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

Weld solidification crack prevention in the laser penetration welding process is essential for the strength of the welded component. -e 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. -e 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. -e 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.


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].
e 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].us, 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.ey also investigated the transient temperature profiles, dimensions of fusion, and heataffected zone (HAZ) by incorporating temperaturedependent 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.ey 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.
ey 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.
e 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.e Gibbs interface thermodynamic method and the Sente Software JMatPro were used in the derivation of the constitutive coupling relation.ird, 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.

Heat Source Model and Chemical Composition in Weld
Bead.
e 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.ey suggested the use of a combined heat source model comprising a 3D cone heat source model and Gaussian surface heat source.is 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.e 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.e 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: where P t is the power of the laser welding machine, W s is the power of the surface heat source, W v is the power of the volume heat source, P l is the power loss caused by the reflection of the workpiece surface, ρ m is the density of the heat flux of the surface heat source, R m 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, r 0 is the effective diameter of the cone, m is the coefficient of the cone shape, and z is the depth of the cone.e schematic diagram of the compound heat source model is illustrated in Figure 1.
In this heat source model, the governing equation of thermal conduction [20] can be expressed as follows: 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.
e 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 2 Advances in Materials Science and Engineering 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.e samples of ultrafine-grained steel were provided by Angang Steel Company Limited.e 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.e mechanical properties of the AN420s-grade steel plate are shown in Table 1, where σ s is the yield strength, σ b is the tensile strength, and δ s is the extensibility.
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.e chemical composition of the weld bead was determined using an FLS980-stm Edinburgh fluorescence spectrometer and an Olympus GX71 metallographic microscope (Figure 2).e instruments used in this study are shown in Figure 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].ere is a stage between the start and end of solidification where the material exhibits brittle behavior, even though the material is ductile.e 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].us, the investigation of the effects of the stress and temperature fields on the mechanical properties of the weld bead was significant in this study.e Gibbs interface thermodynamic method [23] was adopted to establish the constitutive coupling relation between the temperature and material flow stress.
e basic equation for the Gibbs energy of a multicomponent solution phase can be expressed as follows: where  i x i G 0 i is the Gibbs energy of the pure components, RT i x i ln x i is the ideal entropy, and  i  j>i x i x j  V Ω V (x i − x j ) V 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: 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).e relationship between the stress and strain can be determined by the yield strength, hardening exponent, and reference strain [23,24] as follows: where σ 0.2 is the yield strength, n is the hardening exponent, and ε 0 is a reference strain.Using equation ( 5) and Figure 3,    Advances in Materials Science and Engineering a constitutive relation between the temperature and material flow stress can be obtained using JMatPro.
Figure 4 shows the material flow stress of ultrafinegrained 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.
e material flow stress dramatically decreases from 610 MPa to about 50 MPa at a temperature above 500 °C.e region beneath the material flow stress curve in Figure 4 can be considered a safety zone in which cracks will not form.

FEA Model.
e 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.e FEA model is shown in Figure 5, the input data for the FEA model are shown in Table 3, and the welding conditions are shown in Table 4.
As shown in Figure 5(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,  Advances in Materials Science and Engineering four trace points were assigned.As shown in Figure 5(b), the trace points P 1 , P 2 , P 3 , and P 4 were set to collect the residual stress and temperature information in the molten pool.e 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.
e heat source model collation is shown in Figure 6, and the error between the simulated and actual molten pools is shown in Table 5.

Simulated Results under the 1 st Weld Operating Condition.
e effects of the welding process parameters, including the laser power, welding speed, holding force, and defocusing distance, were studied.For the 1 st 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.
As shown in Figure 7, the temperature varied with time at the four trace points.e 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.e residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 6.
According to Table 4, the steady-state residual stress values at the trace points were in the following order: P 2 > P 3 > P 1 > P 4 .Under the 1 st welding condition, the highest residual stress occurred in the middle of the welding plate.

Simulated Results under the 2 nd Weld Operating
Condition.For the 2 nd 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 As shown in Figure 9, the temperature varied with time at the four trace points.Compared to the 1 st welding condition, the highest temperature in the molten pool under the 2 nd 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.e residual stresses at the four trace points eventually stabilized to constant values, and the steady-state values are shown in Table 7.
According to Table 4, the steady-state residual stress values at the trace points were in the following order: P 2 > P 1 > P 4 > P 3 .Under the 2 nd welding condition, the highest residual stress occurred in the middle of the welding plate.

Discussion.
e 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 point P 2 .However, the highest value of residual stress under the 2 nd welding condition was significantly less than that under the 1 st 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.e metallography of the cross sections of the weld beads under the two welding conditions was obtained using the Olympus GX71 metallographic microscope.
Figure 11 shows the cracks observed in the molten pool under the 1 st welding condition.Upon increasing the weld speed from 10.0 to 20.0 mm/s for the 2 nd 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 1 st welding condition were higher than those under the 2 nd welding condition, and high stresses in the molten pool increased the liquid flow.e constitutive coupling relation       Figure 12 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    (1) In the temperature range of interval b, the residual stresses under the two different welding conditions were higher than the material flow stresses.e weld bead was not completely solidified, and the state of the molten pool was a mixture of solid and liquid.e 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.us, for temperatures in the interval b, cracks will occur.(2) In the temperature range of interval a, the weld bead was completely solidified, and the solid cells coalesced.e residual stresses under the 1 st welding condition were higher than the material flow stresses, and cracks will form in this case.e residual stresses under the 2 nd welding condition were lower than the material flow stresses, and cracks will not form in this case.ese conclusions are in good agreement with the experimental results.(3) e residual stresses under the two different welding conditions were nearly equal when the temperature was above 400 °C.e residual stresses under the 1 st welding condition quickly exceeded the residual stresses under the 2 nd welding condition, indicating that cracks will form during the cooling process of the molten pool. is also explains why a reasonable increase of the welding speed can prevent solidification cracks in the laser penetration welding process of ultrafine-grained steel.

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) e 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.

Figure 3 :
Figure 3: Phase transition diagram of the weld bead.
)-10(c) show the transient residual stresses at the trace points at different times.

Figure 6 :
Figure 6: e heat source model collation: the collation under the (a) 1 st and (b) 2 nd welding conditions.

Figure 11 :
Figure 11: Comparison between the measured and the simulated results: the cross section of the weld bead under the (a) 1 st and (b) 2 nd welding conditions; the stress distributions under the (c) 1 st and (d) 2 nd welding conditions.

Figure 12 :
Figure 12: Comparison between the residual stress and the material flow stress.

Table 1 :
Mechanical properties of AN420s-grade steel plate.

Table 3 :
Input data for the FEA model.

Table 4 :
e welding conditions.

Table 5 :
e percentage error between the simulated and actual molten pools.Figure 7: e temperature evolution at the trace points (1 st welding condition).

Table 6 :
Steady-state residual stresses at the trace points.Figure 9: e temperature evolution at the trace points (2 nd welding condition).

Table 7 :
Steady-state residual stresses at the trace points.