Method and program for predicting deformation or residual stress

Abstract

The present invention provides a prediction method (correction thermal shrinkage method) with which it is possible to accurately predict, in a short time, deforming or residual stress occurring due to a heated object returning to normal temperature. A prediction method according to the present invention includes predicting deforming or residual stress occurring due to a heated object returning to normal temperature, the prediction method being characterized by including: a condition-setting step for setting a first shrinkage region and a second shrinkage region in a model for analyzing the object, and setting a first temperature change amount in the first shrinkage region and a second temperature change amount in the second shrinkage region; and an analysis step for imparting a first shrinkage strain calculated from the first temperature change amount to the first shrinkage region, and imparting a second shrinkage strain calculated from the second temperature change amount to the second shrinkage region, to analyze elasticity or elastoplasticity.

Description

[Technical Field]

[0001] The present invention relates to a method and program for predicting deformation or residual stress. [Background technology]

[0002] In recent years, FEM thermo-elastic-plastic analysis has been used as a highly accurate method for predicting deformation during the assembly of large welded structures. This method is capable of predicting the constantly changing temperature, stress, and displacement fields, resulting in highly accurate prediction of welding distortion. However, when the structure is large or complex, the number of elements and nodes required for analysis increases, resulting in enormous calculation times and making analysis extremely difficult. To address this issue, the thermal contraction method was developed (see, for example, Non-Patent Document 1). The thermal contraction method is a method for modeling and analyzing the thermal contraction during the cooling process of a welded structure by setting a contraction region using the mechanical melting temperature as a threshold value, and is capable of predicting angular distortion in a short period of time. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Pressure Technology, 2020, Vol. 58, No. 2, pp. 93-100 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the transverse shrinkage and residual stress distribution calculated by the conventional analysis using the thermal shrinkage method deviate from the transverse shrinkage and residual stress distribution calculated by the thermo-elastic-plastic analysis. The present invention has been made in consideration of the above circumstances, and provides a prediction method (modified thermal shrinkage method) that can accurately predict, in a short time, the deformation or residual stress that occurs when a heated object returns to room temperature. [Means for solving the problem]

[0005] The prediction method (modified thermal shrinkage method) of the present invention is a method for predicting deformation or residual stress caused by a heated object returning to room temperature, and is characterized by including a condition setting step of setting a first shrinkage region and a second shrinkage region in an analytical model of the object, and setting a first temperature change amount in the first shrinkage region and a second temperature change amount in the second shrinkage region, and an analysis step of applying a first shrinkage strain calculated from the first temperature change amount to the first shrinkage region and a second shrinkage strain calculated from the second temperature change amount to the second shrinkage region, and performing elastic analysis or elasto-plastic analysis. [Effects of the Invention]

[0006] According to the prediction method of the present invention, it is possible to accurately predict, in a short time, the deformation or residual stress that occurs when a heated object returns to room temperature. [Brief explanation of the drawings]

[0007] [Figure 1] FIG. 1(a) is an explanatory diagram of a conventional heat shrinkage method, and FIG. 1(b) is an explanatory diagram of the prediction method (modified heat shrinkage method) of the present invention. [Figure 2] 1 is a flowchart of a prediction method according to one embodiment of the present invention. [Figure 3] This is the analytical model used to predict deformation and residual stress. [Figure 4] FIG. 4 is a cross-sectional view of the welded portion of the analysis model shown in FIG. 3, showing the formation sequence of 10 welding passes. [Figure 5] 1 is a graph showing material constants used in the analysis. [Figure 6] (a)(b) shows the maximum temperature distribution, (c)(d) shows the first and second shrinkage regions set in the analysis using the modified heat shrinkage method of the present invention, and (e)(f) shows the shrinkage regions set in the analysis using the conventional heat shrinkage method. [Figure 7] 1 is a graph showing the history of angular distortion when welding passes are formed sequentially. [Figure 8] 10 is a graph showing a history of transverse shrinkage when welding passes are formed sequentially. [Figure 9] FIG. 10 is a contour diagram showing the residual stress distribution calculated for the analysis model after the tenth welding pass has been formed. [Figure 10] 10 is a graph showing the residual stress in the X direction along the dotted line AB shown in FIGS. 9(a) to 9(c). DETAILED DESCRIPTION OF THE INVENTION

[0008] The prediction method (modified thermal shrinkage method) of the present invention is a method for predicting deformation or residual stress caused by a heated object returning to room temperature. The prediction method of the present invention is characterized by including a condition setting step of setting a first shrinkage region and a second shrinkage region in an analytical model of the object, and setting a first temperature change amount in the first shrinkage region and a second temperature change amount in the second shrinkage region, and an analysis step of applying a first shrinkage strain calculated from the first temperature change amount to the first shrinkage region and a second shrinkage strain calculated from the second temperature change amount to the second shrinkage region, and performing an elastic analysis or an elasto-plastic analysis.

[0009] The prediction method of the present invention preferably includes a step of calculating a maximum temperature distribution of the target object, and the condition setting step preferably includes a step of setting a first contraction region, a second contraction region, a first temperature change amount, and a second temperature change amount based on the maximum temperature distribution, thereby making it possible to appropriately set the first contraction region, the second contraction region, the first temperature change amount, and the second temperature change amount. The condition setting step is preferably a step of setting a region whose maximum temperature is equal to or higher than a first temperature T1 as a first contraction region, and setting a region whose maximum temperature is lower than the first temperature T1 and higher than a second temperature T2 as a second contraction region. In the condition setting step, it is preferable to set a third shrinkage region in the analysis model and set a third temperature change amount for the third shrinkage region, and in the analysis step, it is preferable to impart a third shrinkage strain calculated from the third temperature change amount to the third shrinkage region and perform the elastic analysis or the elasto-plastic analysis. This can improve the prediction accuracy of the prediction method of the present invention.

[0010] Preferably, in the condition setting step, a plurality of shrinkage regions are set in the analysis model and a temperature change amount for each shrinkage region is set, and in the analysis step, a shrinkage strain calculated from each temperature change amount is imparted to the corresponding shrinkage region to perform the elastic analysis or the elasto-plastic analysis. The plurality of shrinkage regions include a first, a second, and a third shrinkage region. The condition setting step is preferably a step of setting a plurality of shrinkage regions and the amount of temperature change in each shrinkage region based on the maximum temperature distribution. Preferably, the prediction method of the present invention is a method for predicting deformation or residual stress that occurs when an object that has been heated multiple times returns to room temperature, and the condition setting step is performed for each heating, and the analysis step is performed for each heating in sequence according to the heating order. Preferably, an idealized explicit FEM method is used for the elastic analysis or elasto-plastic analysis in the analysis step. The present invention also provides a program configured to cause a computer to execute the prediction method of the present invention.

[0011] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The configurations shown in the drawings and the following description are merely examples, and the scope of the present invention is not limited to those shown in the drawings and the following description.

[0012] FIG. 1(a) is an explanatory diagram of a conventional heat shrinking method, and FIG. 1(b) is an explanatory diagram of a modified heat shrinking method of this embodiment. In the conventional thermal shrinkage method, as shown in Figure 1(a), only one shrinkage region is set in the analysis model with the mechanical melting temperature as the threshold, and elastic-plastic analysis is performed by uniformly applying shrinkage strain to this shrinkage region. In contrast, the modified thermal shrinkage method (prediction method) of this embodiment sets multiple shrinkage regions (e.g., first and second shrinkage regions) in the analysis model as shown in Figure 1(b), and performs elastic analysis or elasto-plastic analysis by uniformly applying different shrinkage strains to each of these shrinkage regions. This makes it possible to accurately predict deformation or residual stress. This was made clear by simulations performed by the present inventors.

[0013] FIG. 2 is a flowchart of the prediction method of this embodiment, in which multi-layer welding is performed to form the first welding pass through the nth welding pass. The prediction method (modified thermal shrinkage method) of this embodiment is a method for predicting deformation or residual stress caused by a heated object returning to room temperature. The prediction method of this embodiment is characterized by including a condition setting step of setting a first shrinkage region and a second shrinkage region in an analytical model of the object, and setting a first temperature change amount in the first shrinkage region and a second temperature change amount in the second shrinkage region, and an analysis step of applying a first shrinkage strain calculated from the first temperature change amount to the first shrinkage region and a second shrinkage strain calculated from the second temperature change amount to the second shrinkage region, and performing an elastic analysis or an elasto-plastic analysis. The prediction method of this embodiment can include a step of calculating the maximum attained temperature distribution of the target object. The program of this embodiment is provided to cause a computer to execute the prediction method of this embodiment.

[0014] The target object is an object that is the subject of prediction and undergoes a thermal cycle in which locally heated areas return to room temperature. This thermal cycle is, for example, a thermal cycle associated with bead-on welding, groove welding, fillet welding, seam welding, plug welding, slot welding, multi-layer welding, multi-pass welding, metal additive manufacturing (e.g., 3D printing, 3D metal additive manufacturing), thermal strain relief, thermal cutting (e.g., fusion cutting), thermal bending (e.g., line heating), thermal spraying, etc. When the target object undergoes such a thermal cycle, shrinkage strain occurs during the cooling process, resulting in deformation and residual stress in the target object.

[0015] In the prediction method of this embodiment, an analytical model of the target object (point cloud data representing the shape of the target object) can first be created. The analytical model is divided into a plurality of elements (meshes), and each vertex of each element becomes a node. The analytical model can be point cloud data representing the shape of any one of the target objects including a butt joint, a lap joint, a double-sided batten joint, a single-sided batten joint, a corner joint, a T-joint, a cross joint, an edge joint, metal additive manufacturing, strain relief, and bending.

[0016] Next, a heat conduction analysis is performed using the created analytical model, information about the material of the target object (specifically, specific heat, thermal conductivity coefficient, etc.), and heating conditions (specifically, heat input, heat source distribution parameters, torch speed, coordinates of the heating start point, coordinates of the heating end point, etc.) to calculate the maximum temperature distribution. When the target object is heated multiple times (e.g., multi-layer welding, multi-pass welding, metal additive manufacturing, etc.), a heat conduction analysis is performed for each heating, and the maximum temperature distribution can be calculated. In the flowchart of Figure 2, since welding passes 1 through n are formed, the maximum temperature distribution can be calculated for each welding pass. The maximum temperature distribution can also be derived from a theoretical formula, etc.

[0017] Next, a first shrinkage region and a second shrinkage region are set in the analysis model based on the maximum temperature distribution. When the target object is heated multiple times (for example, multi-layer welding, multi-pass welding, metal additive manufacturing, etc.), the first shrinkage region and the second shrinkage region can be set for each heating. In the flowchart of Figure 2, the first to nth welding passes are formed, so the first shrinkage region and the second shrinkage region can be set for each welding pass.

[0018] For example, a region in the maximum temperature distribution where the maximum temperature is equal to or greater than a first temperature T1 can be defined as a first shrinkage region, and a region where the maximum temperature is lower than T1 and higher than a second temperature T2 can be defined as a second shrinkage region. The first temperature T1 can be, for example, the mechanical melting temperature of the material of the object. Furthermore, first, second, and third shrinkage regions can be set in the analysis model based on the maximum temperature distribution. In this case, a region where the maximum temperature is equal to or greater than T1 can be defined as the first shrinkage region, a region where the maximum temperature is lower than T1 and higher than T2 can be defined as the second shrinkage region, and a region where the maximum temperature is lower than T2 and higher than a third temperature T3 can be defined as the third shrinkage region. Similarly, four or more shrinkage regions (e.g., first to fourth shrinkage regions, first to fifth shrinkage regions, first to sixth shrinkage regions, first to seventh shrinkage regions, first to eighth shrinkage regions, first to ninth shrinkage regions, and first to tenth shrinkage regions) can be defined based on the maximum temperature distribution. If the object is heated multiple times, each shrinkage region can be set for each heating.

[0019] Next, the temperature change amount ΔT of the first contraction area is set based on the maximum temperature distribution, and the temperature change amount ΔT of the second contraction area is set. The temperature change amount ΔT of the first contraction area is different from the temperature change amount ΔT of the second contraction area. Furthermore, when three or more contraction areas are set, the temperature change amount ΔT can be set for each set contraction area based on the maximum temperature distribution. The temperature change amount ΔT of each contraction area is different from the temperature change amount ΔT of the other contraction areas. Furthermore, when the target object is heated multiple times, the temperature change amount ΔT of each contraction area can be set based on the maximum temperature distribution for each heating. The temperature change ΔT can be, for example, the temperature difference between the maximum temperature reached in the shrinkage region and room temperature. The maximum temperature reached in the shrinkage region may be the average maximum temperature reached in the shrinkage region, the lower limit of the maximum temperature reached in the shrinkage region, or the median of the temperature range of the maximum temperature reached in the shrinkage region. Furthermore, when the target object is heated multiple times and the temperature of the target object does not drop to room temperature between heatings, the temperature change ΔT can also be the temperature difference between the highest temperature reached in the shrinkage region and a preset temperature.

[0020] Next, a shrinkage strain ε = αΔT (α: linear expansion coefficient) calculated from the set temperature change ΔT is uniformly applied to the shrinkage region, and an elastic or elasto-plastic analysis is performed. For this analysis, for example, an idealized explicit FEM method can be used. The shrinkage strain can also be applied isotropically in three axial directions. For example, if a first shrinkage region and a second shrinkage region are set, a first shrinkage strain is uniformly applied to the first shrinkage region, and a second shrinkage strain is uniformly applied to the second shrinkage region, and then an elastic analysis or an elasto-plastic analysis is performed. This makes it possible to simulate shrinkage during the cooling process of the target object and calculate the deformation and residual stress distribution caused by shrinkage. If multiple shrinkage regions are set, corresponding shrinkage strains are uniformly applied to each shrinkage region, and then an elastic analysis or an elasto-plastic analysis is performed. Furthermore, when a target object is heated multiple times (for example, multi-layer welding, multi-pass welding, metal additive manufacturing, etc.), elastic analysis or elasto-plastic analysis can be performed sequentially for each heating according to the heating order. In this case, the final deformation and residual stress distribution can be calculated by the final elastic analysis or elasto-plastic analysis. In the flowchart of Figure 2, the first to nth welding passes are formed, so elastic analysis or elasto-plastic analysis can be performed sequentially for each welding pass.

[0021] Deformation and residual stress prediction An analytical model (butt multi-layer welding model, length: 200 mm, width: 200 mm, thickness: 25 mm) was created as shown in Figure 3. In this analytical model, 10 welding passes were made by arc welding on a base material that had been groove-prepared, and the joint surfaces of the base material were welded. The material to be analyzed was SM490A steel. Figure 4 is a cross-sectional view of the welded portion of the analytical model shown in Figure 3, showing the order in which the 10 welding passes were made. In this analytical model, the first through seventh welding passes were made on the groove portion from the top side of the analytical model, and after gouging from the bottom side, the eighth through tenth welding passes were made from the bottom side. Next, a heat conduction analysis was performed using this analytical model to calculate the maximum temperature distribution during the formation of each welding pass (from the time the welding pass returns to room temperature after welding). Figure 5 is a graph showing the material constants used in the analysis. Table 1 shows the heat input conditions for each welding pass.

[0022] [Table 1]

[0023] Figure 6(a) shows the maximum temperature distribution when the first welding pass is formed, and Figure 6(b) shows the maximum temperature distribution when the tenth welding pass is formed. The maximum temperature distributions when the second through ninth welding passes are formed were also created (not shown). The maximum temperature in the area where the metal melts when the welding pass is formed is over 800°C, and the further away from this melted area, the lower the maximum temperature becomes.

[0024] Next, in the analysis using the modified heat shrinkage method of the present invention, a first shrinkage region and a second shrinkage region were set in each analysis model after the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, or tenth welding pass was formed based on the calculated maximum temperature distribution. Specifically, the region in the maximum temperature distribution where the maximum temperature was 800°C or higher was defined as the first shrinkage region (maximum temperature T a= 800°C), and the region where the maximum temperature distribution is 300°C or more and less than 800°C is the second contraction region (maximum temperature T b The temperature change ΔT in the first shrinkage region (the temperature change from the maximum temperature reached to the normal temperature) was set to 800°C, and the temperature change ΔT in the second shrinkage region was set to 300°C. Figure 6(c) is a cross-sectional view of an analytical model showing the first and second shrinkage regions set in the analytical model after forming the first welding pass in an analysis using the modified heat shrinkage method of the present invention, and Figure 6(d) is a cross-sectional view of an analytical model showing the first and second shrinkage regions set in the analytical model after forming the tenth welding pass in an analysis using the modified heat shrinkage method of the present invention.

[0025] Next, a first shrinkage strain ε1 = αΔT (α: linear expansion coefficient, ΔT: temperature change in the first shrinkage region) was applied to the first shrinkage region of the analysis model after the first welding pass, and a second shrinkage strain ε2 = αΔT (α: linear expansion coefficient, ΔT: temperature change in the second shrinkage region) was applied to the second shrinkage region, and an elastic-plastic analysis was performed to calculate the deformation and residual stress. After that, a first shrinkage strain ε1 = αΔT (α: linear expansion coefficient, ΔT: temperature change in the first shrinkage region) was applied to the first shrinkage region of the analysis model after the second welding pass, and a second shrinkage strain ε2 = αΔT (α: linear expansion coefficient, ΔT: temperature change in the second shrinkage region) was applied to the second shrinkage region, and an elastic-plastic analysis was performed to calculate the deformation and residual stress. This type of elastic-plastic analysis was also performed sequentially on the analytical model after the third welding pass, the analytical model after the fifth welding pass, the analytical model after the sixth welding pass, the analytical model after the seventh welding pass, the analytical model after the eighth welding pass, the analytical model after the ninth welding pass, and the analytical model after the tenth welding pass, to calculate the deformation (angular distortion and transverse shrinkage) and residual stress. The linear expansion coefficient α was calculated using the values ​​shown in the graph in Figure 5. The elastic-plastic analysis was performed using the idealized explicit FEM method.

[0026] For comparison, an analysis was also conducted using the conventional thermal shrinkage method. In this analysis, only one shrinkage region was set in each analytical model after the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, or tenth welding pass was formed. Specifically, the region in the maximum temperature distribution where the maximum temperature was 800°C or higher was defined as the shrinkage region (maximum temperature T c The temperature change ΔT in the shrinkage region (the temperature change from the maximum temperature reached to the temperature returning to normal) was set to 800°C. Figure 6(e) is a cross-sectional view of an analytical model in which a shrinkage region is set in the analytical model after forming the first welding pass in an analysis using the conventional heat shrinkage method, and Figure 6(f) is a cross-sectional view of an analytical model in which a shrinkage region is set in the analytical model after forming the tenth welding pass in an analysis using the conventional heat shrinkage method. In the analysis using the conventional thermal shrinkage method, shrinkage strain was sequentially applied to the analytical model after the first to tenth welding passes, and elastic-plastic analysis was performed to calculate the deformation (angular distortion and transverse shrinkage) and residual stress. In addition, an idealized explicit FEM was used for the elastic-plastic analysis. In addition, deformation (angular distortion and transverse shrinkage) and residual stress were calculated using thermo-elastic-plastic analysis.

[0027] Figure 7 is a graph showing the angular distortion history when welding passes are formed sequentially, showing the angular distortion history calculated using thermo-elastic-plastic analysis, the angular distortion history calculated using an analysis using a conventional thermal contraction method, and the angular distortion history calculated using an analysis using the modified thermal contraction method of the present invention. As shown in the graph in Figure 7, it was found that the angular distortion calculated using the analysis using the modified thermal contraction method of the present invention was in good agreement with the angular distortion calculated using thermo-elastic-plastic analysis. Furthermore, the angular distortion calculated using the analysis using the conventional thermal contraction method appeared to be larger than the angular distortion calculated using thermo-elastic-plastic analysis.

[0028] Figure 8 is a graph showing the transverse shrinkage history when welding passes are formed sequentially, showing the transverse shrinkage history calculated using thermo-elastic-plastic analysis, the transverse shrinkage history calculated using an analysis using a conventional thermal shrinkage method, and the transverse shrinkage history calculated using an analysis using the modified thermal shrinkage method of the present invention. As shown in the graph in Figure 8, the transverse shrinkage calculated using the analysis using the modified thermal shrinkage method of the present invention was found to be in good agreement with the transverse shrinkage calculated using thermo-elastic-plastic analysis. Furthermore, the transverse shrinkage calculated using the analysis using the conventional thermal shrinkage method appeared to be smaller than the transverse shrinkage calculated using thermo-elastic-plastic analysis. Therefore, it was found that by performing analysis using the modified thermal shrinkage method of the present invention, it is possible to calculate deformation that agrees well with the analysis results of thermo-elastic-plastic analysis in a short time.

[0029] Figures 9(a) to (c) are contour diagrams showing the residual stress distribution calculated for the analysis model after the 10th welding pass was formed, where Figure 9(a) shows the residual stress distribution calculated using thermal elastic-plastic analysis, Figure 9(b) shows the residual stress distribution calculated by analysis using the conventional thermal shrinkage method, and Figure 9(c) shows the residual stress distribution calculated by analysis using the modified thermal shrinkage method of the present invention. FIG. 10 is a graph showing the residual stress in the X direction along the dotted line AB shown in FIGS. 9(a) to 9(c), and shows the residual stress distribution calculated by the thermo-elastic-plastic analysis, the analysis using the conventional heat shrinkage method, and the analysis using the modified heat shrinkage method of the present invention. The residual stress distribution calculated by the analysis using the modified heat shrinkage method of the present invention showed a similar tendency to that calculated by the thermo-elastic-plastic analysis, whereas the residual stress distribution calculated by the analysis using the conventional heat shrinkage method deviated significantly from that calculated by the thermo-elastic-plastic analysis. Therefore, it was found that by performing analysis using the modified thermal shrinkage method of the present invention, it is possible to calculate, in a short time, a residual stress distribution that shows a tendency similar to the analysis results of thermal elastic-plastic analysis.

Claims

1. A method for predicting deformation or residual stress caused by a heated object returning to room temperature, comprising: calculating a maximum temperature distribution of the target object; a condition setting step of setting a first contraction region and a second contraction region in the analytical model of the target object, and setting a first temperature change amount in the first contraction region and a second temperature change amount in the second contraction region; and an analysis step of applying a first shrinkage strain calculated from a first temperature change amount to a first shrinkage region and applying a second shrinkage strain calculated from a second temperature change amount to a second shrinkage region, and performing an elastic analysis or an elasto-plastic analysis, The first temperature change amount is different from the second temperature change amount, The prediction method is characterized in that the condition setting step is a step of setting a first contraction region, a second contraction region, a first temperature change amount, and a second temperature change amount based on the maximum reached temperature distribution.

2. (delete)

3. The condition setting step is performed such that the maximum temperature is a first temperature T １ The region where the temperature is equal to or higher than the first temperature T １ A second temperature T ２ 2. The prediction method according to claim 1, further comprising the step of setting a region having a temperature higher than the first temperature as the second contraction region.

4. In the condition setting step, a third contraction region is set in the analysis model, and a third temperature change amount of the third contraction region is set; The third temperature change amount is different from the first and second temperature change amounts, The prediction method according to claim 1 , wherein in the analysis step, a third shrinkage strain calculated from a third temperature change is applied to a third shrinkage region to perform the elastic analysis or the elasto-plastic analysis.

5. In the condition setting step, a plurality of contraction regions are set in the analysis model, and a temperature change amount of each contraction region is set; In the analysis step, the shrinkage strain calculated from each temperature change amount is assigned to the corresponding shrinkage region, and the elastic analysis or the elasto-plastic analysis is performed; The method of claim 4 , wherein the plurality of contraction regions includes a first, a second, and a third contraction region.

6. The prediction method according to claim 5 , wherein the condition setting step is a step of setting a plurality of contraction regions and a temperature change amount for each contraction region based on the maximum temperature distribution.

7. The prediction method is a method for predicting deformation or residual stress that occurs when an object that has been heated multiple times is returned to room temperature, The condition setting step is performed for each heating; The prediction method according to claim 1 , wherein the analysis step is performed sequentially for each heating in accordance with the heating order.

8. The prediction method according to claim 1 , wherein an idealized explicit FEM method is used for the elastic analysis or elasto-plastic analysis in the analysis step.

9. A program configured to cause a computer to execute the prediction method according to any one of claims 1 and 3 to 8.

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