# Numerical Investigations on Residual Stress in Laser Penetration Welding Process of Ultrafine-Grained Steel

Authors: Dezheng Liu; Yan Li; Haisheng Liu; Zhongren Wang; Yu Wang
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

Weld solidification crack prevention in the laser penetration welding process is essential for the strength of the welded component. The formation of solidification cracks can ultimately be attributed to welding residual stresses, and preventive measures should be taken during welding. In this study, the effects of residual stresses on the laser penetration welding quality of ultrafine-grained steels were investigated. A heat source model was established through the analysis of the metallography of the cross section of the heat-affected zone (HAZ) of ultrafine-grained AN420s-grade steel, and the chemical composition of the weld bead was obtained using an FLS980-stm Edinburgh fluorescence spectrometer. Furthermore, the constitutive coupling relation between the temperature and material flow stress was established based on the Gibbs function, and the welding residual stress was obtained by setting trace points in a finite element analysis (FEA) model based on experimental data of the weld bead cross section under different welding conditions. The results show that weld solidification cracks will form when the residual stresses exceed the material flow stresses in the weld bead, and the residual stresses can be decreased through a reasonable increase of the welding speed. The results indicate that the proposed criterion has high accuracy and can be used to predict the formation of weld solidification cracks in the laser penetration welding process.


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## Body

## 1. Introduction

Laser penetration welding, which is a stable and noncontact joining process, provides high welding speeds, good flexibility (narrow weld width and large weld depth), and high accuracy in process control [1]. The laser penetration welding technology has potential uses in additive manufacturing of ultrafine-grained steels [2, 3]. However, solidification crack formation in the fusion welding process continues to be one of the major challenges in the use of laser penetration welding technology to join ultrafine-grained steels [4]. For example, the use of laser penetration welding for new structural components still requires significant amounts of engineering data to determine its effects on the mechanical properties, such as tensile strength, fatigue strength, and the generation of residual stresses [5]. During the laser penetration welding process, the heat transfer and liquid metal flow in the molten pool affect the grain growth direction, which may affect the weld seam structure and the properties of the weld [6]. If thermomechanical strains caused by the time-dependent temperature distribution during welding and material-specific shrinkage during the liquid- or solid-phase transition cannot be compensated for by the ductility of the weld metal or by reflow of the melt, solidification cracks will appear [7]. Furthermore, the residual stress caused by the changes in the chemical composition and the heating and cooling rates during the welding process can aggravate the initiation and growth of solidification cracks [8]. Measured residual stress data can be used for fracture analysis, safety design, and strength evaluations. However, it is difficult to experimentally measure the evolution of residual stress and solidification cracks due to the strong interference from the arc light, the rapid change in temperature, and the phase transition [5]. Thus, numerical simulations can provide valuable information to understand the laser penetration welding process of ultrafine-grained steels.Numerical simulation methods can use multiple physics models to describe the complex physical phenomena in the molten pool [9, 10]. Many of the studies on the susceptibility to solidification cracking during the welding process using thermomechanical modelling focused on the resulting deformation and residual stresses. Frewin and Scott [11] presented a three-dimensional (3D) finite element (FE) model of the heat flow during pulsed laser beam welding. They also investigated the transient temperature profiles, dimensions of fusion, and heat-affected zone (HAZ) by incorporating temperature-dependent thermophysical properties and experimentally measured beam profiles. Shibahara et al. [12] developed a temperature-dependent interface element technique to analyze solidification cracking for mild steels. They suggested that this technique could be used to predict solidification cracks with a high accuracy. Volpp and Vollertsen [13, 14] presented an analytical method to quickly calculate the keyhole dynamics for different spatial laser intensity distributions during laser deep penetration welding. They concluded that a top hat intensity distribution led to higher maximum frequencies of the keyhole oscillations compared to a Gaussian beam profile. Dong et al. [15] indicated that the prediction of solidification cracking could be obtained by comparing the crack driving force and resistance curves. Fadaei and Mokhtari [16] presented an FE simulation and experimental measurements of the residual stresses in repair butt welds using the Goldak double-ellipsoid heat source model.However, most recent studies on residual stresses in the laser penetration welding process were limited to numerical simulations of the evolution of temperature and residual stress fields and rarely involved the accurate modelling and analysis of the effects of transient residual and material flow stresses for weld solidification cracking.The objective of this study was threefold. First, a heat source model was established through the analysis of the metallography of the cross section of the weld bead of ultrafine-grained AN420s-grade steel, and the chemical composition of the weld bead was measured using an FLS980-stm Edinburgh fluorescence spectrometer. Second, the constitutive coupling relation between temperature and material flow stress in the molten pool was derived. The Gibbs interface thermodynamic method and the Sente Software JMatPro were used in the derivation of the constitutive coupling relation. Third, an FE model of the molten pool was established based on the experimental data of the weld bead cross section under two different welding conditions, and four trace points were used to calculate the residual stresses in different positions of the molten pool. Emphasis was placed on the accuracy of predicting solidification cracking using the proposed criterion. Finally, a comparison between the predicted results and experimental data is given.


## 2. Materials and Methods

### 2.1. Heat Source Model and Chemical Composition in Weld Bead

The material used in the laser penetration welding was ultrafine-grained AN420s-grade steel in the form of a thick plate formed by pressure welding. Due to the dramatic changes in temperature and stress fields, the choice of a heat source model for laser welding should consider the influence of the stability of keyholes and molten pool formation [17]. Sun et al. [18] studied a new type of heat source model for laser deep welding. They suggested the use of a combined heat source model comprising a 3D cone heat source model and Gaussian surface heat source. This model exhibits Gaussian decay of the heat source radius on the surface and an exponential increase in the power density of the heat source with depth, which captures the penetration laser welding screw shape structure observed in actual welding experiments. Hence, a compound [18] cone and Gaussian surface heat source model was adopted in this work. The Gaussian surface heat source controls the surface of the molten pool and the head of the weld bead, and it can capture the effect of fluid agitation at the opening in the molten pool. The cone heat source controls the heat transfer of the liquid in deep layers and the cone body of the weld bead, and it can capture the behavior of a keyhole caused by the beam flow mining. In this compound heat source model, the power of the laser welding machine [19] can be expressed as follows:(1)Pt=Ws+Wv+Pl,Ws=∬ρm⋅e−ar2/σ2ds,Wv=∭Rme−br2/r02⋅mz+r0r0dv,where Pt is the power of the laser welding machine, Ws is the power of the surface heat source, Wv is the power of the volume heat source, Pl is the power loss caused by the reflection of the workpiece surface, ρm is the density of the heat flux of the surface heat source, Rm is the density of the heat flux of the volume heat source, σ is the heat flux distribution parameter, a is the heat flux concentration coefficient, b is the endogenous heat concentration coefficient, r is the diameter of the cone, r0 is the effective diameter of the cone, m is the coefficient of the cone shape, and z is the depth of the cone. The schematic diagram of the compound heat source model is illustrated in Figure 1.Figure 1
The compound heat source model.In this heat source model, the governing equation of thermal conduction [20] can be expressed as follows:(2)ρc∂T∂t=k∂2T∂Δ2+q,where q is the intensity of the laser heating source, T is the temperature, t is the time, Δ is the point spatial vector x,y,z, and ρ, c, and k are the density, specific heat, and thermal conductivity, respectively.The HAZ in the ultrafine-grained steel was a major concern in many studies [21, 22]. In the HAZ, the microstructure of the ultrafine-grained steel undergoes severe transformations due to the influence of the welding thermal cycle, and the structure of the overheated zone changes significantly under the influence of the welding heat [21]. To investigate the microstructure and mechanical properties of the ultrafine-grained steel under laser penetration welding, the metallography of the cross section of the weld bead should be studied. The samples of ultrafine-grained steel were provided by Angang Steel Company Limited. The mechanical properties of the plate of AN420s-grade steel with dimensions of 60 mm × 30 mm × 8 mm were obtained through an experimental tension test using a SUNS UTM5000 electronic tensile testing machine under an ambient temperature of about 0°C. The mechanical properties of the AN420s-grade steel plate are shown in Table 1, where σs is the yield strength, σb is the tensile strength, and δs is the extensibility.Table 1
Mechanical properties of AN420s-grade steel plate.
Steel grade
Thickness (mm)
σ
s (MPa)
σ
b (MPa)
δ
s (%)
Remarks
AN420s
8 mm
950
1080
12
Transverse
940
1050
12
Longitudinal
945
1025
13
45°In this study, an IPG-YSL-10000 fiber laser welder with a minimum spot diameter of 0.72 mm and an argon gas flow rate of 15 L/min were used to weld the samples. The chemical composition of the weld bead was determined using an FLS980-stm Edinburgh fluorescence spectrometer and an Olympus GX71 metallographic microscope (Figure2). The instruments used in this study are shown in Figure 2.Figure 2
The instruments used for the analysis of the chemical composition of the weld bead. (a) FLS980-stm Edinburgh fluorescence spectrometer. (b) Metallographic microscope. (c) The cross section of the weld bead.
(a)
(b)
(c)


### 2.2. Constitutive Coupling Relation

Residual stresses introduced in the weld bead are a consequence of incompatible thermal strains caused by heating and cooling cycles during the laser penetration welding process, and the solidification cracks can ultimately be attributed to the welding residual stresses [5]. There is a stage between the start and end of solidification where the material exhibits brittle behavior, even though the material is ductile. The end of solidification in the molten pool occurs at the temperature where all the material is solidified, which may be below the temperature where the body exhibits solid behavior macroscopically [9]. Thus, the investigation of the effects of the stress and temperature fields on the mechanical properties of the weld bead was significant in this study. The Gibbs interface thermodynamic method [23] was adopted to establish the constitutive coupling relation between the temperature and material flow stress. The basic equation for the Gibbs energy of a multicomponent solution phase can be expressed as follows:(3)Gm=∑ixiGi0+RT∑ixilnxi+∑i∑j>ixixj∑VΩVxi−xjV,where ∑ixiGi0 is the Gibbs energy of the pure components, RT∑ixilnxi is the ideal entropy, and ∑i∑j>ixixj∑VΩVxi−xjV accounts for pairwise interactions of the species. According to the Gibbs interface thermodynamic method [23], the equilibrium pressure of the system is achieved when the Gibbs free energy attains a minimum. Solute mass fraction in the solid can be expressed as follows:(4)τx,T=1β2N/8DΔTq∫0xdxx21−x/31−x2x/3,where τ is the solute mass fraction in the solid for different amounts of undercooling, β is an empirical coefficient, N is the size of a grain, D is an effective diffusion coefficient, ΔT is the undercooling, q is an exponent that depends on the effective diffusion mechanism, and x is the fraction transformed. Based on equations (2)–(4) and the data in Table 2, the phase transition diagram of the weld bead can be calculated using JMatPro using N = 9 scale by ASTM (American Society of Testing Materials).Table 2
Chemical compositions of the weld bead (wt.%).
Al
C
Fe
Mn
Nb
P
S
Si
Ti
V
0.015
0.11
97.062
1.71
0.087
0.22
0.016
0.46
0.15
0.17The relationship between the stress and strain can be determined by the yield strength, hardening exponent, and reference strain [23, 24] as follows:(5)σ=σ0.2ε0n⋅εn,where σ0.2 is the yield strength, n is the hardening exponent, and ε0 is a reference strain. Using equation (5) and Figure 3, a constitutive relation between the temperature and material flow stress can be obtained using JMatPro.Figure 3
Phase transition diagram of the weld bead.Figure4 shows the material flow stress of ultrafine-grained AN420s-grade steel at different temperatures between the solidus and liquidus temperatures. A softening phenomenon occurs at a temperature above 500°C, and liquefaction of the material occurs at a temperature of about 1455°C, at which point the metallic state in the molten pool can be regarded as liquid. The material flow stress dramatically decreases from 610 MPa to about 50 MPa at a temperature above 500°C. The region beneath the material flow stress curve in Figure 4 can be considered a safety zone in which cracks will not form.Figure 4
Material flow stress vs. temperature.


### 2.3. FEA Model

The finite element analysis (FEA) model of the ultrafine-grained AN420s-grade steel in the form of a vehicle component with a joint fabricated by pressure welding was created using the HyperWorks software. Subsequently, the FEA model was imported into the Simufact Welding software to analyze the laser penetration welding process. Two different welding conditions were used in this investigation. The FEA model is shown in Figure5, the input data for the FEA model are shown in Table 3, and the welding conditions are shown in Table 4.Figure 5
The FEA model: (a) the welding model (from top to bottom: two clamps, the welding plate, and the support plate) and (b) trace points.
(a)
(b)Table 3
Input data for the FEA model.
Input data
Welding plate
Clamp
Support plate
Element size
Weld bead: 0.5 mm; base metal: 1.5 mm
2.5 mm
3 mm
Clamping force (kN)
0.3
0.3
0.3
Heat exchange coefficient
Air heat exchange coefficient: 20 W/(m2·K); weldment heat exchange coefficient: 1000W/(m2·K)Table 4
The welding conditions.
Welding parameters
Power (kW)
Speed (mm/s)
Holding force (kN)
Defocusing distance (mm)
1st condition
5.0
10.0
0.3
3
2nd condition
5.0
20.0
0.3
3As shown in Figure5(a), the total number of elements was 20040, and the ambient temperature was 20°C. To investigate the changes in the temperatures and stresses in the molten pool, four trace points were assigned. As shown in Figure 5(b), the trace points P1, P2, P3, and P4 were set to collect the residual stress and temperature information in the molten pool.The characteristics of the laser welding heat source were the local concentration and the instantaneous and heterogeneous temperature field, and an accurate heat source model can improve the accuracy of the FE simulation results [25]. A compound heat source model comprising a cone heat source and Gaussian surface heat source was adopted in this study, and the accurate heat source model was obtained through careful collation from the surface to the root of the weld between the FEA model and the cross section of the weld bead. The heat source model collation is shown in Figure 6, and the error between the simulated and actual molten pools is shown in Table 5.Figure 6
The heat source model collation: the collation under the (a) 1st and (b) 2nd welding conditions.
(a)
(b)Table 5
The percentage error between the simulated and actual molten pools.
Weld width (mm)
Weld depth (mm)
Maximum percentage error (%)
Experimental data
FEA model
Experimental data
FEA model
1st condition
4.0
4.068
5.4
5.387
0.2
2nd condition
3.5
3.523
4.2
4.186
0.3


## 2.1. Heat Source Model and Chemical Composition in Weld Bead

The material used in the laser penetration welding was ultrafine-grained AN420s-grade steel in the form of a thick plate formed by pressure welding. Due to the dramatic changes in temperature and stress fields, the choice of a heat source model for laser welding should consider the influence of the stability of keyholes and molten pool formation [17]. Sun et al. [18] studied a new type of heat source model for laser deep welding. They suggested the use of a combined heat source model comprising a 3D cone heat source model and Gaussian surface heat source. This model exhibits Gaussian decay of the heat source radius on the surface and an exponential increase in the power density of the heat source with depth, which captures the penetration laser welding screw shape structure observed in actual welding experiments. Hence, a compound [18] cone and Gaussian surface heat source model was adopted in this work. The Gaussian surface heat source controls the surface of the molten pool and the head of the weld bead, and it can capture the effect of fluid agitation at the opening in the molten pool. The cone heat source controls the heat transfer of the liquid in deep layers and the cone body of the weld bead, and it can capture the behavior of a keyhole caused by the beam flow mining. In this compound heat source model, the power of the laser welding machine [19] can be expressed as follows:(1)Pt=Ws+Wv+Pl,Ws=∬ρm⋅e−ar2/σ2ds,Wv=∭Rme−br2/r02⋅mz+r0r0dv,where Pt is the power of the laser welding machine, Ws is the power of the surface heat source, Wv is the power of the volume heat source, Pl is the power loss caused by the reflection of the workpiece surface, ρm is the density of the heat flux of the surface heat source, Rm is the density of the heat flux of the volume heat source, σ is the heat flux distribution parameter, a is the heat flux concentration coefficient, b is the endogenous heat concentration coefficient, r is the diameter of the cone, r0 is the effective diameter of the cone, m is the coefficient of the cone shape, and z is the depth of the cone. The schematic diagram of the compound heat source model is illustrated in Figure 1.Figure 1
The compound heat source model.In this heat source model, the governing equation of thermal conduction [20] can be expressed as follows:(2)ρc∂T∂t=k∂2T∂Δ2+q,where q is the intensity of the laser heating source, T is the temperature, t is the time, Δ is the point spatial vector x,y,z, and ρ, c, and k are the density, specific heat, and thermal conductivity, respectively.The HAZ in the ultrafine-grained steel was a major concern in many studies [21, 22]. In the HAZ, the microstructure of the ultrafine-grained steel undergoes severe transformations due to the influence of the welding thermal cycle, and the structure of the overheated zone changes significantly under the influence of the welding heat [21]. To investigate the microstructure and mechanical properties of the ultrafine-grained steel under laser penetration welding, the metallography of the cross section of the weld bead should be studied. The samples of ultrafine-grained steel were provided by Angang Steel Company Limited. The mechanical properties of the plate of AN420s-grade steel with dimensions of 60 mm × 30 mm × 8 mm were obtained through an experimental tension test using a SUNS UTM5000 electronic tensile testing machine under an ambient temperature of about 0°C. The mechanical properties of the AN420s-grade steel plate are shown in Table 1, where σs is the yield strength, σb is the tensile strength, and δs is the extensibility.Table 1
Mechanical properties of AN420s-grade steel plate.
Steel grade
Thickness (mm)
σ
s (MPa)
σ
b (MPa)
δ
s (%)
Remarks
AN420s
8 mm
950
1080
12
Transverse
940
1050
12
Longitudinal
945
1025
13
45°In this study, an IPG-YSL-10000 fiber laser welder with a minimum spot diameter of 0.72 mm and an argon gas flow rate of 15 L/min were used to weld the samples. The chemical composition of the weld bead was determined using an FLS980-stm Edinburgh fluorescence spectrometer and an Olympus GX71 metallographic microscope (Figure2). The instruments used in this study are shown in Figure 2.Figure 2
The instruments used for the analysis of the chemical composition of the weld bead. (a) FLS980-stm Edinburgh fluorescence spectrometer. (b) Metallographic microscope. (c) The cross section of the weld bead.
(a)
(b)
(c)


## 2.2. Constitutive Coupling Relation

Residual stresses introduced in the weld bead are a consequence of incompatible thermal strains caused by heating and cooling cycles during the laser penetration welding process, and the solidification cracks can ultimately be attributed to the welding residual stresses [5]. There is a stage between the start and end of solidification where the material exhibits brittle behavior, even though the material is ductile. The end of solidification in the molten pool occurs at the temperature where all the material is solidified, which may be below the temperature where the body exhibits solid behavior macroscopically [9]. Thus, the investigation of the effects of the stress and temperature fields on the mechanical properties of the weld bead was significant in this study. The Gibbs interface thermodynamic method [23] was adopted to establish the constitutive coupling relation between the temperature and material flow stress. The basic equation for the Gibbs energy of a multicomponent solution phase can be expressed as follows:(3)Gm=∑ixiGi0+RT∑ixilnxi+∑i∑j>ixixj∑VΩVxi−xjV,where ∑ixiGi0 is the Gibbs energy of the pure components, RT∑ixilnxi is the ideal entropy, and ∑i∑j>ixixj∑VΩVxi−xjV accounts for pairwise interactions of the species. According to the Gibbs interface thermodynamic method [23], the equilibrium pressure of the system is achieved when the Gibbs free energy attains a minimum. Solute mass fraction in the solid can be expressed as follows:(4)τx,T=1β2N/8DΔTq∫0xdxx21−x/31−x2x/3,where τ is the solute mass fraction in the solid for different amounts of undercooling, β is an empirical coefficient, N is the size of a grain, D is an effective diffusion coefficient, ΔT is the undercooling, q is an exponent that depends on the effective diffusion mechanism, and x is the fraction transformed. Based on equations (2)–(4) and the data in Table 2, the phase transition diagram of the weld bead can be calculated using JMatPro using N = 9 scale by ASTM (American Society of Testing Materials).Table 2
Chemical compositions of the weld bead (wt.%).
Al
C
Fe
Mn
Nb
P
S
Si
Ti
V
0.015
0.11
97.062
1.71
0.087
0.22
0.016
0.46
0.15
0.17The relationship between the stress and strain can be determined by the yield strength, hardening exponent, and reference strain [23, 24] as follows:(5)σ=σ0.2ε0n⋅εn,where σ0.2 is the yield strength, n is the hardening exponent, and ε0 is a reference strain. Using equation (5) and Figure 3, a constitutive relation between the temperature and material flow stress can be obtained using JMatPro.Figure 3
Phase transition diagram of the weld bead.Figure4 shows the material flow stress of ultrafine-grained AN420s-grade steel at different temperatures between the solidus and liquidus temperatures. A softening phenomenon occurs at a temperature above 500°C, and liquefaction of the material occurs at a temperature of about 1455°C, at which point the metallic state in the molten pool can be regarded as liquid. The material flow stress dramatically decreases from 610 MPa to about 50 MPa at a temperature above 500°C. The region beneath the material flow stress curve in Figure 4 can be considered a safety zone in which cracks will not form.Figure 4
Material flow stress vs. temperature.


## 2.3. FEA Model

The finite element analysis (FEA) model of the ultrafine-grained AN420s-grade steel in the form of a vehicle component with a joint fabricated by pressure welding was created using the HyperWorks software. Subsequently, the FEA model was imported into the Simufact Welding software to analyze the laser penetration welding process. Two different welding conditions were used in this investigation. The FEA model is shown in Figure5, the input data for the FEA model are shown in Table 3, and the welding conditions are shown in Table 4.Figure 5
The FEA model: (a) the welding model (from top to bottom: two clamps, the welding plate, and the support plate) and (b) trace points.
(a)
(b)Table 3
Input data for the FEA model.
Input data
Welding plate
Clamp
Support plate
Element size
Weld bead: 0.5 mm; base metal: 1.5 mm
2.5 mm
3 mm
Clamping force (kN)
0.3
0.3
0.3
Heat exchange coefficient
Air heat exchange coefficient: 20 W/(m2·K); weldment heat exchange coefficient: 1000W/(m2·K)Table 4
The welding conditions.
Welding parameters
Power (kW)
Speed (mm/s)
Holding force (kN)
Defocusing distance (mm)
1st condition
5.0
10.0
0.3
3
2nd condition
5.0
20.0
0.3
3As shown in Figure5(a), the total number of elements was 20040, and the ambient temperature was 20°C. To investigate the changes in the temperatures and stresses in the molten pool, four trace points were assigned. As shown in Figure 5(b), the trace points P1, P2, P3, and P4 were set to collect the residual stress and temperature information in the molten pool.The characteristics of the laser welding heat source were the local concentration and the instantaneous and heterogeneous temperature field, and an accurate heat source model can improve the accuracy of the FE simulation results [25]. A compound heat source model comprising a cone heat source and Gaussian surface heat source was adopted in this study, and the accurate heat source model was obtained through careful collation from the surface to the root of the weld between the FEA model and the cross section of the weld bead. The heat source model collation is shown in Figure 6, and the error between the simulated and actual molten pools is shown in Table 5.Figure 6
The heat source model collation: the collation under the (a) 1st and (b) 2nd welding conditions.
(a)
(b)Table 5
The percentage error between the simulated and actual molten pools.
Weld width (mm)
Weld depth (mm)
Maximum percentage error (%)
Experimental data
FEA model
Experimental data
FEA model
1st condition
4.0
4.068
5.4
5.387
0.2
2nd condition
3.5
3.523
4.2
4.186
0.3


## 3. Results and Discussion

### 3.1. Simulated Results under the 1st Weld Operating Condition

The effects of the welding process parameters, including the laser power, welding speed, holding force, and defocusing distance, were studied. For the 1st welding condition, the parameters were a laser power of 5.0 kW, a weld speed of 10.0 mm/s, a holding force of 0.3 kN, and a defocusing distance of 3.0 mm. Nonuniform thermal expansion and contraction due to different temperatures during the heating and cooling sequence of the welding process resulted in tensile and compressive residual stress fields in and near the weld region [26]. Figure 7 shows the temperature evolution at the trace points in the molten pool. Figures 8(a)–8(c) show the residual stresses at the trace points at different times.Figure 7
The temperature evolution at the trace points (1st welding condition).Figure 8
The residual stresses at the trace points at different times (1st welding condition): (a) 0–1 s; (b) 1–10 s; (c) 10–200 s.
(a)
(b)
(c)As shown in Figure7, the temperature varied with time at the four trace points. The temperature in the molten pool increased dramatically from 20°C to a maximum temperature above 1570°C in a short period of 0.5 s, after which the temperature deceased during the cooling process. As shown in Figure 8, the residual stresses varied with time at the four trace points, and the residual stress curves can be divided into four stages: (1) the metal melted, and the stress value was below 3 MPa; (2) the metal solidified, and the stress value was below 200 MPa; (3) the molten pool began to cool, and the maximum stress occurred at about 7 s; and (4) the stress fluctuated about a certain value and finally reached a steady state. The residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 6.Table 6
Steady-state residual stresses at the trace points.
Trace point
P
1
P
2
P
3
P
4
Steady-state value of stress (MPa)
650
820
800
570According to Table4, the steady-state residual stress values at the trace points were in the following order: P2 > P3 > P1 > P4. Under the 1st welding condition, the highest residual stress occurred in the middle of the welding plate.


### 3.2. Simulated Results under the 2nd Weld Operating Condition

For the 2nd welding condition, the parameters were a laser power of 5.0 kW, a weld speed of 20.0 mm/s, a holding force of 0.3 kN, and a defocusing distance of 3.0 mm. Figure 9 shows the temperature evolution at the trace points in the molten pool. Figures 10(a)–10(c) show the transient residual stresses at the trace points at different times.Figure 9
The temperature evolution at the trace points (2nd welding condition).Figure 10
The residual stresses at the trace points at different times (2nd welding condition): (a) 0–1 s; (b) 1–10 s; (c) 10–200 s.
(a)
(b)
(c)As shown in Figure9, the temperature varied with time at the four trace points. Compared to the 1st welding condition, the highest temperature in the molten pool under the 2nd welding condition increased by about 5% from 1530 to 1600°C. As shown in Figure 10, the residual stresses varied with time at the four trace points, and the residual stress curve can be divided into four stages: (1) the metal melted, and the stress value was below 3 MPa; (2) the metal solidified, and the stress value was below 200 MPa; (3) the molten pool began to cool, and the maximum stress occurred at about 6 s; and (4) the stress fluctuated about a certain value and finally reached a steady state. The residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 7.Table 7
Steady-state residual stresses at the trace points.
Trace point
P
1
P
2
P
3
P
4
Steady-state value of stress (MPa)
475
720
280
410According to Table4, the steady-state residual stress values at the trace points were in the following order: P2 > P1 > P4 > P3. Under the 2nd welding condition, the highest residual stress occurred in the middle of the welding plate.


### 3.3. Discussion

The results from the two different sets of welding parameters indicated that the highest residual stresses occurred in the middle of the welding plate, which corresponds to the trace pointP2. However, the highest value of residual stress under the 2nd welding condition was significantly less than that under the 1st welding condition. When the welding speed increased and the weld pool geometry became tapered, the solidification cracks will be more concentrated and in positions near the centerline. Under this condition, the liquid flow rate was high and the rate of volume change was low. To investigate the effects of the residual stress on the solidification cracking behavior, a comparison between the experimental results and the predicted stress distributions under the two operating conditions is shown in Figure 10. The metallography of the cross sections of the weld beads under the two welding conditions was obtained using the Olympus GX71 metallographic microscope.Figure11 shows the cracks observed in the molten pool under the 1st welding condition. Upon increasing the weld speed from 10.0 to 20.0 mm/s for the 2nd welding condition, no cracks formed. Sheikhi et al. [27] reported that a low solidification rate and a small vulnerable zone were ideal for producing a weld without any cracks. Figures 11(c) and 11(d) show that the stresses in the molten pool under the 1st welding condition were higher than those under the 2nd welding condition, and high stresses in the molten pool increased the liquid flow. The constitutive coupling relation between the temperature and material flow stress is shown in Figure 4. The residual stresses at the trace point P2 at different temperatures were extracted and compared to the material flow stress curve.Figure 11
Comparison between the measured and the simulated results: the cross section of the weld bead under the (a) 1st and (b) 2nd welding conditions; the stress distributions under the (c) 1st and (d) 2nd welding conditions.
(a)
(b)
(c)
(d)Figure12 shows a comparison of the highest residual stress curve under the two welding conditions and the material flow stress curve. Based on Figures 11 and 12, the effects of residual stress on the laser penetration welding process of ultrafine-grained steel can summarized as follows:(1)
In the temperature range of intervalb, the residual stresses under the two different welding conditions were higher than the material flow stresses. The weld bead was not completely solidified, and the state of the molten pool was a mixture of solid and liquid. The liquid still available between the solid cells was continuous and could move easily, since the solid cells have not yet coalesced, and compensates for the deformation induced by shrinkage and thermal stresses. Thus, for temperatures in the interval b, cracks will occur.(2)
In the temperature range of intervala, the weld bead was completely solidified, and the solid cells coalesced. The residual stresses under the 1st welding condition were higher than the material flow stresses, and cracks will form in this case. The residual stresses under the 2nd welding condition were lower than the material flow stresses, and cracks will not form in this case. These conclusions are in good agreement with the experimental results.(3)
The residual stresses under the two different welding conditions were nearly equal when the temperature was above 400°C. The residual stresses under the 1st welding condition quickly exceeded the residual stresses under the 2nd welding condition, indicating that cracks will form during the cooling process of the molten pool. This also explains why a reasonable increase of the welding speed can prevent solidification cracks in the laser penetration welding process of ultrafine-grained steel.Figure 12
Comparison between the residual stress and the material flow stress.


## 3.1. Simulated Results under the 1st Weld Operating Condition

The effects of the welding process parameters, including the laser power, welding speed, holding force, and defocusing distance, were studied. For the 1st welding condition, the parameters were a laser power of 5.0 kW, a weld speed of 10.0 mm/s, a holding force of 0.3 kN, and a defocusing distance of 3.0 mm. Nonuniform thermal expansion and contraction due to different temperatures during the heating and cooling sequence of the welding process resulted in tensile and compressive residual stress fields in and near the weld region [26]. Figure 7 shows the temperature evolution at the trace points in the molten pool. Figures 8(a)–8(c) show the residual stresses at the trace points at different times.Figure 7
The temperature evolution at the trace points (1st welding condition).Figure 8
The residual stresses at the trace points at different times (1st welding condition): (a) 0–1 s; (b) 1–10 s; (c) 10–200 s.
(a)
(b)
(c)As shown in Figure7, the temperature varied with time at the four trace points. The temperature in the molten pool increased dramatically from 20°C to a maximum temperature above 1570°C in a short period of 0.5 s, after which the temperature deceased during the cooling process. As shown in Figure 8, the residual stresses varied with time at the four trace points, and the residual stress curves can be divided into four stages: (1) the metal melted, and the stress value was below 3 MPa; (2) the metal solidified, and the stress value was below 200 MPa; (3) the molten pool began to cool, and the maximum stress occurred at about 7 s; and (4) the stress fluctuated about a certain value and finally reached a steady state. The residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 6.Table 6
Steady-state residual stresses at the trace points.
Trace point
P
1
P
2
P
3
P
4
Steady-state value of stress (MPa)
650
820
800
570According to Table4, the steady-state residual stress values at the trace points were in the following order: P2 > P3 > P1 > P4. Under the 1st welding condition, the highest residual stress occurred in the middle of the welding plate.


## 3.2. Simulated Results under the 2nd Weld Operating Condition

For the 2nd welding condition, the parameters were a laser power of 5.0 kW, a weld speed of 20.0 mm/s, a holding force of 0.3 kN, and a defocusing distance of 3.0 mm. Figure 9 shows the temperature evolution at the trace points in the molten pool. Figures 10(a)–10(c) show the transient residual stresses at the trace points at different times.Figure 9
The temperature evolution at the trace points (2nd welding condition).Figure 10
The residual stresses at the trace points at different times (2nd welding condition): (a) 0–1 s; (b) 1–10 s; (c) 10–200 s.
(a)
(b)
(c)As shown in Figure9, the temperature varied with time at the four trace points. Compared to the 1st welding condition, the highest temperature in the molten pool under the 2nd welding condition increased by about 5% from 1530 to 1600°C. As shown in Figure 10, the residual stresses varied with time at the four trace points, and the residual stress curve can be divided into four stages: (1) the metal melted, and the stress value was below 3 MPa; (2) the metal solidified, and the stress value was below 200 MPa; (3) the molten pool began to cool, and the maximum stress occurred at about 6 s; and (4) the stress fluctuated about a certain value and finally reached a steady state. The residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 7.Table 7
Steady-state residual stresses at the trace points.
Trace point
P
1
P
2
P
3
P
4
Steady-state value of stress (MPa)
475
720
280
410According to Table4, the steady-state residual stress values at the trace points were in the following order: P2 > P1 > P4 > P3. Under the 2nd welding condition, the highest residual stress occurred in the middle of the welding plate.


## 3.3. Discussion

The results from the two different sets of welding parameters indicated that the highest residual stresses occurred in the middle of the welding plate, which corresponds to the trace pointP2. However, the highest value of residual stress under the 2nd welding condition was significantly less than that under the 1st welding condition. When the welding speed increased and the weld pool geometry became tapered, the solidification cracks will be more concentrated and in positions near the centerline. Under this condition, the liquid flow rate was high and the rate of volume change was low. To investigate the effects of the residual stress on the solidification cracking behavior, a comparison between the experimental results and the predicted stress distributions under the two operating conditions is shown in Figure 10. The metallography of the cross sections of the weld beads under the two welding conditions was obtained using the Olympus GX71 metallographic microscope.Figure11 shows the cracks observed in the molten pool under the 1st welding condition. Upon increasing the weld speed from 10.0 to 20.0 mm/s for the 2nd welding condition, no cracks formed. Sheikhi et al. [27] reported that a low solidification rate and a small vulnerable zone were ideal for producing a weld without any cracks. Figures 11(c) and 11(d) show that the stresses in the molten pool under the 1st welding condition were higher than those under the 2nd welding condition, and high stresses in the molten pool increased the liquid flow. The constitutive coupling relation between the temperature and material flow stress is shown in Figure 4. The residual stresses at the trace point P2 at different temperatures were extracted and compared to the material flow stress curve.Figure 11
Comparison between the measured and the simulated results: the cross section of the weld bead under the (a) 1st and (b) 2nd welding conditions; the stress distributions under the (c) 1st and (d) 2nd welding conditions.
(a)
(b)
(c)
(d)Figure12 shows a comparison of the highest residual stress curve under the two welding conditions and the material flow stress curve. Based on Figures 11 and 12, the effects of residual stress on the laser penetration welding process of ultrafine-grained steel can summarized as follows:(1)
In the temperature range of intervalb, the residual stresses under the two different welding conditions were higher than the material flow stresses. The weld bead was not completely solidified, and the state of the molten pool was a mixture of solid and liquid. The liquid still available between the solid cells was continuous and could move easily, since the solid cells have not yet coalesced, and compensates for the deformation induced by shrinkage and thermal stresses. Thus, for temperatures in the interval b, cracks will occur.(2)
In the temperature range of intervala, the weld bead was completely solidified, and the solid cells coalesced. The residual stresses under the 1st welding condition were higher than the material flow stresses, and cracks will form in this case. The residual stresses under the 2nd welding condition were lower than the material flow stresses, and cracks will not form in this case. These conclusions are in good agreement with the experimental results.(3)
The residual stresses under the two different welding conditions were nearly equal when the temperature was above 400°C. The residual stresses under the 1st welding condition quickly exceeded the residual stresses under the 2nd welding condition, indicating that cracks will form during the cooling process of the molten pool. This also explains why a reasonable increase of the welding speed can prevent solidification cracks in the laser penetration welding process of ultrafine-grained steel.Figure 12
Comparison between the residual stress and the material flow stress.


## 4. Conclusions

In this study, the residual stresses in the laser penetration welding process of ultrafine-grained steel were investigated. A constitutive coupling relation between the temperature and material flow stress in the molten pool was developed based on the Gibbs interface thermodynamic method. An FE model of the molten pool was established based on experimental data of the weld bead cross section under two different welding conditions. Lastly, a criterion for assessing the formation of solidification cracks in the laser penetration welding process was proposed. From the experimental work and modelling, the following conclusions were drawn:(1)
At the same temperature and position in the molten pool, when the residual stress is higher than the material flow stress of ultrafine-grained steel, cracks will form in the weld bead.(2)
A reasonable increase of the welding speed can decrease the residual stress in the molten pool and enhance the laser penetration welding quality for ultrafine-grained steel.(3)
The proposed criterion obtained through the comparison of the residual stress and material flow stress curves of the ultrafine-grained steel can provide a new method to evaluate the formation of solidification cracks in weld beads.



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*Source: 8609325-2018-12-26.xml*