JPWO2015037067A1 - Ductile fracture evaluation system and ductile fracture evaluation method - Google Patents

Abstract

Provided is a ductile fracture evaluation system for a structure having a part of a structure or a defect having an arbitrary shape. The present invention includes an input unit, a first storage unit that stores a load and displacement relationship that is a test result of a first test piece, and a load that is a test result of a second test test piece having a shape different from that of the first test piece. And a second storage unit for storing the displacement relationship, and a first numerical analysis unit for obtaining a plurality of load and displacement relationships corresponding to the material constants received from the input unit from a numerical analysis result simulating the test on the first test piece A second numerical analysis unit for obtaining a plurality of loads and displacement relationships corresponding to the material constants from a numerical analysis result simulating a test on the second test piece, and a load stored in the first and second storage units, and From the displacement relationship and the load and displacement relationship, which is a numerical analysis simulating the tests in the first and second numerical analysis units, the material constants of the constitutive equation expressing the fracture are expressed by mathematical statistical processing using the joint probability. Specially identified To.

Description

  The present invention relates to a ductile fracture evaluation system and a ductile fracture evaluation method for evaluating ductile fracture, which is one of fracture modes of a structural material, using numerical analysis.

  Ultimate strength evaluation to determine the breaking load and breaking mode when metal materials constituting various structures such as power plants, chemical plants, transportation equipment and construction equipment are damaged by load is a soundness evaluation at the time of severe event occurrence It is important for the evaluation of actual strength. Ductile fracture is one of the failure modes of structural metal materials excluding high carbon steel and cast iron. To evaluate the ultimate strength of practical structural materials, it is necessary to calculate the failure load due to ductile failure and to evaluate the failure mode. Become. For example, a technique described in Patent Document 1 is known in connection with calculation of the fracture load of a metal material.

  Patent Document 1 discloses the critical interface stress at the fracture limit of the material used, which was measured by performing a destructive test on the material subjected to tensile load from a uniaxial direction or tensile load and compressive load with different load directions. The maximum interfacial stress at the time of fracture of the material used was obtained by numerical analysis performed based on the machining conditions of the above, and the maximum interfacial stress at the time of fracture was compared with the limit interfacial stress at the fracture limit. It is described that the above-mentioned machining conditions are derived so as to be smaller than the critical interface stress, and the machining conditions for the same material used are derived.

  On the other hand, as a method of evaluating ductile fracture by numerical analysis using a constitutive equation expressing fracture, plastic deformation and fracture of a material proceed as a result of the generation and growth of microvoids originating from microscopic defects inside the material. An evaluation method using the modified Gurson model (hereinafter referred to as GTN model: Gurson Tvergaard Needleman model) is known. There are a plurality of material constants in the GTN model, and there is a technique described in Non-Patent Document 1, for example, in connection with identification of material constants of constitutive equations.

JP 2005-283130 A

Tomohiro Noguchi and two others, “Identification of Gurson material property values from simple experiments”, Proceedings of the Japan Society of Mechanical Engineers, Vol.69, No.681 (2003), pp.13-23

  In the technique described in Patent Document 1, an evaluation method in the case where a structure or a defect having an arbitrary shape exists is not disclosed, and only a thin plate is targeted. Further, although it is described that the maximum interface stress is obtained by numerical analysis, details thereof are not disclosed. Therefore, it is difficult to perform ductile fracture evaluation of an arbitrarily shaped structure depending on the technique described in Patent Document 1.

  In the ductile fracture evaluation using the material constant identification method of the GTN model described in Non-Patent Document 1, the past literature values are adopted for many of the material constants. In addition, there are two specimen shapes, but in order to identify material constants by independent mathematical statistical processing, the ductile fracture evaluation of arbitrarily shaped structures, including the case where the stress triaxiality is different, depends on the situation. There is also room for improvement in the identification method because it may be necessary to identify the material constant.

  An object of the present invention is to provide a ductile fracture evaluation system that evaluates the ultimate strength associated with ductile fracture of an arbitrarily shaped structure that undergoes ductile fracture in response to such problems.

  The present invention includes an input unit, a first storage unit that stores a load and displacement relationship that is a test result of the first test piece, a load that is a test result of a second test piece having a shape different from that of the first test piece, and A plurality of material constants received from the input unit from a numerical analysis result using a finite element analysis that implements a constitutive expression that represents a fracture that simulates a test in the first test piece, and a second storage unit that stores a displacement relationship From the numerical analysis results using the first numerical analysis unit for obtaining a plurality of load and displacement relations corresponding to the above and the finite element analysis that implements a constitutive expression that represents a fracture simulating the test in the second test piece Simulates the second numerical analysis unit for obtaining a plurality of load and displacement relationships corresponding to material constants, the load and displacement relationship stored in the first and second storage units, and the test in the first and second numerical analysis units Load that is numerical analysis And a fine displacement relationship, by mathematical statistical processing using the joint probability, and identifying the constitutive equation of the material constants that represent the fracture.

  ADVANTAGE OF THE INVENTION According to this invention, the ductile fracture evaluation system which evaluates the ultimate strength accompanying the ductile fracture of the arbitrarily-shaped structure to which a ductile fracture can be provided.

It is a schematic diagram of the destruction progress process in a GTN model. It is a block diagram which shows the ductile fracture evaluation system of Example 1. It is a flowchart which shows the material constant identification method of a ductile fracture constitutive formula. 1 is a schematic diagram of a smooth round bar test piece used in Example 1. FIG. 2 is a schematic diagram of a round bar test piece with a notch used in Example 1. FIG. It is the stress-plastic strain relationship obtained by the tensile test of the smooth round bar test piece of Example 1. This is an analysis model using axisymmetric elements used in numerical simulation of test simulation. It is a material constant list used for the numerical analysis of the test simulation with respect to material constant identification regarding void generation. It is the numerical analysis result of the test simulation of the combination of 27 material constants regarding void generation. This is a result of inverse analysis of P (x | y ₁ , y ₂ ) when ε _N = 0.00082. It is a material constant list used for the numerical analysis of the test simulation with respect to the material constant identification regarding a correction coefficient. It is the numerical analysis result of the test simulation of the combination of nine material constants regarding the correction coefficient. It is an inverse analysis result of P (x | y ₁ , y ₂ ) regarding the correction coefficient. It is a material constant list used for the numerical analysis of the test simulation with respect to the material constant identification regarding a correction coefficient. It is the numerical-analysis result of the test simulation of the combination of nine material constants regarding damage. It is a figure of the comparison of the numerical analysis result of a test simulation, and a test result in the identified material constant. It is a block diagram which shows the ductile fracture evaluation system in Example 2. FIG. It is explanatory drawing of the computer system which mounted this invention.

  Embodiments of the present invention will be described below with reference to the drawings.

  The ductile fracture evaluation system of the present invention obtains a fracture load and a fracture mode by numerical analysis when materials constituting various structures undergo a ductile fracture. In addition, in the case where a part of the structure has a crack-like defect, it is possible to evaluate the fracture load and the fracture mode. That is, as shown in FIG. 1, when the material 1 constituting the structure is pulled with a load 3 equal to or greater than the breaking load, the microvoids 2 (local thinning and defects) develop and the structural material is destroyed. The system of the present invention for evaluating such fracture behavior by numerical analysis is applied to the evaluation of a structure that is supposed to be ductile fracture. Determining the fracture load and behavior of a structure is important for evaluating the soundness of a severe event and evaluating the actual strength of the structure.

  In the ductile fracture evaluation system, a numerical analysis simulating a test is performed to determine the fracture load and fracture mode. Generally, finite element analysis (hereinafter referred to as FEA) is used for numerical simulation of test simulation. In general-purpose FEA codes, constitutive expressions that express the destruction of some structural materials are generally mounted. In the present invention, a case will be described as an example in which a GTN model in which destruction progresses due to generation and growth of microvoids.

  Next, Equation 1 shows the yield function Φ of the GTN model, which is a ductile fracture constitutive equation implemented in the numerical simulation unit of the test simulation in the processing unit in the ductile fracture evaluation system of the present embodiment.

ここで，σ_eqはボイドの影響を含んだ巨視的な相当応力，ｐは静水圧応力，σ_yは母材の相当応力である。ｑ₁，ｑ₂およびｑ₃はTvergaardおよびNeedlemanによって導入された補正係数である。一般的にｑ₃＝ｑ₁ ²で表わされる。ｆ^*はボイドを含む材料がボイドの合体によって急速に応力負担能力を失う現象を表現するために，Tvergaardにより提案されたパラメータであり，ボイド体積分率ｆの関数である。なお，ＧＴＮモデルにおいてｆ＝０とした場合は，材料内部にボイドが存在しないことを意味し，等方均質のMisesの降伏条件と一致する。

Here, σ _eq is a macroscopic equivalent stress including the influence of voids, p is a hydrostatic pressure stress, and σ _y is an equivalent stress of the base material. q ₁ , q ₂ and q ₃ are correction factors introduced by Tvergaard and Needleman. Generally, q ₃ = q ₁ ² . f ^* is a parameter proposed by Tvergaard in order to express a phenomenon in which a material containing voids rapidly loses the stress bearing ability due to coalescence of voids, and is a function of the void volume fraction f. Note that when f = 0 in the GTN model, it means that no void exists in the material, which is consistent with the isotropic homogeneous Mises yield condition.

ここで初期ボイド体積分率ｆ，母材の体積分率ｒとすると，ｆ＝０（ｒ＝1）は，材料にボイドが存在しないことを意味する。このモデルは，一般にｆ＜0.1（ｒ＞0.9）の場合にのみ妥当な結果を与える。

Here, assuming that the initial void volume fraction f and the base material volume fraction r, f = 0 (r = 1) means that no void exists in the material. This model generally gives reasonable results only when f <0.1 (r> 0.9).

In Equation 2, f _C is the void volume fraction when the voids start to coalesce rapidly, and is called the critical void fraction. _{F F} is the void volume fraction when the material completely loses the stress bearing ability and is called the critical void fraction. When the void volume fraction f exceeds the critical void fraction f _C and is less than the critical void fraction f _F (f _C <f <f _F ), material fracture such as void coalescence is modeled. In addition, when the void volume fraction f exceeds the limit void fraction f _F (f ≧ f _F ), it can be set so that the material is completely destroyed and the element on the analysis model is deleted.

は完全に材料が破壊した時点におけるｆ^*の値であり，以下の式４により表わされる。なお，汎用ＦＥＡコードの種類によっては，以下の式５で表わされることもある。

Is the value of f ^* when the material is completely destroyed, and is expressed by the following equation (4). Depending on the type of general-purpose FEA code, it may be expressed by the following formula 5.

材料中のボイド体積分率は，ボイドの発生および成長によって変化する。すなわち，以下の式６のようにボイド体積分率の時間微分

The void volume fraction in the material changes with the generation and growth of voids. That is, the time derivative of the void volume fraction as shown in Equation 6 below.

は，ボイドの発生および成長によるボイド体積分率の変化

Is the change in void volume fraction due to void generation and growth

および

and

の和で表わされる。

It is expressed as the sum of

ここで，ボイドの成長によるボイド体積率の変化

Here, change of void volume fraction due to void growth

は，塑性変形の非圧縮性の仮定から母材の塑性体積ひずみ増分

Is the plastic volume strain increment of the base metal from the assumption of incompressibility of plastic deformation.

を用いて以下の式７により表わされる。

Is expressed by the following equation (7).

また，ボイドの発生によるボイド体積率の変化

In addition, the change in void volume fraction due to the generation of voids

は，母材に生じる微視的な相当塑性ひずみ増分

Is the microscopic equivalent plastic strain increment occurring in the base metal

を用いて以下の式８により表わされる。

Is represented by the following formula 8.

ここで

here

式９は一次元の正規分布であり，平均ε_N，標準偏差がｓ_Nの形の確率密度関数である。式９において，ボイドが発生する塑性ひずみは，平均値がε_N，標準偏差がｓ_Nおよびボイド発生の核の体積分率がｆ_Nによる正規分布に従うとしている。

Equation 9 is a one-dimensional normal distribution, which is a probability density function having a mean ε _N and a standard deviation s _N. In Equation 9, the plastic strain in which voids are generated follows a normal distribution with an average value of ε _N , a standard deviation of s _N, and a volume fraction of void generation nuclei of f _N.

The material constants in the GTN model shown in Equation 1 to Equation 9 are q ₁ , q ₂ , q ₃ , r, f _F , f _C , ε _N , s _N and f _N. If these material constants are obtained, it is possible to evaluate the ultimate strength associated with the ductile fracture of an arbitrarily shaped structure that undergoes ductile fracture. The identification method of these material constants will be described next. It should be noted that the numerical analysis of the test simulation by FEA requires the Young's modulus E, Poisson's ratio ν, yield stress σ _y and stress-strain relationship of the material. Find from the result.

  It describes about the identification method of the material constant used for the ductile fracture constitutive formula of this invention. This processing is calculated by a mathematical statistical processing unit. In this embodiment, the material constant used for the GTN model is identified from the static tensile test results of a plurality of test pieces having different shapes including a smooth round bar test piece. The load value obtained from the tensile test is defined as a measurement amount y, and the material constant of the GTN model is defined as x. At this time, if h (x) is a load obtained by numerical analysis simulating a tensile test, the relationship between the measured quantity and the system state variable is generally expressed as in the following equation (10).

式１０において，ｙはｍ次元測定量ベクトル，ｘが同定すべきシステムの状態を表すｎ次元ベクトル，ｈは問題を表現するｍ次元の非線形ベクトル関数，νは測定の誤差を表すｍ次元確率変数ベクトルである。νはｘに関して独立であり，式１１で表わされる正規分布に従うと仮定する。式１１や式１２は多次元の正規分布である。

式１１において

In Equation 10, y is an m-dimensional measurement quantity vector, x is an n-dimensional vector representing the state of the system to be identified, h is an m-dimensional nonlinear vector function representing the problem, and ν is an m-dimensional random variable representing a measurement error. Is a vector. It is assumed that ν is independent with respect to x and follows a normal distribution represented by Equation 11. Expressions 11 and 12 are multidimensional normal distributions.

In Equation 11

はνの平均値，Ｒはνの共分散行列を示す。

Is an average value of ν, and R is a covariance matrix of ν.

  Assuming that the stochastic nature of the material constant x to be identified is given by a normal distribution,

，共分散行列がＭで与えられるとすると，ｘの確率密度関数（事前確率）は以下の式１２で表わされる。

If the covariance matrix is given by M, the probability density function (prior probability) of x is expressed by the following Equation 12.

材料定数ｘが与えられた時のｙの条件付き確率密度分布（尤度）は，以下の式１３で表わされる。

The conditional probability density distribution (likelihood) of y when the material constant x is given is expressed by the following Expression 13.

ただし

However,

このときのｙの条件付き確率密度分布（周辺尤度）は，以下の式１５で表わされる。

The conditional probability density distribution (marginal likelihood) of y at this time is expressed by the following Expression 15.

ここでｗはｍ次元ベクトル，Ｓは期待値を表わす行列であり，式１６および式１７で表わされる。

Here, w is an m-dimensional vector, and S is a matrix that represents an expected value, which is expressed by Expression 16 and Expression 17.

式１７におけるＥは期待値を表す。ここで，

E in Equation 17 represents an expected value. here,

で表わされるベイズの定理を用いると，測定量ｙが与えられた時のｘの条件付き確率密度分布関数Ｐ（ｘ｜ｙ）は，以下の式１９のように表わされる。

When the measured quantity y is given, the conditional probability density distribution function P (x | y) of x when the measured quantity y is given is expressed as the following Expression 19.

今，応力三軸度の異なる２つの試験片の試験結果，すなわち測定量ｙ₁およびｙ₂と，材料定数ｘを用いて試験を模擬した解析結果が存在すると，同時確率の観点から式１８および式１９は以下のように書き換えられる。

Now, if there are test results of two specimens with different stress triaxiality, that is, analysis results simulating the test using the measured quantities y ₁ and y ₂ and the material constant x, Equation 18 and Equation 19 can be rewritten as follows:

すなわち

Ie

以上により得られたＰ（ｘ｜ｙ₁，ｙ₂）が最大値を取る時，ｈ（ｘ）とｙ₁およびｙ₂の差が最も小さくなる。すなわち，解析結果と試験結果が最もよく一致することになる。It becomes. here,

When P (x | y ₁ , y ₂ ) obtained as described above takes the maximum value, the difference between h (x) and y ₁ and y ₂ becomes the smallest. In other words, the analysis results and test results are the best match.

Thus, h (x) is rewritten as a function with the components (q ₁ , q ₂ , q ₃ ), (f _F , f _C ) and (ε _N , s _N , f _N ) as arguments as follows: . In the present embodiment, and q ₃ = q ₁ ^2.

In order to determine the value of x when P (x | y ₁ , y ₂ ) takes the maximum value, (q ₁ , q ₂ ), (f _F , f _C ) and (ε _N , s _N , f _N ) To perform numerical analysis simulating a tensile test and obtain h (q ₁ , q ₂ ), h (f _F , f _C ) and h (ε _N , s _N , f _N ). In this case, the number of combinations is enormous, and the computation time is enormous. Therefore, in this embodiment, numerical analysis is performed on some combinations of (q ₁ , q ₂ ), (f _F , f _C ) and (ε _N , s _N , f _N ), and h ( q ₁ , q ₂ ), h (f _F , f _C ) and h (ε _N , s _N , f _N ) are interpolated using a second-order polynomial shown in the following Expression 24 or 25 to obtain h (Q ₁ , q ₂ ), h (f _F , f _C ) and h (ε _N , s _N , f _N ) are defined as continuous functions.
If there are two arguments

また，引数が３つの場合は以下の多項式で補間する。

When there are three arguments, interpolation is performed using the following polynomial.

式２４において，ｎ次元ベクトルの成分（X₁，X₂）は（ｑ₁，ｑ₂），（ｆ_F，ｆ_C）を表わす。また式２５において（X₁，X₂，X₃）は（ε_N，ｓ_N，ｆ_N）を表わす。Ｃ_i（ｉ＝０，１，２）は定数であり，最小二乗法によってｈ（Ｘ₁，Ｘ₂）もしくはｈ（Ｘ₁，Ｘ₂，Ｘ₃）の値が数値解析により得られた離散データに最もよく一致するように決定する。任意の値の範囲内で材料定数の引数が２つの場合は３水準×３水準（９通り），引数が３つの場合は３水準×３水準×３水準（２７通り）を格子状に設定する。例えば，引数が２つである（ｑ₁，ｑ₂）の場合，Ｘ₁およびＸ₂がそれぞれｑ₁およびｑ₂に該当するため，ｑ₁を３水準およびｑ₂を３水準設定して，これら（ｑ₁，ｑ₂）に対するｈ（ｑ₁，ｑ₂）の値，すなわち荷重を解析により求める。同様に（ｆ_F，ｆ_C）および（ε_N，ｓ_N，ｆ_N）に対するｈ（ｆ_F，ｆ_C）およびｈ（ε_N，ｓ_N，ｆ_N）の離散データを求める。求められた離散データを式２４もしくは式２５により補間して，それぞれを連続関数として定義する。式２１および式２２に試験結果および数値解析結果を代入して，Ｐ（ｘ｜ｙ₁，ｙ₂）が最大値を取る時の材料定数を同定値として採用する。なお，ｆ（ｑ₁，ｑ₂）およびｆ（ｆ_F，ｆ_C）に入力する任意範囲の材料定数は，０〜１に正規化する。正規化した材料定数を０。０１刻みでｈ（ｘ₁，ｘ₂）に入力して求めた荷重の推定値は，９通りの解析を実施すると１０，２０１通りの結果が得られる。同様に，ｈ（ε_N，ｓ_N，ｆ_N）の場合，２７通りの解析を実施すると1,030,301通りの結果が得られる。

In Equation 24, the components (X ₁ , X ₂ ) of the n-dimensional vector represent (q ₁ , q ₂ ), (f _F , f _C ). In Expression 25, (X ₁ , X ₂ , X ₃ ) represents (ε _N , s _N , f _N ). C _i (i = 0, 1, 2) is a constant, and the value of h (X ₁ , X ₂ ) or h (X ₁ , X ₂ , X ₃ ) is obtained by numerical analysis by the least square method. Decide to best match the data. Set 3 levels x 3 levels (9 ways) when there are 2 material constant arguments within the range of arbitrary values, and 3 levels x 3 levels x 3 levels (27 ways) when there are 3 arguments. . For example, if there are two arguments (q ₁ , q ₂ ), X ₁ and X ₂ correspond to q ₁ and q ₂ respectively, so q ₁ is set to 3 levels and q ₂ is set to 3 levels, the values of these (q _1, q ₂₎ for h (q _1, q _2), i.e. determined by analyzing the load. Similarly (f _F, f _C) and _{(ε N, s N, f} N) h for (f _F, f _C) and _{h (ε N, s N,} f N) obtaining the discrete data. The obtained discrete data is interpolated by Expression 24 or 25, and each is defined as a continuous function. Substituting the test results and the numerical analysis results into Equation 21 and Equation 22, the material constant when P (x | y ₁ , y ₂ ) takes the maximum value is adopted as the identification value. Note that the material constants in an arbitrary range input to f (q ₁ , q ₂ ) and f (f _F , f _C ) are normalized to 0 to 1. The estimated load values obtained by inputting the normalized material constants into h (x ₁ , x ₂ ) in increments of 0.01 will yield 10,201 results when nine ways of analysis are performed. Similarly, in the case of h (ε _N , s _N , f _N ), if 27 kinds of analysis are performed, 1,030,301 kinds of results are obtained.

  Hereinafter, this embodiment will be described using specific examples.

FIG. 2 is a block diagram showing the ductile fracture evaluation system 50 of this embodiment. Input section 51 for inputting various set values, smooth round bar test piece measurement result storage section 52 for storing measurement results of smooth round bar test pieces, and notches for storing measurement results of notched round bar test pieces A round bar test piece measurement result storage unit 53, a processing unit 54 for performing various calculations, and a display unit 66 for displaying the results are included. The processing unit 54 includes a Young's modulus for obtaining a Young's modulus and a yield stress from the measurement result of the smooth round bar test piece, and a stress for obtaining a relationship between the stress and the strain from the measurement result of the yield stress analysis unit 55 and the smooth round bar test piece. Strain relation analysis unit 56, ε _N , s _N , f _N test simulation numerical analysis unit 57 for obtaining a load-displacement relationship from a numerical analysis simulating a tensile test of a smooth round bar specimen, and a round bar with a notch Ε _N , s _N , f _N test simulation unit 58 for obtaining the load-displacement relationship from numerical analysis simulating the tensile test of the test piece, and each setting of ε _N , s _N , f _N as material constants Analysis results simulating a tensile test of a smooth round bar test piece and a notched round bar test piece in a numerical analysis unit that accepts input of values and inputs a combination of received values of ε _N , s _N , and f _N And smooth round bar specimens and notched round bar specimens The mathematical-statistical processing unit (ε _N , s _N , f _N ) 59 for finding the matching ε _N , s _N , f _N combination and the numerical analysis simulating the tensile test of the smooth round bar specimen show the load-displacement relationship. q _1, q and test numerical analysis portion 60 of the simulated _2, the load from the numerical analysis simulating the tensile test notched round specimens for determining - determining the displacement relationship q _1, numerical analysis of the test simulated q ₂ 61 and accepts input of each set value of q ₁ and q ₂ which are material constants, and receives a combination of received q ₁ and q ₂ numerical values. Mathematical statistical processing unit (q ₁₎ for finding a combination of q ₁ and q ₂ that best matches the analysis result simulating the tensile test of a round bar test piece and the test result of a smooth round bar test piece and a notched round bar test piece , Q ₂ ) 62 and numerical analysis simulating a tensile test of a smooth round bar specimen, load-displacement relationship _{F F} and f _C test simulation numerical analysis unit 63, and f _F and f _C test simulation numerical analysis to obtain a load-displacement relationship from a numerical analysis simulating a tensile test of a notched round bar test piece The smooth round bar test piece and the notch in the numerical analysis unit that accepts the input of each set value of f _F and f _C that is the unit 64 and the material constants and receives the combination of the received values of f _F and f _C Mathematical Statistical Processing Unit (f) for finding a combination of f _F and f _C that best matches the analysis result of a tensile test of a round bar test piece with a smooth round bar test piece and the test result of a round bar test piece with a notch _F , f _C ) 65.

Here, find the material constant that best matches the analysis result of the tensile test of the smooth round bar test piece and the notched round bar test piece with the test result of the smooth round bar test piece and the notched round bar test piece. This is called the mathematical statistical method considering the joint probability because it is necessary to satisfy the analysis result and the measurement result of the two specimens at the same time, and the above calculation is performed with the maximum P (x | y ₁ , y ₂ ). This is a method for obtaining a value when taking a value.

  FIG. 3 shows a flowchart of material constant identification. In this embodiment, a smooth round bar test piece and a notched round bar test piece are used for material constant identification. FIG. 4 shows a smooth round bar tensile test piece 4. FIG. 5 shows a round bar tensile test piece 5 with an R1.5 mm notch. It has a notch 6 of R1.5 mm.

In the numerical analysis, the Young's modulus E, Poisson's ratio ν, yield stress σ _y and stress-strain relationship of the material are necessary. The properties of these materials are preferably determined from the results of a tensile test using a smooth round bar specimen. In addition to the tensile test, it is possible to determine these characteristics from a cylindrical compression test, but in this embodiment, the tensile test result is used. The Young's modulus E, Poisson's ratio ν, and yield stress σ _y are also defined in the Japanese Industrial Standards (JIS: Japanese Industrial Standards). The Young's modulus is determined from the proportional limit of the stress-strain relationship obtained from the axial tensile test. The Poisson's ratio is 0.3, which is generally used for practical materials. If the yield stress is unclear, such as stainless steel or aluminum alloy, 0.2% proof stress σ _0.2 may be used instead of yield stress σ _y . The stress-strain relationship decreases with the generation, growth and coalescence of voids inside the material (the yield surface becomes smaller). That is, the relationship between stress and strain used in the GTN model is shown in FIG. As shown in the figure, in order to take account of the decrease in stress due to the generation of vacancies, the stress for the same strain must be set larger than the relationship between the stress and strain obtained in the test. In FIG. 6, 11 is the nominal stress-nominal plastic strain relationship of the smooth round bar test piece, 12 is the true stress-logarithmic plastic strain relationship of the smooth round bar test piece, and 13 is the Ludwik type hardening law. In this example, the stress-plastic strain relationship after yielding in step S202 was the logarithmic plastic strain of 5. The material constant of the Ludwik type hardening rule was determined from the results up to 0% and used for numerical analysis. Formula 26 shows the Ludwik-type curing rule.

ここで，σ_yは降伏応力，ε^plは塑性ひずみ，Ｃおよびｎは材料定数を示す。本実施例では，Ludwik型硬化則を用いるが応力−ひずみ関係に用いる硬化則はこの限りではない。ここまでの計算により，引張試験を模擬した解析における基本的な変形挙動は評価できるが，最大応力を超えたひずみが加わった場合の応力低下挙動については評価が出来ない。そこで本発明ではGTNモデルを用いて，材料が損傷に至るまでの応力−ひずみ関係を求められるようにする。

Here, σ _y is the yield stress, ε ^pl is the plastic strain, and C and n are the material constants. In this embodiment, the Ludwik type hardening rule is used, but the hardening rule used for the stress-strain relationship is not limited to this. Based on the calculations so far, the basic deformation behavior in an analysis simulating a tensile test can be evaluated, but the stress reduction behavior when a strain exceeding the maximum stress is applied cannot be evaluated. Therefore, in the present invention, the GTN model is used to obtain the stress-strain relationship until the material is damaged.

The material constants ε _N , s _N and f _N relating to the void generation of the GTN model used for the numerical analysis of the ductile fracture evaluation system are identified. First, in step S203, the critical void rate f _C and the critical void rate f _F of material constants related to fracture are set to sufficiently large values so as not to affect other material constants. Further, correction values q ₁ , q ₂ and q ₃ are set to literature values. FIG. 7 is a list of material constants in the numerical simulation of the test simulation. In step S204 and step S205, Young's modulus, Poisson's ratio, yield stress, stress-strain relationship, material properties and ε _N , s _N , f _N shown in FIG. ) Is subjected to numerical analysis simulating a tensile test using FEA. In this embodiment, an axially symmetric element is used for numerical analysis, but numerical analysis using a three-dimensional element may be used. FIG. 7 shows an analysis model used for numerical simulation of test simulation. FIG. 7A shows a smooth round bar test piece, and FIG. 7B shows an R1.5 mm notched round bar tensile test piece. The results of numerical analysis simulating a tensile test for 27 combinations of material constants are shown in FIG. FIG. 9A shows the load-displacement relationship of the smooth round bar test piece, and FIG. 9B shows the load-displacement relationship of the R1.5 mm notched round bar tensile test. FIG. 9 also shows the measurement result 14 of the actual smooth round bar test piece and the measurement result 15 of the notched round bar test piece. In step S206, the value of h (ε _N , s _N , f _N ) is obtained as a continuous function by interpolating the load obtained by the analysis using Equation 25. The measurement result and h (ε _N , s _N , f _N ) are substituted into Equations 21 and 22, and the material constant when P (x | y ₁ , y ₂ ) takes the maximum value is adopted as the identification value. . That is, the material constant is identified using an inverse analysis method considering the joint probability. If no peak appears, review the 27 combinations. FIG. 10 shows the result of P (x | y ₁ , y ₂ ) when normalized ε _N is 0.08. The point showing the maximum value is adopted as the identification value of the material constant. Here, ε _N, s _N and f _N for P | adopted _{(x y 1, y 2)} ε from the peak value showing the maximum value _{N = 0.00082, s N = 0.080} , a f _N = 0.064 as identified values To do.

Next, the correction coefficients q ₁ , q ₂ and q ₃ are identified. FIG. 11 shows a list of material constants in the numerical simulation of the test simulation, including the material constants related to the generation of voids. The range of material constants is narrow because the correction factor is not expected to differ greatly from the literature value. In steps S207 and S208, numerical analysis simulating a tensile test for 3 levels × 3 levels (9 patterns) is performed for q ₁ and q ₂ . FIG. 12 shows the results of numerical analysis simulating a tensile test for nine combinations. FIG. 12A shows the load-displacement relationship of the smooth round bar test piece, and FIG. 12B shows the load-displacement relationship of the R1.5 mm notched round bar tensile test. FIG. 12 also shows the measurement result 16 of an actual smooth round bar test piece and the measurement result 17 of a round bar test piece with a notch. In step S209, the load obtained by the analysis is interpolated by Expression 24, whereby the value of h (q ₁ , q ₂ ) is obtained as a continuous function. By substituting h (q ₁ , q ₂ ) into Equations 21 and 22, the distribution of P (x | y ₁ , y ₂ ) is obtained. FIG. 13 shows the result of P (x | y ₁ , y ₂ ) using the test results and the numerical analysis results. The point showing the maximum value is adopted as the identification value of the material constant. That is, the material constant is identified using an inverse analysis method considering the joint probability. Here, the q ₁ and _{q 2 P (x | y 1} , y 2) is q ₁ = 1.428 from the peak value showing the maximum value, q ₂ = 1.068, the q ₃ = q ₁ ² = 2.039 as identified values adopt.

Similarly, in step S210 and step S211, numerical analysis is performed by simulating a tensile test for 3 levels × 3 levels (9 types) for f _F and f _C using the material physical properties identified so far. By interpolating the load obtained by the numerical analysis using Expression 24, the value of h (f _F , f _C ) is obtained as a continuous function. By substituting h (f _F , f _C ) into Equations 21 and 22, the distribution of P (x | y ₁ , y ₂ ) is obtained. In step S212, the material constant at the time when P (x | y ₁ , y ₂ ) takes the maximum value is adopted as the identification value (the material constant is identified using an inverse analysis method considering the joint probability). If the optimum value is not found, the process returns to step S210, and the numerical analysis is performed again from the combination of 3 levels × 3 levels (9 ways).

  FIG. 16 shows the numerical analysis results and actual test results using FEA evaluated from the GTN model using the material constants obtained by the above-described method. It can be seen that the relationship between the load and the displacement can be accurately evaluated for any of the measurement results of the smooth round bar test piece, the R1.5 mm notched test piece, and the R3.0 mm notched test piece.

  According to this example, the material constant of the GTN model identified using the smooth round bar test piece and the notched round bar test piece is obtained, and the ultimate strength accompanying ductile fracture of the arbitrarily shaped structure that undergoes ductile fracture is evaluated. Therefore, it can be applied to ductile fracture evaluation of various structures.

  A ductile fracture evaluation system in Example 2 of the present invention will be described. FIG. 17 shows a functional block diagram in the second embodiment. The description of the same parts as those in the first embodiment will be omitted.

  As shown in FIG. 17, the ductile fracture evaluation system further analyzes from a structure data as a CAD data storage unit 67 for storing a drawing of a structure to be evaluated and CAD (Computer Aided Design) data, and a structure drawing as CAD data. Numerical value that evaluates ultimate strength such as fracture load and fracture form by performing numerical analysis by FEA from model creation unit 68 that creates model to be used and each material constant obtained by mathematical statistical processing unit and model created by model creation unit An analysis unit 69 is provided. In this embodiment, using the material constants obtained in the first embodiment, the actual structure has a function of evaluating the ultimate strength such as the breaking load and the breaking mode when a load is applied. Different from 1. According to the present embodiment, it is possible to evaluate the ultimate strength such as a breaking load and a breaking mode in an actual structure.

  The ductile fracture evaluation system 50 shown in FIGS. 2 and 17 includes, for example, a CPU 100 (Central Processing Unit), a RAM 101 (Random Access Memory), a ROM 102 (Read Only Memory), an HDD 103 (Hard Disk Drive), an input unit 104, and a display. The computer system including the unit 105 is mounted. The storage area is not limited to the HDD. The processing unit of the present embodiment is embodied by developing a predetermined general-purpose FEA code stored in a ROM, HDD, or the like on a RAM or the like and executing it by a CPU. The input unit may be a mouse, a keyboard, a numeric keypad, or the like. Further, the display unit may be a display, a monitor, or the like.

  Although the present embodiment has been described with specific examples, the present embodiment is not limited to the above contents.

  For example, the constitutive equation expressing the fracture is not limited to the GTN model, and a constitutive equation having a plurality of material constants may be used for the numerical analysis of the ductile fracture evaluation system calculation unit. In addition, in identifying the material constants of the constitutive equation expressing ductile fracture, identification is made from the static tensile test results of a plurality of test pieces with different shapes including smooth round bar test pieces. It is preferable to use test pieces having different values.

In the present embodiment, there are two smooth round bar tensile test pieces and R1.5 mm notched round bar tensile test pieces. When identifying material constants, the concept of coincidence probability is used, so the comparison between numerical analysis results and test results using the same material constants increases the accuracy of the material constant identification values. In the ductile fracture evaluation system in this embodiment, first, material constants related to void generation (ε _N , s _N , f _N ) are identified, and correction coefficients (q ₁ , q _2, q ₃ ) are identified. Finally, material constants (f _F , f _C ) related to fracture were identified. A method for sequentially identifying these material properties one by one or a method for identifying all the arguments at the same time can be developed based on this embodiment. Also, the material constant of the hardening rule that expresses the stress-strain relationship used in the numerical analysis can be set to an optimum value by using the maximum value of P (x | y ₁ , y ₂ ) as the identification value.

  Furthermore, the target for evaluating the ultimate strength such as the fracture load and the fracture mode by the ductile fracture evaluation system may be of any shape. The ductile fracture system of the present embodiment is suitable not only for round bar tensile test pieces but also for shapes that simulate a flat specimen or an actual machine structure, or in a shape in which a crack-shaped defect of an arbitrary shape exists in the structure.

DESCRIPTION OF SYMBOLS 1 ... Material 2 ... Micro void 3 ... Load 4 ... Smooth round bar test piece 5 ... R1.5mm notched round bar test piece 21 ... Analytical model of smooth round bar test piece using axisymmetric element 22 ... Axisymmetric element Analytical model of notched round bar test piece using 50. Ductile fracture evaluation system 51. Input unit 52 ... Smooth round bar test piece measurement result storage unit 53 ... Notched round bar test piece measurement result storage unit 54 ... Processing 55: Young's modulus, yield stress analysis unit 56 ... Stress-strain relationship analysis unit 57, 58 ... Numerical simulation unit 59, 62, 65 ... Mathematical statistical processing unit 60, 61 of ε _N , s _N , f _N ... Q ₁ , q ₂ test simulation numerical analysis unit 63, 64... F _F , f _c test simulation numerical analysis unit 66... Display unit 67... CAD data storage unit 68. ... CPU
101 ... RAM
102 ... ROM
103 ... HDD
104 ... Input unit 105 ... Output unit

Claims (8)

An input section;
A first storage unit for storing a load and displacement relation as a test result of the first test piece;
A second storage unit for storing a load and displacement relationship which is a test result of a second test piece having a shape different from that of the first test piece;
First, a plurality of loads and displacement relationships corresponding to the material constants received from the input unit are obtained from a numerical analysis result using a finite element analysis that implements a constitutive expression that simulates a failure in the first test piece. A numerical analysis section;
A second numerical analysis unit for obtaining a plurality of loads and displacement relationships corresponding to the material constants from a numerical analysis result using a finite element analysis in which a constitutive expression expressing a fracture simulating a test in the second test piece is implemented;
Mathematical statistical processing using simultaneous probabilities from the load and displacement relationship stored in the first and second storage units and the load and displacement relationship which is a numerical analysis simulating the tests in the first and second numerical analysis units A ductile fracture evaluation system characterized by identifying a material constant of a constitutive expression expressing the fracture by: In the ductile fracture evaluation system according to claim 1,
The ductile fracture evaluation system, wherein the first test piece is a smooth round bar test piece, and the second test piece is a notched round bar test piece. In the ductile fracture evaluation system according to claim 1 or claim 2,
A CAD data storage unit for storing the shape of the structure to be evaluated;
A model creation unit for creating a model used for analysis from the CAD data;
A ductile fracture evaluation system that evaluates the ultimate strength of a structural part to be evaluated using finite element analysis from the identified material constants and the created model. In the ductile fracture evaluation system according to claim 3,
The constitutive equation expressing the destruction is a GTN model,
The ductile fracture evaluation system is characterized in that the material constant is identified by using a material constant when the joint probability takes a maximum value as an identification value. Obtaining a load and displacement relationship which is a test result of the first specimen;
Obtaining a load and displacement relationship which is a test result of a second test piece having a shape different from that of the first test piece;
Obtaining a plurality of load and displacement relationships corresponding to the input material constants from a numerical analysis result using a finite element analysis that implements a constitutive equation that represents a fracture simulating a test in the first test piece;
Obtaining a plurality of loads and displacement relationships corresponding to the input material constants from a numerical analysis result using a finite element analysis that implements a constitutive equation that represents a fracture simulating a test in the second specimen;
From the load and displacement relationship, which is the test result in the first and second test pieces, and the load and displacement relationship, which is a numerical analysis simulating the first and second test pieces, by mathematical statistical processing using the joint probability, A ductile fracture evaluation method comprising the step of identifying a material constant of a constitutive expression expressing the fracture. In the ductile fracture evaluation method according to claim 5,
The ductile fracture evaluation method, wherein the first test piece is a smooth round bar test piece, and the second test piece is a notched round bar test piece. In the ductile fracture evaluation method of claim 5 or claim 6,
Acquiring CAD data of the structure to be evaluated;
Creating a model for analysis from the CAD data;
A ductile fracture evaluation method comprising a step of evaluating the ultimate strength of a structural part to be evaluated using finite element analysis from the identified material constant and the created model. In the ductile fracture evaluation method according to claim 7,
The constitutive equation expressing the destruction is a GTN model,
The material constant is identified by adopting a material constant at the time when the joint probability takes a maximum value as an identification value.

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