temperature. This datum was considered to define the minimum value for the molding temperature of recycled fiberglass.

<figure><img src="image_2252.png" /><figcaption>Figure 5: Fiberglass powder DSC curves.</figcaption></figure>

After molding, recycled samples showed a dark yellow surface which was related to surface oxidation (Fig. 6a). However, the surface appearance of all samples is good. There are no particles being released from the surface, which is continuous, smooth and consistent. To evaluate the efficiency of the recycling stage, density and flexural properties were evaluated on the rectangular recycled fiberglass samples. Average sample dimensions and density values after direct molding process are about: 3.5± 0.29 mm in thickness, 16.1±0.26 mm in width and 1.14±0.055 g/cm³ in density. Analyzing the measured data, it was noted that for the same mass of powder inserted into the mold, the average thickness decrease as the process temperature increases (at 250 °C is about 3.2 ±0.08 mm). This trend can be attributed to the increasing viscosity of the polymer as the temperature increases. This allows a better compaction of the powders, therefore a slight increase in the density of the samples (up to 1.19 g/cm³ at 250 °C). This implies that during the heating step in the muffle, a higher setting temperature allowed to obtain a greater agglomeration of particles. The flexural tests depicted in Figure 6b then showed that the higher process temperature has given a greater consolidation to the recycled fiberglass powder, therefore showing major flexural resistance (Fig. 6b).
<figure><img src="image_2262.png" /><figcaption>Figure 6: Molded samples at different temperatures, b) bending curves and calculated values of flexural strength, maximum strain and flexural modulus.</figcaption></figure>

In general, the directly molded samples are quite brittle, but increasing the processing temperature during molding allowed to reach a flexure strength over 25 MPa together with an elastic modulus over 2.9 GPa. These properties can be appealing for various purposes; for example, the result may potentially replace plasterboard. In fact, plasterboard is made by a film of paper and a central part of gypsum. Plasterboard is largely diffused for false ceilings and separation walls; it has low performances and an environmental impact due to the combination of paper and gypsum which are difficult to be separated.

A closer look at the results show how fiberglass particles could be easily used in direct molding. Starting with the same powder with uniform sizes and with identical residual reactivity, only the process parameters are those that contribute to the final cohesion of the material. In direct molding, main process parameters are molding pressure, temperature, and time. Molding pressure should allow contact between particles, so a higher pressure would result in a major connection and higher final performances. On the other hand, restrictions are given by process systems and molds and are also due to the limits of resin compressibility (too high pressure could result in poor improvements). In this study, the pressure was maintained at 2.55 MPa by a compressed spring and it was similar for the different molded samples. The time was fixed for all the samples. Only the temperature of the oven during molding was varied. In fact, the molding temperature has limits given by the material degradation. A limited degradation is necessary to create new links amongst particles, if it exceeds it could result in polymer cracking inside the particles. Likewise, very high temperatures could result in VOCs (Volatile Organic Compounds) and burning [8]. According to all these considerations, different temperatures have been evaluated and the maximum temperature was established at 250 °C to exceed resin mobility.

A comparison with virgin fiberglass samples was not carried out as only the recovered powder was supplied and not the virgin panels of fiberglass. However, in previous studies it has been evaluated as the final properties of the recycled samples are not equivalent to virgin fiberglass, but other industrial applications seem to be possible as replacement for plasterboard panels [15]. At least at a laboratory level, the authors assessed the feasibility of multiple recycling operations [16].

## Summary

A direct molding technology for recycling fiberglass powders has been proposed. Further analyses are crucial to deepen several aspects and understand if this solution is cost-effective. However
<figure><img src="image_2253.png" /><figcaption>Figure 6: Molded samples at different temperatures, b) bending curves and calculated values of flexural strength, maximum strain and flexural modulus.</figcaption></figure>

In general, the directly molded samples are quite brittle, but increasing the processing temperature during molding allowed to reach a flexure strength over 25 MPa together with an elastic modulus over 2.9 GPa. These properties can be appealing for various purposes; for example, the result may potentially replace plasterboard. In fact, plasterboard is made by a film of paper and a central part of gypsum. Plasterboard is largely diffused for false ceilings and separation walls; it has low performances and an environmental impact due to the combination of paper and gypsum which are difficult to be separated.

A closer look at the results show how fiberglass particles could be easily used in direct molding. Starting with the same powder with uniform sizes and with identical residual reactivity, only the process parameters are those that contribute to the final cohesion of the material. In direct molding, main process parameters are molding pressure, temperature, and time. Molding pressure should allow contact between particles, so a higher pressure would result in a major connection and higher final performances. On the other hand, restrictions are given by process systems and molds and are also due to the limits of resin compressibility (too high pressure could result in poor improvements). In this study, the pressure was maintained at 2.55 MPa by a compressed spring and it was similar for the different molded samples. The time was fixed for all the samples. Only the temperature of the oven during molding was varied. In fact, the molding temperature has limits given by the material degradation. A limited degradation is necessary to create new links amongst particles, if it exceeds it could result in polymer cracking inside the particles. Likewise, very high temperatures could result in VOCs (Volatile Organic Compounds) and burning [8]. According to all these considerations, different temperatures have been evaluated and the maximum temperature was established at 250 °C to exceed resin mobility.

A comparison with virgin fiberglass samples was not carried out as only the recovered powder was supplied and not the virgin panels of fiberglass. However, in previous studies it has been evaluated as the final properties of the recycled samples are not equivalent to virgin fiberglass, but other industrial applications seem to be possible as replacement for plasterboard panels [15]. At least at a laboratory level, the authors assessed the feasibility of multiple recycling operations [16].

## Summary

A direct molding technology for recycling fiberglass powders has been proposed. Further analyses are crucial to deepen several aspects and understand if this solution is cost-effective. However
recycled fiberglass has shown good mechanical properties which are dependent on the processing temperature.

The main goal of this study is the demonstration of feasibility of recycling waste fiberglass without adding any virgin material and using industrially wasted fiberglass powder. Moreover, new findings of the present study, indicate good final mechanical properties as outcome of a 4-point bending test and have shown a good molded surface. The final samples surfaces' appearance is an important achievement as it would allow the application of the material without the need to cover it with dedicated coatings. The authors further suggest a study on the utilization of particle functionalization, as several substances could be used to change the particle surface (e.g., ionic liquids or propylene glycol).

The current work, alongside with previous studies from the authors, aim to spark up the interest on the usage of new technical solutions for composite recycling, especially in the context of sustainable manufacturing processes and waste reduction. The current lack of any state-of-art processes to reprocess fiberglass waste without the usage of any additives or virgin materials, underline the importance of the present study. Other common technical solutions, like pyrolysis or burning, could still be used in further recycling steps when already recycled fiberglass would be deteriorated to a point where its residual properties would be unacceptable.

## Acknowledgement

The research leading to the reported results has received funding from the Lazio Region by its initiative "Gruppi di ricerca 2020". Project FERT (Fiberglass Enhanced Recycling Technology): Prot. n. PROT. A0375-2020-36620.

## References

[1] Information on https://www.grandviewresearch.com/industry-analysis/composites-market (Composites Market Size and Share Analysis Report, 2030)

[2] John H. Ferguson, Sr., US Patent no. 5343630, Fibreglass recycling system, 1994

[3] A.K. Bledzki, K. Goracy, The use of recycled fiber composites as reinforcement for thermosets, Mech. Compos. Mater., 29 (4) (1993), 352-356. http://dx.doi.org/10.1007/BF00617160

[4] T. Inot, T. Yokoi, K.I. Sekiyama, N. Kawamura, Y. Mishima, SMC recycling technology J. Thermoplast. Compos. Mater., 7 (1) (1994), 42-55. https://doi.org/10.1177/089270579400700104

[5] K.H. Yoon, A.T. Di Benedetto, S.J. Huang, Recycling of unsaturated polyester resin using propylene glycol. Polymer (1997), 38, 2281-2285. https://doi.org/10.1016/S0032-3861(96)00951-2

[6] S. Kubota, O. Ito, H. Miyamoto, US Patent no. 5620665. Method of recycling unsaturated polyester resin waste and recycling apparatus, 1997

[7] J.R. Kennerley, R.M. Kelly, N.J. Fenwick, S.J. Pickering, C.D. Rudd, The characterization and reuse of glass fibres recycled from scrap composites by the action of fluidized bed process, Composites Part A (1998), 29A, 839-845. https://doi.org/10.1016/S1359-835X(98)00008-6

[8] A.M. Cunliffe, N. Jones, P. Williams, Recycling of fibre-reinforced polymeric waste by pyrolysis: thermo-gravimetric and bench-scale investigations, J Anal Appl Pyrolysis (2003), 70, 315-338. http://dx.doi.org/10.1016/S0165-2370(02)00161-4

[9] W. Kaminsky, M. Predel, A. Sadiki, Feedstock recycling of polymers by pyrolysis in a fluidised bed, Polym. Degrad. Stab (2004), 85, 1045-1050. https://doi.org/10.1016/j.polymdegradstab.2003.05.002
recycled fiberglass has shown good mechanical properties which are dependent on the processing temperature.

The main goal of this study is the demonstration of feasibility of recycling waste fiberglass without adding any virgin material and using industrially wasted fiberglass powder. Moreover, new findings of the present study, indicate good final mechanical properties as outcome of a 4-point bending test and have shown a good molded surface. The final samples surfaces' appearance is an important achievement as it would allow the application of the material without the need to cover it with dedicated coatings. The authors further suggest a study on the utilization of particle functionalization, as several substances could be used to change the particle surface (e.g., ionic liquids or propylene glycol).

The current work, alongside with previous studies from the authors, aim to spark up the interest on the usage of new technical solutions for composite recycling, especially in the context of sustainable manufacturing processes and waste reduction. The current lack of any state-of-art processes to reprocess fiberglass waste without the usage of any additives or virgin materials, underline the importance of the present study. Other common technical solutions, like pyrolysis or burning, could still be used in further recycling steps when already recycled fiberglass would be deteriorated to a point where its residual properties would be unacceptable.

## Acknowledgement

The research leading to the reported results has received funding from the Lazio Region by its initiative "Gruppi di ricerca 2020". Project FERT (Fiberglass Enhanced Recycling Technology): Prot. n. PROT. A0375-2020-36620.

## References

[1] Information on https://www.grandviewresearch.com/industry-analysis/composites-market (Composites Market Size and Share Analysis Report, 2030)

[2] John H. Ferguson, Sr., US Patent no. 5343630, Fibreglass recycling system, 1994

[3] A.K. Bledzki, K. Goracy, The use of recycled fiber composites as reinforcement for thermosets, Mech. Compos. Mater., 29 (4) (1993), 352-356. http://dx.doi.org/10.1007/BF00617160

[4] T. Inot, T. Yokoi, K.I. Sekiyama, N. Kawamura, Y. Mishima, SMC recycling technology J. Thermoplast. Compos. Mater., 7 (1) (1994), 42-55. https://doi.org/10.1177/089270579400700104

[5] K.H. Yoon, A.T. Di Benedetto, S.J. Huang, Recycling of unsaturated polyester resin using propylene glycol. Polymer (1997), 38, 2281-2285. https://doi.org/10.1016/S0032-3861(96)00951-2

[6] S. Kubota, O. Ito, H. Miyamoto, US Patent no. 5620665. Method of recycling unsaturated polyester resin waste and recycling apparatus, 1997

[7] J.R. Kennerley, R.M. Kelly, N.J. Fenwick, S.J. Pickering, C.D. Rudd, The characterization and reuse of glass fibres recycled from scrap composites by the action of fluidized bed process, Composites Part A (1998), 29A, 839-845. https://doi.org/10.1016/S1359-835X(98)00008-6

[8] A.M. Cunliffe, N. Jones, P. Williams, Recycling of fibre-reinforced polymeric waste by pyrolysis: thermo-gravimetric and bench-scale investigations, J Anal Appl Pyrolysis (2003), 70, 315-338. http://dx.doi.org/10.1016/S0165-2370(02)00161-4

[9] W. Kaminsky, M. Predel, A. Sadiki, Feedstock recycling of polymers by pyrolysis in a fluidised bed, Polym. Degrad. Stab (2004), 85, 1045-1050. https://doi.org/10.1016/j.polymdegradstab.2003.05.002
[10] S.J. Pickering, Recycling technologies for thermoset composite materials - current status. Composites: Part A (2006), 37, 1206-1215. https://doi.org/10.1016/j.compositesa.2005.05.030

[11] A. Kamimura, S. Yamamoto, K. Yamada, Depolymerization of unsaturated polyesters and waste fibre-reinforced plastics by using ionic liquids: the use of microwaves to accelerate the reaction rate. Chem. Sus. Chem (2011), 4, 644-649. https://doi.org/10.1002/cssc.201000430

[12] L.V. Silva, C.C. Angrizani, J.R. Souza, S.C. Amico, J.T.N. Medeiros, Use of polyester/glass-fibre residues as fillers for composites, J. Appl. Polym. Sci (2012), 124, 302-310.

[13] M.C.S. Ribeiro, A.C. Meira-Castro, F.G. Silva, J. Santos, J.P. Meixedo, A. Fiúza, M.L. Dinis, M.R. Alvim, Re-use assessment of thermoset composite wastes as aggregate and filler replacement for concrete-polymer composite materials: a case study regarding GFRP pultrusion wastes, Resour Conserv Recycl (2013), https://doi.org/10.1016/j.resconrec.2013.10.001

[14] S. Li, S. Sun, H. Liang, S. Zhong, F. Yang, Production and characterization of polypropylene composites filled with glass fibre recycled from pyrolysed waste printed circuit boards, Environ. Technol. (2014), 35, 2743-2751. https://doi.org/10.1080/09593330.2014.920049

[15] F. Quadrini, Sintering of powders from fiberglass recycling, Proceedings of ASME International Manufacturing Science and Engineering Conference (MSEC) 2014, art. no. V002T02A063. https://doi.org/10.1115/MSEC2014-4097

[16] F. Quadrini, D. Bellisario, L. Santo, Molding articles made of 100% recycled fiberglass, J. Compos. Mater. 50 (2016) 1-11. https://doi.org/10.1177/002199831561519
[10] S.J. Pickering, Recycling technologies for thermoset composite materials - current status. Composites: Part A (2006), 37, 1206-1215. https://doi.org/10.1016/j.compositesa.2005.05.030

[11] A. Kamimura, S. Yamamoto, K. Yamada, Depolymerization of unsaturated polyesters and waste fibre-reinforced plastics by using ionic liquids: the use of microwaves to accelerate the reaction rate. Chem. Sus. Chem (2011), 4, 644-649. https://doi.org/10.1002/cssc.201000430

[12] L.V. Silva, C.C. Angrizani, J.R. Souza, S.C. Amico, J.T.N. Medeiros, Use of polyester/glass-fibre residues as fillers for composites, J. Appl. Polym. Sci (2012), 124, 302-310.

[13] M.C.S. Ribeiro, A.C. Meira-Castro, F.G. Silva, J. Santos, J.P. Meixedo, A. Fiúza, M.L. Dinis, M.R. Alvim, Re-use assessment of thermoset composite wastes as aggregate and filler replacement for concrete-polymer composite materials: a case study regarding GFRP pultrusion wastes, Resour Conserv Recycl (2013), https://doi.org/10.1016/j.resconrec.2013.10.001

[14] S. Li, S. Sun, H. Liang, S. Zhong, F. Yang, Production and characterization of polypropylene composites filled with glass fibre recycled from pyrolysed waste printed circuit boards, Environ. Technol. (2014), 35, 2743-2751. https://doi.org/10.1080/09593330.2014.920049

[15] F. Quadrini, Sintering of powders from fiberglass recycling, Proceedings of ASME International Manufacturing Science and Engineering Conference (MSEC) 2014, art. no. V002T02A063. https://doi.org/10.1115/MSEC2014-4097

[16] F. Quadrini, D. Bellisario, L. Santo, Molding articles made of 100% recycled fiberglass, J. Compos. Mater. 50 (2016) 1-11. https://doi.org/10.1177/002199831561519
# Manufacturing of a shape memory polymer composite actuator with embedded heater

IORIO Leandro<fnref n="1" />,ᵃ*, PROIETTI Alice<fnref n="1" />,ᵇ, BELLISARIO Denise<fnref n="2" />,ᶜ, QUADRINI Fabrizio<fnref n="1" />,ᵈ and SANTO Loredana<fnref n="1" />,ᵉ

**Keywords:** Shape Memory Composite, Carbon Fiber, Non-Explosive Actuator, Smart Composite

**Abstract.** A new architecture of shape memory polymer composite (SMPC) sandwich actuator was developed. High-performance carbon fibre reinforced (CFR) prepreg was used for the external skins, whereas the shape memory functionalities were given by embedding square tablets of epoxy foams in the centre of the actuator. The epoxy foams were obtained by a solid-state process without using a foaming agent. Thermal activation of the smart actuator was induced through a flexible heater embedded during the lamination sequence. Finally, thin layers of the same shape memory (SM) resin used for the foams were deposited at the interface with the constituents. A SMPC actuator in the form of a 2-ply laminate with an embedded heater and with shape memory polymer (SMP) interlayer was also manufactured for comparison. The actuators were manufactured by a single-step hot press moulding process. Optical observations were carried out to evaluate the soundness of the adopted lab-scale manufacturing procedure, whereas shape memory, constrained-recovery and free recovery tests were performed to investigate the shape memory capabilities and the recovery loads of the novel smart device. Comparable actuation loads (1.5N on average) were found for the two SMPC actuators while shape fixity and shape recovery ratios higher than 81% and 99% respectively were measured for the sandwich actuator.

**Introduction**

Shape memory polymer composites (SMPCs) are stimuli-responsive materials that combine the structural performances of conventional laminates and the functionalities given by shape memory polymers (SMPs). These unique properties make them mostly attractive for applications in high-added industrial fields such as aeronautics and aerospace. In fact, they find applications as reflectors, antennas, deployable structures, morphing structures and hinges [1]. SMPCs with epoxy-based matrix commonly exhibit superior mechanical properties compared with their thermoplastic counterpart. Several studies focus on this finding, as in [2], where adding various short and continuous carbon fibers (CFs) within the shape memory epoxies matrix enhanced the elastic modulus and maximum recovery force. Moreover, the shape memory performances were not significantly altered, thus allowing their partial use as innovative structural materials. These findings confirm the continuously increasing interest in SM epoxy-based polymer composites for advanced space applications. A deep investigation of the mechanical, electrical, and thermal properties is required to better understand the deployable capabilities in ambient and vacuum conditions. These requirements are discussed in [3], where great attention is also paid to the deployment of energetic efficiency that can be enhanced by using aluminum coating for the internal radiative heating of intelligent composites. SMPCs can be activated through different external stimuli such as electric fields, pH. changes, humidity variations and heating. Thermal

<figure><img src="image_2263.png" /></figure>

<footnote n="1">¹University of Rome Tor Vergata, via del Politecnico 1, Rome, Italy</footnote>

<footnote n="2">²Mercatorum University, p.zza Mattei 10, Rome, Italy</footnote>

<footnote>ᵃleandro.iorio@uniroma2.it, ᵇalice.proietti@uniroma2.it, ᶜdenise.bellisario@unimercatorum.it,</footnote>

<footnote>ᵈfabrizio.quadrini@uniroma2.it, ᶜloredana.santo@uniroma2.it</footnote>
# Manufacturing of a shape memory polymer composite actuator with embedded heater

IORIO Leandro<fnref n="1" />,ᵃ*, PROIETTI Alice<fnref n="1" />,ᵇ, BELLISARIO Denise<fnref n="2" />,ᶜ, QUADRINI Fabrizio<fnref n="1" />,ᵈ and SANTO Loredana<fnref n="1" />,ᵉ

**Keywords:** Shape Memory Composite, Carbon Fiber, Non-Explosive Actuator, Smart Composite

**Abstract.** A new architecture of shape memory polymer composite (SMPC) sandwich actuator was developed. High-performance carbon fibre reinforced (CFR) prepreg was used for the external skins, whereas the shape memory functionalities were given by embedding square tablets of epoxy foams in the centre of the actuator. The epoxy foams were obtained by a solid-state process without using a foaming agent. Thermal activation of the smart actuator was induced through a flexible heater embedded during the lamination sequence. Finally, thin layers of the same shape memory (SM) resin used for the foams were deposited at the interface with the constituents. A SMPC actuator in the form of a 2-ply laminate with an embedded heater and with shape memory polymer (SMP) interlayer was also manufactured for comparison. The actuators were manufactured by a single-step hot press moulding process. Optical observations were carried out to evaluate the soundness of the adopted lab-scale manufacturing procedure, whereas shape memory, constrained-recovery and free recovery tests were performed to investigate the shape memory capabilities and the recovery loads of the novel smart device. Comparable actuation loads (1.5N on average) were found for the two SMPC actuators while shape fixity and shape recovery ratios higher than 81% and 99% respectively were measured for the sandwich actuator.

**Introduction**

Shape memory polymer composites (SMPCs) are stimuli-responsive materials that combine the structural performances of conventional laminates and the functionalities given by shape memory polymers (SMPs). These unique properties make them mostly attractive for applications in high-added industrial fields such as aeronautics and aerospace. In fact, they find applications as reflectors, antennas, deployable structures, morphing structures and hinges [1]. SMPCs with epoxy-based matrix commonly exhibit superior mechanical properties compared with their thermoplastic counterpart. Several studies focus on this finding, as in [2], where adding various short and continuous carbon fibers (CFs) within the shape memory epoxies matrix enhanced the elastic modulus and maximum recovery force. Moreover, the shape memory performances were not significantly altered, thus allowing their partial use as innovative structural materials. These findings confirm the continuously increasing interest in SM epoxy-based polymer composites for advanced space applications. A deep investigation of the mechanical, electrical, and thermal properties is required to better understand the deployable capabilities in ambient and vacuum conditions. These requirements are discussed in [3], where great attention is also paid to the deployment of energetic efficiency that can be enhanced by using aluminum coating for the internal radiative heating of intelligent composites. SMPCs can be activated through different external stimuli such as electric fields, pH. changes, humidity variations and heating. Thermal

<figure><img src="image_2254.png" /></figure>

<footnote n="1">¹University of Rome Tor Vergata, via del Politecnico 1, Rome, Italy</footnote>

<footnote n="2">²Mercatorum University, p.zza Mattei 10, Rome, Italy</footnote>

<footnote>ᵃleandro.iorio@uniroma2.it, ᵇalice.proietti@uniroma2.it, ᶜdenise.bellisario@unimercatorum.it,</footnote>

<footnote>ᵈfabrizio.quadrini@uniroma2.it, ᶜloredana.santo@uniroma2.it</footnote>
activation is generally the most studied one because of its ease of understanding and applicability, but over the last few years, the development of new applications and devices has made a deep investigation into electric activation necessary. Both actuation methods are used with epoxy-based composite reinforced with unidirectional (UD) and fabric carbon plies [4]. The triggering temperature for epoxy based SMPCs is the glass transition temperature ($T_g$). When it is overcome by thermal or Joule heating, the composite softens, meaning that the molecular mobility of SMP is activated. The break of secondary bonds among molecular chains and the weakening of the main bonds within the same chains are the mechanisms responsible for molecular mobility activation. In other structural applications, molecular mobility is generally reduced, and this leads to a decrease in shape memory capabilities. These microscopic mechanisms justify the macroscopic allowable deformation of smart composites. In fact, when heated up to the glass transition temperature, they can be easily deformed in a temporary non-equilibrium configuration upon applying external constraints. Once the SMPC is cooled, the external constraint can be removed, and the temporary configuration remains fixed. When heated again over $T_g$, the SMPC restores the initial stable equilibrium configuration, and it can be subjected to another memory-recovery cycle if irreversible damages are not present. This thermo-mechanical cycle is the commonly adopted way to give evidence of the shape memory effect typical of smart composites.

Because of these attractive capabilities, SMPCs allow the design and development of new concepts of non-explosive actuators, which can be used in several applications, including soft robotics, where rigid structures at room temperature and soft structures upon activation are generally required. To date, soft actuators are produced by different classes of smart materials, including gels/hydrogels, conductive polymers, dielectric elastomers, and shape memory polymers. The most viable applications deal with soft mechatronics, soft robots, medical devices, haptic devices, flexible devices, and smart optics [5, 6]. Several innovations are also arising; in fact, bi-state shape memory composite soft actuators combining the strength of SMAs and the functionalities of SMPs are under evaluation [7], and numerical models are suitable to predict the behavior in operation. In addition, numerical models can also be used to investigate the thermo-mechanical behavior of one-way and two-way shape memory composite actuators to improve their design and architecture [8]. Following the current trend of innovation, shape memory polymer composites offer a real alternative to developing soft-smart actuators. The use of commercial and high-performance raw materials such as carbon fiber reinforced (CFR) prepregs allows the implementation of the well-consolidated technologies commonly used in composite manufacturing. Recent innovations allow for improved smart functionalities by introducing polystyrene interleaves among prepreg plies during lamination [9]. Following this approach, innovative architectures of SMPCs have been introduced by co-curing an established amount of an uncured shape memory epoxy powder deposited in the form of a thin layer (100µm) between prepreg plies [10]. These laminates can undergo several memory-recovery cycles without incurring premature failure if the maximum allowable deformation is not overcome [11]. Increasing the number of prepreg plies and SMP interlayers allows an increase in the laminate stiffness as well as the recovery force when restoring the original equilibrium configuration, with the risk of affecting the shape memory capabilities. In this optic, SM epoxy foam obtained from the same epoxy powder with an innovative solid-state manufacturing process, which avoids the use of a foaming agent, can be embedded to obtain novel sandwich architecture. They can enhance the shape memory capabilities and minimally affect the stiffness. This architecture has been implemented to manufacture a SMPC unit [12]. In this case, thermal activation was achieved by using a flexible heater placed in the neutral plane of the smart sandwich structure during lamination. The use of flexible heating devices is acquiring great resonance in the composite manufacturing practice [13]. Further heating strategies deal with the single wall carbon nanotube
activation is generally the most studied one because of its ease of understanding and applicability, but over the last few years, the development of new applications and devices has made a deep investigation into electric activation necessary. Both actuation methods are used with epoxy-based composite reinforced with unidirectional (UD) and fabric carbon plies [4]. The triggering temperature for epoxy based SMPCs is the glass transition temperature ($T_g$). When it is overcome by thermal or Joule heating, the composite softens, meaning that the molecular mobility of SMP is activated. The break of secondary bonds among molecular chains and the weakening of the main bonds within the same chains are the mechanisms responsible for molecular mobility activation. In other structural applications, molecular mobility is generally reduced, and this leads to a decrease in shape memory capabilities. These microscopic mechanisms justify the macroscopic allowable deformation of smart composites. In fact, when heated up to the glass transition temperature, they can be easily deformed in a temporary non-equilibrium configuration upon applying external constraints. Once the SMPC is cooled, the external constraint can be removed, and the temporary configuration remains fixed. When heated again over $T_g$, the SMPC restores the initial stable equilibrium configuration, and it can be subjected to another memory-recovery cycle if irreversible damages are not present. This thermo-mechanical cycle is the commonly adopted way to give evidence of the shape memory effect typical of smart composites.

Because of these attractive capabilities, SMPCs allow the design and development of new concepts of non-explosive actuators, which can be used in several applications, including soft robotics, where rigid structures at room temperature and soft structures upon activation are generally required. To date, soft actuators are produced by different classes of smart materials, including gels/hydrogels, conductive polymers, dielectric elastomers, and shape memory polymers. The most viable applications deal with soft mechatronics, soft robots, medical devices, haptic devices, flexible devices, and smart optics [5, 6]. Several innovations are also arising; in fact, bi-state shape memory composite soft actuators combining the strength of SMAs and the functionalities of SMPs are under evaluation [7], and numerical models are suitable to predict the behavior in operation. In addition, numerical models can also be used to investigate the thermo-mechanical behavior of one-way and two-way shape memory composite actuators to improve their design and architecture [8]. Following the current trend of innovation, shape memory polymer composites offer a real alternative to developing soft-smart actuators. The use of commercial and high-performance raw materials such as carbon fiber reinforced (CFR) prepregs allows the implementation of the well-consolidated technologies commonly used in composite manufacturing. Recent innovations allow for improved smart functionalities by introducing polystyrene interleaves among prepreg plies during lamination [9]. Following this approach, innovative architectures of SMPCs have been introduced by co-curing an established amount of an uncured shape memory epoxy powder deposited in the form of a thin layer (100µm) between prepreg plies [10]. These laminates can undergo several memory-recovery cycles without incurring premature failure if the maximum allowable deformation is not overcome [11]. Increasing the number of prepreg plies and SMP interlayers allows an increase in the laminate stiffness as well as the recovery force when restoring the original equilibrium configuration, with the risk of affecting the shape memory capabilities. In this optic, SM epoxy foam obtained from the same epoxy powder with an innovative solid-state manufacturing process, which avoids the use of a foaming agent, can be embedded to obtain novel sandwich architecture. They can enhance the shape memory capabilities and minimally affect the stiffness. This architecture has been implemented to manufacture a SMPC unit [12]. In this case, thermal activation was achieved by using a flexible heater placed in the neutral plane of the smart sandwich structure during lamination. The use of flexible heating devices is acquiring great resonance in the composite manufacturing practice [13]. Further heating strategies deal with the single wall carbon nanotube
electrothermal Joule heating device directly deposited on UD prepreg plies. After deposition, they are integrated during the manufacturing of CFR laminates [14].

In this study, a novel architecture of SMPC sandwich actuator, including all the technological achievements developed in the field of SMPCs, has been designed and prototyped. The achievements include the co-curing of prepreg plies and SMP interlayers with a single-step hot press molding process, the integration of SM foams to enhance laminate deformation capabilities, the embedding of a flexible heating device and using commercial materials and devices. The developed smart soft actuator shows enhanced SM abilities and good mechanical performance.

## Materials and Methods

### Material suppliers and Manufacturing

An innovative carbon fiber reinforced (CFR) shape memory polymer composite (SMPC) sandwich actuator has been manufactured by hot press molding (Fig. 1) starting from commercially available raw materials and devices. A high-performance 0/90 woven fabric prepreg (Solvay Cycom 132 977-2) has been used for the external skins, whereas a thermosetting resin supplied in the form of uncured green powder (3M® Scotchkote 206N) was responsible for the shape memory capabilities and inserted in the forms of thin interlayers and foams. Thermal activation of the smart device was attained through a flexible heater KHLVA-0504/10 acquired by Omega. The heater has a nominal thickness of 150µm and a surface area of 13×90mm²; it is made by an etched copper circuit encapsulated between two polyimide films, and it can be powered with a maximum voltage of 28V corresponding to a power of 19.6W being the resistance of 40Ω.

At the beginning of the manufacturing procedure, the SM epoxy powder was deposited on the bottom CFR ply to form a thin interlayer. A mass of 0.17g has been used to obtain a nominal thickness of 100µm. Then, the flexible heater was placed over the SMP interlayer and covered with a further 100µm thick SMP interlayer. Two epoxy square (13×13mm²) foams, with an average thickness of 1.9mm and obtained by solid-state foaming [15], were placed in the center of the device and covered with another SMP interlayer.

<figure><img src="image_2264.png" /><figcaption>Figure 1. Architecture of CFR-SMPC actuators and adopted lab-scale manufacturing process.</figcaption></figure>
electrothermal Joule heating device directly deposited on UD prepreg plies. After deposition, they are integrated during the manufacturing of CFR laminates [14].

In this study, a novel architecture of SMPC sandwich actuator, including all the technological achievements developed in the field of SMPCs, has been designed and prototyped. The achievements include the co-curing of prepreg plies and SMP interlayers with a single-step hot press molding process, the integration of SM foams to enhance laminate deformation capabilities, the embedding of a flexible heating device and using commercial materials and devices. The developed smart soft actuator shows enhanced SM abilities and good mechanical performance.

## Materials and Methods

### Material suppliers and Manufacturing

An innovative carbon fiber reinforced (CFR) shape memory polymer composite (SMPC) sandwich actuator has been manufactured by hot press molding (Fig. 1) starting from commercially available raw materials and devices. A high-performance 0/90 woven fabric prepreg (Solvay Cycom 132 977-2) has been used for the external skins, whereas a thermosetting resin supplied in the form of uncured green powder (3M® Scotchkote 206N) was responsible for the shape memory capabilities and inserted in the forms of thin interlayers and foams. Thermal activation of the smart device was attained through a flexible heater KHLVA-0504/10 acquired by Omega. The heater has a nominal thickness of 150µm and a surface area of 13×90mm²; it is made by an etched copper circuit encapsulated between two polyimide films, and it can be powered with a maximum voltage of 28V corresponding to a power of 19.6W being the resistance of 40Ω.

At the beginning of the manufacturing procedure, the SM epoxy powder was deposited on the bottom CFR ply to form a thin interlayer. A mass of 0.17g has been used to obtain a nominal thickness of 100µm. Then, the flexible heater was placed over the SMP interlayer and covered with a further 100µm thick SMP interlayer. Two epoxy square (13×13mm²) foams, with an average thickness of 1.9mm and obtained by solid-state foaming [15], were placed in the center of the device and covered with another SMP interlayer.

<figure><img src="image_2255.png" /><figcaption>Figure 1. Architecture of CFR-SMPC actuators and adopted lab-scale manufacturing process.</figcaption></figure>
The square foams were cut from a 2mm thick disk obtained by machining with a CNC facility by Proxon® from an original cylindrical foam 20mm in diameter. The top CFR ply completed the lamination sequence.

The uncured CFR-SMPC sandwich was placed in an aluminum mold and covered with a thin release film to avoid adhesion. Finally, a rubber insert was placed over the top release film to homogeneously distribute the applied load during molding. The cure was led on a heater plate at 200°C for 30min with an applied pressure of 2bar, as stated by a previous study [16]. The presence of the spring as part of the mold assembly allowed for compensation for the thickness reduction due to resin bleeding.

A CFR-SMPC laminate has also been manufactured for comparison. The architecture consisted of a single ply for each one of the external skins and two SMP interlayers with a thickness of 100µm that joined the flexible heater with the external CFR plies. The molding procedure was the same used for the CFR-SMPC actuator, and the cured smart devices are shown in Fig.1.

### Optical observation and SM testing

The soundness of the manufacturing procedure in terms of constituents' adhesion and compaction was assessed by means of an optical stereomicroscope LeicaS9i.

SM tests were instead carried out on an MTS Insight 5 Universal testing machine. These tests allowed us to evaluate the shape memory capabilities of the two actuators by performing memory, constrained-recovery and free-recovery under the three-point bending configuration with a span length of 88mm (the maximum compatible with the length of the actuators). In all these instrumented tests, the flexible heater was powered with a voltage of 26V, corresponding to a power of 16.9W and a current intensity of 0.63A. Moreover, during the tests, a type-J thermocouple was placed on the intrados to record the temperature evolution over time. Memory tests were performed in the hot deformation mode [12].

A scheme of the test is shown in Fig. 2. After reaching the equilibrium temperature induced by the heater, the actuator is inflected by the plunger at a rate of 10mm/min. When the maximum inflection is reached, the heater is powered off, and the actuator is left cooling down to room temperature. Finally, the plunger comes back to the initial position. Two displacements of 5mm and 10mm were set for the memory tests. Constrained-recovery tests were performed by applying a minimum load on the deformed actuator to prevent its recovery. Additionally, the load exerted by the actuator on the plunger upon heating was recorded. Free-recovery tests ended the thermo-mechanical cycling and were able to evaluate not only the shape recovery ratio but also the recovery rate from image elaboration after camera recording.

The shape fixity ($R_f$) and shape recovery ($R_r$) ratios are used in literature to evaluate respectively the ability to fix a deformed configuration and the ability to restore the undeformed one.

<figure><img src="image_2265.png" /><figcaption>Figure 2. Shape memory testing and schematic of a memory curve for two cases of SM behaviour.</figcaption></figure>
The square foams were cut from a 2mm thick disk obtained by machining with a CNC facility by Proxon® from an original cylindrical foam 20mm in diameter. The top CFR ply completed the lamination sequence.

The uncured CFR-SMPC sandwich was placed in an aluminum mold and covered with a thin release film to avoid adhesion. Finally, a rubber insert was placed over the top release film to homogeneously distribute the applied load during molding. The cure was led on a heater plate at 200°C for 30min with an applied pressure of 2bar, as stated by a previous study [16]. The presence of the spring as part of the mold assembly allowed for compensation for the thickness reduction due to resin bleeding.

A CFR-SMPC laminate has also been manufactured for comparison. The architecture consisted of a single ply for each one of the external skins and two SMP interlayers with a thickness of 100µm that joined the flexible heater with the external CFR plies. The molding procedure was the same used for the CFR-SMPC actuator, and the cured smart devices are shown in Fig.1.

Optical observation and SM testing

The soundness of the manufacturing procedure in terms of constituents' adhesion and compaction was assessed by means of an optical stereomicroscope LeicaS9i.

SM tests were instead carried out on an MTS Insight 5 Universal testing machine. These tests allowed us to evaluate the shape memory capabilities of the two actuators by performing memory, constrained-recovery and free-recovery under the three-point bending configuration with a span length of 88mm (the maximum compatible with the length of the actuators). In all these instrumented tests, the flexible heater was powered with a voltage of 26V, corresponding to a power of 16.9W and a current intensity of 0.63A. Moreover, during the tests, a type-J thermocouple was placed on the intrados to record the temperature evolution over time. Memory tests were performed in the hot deformation mode [12].

A scheme of the test is shown in Fig. 2. After reaching the equilibrium temperature induced by the heater, the actuator is inflected by the plunger at a rate of 10mm/min. When the maximum inflection is reached, the heater is powered off, and the actuator is left cooling down to room temperature. Finally, the plunger comes back to the initial position. Two displacements of 5mm and 10mm were set for the memory tests. Constrained-recovery tests were performed by applying a minimum load on the deformed actuator to prevent its recovery. Additionally, the load exerted by the actuator on the plunger upon heating was recorded. Free-recovery tests ended the thermo-mechanical cycling and were able to evaluate not only the shape recovery ratio but also the recovery rate from image elaboration after camera recording.

The shape fixity ($R_f$) and shape recovery ($R_r$) ratios are used in literature to evaluate respectively the ability to fix a deformed configuration and the ability to restore the undeformed one.

<figure><img src="image_2256.png" /><figcaption>Figure 2. Shape memory testing and schematic of a memory curve for two cases of SM behaviour.</figcaption></figure>
$$R_f = \frac{\varepsilon_u}{\varepsilon_m} \times 100 \qquad (1)$$

$$R_r = \frac{\varepsilon_e}{\varepsilon_m} \times 100 \qquad (2)$$

Where $\varepsilon_u$ is the real applied strain after load removal, and $\varepsilon_r$ is the recovered strain, which is calculated as the difference between the maximum applied strain in the memory test $\varepsilon_m$ and the final residual strain after the free recovery test $\varepsilon_p$.

In memory tests, during the holding stage, different behaviors can be obtained considering the material under testing. During cooling, shape memory materials (SMMs) show a stress reduction down to a plateau, which is generally considered to be frozen stress. On the other hand, SMMs with a high elastic contribution can exhibit a partial elastic recovery during the holding stage, as for smart structures where the elastic contribution overcomes the SM one. In the unloading stage, a partial elastic recovery is generally obtained if the material does not exhibit an ideal shape memory behavior. The constrained recovery was performed by fixing samples under the plunger of the testing machine with a minimum applied load of 1N. In this way, it was possible to record the evolution of the stress over time upon heating the sample. Finally, the free recovery tests allowed us to evaluate both the evolution of the obtained final displacement as well as the recovery rate. All the results were shown as normalized curves, so they were evaluated in correspondence with the inflexion section.

## Results and Discussions

The CFR-SMPC laminate and sandwich actuators have a mass of 5.5g and 5.9g, respectively, with the mass of the heater being 3.9g. Moreover, the laminate has an average thickness of 0.89mm, whereas the sandwich has a maximum thickness of 2.6mm in the centre where foams are embedded and an average thickness of 0.785mm on the edges. The heater and foam thickness are respectively 150µm and 1.9mm on average, whereas the thickness of the cured CFR skin is 220µm as stated by a previous study on the same CFR prepreg [16]. A nominal thickness of 150µm and 105µm for each single SMP interlayer, respectively, for the laminate and sandwich actuator can be inferred. The interlayer thicknesses are slightly higher than the nominal designed one, but this discrepancy is acceptable considering the adopted lab scale procedure. The different components and devices used in the manufacturing procedure are shown by the stereomicroscopic images in Fig.3. The components' interfaces are visible, optimal bonding has been obtained, and the closed-cell structure of the foams is also evident. Three-point bending test returned a bending stiffness for the sandwich actuator slightly higher (1.74N/mm) than the laminate one (1.67N/mm), whereas the bending modulus is considerably lower, 1.1GPa compared to 25.7GPa with a reduction of 96%. The proposed sandwich architecture was designed to reduce stress developed during operation, which would exert on the CFR skins, and the mechanisms of cell collapsing that are typical of the SM foams act in this direction.

<figure><img src="image_2266.png" /><figcaption>Figure 3. Stereomicroscopic images of the two CFR-SMPC actuators.</figcaption></figure>
$$R_f = \frac{\varepsilon_u}{\varepsilon_m} \times 100 \qquad (1)$$

$$R_r = \frac{\varepsilon_e}{\varepsilon_m} \times 100 \qquad (2)$$

Where $\varepsilon_u$ is the real applied strain after load removal, and $\varepsilon_r$ is the recovered strain, which is calculated as the difference between the maximum applied strain in the memory test $\varepsilon_m$ and the final residual strain after the free recovery test $\varepsilon_p$.

In memory tests, during the holding stage, different behaviors can be obtained considering the material under testing. During cooling, shape memory materials (SMMs) show a stress reduction down to a plateau, which is generally considered to be frozen stress. On the other hand, SMMs with a high elastic contribution can exhibit a partial elastic recovery during the holding stage, as for smart structures where the elastic contribution overcomes the SM one. In the unloading stage, a partial elastic recovery is generally obtained if the material does not exhibit an ideal shape memory behavior. The constrained recovery was performed by fixing samples under the plunger of the testing machine with a minimum applied load of 1N. In this way, it was possible to record the evolution of the stress over time upon heating the sample. Finally, the free recovery tests allowed us to evaluate both the evolution of the obtained final displacement as well as the recovery rate. All the results were shown as normalized curves, so they were evaluated in correspondence with the inflexion section.

## Results and Discussions

The CFR-SMPC laminate and sandwich actuators have a mass of 5.5g and 5.9g, respectively, with the mass of the heater being 3.9g. Moreover, the laminate has an average thickness of 0.89mm, whereas the sandwich has a maximum thickness of 2.6mm in the centre where foams are embedded and an average thickness of 0.785mm on the edges. The heater and foam thickness are respectively 150µm and 1.9mm on average, whereas the thickness of the cured CFR skin is 220µm as stated by a previous study on the same CFR prepreg [16]. A nominal thickness of 150µm and 105µm for each single SMP interlayer, respectively, for the laminate and sandwich actuator can be inferred. The interlayer thicknesses are slightly higher than the nominal designed one, but this discrepancy is acceptable considering the adopted lab scale procedure. The different components and devices used in the manufacturing procedure are shown by the stereomicroscopic images in Fig.3. The components' interfaces are visible, optimal bonding has been obtained, and the closed-cell structure of the foams is also evident. Three-point bending test returned a bending stiffness for the sandwich actuator slightly higher (1.74N/mm) than the laminate one (1.67N/mm), whereas the bending modulus is considerably lower, 1.1GPa compared to 25.7GPa with a reduction of 96%. The proposed sandwich architecture was designed to reduce stress developed during operation, which would exert on the CFR skins, and the mechanisms of cell collapsing that are typical of the SM foams act in this direction.

<figure><img src="image_2257.png" /><figcaption>Figure 3. Stereomicroscopic images of the two CFR-SMPC actuators.</figcaption></figure>
<figure><img src="image_2267.png" /><figcaption>Figure 4. Memory curves and temperature measures of the SMPC actuators for an applied displacement of 10mm.</figcaption></figure>

The slightly higher stiffness and mass due to the embedded SM foams would help to avoid the development of high stress without affecting the shape memory capabilities typical of SMPC laminates. The shape memory tests performed through a well-consolidated instrumented thermo-mechanical cycle, shown in Fig.2, helped to validate this proposal. A single shape memory test for each applied displacement of 5mm and 10mm was performed. In Fig. 4, the results of SM tests for the applied displacement of 10mm on both actuators are shown.

Results of memory tests are reported as stress evolution over time. Temperature evolution is also reported for the whole duration of the test. The applied voltage of 26V leads to different plateau temperatures, recorded on the intrados, being higher for the sandwich actuator. This difference is due to the higher thermal inertia induced by the SM foams. The CFR-SMPC laminate actuator exhibited higher stresses for every single stage of the test and showed the typical SM behavior of composite laminate with a gradual approach to the stress plateau during the cooling stage. On the other side, the CFR-SMPC sandwich actuator exhibited the discussed elastic recovery during the cooling stage confirming the soundness of the initial proposed goals. Finally, both actuators showed a partial elastic recovery during the unloading stage. Data extracted from the memory tests and listed in Table 1 allow quantitative analysis.

<table><caption>Table 1. Data extracted from memory tests.</caption><thead><tr><th>Sample</th><th>Nominal applied displacement</th><th>Peak load</th><th>Peak stress</th><th>Plateau load</th><th>Plateau stress</th><th>Shape fixity</th></tr><tr><th>ID</th><th>[mm]</th><th>[N]</th><th>[MPa]</th><th>[N]</th><th>[MPa]</th><th>%</th></tr></thead><tbody><tr><td rowspan="2">Laminate</td><td>5</td><td>2.4</td><td>25.4</td><td>1.8</td><td>19.6</td><td>75.5</td></tr><tr><td>10</td><td>3.0</td><td>32.2</td><td>2.2</td><td>23.9</td><td>78.5</td></tr><tr><td rowspan="2">Sandwich</td><td>5</td><td>1.1</td><td>1.4</td><td>1.0</td><td>1.3</td><td>81.8</td></tr><tr><td>10</td><td>1.7</td><td>2.2</td><td>1.5</td><td>1.9</td><td>81.6</td></tr></tbody></table>
<figure><img src="image_2258.png" /><figcaption>Figure 4. Memory curves and temperature measures of the SMPC actuators for an applied displacement of 10mm.</figcaption></figure>

The slightly higher stiffness and mass due to the embedded SM foams would help to avoid the development of high stress without affecting the shape memory capabilities typical of SMPC laminates. The shape memory tests performed through a well-consolidated instrumented thermo-mechanical cycle, shown in Fig. 2, helped to validate this proposal. A single shape memory test for each applied displacement of 5mm and 10mm was performed. In Fig. 4, the results of SM tests for the applied displacement of 10mm on both actuators are shown.

Results of memory tests are reported as stress evolution over time. Temperature evolution is also reported for the whole duration of the test. The applied voltage of 26V leads to different plateau temperatures, recorded on the intrados, being higher for the sandwich actuator. This difference is due to the higher thermal inertia induced by the SM foams. The CFR-SMPC laminate actuator exhibited higher stresses for every single stage of the test and showed the typical SM behavior of composite laminate with a gradual approach to the stress plateau during the cooling stage. On the other side, the CFR-SMPC sandwich actuator exhibited the discussed elastic recovery during the cooling stage confirming the soundness of the initial proposed goals. Finally, both actuators showed a partial elastic recovery during the unloading stage. Data extracted from the memory tests and listed in Table 1 allow quantitative analysis.

<table><caption>Table 1. Data extracted from memory tests.</caption><thead><tr><th>Sample</th><th>Nominal applied displacement</th><th>Peak load</th><th>Peak stress</th><th>Plateau load</th><th>Plateau stress</th><th>Shape fixity</th></tr><tr><th>ID</th><th>[mm]</th><th>[N]</th><th>[MPa]</th><th>[N]</th><th>[MPa]</th><th>%</th></tr></thead><tbody><tr><td rowspan="2">Laminate</td><td>5</td><td>2.4</td><td>25.4</td><td>1.8</td><td>19.6</td><td>75.5</td></tr><tr><td>10</td><td>3.0</td><td>32.2</td><td>2.2</td><td>23.9</td><td>78.5</td></tr><tr><td rowspan="2">Sandwich</td><td>5</td><td>1.1</td><td>1.4</td><td>1.0</td><td>1.3</td><td>81.8</td></tr><tr><td>10</td><td>1.7</td><td>2.2</td><td>1.5</td><td>1.9</td><td>81.6</td></tr></tbody></table>
<figure><img src="image_2268.png" /><figcaption>Figure 5. Recovery load curves and temperature measures of the SMPC actuators during constrained recovery for 10mm of applied displacement.</figcaption></figure>

An average peak stress and plateau stress reduction of 94% were obtained for the sandwich actuator. This reduction is linked to the mechanisms of cell collapsing of the SM foams. On the other side, an increase of 5.7% on average for the shape fixity ratio has been observed for the sandwich actuator underlying the higher elastic contribution of the carbon fibers on the laminate actuator.

Results of constrained recovery tests are shown in Fig. 5 for the same applied displacement of 10mm, whereas the data extracted for both applied displacements are listed in Table 2. As for memory tests, the sandwich actuator exhibited partial elastic recovery during the cooling stage, leading to an increase in the plateau stress, which stabilizes in correspondence with the peak stress. The SMPC laminate confirms the higher stress values for the whole duration of the test. On the other hand, the sandwich actuator shows peak load values slightly lower than the laminate, so underlying that the increase in terms of mass is not paid in terms of high recovery load reduction, which is a fundamental parameter for designing and producing efficient and reliable actuators.

<table><caption>Table 2. Data extracted from recovery tests.</caption><thead><tr><th rowspan="2">Sample</th><th rowspan="2">Nominal applied displacement</th><th colspan="3">Constrained</th><th colspan="3">Free</th></tr><tr><th>Peak load</th><th>Peak stress</th><th>Shape fixity</th><th>Maximum displacement</th><th>Recovery rate</th><th>Shape recovery</th></tr><tr><th>ID</th><th>[mm]</th><th>[N]</th><th>[MPa]</th><th>%</th><th>[mm]</th><th>[mm/s]</th><th>%</th></tr></thead><tbody><tr><td rowspan="2">Laminate</td><td>5</td><td>1.6</td><td>16.7</td><td>60.8</td><td>4.2</td><td>0.04</td><td>97.4</td></tr><tr><td>10</td><td>1.9</td><td>20.7</td><td>65.5</td><td>7.6</td><td>0.06</td><td>98.4</td></tr><tr><td rowspan="2">Sandwich</td><td>5</td><td>0.8</td><td>1.1</td><td>67.4</td><td>4.1</td><td>0.02</td><td>98.6</td></tr><tr><td>10</td><td>1.3</td><td>1.6</td><td>68.6</td><td>8.2</td><td>0.03</td><td>99.3</td></tr></tbody></table>
<figure><img src="image_2259.png" /><figcaption>Figure 5. Recovery load curves and temperature measures of the SMPC actuators during constrained recovery for 10mm of applied displacement.</figcaption></figure>

An average peak stress and plateau stress reduction of 94% were obtained for the sandwich actuator. This reduction is linked to the mechanisms of cell collapsing of the SM foams. On the other side, an increase of 5.7% on average for the shape fixity ratio has been observed for the sandwich actuator underlying the higher elastic contribution of the carbon fibers on the laminate actuator.

Results of constrained recovery tests are shown in Fig. 5 for the same applied displacement of 10mm, whereas the data extracted for both applied displacements are listed in Table 2. As for memory tests, the sandwich actuator exhibited partial elastic recovery during the cooling stage, leading to an increase in the plateau stress, which stabilizes in correspondence with the peak stress. The SMPC laminate confirms the higher stress values for the whole duration of the test. On the other hand, the sandwich actuator shows peak load values slightly lower than the laminate, so underlying that the increase in terms of mass is not paid in terms of high recovery load reduction, which is a fundamental parameter for designing and producing efficient and reliable actuators.

<table><caption>Table 2. Data extracted from recovery tests.</caption><thead><tr><th rowspan="2">Sample</th><th rowspan="2">Nominal applied displacement</th><th colspan="3">Constrained</th><th colspan="3">Free</th></tr><tr><th>Peak load</th><th>Peak stress</th><th>Shape fixity</th><th>Maximum displacement</th><th>Recovery rate</th><th>Shape recovery</th></tr><tr><th>ID</th><th>[mm]</th><th>[N]</th><th>[MPa]</th><th>%</th><th>[mm]</th><th>[mm/s]</th><th>%</th></tr></thead><tbody><tr><td rowspan="2">Laminate</td><td>5</td><td>1.6</td><td>16.7</td><td>60.8</td><td>4.2</td><td>0.04</td><td>97.4</td></tr><tr><td>10</td><td>1.9</td><td>20.7</td><td>65.5</td><td>7.6</td><td>0.06</td><td>98.4</td></tr><tr><td rowspan="2">Sandwich</td><td>5</td><td>0.8</td><td>1.1</td><td>67.4</td><td>4.1</td><td>0.02</td><td>98.6</td></tr><tr><td>10</td><td>1.3</td><td>1.6</td><td>68.6</td><td>8.2</td><td>0.03</td><td>99.3</td></tr></tbody></table>
<figure><img src="image_2269.png" /><figcaption>Figure 6. *Undeformed and highly deformed CFR-SMPC sandwich actuator with an applied radius of curvature of 10mm.*</figcaption></figure>

Moreover, both prototypes reduce the shape fixity ratio at the end of the constrained test, thus confirming that in correspondence with each heating-cooling cycle, a partial elastic recovery should always be expected. Notwithstanding this finding, the sandwich actuator still maintains higher shape fixity values (around 70% on average). Shape recovery ratios are even more high, nearly approaching the ideal value in the case of the sandwich actuator.

This aspect is clearly related to the elastic contribution of the CFs and, even minimally, also by the presence of the embedded heater. The two actuators have the same configuration of CFR skins, and the mass of the sandwich actuator is not highly affected by the presence of the foams (density of 0.67g/cm³ on average), which instead highly influences the shape memory capabilities. At the end of free recovery, the SMPC laminate actuator exhibited a recovery speed of 0.05mm/s on average, double that of the SMPC sandwich actuator (0.025mm/s). These values are typical of shape memory polymer composites, and the lower values obtained for the sandwich actuator are related to the recovery time, 240s, which is 100% higher than the one extracted for the laminate. This result is influenced by the SM foam, which slows down the recovery process due to their inertia upon recovery.

Finally, the high deformation capability inferred for the sandwich device can be clearly visible in Fig. 6, where a deformation with an applied radius of curvature of 10mm has been applied without any appreciable damage. It is evident that most of the deformation is localized within the foam, whereas the external edges tend to maintain the equilibrium planar configuration.

## Summary

The proposed autonomous actuator prototype is one of the largest ever manufactured by using shape memory polymer composites and already shows a high potential to be used at an industrial level for self-deployable structures or grabbing devices. Moreover, it includes all the innovations developed in the field of SMPCs, such as the co-processing of different epoxy systems and the embedding of electrical devices. Commercially available materials and components have been used, thus facilitating the quality control and acceptance procedure typical of high added value industrial fields.

The proposed CFR-SMPC sandwich device exhibits optimal shape memory capabilities compared to standard laminate. Higher shape fixity ratios (85% on average) and even higher shape recovery ratios (also approaching 100% of initial strain) have been obtained. These performances are mainly due to the embedded epoxy foams, which freeze most of the applied deformation, also reducing stress concentration on the CFR skins. The slight increase of mass minimally affects the recovery load, whose values are comparable not only to the peak loads developed during the memory tests but also to the ones extracted for the SMPC laminate.

Small displacements have been applied during testing for a correct comparison between the two devices under bending. On the other side, higher deformation capabilities have been demonstrated by imposing a radius of curvature of 10mm spread over the center of the sandwich actuator in correspondence to the embedded foams. Despite this, no evidence of irreversible damages is present so underlying that the proposed innovative actuator can undergo to severe and multiple
<figure><img src="image_2260.png" /><figcaption>Figure 6. *Undeformed and highly deformed CFR-SMPC sandwich actuator with an applied radius of curvature of 10mm.*</figcaption></figure>

Moreover, both prototypes reduce the shape fixity ratio at the end of the constrained test, thus confirming that in correspondence with each heating-cooling cycle, a partial elastic recovery should always be expected. Notwithstanding this finding, the sandwich actuator still maintains higher shape fixity values (around 70% on average). Shape recovery ratios are even more high, nearly approaching the ideal value in the case of the sandwich actuator.

This aspect is clearly related to the elastic contribution of the CFs and, even minimally, also by the presence of the embedded heater. The two actuators have the same configuration of CFR skins, and the mass of the sandwich actuator is not highly affected by the presence of the foams (density of 0.67g/cm³ on average), which instead highly influences the shape memory capabilities. At the end of free recovery, the SMPC laminate actuator exhibited a recovery speed of 0.05mm/s on average, double that of the SMPC sandwich actuator (0.025mm/s). These values are typical of shape memory polymer composites, and the lower values obtained for the sandwich actuator are related to the recovery time, 240s, which is 100% higher than the one extracted for the laminate. This result is influenced by the SM foam, which slows down the recovery process due to their inertia upon recovery.

Finally, the high deformation capability inferred for the sandwich device can be clearly visible in Fig. 6, where a deformation with an applied radius of curvature of 10mm has been applied without any appreciable damage. It is evident that most of the deformation is localized within the foam, whereas the external edges tend to maintain the equilibrium planar configuration.

## Summary

The proposed autonomous actuator prototype is one of the largest ever manufactured by using shape memory polymer composites and already shows a high potential to be used at an industrial level for self-deployable structures or grabbing devices. Moreover, it includes all the innovations developed in the field of SMPCs, such as the co-processing of different epoxy systems and the embedding of electrical devices. Commercially available materials and components have been used, thus facilitating the quality control and acceptance procedure typical of high added value industrial fields.

The proposed CFR-SMPC sandwich device exhibits optimal shape memory capabilities compared to standard laminate. Higher shape fixity ratios (85% on average) and even higher shape recovery ratios (also approaching 100% of initial strain) have been obtained. These performances are mainly due to the embedded epoxy foams, which freeze most of the applied deformation, also reducing stress concentration on the CFR skins. The slight increase of mass minimally affects the recovery load, whose values are comparable not only to the peak loads developed during the memory tests but also to the ones extracted for the SMPC laminate.

Small displacements have been applied during testing for a correct comparison between the two devices under bending. On the other side, higher deformation capabilities have been demonstrated by imposing a radius of curvature of 10mm spread over the center of the sandwich actuator in correspondence to the embedded foams. Despite this, no evidence of irreversible damages is present so underlying that the proposed innovative actuator can undergo to severe and multiple
shape changes without compromising its mechanical performances. The proposed architecture can also allow tailoring of the whole material's mechanical and shape memory properties through a correct balance of the elastic contribution given by the CFR prepreg and the shape memory abilities given by the shape memory polymer. Further investigations could be carried out to evaluate the maximum applicable deformation before failure and to integrate the proposed actuators in devices to be used in soft robotics. Finally, numerical modelling could be implemented to evaluate alternative architectures of SMPC sandwich actuators aiming to optimize the manufacturing procedures and the required mechanical and shape memory performances.

## References

[1] Y. Liu, H. Du, L. Liu, J. Leng, Shape memory polymers and their composites in aerospace applications: a review, Smart Mater. Struct. 23(2) (2014) art n° 023001.
https://doi.org/10.1088/0964-1726/23/2/023001

[2] Y. Liu, Y. Guo, J. Zhao, X. Chen, H. Zhang, G. Hu, X. Yu, Z. Zhang, Carbon fiber reinforced shape memory polymer composites with superior mechanical performances, Compos. Sci. Technol. 177 (2019) 49-56. https://doi.org/10.1016/j.compoitech.2019.04.014

[3] D. Margoy, I. Gouzman, E. Groessman, A. Bulker, N. Eliaz, R. Verker, Epoxy-based shape memory composites for space applications, Acta Astronaut. 179 (2021) 908-919. https://doi.org/10.1016/j.actaastro.2020.08.026

[4] M.S. Murugan, S. Rao, M.C. Chiranjeevi, A. Revathi, K. V. Rao, S. Srihari, G.N. Dayananda, Actuation of shape memory polymer composites triggered by electrical resistive heating, J. Intel. Mat. Syst Str. 28(17) (2017) 2363-2371. https://doi.org/10.1177/1045389X17689944

[5] J. Kim, J.W. Kim, H.C. Kim, L. Zhai, H.U Ko, R.M. Mutoka, Review of soft actuator materials, International Journal of Precision Engineering and Manufacturing, 20 (2019) 2221-2241. https://doi.org/10.1007/s12541-019-00255-1

[6] M. Sobczyk, S. Wiesenhütter, J.R. Noennig, T. Wallmersperger, Smart materials in architecture for actuator and sensor applications: A review, J. Intel. Mat. Syst Str. 33(3) (2022) 379-399. https://doi.org/10.1177/1045389X211027954

[7] R. Rajagopalan, A.J. Petruska, D. Howard, A bi-state shape memory material composite soft actuator, Actuators, 11(3) (2022) art n° 86. https://doi.org/10.3390/act11030086

[8] Q. Ge, K.K. Westbrook, P.T. Mather, M.L. Dunn, H.J. Qi, Thermomechanical behavior of a two-way shape memory composite actuator, Smart Mater. Struct. 22 (2013) art n° 055009.
https://doi.org/10.1088/0964-1726/22/5/055009

[9] P. Robinson, A. Bismark, B. Zhang, H.A. Maples, Deployable, shape memory carbon fibre composites without shape memory constituents, Compos. Sci. Technol. 145 (2017) 96-104.
https://doi.org/10.1016/j.compscitech.2017.02.024

[10] F. Quadrini, D. Bellisario, L. Iorio, L. Santo, Shape memory polymer composites by molding aeronautical prepregs with shape memory polymer interlayers, Mater. Res. Express. 6(11) (2019) art n° 115711. https://doi.org/10.1088/2053-1591/ab50ad

[11] F. Quadrini, L. Iorio, D. Bellisario, L. Santo, Durability of shape memory polymer composite laminates under thermo-mechanical cycling, J. Compos. Sci. 6(3) (2022) art n° 91.
https://doi.org/10.3390/jcs6030091

[12] F. Quadrini, L. Iorio, D. Bellisario, L. Santo, Shape memory polymer composite unit with embedded heater, Smart Mater. Struct. 30(7) (2021) art n° 075009. https://doi.org/10.1088/1361-665X/ac00cb.
shape changes without compromising its mechanical performances. The proposed architecture can also allow tailoring of the whole material's mechanical and shape memory properties through a correct balance of the elastic contribution given by the CFR prepreg and the shape memory abilities given by the shape memory polymer. Further investigations could be carried out to evaluate the maximum applicable deformation before failure and to integrate the proposed actuators in devices to be used in soft robotics. Finally, numerical modelling could be implemented to evaluate alternative architectures of SMPC sandwich actuators aiming to optimize the manufacturing procedures and the required mechanical and shape memory performances.

## References

[1] Y. Liu, H. Du, L. Liu, J. Leng, Shape memory polymers and their composites in aerospace applications: a review, Smart Mater. Struct. 23(2) (2014) art n° 023001.
https://doi.org/10.1088/0964-1726/23/2/023001

[2] Y. Liu, Y. Guo, J. Zhao, X. Chen, H. Zhang, G. Hu, X. Yu, Z. Zhang, Carbon fiber reinforced shape memory polymer composites with superior mechanical performances, Compos. Sci. Technol. 177 (2019) 49-56. https://doi.org/10.1016/j.compoitech.2019.04.014

[3] D. Margoy, I. Gouzman, E. Groessman, A. Bulker, N. Eliaz, R. Verker, Epoxy-based shape memory composites for space applications, Acta Astronaut. 179 (2021) 908-919. https://doi.org/10.1016/j.actaastro.2020.08.026

[4] M.S. Murugan, S. Rao, M.C. Chiranjeevi, A. Revathi, K. V. Rao, S. Srihari, G.N. Dayananda, Actuation of shape memory polymer composites triggered by electrical resistive heating, J. Intel. Mat. Syst Str. 28(17) (2017) 2363-2371. https://doi.org/10.1177/1045389X17689944

[5] J. Kim, J.W. Kim, H.C. Kim, L. Zhai, H.U Ko, R.M. Mutoka, Review of soft actuator materials, International Journal of Precision Engineering and Manufacturing, 20 (2019) 2221-2241. https://doi.org/10.1007/s12541-019-00255-1

[6] M. Sobczyk, S. Wiesenhütter, J.R. Noennig, T. Wallmersperger, Smart materials in architecture for actuator and sensor applications: A review, J. Intel. Mat. Syst Str. 33(3) (2022) 379-399. https://doi.org/10.1177/1045389X211027954

[7] R. Rajagopalan, A.J. Petruska, D. Howard, A bi-state shape memory material composite soft actuator, Actuators, 11(3) (2022) art n° 86. https://doi.org/10.3390/act11030086

[8] Q. Ge, K.K. Westbrook, P.T. Mather, M.L. Dunn, H.J. Qi, Thermomechanical behavior of a two-way shape memory composite actuator, Smart Mater. Struct. 22 (2013) art n° 055009.
https://doi.org/10.1088/0964-1726/22/5/055009

[9] P. Robinson, A. Bismark, B. Zhang, H.A. Maples, Deployable, shape memory carbon fibre composites without shape memory constituents, Compos. Sci. Technol. 145 (2017) 96-104.
https://doi.org/10.1016/j.compscitech.2017.02.024

[10] F. Quadrini, D. Bellisario, L. Iorio, L. Santo, Shape memory polymer composites by molding aeronautical prepregs with shape memory polymer interlayers, Mater. Res. Express. 6(11) (2019) art n° 115711. https://doi.org/10.1088/2053-1591/ab50ad

[11] F. Quadrini, L. Iorio, D. Bellisario, L. Santo, Durability of shape memory polymer composite laminates under thermo-mechanical cycling, J. Compos. Sci. 6(3) (2022) art n° 91.
https://doi.org/10.3390/jcs6030091

[12] F. Quadrini, L. Iorio, D. Bellisario, L. Santo, Shape memory polymer composite unit with embedded heater, Smart Mater. Struct. 30(7) (2021) art n° 075009. https://doi.org/10.1088/1361-665X/ac00cb.
[13] X. Guo, Q. Yang, H. Zheng, W. Dong, Integrated composite electrothermal de-icing system based on ultra-thin flexible heating film, Appl. Therm. Eng. 236 (2024) art n° 121723.
https://doi.org/10.1016/j.applthermaleng.2023.121723

[14] G. Karalis, L. Tzounis, E. Dimos, C.K. Mytafides, M. Liebscher, A. KarydisMessinis, N.E. Zafeiropoulos, A.S. Paipetis, Printed single-wall carbon nanotube-based joule heating devices integrated as functional laminae in advanced composites, ACS Appl. Mater. Interfaces. 13 (2021) 39880-39893. https://doi.org/10.1021/acsami.1c10001

[15] E.A. Squeo, F. Quadrini, Shape memory epoxy foams by solid-state foaming, Smart Mater. Struct. 19(10) (2010) art n° 105002. https://doi.org/10.1088/0964-1726/19/10/105002

[16] L. Iorio, D. Bellisario, F. Quadrini, Manufacturing and testing of shape memory polymer composite actuators, in: Carrino, L., Galantucci, L.M., Settineri, L. (Eds), Lecture Notes in Mechanical Engineering, Springer, E-Publishng Inc., Cham, 2023, pp. 141-157. https://doi.org/10.1007/978-3-031-41163-2_9
[13] X. Guo, Q. Yang, H. Zheng, W. Dong, Integrated composite electrothermal de-icing system based on ultra-thin flexible heating film, Appl. Therm. Eng. 236 (2024) art n° 121723.
https://doi.org/10.1016/j.applthermaleng.2023.121723

[14] G. Karalis, L. Tzounis, E. Dimos, C.K. Mytafides, M. Liebscher, A. KarydisMessinis, N.E. Zafeiropoulos, A.S. Paipetis, Printed single-wall carbon nanotube-based joule heating devices integrated as functional laminae in advanced composites, ACS Appl. Mater. Interfaces. 13 (2021) 39880-39893. https://doi.org/10.1021/acsami.1c10001

[15] E.A. Squeo, F. Quadrini, Shape memory epoxy foams by solid-state foaming, Smart Mater. Struct. 19(10) (2010) art n° 105002. https://doi.org/10.1088/0964-1726/19/10/105002

[16] L. Iorio, D. Bellisario, F. Quadrini, Manufacturing and testing of shape memory polymer composite actuators, in: Carrino, L., Galantucci, L.M., Settineri, L. (Eds), Lecture Notes in Mechanical Engineering, Springer, E-Publishng Inc., Cham, 2023, pp. 141-157. https://doi.org/10.1007/978-3-031-41163-2_9
# Cellular automata and crystal plasticity modelling for metal additive manufacturing

KAVOUSI Majid<fnref n="1" />,ᵃ*, MCGARRY Patrick<fnref n="2" />,ᵇ, MCHUGH Peter<fnref n="2" />,ᶜ and LEEN Seán<fnref n="1" />,ᵈ

**Keywords:** Additive Manufacturing, Cellular Automaton, Crystal Plasticity

**Abstract.** This paper presents a methodology to establish a process-structure-property (PSP) relationship for the additive manufacturing (AM) of small AISI 316L parts, as might be used in coronary stent applications. The methodology includes a physically based process-structure model based on cellular automata (CA) for microstructure characterization and generation, coupled with crystal plasticity finite element (CPFE) structure-property modelling to predict the mechanical response of the AM part under tensile loading. The effect of AM process variables, such as laser power and scanning speed, are reflected in the PSP modelling through the thermal modelling of AM feeding into the CA model. The CA method is shown to be able to capture microstructure texture, which is key to anisotropic behavior of AM parts. The present study aims to (i) establish a practical link between CA and CPFE models and (ii) identify optimal process variables with respect to ductility.

## Introduction

Metal additive manufacturing (AM) is revolutionizing the manufacturing industry through a layer-by-layer built process, enabling highly complex, bespoke, and customizable designs, especially in biomedical application. However, the characteristic microstructures resulting from metal AM processes, including grain morphologies and texture distributions, as well as void distributions, for example, are quite different from those of more conventional manufacturing processes. These AM-induced microstructures and defects in turn have a strong influence on resulting mechanical behavior. This can lead to undesirable and hard-to-predict mechanical properties [1].

The texture associated with AM parts and the build direction have been shown to result in orientation-dependent and anisotropic mechanical properties, such as ductility and tensile strength [2,3]. This may be attributed to the directional and high cooling rates in powder bed fusion (PBF) and the epitaxial and directional solidification of cubic crystals (such as FCC for 316L stainless steel).

It is difficult to predict the relationships between process variables and the mechanical response of the printed part or to design the process to achieve specific mechanical performance. Computational simulation is a possible methodology to help understand these relationships and thus the micro-mechanical characteristics of metal AM parts.

The present work is focused on development of a physically based process-structure-property (PSP) methodology for powder bed fusion (PBF), to provide a better understanding of the effects of process variables, and hence facilitate improved process design to avoid detrimental defects and achieve specific mechanical response.

In this study, a cellular automata (CA) process-structure model, for simulation of AM-induced microstructure for thin stainless-steel members [4], is sequentially coupled with a crystal plasticity

<figure><img src="image_2270.png" /></figure>

<footnote n="1">¹Mechanical Engineering, School of Engineering, University of Galway, Galway, Ireland</footnote>

<footnote n="2">²Biomedical Engineering, School of Engineering, University of Galway, Galway, Ireland</footnote>

<footnote>ᵃm.kavousi1@universityofgalway.ie, ᵇpatrick.mcgarry@universityofgalway.ie,</footnote>

<footnote>ᶜpeter.mchugh@universityofgalway.ie, ᵈsean.leen@universityofgalway.ie</footnote>
# Cellular automata and crystal plasticity modelling for metal additive manufacturing

KAVOUSI Majid<fnref n="1" />,ᵃ*, MCGARRY Patrick<fnref n="2" />,ᵇ, MCHUGH Peter<fnref n="2" />,ᶜ and LEEN Seán<fnref n="1" />,ᵈ

**Keywords:** Additive Manufacturing, Cellular Automaton, Crystal Plasticity

**Abstract.** This paper presents a methodology to establish a process-structure-property (PSP) relationship for the additive manufacturing (AM) of small AISI 316L parts, as might be used in coronary stent applications. The methodology includes a physically based process-structure model based on cellular automata (CA) for microstructure characterization and generation, coupled with crystal plasticity finite element (CPFE) structure-property modelling to predict the mechanical response of the AM part under tensile loading. The effect of AM process variables, such as laser power and scanning speed, are reflected in the PSP modelling through the thermal modelling of AM feeding into the CA model. The CA method is shown to be able to capture microstructure texture, which is key to anisotropic behavior of AM parts. The present study aims to (i) establish a practical link between CA and CPFE models and (ii) identify optimal process variables with respect to ductility.

**Introduction**

Metal additive manufacturing (AM) is revolutionizing the manufacturing industry through a layer-by-layer built process, enabling highly complex, bespoke, and customizable designs, especially in biomedical application. However, the characteristic microstructures resulting from metal AM processes, including grain morphologies and texture distributions, as well as void distributions, for example, are quite different from those of more conventional manufacturing processes. These AM-induced microstructures and defects in turn have a strong influence on resulting mechanical behavior. This can lead to undesirable and hard-to-predict mechanical properties [1].

The texture associated with AM parts and the build direction have been shown to result in orientation-dependent and anisotropic mechanical properties, such as ductility and tensile strength [2,3]. This may be attributed to the directional and high cooling rates in powder bed fusion (PBF) and the epitaxial and directional solidification of cubic crystals (such as FCC for 316L stainless steel).

It is difficult to predict the relationships between process variables and the mechanical response of the printed part or to design the process to achieve specific mechanical performance. Computational simulation is a possible methodology to help understand these relationships and thus the micro-mechanical characteristics of metal AM parts.

The present work is focused on development of a physically based process-structure-property (PSP) methodology for powder bed fusion (PBF), to provide a better understanding of the effects of process variables, and hence facilitate improved process design to avoid detrimental defects and achieve specific mechanical response.

In this study, a cellular automata (CA) process-structure model, for simulation of AM-induced microstructure for thin stainless-steel members [4], is sequentially coupled with a crystal plasticity

<figure><img src="image_2261.png" /></figure>

<footnote n="1">¹Mechanical Engineering, School of Engineering, University of Galway, Galway, Ireland</footnote>

<footnote n="2">²Biomedical Engineering, School of Engineering, University of Galway, Galway, Ireland</footnote>

<footnote>ᵃm.kavousi1@universityofgalway.ie, ᵇpatrick.mcgarry@universityofgalway.ie,</footnote>

<footnote>ᶜpeter.mchugh@universityofgalway.ie, ᵈsean.leen@universityofgalway.ie</footnote>
finite element (CPFE) structure-property model to predict mechanical response of the synthetically-generated CA microstructure-sensitive models under tensile loading.

## Methodology

### Cellular automata solidification growth model

A single dendrite with a face-centered cubic (fcc) lattice structure is shown to grow with an octahedral grain morphology in an undercooled melt, in both experiments [5] and simulations [6]. <100> directions represent the half diagonals of the octahedron. All the diagonals of the octahedron are of the same length under uniform thermal conditions as shown in Fig. 1 (a). For a 2D representation of the growth envelope, one of the <100> directions of the grain is assumed to be normal to the 2D simulation plane (Fig. 1 (b))

<figure><img src="image_2271.png" /><figcaption>Fig. 1 The growth envelope under uniform thermal conditions in (a) 3D and (b) 2D, (c) thermal gradient in y direction in 2D.</figcaption></figure>

The basic cellular automata (CA) algorithm for modelling solidification growth is described in terms of the growth of a single nucleus in a melt pool with uniform temperature distribution. The physical and thermal parameters are the same as those used in [7]. A rectangular domain of size $L_x \times L_y$ is assumed in the x-y plane. The domain is divided into a grid of square cells of size $\Delta x$, resulting in $n_x$ and $n_y$ cells in the x and y directions, respectively. $T_{ij}$ denotes the temperature of cell ij where $i \in \{1, ..., n_y\}$ and $j \in \{i, ..., n_x\}$. The undercooling is defined as:

$$ \Delta T = T_{liq} - T_{ij} \qquad (1) $$

where $T_{liq}$ is liquidus temperature. The initial state of the cells is set as liquid. An initial undercooling of 2K is assigned to all cells to initiate the growth of the nuclei [7]. A nucleus is assumed to be developed from the centre of cell $\eta$. The initial shape of the grain in 2D is a square where the [100] direction is rotated by an angle $\theta$ about the x-axis. The square engulfs the dendrite main trunks and arms. The size of the square depends on speed of the dendrite tip, $v_{tip}$, which itself is a function of local undercooling, $\Delta T$. The following relationship is proposed by Kurz et al. [8] between $v_{tip}$ and $\Delta T$:

$$ v_{tip} = A(\Delta T)^2 \qquad (2) $$

where A is a material dependent constant. The half size of the growth square of the nucleus centered on cell $\eta$ (see Fig. 2 (a)) at time t can be calculated from Eq. (3) or Eq. (4), as below:

$$ L_{\eta}^{t} = \frac{1}{\sqrt{2}} \int_{t_0}^{t} v[\Delta T_{\eta}(\tau)] \cdot d\tau \qquad (3) $$
finite element (CPFE) structure-property model to predict mechanical response of the synthetically-generated CA microstructure-sensitive models under tensile loading.

## Methodology

### Cellular automata solidification growth model

A single dendrite with a face-centered cubic (fcc) lattice structure is shown to grow with an octahedral grain morphology in an undercooled melt, in both experiments [5] and simulations [6]. <100> directions represent the half diagonals of the octahedron. All the diagonals of the octahedron are of the same length under uniform thermal conditions as shown in Fig. 1 (a). For a 2D representation of the growth envelope, one of the <100> directions of the grain is assumed to be normal to the 2D simulation plane (Fig. 1 (b))

<figure><img src="image_2262.png" /><figcaption>Fig. 1 The growth envelope under uniform thermal conditions in (a) 3D and (b) 2D, (c) thermal gradient in y direction in 2D.</figcaption></figure>

The basic cellular automata (CA) algorithm for modelling solidification growth is described in terms of the growth of a single nucleus in a melt pool with uniform temperature distribution. The physical and thermal parameters are the same as those used in [7]. A rectangular domain of size $L_x \times L_y$ is assumed in the x-y plane. The domain is divided into a grid of square cells of size $\Delta x$, resulting in $n_x$ and $n_y$ cells in the x and y directions, respectively. $T_{ij}$ denotes the temperature of cell ij where $i \in \{1, ..., n_y\}$ and $j \in \{i, ..., n_x\}$. The undercooling is defined as:

$$ \Delta T = T_{liq} - T_{ij} \qquad (1) $$

where $T_{liq}$ is liquidus temperature. The initial state of the cells is set as liquid. An initial undercooling of 2K is assigned to all cells to initiate the growth of the nuclei [7]. A nucleus is assumed to be developed from the centre of cell $\eta$. The initial shape of the grain in 2D is a square where the [100] direction is rotated by an angle $\theta$ about the x-axis. The square engulfs the dendrite main trunks and arms. The size of the square depends on speed of the dendrite tip, $v_{tip}$, which itself is a function of local undercooling, $\Delta T$. The following relationship is proposed by Kurz et al. [8] between $v_{tip}$ and $\Delta T$:

$$ v_{tip} = A(\Delta T)^2 \qquad (2) $$

where A is a material dependent constant. The half size of the growth square of the nucleus centered on cell $\eta$ (see Fig. 2 (a)) at time t can be calculated from Eq. (3) or Eq. (4), as below:

$$ L_{\eta}^{t} = \frac{1}{\sqrt{2}} \int_{t_0}^{t} v[\Delta T_{\eta}(\tau)]. d\tau \qquad (3) $$
$$L_{\eta}^{t} = \frac{1}{\sqrt{2}} \sum_{\tau=t_0}^{t} v[\Delta T_{\eta}(\tau)] \cdot \Delta \tau \quad (4)$$

New cells are captured as soon as their centre is engulfed by a growth square. The time increment at which four neighbors of cell $\eta$, one highlighted as cell $\mu$ for further explanation, are captured as shown in Fig. 2 (b). Once a new cell is captured, it inherits the properties of the parent cell, i.e., the grain identification number (grain ID) and misorientation, and its state changes liquid to solid. So far, the centre of the growth square is fixed at its initial location, and it keeps growing as long as $\Delta T > 0$, resulting into two issues: (i) the growth square becomes so large that it captures cells that should have been captured by other grains, as in Fig. 2 (c), and (ii) failure to take into account the local undercooling as the growth square grows.

<figure><img src="image_2272.png" /><figcaption>Fig. 2. The cell capturing mechanism in 2D CA: (a) the growth square, $S_{\eta}^t$, of the nucleus placed on the centre of cell $\eta$ with a misorientation angle of $\theta$ and its half size, $L_{\eta}^t$, shown, (b) the time increment at which the cell $\mu$ is captured by the growth square of cell $\eta$. The new truncated decentred growth square for the newly captured cell $\mu$, with is half size of $L_{\mu}^t$ is shown as well ($S_{\mu}^t$), and (c) capturing wrong cells by the yellow growth square when it keeps growing.</figcaption></figure>

To overcome this problem, the decentered square algorithm is introduced. Whenever a new cell is captured, a new growth square is defined for that cell with the following criteria:

1. The new square is fully inside the parent square.

2. A corner of the new square coincides with a corner of the parent square which is closest to the centre of the newly captured cell.

3. The half size of the new square is calculated as below (considering the capture of cell $\mu$ as shown in Fig. 2 (b)):

$$L_{\mu}^{t} = \frac{1}{2} [\min(L_{\mu 1}^{t}, \sqrt{2}\Delta x) + \min(L_{\mu 2}^{t}, \sqrt{2}\Delta x)] \quad (5)$$

where $L_{\mu 1}^t$ and $L_{\mu 2}^t$ are the distances of centre of cell $\mu$ from the two opposite faces of the parent square along the capturing face (the face that has captured cell $\mu$). The growth squares of cell $\eta$ at times $t$ and $t - \delta t$, and the growth square of the captured cell $\mu$ are shown in Fig. 2(b) as $S_{\eta}^t$, $S_{\eta}^{t-\delta t}$, and $S_{\mu}^t$, respectively. The newly defined growth squares will grow similarly in each time increment, except with the undercooling associated with their own cell. Once all cells in the Moore neighborhood [9] of a cell are captured, its growth square is deactivated. In the case that multiple squares try to capture a particular cell at the same time step, the first capture in the iteration order
$$L_{\eta}^{t} = \frac{1}{\sqrt{2}} \sum_{\tau=t_0}^{t} v[\Delta T_{\eta}(\tau)] \cdot \Delta \tau \quad (4)$$

New cells are captured as soon as their centre is engulfed by a growth square. The time increment at which four neighbors of cell $\eta$, one highlighted as cell $\mu$ for further explanation, are captured as shown in Fig. 2 (b). Once a new cell is captured, it inherits the properties of the parent cell, i.e., the grain identification number (grain ID) and misorientation, and its state changes liquid to solid. So far, the centre of the growth square is fixed at its initial location, and it keeps growing as long as $\Delta T > 0$, resulting into two issues: (i) the growth square becomes so large that it captures cells that should have been captured by other grains, as in Fig. 2 (c), and (ii) failure to take into account the local undercooling as the growth square grows.

<figure><img src="image_2263.png" /><figcaption>Fig. 2. The cell capturing mechanism in 2D CA: (a) the growth square, $S_{\eta}^t$, of the nucleus placed on the centre of cell $\eta$ with a misorientation angle of $\theta$ and its half size, $L_{\eta}^t$, shown, (b) the time increment at which the cell $\mu$ is captured by the growth square of cell $\eta$. The new truncated decentred growth square for the newly captured cell $\mu$, with is half size of $L_{\mu}^t$ is shown as well ($S_{\mu}^t$), and (c) capturing wrong cells by the yellow growth square when it keeps growing.</figcaption></figure>

To overcome this problem, the decentered square algorithm is introduced. Whenever a new cell is captured, a new growth square is defined for that cell with the following criteria:

1. The new square is fully inside the parent square.

2. A corner of the new square coincides with a corner of the parent square which is closest to the centre of the newly captured cell.

3. The half size of the new square is calculated as below (considering the capture of cell $\mu$ as shown in Fig. 2 (b)):

$$L_{\mu}^{t} = \frac{1}{2} [\min(L_{\mu1}^{t}, \sqrt{2\Delta x}) + \min(L_{\mu2}^{t}, \sqrt{2\Delta x})] \quad (5)$$

where $L_{\mu1}^t$ and $L_{\mu2}^t$ are the distances of centre of cell $\mu$ from the two opposite faces of the parent square along the capturing face (the face that has captured cell $\mu$). The growth squares of cell $\eta$ at times $t$ and $t - \delta t$, and the growth square of the captured cell $\mu$ are shown in Fig. 2(b) as $S_{\eta}^t, S_{\eta}^{t-\delta t}$, and $S_{\mu}^t$, respectively. The newly defined growth squares will grow similarly in each time increment, except with the undercooling associated with their own cell. Once all cells in the Moore neighborhood [9] of a cell are captured, its growth square is deactivated. In the case that multiple squares try to capture a particular cell at the same time step, the first capture in the iteration order
takes precedence. In some cases, the square of the captured cell completely overlaps with the parent square; in such cases, the new square is deactivated for computational efficiency.

### Grain growth algorithm validation

The CA model for the decentered square grain growth algorithm is validated against the analytical model [10] which, in turn, was validated against experiments [11]. A 10 mm × 10 mm square domain is considered with a cell size of $Δx = 5 × 10^{-5}$ m resulting in $4 × 10^4$ cells. A nucleus is placed on the cell in the centre of the domain with a misorientation angle of $θ = 30°$. Three different thermal conditions are defined based on the work of Gandin et al. [10], including spatially isothermal cooling, static thermal field, and Bridgman condition with a fourth condition as static temperature for comparison, as listed in Table 1. A cooling rate of $\dot{T} = -0.1$ Ks$^{-1}$ and a thermal gradient of $G = 250$ Km$^{-1}$ in the Y-direction is used where needed. For all cases, the initial undercooling is 2K, and the time increment is 0.01s.

<table><caption>Table 1. Different modes of thermal conditions for the simulation of growth of a single nucleus using decentered square algorithm.</caption><thead><tr><th>Mode 1:<br>Spatially isothermal cooling</th><th>Mode 2:<br>Static thermal field</th><th>Mode 3:<br>Bridgman condition</th><th>Mode 4:<br>Static temperature</th></tr></thead><tbody><tr><td>$G = 0.0$ Km$^{-1}$<br>$\dot{T} = -0.1$ Ks$^{-1}$</td><td>$G = 250$ Km$^{-1}$ (Y dir.)<br>$\dot{T} = 0.0$ Ks$^{-1}$</td><td>$G = 250$ Km$^{-1}$ (Y dir.)<br>$\dot{T} = -0.1$ Ks$^{-1}$</td><td>$G = 0.0$ Km$^{-1}$<br>$\dot{T} = 0.0$ Ks$^{-1}$</td></tr></tbody></table>

The evolution of the grain boundary in the CA decentered square algorithm is visualized with 1 s time intervals for all thermal modes listed in Table 1 in Fig. 3 (a-d). The first three modes match perfectly with the analytical results [10], while the fourth mode is also a consistent result. For spatially isothermal cooling, the grain grows uniformly, and the growth rate increases over time as the undercooling increases (see Fig. 3(a)). The static thermal field and Bridgman condition resulted in non-uniform grain growth induced by the thermal gradient, $G$, where grains grow faster in the Bridgman condition because of the presence of cooling rate, $\dot{T}$, as in Fig. 3(b,c). The static temperature mode, on the other hand, produces uniform grain growth with constant growth rate (i.e., equally spaced grain boundaries in 1 s time intervals) as the only reason of grain growth in the initial undercooling (see Fig. 3(d)). The decentered square CA algorithm is developed using MATLAB.

<figure><img src="image_2273.png" /><figcaption>Fig. 3. The grain boundary of the growing grain associated with the single nucleus on the centre of the domain plotted at 1 s time intervals for different thermal conditions: (a) spatially isothermal cooling, (b) static thermal field, (c) Bridgman condition, and (d) static temperature.</figcaption></figure>
takes precedence. In some cases, the square of the captured cell completely overlaps with the parent square; in such cases, the new square is deactivated for computational efficiency.

### Grain growth algorithm validation

The CA model for the decentered square grain growth algorithm is validated against the analytical model [10] which, in turn, was validated against experiments [11]. A 10 mm × 10 mm square domain is considered with a cell size of $Δx = 5 × 10^{-5}$ m resulting in $4 × 10^4$ cells. A nucleus is placed on the cell in the centre of the domain with a misorientation angle of $θ = 30°$. Three different thermal conditions are defined based on the work of Gandin et al. [10], including spatially isothermal cooling, static thermal field, and Bridgman condition with a fourth condition as static temperature for comparison, as listed in Table 1. A cooling rate of $\dot{T} = -0.1$ Ks$^{-1}$ and a thermal gradient of $G = 250$ Km$^{-1}$ in the Y-direction is used where needed. For all cases, the initial undercooling is 2K, and the time increment is 0.01s.

<table><caption>Table 1. Different modes of thermal conditions for the simulation of growth of a single nucleus using decentered square algorithm.</caption><thead><tr><th>Mode 1:<br>Spatially isothermal cooling</th><th>Mode 2:<br>Static thermal field</th><th>Mode 3:<br>Bridgman condition</th><th>Mode 4:<br>Static temperature</th></tr></thead><tbody><tr><td>$G = 0.0$ Km$^{-1}$<br>$\dot{T} = -0.1$ Ks$^{-1}$</td><td>$G = 250$ Km$^{-1}$ (Y dir.)<br>$\dot{T} = 0.0$ Ks$^{-1}$</td><td>$G = 250$ Km$^{-1}$ (Y dir.)<br>$\dot{T} = -0.1$ Ks$^{-1}$</td><td>$G = 0.0$ Km$^{-1}$<br>$\dot{T} = 0.0$ Ks$^{-1}$</td></tr></tbody></table>

The evolution of the grain boundary in the CA decentered square algorithm is visualized with 1 s time intervals for all thermal modes listed in Table 1 in Fig. 3 (a-d). The first three modes match perfectly with the analytical results [10], while the fourth mode is also a consistent result. For spatially isothermal cooling, the grain grows uniformly, and the growth rate increases over time as the undercooling increases (see Fig. 3(a)). The static thermal field and Bridgman condition resulted in non-uniform grain growth induced by the thermal gradient, $G$, where grains grow faster in the Bridgman condition because of the presence of cooling rate, $\dot{T}$, as in Fig. 3(b,c). The static temperature mode, on the other hand, produces uniform grain growth with constant growth rate (i.e., equally spaced grain boundaries in 1 s time intervals) as the only reason of grain growth in the initial undercooling (see Fig. 3(d)). The decentered square CA algorithm is developed using MATLAB.

<figure><img src="image_2264.png" /><figcaption>Fig. 3. The grain boundary of the growing grain associated with the single nucleus on the centre of the domain plotted at 1 s time intervals for different thermal conditions: (a) spatially isothermal cooling, (b) static thermal field, (c) Bridgman condition, and (d) static temperature.</figcaption></figure>
To model the micro-mechanical behaviour of individual grains of 316L austenitic stainless steel, with a face-centered-cubic (FCC) crystal microstructure and 12 slip systems, single crystal plasticity theory was employed, based on the work of Hill [12], Rice [13], and Asaro [14]. This constitutive behavior has been implemented in a user-defined material (UMAT) for Abaqus [15,16] and is adopted here. More detailed description of the constitutive model is given in our previous work [4].

## Results and discussion

The proposed CA model when combined with the thermal histories of PBF for metal can produce microstructures that represent AM parts. As a preliminary study, a rectangular model representing a single track-like laser scan, with a thermal gradient in the y direction, is modelled, as depicted in Fig. 4(a) with grains y-color map according to the IPF color key. It is apparent from the model that the grains with <100> crystallographic orientations almost parallel to the y-axis (build direction) tend to grow faster and eliminate neighboring grains that are not suitable for fast growth (grains with green colors or with <101> direction parallel to the y-axis).

<figure><img src="image_2274.png" /><figcaption>Fig. 4. CA microstructure model: (a) a sample CA microstructure with grains colored (in direction) according to (b) IPF color key, (c) jagged grain boundaries in a three grain CA growth model, and (d) the grain boundaries after smoothing.</figcaption></figure>

## CA model optimization for meshing

In a multi-grain CA model, the grain boundaries may exhibit artificial (synthetic) roughness, as illustrated in Fig. 4(d) for the case of three grains. To mitigate this artifice, a smoothing algorithm is employed to refine the grain boundaries. To achieve this, the grain identification number assigned to each cell is compared with the numbers attributed to the majority of its neighboring cells and changed accordingly. This process eliminates isolated cells and effectively smoothens the jagged grain boundaries, as depicted in Fig. 4(e).

As part of the process-structure-property methodology, the CA microstructure should be converted into a suitable mesh for crystal plasticity finite element (CPFE) analysis. The pixels or cells (voxels in 3D) in the CA model can be converted into regular quadrilateral (hexahedral in
To model the micro-mechanical behaviour of individual grains of 316L austenitic stainless steel, with a face-centered-cubic (FCC) crystal microstructure and 12 slip systems, single crystal plasticity theory was employed, based on the work of Hill [12], Rice [13], and Asaro [14]. This constitutive behavior has been implemented in a user-defined material (UMAT) for Abaqus [15,16] and is adopted here. More detailed description of the constitutive model is given in our previous work [4].

## Results and discussion

The proposed CA model when combined with the thermal histories of PBF for metal can produce microstructures that represent AM parts. As a preliminary study, a rectangular model representing a single track-like laser scan, with a thermal gradient in the y direction, is modelled, as depicted in Fig. 4(a) with grains y-color map according to the IPF color key. It is apparent from the model that the grains with <100> crystallographic orientations almost parallel to the y-axis (build direction) tend to grow faster and eliminate neighboring grains that are not suitable for fast growth (grains with green colors or with <101> direction parallel to the y-axis).

<figure><img src="image_2265.png" /><figcaption>Fig. 4. CA microstructure model: (a) a sample CA microstructure with grains colored (in direction) according to (b) IPF color key, (c) jagged grain boundaries in a three grain CA growth model, and (d) the grain boundaries after smoothing.</figcaption></figure>

## CA model optimization for meshing

In a multi-grain CA model, the grain boundaries may exhibit artificial (synthetic) roughness, as illustrated in Fig. 4(d) for the case of three grains. To mitigate this artifice, a smoothing algorithm is employed to refine the grain boundaries. To achieve this, the grain identification number assigned to each cell is compared with the numbers attributed to the majority of its neighboring cells and changed accordingly. This process eliminates isolated cells and effectively smoothens the jagged grain boundaries, as depicted in Fig. 4(e).

As part of the process-structure-property methodology, the CA microstructure should be converted into a suitable mesh for crystal plasticity finite element (CPFE) analysis. The pixels or cells (voxels in 3D) in the CA model can be converted into regular quadrilateral (hexahedral in
3D) elements. However, this has two main drawbacks: (i) stepped grain boundaries (GBs) which are not appropriate for simulating phenomena like GB sliding, and (ii) a large number of elements due to the relatively small cell size required for CA growth modelling [17]. Alternatively, the CA microstructure model can be meshed using 2D triangular (or 3D tetrahedral) elements within the MATLAB code. For this purpose, GBs in the CA model are extracted for all grains (see Fig. 5(a)). Then, for each grain, the initial GB is rearranged to represent the correct connectivity order, creating a polygon for each grain. This polygon can be meshed straight away. But, since the GB polygons are comprised of the cell edges, the issue with the stepped grain boundaries persists and results in non-uniform mesh distribution with very small elements near the GBs as depicted in Fig. 5(b). To rectify this problem, a Ramer-Douglas-Peucker (RDP) algorithm [18,19] is utilized to simplify the GBs. The triple points for each grain are used as the initial points to start the RDP algorithm. Fig. 5(c) shows the simplified GBs along with the initial ones for the same 10 grain CA microstructure model shown in Fig. 5(c). The significant improvement of the mesh quality using the simplified GBs as input is evident, not only near the GBs but also inside the grain, as illustrated in Fig. 5(d).

<figure><img src="image_2275.png" /><figcaption>Fig. 5. CA model optimization for FE meshing: (a) the initial grain boundaries (GB) of a CA model with 10 grains with a portion magnified to show the stepped grain boundaries, (b) the non-uniform mesh generated using the initial GBs with very small mesh close to GBs, (c) the simplified GBs using the RDP algorithm, and (d) the generated mesh using the simplified GBs.</figcaption></figure>

### CPFE tensile analysis of CA model

A tensile macroscopic strain of up to 50% has been applied to the microstructure produced with the CA model as shown Fig. 4(a) and the tensile response is analyzed using the CPFE material model. The strain contour plot of the deformed microstructure is depicted in Fig. 6. The FE model is constrained from the two ends and the upper and lower sides are unconstrained, mimicking minuscule components such as cardiovascular stent struts, resulting in free deformation along the
3D) elements. However, this has two main drawbacks: (i) stepped grain boundaries (GBs) which are not appropriate for simulating phenomena like GB sliding, and (ii) a large number of elements due to the relatively small cell size required for CA growth modelling [17]. Alternatively, the CA microstructure model can be meshed using 2D triangular (or 3D tetrahedral) elements within the MATLAB code. For this purpose, GBs in the CA model are extracted for all grains (see Fig. 5(a)). Then, for each grain, the initial GB is rearranged to represent the correct connectivity order, creating a polygon for each grain. This polygon can be meshed straight away. But, since the GB polygons are comprised of the cell edges, the issue with the stepped grain boundaries persists and results in non-uniform mesh distribution with very small elements near the GBs as depicted in Fig. 5(b). To rectify this problem, a Ramer-Douglas-Peucker (RDP) algorithm [18,19] is utilized to simplify the GBs. The triple points for each grain are used as the initial points to start the RDP algorithm. Fig. 5(c) shows the simplified GBs along with the initial ones for the same 10 grain CA microstructure model shown in Fig. 5(c). The significant improvement of the mesh quality using the simplified GBs as input is evident, not only near the GBs but also inside the grain, as illustrated in Fig. 5(d).

<figure><img src="image_2266.png" /><figcaption>Fig. 5. CA model optimization for FE meshing: (a) the initial grain boundaries (GB) of a CA model with 10 grains with a portion magnified to show the stepped grain boundaries, (b) the non-uniform mesh generated using the initial GBs with very small mesh close to GBs, (c) the simplified GBs using the RDP algorithm, and (d) the generated mesh using the simplified GBs.</figcaption></figure>

## CPFE tensile analysis of CA model

A tensile macroscopic strain of up to 50% has been applied to the microstructure produced with the CA model as shown Fig. 4(a) and the tensile response is analyzed using the CPFE material model. The strain contour plot of the deformed microstructure is depicted in Fig. 6. The FE model is constrained from the two ends and the upper and lower sides are unconstrained, mimicking minuscule components such as cardiovascular stent struts, resulting in free deformation along the
length of the model. Due to heterogeneity of crystallographic orientation, the deformation is also non-uniform (heterogeneous) with regions of localized strains and macroscopic shear band aligned at 45° of the tensile direction.

<figure><img src="image_2276.png" /><figcaption>Fig. 6. The CPFE strain contour plot of the CA microstructure model under 50% macroscopic tensile deformation.</figcaption></figure>

## Conclusion

A cellular automata process-structure methodology for grain growth was developed, simulating dendritic growth under different thermal conditions – suitable for PBF microstructure morphology and texture modelling; this was linked to CPFE for tensile structure-property simulation, with 50% macroscopic elongation applied to the CA-CPFE model, revealing localized deformation and shear bands. Future and ongoing work includes CA-CPFE sensitivity studies to understand process variable effects on AM part performance, continuing our recent work on PSP modelling of AM 316L struts.

## Acknowledgements

This publication has emanated from research conducted with the financial support of University of Galway Hardiman PhD Scholarship (M. Kavousi) and Science Foundation Ireland under Grant number SFI/16/RC/3872. For the purpose of Open Access, the author has applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission.

## References

[1] T. Ronneberg, C.M. Davies, P.A. Hooper, Revealing relationships between porosity, microstructure and mechanical properties of laser powder bed fusion 316L stainless steel through heat treatment, Mater. Des. 189 (2020). https://doi.org/10.1016/j.matdes.2020.108481

[2] X. Yang, X. Wang, M. Brochu, X. Wang, N.M. Harrison, S.B. Leen, J. Segurado, Understanding orientation-dependent plasticity in laser beam powder bed fusion stainless steel through crystal plasticity modelling, Mater. Sci. Eng. A 852, (2022). https://doi.org/10.1016/j.msea.2022.143682

[3] X. Wang, J.A. Muñiz-Lerma, O. Sánchez-Mata, M.A. Shandiz, M. Brochu, Microstructure and mechanical properties of stainless steel 316L vertical struts manufactured by laser powder bed fusion process, Mater. Sci. Eng. A 736, (2018) 27-40. https://doi.org/10.1016/j.msea.2018.08.069

[4] M. Kavousi, P. McGarry, P. McHugh, S. Leen, Geometrical and crystal plasticity modelling: Towards the establishment of a process-structure-property relationship for additively manufactured 316L struts, Eur J Mech A Solids 102 (2023). https://doi.org/10.1016/j.euromechsol.2023.105115

[5] D.E. Ovsienko, G. A. Alfintsev, Crystal Growth from the Melt Experimental Investigation of Kinetics and Morphology, *Crystals: growth and properties*. Berlin: Springer-Verlag (1980): 119-70.

[6] G. I. Tóth, G. Tegze, T. Pusztai, G. Tóth, L. Gránásy, Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D, J. Phys. Condens. Matter 22 (2010). https://doi.org/10.1088/0953-8984/22/36/364101

[7] C.A. Gandin, M. Rappaz, A 3D cellular automaton algorithm for the prediction of dendritic grain growth, Acta Mater. 45 (1997) 2187-2195. https://doi.org/10.1016/S1359-6454(96)00303-5
length of the model. Due to heterogeneity of crystallographic orientation, the deformation is also non-uniform (heterogeneous) with regions of localized strains and macroscopic shear band aligned at 45° of the tensile direction.

<figure><img src="image_2267.png" /><figcaption>Fig. 6. The CPFE strain contour plot of the CA microstructure model under 50% macroscopic tensile deformation.</figcaption></figure>

## Conclusion

A cellular automata process-structure methodology for grain growth was developed, simulating dendritic growth under different thermal conditions – suitable for PBF microstructure morphology and texture modelling; this was linked to CPFE for tensile structure-property simulation, with 50% macroscopic elongation applied to the CA-CPFE model, revealing localized deformation and shear bands. Future and ongoing work includes CA-CPFE sensitivity studies to understand process variable effects on AM part performance, continuing our recent work on PSP modelling of AM 316L struts.

## Acknowledgements

This publication has emanated from research conducted with the financial support of University of Galway Hardiman PhD Scholarship (M. Kavousi) and Science Foundation Ireland under Grant number SFI/16/RC/3872. For the purpose of Open Access, the author has applied a CC BY public copyright license to any Author Accepted Manuscript version arising from this submission.

## References

[1] T. Ronneberg, C.M. Davies, P.A. Hooper, Revealing relationships between porosity, microstructure and mechanical properties of laser powder bed fusion 316L stainless steel through heat treatment, Mater. Des. 189 (2020). https://doi.org/10.1016/j.matdes.2020.108481

[2] X. Yang, X. Wang, M. Brochu, X. Wang, N.M. Harrison, S.B. Leen, J. Segurado, Understanding orientation-dependent plasticity in laser beam powder bed fusion stainless steel through crystal plasticity modelling, Mater. Sci. Eng. A 852, (2022). https://doi.org/10.1016/j.msea.2022.143682

[3] X. Wang, J.A. Muñiz-Lerma, O. Sánchez-Mata, M.A. Shandiz, M. Brochu, Microstructure and mechanical properties of stainless steel 316L vertical struts manufactured by laser powder bed fusion process, Mater. Sci. Eng. A 736, (2018) 27-40. https://doi.org/10.1016/j.msea.2018.08.069

[4] M. Kavousi, P. McGarry, P. McHugh, S. Leen, Geometrical and crystal plasticity modelling: Towards the establishment of a process-structure-property relationship for additively manufactured 316L struts, Eur J Mech A Solids 102 (2023). https://doi.org/10.1016/j.euromechsol.2023.105115

[5] D.E. Ovsienko, G. A. Alfintsev, Crystal Growth from the Melt Experimental Investigation of Kinetics and Morphology, *Crystals: growth and properties*. Berlin: Springer-Verlag (1980): 119-70.

[6] G. I. Tóth, G. Tegze, T. Pusztai, G. Tóth, L. Gránásy, Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D, J. Phys. Condens. Matter 22 (2010). https://doi.org/10.1088/0953-8984/22/36/364101

[7] C.A. Gandin, M. Rappaz, A 3D cellular automaton algorithm for the prediction of dendritic grain growth, Acta Mater. 45 (1997) 2187-2195. https://doi.org/10.1016/S1359-6454(96)00303-5
[8] W. Kurz, B. Giovanola, R. Trivedi, Theory of microstructural development during rapid solidification, Acta metall. 34 (1986) 823-830. https://doi.org/10.1016/0001-6160(86)90056-8

[9] D.A. Zaitsev, A generalized neighborhood for cellular automata, Theor Comput Sci 666 (2017) 21-35. https://doi.org/10.1016/j.tcs.2016.11.002

[10] C.A. Gandin, R.J. Schaefer, M. Rappaz, Analytical and numerical predictions of dendritic grain envelopes, Acta mater. 44.8 (1996) 3339-3347. https://doi.org/10.1016/1359-6454(95)00433-5

[11] D.E. Ovsienko, G.A. Alfintsev, V.V. Maslov, Kinetics and shape of crystal growth from the melt for substances with low L/kT values, J. Cryst. Growth 26 (1974) 233-238. https://doi.org/10.1016/0022-0248(74)90251-6

[12] R. Hill, Generalized constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids 14 (1966) 95-102. https://doi.org/10.1016/0022-5096(66)90040-8

[13] J.R. Rice, Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids 19 (1971) 433-455. https://doi.org/10.1016/0022-5096(71)90010-X

[14] R.J. Asaro, Micro Mechanics of Crystals and Polycrystals, Adv. Appl. Mech. 23 (1983) 1-115. https://doi.org/10.1016/S0065-2156(08)70242-4

[15] Y. Huang, A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Harvard Univ. Cambridge, MA, 1991.

[16] J. W. Kysar and P. Hall, Addendum to a User-material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program: Mech Report 178., Cambridge, 1997.

[17] J. Segurado, R.A. Lebensohn, J. Llorca, Computational Homogenization of Polycrystals, Adv. Appl. Mech. 51 (2018) 1-114. https://doi.org/10.1016/bs.aams.2018.07.001

[18] D.H. Douglas T.K. Peucker, Algorithms for the reduction of the number of points required to represent a digitized line or its caricature, Int J Geogr Inf Sci 10 (1973) 112-122. https://doi.org/10.3138/FM57-6770-U75U-7727

[19] U. Ramer, An Iterative Procedure for the Polygonal Approximation of Plane Curves, Comput. graph. image process 1 (1972) 244-256. https://doi.org/10.1016/S0146-664X(72)80017-0
[8] W. Kurz, B. Giovanola, R. Trivedi, Theory of microstructural development during rapid solidification, Acta metall. 34 (1986) 823-830. https://doi.org/10.1016/0001-6160(86)90056-8

[9] D.A. Zaitsev, A generalized neighborhood for cellular automata, Theor Comput Sci 666 (2017) 21-35. https://doi.org/10.1016/j.tcs.2016.11.002

[10] C.A. Gandin, R.J. Schaefer, M. Rappaz, Analytical and numerical predictions of dendritic grain envelopes, Acta mater. 44.8 (1996) 3339-3347. https://doi.org/10.1016/1359-6454(95)00433-5

[11] D.E. Ovsienko, G.A. Alfintsev, V.V. Maslov, Kinetics and shape of crystal growth from the melt for substances with low L/kT values, J. Cryst. Growth 26 (1974) 233-238. https://doi.org/10.1016/0022-0248(74)90251-6

[12] R. Hill, Generalized constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids 14 (1966) 95-102. https://doi.org/10.1016/0022-5096(66)90040-8

[13] J.R. Rice, Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids 19 (1971) 433-455. https://doi.org/10.1016/0022-5096(71)90010-X

[14] R.J. Asaro, Micro Mechanics of Crystals and Polycrystals, Adv. Appl. Mech. 23 (1983) 1-115. https://doi.org/10.1016/S0065-2156(08)70242-4

[15] Y. Huang, A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Harvard Univ. Cambridge, MA, 1991.

[16] J. W. Kysar and P. Hall, Addendum to a User-material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program: Mech Report 178., Cambridge, 1997.

[17] J. Segurado, R.A. Lebensohn, J. Llorca, Computational Homogenization of Polycrystals, Adv. Appl. Mech. 51 (2018) 1-114. https://doi.org/10.1016/bs.aams.2018.07.001

[18] D.H. Douglas T.K. Peucker, Algorithms for the reduction of the number of points required to represent a digitized line or its caricature, Int J Geogr Inf Sci 10 (1973) 112-122. https://doi.org/10.3138/FM57-6770-U75U-7727

[19] U. Ramer, An Iterative Procedure for the Polygonal Approximation of Plane Curves, Comput. graph. image process 1 (1972) 244-256. https://doi.org/10.1016/S0146-664X(72)80017-0
# Influences of line and contact impedance of the efficiency by non-conventional processes

HERZIG Mathias¹,ᵃ*, SCHULZE Hans-Peter¹,ᵇ and KRÖNING Oliver¹,ᶜ

¹Leukhardt Schaltanlagen Systemtechnik GmbH, Magdeburg, Gustav-Ricker-Straße 62, Germany

ᵃmathias.herzig@leukhardt-system.de, ᵇhans-peter.schulze@leukhardt-system.de, ᶜoliver.kroening@leukhardt-system.de

**Keywords:** Impedance, EDM, ECM, Hybrid Processes

**Abstract.** The basis for an efficient application of the non-conventional processing methods Electric Discharge Machining (EDM), Electrochemical Machining (ECM), or a hybrid ED-EC-processes are the right and stable operating points. Correct matching between source, line and process is necessary for that. In general, the conductivity of transition points can shift the operating point. Especially for pulsed processing ECM and hybrid, the frequency response of the supply configuration is essential. The supply impedance depends on the working frequency, the electrical conductivity, and the capacity of the working medium used. The following examination should analyze which influences, in particular, have the supply lines and the contacts on the process. Using an experimental test setup, the contacts under various forces, frequencies, materials and surface scratches. Fundamentals of contact impedance measurements, surface film, and roughness are discussed, as well as the influence of impedance on an operating point. Especially for ECM, the intention to strike a particular operating point must consider the used medium's nonlinear characteristic line. The results are significant in building experimental testing facilities and changing industrial systems for special inserts. By analyzing the impedances, particularly the process energy source used, to avoid misinterpretations regarding process control.

**Introduction**

The system technologies of non-conventional processing methods are mostly machines geared towards the application process. This means that the impedances of sources and connection configuration must also be adapted to the application. For test systems knowing the impedances and being transparent about their relationships is necessary. Otherwise, questions related to the process configuration are impossible, or the interpretation of the results is impossible. Another source of error is that the system technology is changed. After the change, the integrated measurement and control technology incorrectly interprets the process state and reacts accordingly. A simple example of this is extended connecting cables. Fig. 1 shows the relationships between the essential sections influencing the overall impedance and, thus, the real effect of the PES pulses on the working gap. Block S is the process energy source with its internal resistance, which can be a voltage source, a current source or a hybrid source. Block P represents the variable resistance of the EC process, although the double layers as a parallel connection of resistance and capacitance are not considered here.

<figure><img src="image_2277.png" /></figure>
# Influences of line and contact impedance of the efficiency by non-conventional processes

HERZIG Mathias¹,ᵃ*, SCHULZE Hans-Peter¹,ᵇ and KRÖNING Oliver¹,ᶜ

¹Leukhardt Schaltanlagen Systemtechnik GmbH, Magdeburg, Gustav-Ricker-Straße 62, Germany

ᵃmathias.herzig@leukhardt-system.de, ᵇhans-peter.schulze@leukhardt-system.de, ᶜoliver.kroening@leukhardt-system.de

**Keywords:** Impedance, EDM, ECM, Hybrid Processes

**Abstract.** The basis for an efficient application of the non-conventional processing methods Electric Discharge Machining (EDM), Electrochemical Machining (ECM), or a hybrid ED-EC-processes are the right and stable operating points. Correct matching between source, line and process is necessary for that. In general, the conductivity of transition points can shift the operating point. Especially for pulsed processing ECM and hybrid, the frequency response of the supply configuration is essential. The supply impedance depends on the working frequency, the electrical conductivity, and the capacity of the working medium used. The following examination should analyze which influences, in particular, have the supply lines and the contacts on the process. Using an experimental test setup, the contacts under various forces, frequencies, materials and surface scratches. Fundamentals of contact impedance measurements, surface film, and roughness are discussed, as well as the influence of impedance on an operating point. Especially for ECM, the intention to strike a particular operating point must consider the used medium's nonlinear characteristic line. The results are significant in building experimental testing facilities and changing industrial systems for special inserts. By analyzing the impedances, particularly the process energy source used, to avoid misinterpretations regarding process control.

**Introduction**

The system technologies of non-conventional processing methods are mostly machines geared towards the application process. This means that the impedances of sources and connection configuration must also be adapted to the application. For test systems knowing the impedances and being transparent about their relationships is necessary. Otherwise, questions related to the process configuration are impossible, or the interpretation of the results is impossible. Another source of error is that the system technology is changed. After the change, the integrated measurement and control technology incorrectly interprets the process state and reacts accordingly. A simple example of this is extended connecting cables. Fig. 1 shows the relationships between the essential sections influencing the overall impedance and, thus, the real effect of the PES pulses on the working gap. Block S is the process energy source with its internal resistance, which can be a voltage source, a current source or a hybrid source. Block P represents the variable resistance of the EC process, although the double layers as a parallel connection of resistance and capacitance are not considered here.

<figure><img src="image_2268.png" /></figure>
<figure><img src="image_2278.png" /><figcaption>Fig. 1: Equivalent circuit for ECM machine</figcaption></figure>

Block Me is an active influence by a measuring sensor, for example, a measuring shunt for current measurement. Their structure determines the impedance of the supply line and its components, as connecting cables are often used as double wires. Coaxial and braided cables are also conceivable. For AC or pulsed applications, the weighting of the reactive components shifts depending on the type of cable selected. This results in overshoot, resonance, damping and other phenomena.

This paper will primarily deal with block Co (the contact transition resistance) because it has always been neglected. It can be assumed that in industrial systems and test systems, the process energy source, the supply lines, and the measuring sensors are known, so the contact of the structure is known but can vary greatly depending on the individual and application.

Fig. 2 compares an optimal supply line of approx. 100 mΩ (dashed red) with different gap widths and electrolyte conductivities. A critical working condition arises from around 8 cm² of the work area because the resistances from the process, the supply line and, as can be seen later, also from the contacting are of the same magnitude. For smaller working surfaces, it is possible to balance is fact by electrolyte conductivity and working gap.

<figure><img src="image_2279.png" /><figcaption>Fig. 2: Comparison of different working parameters with the optimal connecting lines – Legend are working gap / electrical conductivity. Legend ranking is identical with calculated curve ranking</figcaption></figure>
<figure><img src="image_2269.png" /><figcaption>Fig. 1: Equivalent circuit for ECM machine</figcaption></figure>

Block Me is an active influence by a measuring sensor, for example, a measuring shunt for current measurement. Their structure determines the impedance of the supply line and its components, as connecting cables are often used as double wires. Coaxial and braided cables are also conceivable. For AC or pulsed applications, the weighting of the reactive components shifts depending on the type of cable selected. This results in overshoot, resonance, damping and other phenomena.

This paper will primarily deal with block Co (the contact transition resistance) because it has always been neglected. It can be assumed that in industrial systems and test systems, the process energy source, the supply lines, and the measuring sensors are known, so the contact of the structure is known but can vary greatly depending on the individual and application.

Fig. 2 compares an optimal supply line of approx. 100 mΩ (dashed red) with different gap widths and electrolyte conductivities. A critical working condition arises from around 8 cm² of the work area because the resistances from the process, the supply line and, as can be seen later, also from the contacting are of the same magnitude. For smaller working surfaces, it is possible to balance is fact by electrolyte conductivity and working gap.

<figure><img src="image_2270.png" /><figcaption>Fig. 2: Comparison of different working parameters with the optimal connecting lines – Legend are working gap / electrical conductivity. Legend ranking is identical with calculated curve ranking</figcaption></figure>
More generally, the current density-potential curves of anodic metal dissolution describe the situation in Fig. 3. A change in the overall impedance causes a shift in the process potentials and/or the current density. The shifting of operating point is described in [1,2].

<figure><img src="image_2280.png" /><figcaption>Fig. 3: General current density-potential curve for passivating electrolyte as a criterion for a possible potential shift due to a change in contact resistance</figcaption></figure>

## Experimental Setup

The explanations and descriptions in [3,4] were the inspiration for the experimental setup. The aim of the experimental setup (Fig. 4) was a test section that was as reproducible as possible so that the different cable lugs made of different materials could be sufficiently comparable. Seven to nine measurements in chronological order and at least two series of measurements were evaluated.

<figure><img src="image_2281.png" /><figcaption>Fig. 2: Experimental setting for measurement of contact resistance</figcaption></figure>

The cable lug is on a 10 mm diameter brass base positioned. A wire on 4 mm is pressed onto the cable lug from above. The deflection of a spring creates the force on the wire. A scale (Fig. 4) is used as a force sensor, and the displayed weight values are converted. For each set force, the resistance for the DC measurements was done using an mΩ-meter, the impedance amount |ZCo| was measured using an LCR-meter, and additional the phase angle for the AC arrangements was measured. For the correct contact impedance, the arrangement without a cable lug is determined
More generally, the current density-potential curves of anodic metal dissolution describe the situation in Fig. 3. A change in the overall impedance causes a shift in the process potentials and/or the current density. The shifting of operating point is described in [1,2].

<figure><img src="image_2271.png" /><figcaption>Fig.3: General current density-potential curve for passivating electrolyte as a criterion for a possible potential shift due to a change in contact resistance</figcaption></figure>

## Experimental Setup

The explanations and descriptions in [3,4] were the inspiration for the experimental setup. The aim of the experimental setup (Fig. 4) was a test section that was as reproducible as possible so that the different cable lugs made of different materials could be sufficiently comparable. Seven to nine measurements in chronological order and at least two series of measurements were evaluated.

<figure><img src="image_2272.png" /><figcaption>Fig. 2: Experimental setting for measurement of contact resistance</figcaption></figure>

The cable lug is on a 10 mm diameter brass base positioned. A wire on 4 mm is pressed onto the cable lug from above. The deflection of a spring creates the force on the wire. A scale (Fig. 4) is used as a force sensor, and the displayed weight values are converted. For each set force, the resistance for the DC measurements was done using an mΩ-meter, the impedance amount |ZCo| was measured using an LCR-meter, and additional the phase angle for the AC arrangements was measured. For the correct contact impedance, the arrangement without a cable lug is determined
and subtracted from the measured values. The arrangement without a cable lug is determined and subtracted from the measured values for the correct contact impedance. Open and short calibration will support a newer four-wired measuring device. However, it is also possible to determine the impedance of the measuring arrangement and then implement the compensation in post-processing.

<figure><img src="image_2282.png" /><figcaption>Fig. 3: Cable lugs for the investigation</figcaption></figure>

The measuring range for the contact force was limited by the secure contact up to 80% of the scale load, corresponding to a contact force of 5 N to 45 N. Copper and aluminum were preferred as materials. Surfaces cleaned with acetone and roughened with 1000-grit sandpaper or plasma-electrolytic polished were tested. Attempts by increasing and decreasing contact force verify selected measurements. The different cable lugs for investigation are to be seen in Fig. 5.

The linear load in the test setup makes a comparison between different contact surfaces possible. However, it can be seen from Fig. 2 that for contact resistances less than 5 mΩ, the influence of the contact can be neglected. Influences up to 10 mΩ are very dependent on the gap width and electrolyte conductivity; up to a limit of 20 mΩ, the gap voltage has to be corrected. Beyond 20 mΩ, it is essential to determine the real gap voltage and the possibly changing working current so that the results remain comparable to other experiments. Under certain circumstances, the conditions can mean that the removal process (ECM or Electro-Discharge Chemical Machining (EDCM)) is no longer possible (Fig. 3).

Galvanized copper cable lugs and gold-plated cable lugs were examined as further comparison materials (Fig. 5). To preserve the coating, these parts were only cleaned with acetone.

## Experiments with a direct voltage source (DC arrangement)

Processing with DC voltage is still important for the ECM. Therefore, cable lugs were measured in the DC arrangement. The DC arrangement shows three characteristic phases in the dependence of the contact resistance $R_{Co}$ on the contact force $F_{Co}$.
and subtracted from the measured values. The arrangement without a cable lug is determined and subtracted from the measured values for the correct contact impedance. Open and short calibration will support a newer four-wired measuring device. However, it is also possible to determine the impedance of the measuring arrangement and then implement the compensation in post-processing.

<figure><img src="image_2273.png" /><figcaption>Fig. 3: Cable lugs for the investigation</figcaption></figure>

The measuring range for the contact force was limited by the secure contact up to 80% of the scale load, corresponding to a contact force of 5 N to 45 N. Copper and aluminum were preferred as materials. Surfaces cleaned with acetone and roughened with 1000-grit sandpaper or plasma-electrolytic polished were tested. Attempts by increasing and decreasing contact force verify selected measurements. The different cable lugs for investigation are to be seen in Fig. 5.

The linear load in the test setup makes a comparison between different contact surfaces possible. However, it can be seen from Fig. 2 that for contact resistances less than 5 mΩ, the influence of the contact can be neglected. Influences up to 10 mΩ are very dependent on the gap width and electrolyte conductivity; up to a limit of 20 mΩ, the gap voltage has to be corrected. Beyond 20 mΩ, it is essential to determine the real gap voltage and the possibly changing working current so that the results remain comparable to other experiments. Under certain circumstances, the conditions can mean that the removal process (ECM or Electro-Discharge Chemical Machining (EDCM)) is no longer possible (Fig. 3).

Galvanized copper cable lugs and gold-plated cable lugs were examined as further comparison materials (Fig. 5). To preserve the coating, these parts were only cleaned with acetone.

## Experiments with a direct voltage source (DC arrangement)

Processing with DC voltage is still important for the ECM. Therefore, cable lugs were measured in the DC arrangement. The DC arrangement shows three characteristic phases in the dependence of the contact resistance $R_{Co}$ on the contact force $F_{Co}$.
<figure><img src="image_2283.png" /><figcaption>Fig. 4: Contact resistance for different Cable lug materials using the DC application</figcaption></figure>

Samples without coating have a 500 mΩ to 600 mΩ contact resistance at low contact forces of less than 20 N. This is, therefore, significantly larger than the supply line resistances and the process state. In the second phase, there is a bend in the RCo curve. The contact force is increased by 10 N, so the contact resistance is below 100 mΩ. The exceptions are the coated cable lugs; their transition to complete contact occurs below 10 N. What they have in common is the use of an intermediate medium that is ductile enough to adapt to the surface of the contact partner, even at low forces. The examples chosen here also deal with oxidation. With R<sub>C</sub> values of 40 mΩ to 80 mΩ and the requirement that there are at least two contacts, significant corrections to the actual Process Energy Source (PES) voltage are necessary in order to achieve the desired gap voltages. The repetitions of the measurements with DC show qualitatively the same behavior and quantitatively larger deviations. Contact forces of greater than 25 N are necessary to achieve contact resistances of less than 80 mΩ for pure materials.

## Experiments with AC applications at different frequencies

In the case of AC applications, the magnitude and the phase angle Φ of the impedance was |ZCo|, was measured. By this, it can be determined how large the resistance component and the capacitive component are.

Contact impedances of 20 mΩ to less than 1 mΩ were determined for the coated cable lugs. Since the phase angle was consistently close to 0° (100 Hz), this corresponds to a purely ohmic contact resistance in this range. From 15 N upwards, the contact resistance values are below 5 mΩ, and the ohmic component can therefore be neglected. Since the pulse durations of 10 ms correspond to this frequency, there are no corrections for the gap voltage for the ECM.

For the 100 kHz test frequency, the result is a very low-value level of less than 15 mΩ, as shown in Fig. 7. This frequency corresponds to a pulsation of 10 µs, which is below the pulse durations primarily used today. The two materials show very different behavior. The galvanized cable lug
<figure><img src="image_2274.png" /><figcaption>Fig. 4: Contact resistance for different Cable lug materials using the DC application</figcaption></figure>

Samples without coating have a 500 mΩ to 600 mΩ contact resistance at low contact forces of less than 20 N. This is, therefore, significantly larger than the supply line resistances and the process state. In the second phase, there is a bend in the RCo curve. The contact force is increased by 10 N, so the contact resistance is below 100 mΩ. The exceptions are the coated cable lugs; their transition to complete contact occurs below 10 N. What they have in common is the use of an intermediate medium that is ductile enough to adapt to the surface of the contact partner, even at low forces. The examples chosen here also deal with oxidation. With R<sub>C</sub> values of 40 mΩ to 80 mΩ and the requirement that there are at least two contacts, significant corrections to the actual Process Energy Source (PES) voltage are necessary in order to achieve the desired gap voltages. The repetitions of the measurements with DC show qualitatively the same behavior and quantitatively larger deviations. Contact forces of greater than 25 N are necessary to achieve contact resistances of less than 80 mΩ for pure materials.

## Experiments with AC applications at different frequencies

In the case of AC applications, the magnitude and the phase angle Φ of the impedance was |ZCo|, was measured. By this, it can be determined how large the resistance component and the capacitive component are.

Contact impedances of 20 mΩ to less than 1 mΩ were determined for the coated cable lugs. Since the phase angle was consistently close to 0° (100 Hz), this corresponds to a purely ohmic contact resistance in this range. From 15 N upwards, the contact resistance values are below 5 mΩ, and the ohmic component can therefore be neglected. Since the pulse durations of 10 ms correspond to this frequency, there are no corrections for the gap voltage for the ECM.

For the 100 kHz test frequency, the result is a very low-value level of less than 15 mΩ, as shown in Fig. 7. This frequency corresponds to a pulsation of 10 µs, which is below the pulse durations primarily used today. The two materials show very different behavior. The galvanized cable lug
<figure><img src="image_2284.png" /><figcaption>Fig. 5: Magnitude of impedance for the coated cable lugs at 100 Hz</figcaption></figure>

shows an almost constant contact impedance of 7 mΩ, while the phase angle increases from 70° to 87°. This means that the ohmic component at 10 N is approximately 2.40 mΩ, while at 35 N it drops to 0.37 mΩ. The contacting has a primarily capacitive effect for all contact forces. For the gold-plated cable lug, there is a slightly increased RCo value of 15 mΩ for 3 N, while it then drops almost to 3 mΩ to 1 mΩ. In the case of the phase angle, there is a sharp increase from 5° at 8 N to 87° at 37 N. Therefore, there is a change from the purely ohmic component (14.8 mΩ) to an almost purely capacitive behavior with an ohmic component of 0.06 mΩ. For an RCo value of 1.7 m, there will be an average contact force of 20 N.

<figure><img src="image_2285.png" /><figcaption>Fig. 6: Magnitude and phase of contact impedance at 100 kHz – Square is Zn/Cu and circle is Au/Cu</figcaption></figure>

## AC application by different surface characters for Al

Using aluminum as an example, we want to show the influence of surface formation on contact resistance. Three different surface conditions were examined. Firstly, with acetone cleaned, Al. Secondly, it was roughened with 1000 grit sandpaper and thirdly, the contact surfaces were plasma electrolytic polished.
<figure><img src="image_2275.png" /><figcaption>Fig. 5: Magnitude of impedance for the coated cable lugs at 100 Hz</figcaption></figure>

shows an almost constant contact impedance of 7 mΩ, while the phase angle increases from 70° to 87°. This means that the ohmic component at 10 N is approximately 2.40 mΩ, while at 35 N it drops to 0.37 mΩ. The contacting has a primarily capacitive effect for all contact forces. For the gold-plated cable lug, there is a slightly increased RCo value of 15 mΩ for 3 N, while it then drops almost to 3 mΩ to 1 mΩ. In the case of the phase angle, there is a sharp increase from 5° at 8 N to 87° at 37 N. Therefore, there is a change from the purely ohmic component (14.8 mΩ) to an almost purely capacitive behavior with an ohmic component of 0.06 mΩ. For an RCo value of 1.7 m, there will be an average contact force of 20 N.

<figure><img src="image_2276.png" /><figcaption>Fig. 6: Magnitude and phase of contact impedance at 100 kHz – Square is Zn/Cu and circle is Au/Cu</figcaption></figure>

## AC application by different surface characters for Al

Using aluminum as an example, we want to show the influence of surface formation on contact resistance. Three different surface conditions were examined. Firstly, with acetone cleaned, Al. Secondly, it was roughened with 1000 grit sandpaper and thirdly, the contact surfaces were plasma electrolytic polished.
<figure><img src="image_2286.png" /><figcaption>Fig. 7: Comparison of different contact surface modifications for Al by 100 Hz</figcaption></figure>

The 100 Hz investigations show an almost purely ohmic load, because the phase shift is close to zero. Then, in Fig. 9, the impedance can also be replaced by the value of $R_{Co}$. The simply cleaned cable lug (circle) shows increased contact resistances between 70 mΩ and 25 mΩ, which does not correspond to the ideal contact resistance requirements. This may be because the aluminum surface oxidizes easily in the air, resulting in an increase in $R_{Co}$. The cleaned and corrosion-resistant surface created by PeP treatment (triangle) still has contact resistances of 150 mΩ to 60 mΩ at small contact forces of less than 15 N. Above, it falls below 20 mΩ and can, therefore, be neglected. The most favorable behavior is the roughened cable lugs, which are 20 mΩ and smaller in the tested contact force range. From 25 N, the contact resistance drops to less than 10 mΩ. Phase response and impedances have to be considered separately for a frequency of 100 kHz. For the cleaned Al, the absolute impedance at 10 N is approx. 45 mΩ and the phase angle is 20° so the contact resistance is 42.3 mΩ. Already from 20 N, the absolute impedance is only 12 mΩ and the phase angle is 40°, which results in a contact resistance of 9.2 mΩ. The worst is the roughened cable lug surface, which almost always fluctuates between 40 mΩ and 60 mΩ for the absolute impedance and whose phase angle is between 35° and 20°. The amount of contact resistance, therefore, reaches values of 32.8 mΩ to 56.4 mΩ. These values are far from the optimally required ones. The behavior of the PeP-processed cable lugs is qualitatively interesting. Above 10 N, complete contact has been formed, and the phase behaves constantly.

<figure><img src="image_2287.png" /><figcaption>Fig. 8: Comparison of different contact surface modifications for Al by 100 kHz.</figcaption></figure>
<figure><img src="image_2277.png" /><figcaption>Fig. 7: Comparison of different contact surface modifications for Al by 100 Hz</figcaption></figure>

The 100 Hz investigations show an almost purely ohmic load, because the phase shift is close to zero. Then, in Fig. 9, the impedance can also be replaced by the value of $R_{Co}$. The simply cleaned cable lug (circle) shows increased contact resistances between 70 mΩ and 25 mΩ, which does not correspond to the ideal contact resistance requirements. This may be because the aluminum surface oxidizes easily in the air, resulting in an increase in $R_{Co}$. The cleaned and corrosion-resistant surface created by PeP treatment (triangle) still has contact resistances of 150 mΩ to 60 mΩ at small contact forces of less than 15 N. Above, it falls below 20 mΩ and can, therefore, be neglected. The most favorable behavior is the roughened cable lugs, which are 20 mΩ and smaller in the tested contact force range. From 25 N, the contact resistance drops to less than 10 mΩ. Phase response and impedances have to be considered separately for a frequency of 100 kHz. For the cleaned Al, the absolute impedance at 10 N is approx. 45 mΩ and the phase angle is 20° so the contact resistance is 42.3 mΩ. Already from 20 N, the absolute impedance is only 12 mΩ and the phase angle is 40°, which results in a contact resistance of 9.2 mΩ. The worst is the roughened cable lug surface, which almost always fluctuates between 40 mΩ and 60 mΩ for the absolute impedance and whose phase angle is between 35° and 20°. The amount of contact resistance, therefore, reaches values of 32.8 mΩ to 56.4 mΩ. These values are far from the optimally required ones. The behavior of the PeP-processed cable lugs is qualitatively interesting. Above 10 N, complete contact has been formed, and the phase behaves constantly.

<figure><img src="image_2278.png" /><figcaption>Fig. 8: Comparison of different contact surface modifications for Al by 100 kHz.</figcaption></figure>
## AC application by different surface characters for Cu

For the material Cu, only two surface modifications have been investigated: the slightly roughened surface with 1000-grid sandpaper and the PeP-processed contact surface. The oxidation here has a different effect on the contact resistance. For the 100 Hz tests, the phase angle is again 0°, and therefore, the measured impedance is equal to the ohmic component. Similar to Al<sub>PeP</sub>, the contact resistances of Cu<sub>PeP</sub> show constant behavior in the range from 5 N to 45 N. The roughened Cu<sub>1000</sub> shows contact resistances of 100 mΩ to 60 mΩ at small contact forces (< 10 N), which do not meet the requirements of neglect. From 20 N, the contact resistance drops to 20 mΩ to 30 mΩ and only after 35 N falls below to 10 mΩ. The waviness in the curve can result from the ductile behavior of the copper under higher forces. This means that the optimal area of application is very limited to the high contact forces.

<figure><img src="image_2288.png" /><figcaption>Fig. 9: Comparison of different contact surface modifications for Cu by 100 Hz.</figcaption></figure>

In the case of the 100 kHz study, the contact resistance drops significantly, and the phase angle influences the contact resistance. The impedance amounts are between 27 mΩ and 3 mΩ and the phase angles are in a range of 20°. The PeP-processed cable lug already has an impedance of less than 10 mΩ and improves the phase angle to 8.5 mΩ. Simply roughening the surface results in small, better ohmic contact resistances of 4.7 mΩ to 4.2 mΩ.

<figure><img src="image_2289.png" /><figcaption>Fig. 10: Comparison of different contact surface modifications for Cu by 100 kHz.</figcaption></figure>
## AC application by different surface characters for Cu

For the material Cu, only two surface modifications have been investigated: the slightly roughened surface with 1000-grid sandpaper and the PeP-processed contact surface. The oxidation here has a different effect on the contact resistance. For the 100 Hz tests, the phase angle is again 0°, and therefore, the measured impedance is equal to the ohmic component. Similar to Al<sub>PeP</sub>, the contact resistances of Cu<sub>PeP</sub> show constant behavior in the range from 5 N to 45 N. The roughened Cu<sub>1000</sub> shows contact resistances of 100 mΩ to 60 mΩ at small contact forces (< 10 N), which do not meet the requirements of neglect. From 20 N, the contact resistance drops to 20 mΩ to 30 mΩ and only after 35 N falls below to 10 mΩ. The waviness in the curve can result from the ductile behavior of the copper under higher forces. This means that the optimal area of application is very limited to the high contact forces.

<figure><img src="image_2279.png" /><figcaption>Fig. 9: Comparison of different contact surface modifications for Cu by 100 Hz.</figcaption></figure>

In the case of the 100 kHz study, the contact resistance drops significantly, and the phase angle influences the contact resistance. The impedance amounts are between 27 mΩ and 3 mΩ and the phase angles are in a range of 20°. The PeP-processed cable lug already has an impedance of less than 10 mΩ and improves the phase angle to 8.5 mΩ. Simply roughening the surface results in small, better ohmic contact resistances of 4.7 mΩ to 4.2 mΩ.

<figure><img src="image_2280.png" /><figcaption>Fig. 10: Comparison of different contact surface modifications for Cu by 100 kHz.</figcaption></figure>
## Conclusion

The relationship between contact force and contact impedance is discussed in relation to workpiece clamping in ECM. The situation is problematic, when the contact resistance is in the same order of magnitude as the gap impedance of the ECM. In this case, the resulting current limitation limits machining productivity. A distinction must be made between the influence on DC processing and AC/pulse processing. As described in [3,4], there is a point at which the apparent and actual contact surfaces correspond to each other. For our DC studies, this range shows three above a contact force between 20 N and 30 N.

For AC or pulsed applications, in addition to the contact resistance, the influence of impurity or oxide layers must also be taken into account. These form an additional parallel capacitance to the ohmic contact resistance. Test specimens with different surface modifications are compared in order to work out this influence. Tin-plated and gold-plated cable lugs show the advantages of appropriately chosen coatings. If they are ductile enough and control the oxidation behavior for the environment.

Cu and Al samples show the influence of oxide layers on the impedance. For Al samples, the ohmic component of the contact resistance collapses when the contact force is sufficient. However, the parallel capacitance increases according to the contact force. The Cu oxide layer is more ductile than the Al oxide layer. The increase in pressure at Al shows a reduction in distance. For Cu, the reduction in distance and the increase in contact area work against each other.

Own investigations on plasma-polished surfaces show a reduction in these influences. Levelling the surface reduces oxide formation and foreign layer adhesion. However, the improvement in the ohmic component also depends on the roughness of the contact partner.

## References

[1] O. Kröning, H.-P. Schulze, M. Herzig. Process source analysis of the regulation parameters for simultaneous hole widening. Proceedings of INSECT 2020 Chemnitz, Germany

[2] DeSilva, A.K.M., Schulze, H.-P, McGeough, J.A., M.Zybura,. (2010). Process control and power systems for Electrochemical-Erosion Sinking (ELESIN). Proceedings of the 16th ISEM. 389-392.

[3] A. Kreil, W. A. Merl, E. Vinaricky: Elektrische Kontakte und ihre Werkstoffe; Springer Berlin, 1984. https://doi.org/10.1002/mawe.19840150310

[4] R. Holm: Electrical Contacts, Springer Berlin, 2000
## Conclusion

The relationship between contact force and contact impedance is discussed in relation to workpiece clamping in ECM. The situation is problematic, when the contact resistance is in the same order of magnitude as the gap impedance of the ECM. In this case, the resulting current limitation limits machining productivity. A distinction must be made between the influence on DC processing and AC/pulse processing. As described in [3,4], there is a point at which the apparent and actual contact surfaces correspond to each other. For our DC studies, this range shows three above a contact force between 20 N and 30 N.

For AC or pulsed applications, in addition to the contact resistance, the influence of impurity or oxide layers must also be taken into account. These form an additional parallel capacitance to the ohmic contact resistance. Test specimens with different surface modifications are compared in order to work out this influence. Tin-plated and gold-plated cable lugs show the advantages of appropriately chosen coatings. If they are ductile enough and control the oxidation behavior for the environment.

Cu and Al samples show the influence of oxide layers on the impedance. For Al samples, the ohmic component of the contact resistance collapses when the contact force is sufficient. However, the parallel capacitance increases according to the contact force. The Cu oxide layer is more ductile than the Al oxide layer. The increase in pressure at Al shows a reduction in distance. For Cu, the reduction in distance and the increase in contact area work against each other.

Own investigations on plasma-polished surfaces show a reduction in these influences. Levelling the surface reduces oxide formation and foreign layer adhesion. However, the improvement in the ohmic component also depends on the roughness of the contact partner.

## References

[1] O. Kröning, H.-P. Schulze, M. Herzig. Process source analysis of the regulation parameters for simultaneous hole widening. Proceedings of INSECT 2020 Chemnitz, Germany

[2] DeSilva, A.K.M., Schulze, H.-P, McGeough, J.A., M.Zybura,. (2010). Process control and power systems for Electrochemical-Erosion Sinking (ELESIN). Proceedings of the 16th ISEM. 389-392.

[3] A. Kreil, W. A. Merl, E. Vinaricky: Elektrische Kontakte und ihre Werkstoffe; Springer Berlin, 1984. https://doi.org/10.1002/mawe.19840150310

[4] R. Holm: Electrical Contacts, Springer Berlin, 2000
# Process analysis using adapted Rogowski coil for non-conventional processes

DARAWISH Haytham¹,*, HERZIG Mathias¹,†, SCHULZE Hans-Peter¹,‡
and KRÖNING Oliver¹,‡

¹Leukhardt Schaltanlagen Systemtechnik GmbH, Gustav-Ricker-Straße 62, 39120 Magdeburg, Germany

ªhaytham.darawish@leukhardt-system.de, ᵇmathias.herzig@leukhardt-system.de,

ᶜhans-peter.schulze@leukhardt-system.de, ᵈoliver.kroening@leukhardt-system.de

**Keywords:** Rogowski Coil, Hybrid Processes, Process Analysis, Current Rise Time

**Abstract.** The process analysis of non-conventional processes is very complex because many critical subprocesses can occur. These subprocesses can be determined among other things, by their positive and negative current increases. A process adapted Rogowski coil is particularly suitable for analyzing the current increases. Using the example of plasma electrolytic polishing, it will be shown how pulse typical effects can be distinguished from process typical effects. The boundary condition for this development was that the size of the measuring sensor had to be adapted to the system conditions of the plasma electrolytic polishing process. It was not necessary to calculate the real current, but rather to recognize the process situation very quickly. For this purpose, a higher signal amplification must be carried out during the polishing process and the initialization phase must be hidden. The example of experimental test setup shows, which analyzes can be carried out. The influence of the process disruption on the result can also be determined through comparisons with the processed final results.

**Introduction**

Process monitoring and process control are important components of process optimization for non-conventional machining processes such as electrical discharge machining (EDM), electrochemical machining (ECM), Plasma-electrolytic polishing (PeP), and the hybrid derivatives of these processes. The primary pulse analyses for these processes are performed by determining the measurable current and voltage pulses [1-3]. Another way to characterize the process is to measure the current changes. The current increases di/dt are typical for certain ablation mechanisms or process disturbances and can be recorded quickly. Fast data acquisition also makes it possible to react to the process disturbance or process change more quickly than with the usual parameters.

Rogowski coils are best suited for measuring these current increases, which ever have to be adapted to the process and the system technology. For this purpose, a study was conducted to investigate the possibilities of size adjustment and process parameter acquisition. Plasma-electrolytic polishing (PeP) was used as a test procedure on a test system.

Figure 1 shows how the current change can be considered as a part of the process analysis. It is also crucial whether the process is directly influenced by the sensor or not. Only current measurement using shunts directly influences the process, but it has the advantage that all frequency components can be recorded.

The current measurement with the Rogowski coil is indirect. It has no influence on the process but is frequency-dependent and shows linear behavior up to the cutoff frequency. Up to this frequency, the output signal of the Rogowski coil is proportional to the derivative of the current di/dt. Certain process types such as EDM and arc can be analyzed by the current rise. Similarly, there are differences in the different types of short circuits resulting from a metallic short circuit

<figure><img src="image_2290.png" /></figure>
# Process analysis using adapted Rogowski coil for non-conventional processes

DARAWISH Haytham¹,*, HERZIG Mathias¹,†, SCHULZE Hans-Peter¹,‡
and KRÖNING Oliver¹,‡

¹Leukhardt Schaltanlagen Systemtechnik GmbH, Gustav-Ricker-Straße 62, 39120 Magdeburg, Germany

ªhaytham.darawish@leukhardt-system.de, ᵇmathias.herzig@leukhardt-system.de,

ᶜhans-peter.schulze@leukhardt-system.de, ᵈoliver.kroening@leukhardt-system.de

**Keywords:** Rogowski Coil, Hybrid Processes, Process Analysis, Current Rise Time

**Abstract.** The process analysis of non-conventional processes is very complex because many critical subprocesses can occur. These subprocesses can be determined among other things, by their positive and negative current increases. A process adapted Rogowski coil is particularly suitable for analyzing the current increases. Using the example of plasma electrolytic polishing, it will be shown how pulse typical effects can be distinguished from process typical effects. The boundary condition for this development was that the size of the measuring sensor had to be adapted to the system conditions of the plasma electrolytic polishing process. It was not necessary to calculate the real current, but rather to recognize the process situation very quickly. For this purpose, a higher signal amplification must be carried out during the polishing process and the initialization phase must be hidden. The example of experimental test setup shows, which analyzes can be carried out. The influence of the process disruption on the result can also be determined through comparisons with the processed final results.

**Introduction**

Process monitoring and process control are important components of process optimization for non-conventional machining processes such as electrical discharge machining (EDM), electrochemical machining (ECM), Plasma-electrolytic polishing (PeP), and the hybrid derivatives of these processes. The primary pulse analyses for these processes are performed by determining the measurable current and voltage pulses [1-3]. Another way to characterize the process is to measure the current changes. The current increases di/dt are typical for certain ablation mechanisms or process disturbances and can be recorded quickly. Fast data acquisition also makes it possible to react to the process disturbance or process change more quickly than with the usual parameters.

Rogowski coils are best suited for measuring these current increases, which ever have to be adapted to the process and the system technology. For this purpose, a study was conducted to investigate the possibilities of size adjustment and process parameter acquisition. Plasma-electrolytic polishing (PeP) was used as a test procedure on a test system.

Figure 1 shows how the current change can be considered as a part of the process analysis. It is also crucial whether the process is directly influenced by the sensor or not. Only current measurement using shunts directly influences the process, but it has the advantage that all frequency components can be recorded.

The current measurement with the Rogowski coil is indirect. It has no influence on the process but is frequency-dependent and shows linear behavior up to the cutoff frequency. Up to this frequency, the output signal of the Rogowski coil is proportional to the derivative of the current di/dt. Certain process types such as EDM and arc can be analyzed by the current rise. Similarly, there are differences in the different types of short circuits resulting from a metallic short circuit

<figure><img src="image_2281.png" /></figure>
between anode and cathode, metallic bridging from ablation particles/additives or partial discharges between metallic particles/gas bubbles.

<figure><img src="image_2291.png" /><figcaption>Figure 1: Components of process analysis for non-conventional machining processes [4]</figcaption></figure>

The analysis of the machining process is not only used for process control but also allows conclusions to be drawn about the machining quality, for example by determining the frequency of the process types during machining. The short circuit types, the discharges, and the main removal types play a decisive role here.

The second possible use of the Rogowski coil is as a safety sensor in processes in which the di/dt can be used to detect and prevent very high current values from being reached at an early stage. In order to prevent very high current values from being reached, the output signal of the Rogowski coil will be transmitted to the control element, whereby purely mechanical solutions have a response time in the higher ms range, hydraulic solutions in the higher µs-range, and the electrical solution in the lower µs-range. The excess power must be then stored or disposed.

## Fundamentals of the Rogowski coil

The characteristics of the Rogowski coil can be derived from the equivalent circuit diagram (Figure 2).

<figure><img src="image_2292.png" /><figcaption>Figure 2: Geometric parameters of the Rogowski coil and characteristics of the output voltage vs. frequency with the first resonance frequency</figcaption></figure>

The equivalent circuit diagram contains the parameters mutual inductance $M$, inductance $L_0$, capacitance $C_0$, ohmic resistance $R_0$, operating current $i$, and measuring voltage $u_2$. The geometric parameters of the Rogowski coil are shown in Figure 3 as well as the qualitative characteristic curve of the amplitude as a function of frequency. The following equations apply to a coil with rectangular windings and are valid only up to the first resonant frequency [1-3].
between anode and cathode, metallic bridging from ablation particles/additives or partial discharges between metallic particles/gas bubbles.

<figure><img src="image_2282.png" /><figcaption>Figure 1: Components of process analysis for non-conventional machining processes [4]</figcaption></figure>

The analysis of the machining process is not only used for process control but also allows conclusions to be drawn about the machining quality, for example by determining the frequency of the process types during machining. The short circuit types, the discharges, and the main removal types play a decisive role here.

The second possible use of the Rogowski coil is as a safety sensor in processes in which the di/dt can be used to detect and prevent very high current values from being reached at an early stage. In order to prevent very high current values from being reached, the output signal of the Rogowski coil will be transmitted to the control element, whereby purely mechanical solutions have a response time in the higher ms range, hydraulic solutions in the higher µs-range, and the electrical solution in the lower µs-range. The excess power must be then stored or disposed.

## Fundamentals of the Rogowski coil

The characteristics of the Rogowski coil can be derived from the equivalent circuit diagram (Figure 2).

<figure><img src="image_2283.png" /><figcaption>Figure 2: Geometric parameters of the Rogowski coil and characteristics of the output voltage vs. frequency with the first resonance frequency</figcaption></figure>

The equivalent circuit diagram contains the parameters mutual inductance $M$, inductance $L_0$, capacitance $C_0$, ohmic resistance $R_0$, operating current $i$, and measuring voltage $u_2$. The geometric parameters of the Rogowski coil are shown in Figure 3 as well as the qualitative characteristic curve of the amplitude as a function of frequency. The following equations apply to a coil with rectangular windings and are valid only up to the first resonant frequency [1-3].
<figure><img src="image_2293.png" /><figcaption>Figure 3: Geometric parameters of the Rogowski coil and characteristics of the output voltage vs. frequency with the first resonance frequency</figcaption></figure>

$$ M = N \frac{\mu_0 \mu_r}{2\pi} a \ln \left( \frac{r_2}{r_1} \right) \qquad (1) $$

$$ L_0 = N \frac{\mu_0 \mu_r}{2\pi} a \ln \left( \frac{r_2}{r_1} \right) \qquad (2) $$

$$ C_0 = 4\pi^2 \epsilon_0 \epsilon_r \frac{r_1+r_2}{\ln\left(\frac{r_1+r_2}{r_2-r_1}\right)} \qquad (3) $$

$$ R_0 = \frac{1}{\kappa A} \qquad (4) $$

$$ \frac{U_2}{I} = \frac{\frac{R}{R+R_0} j\omega M}{\frac{RL_0C_0}{R+R_0}(j\omega)^2 + \frac{L_0+RR_0C_0}{R+R_0}j\omega+1} \qquad (5) $$

$$ f_{r1} = \frac{1}{2\pi} \sqrt{\frac{R+R_0}{RL_0C_0}} \qquad (6) $$

$$ \sigma = \pi \frac{L_0+RR_0C_0}{R+R_0} f_{r1} \qquad (7) $$

The parameters in Equations (1) to (7) are shown in Figure 2 and Figure 3, where N represents the number of turns, σ denotes attenuation and f<sub>r1</sub> is the resonant frequency.

Specific requirements were defined for the development of a suitable process analysis sensor. These include a sensor size that allows integration into industrial systems, a wide operating frequency of up to 10 MHz, very good linearity of the sensor output voltage with the frequencies, and an analyzable, measurable output signal.

## Structure of various Rogowski coils

As part of the study, various sensors (Rogowski coils) were constructed and tested using a test procedure (PeP). Figure 4 shows the three most important solutions with their geometric parameters.

Coil 1 has a non-ferromagnetic printed core with guide slots for the winding. The advantage of this coil is the geometrically exact and homogeneous winding, which can also be implemented in a concrete calculation or simulation. Comparisons between calculations and measurements are provided below.
<figure><img src="image_2284.png" /><figcaption>Figure 3: Geometric parameters of the Rogowski coil and characteristics of the output voltage vs. frequency with the first resonance frequency</figcaption></figure>

$$M = N \frac{\mu_0 \mu_r}{2\pi} a \ln \left( \frac{r_2}{r_1} \right) \qquad (1)$$

$$L_0 = N \frac{\mu_0 \mu_r}{2\pi} a \ln \left( \frac{r_2}{r_1} \right) \qquad (2)$$

$$C_0 = 4\pi^2 \epsilon_0 \epsilon_r \frac{r_1+r_2}{\ln\left(\frac{r_1+r_2}{r_2-r_1}\right)} \qquad (3)$$

$$R_0 = \frac{1}{\kappa A} \qquad (4)$$

$$\frac{U_2}{I} = \frac{\frac{R}{R+R_0} j\omega M}{\frac{R L_0 C_0}{R+R_0} (j\omega)^2 + \frac{L_0+R R_0 C_0}{R+R_0} j\omega + 1} \qquad (5)$$

$$f_{r1} = \frac{1}{2\pi} \sqrt{\frac{R+R_0}{RL_0C_0}} \qquad (6)$$

$$\sigma = \pi \frac{L_0+R R_0 C_0}{R+R_0} f_{r1} \qquad (7)$$

The parameters in Equations (1) to (7) are shown in Figure 2 and Figure 3, where N represents the number of turns, σ denotes attenuation and f<sub>r1</sub> is the resonant frequency.

Specific requirements were defined for the development of a suitable process analysis sensor. These include a sensor size that allows integration into industrial systems, a wide operating frequency of up to 10 MHz, very good linearity of the sensor output voltage with the frequencies, and an analyzable, measurable output signal.

## Structure of various Rogowski coils

As part of the study, various sensors (Rogowski coils) were constructed and tested using a test procedure (PeP). Figure 4 shows the three most important solutions with their geometric parameters.

Coil 1 has a non-ferromagnetic printed core with guide slots for the winding. The advantage of this coil is the geometrically exact and homogeneous winding, which can also be implemented in a concrete calculation or simulation. Comparisons between calculations and measurements are provided below.
<figure><img src="image_2294.png" /></figure>

Coil 1

$r_1 = 5.5 \text{ mm}$

$r_2 = 10.5 \text{ mm}$

$a = 2 \text{ mm}$

$N = 17$

<figure><img src="image_2295.png" /></figure>

Coil 2

$r_1 = 3.5 \text{ mm}$

$r_2 = 12 \text{ mm}$

$a = 2 \text{ mm}$

$N = 69$

<figure><img src="image_2296.png" /></figure>

Coil 3

$r_1 = 5.5 \text{ mm}$

$r_2 = 10.5 \text{ mm}$

$a = 1.6 \text{ mm}$

$N = 30$

<caption>Figure 4: Test coils for different application</caption>

Coil 2 has a larger ratio between outer and inner diameters with a significantly higher number of turns, which leads to overlaps on the inside radius and unequal spacing on the outside radius. This means that the calculation equations for the equivalent circuit diagram (ECD) in Figure 2 are only partially applicable.

Coil 3 is a printed circuit board Rogowski coil. The advantage of this coil is the higher manufacturing accuracy, which leads to a more precise calculation or simulation.

<figure><img src="image_2297.png" /><figcaption>Figure 5: Amplitude response for the three test coils up to 1 MHz</figcaption></figure>

In Figure 5 the linearity of the three coils was tested from 10 kHz up to 1 MHz, as a result. All tested coils have been shown a very good linearity. The influence of increasing the number of turns on the sensitivity can be clearly seen in Figure 5. The sensitivity M of coils 1 and 3 are almost similar, where the sensitivity M of coil 1 is 1.6 dB higher than that of coil 3. Coil 2 has a significantly higher sensitivity M than both coils 1 and 3. The sensitivity M of coil 3 is 17.7 dB higher than that of coil 1 and 16.1 dB higher than that of coil 3. Therefore, a higher number of windings is preferred. However, due to manufacturing limitations during the 3D printing of coil 1 and the PCB fabrication of coil 3, a higher number N of windings could not be achieved. In Figure 6 the calculated and measured frequency response for coil 1 are compared.
<figure><img src="image_2285.png" /></figure>

Coil 1

$r_1 = 5.5 \text{ mm}$

$r_2 = 10.5 \text{ mm}$

$a = 2 \text{ mm}$

$N = 17$

<figure><img src="image_2286.png" /></figure>

Coil 2

$r_1 = 3.5 \text{ mm}$

$r_2 = 12 \text{ mm}$

$a = 2 \text{ mm}$

$N = 69$

<figure><img src="image_2287.png" /></figure>

Coil 3

$r_1 = 5.5 \text{ mm}$

$r_2 = 10.5 \text{ mm}$

$a = 1.6 \text{ mm}$

$N = 30$

<caption>Figure 4: Test coils for different application</caption>

Coil 2 has a larger ratio between outer and inner diameters with a significantly higher number of turns, which leads to overlaps on the inside radius and unequal spacing on the outside radius. This means that the calculation equations for the equivalent circuit diagram (ECD) in Figure 2 are only partially applicable.

Coil 3 is a printed circuit board Rogowski coil. The advantage of this coil is the higher manufacturing accuracy, which leads to a more precise calculation or simulation.

<figure><img src="image_2288.png" /><figcaption>Figure 5: Amplitude response for the three test coils up to 1 MHz</figcaption></figure>

In Figure 5 the linearity of the three coils was tested from 10 kHz up to 1 MHz, as a result. All tested coils have been shown a very good linearity. The influence of increasing the number of turns on the sensitivity can be clearly seen in Figure 5. The sensitivity M of coils 1 and 3 are almost similar, where the sensitivity M of coil 1 is 1.6 dB higher than that of coil 3. Coil 2 has a significantly higher sensitivity M than both coils 1 and 3. The sensitivity M of coil 3 is 17.7 dB higher than that of coil 1 and 16.1 dB higher than that of coil 3. Therefore, a higher number of windings is preferred. However, due to manufacturing limitations during the 3D printing of coil 1 and the PCB fabrication of coil 3, a higher number N of windings could not be achieved. In Figure 6 the calculated and measured frequency response for coil 1 are compared.
<figure><img src="image_2298.png" /><figcaption>Figure 6: Amplitude response and phase response in the frequency range from 10 kHz to 10 MHz, calculated (blue, red) and measured (green) for coil 1</figcaption></figure>

Figure 6 shows an agreement between the measured and calculated amplitude response up to 10 MHz. The cutoff frequency is around 10 MHz. The requirement for the measuring sensor (coil) has been met.

## Experimental setup

The experimental setup is intended to show that both the initialization conditions of plasma electrolytic polishing (PeP) and the process transitions of the ECM can be determined at different voltage levels. PeP initialization requires the use of higher currents and larger voltage changes. In this case, the coil can be used without further amplification. With EC processing, however, significantly smaller current changes are to be expected, so that amplification of the coil output signal is necessary.

<figure><img src="image_2299.png" /><figcaption>Figure 7: Experimental setup for PeP/ECM</figcaption></figure>

The basic structure of the experiment corresponds to that of a PeP and the electrolyte used (Beckmann Institute) is also used for PeP processing. Figure 7 shows the key elements of the experiment.
<figure><img src="image_2289.png" /><figcaption>Figure 6: Amplitude response and phase response in the frequency range from 10 kHz to 10 MHz, calculated (blue, red) and measured (green) for coil 1</figcaption></figure>

Figure 6 shows an agreement between the measured and calculated amplitude response up to 10 MHz. The cutoff frequency is around 10 MHz. The requirement for the measuring sensor (coil) has been met.

## Experimental setup

The experimental setup is intended to show that both the initialization conditions of plasma electrolytic polishing (PeP) and the process transitions of the ECM can be determined at different voltage levels. PeP initialization requires the use of higher currents and larger voltage changes. In this case, the coil can be used without further amplification. With EC processing, however, significantly smaller current changes are to be expected, so that amplification of the coil output signal is necessary.

<figure><img src="image_2290.png" /><figcaption>Figure 7: Experimental setup for PeP/ECM</figcaption></figure>

The basic structure of the experiment corresponds to that of a PeP and the electrolyte used (Beckmann Institute) is also used for PeP processing. Figure 7 shows the key elements of the experiment.
The workpiece electrode (anode) is located in the center of a 61 mm radius work cup filled with a special electrolyte from the Beckmann Institute. The cathode plate is placed circumferentially against the inner wall of the cup. This configuration results in an anode-to-cathode ratio of 1 to 10, which is required for plasma polishing. Two series-connected programmable power supplies were used, each capable of supplying 300 VDC for the process. The cup filled with the electrolyte was brought to a temperature of 80 °C ± 5 °C using a heating plate. The coil was placed around the wire connected to the anode. Voltage, current and current change di/dt were recorded with an oscilloscope.

To analyze the switching behavior of the process, the voltage provided by the two power supplies was switched from an offset of 100 V/6 A to a typical PeP voltage of 348 V/396 V, pulsed for repeated generation of current increases.

## Results of the current change analysis at different voltage jumps in arrangements (PeP/ECM)

Figure 8 shows the performance of test coil 1 and test coil 3 when the supply voltage changed from 100 V to 348 V. The current changes di/dt were measured in two different experiments under the same conditions, resulting same process current and process voltage. It can be seen that the measured current changes with test coil 3 lead to significantly larger peak values. The beat (~8 kHz) on the di/dt peaks (~40 kHz) can be seen with the coil 3 also more clearly. There is still no clear initialization of the PeP process in the voltage switching range. There is no light effect on the anode that would indicate plasma formation. The di/dt peaks are caused by the power supplies used. This also proves the high performance of the test coil.

<figure><img src="image_2300.png" /><figcaption>Figure 8: Voltage changes from 100 V to 348 V measured with test coils 1 and 3 for two different tests</figcaption></figure>

On the 100 V level, a pure heating effect of the electrolyte can be assumed. The introduced power is approximately 600 W. In the 348 V level, the current density increases to 2 A/cm², and the power rises to approximately 5.9 kW after reaching a steady state. Due to the 6.1 cm distance between the anode and cathode, a low current yield is expected, minimizing the possibility of an electrochemical effect.
The workpiece electrode (anode) is located in the center of a 61 mm radius work cup filled with a special electrolyte from the Beckmann Institute. The cathode plate is placed circumferentially against the inner wall of the cup. This configuration results in an anode-to-cathode ratio of 1 to 10, which is required for plasma polishing. Two series-connected programmable power supplies were used, each capable of supplying 300 VDC for the process. The cup filled with the electrolyte was brought to a temperature of 80 °C ± 5 °C using a heating plate. The coil was placed around the wire connected to the anode. Voltage, current and current change di/dt were recorded with an oscilloscope.

To analyze the switching behavior of the process, the voltage provided by the two power supplies was switched from an offset of 100 V/6 A to a typical PeP voltage of 348 V/396 V, pulsed for repeated generation of current increases.

## Results of the current change analysis at different voltage jumps in arrangements (PeP/ECM)

Figure 8 shows the performance of test coil 1 and test coil 3 when the supply voltage changed from 100 V to 348 V. The current changes di/dt were measured in two different experiments under the same conditions, resulting same process current and process voltage. It can be seen that the measured current changes with test coil 3 lead to significantly larger peak values. The beat (~8 kHz) on the di/dt peaks (~40 kHz) can be seen with the coil 3 also more clearly. There is still no clear initialization of the PeP process in the voltage switching range. There is no light effect on the anode that would indicate plasma formation. The di/dt peaks are caused by the power supplies used. This also proves the high performance of the test coil.

<figure><img src="image_2291.png" /><figcaption>Figure 8: Voltage changes from 100 V to 348 V measured with test coils 1 and 3 for two different tests</figcaption></figure>

On the 100 V level, a pure heating effect of the electrolyte can be assumed. The introduced power is approximately 600 W. In the 348 V level, the current density increases to 2 A/cm², and the power rises to approximately 5.9 kW after reaching a steady state. Due to the 6.1 cm distance between the anode and cathode, a low current yield is expected, minimizing the possibility of an electrochemical effect.
In Figure 9, the transient conditions are compared for two different voltage steps. In the left diagram, the voltage step of 248 V is smaller. After a current peak of 17 A, the current drops to approximately 7.5 A before approaching the stable final value of 17 A. The $u_3$ value in this case is 2.55 V. In the case of the 296 V voltage step, the current peak is 62 A, and the later settling final value is 17 A. The maximum $u_3$ value is 3.35 V. After reaching the stable final value, the di/dt peaks remain constant, indicating no additional processes contributing to the electrolyte's warming.

<figure><img src="image_2301.png" /><figcaption>Figure 9: Transient behavior of the working current with different voltage jumps</figcaption></figure>

Compared to the initialization characteristic of Bath-PeP [5], only the first two phases of this characteristic are present. This implies that no plasma area can be created. Furthermore, based on [5], it can be inferred that the absolute voltage peak value is not crucial for initialization; instead, it is the du/dt value that matters. This is evident in the fact that a voltage value of 396 V with a rise of 0 V is ideal for PeP processing. In the examined example, however, the voltage change from 100 V to 396 V is not sufficient.

## Important measuring ranges of the Rogowski sensor for the Bath-PeP

In [5] different initialization curves were recorded for different voltage levels, as shown in Figure 10. The experiments involve stable PeP processing as well as unstable processes. Depending on the process energy source used to provide the voltage for the process, it is essential to initially verify whether the current overshoot in the first 50 µs is within the safe operating state and does not exceed the current limit that the process energy source can provide. Since this current value is also dependent on the immersion process, there may be larger deviations compared to the present diagram. With the di/dt sensor presented, the current overshoot can be detected within a few microseconds and appropriate measures can then be taken.

The second use of the coil occurs after the current drops after the initial current plateau, which provides information about the stability of the plasma ignition. A lower supply voltages lead to greater instabilities in the polishing process; thus, depending on the materials and electrolyte used, there must be a minimum changes in the process current di/dt to ensure a rapid and stable PeP process. For processes with greater instability, indicating potential reinitializations (plasma disruptions), as shown in Figure 10 for voltages of 200 V and 225 V, a third process evaluation can be conducted. For these process analyses and system safety considerations, Rogowski coils without amplification can be used. It is recommended to position the windings on a printed core with guide slots for the winding (coil 1) to enable the creation of reliable process analysis programs.
In Figure 9, the transient conditions are compared for two different voltage steps. In the left diagram, the voltage step of 248 V is smaller. After a current peak of 17 A, the current drops to approximately 7.5 A before approaching the stable final value of 17 A. The $u_3$ value in this case is 2.55 V. In the case of the 296 V voltage step, the current peak is 62 A, and the later settling final value is 17 A. The maximum $u_3$ value is 3.35 V. After reaching the stable final value, the di/dt peaks remain constant, indicating no additional processes contributing to the electrolyte's warming.

<figure><img src="image_2292.png" /><figcaption>Figure 9: Transient behavior of the working current with different voltage jumps</figcaption></figure>

Compared to the initialization characteristic of Bath-PeP [5], only the first two phases of this characteristic are present. This implies that no plasma area can be created. Furthermore, based on [5], it can be inferred that the absolute voltage peak value is not crucial for initialization; instead, it is the du/dt value that matters. This is evident in the fact that a voltage value of 396 V with a rise of 0 V is ideal for PeP processing. In the examined example, however, the voltage change from 100 V to 396 V is not sufficient.

## Important measuring ranges of the Rogowski sensor for the Bath-PeP

In [5] different initialization curves were recorded for different voltage levels, as shown in Figure 10. The experiments involve stable PeP processing as well as unstable processes. Depending on the process energy source used to provide the voltage for the process, it is essential to initially verify whether the current overshoot in the first 50 µs is within the safe operating state and does not exceed the current limit that the process energy source can provide. Since this current value is also dependent on the immersion process, there may be larger deviations compared to the present diagram. With the di/dt sensor presented, the current overshoot can be detected within a few microseconds and appropriate measures can then be taken.

The second use of the coil occurs after the current drops after the initial current plateau, which provides information about the stability of the plasma ignition. A lower supply voltages lead to greater instabilities in the polishing process; thus, depending on the materials and electrolyte used, there must be a minimum changes in the process current di/dt to ensure a rapid and stable PeP process. For processes with greater instability, indicating potential reinitializations (plasma disruptions), as shown in Figure 10 for voltages of 200 V and 225 V, a third process evaluation can be conducted. For these process analyses and system safety considerations, Rogowski coils without amplification can be used. It is recommended to position the windings on a printed core with guide slots for the winding (coil 1) to enable the creation of reliable process analysis programs.
<figure><img src="image_2302.png" /><figcaption>Figure 10: PeP initialization diagrams for Bath-PeP at different working voltages [5]</figcaption></figure>

Due to the very small current changes in the steady state, an amplifier circuit may be required for coils in order to monitor the current changes. When amplifying the coil output signal, the cutoff frequency of the amplifier circuit must be considered. To avoid influencing the cutoff frequency of the coil, the cutoff frequency of the amplifier circuits must be higher than the cutoff frequency of the coil, ensuring that the overall system's cutoff frequency remains equal to that of the coil itself. In the examples examined, the shifts in cutoff frequency were close to the required 10 MHz cutoff frequency in the worst case.

## Summary

This paper demonstrates the effectiveness of the Rogowski coil in measuring transients and fast current changes. All the coils studied have shown very good linearity up to an operating frequency of 10 MHz, measuring transients as short as 100 ns. The electrical properties of the Rogowski coil are significantly influenced by its geometrical parameters. To increase the accuracy of the calculation and simulation, it is recommended to wind the coil around a printed core with guide slots or to realize a circuit board with fixed geometric dimensions. Coil parameters such as mutual inductance, inductance, resistance and capacitance have been calculated analytically. The practicality of three Rogowski coils has been tested experimentally. The function of a Rogowski coil is to recognize current changes. For processes with direct correlation to current, such as ECM or PEP, the Rogowski coil can help protect processes against overcurrent, analyze the stability of processes and act as an event detector for monitoring processes over time. Known for its scalability, the Rogowski coil offers an industrially scalable solution for accurately measuring current changes across various applications. Its adaptability to different current levels, ease of installation and precision make it an effective choice for industrial environments with different current levels and operating conditions.

## References

[1] Darawish, H, Auslegung einer Prozessfehlererkennung auf Basis der Prozessstromänderungsrate. BA Thesis OVGU Magdeburg, 2023

[2] M. H. Samimi, A. Mahari, M. A. Farahnakian and H. Mohseni, "The Rogowski Coil Principles and Applications: A Review," in *IEEE Sensors Journal*, vol. 15, no. 2, pp. 651-658, Feb. 2015. https://doi.org/10.1109/JSEN.2014.2362940

[3] Hashmi, G. M., Lehtonen, M., and Elhaffar, A. (2007). Modeling of Rogowski coil for online PD monitoring in covered-conductor overhead distribution networks. *Pulse, 1*, P2.
<figure><img src="image_2293.png" /><figcaption>Figure 10: PeP initialization diagrams for Bath-PeP at different working voltages [5]</figcaption></figure>

Due to the very small current changes in the steady state, an amplifier circuit may be required for coils in order to monitor the current changes. When amplifying the coil output signal, the cutoff frequency of the amplifier circuit must be considered. To avoid influencing the cutoff frequency of the coil, the cutoff frequency of the amplifier circuits must be higher than the cutoff frequency of the coil, ensuring that the overall system's cutoff frequency remains equal to that of the coil itself. In the examples examined, the shifts in cutoff frequency were close to the required 10 MHz cutoff frequency in the worst case.

## Summary

This paper demonstrates the effectiveness of the Rogowski coil in measuring transients and fast current changes. All the coils studied have shown very good linearity up to an operating frequency of 10 MHz, measuring transients as short as 100 ns. The electrical properties of the Rogowski coil are significantly influenced by its geometrical parameters. To increase the accuracy of the calculation and simulation, it is recommended to wind the coil around a printed core with guide slots or to realize a circuit board with fixed geometric dimensions. Coil parameters such as mutual inductance, inductance, resistance and capacitance have been calculated analytically. The practicality of three Rogowski coils has been tested experimentally. The function of a Rogowski coil is to recognize current changes. For processes with direct correlation to current, such as ECM or PEP, the Rogowski coil can help protect processes against overcurrent, analyze the stability of processes and act as an event detector for monitoring processes over time. Known for its scalability, the Rogowski coil offers an industrially scalable solution for accurately measuring current changes across various applications. Its adaptability to different current levels, ease of installation and precision make it an effective choice for industrial environments with different current levels and operating conditions.

## References

[1] Darawish, H, Auslegung einer Prozessfehlererkennung auf Basis der Prozessstromänderungsrate. BA Thesis OVGU Magdeburg, 2023

[2] M. H. Samimi, A. Mahari, M. A. Farahnakian and H. Mohseni, "The Rogowski Coil Principles and Applications: A Review," in *IEEE Sensors Journal*, vol. 15, no. 2, pp. 651-658, Feb. 2015. https://doi.org/10.1109/JSEN.2014.2362940

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