KR100948035B1 - Method of Acquisition of True Stress-Strain Curves over Large Strain by the Tensile Test and its Finite Element Analysis, and Tensile Test Device using it - Google Patents

Abstract

The method of obtaining the true strain-true stress curve for high strain using the tensile test and the finite element method according to the present invention, the finite element analysis using the elongation-tensile load curve or nominal strain-nominal stress curve obtained by the tensile test It can be configured to acquire the true strain-stress curve of the input information as well as an independent module with a finite element analysis program, that is, a finite element analysis program (including a material property acquisition module) dedicated to tensile test and commercial computer use engineering ( It can be developed as a material information acquisition program of the CAE) program and can be mounted on the tensile tester to provide the user with a very fast and accurate true strain-true stress curve, and also to researchers such as fracture mechanics By providing more accurate deformation behavior up to failure, There is an effect that technology can contribute in associated industries.

Tensile test, finite element analysis, true strain-true stress curve, necking, tensile tester

Description

Method of Acquisition of True Stress-Strain Curves over Large Strain by the Tensile Test and its Finite Element Analysis, and Tensile Test Device using it}

1 is a graph showing the nominal strain-nominal stress curve obtained by the tensile test,

2 is a graph showing a reference true strain-true stress curve obtained from a nominal strain-nominal stress curve;

3 is a view showing a complete tensile test analysis model,

4 is a graph comparing the results of the finite element analysis predicted by the tensile test results and the reference true strain-true stress curve,

5 is a graph showing the first improved true strain-true stress curve,

6 is a comparative graph of the results of the elongation-tensile load curve obtained from the first improved true strain-true stress curve and the experimental results;

7 is a graph showing true strain-true stress curves over 2nd, 3rd, and 4th orders.

FIG. 8 is a comparison graph of the results of the elongation-tensile load curve obtained from the true strain-true stress curves over the second, third, and fourth orders.

9 is a view illustrating a state in connection with a tensile tester to obtain a true strain-true stress curve according to the present invention;

FIG. 10 is a diagram illustrating a case where a method for obtaining strain-stress curves according to the present invention is used as a material property acquisition module of engineering analysis software.

The present invention relates to a method of obtaining a true strain-true stress curve of a metallic material using only an elongation-tensile load curve obtained from a tensile test result, by considering deformation behavior after necking based on accurate necking prediction using a finite element method. And a true strain-true stress curve at high strain.

Generalized plastic processing process analysis techniques have made the true strain-true stress relations or curves of metal materials necessary for process design technicians, but they are not easy to acquire experimentally, so field engineers and researchers often do not know the exact material information. Most technicians use limited information from the literature.

This is especially true when flow stresses at high strain rates are required, such as forging. Although it has been studied by many researchers to date, no system has been commercialized for obtaining high-strain flow stress (true stress) based on tensile tests, and at the laboratory level to obtain true strain-true stress curves at high strain rates. Compression tests are being conducted.

There is no easier and easier way to test a material than a tensile test. Acquiring the true strain-true stress curve is one of the main purposes of the tensile test. If strain and stress information at the minimum cross section of the necking area is available, even a tensile test can provide reliable flow stress for high strain. Already, a method of inferring true strain-true stress curves by measuring the deformation shape of the necking area has been developed. However, since the accuracy is not easy and the measurement itself is not easy, there is no commercialized result in connection with the tensile tester.

One way to avoid the problem of measurement is to use the finite element method. However, many researchers have tried to interpret necking phenomena, but none of the results have been solved by the full tensile test model (simple bar analysis model without imposing artificial defects or displacement constraints). Recently, the inventors have predicted precisely the timing of necking from an engineering point of view in the tensile test of a circular cross-section bar using a full tensile test analysis model of a simple bar modeling the gap between the marks.

The true strain-true stress curve is often formulated by the following strength factor-strain hardening index model: Hollomon's constitutive equation.

(1)

(One)

와

는 각각 진응력과 진변형률을 의미하며, K와 n은 강도계수와 변형경화지수이다. 그런데 일반적으로 관련 문헌에서 강도계수와 변경경화지수를 찾아 인장시험에 관하여 유한요소해석을 실시해 보면, 네킹 시점을 정확하게 예측하지 못한다. 그 이유는 시편의 형상비가 일정 이상일 경우 네킹의 발생 관점에서 볼 때, Considere 조건으로부터 변형경화지수는 최대공칭응력점에 대응하는 진변형률과 동일해야 하는데 대부분 이 값과 일치하지 않기 때문이다. 그리고 비록 네킹을 정확하게 예측하였더라도 네킹 발생 이후의 연신량-인장하중 곡선의 실험치와 유한요소해석 결과(예측치) 간에는 상당한 차이가 발생한다. 이것은 Hollomon의 구성방정식의 한계를 보여주는 결과이다.here

Wow

Are the true stress and true strain, respectively, and K and n are the strength coefficient and the strain hardening index. In general, however, when finite element analysis is performed on the tensile test by finding the strength coefficient and the change hardening index in the relevant literature, the necking point cannot be accurately predicted. This is because from the point of view of the necking when the aspect ratio of the specimen is above a certain level, from the Considere condition, the Strain Hardening Index should be equal to the true strain corresponding to the maximum nominal stress point, which is mostly inconsistent with this value. And even though the necking is accurately predicted, there is a significant difference between the experimental value of the elongation-tensile load curve after the necking and the finite element analysis (prediction). This is the result of the limitations of Hollomon's construction equation.

The true strain-true stress curve is mainly obtained by tensile test, compression test, indentation test, punch test, torsion test, notch tensile test, etc., and is often expressed by mathematical model such as Hollomon's constitutive equation.

Tensile tests are relatively easy to perform and provide the technician with a great deal of information about the material properties. However, there is a limit in obtaining the correlation between strain and stress, which is essential in plastic flow analysis, because of necking phenomenon in tensile test. Until necking, true strain-true stress curves or functions can be obtained from tensile test results under the assumption of incompressibility, but no further information can be obtained from this condition if necking occurs. In the case of steel, necking usually occurs at a strain of 0.15 or less, while strain in plastic processing such as forging is often more than 1.0. In particular, in the case of automatic multi-forging, in-process annealing cannot be performed, so the strain rate in the main deformation section is more than 2.0. Therefore, the true strain-true stress curve before the necking cannot be a major concern in terms of plastic processing involving large strains, and the true strain-true stress curve after the necking is extrapolated by extrapolating the strain-stress curve before the necking. Use may be very inappropriate in some situations. Some researchers have obtained strain-stress curves that fall within an error range of about 10% based on the tension-tensile load curve and the shape of the necking region, which are the result of the tensile test, but it is necessary to measure the deformation shape of the necking region or material There is a disadvantage that does not reflect the characteristics of the details.

Compression tests allow the flow stress (true stress) to be obtained for relatively large strains, but low solution accuracy due to the uncertainty of the boundary conditions is a problem. For this reason, it is not easy to obtain true strain-true stress curves from compression tests unless they have all the expertise, experience, and equipment.

The indentation test has some advantages in terms of test location and specimen preparation, but this method is applicable to true strains below 0.3.

Punch tests are also used to find true stress for relatively low strains below 0.3.

Torsional tests give true stress at relatively high strain rates, but no flow stress at high strain at room temperature.

Notch test is inevitably low strain results compared to the tensile test, and has the disadvantage of poor reproducibility.

Most of the methods for obtaining the true strain-true stress curves of metal materials, which are being studied recently, use analytical techniques, particularly finite element analysis techniques. In the tensile test, the true strain rate is the maximum at the minimum cross section of the necking area, and the true strain rate is 1.5 in mild steel. Therefore, by utilizing the deformation behavior of the necking region predicted by the finite element method, it is possible to obtain true or flow stress for high strain. This attempt has been attempted by some researchers, but its use is extremely limited. The reason for this is as follows.

First, the finite element analysis model used in all studies using simple bar as the analysis area requires artificial defects (shape defects, assumption of boundary conditions, strain manipulation, etc.) or the entire tensile test specimen is selected as the analysis area.

Second, generalization is impossible because the approach is not organized.

Third, some methods require deformation information of the specimen.

Fourth, the necking prediction is not accurate and the accuracy of the result is not high.

Accurate prediction of necking phenomena by numerical or analytical methods is required to obtain flow stress at high strain from tensile test results. Various studies have been conducted for the numerical analysis of necking phenomena. However, in all studies that considered the marks between tensile specimens as an analysis domain, artificial defects were added to the analytical model to induce necking, or in one direction perpendicular to the tensile direction. The displacement was restrained. In some cases, the entire tensile specimen is used as the analysis area, but there are many limitations in terms of application of properties. The objective of satisfying the condition of consid ㅸ re as a result of finite element analysis by modeling between the marks of tensile specimens of circular cross-section bar with perfect tensile test analysis model of defect and shear strength. No results have been published.

For the reasons mentioned above, the true material strain-strain curves that actual process design and analysis researchers and technicians are looking for are not provided in the relevant material handbooks and are not provided as a function of the tensile tester. In addition, the plastic mechanical engineering S / W does not provide a material property acquisition module using tensile test information.

The present invention has been made to solve the above problems, so that the elongation-tensile load curve after the necking resulting from the finite element analysis of the tensile test is in agreement with the elongation-tensile load curve obtained by the tensile test. It is an object of the present invention to provide a method of obtaining a true strain-true stress curve for a high strain using a tensile test and a finite element method to obtain a true strain-true stress curve at a high strain.

과 기준 강도계수

을 구하고, 네킹 발생 이후의 연신량 중에서 시험 연신량

(

)를 결정하는 제1단계와;
상기 기준 변형경화지수

과 기준 강도계수

을 아래의 식을 이용하여 산출된 기준 변형률-응력 곡선을 사용하여 인장시험을 해석한 후 대표 변형률

(

) 을 구하는 제2단계와;

(이때,

,

)
반복 개선 작업을 위하여 초기 조건을

,

,

으로 설정하는 제3단계와;

를

로 두고,

,

로 설정하는 제4단계와;

,

,

(

)에 의하여 정의된 재료의 유동응력 정보와 완전 인장시험 해석모델을 이용하여 인장시험을 해석하고,

(

)에서 인장하중의 실험치

와 예측치

를 비교하여 수렴 여부를 확인한 다음, 수렴되지 않았을 경우 해석결과로부터

을 구하여

로 치환하고

(

)를 계산하고, 수렴되었을 경우 반복 개선 작업을 종료하는 제5단계와;

(

)에서

(

)을 선형 보간하여 응력

을 구하고,

에서의 수정된

를 아래와 같이 계산하는 제6단계와;

다시 상기 제4단계로 돌아가서 n회 반복하여 진행하는 제7단계를 포함한 것을 특징으로 한다.
또한, 본 발명에 따른 인장 시험기는, 상기한 바와 같은 인장시험과 유한요소법을 이용한 고 변형률에 대한 진변형률-진응력 곡선의 획득 방법을 연계하여 이용하는 것을 특징으로 한다.The method of obtaining a true strain-true stress curve for high strain using the tensile test and the finite element method according to the present invention for realizing the above object,
Reference strain hardening index of necking point from tensile test result

And reference strength factors

To obtain the test draw amount from the draw amount after the necking occurrence.

(

Determining a first step;
The standard strain hardening index

And reference strength factors

Representative strain after analysis of tensile test using the standard strain-stress curve

(

Obtaining a second step;

(At this time,

,

)
Initial conditions for iterative improvement

,

,

Setting a third step;

To

Leave as,

,

Setting a fourth step;

,

,

(

Analyze the tensile test by using the flow stress information of the material defined by

(

Experimental value of tensile load at

And estimates

Check the convergence by comparing with, and from the analysis result

To obtain

Replace with

(

Calculating a step (5) and ending the iterative improvement work if it converges;

(

)in

(

) By linear interpolation

Obtaining

Modified in

Calculating a sixth step as follows;

It is characterized by including a seventh step of going back to the fourth step and repeating n times.
In addition, the tensile tester according to the present invention is characterized in that it is used in conjunction with the method of obtaining a true strain-true stress curve for high strain using the tensile test as described above and the finite element method.

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As described above, the present invention reduces the difference between the experimental value of the elongation-tensile load and the predicted value by the iterative improvement algorithm based on the general approach for the prediction of the necking occurrence accuracy using the finite element method. A systematic and general method of acquiring curves and a true strain-true stress acquisition system based on it can be constructed.

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.

)-공칭변형률(

) 곡선으로부터 소재의 물성치를 직접 얻을 수 있는 것은 탄성계수

, 항복강도

, 인장강도

, 연신율

등이다. Tensile test results, ie nominal stress of FIG.

) -Nominal strain (

The elastic modulus can be obtained directly from the curve

Yield strength

, The tensile strength

Elongation

And so on.

와 진변형률

는 공칭응력 및 공칭변형률 와 다음의 관계에 있다. Ignoring the volume change during plastic deformation, true stress

And true strain

Is related to the nominal stress and nominal strain.

(2)

(2)

(3)

(3)

Equations (2) and (3) can be applied until necking occurs, so the true stress-strain curves before necking are obtained from equations (2) and (3) under incompressible conditions.

으로 표현하면,The strain hardening index obtained from the true strain at the time of necking is called the reference strain hardening exponent.

In terms of

(4)

(4)

은 네킹 발생 시점에서 공칭변형률이다. 그리고 식 (1)의 진변형률-진응력 곡선이 네킹 발생 때의 진변형률과 진응력을 정확하게 만족하게 함으로써 강도계수

를 구할 수 있다. 이 때의 강도계수를 기준 강도계수(reference strength coefficient)라고 칭하고

으로 표시하면,to be. In this expression

Is the nominal strain at the time of necking. And the true strain-true stress curve of equation (1) satisfies the true strain and true stress at the time of necking.

Can be obtained. The strength coefficient at this time is called a reference strength coefficient

If you mark

(5)

(5)

는 네킹 발생 시점에서 공칭응력을 의미한다.to be. In this expression

Is the nominal stress at the time of necking.

모델(구성방정식)에서

,

을 사용할 경우, 식 (1)의 진변형률-진응력 곡선을 기준 변형률-응력 곡선(reference stress-strain curve)이라 칭한다. 기준 변형률-응력 곡선을 사용하여 인장시험을 해석할 경우, 진변형률이

에 도달하면, 이론적으로 네킹이 발생하게 된다. 네킹 이후의 연신량-인장하중 정보로부터 진변형률-진응력 곡선을 획득하기 위한 목적으로 인장시험을 유한요소해석할 때 이 점을 만족시키는 것은 매우 중요하다. 본 발명에 사용될 유한요소해석 프로그램은 네킹 발생 시점을 공학적으로 정확하게 예측해야 한다. 실제 네킹 발생 시점의 예측 사례를 다음에 설명한다.Hollomon of formula (1)

In Model (Equation)

,

When using, the true strain-true stress curve of Equation (1) is referred to as a reference stress-strain curve. When the tensile test is analyzed using the standard strain-stress curve, the true strain

Is reached, theoretically necking occurs. It is very important to satisfy this point in finite element analysis of tensile tests for the purpose of obtaining true strain-true stress curves from elongation-tensile load information after necking. The finite element analysis program to be used in the present invention should accurately predict the timing of necking. An example of the prediction at the time of actual necking occurrence is described below.

과

는 각각 0.127와 526.35로 계산되며, 도 2에서 진변형률-진응력 곡선을 나타내었다. 도 2에서 실선은 네킹 이전까지를 나타내며, 네킹 이전까지의 결과를 외삽하여 구한 네킹 발생 이후의 진변형률-진응력 곡선을 점선으로 나타내 었다. 따라서 네킹 발생 이후의 정보는 추정치에 불과하다. 비록 네킹 이전까지의 결과는 맞지 않더라도 이에 관한 상세한 값은 인장시험 결과를 식 (2)와 식(3)에 대입하여 구할 수 있다. 앞에서 구한

과

를 식 (1)에 대입하여 인장시험을 유한요소해석하면, 네킹 발생 시점은 공학적 관점에서 정확하게 계산되어야 한다. 이러한 사실은 인장시편의 그립을 포함한 모델에서도 예측이 되며, 접근 방법의 체계화 관점에서는 해석 대상 영역을 표점과 상하대칭면 사이로 하는 것이 바람직하다. 후자의 경우, 양 끝은 무마찰 속도 지정 경계로 간주되어야 한다. 유한요소 해석모델에 인위적 결함을 부과하지 않았으며, 양 끝단에서 표면력의 반경방향 성분이 0인 도 3의 완전 인장시험 해석모델을 사용하였다. 유한요소의 크기를 균일하게 하였다. 해석중 상태변수의 순화로 인한 영향을 배제시키기 위하여 요소망 재구성을 실시하지 않았다.As shown in FIG. 1, since the tensile strength of the necking point in the tensile test selected as an example is 357 MPa and the necking occurred at a nominal strain of 0.135, equations (4) and (5)

and

Are calculated as 0.127 and 526.35, respectively, and the true strain-true stress curve is shown in FIG. 2. In FIG. 2, the solid line represents before the necking, and the true strain-true stress curve after the occurrence of the necking obtained by extrapolating the results until the necking is indicated by the dotted line. Therefore, the information after necking is only an estimate. Although the results before the necking are not correct, the detailed values can be obtained by substituting the tensile test results in equations (2) and (3). Obtained earlier

and

When finite element analysis of the tensile test is made by substituting Eq. (1), the timing of necking should be calculated accurately from an engineering point of view. This fact is also predicted by the model including the grip of tension specimens, and from the viewpoint of systematization of the approach, it is desirable to place the area of analysis between the gauge and the symmetry plane. In the latter case, both ends shall be regarded as frictionless speed specification boundaries. No artificial defects were imposed on the finite element model, and the full tensile test model of FIG. 3 with zero radial force at both ends was used. The size of the finite element was made uniform. The mesh reconstruction was not carried out to exclude the effects of the state variables during the analysis.

As a result of comparing the predicted tensile load according to the elongation in FIG. 4 with the experimental value, the experimental value and the predicted maximum tensile load were 10,950 N and 10,951 N, respectively. mm. Therefore, it can be seen from the engineering point of view that the experimental and analysis results for the necking point are consistent.

As described above, when the aspect ratio of the specimen is above a certain level, the start of the necking is governed by the reference strain hardening index. The reference true strain-true stress curve of FIG. 2 is obtained by emphasizing the occurrence of necking and accurately predicts the timing and maximum load of the necking as described above. It should be emphasized that it is preferable to use the reference strain-stress curve of FIG. 2 to predict the process leading to the occurrence and fracture of the necking, in particular the shape change of the tensile specimen. As shown in FIG. 4, the difference between the experimental value and the finite element prediction value for the tensile test increases as the amount of elongation after the necking occurs, and the strain of the material during forging is usually 10 times larger than the strain at the necking. There is. Therefore, there is a limit in directly using the reference strain-stress curve of FIG. 2 as a material property of the material after the necking, and proper correction of the flow stress is required.

(

,

은 점 데이타의 수)에 대하여 최소단면을 구할 수 있으며, 그 때의 변형률 대표값

의 결정이 가능하다. 그러므로 시험 연신량

에서 측정한 인장하중

와 해석으로 예측한 인장하중

의 차이를

에서의 응력

을 보정하여 최소화시킴으로써 네킹 이후에도 진변형률(

)-진응력(

)의 관계를 구할 수 있다.When necking occurs, the heterogeneity of the true strain distribution increases sharply, especially at the smallest cross section, the true strain reaches its maximum. In the smallest section, the shear force does not work due to the up and down symmetry, and the uniformity of the strain distribution is relatively high in the plastic deformation region. Therefore, the strain that can represent the smallest section can be easily defined from the finite element analysis results. That is, the draw amount of a particular point data, that is, the test draw amount

(

,

Is the minimum cross-section for the number of point data, and the representative strain value at that time

It is possible to decide. Therefore test draw

Tensile load measured in

And predicted tensile loads

The difference

Stress at

By correcting and minimizing the

)-True stress (

) Can be obtained.

을 구하였다. 즉, 다음 식에 의하여 변형률 대표값

을 계산하였다.In the present invention, using the area average method

Was obtained. That is, the representative strain value according to the following equation

Was calculated.

(6)

(6)

는 시험 연신량

에서의 인장시편의 최소단면 또는 최소단면적을 나타내며,

는 진변형률에 해당하는 유효변형률이다.here

Test draw

Represents the minimum or minimum cross-sectional area of the tension specimen at

Is the effective strain corresponding to true strain.

에 대응하는 변형률 대표값이

이고 인장하중에 관한 실험치와 해석치가 각각

와

일 때,

에서의 응력을 보정하였다.In the present invention, the test draw amount

The representative strain value for

The experimental and analysis values for tensile load are

Wow

when,

The stress at was corrected.

에서 정의된 (

,

)를 선형보간하여 진변형률-진응력 곡선으로 사용하였다.Before describing the true strain-true stress curve acquisition method, a representation of the true strain-true stress relationship will be described. The reference strain-stress curve is used as the true strain-true stress curve before the necking occurs, and after the necking occurs, the test draw amount as shown in FIG. 5.

Defined in (

,

) Was used as a true strain-true stress curve by linear interpolation.

에서의 개선된 (

,

)를 구하는 구체적인 절차, 즉 반복개선 알고리즘은 다음과 같다. 다음에서

와

는

번 수정된 변형률과 응력을 각각 의미한다.Test draw

Improved on

,

), The iterative improvement algorithm is as follows. From

Wow

Is

Mean strain and stress, respectively.

과 기준 강도계수

을 구하고, 네킹 발생 이후의 연신량 중에서 시험 연신량

(

)를 결정한다. Step 1 : Standard strain hardening index from tensile test results

And reference strength factors

To obtain the test draw amount from the draw amount after the necking occurrence.

(

Is determined.

에 대한 대표 변형률

(

) 등을 구한다. Step 2 : Test Elongation after Analyzing the Tensile Test Using the Standard Strain-Stress Curve

Representative strain for

(

), Etc.

,

,

으로 설정한다. Step 3 : Initial conditions for repeated improvement

,

,

Set to.

를

로 두고,

,

로 둔다. 반복개선 작업을 실시한다. Step 4 :

To

Leave as,

,

Leave it as. Carry out repetitive improvement work.

,

,

(

) 등에 의하여 정의된 재료의 유동응력 정보와 완전 인장시험 해석모델을 이용하여 인장시험을 해석하고

(

)에서 인장하중의 실험치와 예측치를 비교하여 수렴 여부를 확인하며, 수렴되지 않았을 경우 해석결과로부터

을 구하여

로 치환하고

(

)를 계산한다. 수렴되었을 경우, 관련 정보를 출력하고 반복개선 작업을 중단한다. Step 5 :

,

,

(

Analyze tensile test using flow stress information of material and full tensile test model

(

), Compare the experimental value and the predicted value of the tensile load and check the convergence.

To obtain

Replace with

(

Calculate If it has converged, it prints out relevant information and stops repetitive work.

(

)에서

(

)을 선형보간하여 응력

을 구하고,

에서의 수정된

를 다음 식에 의하여 같이 구한다. Step 6 :

(

)in

(

) By linear interpolation

Obtaining

Modified in

Is obtained by the following equation.

(7)

(7)

Step 7 : Go to step 4.

에서 전술한 방식으로 1차 보정된 진변형률-진응력 곡선을 기준 진변형률-진응력 곡선과 함께 도 5에 나타내었으며, 계산 과정을 아래의 표 1에 정리하였다.Each test draw amount

The true strain-true stress curve first corrected in the above-described manner is shown in FIG. 5 together with the reference true strain-true stress curve, and the calculation process is summarized in Table 1 below.

TABLE 1

i

(N)

(N)

One 0.128 405.34 10950 10951 405.34 0.00% 2 0.209 431.39 10867 10820 433.24 0.43% 3 0.279 447.48 10799 10611 455.4 1.74% 4 0.385 466.28 10646 10194 486.94 4.25% 5 0.486 480.29 10448 9741 515.16 6.77% 6 0.608 494.14 10170 9155 548.94 9.98% 7 0.779 509.96 9697 8308 595.23 14.32% 8 0.977 524.77 9119 7341 651.87 19.50% 9 1.203 538.86 8429 6282 723.04 25.47% 10 1.390 548.84 7850 5472 787.37 30.29%

In order to investigate the validity of the first modified true strain-true stress curve of FIG. 5, an analysis of the tensile test was performed, and the analysis results of FIG. 6 were compared with the results predicted using the experimental results and the reference strain-stress curve. It was. As a result of the comparison of FIG. 6, it can be seen that the prediction accuracy of the tensile load is greatly improved by the first-modified true strain-true stress curve. The error tends to increase as the draw amount increases, but the maximum value stays below 474N (6.04%). Therefore, the 30.29% error was improved to 6.04% by the first improvement.

Although the material used in the present invention has a relatively large elongation, it showed an accuracy of about 94% in one calibration operation. Of course, a more reliable result can be obtained by repeating the calibration process, considering the true strain-true stress curve as already described in the approach, as a new criterion. 7 and 8 show strain-stress curves modified by repeated calculations of two, three and four times, and an elongation-tensile load curve predicted using the same.

Table 2 shows the change in the maximum error of the predicted value compared to the experimental value of the draw-tensile load curve according to the number of repeated improvements.

TABLE 2

Number of iterations Maximum error 0 30.29% One 6.04% 2 3.96% 3 0.89% 4 0.38%

As shown in this table, it can be seen that the convergence characteristic is very good, and the result of the maximum error of 0.38% or less was obtained through four iteration calculations, that is, the engineering correct answer was obtained.

Based on these results, it is possible to develop a true strain-true stress curve acquisition function and system in connection with a tensile tester as shown in FIG. 9, and can be used as a material information acquisition module of engineering analysis software as shown in FIG. 10. .

And the accurate analysis result of tensile test using the obtained true strain-stress curve can replace the shape change of tensile test specimen, and it is possible to develop engineering analysis S / W for the purpose of grasping the material's internal deformation characteristics and fracture phenomenon. Do.

On the other hand, fitting the true strain-true stress curve obtained based on the example applied in the present invention, after necking, it was found that the following mathematical model is most suitable.

(8)

(8)

The method of obtaining the true strain-true stress curve for high strain using the tensile test and the finite element method according to the present invention as described above has the following effects.

In general, the strain rate of the material during the plastic processing process with a large deformation is more than 1.0, whereas the necking of the steel occurs at a strain rate of less than 0.15. Therefore, the flow stress obtained by extrapolating the results before the necking obtained in the tensile test is not suitable for the purpose of analyzing the high strain forging process.

However, using the method used in the present invention as described above, it is possible to obtain a true strain-true stress curve of high accuracy at a high strain rate (the degree is increased as the number of improvement iterations is increased).

Since the approach in the present invention is very systematic and generalized, it can be developed as an independent module with a finite element analysis program, that is, a finite element analysis program (including material property acquisition module) dedicated to tensile test linkage, and can be mounted on a tensile tester. This gives the user a very fast and accurate true strain-true stress curve.

In addition, the present invention provides a researcher, such as fracture mechanics, more accurate deformation behavior at the necking just before the break, it is possible to contribute significantly to the industrial development associated with the relevant science as well as related technologies.

Claims (6)

Reference strain hardening index of necking point from tensile test result

And reference strength factors

To obtain the test draw amount from the draw amount after the necking occurrence.

(

Determining a first step; The standard strain hardening index

And reference strength factors

Representative strain after analysis of tensile test using the standard strain-stress curve

(

Obtaining a second step;

(At this time,

,

) Initial conditions for iterative improvement

,

,

Setting a third step;

To

Leave as,

,

Setting a fourth step;

,

,

(

Analyze the tensile test by using the flow stress information of the material defined by

(

Experimental value of tensile load at

And estimates

Check the convergence by comparing with, and from the analysis result

To obtain

Replace with

(

Calculating a step (5) and ending the iterative improvement work if it converges;

(

)in

(

) By linear interpolation

Obtaining

Modified in

Calculating a sixth step as follows;

A method of obtaining a true strain-true stress curve for high strain using a tensile test and a finite element method, comprising a seventh step of returning to the fourth step and repeating n times. A tensile tester, which is used in connection with a method for obtaining a true strain-true stress curve for high strain using the tensile test according to claim 1 and the finite element method. delete delete delete delete

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