# Investigation on Temperature-Dependent Multiaxial Ratchetting of Polycarbonate by a Novel Experimental Method

Authors: Fucong Lu; Kun Zhang; Yuhang Hou; Zhiwen Wu
Journal: Advances in Materials Science and Engineering
 (2022)

---

## Abstract

A novel method to heat the multiaxial hollow thin-wall specimen was proposed, where its gauge length section can be heated by the liquid (i.e., water) filled inside the specimen instead of the closed furnace. This method realizes the direct measurement of multiaxial strain on the surface of specimen at different temperatures by the noncontact digital image correlation. By utilizing the proposed method, the multiaxial stress-control cyclic tests were performed to investigate the multiaxial ratchetting of polycarbonate (PC) at different temperatures. It is found that the multiaxial ratchetting of PC depends greatly on the test temperatures and the multiaxial ratchetting strain increases with increasing the test temperature. The temperature-dependent multiaxial ratchetting is also influenced by valley stresses. The unrecoverable part of deformation in the multiaxial ratchetting strain increases with increasing temperature.


---

## Body

## 1. Introduction

Polycarbonate (PC) is widely used in various engineering components due to its excellent physical and mechanical properties such as high specific strength, high fracture toughness, and good impact resistance [1–4]. In practical applications, PC components are often subjected to cyclic loading, especially the nonzero mean stress cyclic loading. Thus, ratchetting of these components may occur during cyclic loading. The ratchetting of polymers is influenced by many factors, such as stress level, stress rate, loading path, and temperature. To achieve the reliability assessment and design of the components reasonably, it is necessary to investigate the multiaxial ratchetting of PC at different temperatures.In the last decades, extensive research on the uniaxial ratchetting of polymer materials at room temperature has been conducted. For example, Li et al. [5] studied the uniaxial ratchetting of vulcanized natural rubber and discussed the influence of stress level, loading rate, and stress history on ratchetting of the material. Pan et al. [6] performed the stress-controlled cyclic test with different holding times at valley/peak stress and studied the time-dependent uniaxial ratchetting behavior of polyetherimide. Jiang et al. [7] investigated the uniaxial ratchetting of PC and proposed an experimental method to quantitative analysis of the recoverable part of deformation in the ratchetting strain. Xi et al. [8] discussed the influence of molecular weight on the uniaxial ratchetting of two kinds of PCs. The uniaxial ratchetting-fatigue interaction of polymers (i.e., epoxy resin and polyacetal resin) was investigated and found the ratchetting strain will accelerate the fatigue failure of polymers [9, 10]. Zhang et al. [11] investigated the uniaxial compression ratchetting of polytetrafluoroethylene and proposed a constitutive model for the material. Much effort on the observations to the uniaxial ratchetting of polymers/polymer composites and its dependences on the loading level, loading rate, and loading history as well as control mode can be referred to [12–15].The effect of environmental conditions (i.e., temperature) on the uniaxial ratchetting of polymer materials has attracted the attention of researchers. Zhang et al. [16, 17] systematically studied the cyclic compression ratchetting of polytetrafluoroethylene at different temperatures and found that the ratchetting strain increases with increasing temperature. Chen et al. [18] investigated the temperature-dependent uniaxial ratchetting of ultrahigh molecular weight polyethylene and found the relationship between ratchetting strain and temperature is not monotonic. Lu et al. [19] investigated the effect of valley stress on the temperature-dependent ratchetting of PC and found that the fatigue life in the load cases with negative valley stresses is lower than that with positive valley stresses. Jeya et al. [20] studied the thermal cyclic ratchetting of high-density polyethylene and discussed the effects of compression stress, cyclic temperature amplitude, and the number of thermal cycles on ratchetting.The multiaxial ratchetting of polymer materials was focused on in recent years. Chen et al. [21] performed the multiaxial stress-control cyclic test on acrylonitrile-butadiene-styrene polymer and studied the multiaxial ratchetting-fatigue interaction. Lu et al. [22] systematically investigated multiaxial ratchetting of PC at room temperature, including the effect of peak/valley stress, loading path, and loading history. Chen et al. [23] studied the nonproportional multiaxial ratchetting of ultrahigh molecular weight polyethylene polymer and proposed a cyclic constitutive model considering the nonproportional loading effect based on the experimental results.Although the ratchetting of polymer materials has been extensively investigated, no studies have been reported on multiaxial ratchetting of polymer materials considering the effect of temperature. One main challenge is that there is little suitable testing equipment for performing multiaxial ratchetting of polymeric materials at high temperatures. Note that the existing multiaxial strain extensometer is mainly designed for metallic materials. When the multiaxial strain extensometer is applied to polymers, it will damage the multiaxial hollow thin-wall specimen because polymers are much softer than metals.In this work, a novel method to heat the multiaxial hollow thin-wall specimen was presented and the validity of the proposed heating method was verified. This method realizes the direct measurement of the multiaxial strain on the surface of the specimen at different temperatures by the noncontact digital image correlation (DIC). The multiaxial stress-controlled cyclic tests were performed to investigate multiaxial ratchetting of PC at different temperatures. The effects of loading path and valley stress on the temperature-dependent multiaxial ratchetting of PC were discussed. Note that this work is a supplement to our previous studies on the uniaxial ratchetting at different temperatures and the multiaxial ratchetting behavior at room temperature for the same PC material. These experimental results combined with the previous data will provide sufficient data support for the establishment of a suitable cyclic constitutive model of the material.


## 2. Experimental Procedures

### 2.1. Testing Method

A noncontact DIC method has certain advantages in measuring the deformation of materials because it does not damage the surface of the specimen and can obtain the strain field of the measured area. However, this method is hard to measure the strain on the surface of specimens at different temperatures because the experiments at different temperatures generally need to perform in the closed environment box and DIC camera cannot take pictures of the specimen’s surface during testing. Some scholars [24] modified the environmental box with a glass window and recalibrated the DIC system. Although the strain field on the surface of specimen can be obtained in the method, the strain measurement accuracy decreases due to the refraction of the glass. To solve this problem, a novel method is proposed to measure the strain field on the surface of specimen at different temperatures. The schematic diagram of the proposed test system is shown in Figure 1.Figure 1
The schematic diagram of the proposed experimental method.The testing system includes an MTS858-BIONIX test machine (MTS System Corp., USA), a DIC system ARAMIS 5M (GOM mhH Ltd., Germany), and a novel heating device. For the heating device, the water filled inside the cavity of the specimen is considered as a continuous heat source. To control the water temperature, a set of the temperature control devices is specially designed for this purpose. Its schematic diagram is shown in Figure1. The core components are heating resistance wire, thermocouple, direct current (DC) power supply, temperature controller, and relay. The metal blocker on the upper end of the specimen has three perforated holes for installing power cable and thermocouple. A DC power supply is used to provide a heating current. The thermocouple probe is placed in water inside the specimen to detect the temperature of water. The relay works with the temperature controller to control the current on and off. When the water temperature is lower than the target value, the heating current is switched on. When the water temperature reaches the target value, the relay is disconnected and stops heating. Once the water temperature drops below the target value due to the thermal convection and thermal radiation, the temperature controller will turn on the heating current to keep the water temperature at a constant value.To verify the validity of the proposed heating method, a multistage temperature control test was carried out. The polymer material used was Bayer Makrolon® ET3113 extruded PC. The raw material used is not a solid polycarbonate bar, but a hollow polycarbonate tube, whose inner diameter is the same as that of the received hollow sample. In the machining process, only the outer contour of the sample was processed. After the sample is machined, the sample is placed for a period of time to eliminate residual stress. To prevent deformation from affecting the processing accuracy, a steel rod with diameter as the inner diameter of the tube was inserted into the raw polycarbonate tube before processed. According to our previous work [22], the final performances of the sample are hardly affected by processing. The dimension of the multiaxial specimen is shown in Figure 2. The target temperatures of water were set at 35, 50, 65, and 80°C and kept at each temperature for 5 minutes. Meanwhile, the temperature field of the external surface on the specimen was measured by a thermal infrared imager (FLIR S650, USA). The test results are shown in Figure 3. As shown in Figure 3(a), the water temperature (internal temperature) agrees well with the target setting value, indicating the temperature system was well controlled. After holding at the target temperature for 5 minutes, the temperature of the internal surface of the gauge section of the specimen should be consistent with that of the thermocouple probe (water temperature). The temperature difference between internal and external surfaces of the specimen increases with the increase of temperature. However, when the internal temperature reaches a certain value, the external temperature is also reaching a certain level and stable. Besides, it can be observed that the temperature field of the external surface of the specimen is uniform for all the testing temperatures, as shown in Figure 3(b). Note that the temperature value of the thermocouple probe is taken as the testing temperature of the material in this work. Although the temperature values for the internal and external surfaces on the gauge section of specimen are not consistent, the temperature difference is relatively small as the thickness on the gauge section of specimen is very thin (1 mm).Figure 2
Sketch of the multiaxial specimen (unit: mm).Figure 3
Verification of temperature control. (a) Temperature difference between inner surface and outer surface of the specimen at different temperatures. (b) Thermal image of temperature distribution on the outer surface of the specimen at different temperatures.
(a)(b)Note that the validity of the method to measure the multiaxial strain of hollow thin-wall specimen at room temperature has been verified in our previous work [22]. In this work, the method to measure the multiaxial strain of the specimen at different temperatures is similar to that at room temperature, indicating that the proposed multiaxial strain measurement method at different temperatures is reliable.


### 2.2. Loading Cases

This work mainly investigated the multiaxial ratchetting of PC at different temperatures (i.e., 35, 60, 75, and 90°C). Three loading paths were selected for performing multiaxial stress-control tests, as shown in Figure4. The design of the loading cases was similar to that of uniaxial ratchetting at different temperatures. The loading case (i.e., peak stress and valley stress) was set based on the ratio of yield stress. The yield stress was defined as the ultimate stress before softening, which was determined by the uniaxial tensile tests at a speed of 0.01 mm/min and equaled to 66, 57, 49, and 45 MPa at 35, 60, 75, and 90°C, respectively. The axial (or torsional equivalent) peak stress keeps the same value, and the axial (or torsional equivalent) valley stress varies at each temperature. The peak and valley stresses refer to the axial (or equivalent torsional) maximum or minimum stress value of the external circular of the loading path, respectively. The prescribed loading cases are given in Table 1. A constant stress rate of 1 MPa/s is applied for all loading cases. The number of cycles is 50. After the end of cyclic tests, they were held at the zero-stress level for half hour to assess the recoverable feature of the residual strain produced immediately after unloading.Figure 4
Diagram of nonproportional multiaxial stress-control loading path: (a) rhombic-type 1, (b) butterfly-type, and (c) rhombic-type 2.
(a)(b)(c)Table 1
Multiaxial stress-control cyclic loading cases.
Loading caseLoading pathPeak stress (×σy)Valley stress (×σy)Temperature (°C)1Rhombic-type 10.80.3352Rhombic-type 10.80.0353Rhombic-type 10.8−0.3354Rhombic-type 10.80.3605Rhombic-type 10.80.0606Rhombic-type 10.8−0.3607Butterfly-type0.80.3608Butterfly-type0.8−0.3609Butterfly-type0.8−0.66010Rhombic-type 10.80.37511Rhombic-type 10.8−0.37512Rhombic-type 20.80.07513Rhombic-type 20.8−0.37514Rhombic-type 20.8−0.67515Rhombic-type 10.80.39016Rhombic-type 10.8−0.390To discuss the relationship between stress and strain under multiaxial loading conditions, the equivalent stressσeq and the equivalent strain εeq are used and defined as follows:(1)σeq=σ2+τe2=σ2+3τ2,εeq=ε2+γ32,where σ, ε, 3τ, and γ/3 are the nominal axial and equivalent shear stresses and strains, respectively.The multiaxial stress-control loading cases (i.e., combined tension-torsion with three loading paths shown in Figure4) are given in Table 1. To illustrate the uniaxial and multiaxial ratchetting more clearly, the axial ratchetting strain εr and equivalent torsional ratchetting strain γer are defined as(2)εr=εmax+εmin2,γer=γemax+γemin2,where εmax (or γemax) is the maximum axial (or equivalent torsional) strain in each cycle, and εmin (or γemin) is the minimum one. The ratchetting strain rate is defined as the increment of ratchetting strain per cycle.


## 2.1. Testing Method

A noncontact DIC method has certain advantages in measuring the deformation of materials because it does not damage the surface of the specimen and can obtain the strain field of the measured area. However, this method is hard to measure the strain on the surface of specimens at different temperatures because the experiments at different temperatures generally need to perform in the closed environment box and DIC camera cannot take pictures of the specimen’s surface during testing. Some scholars [24] modified the environmental box with a glass window and recalibrated the DIC system. Although the strain field on the surface of specimen can be obtained in the method, the strain measurement accuracy decreases due to the refraction of the glass. To solve this problem, a novel method is proposed to measure the strain field on the surface of specimen at different temperatures. The schematic diagram of the proposed test system is shown in Figure 1.Figure 1
The schematic diagram of the proposed experimental method.The testing system includes an MTS858-BIONIX test machine (MTS System Corp., USA), a DIC system ARAMIS 5M (GOM mhH Ltd., Germany), and a novel heating device. For the heating device, the water filled inside the cavity of the specimen is considered as a continuous heat source. To control the water temperature, a set of the temperature control devices is specially designed for this purpose. Its schematic diagram is shown in Figure1. The core components are heating resistance wire, thermocouple, direct current (DC) power supply, temperature controller, and relay. The metal blocker on the upper end of the specimen has three perforated holes for installing power cable and thermocouple. A DC power supply is used to provide a heating current. The thermocouple probe is placed in water inside the specimen to detect the temperature of water. The relay works with the temperature controller to control the current on and off. When the water temperature is lower than the target value, the heating current is switched on. When the water temperature reaches the target value, the relay is disconnected and stops heating. Once the water temperature drops below the target value due to the thermal convection and thermal radiation, the temperature controller will turn on the heating current to keep the water temperature at a constant value.To verify the validity of the proposed heating method, a multistage temperature control test was carried out. The polymer material used was Bayer Makrolon® ET3113 extruded PC. The raw material used is not a solid polycarbonate bar, but a hollow polycarbonate tube, whose inner diameter is the same as that of the received hollow sample. In the machining process, only the outer contour of the sample was processed. After the sample is machined, the sample is placed for a period of time to eliminate residual stress. To prevent deformation from affecting the processing accuracy, a steel rod with diameter as the inner diameter of the tube was inserted into the raw polycarbonate tube before processed. According to our previous work [22], the final performances of the sample are hardly affected by processing. The dimension of the multiaxial specimen is shown in Figure 2. The target temperatures of water were set at 35, 50, 65, and 80°C and kept at each temperature for 5 minutes. Meanwhile, the temperature field of the external surface on the specimen was measured by a thermal infrared imager (FLIR S650, USA). The test results are shown in Figure 3. As shown in Figure 3(a), the water temperature (internal temperature) agrees well with the target setting value, indicating the temperature system was well controlled. After holding at the target temperature for 5 minutes, the temperature of the internal surface of the gauge section of the specimen should be consistent with that of the thermocouple probe (water temperature). The temperature difference between internal and external surfaces of the specimen increases with the increase of temperature. However, when the internal temperature reaches a certain value, the external temperature is also reaching a certain level and stable. Besides, it can be observed that the temperature field of the external surface of the specimen is uniform for all the testing temperatures, as shown in Figure 3(b). Note that the temperature value of the thermocouple probe is taken as the testing temperature of the material in this work. Although the temperature values for the internal and external surfaces on the gauge section of specimen are not consistent, the temperature difference is relatively small as the thickness on the gauge section of specimen is very thin (1 mm).Figure 2
Sketch of the multiaxial specimen (unit: mm).Figure 3
Verification of temperature control. (a) Temperature difference between inner surface and outer surface of the specimen at different temperatures. (b) Thermal image of temperature distribution on the outer surface of the specimen at different temperatures.
(a)(b)Note that the validity of the method to measure the multiaxial strain of hollow thin-wall specimen at room temperature has been verified in our previous work [22]. In this work, the method to measure the multiaxial strain of the specimen at different temperatures is similar to that at room temperature, indicating that the proposed multiaxial strain measurement method at different temperatures is reliable.


## 2.2. Loading Cases

This work mainly investigated the multiaxial ratchetting of PC at different temperatures (i.e., 35, 60, 75, and 90°C). Three loading paths were selected for performing multiaxial stress-control tests, as shown in Figure4. The design of the loading cases was similar to that of uniaxial ratchetting at different temperatures. The loading case (i.e., peak stress and valley stress) was set based on the ratio of yield stress. The yield stress was defined as the ultimate stress before softening, which was determined by the uniaxial tensile tests at a speed of 0.01 mm/min and equaled to 66, 57, 49, and 45 MPa at 35, 60, 75, and 90°C, respectively. The axial (or torsional equivalent) peak stress keeps the same value, and the axial (or torsional equivalent) valley stress varies at each temperature. The peak and valley stresses refer to the axial (or equivalent torsional) maximum or minimum stress value of the external circular of the loading path, respectively. The prescribed loading cases are given in Table 1. A constant stress rate of 1 MPa/s is applied for all loading cases. The number of cycles is 50. After the end of cyclic tests, they were held at the zero-stress level for half hour to assess the recoverable feature of the residual strain produced immediately after unloading.Figure 4
Diagram of nonproportional multiaxial stress-control loading path: (a) rhombic-type 1, (b) butterfly-type, and (c) rhombic-type 2.
(a)(b)(c)Table 1
Multiaxial stress-control cyclic loading cases.
Loading caseLoading pathPeak stress (×σy)Valley stress (×σy)Temperature (°C)1Rhombic-type 10.80.3352Rhombic-type 10.80.0353Rhombic-type 10.8−0.3354Rhombic-type 10.80.3605Rhombic-type 10.80.0606Rhombic-type 10.8−0.3607Butterfly-type0.80.3608Butterfly-type0.8−0.3609Butterfly-type0.8−0.66010Rhombic-type 10.80.37511Rhombic-type 10.8−0.37512Rhombic-type 20.80.07513Rhombic-type 20.8−0.37514Rhombic-type 20.8−0.67515Rhombic-type 10.80.39016Rhombic-type 10.8−0.390To discuss the relationship between stress and strain under multiaxial loading conditions, the equivalent stressσeq and the equivalent strain εeq are used and defined as follows:(1)σeq=σ2+τe2=σ2+3τ2,εeq=ε2+γ32,where σ, ε, 3τ, and γ/3 are the nominal axial and equivalent shear stresses and strains, respectively.The multiaxial stress-control loading cases (i.e., combined tension-torsion with three loading paths shown in Figure4) are given in Table 1. To illustrate the uniaxial and multiaxial ratchetting more clearly, the axial ratchetting strain εr and equivalent torsional ratchetting strain γer are defined as(2)εr=εmax+εmin2,γer=γemax+γemin2,where εmax (or γemax) is the maximum axial (or equivalent torsional) strain in each cycle, and εmin (or γemin) is the minimum one. The ratchetting strain rate is defined as the increment of ratchetting strain per cycle.


## 3. Results and Discussion

### 3.1. Evolution of Multiaxial Ratchetting

Figure5 shows the curves of responding equivalent shear strain vs. axial strain of PC obtained by the proposed test method at different temperatures (i.e., 35 and 90°C). The multiaxial ratchetting of PC mainly occurs in loading cases with nonzero average stress in the axial direction and progressively evolves with the increasing number of cycles. As shown in Figure 6, it is seen that the ratchetting strain obviously increases with the increasing number of cycles and the ratchetting strain rate almost keeps a constant rate. Furthermore, ratchetting depends on the temperature and the ratchetting strain rate increases with the increase of temperature.Figure 5
The curve of responding equivalent shear strain and axial strain of PC under the rhombic-type 1 loading path at different temperatures: (a) 35°C; (b) 90°C.
(a)(b)Figure 6
The evolution of multiaxial ratchetting strain of polycarbonate with the number of cycles under the rhombic-type 1 loading path condition with a constant peak stress of 0.8 ×σy and a constant valley stress of −0.3 × σy at different temperatures.The effect of valley stress on the multiaxial ratchetting of PC at different temperatures was investigated. The results are shown in Figures7 and 8. It is ready to conclude as follows: (1) at different temperatures, the initial ratchetting strain increases, while the ratchetting strain rate decreases with the increasing valley stress. (2) When the valley stress is negative (i.e., −0.6 × σy), the material fractured within 50 cycles; while when the valley stress is positive, the material did not fracture within the prescribed number of cycles. These phenomena are similar to the behavior of the uniaxial ratchetting at high temperature, which is because under the condition of a constant peak stress, the lower the valley stress is, the greater the stress amplitude is. The plastic dissipation increases with the increases of stress amplitude in the cycling loading. The higher plastic dissipation will result in larger damage and a shorter fatigue life of the material.Figure 7
Ratchetting of PC in multiaxial stress-controlled cyclic tests under the rhombic-type 1 loading path and with different valley stresses at a constant peak stress of 0.8 ×σy and at various temperatures: (a) 35°C, (b) 60°C, (c) 75°C, and (d) 90°C.
(a)(b)(c)(d)Figure 8
Ratchetting of PC in multiaxial stress-controlled cyclic tests with different valley stresses at a constant peak stress of 0.8 ×σy and with different loading paths: (a) butterfly-type; (b) rhombus-type 2.
(a)(b)


### 3.2. Evolution of the Residual Strain after Unloading

The recovery of the residual strain at the end of the multiaxial ratchetting test was measured and discussed. The results are shown in Figure9. The residual strain after the multiaxial ratchetting test is partially recovered, and the recovering rate decreases gradually with the increase of holding time. The residual strain of the loading case with lower valley stress is higher than that with higher valley stress at different temperatures. The residual strain at 1800 s can be considered as the irrecoverable plastic strain because the recovering rate is small after holding at the zero-stress level for half hour. It indicates that the multiaxial ratchetting strain in the loading case with a lower value of valley stress contains a greater amount of irrecoverable plastic strain. Besides, the irrecoverable plastic strain increases with the increasing temperature as the movement of molecular segments of polymers is easier to occur at a higher temperature, indicating that the accumulated plastic deformation during the cyclic loading at high temperature is more significant than that at the low temperature.Figure 9
The axial strain evolving with time during the zero-stress holding after the multiaxial ratchetting tests of PC at different temperatures: (a) 35°C, (b) 60°C, and (c) 90°C.
(a)(b)(c)


## 3.1. Evolution of Multiaxial Ratchetting

Figure5 shows the curves of responding equivalent shear strain vs. axial strain of PC obtained by the proposed test method at different temperatures (i.e., 35 and 90°C). The multiaxial ratchetting of PC mainly occurs in loading cases with nonzero average stress in the axial direction and progressively evolves with the increasing number of cycles. As shown in Figure 6, it is seen that the ratchetting strain obviously increases with the increasing number of cycles and the ratchetting strain rate almost keeps a constant rate. Furthermore, ratchetting depends on the temperature and the ratchetting strain rate increases with the increase of temperature.Figure 5
The curve of responding equivalent shear strain and axial strain of PC under the rhombic-type 1 loading path at different temperatures: (a) 35°C; (b) 90°C.
(a)(b)Figure 6
The evolution of multiaxial ratchetting strain of polycarbonate with the number of cycles under the rhombic-type 1 loading path condition with a constant peak stress of 0.8 ×σy and a constant valley stress of −0.3 × σy at different temperatures.The effect of valley stress on the multiaxial ratchetting of PC at different temperatures was investigated. The results are shown in Figures7 and 8. It is ready to conclude as follows: (1) at different temperatures, the initial ratchetting strain increases, while the ratchetting strain rate decreases with the increasing valley stress. (2) When the valley stress is negative (i.e., −0.6 × σy), the material fractured within 50 cycles; while when the valley stress is positive, the material did not fracture within the prescribed number of cycles. These phenomena are similar to the behavior of the uniaxial ratchetting at high temperature, which is because under the condition of a constant peak stress, the lower the valley stress is, the greater the stress amplitude is. The plastic dissipation increases with the increases of stress amplitude in the cycling loading. The higher plastic dissipation will result in larger damage and a shorter fatigue life of the material.Figure 7
Ratchetting of PC in multiaxial stress-controlled cyclic tests under the rhombic-type 1 loading path and with different valley stresses at a constant peak stress of 0.8 ×σy and at various temperatures: (a) 35°C, (b) 60°C, (c) 75°C, and (d) 90°C.
(a)(b)(c)(d)Figure 8
Ratchetting of PC in multiaxial stress-controlled cyclic tests with different valley stresses at a constant peak stress of 0.8 ×σy and with different loading paths: (a) butterfly-type; (b) rhombus-type 2.
(a)(b)


## 3.2. Evolution of the Residual Strain after Unloading

The recovery of the residual strain at the end of the multiaxial ratchetting test was measured and discussed. The results are shown in Figure9. The residual strain after the multiaxial ratchetting test is partially recovered, and the recovering rate decreases gradually with the increase of holding time. The residual strain of the loading case with lower valley stress is higher than that with higher valley stress at different temperatures. The residual strain at 1800 s can be considered as the irrecoverable plastic strain because the recovering rate is small after holding at the zero-stress level for half hour. It indicates that the multiaxial ratchetting strain in the loading case with a lower value of valley stress contains a greater amount of irrecoverable plastic strain. Besides, the irrecoverable plastic strain increases with the increasing temperature as the movement of molecular segments of polymers is easier to occur at a higher temperature, indicating that the accumulated plastic deformation during the cyclic loading at high temperature is more significant than that at the low temperature.Figure 9
The axial strain evolving with time during the zero-stress holding after the multiaxial ratchetting tests of PC at different temperatures: (a) 35°C, (b) 60°C, and (c) 90°C.
(a)(b)(c)


## 4. Conclusion

A novel method to heat the multiaxial hollow thin-wall specimen was proposed, which enables the direct measurement of the multiaxial strain on the surface of the specimen at different temperatures by the noncontact DIC. The feasibility of the test method is demonstrated. The multiaxial ratchetting behavior of PC at different temperatures was studied by utilizing the proposed testing method. The results show that multiaxial ratchetting of PC is greatly affected by the temperature, and the higher the temperature is, the higher the ratchetting strain rate is. The ratchetting strain includes both the recoverable viscoelastic strain and the unrecoverable plastic strain. The amount of unrecoverable plastic part in the ratchetting strain increases with the increasing temperature.



---

*Source: 6577569-2022-05-13.xml*