Mechanical Properties Improvement of Laser Tailor Welded Blanks of Dp600 Steel by Magnetic Treatment

The influence of magnetic treatment on the yield strength, the ultimate tensile strength and the elongation of laser tailor welded blanks (TWBs) of DP600 steel was investigated by uniaxial tensile tests. The experimental results showed that the yield strength and the ultimate tensile strength of the TWBs had only a slight change, but the elongation increased by 13.90%–36.23% after the magnetic treatment. The dislocation distributions in the fusion zone (FZ) and the heat-affected zone (HAZ) were observed respectively by transmission electron microscopy (TEM). It was found that after magnetic treatment, the dislocations in both the FZ and the HAZ of the TWBs increased and showed a relatively uniform distribution. The mechanism of the mechanical property improvement of the TWBs by the magnetic treatment was then revealed on the basis of the relationship model between the dislocation and shear strain, considering the evolution of magnetic domains and Frank-Read dislocation multiplication in a magnetic field.


Introduction
Tailor welded blanks (TWBs) are made up of several steels with different materials, thicknesses and/or coatings to meet the diverse requirements of the components on the properties and thickness of the material [1].Compared to other welding methods, laser welding can create a narrow fusion zone (FZ) and heat-affected zone (HAZ), and has become a widely used welding method of TWBs in the modern automobile industry [2,3].However, the performance of laser TWBs is greatly reduced due to the existence of welded joints, which limits their application in automobiles [4][5][6][7][8].Farabi [9] researched the tensile properties of laser TWBs of DP600 steel and the results showed that the hardness increased significantly in the FZ, the yield strength increased and the ultimate tensile strength remained almost unchanged after welding.Kang [10] investigated the mechanical properties and formability of laser-welded 600 MPa grade TRIP (Transformation Induced Plasticity) steel and DP (Dual Phase) steel and the results showed that the FZ hardness increased, the yield strength and ultimate tensile strength increased, but the elongation and the formability decreased.Therefore, it is important to find approaches to improve the ductility of TWBs, especially for those made of high-strength steels.
Magnetic treatment is an advanced method used to improve the mechanical properties of metallic materials [11].At present, many scientific studies are being carried out to explore the rules and mechanisms of magnetic treatment.Zhao [12] detected the micro-hardness of high-speed steel for cutting tools under a pulsed magnetic field, and found that magnetic treatment with appropriate The samples in two different dimensions in length and width were fabricated referred to the Chinese standard GB/228.1-2010[17] and their sketches are shown in Figure 1.To reduce the measuring error, each group with the same dimension included three non-magnetic treated samples and three magnetic treated ones.and mechanisms of magnetic treatment.Zhao [12] detected the micro-hardness of high-speed steel for cutting tools under a pulsed magnetic field, and found that magnetic treatment with appropriate parameters clearly improved the micro-hardness of the high-speed steel.Celik [13] investigated the fatigue life of AISI 4140 steel under different magnetic field intensities and found that the fatigue life increased when the magnetic field was applied up to 30% of the fatigue fracture cycle of the untreated samples, and the treated effects also varied according to different magnetic field intensities.Klamechi [14] researched the residual stress of curved strip samples with and without applying an external magnetic field and the results showed that the residual stress was reduced by 4%-13% after the particular pulsed magnetic treatment.Cai [15] studied the effects of the magnetic field intensity orientation on the welding residual stress release by the pulsed magnetic field treatment and the results showed that the welding residual stress was reduced by up to 26% when the magnetic field was oriented along the blank thickness.Song [16] investigated the welding residual stress in low-alloy steel with a low-frequency alternating magnetic treatment and the experimental results revealed that the welding residual stress was reduced by 20%-24%.
Besides the aforementioned welding residual stress relief caused by magnetic treatment, other changes in the microstructures and properties of TWBs under a magnetic field are still not clear.Due to the critical role of the mechanical properties on the formability of TWBs, in this work the influences of magnetic treatment on the strength and ductility of TWBs are detected and the mechanism is explained with the combination effect of the magnetic domain and dislocation.

Experimental
In this work, the DP600 steel sheet with 1.6 mm in thickness was chosen as the base material of the TWBs.The main parameters of laser welding are shown in Table 1.After the laser welding, a weld seam with a good surface quality, even width (nearly 2 mm) and high straightness is formed.

Welding Power/(W) Welding Speed/(m/s)
Defocusing Amount/(m) Shielding Gas 1500 0.05 0 Argon The samples in two different dimensions in length and width were fabricated referred to the Chinese standard GB/228.1-2010[17] and their sketches are shown in Figure 1.To reduce the measuring error, each group with the same dimension included three non-magnetic treated samples and three magnetic treated ones.The magnetic device used here comprises a coil and an AC (Alternating Current) variable frequency power supply, as shown in Figure 2. The inner diameter and height of the coil are about 80 and 201 mm, respectively.The tensile samples were placed in the center of the coil vertically for magnetic treatment.The parameters of magnetic treatment were set as follows: the peak value of magnetic intensity was about 10 4 A/m, the frequency was 50 Hz and the processing time was 90 s.After the magnetic treatment, the mechanical properties of both the non-magnetic treated and magnetic treated samples were measured by a series of uniaxial tensile tests via a material testing The magnetic device used here comprises a coil and an AC (Alternating Current) variable frequency power supply, as shown in Figure 2. The inner diameter and height of the coil are about 80 and 201 mm, respectively.The tensile samples were placed in the center of the coil vertically for magnetic treatment.The parameters of magnetic treatment were set as follows: the peak value of magnetic intensity was about 10 4 A/m, the frequency was 50 Hz and the processing time was 90 s.After the magnetic treatment, the mechanical properties of both the non-magnetic treated and magnetic treated samples were measured by a series of uniaxial tensile tests via a material testing machine (Mode: MTS810, MTS, Eden Prairie, MN, USA).All the strain rate used in this work was 0.01/s.

Results
The broken tensile samples with and without magnetic treatment are shown in Figure 3 and the measured engineering stress-engineering strain curves are given in Figure 4.

Results
The broken tensile samples with and without magnetic treatment are shown in Figure 3 and the measured engineering stress-engineering strain curves are given in Figure 4.

Results
The broken tensile samples with and without magnetic treatment are shown in Figure 3 and the measured engineering stress-engineering strain curves are given in Figure 4.The mechanical properties including the yield strength, ultimate tensile strength and elongation before and after the magnetic treatment are compared in Figure 5.According to the data in Figure 5a, the average yield strength of TWB samples in both large and small sizes after magnetic treatment increased (or decreased) by less than 5%.Similarly, it can be found from Figure 5b that the average ultimate strength of TWB samples in both large and small sizes after magnetic treatment increased by less than 5%.This indicates that the magnetic treatment has little effect on the strength of the laser TWBs.
As can be seen from Figure 5c, however, the average elongations of the samples after the magnetic treatment were increased by 36.23% and 13.90% for the TWB samples in large and small sizes, respectively.The results show that the magnetic treatment can effectively improve the ductility of the laser TWBs.The mechanical properties including the yield strength, ultimate tensile strength and elongation before and after the magnetic treatment are compared in Figure 5.According to the data in Figure 5a, the average yield strength of TWB samples in both large and small sizes after magnetic treatment increased (or decreased) by less than 5%.Similarly, it can be found from Figure 5b that the average ultimate strength of TWB samples in both large and small sizes after magnetic treatment increased by less than 5%.This indicates that the magnetic treatment has little effect on the strength of the laser TWBs.The mechanical properties including the yield strength, ultimate tensile strength and elongation before and after the magnetic treatment are compared in Figure 5.According to the data in Figure 5a, the average yield strength of TWB samples in both large and small sizes after magnetic treatment increased (or decreased) by less than 5%.Similarly, it can be found from Figure 5b that the average ultimate strength of TWB samples in both large and small sizes after magnetic treatment increased by less than 5%.This indicates that the magnetic treatment has little effect on the strength of the laser TWBs.

Discussion
As can be seen from Figure 5c, however, the average elongations of the samples after the magnetic treatment were increased by 36.23% and 13.90% for the TWB samples in large and small sizes, respectively.The results show that the magnetic treatment can effectively improve the ductility of the laser TWBs.As can be seen from Figure 5c, however, the average elongations of the samples after the magnetic treatment were increased by 36.23% and 13.90% for the TWB samples in large and small sizes, Metals 2017, 7, 85 5 of 10 respectively.The results show that the magnetic treatment can effectively improve the ductility of the laser TWBs.

Discussion
Since the plastic deformation is carried out by the movement of dislocations, the change in the mechanical properties of the TWBs after the magnetic treatment can be explained from the evolution of dislocations under a magnetic field.Hence, the dislocations of TWBs before and after magnetic treatment were observed by the transmission electron microscope (TEM, mode: JEM-2100F, JEOL, Tokyo, Japan).Before the TEM test, the thin films with thicknesses of less than 60 µm in the center were obtained by an ion beam thinner for observation.
Figure 6a,b show the microstructures in the FZ of the non-magnetically and magnetically treated TWBs, respectively.As can be seen from the photographs, the microstructure of the FZ was predominantly martensite.The formation of martensite in the FZ was due to the rapid cooling speed of the weld pool during the laser welding process [9].Before the magnetic treatment, the dislocation density in the FZ was relatively low.After the magnetic treatment, the density of dislocation density increased distinctly with a relatively uniform distribution.
Metals 2017, 7, 85 5 of 10 Since the plastic deformation is carried out by the movement of dislocations, the change in the mechanical properties of the TWBs after the magnetic treatment can be explained from the evolution of dislocations under a magnetic field.Hence, the dislocations of TWBs before and after magnetic treatment were observed by the transmission electron microscope (TEM, mode: JEM-2100F, JEOL, Tokyo, Japan).Before the TEM test, the thin films with thicknesses of less than 60 μm in the center were obtained by an ion beam thinner for observation.
Figure 6a,b show the microstructures in the FZ of the non-magnetically and magnetically treated TWBs, respectively.As can be seen from the photographs, the microstructure of the FZ was predominantly martensite.The formation of martensite in the FZ was due to the rapid cooling speed of the weld pool during the laser welding process [9].Before the magnetic treatment, the dislocation density in the FZ was relatively low.After the magnetic treatment, the density of dislocation density increased distinctly with a relatively uniform distribution.Figure 7a,b show the microstructures in the HAZ of the non-magnetically and magnetically treated TWBs, respectively.It can be seen that, similar to that of the weld zone, after the magnetic treatment, the dislocation density in the HAZ increased obviously and dislocation nets were formed in some local areas.
The dislocation multiplication after the magnetic treatment is thought to be related to the evolution of magnetic domains for a ferromagnetic material.There are five main interactions in a ferromagnetic material, namely the exchange energy, the magnetocrystalline anisotropy energy, the magnetic and elasticity interaction energy, the demagnetizing field energy and the external magnetic field energy.In order to reduce the demagnetizing energy, self-magnetization magnetic domains are formed in a ferromagnetic material (Figure 8a).Vector M s is used to represent the average value of the self-magnetization intensity in a single magnetic domain.The directions of M s in different magnetic domains are disordered before magenization [18].Therefore, a ferromagnetic material does not exhibit magnetic properties at the macro level without an external magnetic field.Thus the total magnetization intensity of each domain is [19 where v i is the volume of magnetic domain i, θ i is the angle between M s and H. Figure 7a,b show the microstructures in the HAZ of the non-magnetically and magnetically treated TWBs, respectively.It can be seen that, similar to that of the weld zone, after the magnetic treatment, the dislocation density in the HAZ increased obviously and dislocation nets were formed in some local areas.The dislocation multiplication after the magnetic treatment is thought to be related to the evolution of magnetic domains for a ferromagnetic material.There are five main interactions in a ferromagnetic material, namely the exchange energy, the magnetocrystalline anisotropy energy, the magnetic and elasticity interaction energy, the demagnetizing field energy and the external magnetic field energy.In order to reduce the demagnetizing energy, self-magnetization magnetic domains are formed in a ferromagnetic material (Figure 8a).Vector Ms is used to represent the average value of the self-magnetization intensity in a single magnetic domain.The directions of Ms in different magnetic domains are disordered before magenization [18].Therefore, a ferromagnetic material does not exhibit magnetic properties at the macro level without an external magnetic field.Thus the total magnetization intensity of each domain is [19] ∑     cos θ  = 0  (1) where   is the volume of magnetic domain i, θ  is the angle between Ms and H.When an external magnetic field is applied, the directions of Ms in different magnetic domains become ordered and the ferromagnetic material is then magnetized (Figure 8b).Here, H represents the magnetic field intensity.Then magnetization intensity δ  along the direction of the external magnetic field can be expressed as follows δ  = ∑(  cos θ  δ  −     sin θ  δθ  +   cos θ  δ  )  (2) where the expression   cos θ  δ  is related to the movement of domain walls due to the growth of magnetic domains.The expression     sin θ  δθ  is related to the change of the direction of the vector   due to the rotation of the magnetic domains.The expression   cos θ  δ  is related to the increase of vector   .The evolution of the magnetic domains in a ferromagnetic material will certainly cause local stress.For example, the stress caused by the movement of domain walls in a local area was deduced in our former work [20] and can be expressed by The above stress further causes local strain and micro-deformations in the ferromagnetic material and thus contributes to the multiplication of dislocations.
Based on the above, the increase of the dislocation density in TWBs after magnetic treatment can be illustrated by the mechanism of Frank-Read dislocation multiplication.In Figure 9a, DD′ is a dislocation line and it cannot move because of its two fixed endpoints and the obstacles may be a fixed dislocation, impurities or foreign particles, and so on.When the external magnetic field is When an external magnetic field is applied, the directions of M s in different magnetic domains become ordered and the ferromagnetic material is then magnetized (Figure 8b).Here, H represents the magnetic field intensity.Then magnetization intensity δM H along the direction of the external magnetic field can be expressed as follows where the expression M s cos θ i δv i is related to the movement of domain walls due to the growth of magnetic domains.The expression M s v i sin θ i δθ i is related to the change of the direction of the vector M s due to the rotation of the magnetic domains.The expression v i cos θ i δM s is related to the increase of vector M s .The evolution of the magnetic domains in a ferromagnetic material will certainly cause local stress.For example, the stress caused by the movement of domain walls in a local area was deduced in our former work [20] and can be expressed by Metals 2017, 7, 85 7 of 10 The above stress further causes local strain and micro-deformations in the ferromagnetic material and thus contributes to the multiplication of dislocations.
Based on the above, the increase of the dislocation density in TWBs after magnetic treatment can be illustrated by the mechanism of Frank-Read dislocation multiplication.In Figure 9a, DD is a dislocation line and it cannot move because of its two fixed endpoints and the obstacles may be a fixed dislocation, impurities or foreign particles, and so on.When the external magnetic field is applied, the component of stress, τ, starts to act on the dislocation line DD .Due to the fixed nodes D and D , the line dislocation DD can only bend forward, as shown in Figure 9b.Once the dislocation line bends to more than a semicircle, it curls and forms helical branches m and n around D and D , as shown in Figure 9c,d.When the two bending lines gradually approach, helical branches m and n, whose Burgers vectors, b, are opposite, annihilate after meeting.Thus the dislocation line is divided into two parts, as shown in Figure 9e.After that, the dislocation DD goes back to its original position and repeats the above process and finally results in the increase of the dislocation density [21,22].The increase of the dislocation density is the main cause of the ductility improvement of the TWBs.The mechanism is deduced by the relationship model between the dislocation and shear strain as shown in Figure 10.Using b to represent the value of Burgers vector b, when the dislocation moves through an element in a unit length along the slip plane, the shear strain can be expressed as [23] γ =  ℎ (4) Assuming that the dislocation slip distance is xi, and the displacement at the top of the element, relative to its bottom, is The total displacement produced by the slip of N dislocations on many parallel slip planes is The increase of the dislocation density is the main cause of the ductility improvement of the TWBs.The mechanism is deduced by the relationship model between the dislocation and shear strain as shown in Figure 10.Using b to represent the value of Burgers vector b, when the dislocation moves through an element in a unit length along the slip plane, the shear strain can be expressed as [23]   The increase of the dislocation density is the main cause of the ductility improvement of the TWBs.The mechanism is deduced by the relationship model between the dislocation and shear strain as shown in Figure 10.Using b to represent the value of Burgers vector b, when the dislocation moves through an element in a unit length along the slip plane, the shear strain can be expressed as [23] γ =  ℎ (4) Assuming that the dislocation slip distance is xi, and the displacement at the top of the element, relative to its bottom, is The total displacement produced by the slip of N dislocations on many parallel slip planes is Assuming that the dislocation slip distance is x i , and the displacement at the top of the element, relative to its bottom, is The total displacement produced by the slip of N dislocations on many parallel slip planes is The corresponding shear strain is The average displacement of dislocations x can be expressed as Then the shear strain caused by the slip of N dislocations on a series of parallel slip planes is Thus, the average displacement of the dislocations can be further written as where ρ = N/(hL) is the dislocation density.
Considering the plastic deformation at a certain moment of the uniaxial tensile test, the average displacements of dislocations at the beginning and end of the deformation are supposed to be x 0 and x b , respectively.According to Equation (10), different dislocation density values bring different line slopes and shear strains in Figure 11.Therefore, a higher dislocation density causes a smaller slope and thus a larger shear strain, i.e., γ t > γ u .Since the dislocation density of the magnetically treated TWBs is much higher than that of non-magnetically treated ones according to the results of TEM, the former has a much larger strain for a certain average displacement of dislocations.The displacement, in the plastic deformation process, is continuous from the beginning to the fracture of the TWB.Namely, the process of the dislocation slip is continuous.Therefore, it can be concluded that the magnetically treated TWBs have a higher elongation.
The corresponding shear strain is The average displacement of dislocations ̅ can be expressed as Then the shear strain caused by the slip of N dislocations on a series of parallel slip planes is Thus, the average displacement of the dislocations can be further written as where ρ = N/(hL) is the dislocation density.
Considering the plastic deformation at a certain moment of the uniaxial tensile test, the average displacements of dislocations at the beginning and end of the deformation are supposed to be  0 ̅̅̅ and   ̅̅̅, respectively.According to Equation (10), different dislocation density values bring different line slopes and shear strains in Figure 11.Therefore, a higher dislocation density causes a smaller slope and thus a larger shear strain, i.e., γ t > γ u .Since the dislocation density of the magnetically treated TWBs is much higher than that of non-magnetically treated ones according to the results of TEM, the former has a much larger strain for a certain average displacement of dislocations.The displacement, in the plastic deformation process, is continuous from the beginning to the fracture of the TWB.Namely, the process of the dislocation slip is continuous.Therefore, it can be concluded that the magnetically treated TWBs have a higher elongation.The increase of the dislocation density leads to the formation of dislocation cells, which further affects the local stress/strain field and thus the ductility of TWBs.At the same time, the evolution of the magnetic domain under the magnetic field and the dimensions of the uniaxial tensile samples also increase the complexity of magnetic treatment effects on TWBs.The increase of the dislocation density leads to the formation of dislocation cells, which further affects the local stress/strain field and thus the ductility of TWBs.At the same time, the evolution of the magnetic domain under the magnetic field and the dimensions of the uniaxial tensile samples also increase the complexity of magnetic treatment effects on TWBs.

Conclusions
(1) The yield strengths and the ultimate tensile strength of the TWBs changed slightly (less than 5%), but the elongation increased by 13.90%-36.23%after the magnetic treatment.
(2) The increase in the elongation of laser TWBs is mainly caused by the increase of the dislocation density, which is explained by the relationship model between the dislocation and shear strain.
(3) The evolution of the magnetic domain of ferromagnetic materials under the magnetic field produces local stress and strain, which can promote the multiplication of dislocations.
(4) The comprehensive effect of the magnetic domain evolution, the dislocation evolution and the corresponding changes in the stress/strain field increases the complexity of property changes under the magnetic field.

Figure 1 .
Figure 1.Sketches of the uniaxial tensile test samples with two different dimensions: (a) large size; and (b) small size.

Figure 1 .
Figure 1.Sketches of the uniaxial tensile test samples with two different dimensions: (a) large size; and (b) small size.
: MTS810, MTS, Eden Prairie, MN, USA).All the strain rate used in this work was 0.01/s.

Figure 2 .
Figure 2.The setup of the magnetic treatment.

Figure 3 .
Figure 3.The test samples after uniaxial tensile tests: (a) large size; and (b) small size.

Figure 2 .
Figure 2. The setup of the magnetic treatment.
: MTS810, MTS, Eden Prairie, MN, USA).All the strain rate used in this work was 0.01/s.

Figure 2 .
Figure 2.The setup of the magnetic treatment.

Figure 3 .
Figure 3.The test samples after uniaxial tensile tests: (a) large size; and (b) small size.Figure 3. The test samples after uniaxial tensile tests: (a) large size; and (b) small size.

Figure 3 .Figure 4 .
Figure 3.The test samples after uniaxial tensile tests: (a) large size; and (b) small size.Figure 3. The test samples after uniaxial tensile tests: (a) large size; and (b) small size.

Figure 5 .
Figure 5. Mechanical properties before and after magnetic treatment: (a) yield strength; (b) ultimate tensile strength; and (c) elongation.Groups A and B represents the samples in large and small sizes, respectively.The blue line segments denote the standard deviation of measured data of three samples in each case.

Figure 4 .
Figure 4. Engineering stress-engineering strain curves before and after magnetic treatments: (a) large size; and (b) small size.

Figure 4 .
Figure 4. Engineering stress-engineering strain curves before and after magnetic treatments: (a) large size; and (b) small size.

Figure 5 .
Figure 5. Mechanical properties before and after magnetic treatment: (a) yield strength; (b) ultimate tensile strength; and (c) elongation.Groups A and B represents the samples in large and small sizes, respectively.The blue line segments denote the standard deviation of measured data of three samples in each case.

Figure 5 .
Figure 5. Mechanical properties before and after magnetic treatment: (a) yield strength; (b) ultimate tensile strength; and (c) elongation.Groups A and B represents the samples in large and small sizes, respectively.The blue line segments denote the standard deviation of measured data of three samples in each case.

Figure 6 .
Figure 6.Dislocation distribution in the FZ of TWBs: (a) before and (b) after the magnetic treatment.In to exhibit the distribution of dislocations, the enlarged images at local positions A and B are shown at the top right corner of each photograph.FZ: fusion zone; TWBs: laser tailor welded blanks.

FigureFigure 6 .
Figure7a,b show the microstructures in the HAZ of the non-magnetically and magnetically treated TWBs, respectively.It can be seen that, similar to that of the weld zone, after the magnetic treatment, the dislocation density in the HAZ increased obviously and dislocation nets were formed in some local areas.

Figure 6 .
Figure 6.Dislocation distribution in the FZ of TWBs: (a) before and (b) after the magnetic treatment.In order to exhibit the distribution of dislocations, the enlarged images at local positions A and B are shown at the top right corner of each photograph.FZ: fusion zone; TWBs: laser tailor welded blanks.

Figure 7 .
Figure 7. Dislocation distribution in the HAZ of TWBs: (a) before and (b) after the magnetic treatment.HAZ: heat-affected zone; TWBs: laser tailor welded blanks.

Figure 7 .
Figure 7. Dislocation distribution in the HAZ of TWBs: (a) before and (b) after the magnetic treatment.HAZ: heat-affected zone; TWBs: laser tailor welded blanks.

Figure 8 .
Figure 8. Evolution of magnetic domains: (a) before and (b) after applying a magnetic field.

Figure 8 .
Figure 8. Evolution of magnetic domains: (a) before and (b) after applying a magnetic field.
component of stress, τ, starts to act on the dislocation line DD′.Due to the fixed nodes D and D′, the line dislocation DD′ can only bend forward, as shown in Figure9b.Once the dislocation line bends to more than a semicircle, it curls and forms helical branches m and n around D and D′, as shown in Figure9c,d.When the two bending lines gradually approach, helical branches m and n, whose Burgers vectors, b, are opposite, annihilate after meeting.Thus the dislocation line is divided into two parts, as shown in Figure9e.After that, the dislocation DD′ goes back to its original position and repeats the above process and finally results in the increase of the dislocation density[21,22].

Figure 9 .
Figure 9. Frank-Read dislocation multiplication [22]: (a)-(e) the process of dislocation multiplication.In the figure, b is the Burgers vector and τ is the component of stress applied on the dislocation line DD′ under a magnetic field.

Figure 10 .
Figure 10.Relationship model between dislocation and shear strain.b: the value of Burgers vector b; h: the width of element; L: the length of element.

Figure 9 .
Figure 9. Frank-Read dislocation multiplication [22]: (a)-(e) the process of dislocation multiplication.In the figure, b is the Burgers vector and τ is the component of stress applied on the dislocation line DD under a magnetic field.
component of stress, τ, starts to act on the dislocation line DD′.Due to the fixed nodes D and D′, the line dislocation DD′ can only bend forward, as shown in Figure9b.Once the dislocation line bends to more than a semicircle, it curls and forms helical branches m and n around D and D′, as shown in Figure9c,d.When the two bending lines gradually approach, helical branches m and n, whose Burgers vectors, b, are opposite, annihilate after meeting.Thus the dislocation line is divided into two parts, as shown in Figure9e.After that, the dislocation DD′ goes back to its original position and repeats the above process and finally results in the increase of the dislocation density[21,22].

Figure 9 .
Figure 9. Frank-Read dislocation multiplication [22]: (a)-(e) the process of dislocation multiplication.In the figure, b is the Burgers vector and τ is the component of stress applied on the dislocation line DD′ under a magnetic field.

Figure 10 .
Figure 10.Relationship model between dislocation and shear strain.b: the value of Burgers vector b; h: the width of element; L: the length of element.

Figure 10 .
Figure 10.Relationship model between dislocation and shear strain.b: the value of Burgers vector b; h: the width of element; L: the length of element.

Figure 11 .
Figure 11.Relationship between average displacement of dislocations ̅ and shear strain γ.

Figure 11 .
Figure 11.Relationship between average displacement of dislocations x and shear strain γ.

Table 1 .
The main parameters of laser welding.

Table 1 .
The main parameters of laser welding.