This paper describes the development of fracture finite element (FE)
Laser Spiral welding (LSW)
The model was verified through experiments.
The LSW was developed and introduced to production vehicles by Toyota Motor in 2013.
LSW has the advantages of high production efficiency and short welding time.
Although the author has previously developed broken FEmodels for traditional resistance welding points (RSW)
The fracture model of LSW has not been developed yet.
Many comprehensive experiments were carried out to establish this fracture model.
The results showed that LSWhad changed twice as much in fracture pattern as RSW compared to RSW.
In addition, it was found that the fracture mode bifurcation was caused by the difference in the gap between the welded plates.
In order to analyze the phenomenon of LSWfracture, a detailed finite element model is established by using the fine hexagonal elements.
The analysis results show that the fracture mode is determined not only by the equivalent plastic strain on the element, but also by the stress three-axis state of the element.
It was observed in the experiment that a model with a new fracture criterion allows for the bifurcation of the fracture mode in different clearance situations.
Based on the above results, a simplified LSW efficient fracture model was developed for large scale
The new model consists of the nuggetpart of the heat-affected zone and the six-sided element of the shell element (HAZ).
The new LSWfracture model has a good correlation with the experimental results of the fracture mode bifurcation.
Citation: Kumagai, K. , Kuwahara, M. , Yasuki, T.
And N. Koreishi
"Development of fracture model for laser screw welding", SAEInt. J. Passeng. Cars -Mech. Syst. 9(1):2016.
Introduction in recent years, due to the strengthening of safety standards and rating agreements in various countries, the safety requirements of vehicles have been continuously improved.
Therefore, the role of vehicles using collision finite element analysis to develop safety performance improvements is increasing year by year.
It is believed that not only the deformation of the vehicle structure should be simulated, but also the joint fracture including RSW [should be simulated and evaluated]2,9].
The reason is in the body-in-white (BiW)
The vehicle in the development phase consists of hundreds of steel parts, which are connected by welding, mainly using the overall structure.
Due to the use of body deformation for energy absorption of collision events, in many cases the joint may break first.
This is because the connection efficiency is more than 100%, so the joint may break before the base part.
In particular, due to the bifurcation of joint fracture phenomenon, joint fracture may lead to instability of collision events.
Therefore, in order to create a robust car design, not only the joint fracture must be simulated, but the ratio of the load to the fracture criterion must also be evaluated (fracture risk).
The authors have previously reported how they simulated the fracture of the RSW [1,2,3]
Their method produced the fracturerisk 
RSW is represented by a beam element.
Recently, LSW has been introduced as a new joining process, using laser welding of circular points with a diameter of several mmin between metal plates.
This technology began to be applied to body-in-white vehicles worldwide, as it has many advantages compared to RSW [s], such as increasing the productivity and capability of short pitch welding5].
However, the LSW model has not been developed even if the traditional line laser welding model exists .
Many comprehensive static experiments were carried out to establish the LSW fracture model.
The fracture mode of LSW is compared with the fracture mode of RSW.
It is revealed that there are many additional fracture patterns in LSW as described below.
The fracture pattern variation Figure 1 shows a schematic diagram comparing the fracture patterns observed during the RSW and LSW experiments.
The RSW sample broke in three modes, but the LSW sample broke in six modes.
The significant characteristic of the LSW fracture pattern is the change of complex faults through gold blocks, such (4)through (6)inFigure 1.
In the production application of LSW, according to the load conditions and clearance, the change of the fracture mode and resistance is difficult to avoid creating a gap between the welded plates (clearance)
Because unlike the traditional RSW, no clamping force is applied between the plates.
For this experimental series, peel and loop-
The shear joint samples shown in Figure 2 and Figure 3 include changes in the clearance.
The arrow indicates the direction of loading.
The holder is welded at each end of the sample in order to put it into the experimental device.
The outer board is very small, and the contribution to the overall power transmission is very small.
The fracture position observed in this experimental series is represented by the bold red line in the schematic diagram of the welded part shown in figure 4.
Tensile strength grade of steel (MPa)
Displayed on the right side of the number.
1 specimen drawing.
H/S indicates grade 500 hot stamping steel.
As shown in figure 4, when learning to change between the maximum and minimum values, the fracture mode bifurcation is observed in each sample loading type.
In the maximum gap sample for both load types, both lswundersent experienced a plug break.
In the minimum gap sample type, LSWfractured in the gold block section with stripping and overlapping-
The shear samples experienced gold block fracture and interface fracture respectively.
Figure 5 shows the fracture resistance results of stripping and overlapping
Shear specimen between the maximum gap and the minimum gap.
The hydraulic resistance in the case of maximum clearance is greater than that in the case of minimum clearance.
However, this relationship was not observed in RSW.
LSW showed more fracture patterns than RSW.
In addition, differences in clearance can lead to differences in fracture patterns and resistance.
Due to these differences, it is considered that LSW needs a more complex fracture model to simulate its complex fracture pattern and bifurcation.
In order to clarify the cause of the bifurcation of the fracture mode, the cause of the hardness distribution of the lsws multi-fracture mode was studied.
As shown in Table 1, the plates of the combination of thickness and material grade are welded byLSW.
The maximum hardness and the ratio of the minimum hardness of the HAZ part to the raw material, as shown in figure 6.
It was found that the hardness distribution in HAZwas changed in a large range.
On the other hand, since there is no material mixing in the heat affected zone part, it is conceivable that the cooling rate after LSW heating will affect the mechanical properties of the heat affected zone part.
In particular, in 270 MPa Steel, the hardness increased significantly by quenching and decreased by annealing in H/S materials.
The hardness distribution through the gold block part shows almost uniform.
Considering the volume fraction of the material combination in the gold block part, the ratio of the average hardness to the average hardness of the fusion material is shown in figure 6.
It is found that for this material combination, the hardness of the gold block part can be estimated by the average hardness of the melted metal, although the hardness is about 20% lower than the average hardness.
The results show that the hardness of the LSW gold block is affected by the fusion and mixing of all materials, and different material combinations produce materials with different properties.
The development of a detailed model of the maximum gap and the minimum gap consists of a detailed model of 0.
Six elements of 03mm or greater 
It was developed to study the complex fracture mode bifurcation due to the difference in the gap between welded plates.
For this model, in order to avoid expressing differences in plastic deformation strain gauge calculations, only the elements of the parallelepiped elements are used.
The development method is the same as that reported by Kuwahara 
According to the hardness distribution, yield stress and tensile strength are assigned to five or six HAZ parts and one gold block part.
The center of mass part of the detailed model is shown in Figure 7.
The left side of Figure 7 shows a huge rupture of the gold block connected to the plate.
Figure 8 shows the specified material property definition.
Study on the influence of clearance on the change of fracture mode figure 9 (a)and (b)
The stripping experimental results of the minimum and maximum gap samples are expressed, respectively.
Head displacement of testing machine.
In both figures, the comparison between the experimental results and the FEanalysis using the detailed model is shown.
The solid line represents the FE result and the dotted line represents the experimental result.
For each type of sample, the physical experiment was repeated three times.
In these FE simulations, the fracture criteria were not assigned to the model.
Therefore, the reduction of the force caused by the fracture in the experiment was not expressed.
Before the fracture begins, the force
The stroke relationship in the FE results is very relevant to the experimental results, as shown in Figure 9.
This shows that a highly correlated model can be obtained if the appropriate fracture criterion is assigned to the FE model to recreate the same fracture pattern and maximum fracture resistance.
Figure 10 shows the equivalent plastic strain of the fracture position minimum and maximum gap sample at 2mm stroke.
Three points are stated;
A point where the fracture begins in the minimum gap sample;
Point B, corresponding to point A in the maximum gap sample;
And point C, in the maximum gap sample, the fracture begins again.
As shown in Figure 10, in the finite element analysis, the equivalent plastic strain distribution in each case is not much different, although in the actual sample experiment, the starting point of the fracture is very different.
Figure 11 shows the relationship between the travel and equivalent plastic strain of points A, B and C in FE analysis shown in Figure 10.
The point at which the crack begins in the experiment is marked with x in the figure.
Although the path of point A and point Boverlap, the break occurs only at point A, while there is no break at point B, although the final equivalent strain at point B is much higher than that at point.
Therefore, the equivalent plastic strain cannot be used to predict fracture initiation, and it is clear that a new fracture criterion is required to evaluate the fracture initiation of LSW.
In addition, in the maximum gap sample, it is determined that the equivalent plastic strain of HAZ at the start of the C-point fracture is greater than the equivalent plastic strain in the gold block.
This means that different fracture criteria are required for the heat affected zone part and the gold block part.
The study of a new fracture criterion depends on the fracture criterion of stress triaxiality (
Effective stress divided by static pressure)[8, 9]
Being investigated as a new standard.
FE simulation evaluates the fracture of each integral point of each element.
This fracture criterion gives the maximum integral point values in the elements at points A, B, and C, as shown in Figure 12.
The results of the calculation of the equivalent plastic strain based on the stress three-axis criterion show that the stress stripe at point A is higher than point B, and the line does not overlap, as shown in Figure 12.
It is reported that with the increase of the triaxiality of the internal stress in the region, the power mathematical function can better predict the decrease of the fracture strain .
Therefore, the fracture criterion in nugget is presumed to be a curve represented by a power mathematical function of a point above the trajectory of a and B points in Figure 12.
As mentioned earlier, the HAZ fracture criterion and the gold block fracture criterion can be represented by different functions.
Therefore, the fracture criterion for the C-point of the HAZ part is presumed to be a curve represented by the power mathematical function of the C-point threshold point in Figure 12.
FE analysis was carried out on the stripping experiment, in which the stress triaxiality-related fracture criteria of HAZ and nuggetpart were realized.
Figure 13 and Figure 14 show the model results of the minimum and maximum gap samples, respectively.
It is confirmed that the starting point of the fracture corresponds to point a in the minimum clearance experimental results shown in Figure 13, and point C in the maximum clearance experimental results, as shown in Figure 14.
Based on the results of the previous section, a simplified LSW model is developed for LSW fracture model, which can be used in large-
As shown in Figure 15, a proportional vehicle model is developed.
The development of the gold block part is modeled with a hexagonal element to express various fracture patterns.
In addition, the center groove is simulated in the gold block section to represent the geometric effect of the groove.
Using stress 3D degree related fracture criteria, the fracture criteria for assignment are the same as in the detailed model.
Development of HAZ parts are modeled with shell elements in accordance with the current RSWmodeling modeling program.
Li [report] Criterion for stress triaxiality-related fracture of shell unit11]
The applicability of HAZ parts was investigated.
Li reported that, assuming plane stress, the fracture criterion of the shell unit has two peaks of equivalent fracture suppression at 1/3 and 2/3 of the three coaxiality of the stress.
Thus, the HAZ part is assigned a fracture constraint criterion as a function of stress triaxiality with two peaks, 1/3 and 2/3.
The direct connection between the shell unit and the six-surface unit node and the shell unit node concentrates the force on the six-surface unit node.
In general, the concentration of these forces is no different from the physical response.
Therefore, by implementing constraint interpolation [,] the parallelepiped element is connected to the shell element12]
In the general purpose analysis code (
Crash analysis code.
Development model validation of HAZ part fracture criteria simplified LSW models described in the previous section are used to compare the fracture patterns and resistance between the current used fracture criterion and stress for a simple stripping sample, the three dimensional degree depends on the fracture standard.
The simulation results are then compared with the experimental results.
Figure 16 shows the model used in the comparison.
First, the simulation was completed using the constant fracture equivalent plastic strain criterion.
Next, the simulation was completed using the fracture equivalent plastic strain criterion associated with stress triaxiality.
Since HAZconsists are composed of the shell unit [s], plane stress is assumed12].
Figure 17 shows a three-way dependent fracture criterion for specified stress with two peaks at 1/3 and 2/3.
Figure 18 shows the results of modeling fracture patterns using current fracture rules.
The fracture mode is a plug-shaped fracture.
The resistance ratio comparison between the experimental results and the Peel mode analysis results is shown in Figure 19.
The blue line indicates the simulation results using the constant fracture criterion, and the red line indicates the stress three-way related fracture criterion.
Vertical Drop in resistance-
The displacement curve indicates the elimination of elements.
Figure 20 shows the resistance comparison at the beginning of the fracture, and the limit resistance comparison between experiments and analyses conducted using current and new fracture criteria.
The resistance at the beginning of the fracture increased significantly, and the final resistance improved slightly.
Therefore, it is confirmed that the stress triaxiality-related fracture criterion that assumes that the plane stress is effective for the thermal impact zone part modeled using the shell unit.
As mentioned earlier, validation of the entire LSW model indicates that LSW fracturemode changes depending on the gap and loading method.
Table 2 shows the ratio of fracture resistance analysis results to similar experimental results.
The fracture patterns found in the four configuration experiments are shown in figure 4.
As shown in the figure, the correlation between the resistance of FE analysis and the resistance in the experimental results is confirmed within an estimated error of 7%.
The finite element analysis coincides with the fracture pattern of the experimental results.
A comparison of the fracture patterns in each experiment is shown in Figures 21 to 24.
The left side of figure 21 and figure 22 shows the fracture start of the peel off FE analysis model.
The left side of figure 23 and Figure 24 shows the gold block portion of the central area of the lap shear FE analysis model where the fracture occurred.
The overlay numbers and letters in each graphic photo represent the material used in the part.
The plug breakage found in the analysis results of the maximum clearance peelspecimen corresponds to the experimental results, as shown in Figure 21, but in the experiment, the crack extends along the heat-affected zone to the edge of the specimen.
The gold block fracture found in the analysis results of Peel samples with minimum clearance is in response to the experimental results, as shown in Figure 22.
The plug found in the analysis results of the loop is broken
The arrow in Figure 23 indicates that the shear specimen for the maximum gap begins on the 440 MPa plate.
In the experimental sample, as shown in Figure 23, the holes left by the break of the plug are formed on the 440 MPa plate.
The fracture pattern in the analysis is consistent with the experimental results.
Interface fracture patterns found in lap analysis results
The shear sample of the minimum gap is also consistent with the experimental results, as shown in Figure 24.
Therefore, it is confirmed that the analysis results using the developed model are consistent with the experimental results of the combination of the two sample types and the two load types.
Generally speaking, the collision analysis code developed a fracture risk output method with the function of determining the ratio of equivalent plastic strain to fracture straine.
Risk of fracture. 
To simplify the analysis of the LSW model, a function was developed that generates a special finite post file containing the highest break between all integration points that make up the elements of each LSW model
The function then reads these fracture risks from the post file and displays them using a note, throughout the model, the LSWs fracture and/or fracture risk from the highest to lowest levels is high.
The developed system can reduce the amount of human working time required for comparison, as it can simultaneously display the hexipes and shell elements associated with the fracture risk profile.
Figure 25 shows the fracture risk profile of the maximum gap sample subjected to the Peel load before the start of the fracture.
Compared with the experimental results shown in Figure 21, the risk of fracture shown in Figure 25 is the largest in the HAZ part of the right plate, corresponding to the experimental results of the specimen that broke in the plug fracture mode.
The notes shown near the top left corner of figure 25 include Rank, join part, coordinates, identification number, and break time.
The discussion gap allowance of LSW and line laser welding is studied.
The horizontal coordinates in Figure 26 represent the ratio of the gap to the LSW mean, and the longitudinal coordinates represent the ratio of the maximum breaking resistance to the mean in the stripping experiment.
The solid line of LSWindicates linear interpolation and the dotted line of line laser welding indicate the estimated line taking into account the upper and lower limits of the gap margin of 0. 2 and 0.
In the case of online laser welding, the gap is limited by the melting of the pores and the maximum gap [caused by the surface zinc vapor at the minimum gap]13].
The clearance allowance of the LSW is several times larger than the clearance allowance of the line laser welding, as shown in Figure 26.
The wide gap of the LSW indicates that this welding method can simplify production, as it is easier for the LSW to achieve fixation during welding.
The hardness of the gold block depends on the performance of the plate. 2.
The gap affects the resistance of the break and the mode of the break. 3.
In view of the problem that the current commonly used evaluation methods cannot predict the bifurcation of the fracture mode, a new evaluation method based on stress stripe degree is proposed. 4.
The newly developed detailed model for implementing stress stripe-related fracture criteria is capable of simulating the bifurcation and resistance variation of the fracture mode. 5.
Based on the detailed model, a simplified model for vehicle simulation is developed.
The stress triaxiality-related criterion assuming plane stress is confirmed to be effective for Shell units. 6.
A display system is developed, which can display the fractal diagram of the shell and the hexagonal element at the same time. 7.
The LSW has a wide gap allowance, which is more conducive to increasing productivity than laser wire welding.
Future research is expected as follows. 1.
Verification of LSW in component and vehicle FE analysis 2.
Evaluation of the development of LSW 3 non-uniformity methods.
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Toyota Motor Company Contact Information: Toyota Motor Company's senior CAE Department of Safety CAE development, kumage, Jinji and nori Chaoxi Toyota Motor Company Contact Information: kumage
Cho, Toyota, Aichi, 471-
8572 Japan Kou _ Kumagai @ mail. toyota. co.