JPH10320432A - Method and system for plasticity analysis using finite element method, and recording medium where plasticity analyzing program using finite element method is recorded - Google Patents

Abstract

PROBLEM TO BE SOLVED: To carry out an analysis of the plasticity of a structure using the finite element method in a short time without repetitive calculation or complicated calculation. SOLUTION: Data on the correlation between stress σ and strain ε is taken in from a stress-strain curve (S5). The elastic limit load FA in an elastic deformation area is calculated from the correlation data (S8), the elastic modulus EB in a plastic deformation area up to a maximum load Fa is approximated with a straight line according to the correlation data (S11), and further respective elements are sorted into an element group A which exceeds strain εA where plastic deformation starts when the maximum load Ff is placed and another element group B are sorted (S9). Those results are used to carry out linear analyses (S14, S15) of the elastic deformation area and plastic deformation area by using the finite element method, and the analytic results of the both are added together (S16).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a plasticity analysis method and system for efficiently obtaining the stress and strain generated when a certain structure is deformed by a load such as heat or load using a finite element analysis. About.

[0002]

2. Description of the Related Art The finite element method (FEM) divides a structure (analysis object) that is deformed by a load such as heat or load into a number of small areas (elements), and determines the force and displacement of each element. Approximate the solution piecewise by a function with finite values,
This is a method of calculating the overall deformation, strain distribution, and stress distribution by numerical calculation. This finite element method is based on the shape, dimensions, material constants and detention conditions. By changing the input parameters such as the load conditions, the deformation and stress of the structure under various conditions. Since distortion can be obtained, it is widely used in the field of strength design and the like (for example, Japanese Patent Laid-Open No. 6-18027).
No. 1, JP-A-8-339396).

[0003] Also, in the case where so-called plastic deformation in which the amount of deformation such as heat or load increases and the amount of deformation gradually increases, various application methods have been proposed, which is called plastic analysis. It should be noted that plastic deformation is always called elasto-plastic analysis because it always involves elastic deformation.

In general, a plastic analysis requires a stress-strain curve indicating the deformation characteristics of a material. In the elastic deformation (linear) region where strain ε and stress σ or deformation and load F are proportional,
The elastic modulus E, which is the ratio of stress to strain, is constant, but in the plastic deformation region, the elastic modulus changes every moment as the load increases. Therefore, it is necessary to perform linear analysis after linearly approximating the stress-strain curve by some method. What is linear analysis 1
This is an analysis that does not change the material constant during the numerical calculations.

In the conventional plastic analysis, a plurality of load steps are set by equally dividing a load condition from a zero load to a load condition to be obtained (final load), and an elastic modulus is calculated for each of these load steps. It has been widely practiced to repeat the linear analysis.

FIG. 8 shows a case where a load is applied as a load.
FIG. 9 is a diagram for explaining an example of a conventional plastic analysis method.

In this example, up to the final load is divided into six load steps. Based on the stress-strain curve of the material, the coordinates (σ1, ε1) of stress and strain at each load step,
(Σ2, ε2),..., (Σf, εf) are given as material constants in advance.

[0008] The elastic moduli E1, E2,
.., Ef are calculated, for example, as in the following equation. E1 = σ1 / ε1, E2 = (σ2−σ1) / (ε2−ε1),..., Ef = (σf−σ5) / (εf−ε5) The elastic modulus E1, E2,. Then, first, the elastic modulus E1 in the first load step is set.
Is used to perform a linear analysis to calculate the increment of stress and strain. Next, a linear analysis is performed under the condition of the elastic modulus E2 in the second load step, and the obtained increments of the stress and strain are added to the values of the stress and strain up to that time. The linear analysis is performed using general-purpose analysis software based on the finite element method.

When the load is large, the position (element) of the structure
In some cases, the strain reaches the plastic deformation region, and the element has a smaller elastic modulus than the element that is the elastic deformation region. For this reason, the elastic modulus E is calculated for each element by a method as in the above equation.

In this way, the same operation is repeated until the load step reaches the final load, and finally the stress and strain after plastic deformation are obtained.

This procedure will be described in detail with reference to the flowchart of FIG. FIG. 9 is a flowchart showing a procedure of a conventional plastic analysis method.

First, a folding model for obtaining stress and strain generated by deformation due to a load such as heat or load is created. This operation is performed by the user himself based on the shape, dimensions, material constants, and the like of the structure to be analyzed. Usually, to reduce the burden of repeated calculations,
Create a two-dimensional model using plane stress elements, plane strain elements, shell elements, etc.

Next, stress and strain data (σ, ε) are input as material constants based on the stress-strain curve of the material (S51). This input operation is also performed by the user himself.

Next, a part of the load condition such as load and temperature is given as a first load step to the created analysis model (S52), and the elastic modulus E is calculated for all the elements (S53). Some elements are in the plastic deformation region and the elastic modulus may be small.

A linear analysis is performed under the above conditions (S54).
Calculate the increment of stress and strain for each element. (S5
5). In the first load step, these values are stored, and after the second load step, the obtained increments of stress and strain are added to the values of stress and strain of each element stored so far and stored (S56). ). The linear analysis is performed by directly operating general-purpose analysis software based on the finite element method.

Next, it is determined whether the load condition has reached the final load (S57). If not, the load step is increased (S58), and the load condition at the next load step is given, and The elastic modulus is calculated and a linear analysis is performed.
The obtained stress and strain increments are added to the stress and strain values of each element stored so far.

In the same manner, this operation is repeated until the load step reaches the final load. When the load step reaches the final load, the stress and strain of each element at that time are obtained (S59).

When graphing the analysis result,
The user himself / herself aggregates the analysis results and creates a graph using a separate graph creation tool.

As described above, conventionally, a method has been adopted in which a load is applied little by little to calculate the elastic modulus of each element, and the analysis is repeated.

As a conventional plastic analysis method, there is a method of approximating a stress-strain curve with two straight lines in addition to the above-described method. For example, ignoring work hardening and the like peculiar to plastic materials, an elastic perfect plastic approximation method in which stress does not increase at a deformation exceeding a certain strain, or work hardening as disclosed in JP-A-58-162838. There is a method of performing two-line approximation in consideration of the Bauschinger effect.

[0021]

However, the conventional plastic analysis method as described above has the following problems.

The method of repeatedly performing the calculation while increasing the load little by little takes a long time until a result is obtained.
In addition, the number of files generated during the analysis becomes enormous as the number of repetitive calculations increases. Further, the setting of the load step requires a long time and skill because preparation of the analysis is complicated, for example, when the step is coarse, the analysis accuracy is extremely reduced, and when the step is fine, a long time is required until a final result is obtained. For example, in the case of the stress-strain curve of FIG. 8, approximation is performed by six steps of linear analysis up to the final load, but the load steps relating to the plastic deformation region are the last two steps. The analysis accuracy is relatively low.

In the method of two-line approximation, the simultaneous ternary 1
Solving the following equations and simultaneous 6-element linear equations requires complicated calculations. In particular, although plastic deformation occurs only in some areas of the structure to be analyzed, since the elastic modulus is calculated for all elements including elements in the area where plastic deformation does not occur, the amount of calculation becomes enormous, That takes time. For example, in the case shown in FIG. 8, E1 = E2 =
E3 = E4, and the elastic modulus of all the elements is the elastic modulus E1 of the elastic deformation region without performing the repetitive analysis of the four load steps. Thus, as a result of the calculation, for many elements, the elastic modulus of the elastic deformation region is sufficient.
As a result, there are many useless calculations.

Further, in reality, a three-dimensional constraint condition or load condition cannot be accurately represented by a two-dimensional model, but a two-dimensional model must be used to reduce the amount of calculation. Furthermore, since it is necessary for the user to directly operate general-purpose analysis software based on the finite element method, specialized knowledge is required for analysis such as commands specific to the software to be used.

On the other hand, data on the correlation between stress and strain, which are indispensable for plastic analysis, are input by the user after reading from a stress-strain curve, or a strain gauge is attached to a deformed position of a material. Since it is necessary to directly measure the deformation amount, it takes time to prepare for analysis.

Further, since there is no support function for creating an analysis model, it takes much time and effort to create an analysis model. In particular, when performing plastic analysis on a lead frame of a semiconductor package, it takes a lot of time and effort to create several three-dimensional analysis models with different numbers of leads.

Further, since there is no support function for graphing the analysis results, it is necessary to troubleshoot the analysis results and create a necessary graph.

Therefore, the present invention provides a plastic analysis method and system capable of executing an analysis process in a short time without performing repetitive calculations or complicated calculations, and a recording medium storing a plastic analysis program using a finite element method. The main purpose is to provide. A second object of the present invention is to reduce the labor required for preparing for analysis by the finite element method, and further to reduce the labor of graphing the analysis result.

[0029]

In order to achieve the above object, a plastic analysis method according to the present invention comprises the steps of: creating a model obtained by dividing a structure into a plurality of elements; This is a plastic analysis method for determining the stress and strain generated when a load acts on an object.From the stress-strain curve, which is the result of a fracture test of the material of the structure to be analyzed, the stress and strain at which plastic deformation starts are calculated. The step of obtaining and performing a linear analysis on the model using the finite element method under the condition of the final load to be obtained, the maximum strain, the element and the maximum stress that become the maximum strain, and each element of the model, A first element group that exceeds the strain at which plastic deformation starts, and a remaining second element group, and further, an elastic limit load when the strain of the element having the maximum strain becomes the strain at which the plastic deformation starts. Obtaining a first elastic modulus that is an elastic modulus in an elastic deformation region from the stress and strain at which the plastic deformation starts, and calculating the plastic deformation region from the maximum stress and the maximum strain and the stress and strain at which the plastic deformation starts. Obtaining a second elastic modulus approximated by a straight line;
For the elastic deformation region, a step of performing a linear analysis using a finite element method under the condition of the elastic limit load and the first elastic modulus, and, for the plastic deformation region, changing the load condition to the final load and the elastic limit load. And the elastic modulus condition is defined as the second elastic modulus for the first element group and the first elastic modulus for the second element group, using a finite element method for linear analysis. And adding a linear analysis result of the elastic deformation region and a linear analysis result of the plastic deformation region for all the elements of the model.

Further, the stress-strain curve is read as image data, and the stress and strain at which the plastic deformation starts are obtained from the image data, and a plurality of typical models for analysis using the finite element method. Is prepared in advance, and a material file storing material data including material constants and material strengths for a plurality of typical types of materials is prepared in advance, and the structure is selected from the model file and the material file. May be selected to generate an analysis model for the finite element analysis based on the selected model and material data.

The plastic analysis system of the present invention creates a model in which a structure is divided into a plurality of elements, and applies stress to the model by applying a load to the structure using the finite element method. A plastic analysis system for obtaining strain, an image reading means for reading, as image data, a stress-strain curve which is a fracture test result of a material of a structure to be analyzed, and a finite element method in accordance with conditions given to the model. Finite element method analysis means for performing a linear analysis using, based on the image data read by the image reading means, to determine the stress and strain at which plastic deformation starts, each element of the model, the strain at which the plastic deformation starts The first element group and the remaining second element group are divided into
The condition of the final load to be obtained is given to the finite element method analysis means, the linear analysis is performed, the maximum strain and the element that becomes the maximum strain are obtained, and the maximum stress when the obtained maximum strain occurs is obtained. Further, an elastic limit load when the strain of the element having the maximum strain becomes a strain at which the plastic deformation starts is obtained, and a first elasticity which is an elastic modulus in an elastic deformation region from the stress and strain at which the plastic deformation starts is obtained. Calculating the modulus, the maximum stress and the maximum strain and the image processing means for calculating a second elastic modulus by approximating a plastic deformation region with a straight line from the stress and the strain at which the plastic deformation starts, and the finite element method analysis means For the elastic deformation region, the linear analysis is performed under the condition of the elastic limit load and the first elastic modulus, and the load condition is set to the final load and the final load for the plastic deformation region. The linear analysis is performed with the difference from the limiting load and the elastic modulus condition as the second elastic modulus for the first element group and the first elastic modulus for the second element group. And a function of adding a linear analysis result of the elastic deformation region and a linear analysis result of the plastic deformation region for all the elements of the model.

Also, a model file storing a plurality of types of models for analysis using the finite element method, a material file storing material data including material constants and material strengths for a plurality of types of materials, Model generating means for generating an analysis model for the finite element method analysis according to the model and material data corresponding to the structure selected from the file and the material file, In this case, the analysis result by the finite element method analysis means is further graphed in accordance with a graph creation condition file storing creation conditions for a plurality of types of graphs and a creation condition selected from the graph creation condition file. May have a graph creating means for displaying the data on a display device.

The recording medium on which the plasticity analysis program of the present invention is recorded is formed by a computer by creating a model obtained by dividing a structure into a plurality of elements, and applying a load to the structure using the finite element method. A recording medium on which a plastic analysis program for obtaining stress and strain generated by acting is recorded, wherein the plastic analysis program is provided to a computer from a stress-strain curve which is a fracture test result of a material of a structure to be analyzed. Performing a linear analysis on the model using the finite element method under the conditions of the stress and strain at which plastic deformation starts and the final load to be determined, and determining the maximum strain, the element and the maximum stress that are the maximum strain At the same time, each element of the model is divided into a first group of elements exceeding the strain at which plastic deformation starts and a second group of remaining elements. The procedure for determining the elastic limit load when the strain of the element becomes the strain at which the plastic deformation starts, and the first modulus of elasticity in the elastic deformation region from the stress and strain at which the plastic deformation starts, A procedure for obtaining a second elastic modulus by linearly approximating a plastic deformation region from the maximum stress and the maximum strain and the stress and strain at which the plastic deformation starts, and for the elastic deformation region, the elastic limit load and the first elasticity. The procedure for performing a linear analysis using a finite element method with a condition as a condition, and for the plastic deformation region, the load condition is the difference between the final load and the elastic limit load, and
A step of performing a linear analysis using a finite element method on elasticity conditions as the second elastic modulus for the first element group and the first elastic modulus for the second element group; And a procedure for adding the linear analysis result of the elastic deformation region and the linear analysis result of the plastic deformation region.

In the present invention configured as described above, stress, strain, deformation, and the like due to plastic deformation can be obtained only by performing linear analysis three times or less without performing repeated calculations. Further, by reading the stress-strain curve as image data, it is possible to easily obtain a correlation between stress and strain required for a plastic trace from the image data.

[0035]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1 is a block diagram of one embodiment of the plasticity analysis system using the finite element method of the present invention.

This plastic analysis system comprises a data processing device 1 and a three-dimensional model file 2, a graph preparation condition file 3, a material file 4, an input device 5,
It comprises an image scanner 6 and a display device 7.

The data processing device 1 includes an image processing unit 10
, Selecting means 11, and three-dimensional model generating means for analysis 12
And a finite element method analysis means 13 and a graph creation means 14. The data processing device 1 is composed of, for example, a workstation. The image processing unit 10, the selection unit 11, the analysis model generation unit 12, the finite element method analysis unit 13, and the graph creation unit 14 may be incorporated in the data processing device 1 in advance, or may be included in the data processing device 1. It may be realized by installed software.

The input device 5 has a keyboard 5a and a mouse 5b for data input by the user.

The three-dimensional model file 2 stores three-dimensional models 2a to 2p for plastic analysis of some typical shapes of structures using the finite element method. The material file 4 includes several kinds of data including representative material names of the structures, material constants such as thermal expansion coefficients and material strengths, and (stress, strain) correlation data transferred from the image processing means 10. Material data 4a to 4r are stored. In addition, the graph creation condition file 3 contains several typical graphs that are frequently used.
Graph creation conditions such as how to take the horizontal axis are stored as graph creation conditions 3a to 3q.

FIG. 2 is a flowchart showing a processing example of the data processing device 1 in the plastic analysis system shown in FIG. Hereinafter, the operation of the present embodiment will be described with reference to FIGS.

When the user performs a plastic analysis on a certain structure, the data processing device 1 is operated by the input operation of the input device 5.
Start

When the data processing device is started, first, the selecting means 11 displays the three-dimensional model 2a on the screen of the display device 7.
2p and a list of graph creation conditions 3a to 3q are displayed, and the user is prompted to select an appropriate one (S1). When the user selects a three-dimensional model from the three-dimensional model list on the screen, the selection means 11 inputs the selected three-dimensional model from the three-dimensional model file 2 and transmits it to the analysis model generation means 12. When the user selects a graph creation condition from the list of graph creation conditions on the screen, the selection unit 11 inputs the selected graph creation condition from the graph creation condition file 3 and transmits it to the graph creation unit 14.

Next, the analysis model generation means 12 displays the three-dimensional model transmitted from the selection means 11 on the display device 7 and prompts the user to rewrite the dimensions of the components in the three-dimensional model. Request (S2). The user corrects the dimensions of the structural components in the three-dimensional model displayed on the display device 7 by input from the input device 5 so as to match the structure to be analyzed.

Further, the analysis model generation means 12 displays a list of the material data on the display device 7 to urge the selection (S
3). When the user selects the corresponding material data from the list of material data on the screen, the analysis model generating means 12 inputs the selected material data from the material file 4, and sets the material constant in the material data to Set as the material constant in the selected 3D model. Further, the strength of the material included in the selected material data is transmitted to the graph creating means 14.

Next, the analysis model generation means 12 prompts the user to set a constraint condition, and sets the input constraint condition in the three-dimensional model (S4). by this,
The generation of the analysis model is completed, and the analysis model is transmitted to the finite element method analysis means 13.

With the above, setting of various conditions for the finite element method analysis is completed. Next, the user causes the image scanner 6 to read the stress-strain curve and the coordinate axis, which are the results of the material fracture test.

Then, the image processing means 10 converts the image of the stress-strain curve obtained by the image scanner 6 into (stress, strain) coordinates and stores it as material data. (S5). Further, from the image obtained by the image scanner 6, the strain εA at the time when the plastic deformation starts and the stress σA at this time are detected from the coordinates and stored (S6).

On the other hand, the finite element method analysis means 13 performs a linear analysis when the maximum load Ff to be obtained is given (S12), and sends the distortion of each position (element) at that time to the image processing means 10. Can be Further, the maximum distortion εf is calculated by this linear analysis (S13).

The image processing means 10 calculates the maximum distortion εf calculated by the finite element method analysis means 13 and its position (element).
Is detected, the stress σf corresponding to the maximum strain εf is detected from the previously stored (stress, strain) data (S7), and the stress at the position where the maximum strain εf occurs becomes εA. A certain elastic limit load FA = Ff × εA / εf is calculated (S8). The elastic limit load FA means a load at which the structure to be analyzed does not plastically deform at any position.
Further, each element is sorted into an element group A whose distortion exceeds εA when the maximum load Ff is applied and a remaining element group B (S9).

From the above data, the elastic modulus EA = σA / εA of the elastic deformation region and the elastic modulus EB = (σf−σA) / (εf−εA) when the plastic deformation region is approximated by a straight line. It is calculated (S10, S11) and transmitted to the finite element method analysis means 13 as analysis conditions. The steps from S8 to S11 may be performed in any order.

The finite element method analysis means 13 includes an analysis model generated previously and a finite element method program (for example, Sw
anson Analysis Inc. ANSY
S (registered trademark)) and a plastic analysis is performed as follows.

First, as described above, the finite element method program is started under the final load conditions (final values such as temperature and load) Ff input by the user through the input device 5, and the finite element method is started. Perform linear analysis by the method (S1
2) The maximum distortion εf and its position (element) are obtained (S13) and transmitted to the image processing means 10.

Then, the elastic modulus EA = σA / εA of the elastic deformation region and the elastic modulus EB = (σf−σA) / (εf−εA) of the plastic deformation region are received from the image processing means 10. First,
A linear analysis is performed on the elastic deformation region under the conditions of the elastic modulus EA and the elastic limit load FA for all the elements (S14), and the stress σAj and the strain εAj of each element are stored. Here, when the number of elements is n, j = 1, 2,..., N. Similarly,
With respect to the plastic deformation region, the element group A is set to the elastic modulus EB, the element group B is set to the elastic modulus EA, and a linear analysis is performed under a load (Ff-FA) condition (S15), and the stress σBj and strain εBj of each element are stored. In the linear analysis of the plastic deformation region, the analysis conditions are changed between the element group A and the element group B. The element group A has a plastic deformation region extending to the final load, whereas the element group B has a final deformation region. This is because only elastic deformation occurs until the load.

Finally, for all the elements, the analysis results of the elastic deformation region and the analysis results of the plastic deformation region are added (S16), and the stress σ and strain ε generated by the final load such as heat and load are calculated. , Σ = σAj + σBj, ε = εAj + ε
Calculate as Bj.

The result of the analysis is transmitted to the graph creating means 14. The graph creating means 14 graphs the transmitted analysis result in a format determined by the graph creating conditions transmitted from the selecting means 11, and displays the graph on the screen of the display device 7 (S17). Further, the data of the material strength transmitted from the analysis model generating means 12 is displayed together with the screen of the display device 7.

Generally, plastic breaking can be roughly divided into three stages: creation of an analysis model, finite element method analysis, and display of results.

According to the present embodiment, the analysis model is created by storing a file in which some typical three-dimensional model shapes and material constants are registered. Select, rewrite the dimensions of the components, specify the material, and especially in the case of plastic analysis of the lead frame of a semiconductor package, specify the number of leads and apply constraints to easily create a 3D model for analysis. Can be created. Material file 4
Can be performed simply by designating any of the material data 4a to 4r stored in. Therefore, the work time required for creating the analysis model can be significantly reduced as compared with the conventional case.
Since the data of the correlation between stress and strain, which are indispensable for plastic breaking, are also read and processed by the image scanner 6 and the image processing means 10, all data necessary for plastic analysis such as strain at which plastic deformation starts can be easily calculated. it can.

Since the plastic analysis using the analysis model and the finite element method program is automatically advanced by the finite element method analysis means 13, the user who lacks specialized knowledge such as commands unique to the finite element method program. However, plastic analysis can be performed. Therefore, unlike the conventional technique, specialized knowledge such as a command for analysis is not required, and a result can be obtained in a single time because a result can be obtained by three or less linear analyzes without performing repetitive calculations.

Further, for a graph for outputting stress and deformation as analysis results, by selecting desired graph creation conditions from the graph creation condition file 3, the user can compile the analysis results and obtain necessary graphs. The graph of the analysis result is automatically output from the display device 7 without creating the graph by itself, so that the graph can be displayed on the same system as the analysis is performed, and even a beginner can easily generate the graph. it can. Furthermore, since the value of the material strength of the component is also displayed on the graph showing the stress value of the analysis result by the finite element method, it is easy to check whether the stress caused by plastic deformation exceeds the strength of the material be able to.

Next, a specific analysis example using the above-described plastic analysis method will be described.

(Analysis Example 1) In this example, a load is applied as a load.
In this case, the bending test of the beam supported at both ends as shown in FIG.
The amount of deflection of the beam 31 generated in the experiment was determined. Needle
31 is 5 × 10 ^-3Alloy material that begins plastic deformation due to strain
And the maximum load applied to the beam 31 is 100 kg
f. FIG. 3 (a) is used for this plastic breaking.
FIG. 3B shows the initial state of the analysis model.
This shows the state when a load is applied.

In the plastic analysis system shown in FIG. 1, first, the image processing means 10
Data necessary for 3 is prepared.

FIG. 4 shows a stress-strain curve of the alloy material used in this example, which is read by the image scanner 6 and stored as (stress, strain) coordinates by the image processing means 10. Further, the image processing means 10 causes the strain εA = 2.5 × 10 ^{−3 at which the} plastic deformation starts and the stress σA = 1
0 kgf / mm ² has been detected. Thereby, the elastic modulus EA of the elastic deformation region EA = σA / εA = 4000 kgf / m
m ² is calculated and sent to the finite element method analysis means 13.

The finite element method analysis means 13 receives the value of EA, and first performs 100 kgf as the maximum load Ff to perform a linear analysis by the finite element method. Since this analysis does not take into account changes in elastic modulus due to plastic deformation, stress increases in proportion to strain. As a result of the analysis, the maximum strain at this time was εf = 5 × 10 ⁻³ , and the position where the maximum strain occurred was an element immediately below the load on the opposite side of the portion to which the load was applied. FIG. 3B schematically shows the state of the analysis model at this time. For those elements near where the maximum distortion occurs, the distortion is greater than εA,
In practice, this means that plastic deformation occurs.

The distortion of each element is sent to the image processing means 10 and the data necessary for the finite element method analysis means 13 is calculated.

First, the image processing means 10 detects the stress σf = 14 kgf / mm ² corresponding to the maximum strain εf using the (stress, strain) data stored previously. Next, as a result of the above linear analysis, each element is classified into an element group A, which is an element having a strain larger than εA, and an element group B, which is a remaining element that does not undergo plastic deformation until a final load. .
Furthermore, the load FA when the maximum strain is just εA
Is calculated using the following equation.

FA = Ff × εA / εf = 50 kgf FA means a load at which the beam 31 does not plastically deform at any position.

Finally, based on these values, the elastic modulus EB of the plastic deformation region is calculated by the following equation.

EB = (σf−σA) / (εf−εA) = 16
00 kgf / mm ² These values are transferred to the finite element method analysis means 13.

The finite element method analysis means 13 receives the values of FA and EB, and first, for all the elements, the elastic modulus EA
= 4000 kgf / mm ² and load FA = 50 kgf, a linear analysis is performed on the elastic deformation region by the finite element method. And the resulting stress σAj of each element,
The distortion εAj and the amount of deflection ΔA at the maximum distortion position are stored. Next, for the plastic deformation region, the load Ff-FA = 50
kgf, the element group A has an elastic modulus EB of 1600 kgf / m.
m ² , the element group B is subjected to linear analysis under the condition of the elastic modulus EB = 4000 kgf / mm ² , and the stress σBj, the strain εBj, and the deflection δB at the maximum strain position of each element are stored.

Finally, for each element, the analysis result of the elastic deformation region and the analysis result of the plastic deformation region are added as in the following equation.

Σ = σAj + σBj ε = εAj + εBj δ = δA + δB The deflection amount thus obtained was δ = 12 mm. The amount of deflection when plastic deformation does not occur is 8 mm, and it can be seen that the amount of deflection is increased by the amount of plastic deformation.

As described above, according to the plasticity analysis system of the present invention, the stress and strain at each position of the structure caused by plastic deformation due to the final load such as heat and load are usually calculated by three linear solutions. You can get it just by folding.

(Analysis Example 2) This example is a case where heat is applied as a load, and a semiconductor chip and a glass / epoxy substrate (hereinafter simply referred to as a substrate) are formed using a solder-based alloy.
After connecting at a temperature of ° C, the amount of deformation of the solder alloy that occurred when cooled to room temperature (20 ° C) was determined.

FIGS. 5A and 5B schematically show the analysis model used for the plasticity analysis. FIG. 5A shows the initial state (320 ° C.), and FIG. 5B shows the maximum load state (20 ° C.).
° C).

As shown in FIG. 5A, in the initial state, neither the semiconductor chip 33 nor the substrate 32 is warped, and as a result, the solder alloy is not deformed. When cooled from this state to room temperature, as shown in FIG.
Warps toward the semiconductor chip 33 side. This is semiconductor chip 3
This is because the substrate 32 has a larger thermal expansion coefficient than that of the substrate 32. The easily deformable solder alloy 34 is deformed by being sandwiched between them.

FIG. 6 shows a stress-strain curve of the solder alloy 34 used in this embodiment, which is read by the image scanner 6 and stored by the image processing means 10 as coordinates of (stress, strain). Further, the image processing means 10 causes the strain εA = 14 × 10 ^{−3 at which the} plastic deformation starts and the stress σA = 2
1 kgf / mm ² is detected. Thus, the elastic modulus EA = σA / εA = 1500 kgf / mm ² of the elastic deformation region is calculated and sent to the finite element method analysis means 13.

The finite element method analysis means 13 uses the value of EA as the elastic modulus of the solder alloy 34 and determines the maximum load Ff as the temperature difference ΔT between the initial state and room temperature ΔT = 320-20 ° C. = 3
At a temperature of 00 ° C., linear analysis was performed by the finite element method.
As a result of the analysis, the maximum strain generated in the solder alloy 34 is εf =
10 × 10 ⁻³ , which is smaller than the strain εA at which plastic deformation starts. This means that the solder alloy 34 does not undergo plastic deformation even when cooled from 320 ° C. to 20 ° C. In the system, the distortion of each element is sent to the image processing unit 10 as in the first analysis example.

The image processing means 10 detects the stress σf = 21 kgf / mm ² corresponding to the maximum strain εf using the previously stored (stress, strain) data. Next, from the previous linear analysis, there is no element whose distortion is larger than εA,
Element group A is empty. All the elements are recognized as an element group B that does not undergo plastic deformation until the final load. Further, when the maximum strain is just εA, the load is FA = F
f × εA / εf = 300 ° C. × 14 × 10 ⁻³ / 10 × 10 ⁻³
= 420 ° C.

Finally, from these values, the elastic modulus of the plastic deformation region is EB = (σf−σA) / (εf−εA) = 1500
It is calculated as kgf / mm ² . Since the solder alloy does not undergo plastic deformation, this value is the same as the elastic modulus EA of the elastic deformation area. These values are transferred to the finite element method analysis means 13.

The finite element method analysis means 13 receives these values, and the elastic modulus EA = 15000 for all the elements.
Under the condition of kgf / mm ² and FA (that is, temperature difference) = 420 ° C., linear analysis is performed on the elastic deformation region by the finite element method. The resulting stress σAj, strain ε of each element
Aj and the deformation amount ΔA are stored. Next, regarding the plastic deformation region, the load Ff−FA = 300−420 ° C. = − 120.
° C., the element group A modulus EB = 1500kgf / mm ^2, even element group B linear Kaiori the plastic deformation region in conditions of elastic modulus EA = 15000kgf / mm ^2, for each element応Ka ShigumaBj,
The distortion εBj and the deformation amount δB are stored.

Finally, for each element, the result of analysis of the elastic deformation region and the result of breaking of the plastic deformation region are added as in the following equation.

Σ = σAj + σBj ε = εAj + εBj δ = δA + δB Here, since the load condition is a negative value, the analysis result of the plastic deformation region has a negative value.

The amount of deformation of the solder alloy thus obtained is δ
= 5 mm. This was confirmed to be the same as the result of the elasticity analysis.

As described above, in the plastic analysis system of the present invention, a solution can be obtained by a similar method even when there is only elastic deformation.

In order to further reduce the analysis time, the maximum strain εf obtained in S13 is compared with the plastic deformation starting strain εA detected in S6, and if εf <εA, it is determined that no plastic deformation occurs. And without analyzing the plastic deformation area
It is also conceivable to find a solution only by performing the linear analysis twice.

Further, a linear analysis of the elastic deformation region (S1
Instead of performing 4), a method of obtaining a solution by a proportional calculation from the result of the linear analysis (S12) of the maximum load may be adopted.

In the present plasticity analysis system, an analysis using a three-dimensional model is performed. However, a system using a two-dimensional model may be used to further improve the calculation speed.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above embodiments, and various other modifications can be made. For example, assuming that beginners who have no experience in plastic analysis use it, guides that inform the order of work are displayed at each stage of creation of analysis models, finite element method analysis, etc. A configuration may be adopted in which a screen showing the current work state by flashing is displayed on the flowchart shown.

The present invention may be in the form of a recording medium on which a plastic analysis program for causing a computer to execute the above-described procedure is recorded.

In this case, as shown in FIG. 7, the data processing device 21 such as a workstation or a personal computer reads the plastic analysis program recorded on the recording medium 22, and the data processing device 21 according to the plastic analysis program. Control the operation of. The recording medium 22 may be a magnetic disk, a semiconductor memory, or another recording medium. The three-dimensional model file 2, the graph creation condition file 3, the material file 5, the input device 5, the image scanner 6, and the display device 7
Since each is the same as that shown in FIG. 1, the same reference numerals as those in FIG. 1 are given, and the description thereof is omitted here. The data processing device 21 controls the plastic analysis program read from the recording medium 22 to execute the processing described with reference to FIG.
The processing from 1 to S17 is executed.

Further, according to the present invention, since only linear analysis is performed without performing complicated calculations associated with repetitive calculations, it is possible to use it in combination with various general-purpose analysis software including an analysis solver, including elementary ones. The finite element method analysis function can be used in combination with general-purpose analysis software installed on the same processing device (machine) or a personal computer or another machine connected by a computer network. Further, the present invention is effective not only for plastic analysis but also for efficient model creation and complicated graph creation as a pre / post processor of finite element method analysis software such as heat conduction, vibration, and fluid analysis. .

[0094]

As described above, according to the present invention, the following effects can be obtained.

Since the stress, strain, deformation, and the like due to plastic deformation can be obtained only by three or less linear analyses without performing repetitive calculations, the analysis time can be greatly reduced. Further, since the number of calculations is reduced, the capacity of a file generated during the analysis can be reduced.

Further, by reading the stress-strain curve as image data, the correlation between the stress and the strain required for the plastic trace can be easily obtained from the image data, and the elastic modulus required for the plastic analysis can be obtained. Can also be automatically calculated using this image data. Furthermore, a model for analysis can be easily created by selecting an appropriate model and material data from the model file and the material file. By having all of these functions, even users with little specialized knowledge can easily perform plastic analysis, eliminating the need to train skilled design engineers with general-purpose analysis software.
Human costs can be reduced.

Further, by providing a graph creation means as a support function for graphing, it is possible to easily graph the analysis result.

[Brief description of the drawings]

FIG. 1 is a block diagram of an embodiment of a plastic analysis system using a finite element method according to the present invention.

FIG. 2 is a flowchart illustrating a processing example of the data processing device illustrated in FIG. 1;

FIG. 3 is a schematic diagram of an analysis model for explaining an analysis example 1 using the plasticity analysis method of the present invention.

FIG. 4 is a stress-strain curve of the alloy material used in Analysis Example 1.

FIG. 5 is a schematic diagram of an analysis model for explaining an analysis example 2 of the plasticity analysis method of the present invention.

FIG. 6 is a stress-strain curve of the solder alloy used in Analysis Example 2.

FIG. 7 is a block diagram of another embodiment of the present invention.

FIG. 8 is a graph showing stress-values for explaining a conventional plasticity analysis method.
It is a distortion curve.

FIG. 9 is a flowchart showing a procedure of a conventional plasticity analysis method.

[Explanation of symbols]

 1, 21 Data processing device 2 3D model file 3 Graph creation file 4 Material file 5 Input device 6 Image scanner 7 Display device 11 Selection means 12 Analysis model creation means 13 Finite element method analysis means 14 Image processing means 31 Beam 32 Substrate 33 Semiconductor chip 34 Solder alloy

Claims (7)

[Claims] 1. A plastic analysis method for creating a model in which a structure is divided into a plurality of elements, and using a finite element method on the model to determine stress and strain generated when a load acts on the structure. A step of obtaining stress and strain at which plastic deformation starts from a stress-strain curve which is a result of a fracture test of a material of a structure to be analyzed; and a finite element for the model under a condition of a final load to be obtained. The maximum strain, the element that becomes the maximum strain, and the maximum stress are obtained by performing a linear analysis using the method, and each element of the model is replaced with a first element group exceeding the strain at which plastic deformation starts and a second second element. A step of obtaining an elastic limit load when the strain of the element having the maximum strain becomes the strain at which the plastic deformation starts, and an elastic limit from the stress and the strain at which the plastic deformation starts. Obtaining a first elastic modulus which is an elastic modulus in the elastic deformation region, and obtaining a second elastic modulus which approximates a plastic deformation region with a straight line from the maximum stress and the maximum strain and the stress and the strain at which the plastic deformation starts, A step of performing a linear analysis using a finite element method on the elastic deformation region under the condition of the elastic limit load and the first elastic modulus; and, for the plastic deformation region, changing a load condition to the final load and the elastic limit load. And the elastic modulus condition is defined as the second elastic modulus for the first element group and the first elastic modulus for the second element group, using the finite element method. A plastic analysis method comprising: analyzing; and for all elements of the model, adding a linear analysis result of the elastic deformation region and a linear analysis result of the plastic deformation region. 2. The plasticity analysis method according to claim 1, wherein the stress-strain curve is read as image data, and a stress and a strain at which the plastic deformation starts are obtained from the image data. 3. A model file storing a plurality of typical models used for analysis using the finite element method, and material data including material constants and material strengths of the plurality of typical materials are stored. Prepare a material file in advance, select a model and material data corresponding to the structure from the model file and material file, and use the selected model and material data for analysis for finite element analysis. The method according to claim 1, wherein the model is generated. 4. A plastic analysis system for creating a model in which a structure is divided into a plurality of elements, and using a finite element method on the model to determine stress and strain generated by applying a load to the structure. An image reading means for reading a stress-strain curve which is a result of a fracture test of a material of a structure to be analyzed as image data, and a linear analysis using a finite element method according to conditions given to the model. Based on the finite element method analysis means to be performed, based on the image data read by the image reading means, to determine the stress and strain at which plastic deformation starts, each element of the model, the first exceeding the strain at which the plastic deformation begins
And the remaining second element group, and the condition of the final load to be obtained is given to the finite element method analysis means and the linear analysis is performed to obtain the maximum distortion and the element having the maximum distortion. To obtain the maximum stress when the obtained maximum strain occurs, and further obtain the elastic limit load when the strain of the element that becomes the maximum strain becomes the strain at which the plastic deformation starts, and the stress at which the plastic deformation starts And a first elastic modulus which is an elastic modulus in an elastic deformation region from the strain and a second elastic modulus which approximates a plastic deformation region with a straight line from the maximum stress and the maximum strain and the stress and the strain at which the plastic deformation starts, and The finite element method analysis means performs the linear analysis on the elastic deformation region under the conditions of the elastic limit load and the first elastic modulus, For the sexual deformation region, the load condition is defined as the difference between the final load and the elastic limit load, and the elasticity condition is defined as the second elastic modulus for the first element group and the second elastic group for the second element group. Is a plastic analysis system having a function of performing the linear analysis as the first elastic modulus, and adding a linear analysis result of the elastic deformation region and a linear analysis result of the plastic deformation region for all elements of the model. 5. A model file storing a plurality of types of models for analysis using the finite element method; a material file storing material data including material constants and material strengths for a plurality of types of materials; 5. The plastic analysis according to claim 4, further comprising: model generation means for generating an analysis model for a finite element method analysis in accordance with a model and material data corresponding to the structure selected from a file and a material file. system. 6. A graph creation condition file storing a plurality of types of graph creation conditions, and an analysis result by the finite element method analysis means in a graph form according to a creation condition selected from the graph creation condition file. The plastic analysis system according to claim 5, further comprising a graph creating unit for displaying the graph on an apparatus. 7. A computer creates a model in which a structure is divided into a plurality of elements, and obtains stress and strain generated by applying a load to the structure using a finite element method on the model. A recording medium on which a plastic analysis program is recorded, wherein the plastic analysis program is a computer that obtains stress and strain at which plastic deformation starts from a stress-strain curve that is a fracture test result of a material of a structure to be analyzed. Under the condition of the final load to be obtained, a linear analysis is performed on the model using the finite element method to obtain the maximum strain, the element that becomes the maximum strain and the maximum stress, and each element of the model is subjected to plastic deformation. Is divided into a first element group exceeding the strain at which the deformation starts and a remaining second element group, and the strain of the element having the maximum strain is changed to the strain at which the plastic deformation starts. And a procedure for obtaining an elastic limit load, and obtaining a first elastic modulus which is an elastic modulus in an elastic deformation region from the stress and strain at which the plastic deformation starts, and obtaining the maximum stress and the maximum strain and the stress at which the plastic deformation starts. And a procedure for obtaining a second elastic modulus by approximating the plastic deformation region with a straight line from the strain and the strain, and linearly analyzing the elastic deformation region using a finite element method under the condition of the elastic limit load and the first elastic modulus. Procedures: For the plastic deformation region, a load condition is defined as a difference between the final load and the elastic limit load, and an elastic modulus condition is defined as the second elastic modulus and the second elastic modulus for the first element group. A linear analysis using the finite element method as the first elastic modulus for the group of elements; and a linear analysis result of the elastic deformation area and the plastic deformation area for all the elements of the model. And a step of adding the result of the linear analysis of the recording medium.