Method for estimating fracture strain, CAE fracture estimation method, fracture estimation program, and product production method.

Abstract

This invention provides a fracture strain estimation method, a CAE fracture estimation method, a fracture estimation program, and a product production method that can accurately estimate the fracture strain of a material and reduce the need to conduct material tests. [Solution] A susceptibility constant acquisition step of obtaining a susceptibility constant α based on the crystal structure of the material and the work hardening ability of the material; an adjustment coefficient acquisition step of obtaining an adjustment coefficient K based on the susceptibility constant α and the stress triaxiality η of the material; and an adjustment coefficient acquisition step of obtaining an adjustment coefficient K and the nominal elongation at break ε of the material. f,nom Based on the above, the fracture strain ε of the material f A fracture strain estimation step that estimates the fracture strain, and a fracture strain estimation method comprising the steps of estimating the fracture strain.

Description

[Technical Field]

[0001] The present invention relates to a fracture strain estimation method, a CAE fracture estimation method, a fracture estimation program, and a product production method. [Background technology]

[0002] Various research results related to methods for estimating fracture strain of materials are known, for example, in Non-Patent Documents 1 to 11. [Prior art documents] [Patent Documents]

[0003] [Non-Patent Document 1] Bao, Y. and Wierzbicki, T., "On fracture locus in the equivalent strain and stress triaxiality space," International Journal of Mechanical Sciences, Vol.46, Issue 1, pp.81-98, 2004. [Non-Patent Document 2] Rice, JR and Tracey, DM, "On the ductile enlargement of voids in triaxial stress fields," Journal of the Mechanics and Physics of Solids, Vol.17, Issue 3, pp.201-217, 1969. [Non-Patent Document 3] Bai, Y. and Wierzbicki, T., "A new model of metal plasticity and fracture with pressure and Lode dependence," International Journal of Plasticity, Vol.24, Issue 6, pp.1071-1096, 2008. [Non-Patent Document 4] Kondori, B. and Benzerga, A.A., "Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31," Metallurgical and Materials Transactions A, Vol.45, pp.3292-3307, 2014.

Non-Patent Document 5

Non-Patent Document 6

Non-Patent Document 7

Non - Patent Document 8

Non - Patent Document 9

Non - Patent Document 10

Non - Patent Document 11

[0004] The object of the present invention is to provide a fracture strain estimation method, a CAE fracture estimation method, a fracture estimation program, and a product production method that can accurately estimate the fracture strain of a material and reduce the need to conduct material tests. [Means for solving the problem]

[0005] One aspect of the present invention is as follows:

[0006] [1] A susceptibility constant acquisition step in which a susceptibility constant α is obtained based on the crystal structure of the material and the work hardening ability of the material, A step of obtaining an adjustment coefficient K based on the sensitivity constant α and the stress triaxiality η of the material, The adjustment coefficient K and the nominal fracture elongation ε of the material. f,nom Based on the above, the fracture strain ε of the material f A fracture strain estimation step that estimates the fracture strain, A fracture strain estimation method having [a certain characteristic].

[0007] [2] The fracture strain estimation method according to [1], wherein the susceptibility constant acquisition step involves acquiring the susceptibility constant α based on whether the crystal structure is a body-centered cubic lattice structure, a face-centered cubic lattice structure, or a hexagonal close-packed structure.

[0008] [3] The sensitivity constant acquisition step is the fracture strain estimation method according to [2], which acquires a crystal structure constant α0 based on which of the body-centered cubic lattice structure, face-centered cubic lattice structure, and hexagonal close-packed structure the crystal structure is, and acquires the sensitivity constant α based on the crystal structure constant α0.

[0009] [4] The sensitivity constant acquisition step is the fracture strain estimation method according to [3], which sets the crystal structure constant α0 to a value of 0.5 or more and 1.5 or less when the crystal structure is the body-centered cubic lattice structure, sets the crystal structure constant α0 to a value of 1.0 or more and 2.0 or less when the crystal structure is the face-centered cubic lattice structure, and sets the crystal structure constant α0 to a value of 0.0 or more and 1.0 or less when the crystal structure is the hexagonal close-packed structure.

[0010] [5] The sensitivity constant acquisition step y and the tensile strength σ u of the material, and acquires the sensitivity constant α based thereon. The fracture strain estimation method according to any one of [1] to [4].

[0011] [6] The sensitivity constant acquisition step y and the tensile strength σ u of the material, and acquires the sensitivity constant α based on the work hardening constant σ y / σ u which is the ratio of and. The fracture strain estimation method according to [5].

[0012] [7] The sensitivity constant acquisition step is the fracture strain estimation method according to [6], which acquires a crystal structure constant α0 based on which of the body-centered cubic lattice structure, face-centered cubic lattice structure, and hexagonal close-packed structure the crystal structure is, and acquires the sensitivity constant α based on the sum of the crystal structure constant α0 and the work hardening constant σ y / σ u

[0013] [8] The aforementioned step of obtaining the sensitivity constant is α = α0 + σ y / σ u A fracture strain estimation method according to [7], wherein the susceptibility constant α is obtained by calculation using the formula [formula].

[0014] [9] The yield stress of the aforementioned yield stress y , the tensile strength σ u and the nominal elongation at break ε f,nom It has a public information acquisition step that obtains information from publicly available information, The aforementioned step of obtaining the susceptibility constant involves obtaining the yield stress σ from the publicly available information. y and the tensile strength σ u Using The fracture strain estimation step involves the nominal fracture elongation ε obtained from the publicly available information. f,nom A fracture strain estimation method described in any one of items [5] to [8], using the following.

[0015]

[10] The yield stress of the aforementioned yield stress y , the tensile strength σ u and the nominal elongation at break ε f,nom It has an examination step to obtain through an examination, The susceptibility constant acquisition step involves the yield stress σ obtained by the test. y and the tensile strength σ u Using The fracture strain estimation step involves the nominal fracture elongation ε obtained by the test. f,nom A fracture strain estimation method described in any one of items [5] to [8], using the following.

[0016]

[11] The aforementioned test is a uniaxial tensile test, as described in

[10] for estimating fracture strain.

[0017]

[12] The fracture strain estimation method described in any one of [1] to

[11] , wherein the adjustment coefficient acquisition step involves acquiring the adjustment coefficient K based on the product of the sensitivity constant α and the stress triaxiality η.

[0018]

[13] The fracture strain estimation method described in

[12] , wherein the adjustment coefficient acquisition step involves obtaining the adjustment coefficient K by calculation using the formula K = exp[-α(η - 1 / 3)].

[0019]

[14] The fracture strain estimation step involves the adjustment coefficient K and the nominal fracture elongation ε of the material. f,nom Based on the product of the above, the fracture strain ε f A fracture strain estimation method described in any one of the items [1] to

[13] for estimating the fracture strain.

[0020]

[15] The fracture strain estimation step is ε f = Kε f,nom The fracture strain ε is calculated using the formula shown above. f A fracture strain estimation method described in

[14] for estimating the fracture strain.

[0021]

[16] A CAE fracture estimation method that uses the fracture strain estimation method described in any one of items [1] to

[15] , A stress triaxiality η calculation step in which a computer calculates the stress state of each element of the material and calculates the stress triaxiality η of each element, The computer performs the adjustment coefficient acquisition step for each of the elements and calculates the adjustment coefficient K in the adjustment coefficient calculation step, The computer performs the fracture strain estimation step for each element and calculates the fracture strain ε f A fracture strain calculation step to calculate the fracture strain, The computer calculates the equivalent plastic strain ε for each of the elements. peq A step to calculate the equivalent plastic strain, The computer calculates the equivalent plastic strain ε for each of the elements. peq and the fracture strain ε f A fracture estimation step that estimates the likelihood of fracture based on the above, A CAE fracture estimation method having the following characteristics.

[0022]

[17] A fracture estimation program, which is a computer program that causes the computer to execute the CAE fracture estimation method described in

[16] .

[0023]

[18] A design step in which the product is designed using the CAE fracture estimation method described in

[16] , A production step for producing the product designed in the above design step, A method for producing a product having [a certain characteristic]. [Effects of the Invention]

[0024] According to the present invention, it is possible to provide a fracture strain estimation method, a CAE fracture estimation method, a fracture estimation program, and a product production method that can accurately estimate the fracture strain of a material and reduce the need to conduct material tests. [Brief explanation of the drawing]

[0025] [Figure 1] This is an explanatory diagram illustrating a fracture strain estimation method and a CAE fracture estimation method in one embodiment of the present invention. [Modes for carrying out the invention]

[0026] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0027] As shown in Figure 1, in one embodiment of the present invention, the fracture strain estimation method includes a sensitivity constant acquisition step of obtaining a sensitivity constant α based on the crystal structure of the material and the work hardening ability of the material, an adjustment coefficient acquisition step of obtaining an adjustment coefficient K based on the sensitivity constant α and the stress triaxiality η of the material, and an adjustment coefficient acquisition step of obtaining an adjustment coefficient K and the nominal fracture elongation ε of the material. f,nom Based on this, the fracture strain ε of the material f The system includes a fracture strain estimation step that estimates the fracture strain.

[0028] As shown in Figure 1, in this embodiment, the CAE fracture estimation method uses the fracture strain estimation method of this embodiment. The CAE fracture estimation method of this embodiment includes a stress triaxiality calculation step in which a computer calculates the stress state of each element of the material and calculates the stress triaxiality η of each element; an adjustment coefficient calculation step in which the computer performs an adjustment coefficient acquisition step for each element and calculates the adjustment coefficient K; and a fracture strain estimation step in which the computer performs a fracture strain estimation step for each element and calculates the fracture strain ε. f A fracture strain calculation step calculates the fracture strain, and the computer calculates the equivalent plastic strain ε for each element. peq A step to calculate the equivalent plastic strain, and a computer calculates the equivalent plastic strain ε for each element. peq and fracture strain ε f The method includes a fracture estimation step that estimates the possibility of fracture based on the following. The stress triaxiality η calculation step may involve a computer performing a stress analysis using the finite element method (FEM) to calculate the stress state of each element. The CAE fracture estimation method may also include a susceptibility constant calculation step in which a computer performs a susceptibility constant acquisition step to calculate the susceptibility constant α.

[0029] The fracture estimation step involves the equivalent plastic strain ε peq Fracture strain ε f It can be assumed that fracture will occur when the value exceeds the specified limit. The mechanical property values ​​(spec values) listed in the material standard are usually set as lower guaranteed values. This guarantees that a material that meets the standard will have performance equal to or greater than these values. Therefore, the yield stress σ described later in the material standard y , tensile strength σ u and nominal elongation at fracture ε f,nom The fracture strain ε was estimated by obtaining the data. f This value is conservative (on the safe side) for actual materials. When using actual materials, the performance will exceed the standard value, resulting in a higher fracture strain ε than the estimated value. f This is achieved, and a high safety margin is naturally ensured.

[0030] The fracture estimation step involves the equivalent plastic strain ε peq The product of this strain and the safety factor S is the fracture strain εf It may be estimated that fracture will occur when the above conditions are met. In this case, the fracture estimation step is the equivalent plastic strain ε peq The design allowable strain ε allow It can be assumed that fracture will occur when the above conditions are met. Design allowable strain ε allow is fracture strain ε f It can be taken as the value obtained by dividing by the safety factor S. For example, if the safety factor S = 2.0, then ε allow = ε f S = ε f This results in a value of 2.0. In this way, the reliability of the design can be further enhanced.

[0031] In this embodiment, the fracture estimation program is a computer program that causes a computer to execute the CAE fracture estimation method of this embodiment.

[0032] In this embodiment, the product production method comprises a design step of designing a product using the CAE fracture estimation method of this embodiment, and a production step of producing the product designed in the design step.

[0033] According to this embodiment, the fracture strain of a material can be accurately estimated based on its crystal structure, work hardening ability, and stress triaxiality η, and the need to conduct material tests can be reduced. Therefore, the likelihood of material fracture can be advantageously estimated, and the product can be produced more efficiently.

[0034] In the susceptibility constant acquisition step, it is preferable to acquire the susceptibility constant α based on whether the crystal structure is a body-centered cubic structure (BCC structure), a face-centered cubic structure (FCC structure), or a hexagonal close-packed structure (HCP structure). In this case, it is preferable to acquire the crystal structure constant α0 based on whether the crystal structure is a body-centered cubic structure, a face-centered cubic structure, or a hexagonal close-packed structure, and then acquire the susceptibility constant α based on the crystal structure constant α0. In this case, it is preferable to set the crystal structure constant α0 to a value of 0.5 or more and 1.5 or less when the crystal structure is a body-centered cubic structure, set the crystal structure constant α0 to a value of 1.0 or more and 2.0 or less when the crystal structure is a face-centered cubic structure, and set the crystal structure constant α0 to a value of 0.0 or more and 1.0 or less when the crystal structure is a hexagonal close-packed structure. More preferably, when the crystal structure is a body-centered cubic lattice structure, the crystal structure constant α0 is set to a value of 0.8 or more and 1.3 or less; when the crystal structure is a face-centered cubic lattice structure, the crystal structure constant α0 is set to a value of 1.3 or more and 1.8 or less; and when the crystal structure is a hexagonal close-packed structure, the crystal structure constant α0 is set to a value of 0.3 or more and 1.0 or less.

[0035] The susceptibility constant acquisition step involves the yield stress σ of the material. y and the tensile strength σ of the material u It is preferable to obtain the susceptibility constant α based on the following. In this case, the susceptibility constant acquisition step is the yield stress σ y and tensile strength σ u The work hardening constant σ is the ratio of to y / σ u It is preferable to obtain the sensitivity constant α based on the following. In this case, the sensitivity constant acquisition step involves obtaining the crystal structure constant α0 based on whether the crystal structure is a body-centered cubic structure, a face-centered cubic structure, or a hexagonal close-packed structure, and then obtaining the crystal structure constant α0 and the work hardening constant σ y / σ u It is preferable to obtain the sensitivity constant α based on the sum of the following. In this case, the sensitivity constant acquisition step is α = α0 + σ y / σ u It is preferable to obtain the sensitivity constant α by calculation using the formula shown.

[0036] The ductility and fracture behavior of metallic materials strongly depend on their crystal structure. In this embodiment, the crystal structure constant α0, which strongly influences the susceptibility constant α representing the susceptibility to stress triaxiality η, is determined based on the crystal structure.

[0037] Body-centered cubic (BCC) structures have a large number of slip systems (48), resulting in a high degree of deformation freedom. However, they exhibit high Peierls stress and strong dependence on temperature and strain rate. Typical materials include carbon steel (SS400, S45C, etc.), low-alloy steel, and stainless steel (SUS430, etc.). The crystal structure constant α0 of BCC structures is in the range of 0.8 ≤ α0 ≤ 1.3, and α0 = 1.0 can be used as a representative value.

[0038] Face-centered cubic (FCC) structure: Although it has 12 slip systems, fewer than BCC, it exhibits low Peierls stress and readily undergoes slip deformation even at room temperature. Typical materials include aluminum alloys (A6061, A5052, etc.), copper alloys, stainless steel (SUS304, SUS316, etc.), and nickel-based alloys. The crystal structure constant α0 of the FCC structure is in the range of 1.3 ≤ α0 ≤ 1.8, and α0 = 1.5 can be used as a representative value. This is consistent with the theoretical value of 1.5 in Rice & Tracey (Non-Patent Literature 2).

[0039] Hexagonal close-packed (HCP) structure: This structure has the fewest slip systems (3), and in addition to slip at the basal plane {0001}, twinning deformation is also an important deformation mechanism. Twinning deformation has the effect of mitigating stress concentration and has the lowest sensitivity to stress triaxiality η. Typical materials include pure titanium, titanium alloys (Ti-6Al-4V, etc.), magnesium alloys, and zinc. The crystal structure constant α0 of the HCP structure is in the range of 0.3 ≤ α0 ≤ 1.0, and α0 = 0.5 can be used as a representative value.

[0040] Rice & Tracey (Non-Patent Literature 2) theoretically demonstrated that the growth rate of spherical voids depends exponentially on the stress triaxiality η. According to their analysis, the growth rate of the void radius is expressed by the following equation: dR / dε eq = CR exp(1.5η) Here, R is the void radius, ε eq is the equivalent plastic strain, and C is a material constant. The exponential coefficient of 1.5 is the theoretical value for a perfectly plastic (non-hardening) material. It is known that the sensitivity of fracture strain to stress triaxiality differs depending on the work hardening characteristics of the material.

[0041] Generally, materials with high work hardening ability (tensile strength σ u The yield stress σ y A material that is larger than σ u / σ y In materials with a large stress triaxiality (η), the material hardens as plastic deformation progresses, and stress concentration around the voids is relieved. As a result, the void growth rate is suppressed, and the fracture strain ε with respect to the increase in stress triaxiality η decreases. f The rate of decrease becomes smaller. Conversely, materials with low work hardening ability (σ u / σ y In materials with a small stress triaxiality (η), sufficient hardening does not occur during plastic deformation, so stress concentration around voids persists, promoting void growth. As a result, the fracture strain ε increases with increasing stress triaxiality η. f The rate of decrease becomes larger. This phenomenon is quantitatively demonstrated in the void growth theory by Tvergaard (Non-Patent Documents 9, 10) and in the review paper by Benserga & Leblond (Non-Patent Document 11), where it is stated that "the larger the work hardening index n, the lower the void growth rate."

[0042] In this embodiment, this theory is extended to also consider the crystal structure, and the crystal structure (crystal structure constant α0) and work hardening ability (work hardening constant σ) are defined. y / σ u The susceptibility constant α is accurately determined based on the following: work hardening constant σ y / σ u σ corresponds to the reciprocal of the work hardening ability.y / σ u The larger the material (the material with a smaller work hardening ability) with respect to / σ, the larger the sensitivity constant α becomes, and the higher the sensitivity to the stress triaxiality η.

[0043] The fracture strain estimation method preferably has a public information acquisition step of obtaining the yield stress σ y , the tensile strength σ u and the nominal fracture elongation ε f,nom from public information. In this case, the sensitivity constant acquisition step may use the yield stress σ y and the tensile strength σ u obtained from public information, and the fracture strain estimation step may use the nominal fracture elongation ε f,nom obtained from public information. The public information is, for example, information described in material specifications or documents. The material specifications are, for example, JIS standards, ISO standards, ASTM standards, etc. Such information can be easily obtained from the catalogs or databases of material manufacturers. Therefore, fracture evaluation can be immediately performed without conducting a material test.

[0044] The fracture strain estimation method may have a test step of obtaining the yield stress σ y , the tensile strength σ u and the nominal fracture elongation ε f,nom by tests. In this case, the sensitivity constant acquisition step may use the yield stress σ y and the tensile strength σ u obtained by tests, and the fracture strain estimation step may use the nominal fracture elongation ε f,nom obtained by tests. The test is preferably a uniaxial tensile test. When a more precise evaluation than when using public information is required, or in the case of a material for which no public value exists, by conducting a uniaxial tensile test (stress triaxiality η = 1 / 3) once, evaluation based on measured values becomes possible.

[0045] The adjustment coefficient acquisition step preferably obtains the adjustment coefficient K based on the product of the sensitivity constant α and the stress triaxiality η. In this case, the adjustment coefficient acquisition step preferably obtains the adjustment coefficient K by calculation using the calculation formula K = exp[-α(η - 1 / 3)].

[0046] The fracture strain estimation step preferably estimates the fracture strain ε f,nom based on the product of the adjustment coefficient K and the nominal fracture elongation ε f of the material. In this case, the fracture strain estimation step preferably estimates the fracture strain ε f by calculation using the calculation formula ε f,nom = Kε f .

[0047] The above calculation formula has the following physical meanings. (1) When η = 1 / 3 (uniaxial tension), K = 1, ε f = ε f,nom , and the fracture elongation of the published value or measured value is reproduced. (2) When η > 1 / 3, K < 1, ε f < ε f,nom , and the more tensile stress is dominant, the fracture strain ε f decreases. (3) When η < 1 / 3, K > 1, ε f > ε f,nom , and the more shear stress is dominant, the fracture strain ε f increases. (4) The larger the sensitivity constant α is, the higher the sensitivity to the stress triaxiality η, and the greater the change in the fracture strain ε f with respect to the change in the stress triaxiality η.

[0048] The stress triaxiality η (stress triaxiality) is defined as the ratio of the hydrostatic stress σ m to the equivalent stress σ eq . That is, η = σ m / σ eq Here, σ m = (σ1 + σ2 + σ3) / 3 (hydrostatic stress) σ eq = √[(σ1-σ2) 2 + (σ2-σ3) 2 + (σ3-σ1) 2 ] / √2 (equivalent stress of von Mises) σ1, σ2, and σ3 are principal stresses.

[0049] The stress triaxiality η is an important parameter that characterizes the stress state within a material. η = 1 / 3 represents a uniaxial tensile state, η < 1 / 3 represents a state where shear is dominant, and η > 1 / 3 represents a state where tension is dominant.

[0050] The yield stress σ corresponding to the strain rate when strain occurs in a material. y , tensile strength σ u and nominal elongation at fracture ε f,nom You may use this. The strain rate generated in the material is 100 s. -1 Under the above high-speed deformation conditions, the yield stress σ corresponding to the high-speed deformation conditions is y , tensile strength σ u and nominal elongation at fracture ε f,nom It is also possible to use the following. It is preferable to set the crystal structure constant α0 independently of the strain rate. Thus, the crystal structure constant α0 and the yield stress σ y , tensile strength σ u and nominal elongation at fracture ε f,nom By setting this, the sensitivity constant α, which takes strain rate into account, can be accurately determined.

[0051] The yield stress σ corresponding to the temperature of the material when strain occurs in the material. y , tensile strength σ u and nominal elongation at fracture ε f,nom You may use this. When the temperature of the material at which strain occurs is above a predetermined value, the yield stress σ corresponding to the high temperature condition is used. y , tensile strength σ u and nominal elongation at fracture ε f,nom You may use the following: When the temperature of the material at which strain occurs is below a predetermined value, the yield stress σ corresponding to the low temperature conditions is used. y , tensile strength σ uand nominal elongation at fracture ε f,nom It is also possible to use the following. It is preferable to set the crystal structure constant α0 independently of the material temperature. Thus, the crystal structure constant α0 and the yield stress σ are used. y , tensile strength σ u and nominal elongation at fracture ε f,nom By setting this, the sensitivity constant α, which takes into account the material's temperature, can be accurately determined.

[0052] The above range and typical values ​​of the crystal structure constant α0, depending on the crystal structure, are based on quasi-static conditions (room temperature, strain rate 0.001-0.01 s). -1 This assumes a certain degree of [condition]. However, the crystal structure constant α0 is a physical constant based on the crystal structure and does not change depending on the usage conditions (strain rate, temperature, etc.).

[0053] On the other hand, yield stress σ y , tensile strength σ u and nominal elongation at fracture ε f,nom These are the mechanical property values ​​of the material, and they change depending on the usage conditions. When considering the effects of special conditions (high-speed deformation, high temperature, low temperature, etc.), these values ​​can be modified based on published or measured values.

[0054] This embodiment can be used in the following industrial fields, for example. (1) Automotive industry: Fracture evaluation of vehicle bodies, chassis, engine parts, etc. (2) Aerospace industry: Fracture evaluation of aircraft structures, engine components, etc. (3) Construction and Civil Engineering: Fracture evaluation of steel structures, bridges, etc. (4) Machinery industry: Fracture evaluation of various machine parts (5) Electrical and electronics industry: Fracture evaluation of enclosures, connectors, etc.

[0055] This embodiment can contribute to shortening development time and reducing costs, particularly in the early stages of design, by enabling rapid evaluation of fracture risk with no material testing or minimal testing (one uniaxial tensile test). Furthermore, this embodiment can be implemented as a module in CAE analysis software, making it easily accessible to designers. In addition, the fracture strain ε estimated by this embodiment... fSince this is a conservative value based on standard values, it ensures the reliability of the design.

[0056] This embodiment also contributes to the Sustainable Development Goals (SDGs). By reducing material testing, material consumption and energy consumption of test specimens can be reduced. Furthermore, by optimizing the design, material usage can be reduced, contributing to the efficient use of resources.

[0057] Although embodiments of the present invention have been described above, the present invention is not limited to the embodiments described above, and the embodiments described above can be modified in various ways without departing from the spirit of the present invention. [Examples]

[0058] <Example 1: SS400 (BCC structure)> • Material: General structural rolled steel SS400 (JIS G 3101) ·Crystal structure: Body-centered cubic lattice (BCC) ·Based on JIS standard values ​​(from JIS G 3101), Yield stress σ y = 245 MPa (lower limit) Tensile strength σ u = 400 MPa (lower limit) Elongation at break ε f,nom = 0.21(21%, lower limit) (1) Since SS400 has a BCC structure, we select the representative value α0 = 1.0. (2) σ y / σ u = 245 / 400 = 0.613 (3) α = α0 + σ y / σ u = 1.0 + 0.613 = 1.613 (4) ε f,nom = 0.21 (JIS standard value) (5) When η = 1 / 3 (uniaxial tension): ε f = 0.21 exp[-1.613 (1 / 3 - 1 / 3)] = 0.21 exp[0] = 0.21 (6) When η = 1 / 2: ε f = 0.21 exp[-1.613 (1 / 2 - 1 / 3)] = 0.21 exp[-1.613 × 1 / 6] = 0.21 exp[-0.269] = 0.21 × 0.764 = 0.160 (7) When η = 2 / 3: ε f = 0.21 exp[-1.613 (2 / 3 - 1 / 3)] = 0.21 exp[-1.613 × 1 / 3] = 0.21 exp[-0.538] = 0.21 × 0.584 = 0.123

[0059] Thus, as the stress triaxiality η increases, the fracture strain ε f A decrease is predicted. These predicted values ​​(estimates) were calculated solely from JIS standard values, without any material testing.

[0060] This example was conducted under quasi-static conditions (room temperature, strain rate 0.001-0.01 s). -1 While the evaluation focuses on the degree of performance, it can be extended as follows: (1) Consideration of temperature effects: When use at high or low temperatures is anticipated, temperature dependence can be considered. In this case, the susceptibility constant α or nominal elongation at break ε f,nom Express this as a function of temperature. (2) Consideration of dynamic effects: When dealing with high-speed deformation (collision, explosion, etc.), the effect of strain rate can be considered.

[0061] The coefficient α0 is a physical constant determined by the crystal structure and is not modified. Dynamic effects are considered by modifying the following material properties. (i) Tensile strength σ u and yield stress σ y : At high-speed deformation, strength increases due to strain rate hardening. Based on published values ​​or limited experiments, σ ​​under high-speed conditions u , σ y You can obtain it. (ii) Elongation at break ε f,nomUnder high-speed deformation, ductility changes. If the published value falls below the specification value, adopting the published value allows for a more conservative evaluation.

[0062] For example, in the titanium alloy described by Skripnyak et al. (Non-Patent Document 7), ·Quasi-static:σ y Approximately 800 MPa, σ u Approximately 1000 MPa, ε f,nom Approximately 0.14 ·High speed (833s -1 ): Increased intensity, ε f,nom Approximately 0.13 (high stress triaxiality condition)

[0063] Thus, α0 = 0.5(HCP) is fixed, and σ u , σ y , ε f,nom By correcting these values ​​based on the values ​​described in the literature (literature values), the dynamic effects can be accurately evaluated.

[0064] The basic form of this embodiment (using only standard values) offers a step-by-step approach that allows for immediate evaluation without material testing and modification using publicly available values ​​as needed.

[0065] If a more detailed evaluation is required, the Lode angle parameter can be introduced to more precisely assess the effect of the shear component.

[0066] These extensions are based on the fundamental concepts of this embodiment (crystal structure constant α0 and work hardening constant σ based on crystal structure). y / σ u This approach addresses more complex conditions while maintaining the (determining the sensitivity constant α as the sum of) factor.

[0067] <Example 2: A6061-T6 (FCC structure)> • Material: Aluminum alloy A6061-T6 (JIS H 4040) ·Crystal structure: Face-centered cubic lattice (FCC) ·Based on JIS standard values ​​(from JIS H 4040), Yield stress σ y= 240 MPa (lower limit) Tensile strength σ u = 290 MPa (lower limit) Elongation at break ε f,nom = 0.10(10%, lower limit) (1) Since A6061-T6 has an FCC structure, we select the representative value α0 = 1.5. (2) σ y / σ u = 240 / 290 = 0.828 (3) α = α0 + σ y / σ u = 1.5 + 0.828 = 2.328 (4) ε f,nom = 0.10 (JIS standard value) (5) When η = 1 / 3 (uniaxial tension): ε f = 0.10 × exp[-2.328 × (1 / 3 - 1 / 3)] = 0.10 × exp[0] = 0.10 (6) When η = 1 / 2: ε f = 0.10 exp[-2.328 (1 / 2 - 1 / 3)] = 0.10 exp[-2.328 × 1 / 6] = 0.10 × exp[-0.388] = 0.10 × 0.678 = 0.068 (7) When η = 2 / 3: ε f = 0.10 exp[-2.328 (2 / 3 - 1 / 3)] = 0.10 exp[-2.328 × 1 / 3] = 0.10 × exp[-0.776] = 0.10 × 0.460 = 0.046

[0068] This predicted value is that fracture strain ε increases with increasing stress triaxiality η. f This qualitatively agrees with the behavior of aluminum alloys reported in the literature (Non-Patent Documents 3, 4, etc.) where the amount of fracture strain decreases. In this embodiment, the standard value (lower guaranteed value) is used, so the predicted fracture strain ε fThis value is more conservative compared to the measured value. For example, the experimental value for 6061 aluminum alloy reported by Kou et al. (Non-Patent Literature 6) is approximately four times higher than the predicted value (based on the standard value) in this embodiment, demonstrating that a high safety factor is naturally ensured when using actual materials.

[0069] <Example 3: Pure Titanium (HCP Structure)> • Material: Pure titanium (JIS H 4600 Class 1) ·Crystal structure: Hexagonal close packed (HCP) ·Based on JIS standard values ​​(from JIS H 4600), Yield stress σ y = 275 MPa (lower limit) Tensile strength σ u = 345 MPa (lower limit) Elongation at break ε f,nom = 0.27(27%, lower limit) (1) Since pure titanium has an HCP structure, we select the representative value α0 = 0.5. (2) σ y / σ u = 275 / 345 = 0.797 (3) α = α0 + σ y / σ u = 0.5 + 0.797 = 1.297 (4) ε f,nom = 0.27 (JIS standard value) (5) When η = 1 / 3 (uniaxial tension): ε f = 0.27 exp[-1.297 (1 / 3 - 1 / 3)] = 0.27 exp[0] = 0.27 (6) When η = 1 / 2: ε f = 0.27 exp[-1.297 (1 / 2 - 1 / 3)] = 0.27 exp[-1.297 × 1 / 6] = 0.27 exp[-0.216] = 0.27 × 0.806 = 0.218 (7) When η = 2 / 3: ε f= 0.27 exp[-1.297 (2 / 3 - 1 / 3)] = 0.27 exp[-1.297 × 1 / 3] = 0.27 exp[-0.432] = 0.27 × 0.649 = 0.175

[0070] Pure titanium has a smaller susceptibility constant α (1.297) compared to SS400 and A6061-T6, and is less susceptible to stress triaxiality η. This reflects the stress relaxation effect due to twinning deformation of the HCP structure.

[0071] <Example 4: Comparison based on differences in sensitivity constant α> The values ​​of the susceptibility constant α calculated in Examples 1 to 3 are compared as follows: SS400(BCC):α = 1.613 · A6061-T6(FCC): α = 2.328 Pure titanium (HCP): α = 1.297

[0072] A6061-T6 has the largest FCC structure reference value α0 = 1.5, σ y / σ u Since = 0.828 is also relatively large, the overall sensitivity constant α is the largest. On the other hand, pure titanium has a small α0 = 0.5, and σ y / σ u Since = 0.797 is also relatively small, the sensitivity constant α is the smallest.

[0073] <Example 5: Practical evaluation using uniaxial tensile testing with JIS No. 5 test specimen> This embodiment describes an evaluation method for a uniaxial tensile test performed on a No. 5 test specimen, as specified in JIS Z 2241, prepared from a sheet material widely used in practical applications. • Test specimen: JIS No. 5 test specimen (parallel section length 50 mm, parallel section width 25 mm) • Test conditions: Room temperature, strain rate 0.001 s -1 (semi-static) • Stress triaxiality η = 1 / 3 (uniaxial tension)

[0074] For the following five types of materials, this embodiment yields fracture strain ε at other stress triaxial degrees η. f To predict.

[0075] <<Material 1: SS400 (BCC structure), plate thickness 1.6mm>> Based on JIS standard values ​​(from JIS G 3101), · Yield stress σ y = 245 MPa (lower limit) • Tensile strength σ u = 400 MPa (lower limit) • Elongation at break ε f,nom = 0.21(21%, lower limit) (1) α0 = 1.0 (BCC structure, fixed value) (2) σ y / σ u = 245 / 400 = 0.613 (3) α = 1.0 + 0.613 = 1.613 (4) ε f,nom = 0.21 (JIS standard value)

[0076] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 407 MPa, σ u = 459 MPa, ε f The value was 0.29. The measured value exceeds the JIS standard value, indicating that the material has higher strength and ductility.

[0077] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.21 × exp[-1.613×0.167] = 0.160 (6) η = 0.667: ε f = 0.21 × exp[-1.613×0.334] = 0.123

[0078] <<Material 2: SS400 (BCC structure), plate thickness 3.2mm>> Based on JIS standard values ​​(from JIS G 3101), · Yield stress σ y = 245 MPa (lower limit) • Tensile strength σ u = 400 MPa (lower limit) • Elongation at break ε f,nom = 0.21(21%, lower limit) (1) α0 = 1.0 (BCC structure, fixed value) (2) σ y / σ u = 245 / 400 = 0.613 (3) α = 1.0 + 0.613 = 1.613 (4) ε f,nom = 0.21 (JIS standard value)

[0079] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 251 MPa, σ u = 359 MPa, ε f = 0.44. This measured value corresponds to the tensile strength σ u = 359 MPa is below the JIS standard (400 MPa or more), but the elongation at break ε f A value of 0.44 indicates high ductility, approximately twice the standard value. Such variations in material properties can occur due to differences in manufacturing lots, chemical composition, cooling conditions, etc.

[0080] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.21 × exp[-1.613×0.167] = 0.160 (6) η = 0.667: ε f = 0.21 × exp[-1.613×0.334] = 0.123

[0081] <<Material 3: SUS304 (FCC structure), plate thickness 3mm>> From the JIS standard values ​​(from JIS G 4305), · Yield stress σ y = 205 MPa (lower limit, yield strength) • Tensile strength σ u = 520 MPa (lower limit) • Elongation at break ε f,nom = 0.40(40%, lower limit) (1) α0 = 1.5 (FCC structure, fixed value) (2) σ y / σ u = 205 / 520 = 0.394 (3) α = 1.5 + 0.394 = 1.894 (4) ε f,nom = 0.40 (JIS standard value)

[0082] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 298 MPa, σ u = 702 MPa, ε f The value was 0.650. The measured value exceeds the JIS standard value, indicating that the material has higher strength and ductility.

[0083] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.40 × exp[-1.894×0.167] = 0.290 (6) η = 0.667: ε f = 0.40 × exp[-1.894×0.334] = 0.210

[0084] <<Material 4: A5052-H34 (FCC structure), plate thickness 3mm>> From JIS standard values ​​(from JIS H 4000), · Yield stress σ y = 180 MPa (lower limit, yield strength) • Tensile strength σ u = 235 MPa (lower limit) • Elongation at break ε f,nom = 0.06(6%, lower limit) (1) α0 = 1.5 (FCC structure, fixed value) (2) σ y / σ u= 180 / 235 = 0.766 (3) α = 1.5 + 0.766 = 2.266 (4) ε f,nom = 0.06 (JIS standard value)

[0085] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 190 MPa, σ u = 253 MPa, ε f The value was 0.12. The measured value exceeds the JIS standard value, indicating that the material has higher ductility.

[0086] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.06 × exp[-2.266×0.167] = 0.041 (6) η = 0.667: ε f = 0.06 × exp[-2.266×0.334] = 0.028

[0087] <<Material 5: A1050-H24 (FCC structure), plate thickness 3mm>> From JIS standard values ​​(from JIS H 4000), · Yield stress σ y = 75 MPa (lower limit, yield strength) • Tensile strength σ u = 95 MPa (lower limit) • Elongation at break ε f,nom = 0.06(6%, lower limit) (1) α0 = 1.5 (FCC structure, fixed value) (2) σ y / σ u = 75 / 95 = 0.789 (3) α = 1.5 + 0.789 = 2.289 (4) ε f,nom = 0.06 (JIS standard value)

[0088] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 10⁹ MPa, σ u = 113 MPa, ε f The value was 0.20. The measured value exceeds the JIS standard value, indicating that the material has higher ductility.

[0089] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.06 × exp[-2.289×0.167] = 0.041 (6) η = 0.667: ε f = 0.06 × exp[-2.289×0.334] = 0.028

[0090] <<Material 6: Pure titanium (HCP structure), plate thickness 3mm>> From JIS standard values ​​(from JIS H 4600), · Yield stress σ y = 215 MPa (lower limit, yield strength) • Tensile strength σ u = 345 MPa (lower limit) • Elongation at break ε f,nom = 0.23(23%, lower limit) (1) α0 = 0.5 (HCP structure, fixed value) (2) σ y / σ u = 215 / 345 = 0.623 (3) α = 0.5 + 0.623 = 1.123 (4) ε f,nom = 0.23 (JIS standard value)

[0091] In contrast, the results of a uniaxial tensile test conducted by a public institution (Saitama Prefectural Industrial Technology Center) were as follows: σ y = 296 MPa, σ u = 419 MPa, ε f= 0.34. The measured value exceeds the JIS standard value, indicating that the material has higher strength and ductility. Pure titanium has an HCP structure, a crystal structure with few slip systems and generally considered to have low ductility, but this material has ε f It exhibits considerable ductility, with a ratio of 0.34.

[0092] • Prediction for other stress triaxial values ​​η (according to JIS standard values): (5) η = 0.50: ε f = 0.23 × exp[-1.123×0.167] = 0.189 (6) η = 0.667: ε f = 0.23 × exp[-1.123×0.334] = 0.155

[0093] <<Summary of differences based on crystal structure>> Fracture strain ε at η = 0.50 f (In descending order according to JIS standard values): 1. SUS304 (FCC): 0.290 2. Pure Titanium (HCP): 0.189 3. SS400 (BCC): 0.160 (common to 1.6mm and 3.2mm) 4. A5052-H34(FCC):0.041 5. A1050-H24(FCC):0.041

[0094] In this embodiment, the fracture strain ε in uniaxial tension is obtained for all major crystal structures of BCC, FCC, and HCP. f It has been shown that practical fracture evaluation is possible with only a prediction or a single uniaxial tensile test.

[0095] <Example 6: Evaluation of special conditions using publicly available values> Examples 1-5 demonstrate basic evaluations using standard values ​​or measured values ​​under quasi-static conditions. Standard values ​​are for quasi-static conditions (room temperature, strain rate 0.001-0.01 s). -1This is the lower limit of guaranteed values ​​and provides a conservative evaluation under typical design conditions. If a more precise evaluation is required, or if special operating conditions (high-speed deformation, high temperature, low temperature, etc.) are considered, the material property values ​​can be modified by referring to the published values.

[0096] The important principles are as follows: (1) The crystal structure constant α0 is a physical constant determined by the crystal structure and is not modified. (2) If the literature value is below the standard value, the literature value may be adopted. (3) If the literature value exceeds the standard value, the standard value will be maintained (conservative evaluation).

[0097] For example, in the case of the Ti-5Al-2.5Sn alloy (HCP structure) described by Skripnyak et al. (Non-Patent Document 7), the following applies: << Quasi-static condition (0.01 s -1 )>> • α0 = 0.5 (HCP fixed value) ·σ y / σ u = 0.80 ·α = 0.5 + 0.80 = 1.30 ·ε f,nom = 0.14 (equivalent to literature value and specification value) <<High-speed deformation conditions (833 s -1 ) Rating >> Skripnyak et al. reported an experimental fracture strain of approximately 0.12-0.13 under high-speed deformation conditions with stress triaxiality η = 0.549. Since this value is below the quasi-static specification value of 0.14, the literature value ε is used when performing a more conservative evaluation under high-speed conditions. f,nom We can adopt = 0.13. • α0 = 0.5 (HCP fixed value, no change) ·σ y / σ u = 0.80 (material eigenvalue, unchanged) ·α = 1.30 (same as above) ·ε f,nom = 0.13 (Adopting the literature value, more conservative than the standard value of 0.14) Prediction at η=0.549: ε f = 0.13 exp[-1.30 (0.549-0.333)] = 0.13 exp[-1.30×0.216] = 0.13 exp[-0.281] = 0.13 × 0.755 = 0.098

[0098] Skripnyak et al. conducted the study under the same conditions (η=0.549, strain rate 833 s) -1 The measured fracture strain reported in the study was approximately 0.12-0.13, and the predicted value of 0.098 in this invention is a conservative evaluation with a safety margin of approximately 25% compared to the measured value.

[0099] Thus, if the literature value is below the standard value, the literature value is adopted, and the sensitivity constant α(= α0 + σ) y / σ u By maintaining this value as a material-specific value, it becomes possible to perform conservative evaluations even under special conditions.

[0100] The advantage of this embodiment lies in its step-by-step approach: in the basic form (using only standard values), material testing is unnecessary, and modifications based on literature values ​​can be made as needed.

Claims

1. A susceptibility constant acquisition step in which a susceptibility constant α is obtained based on the crystal structure of the material and the work hardening ability of the material, A step of obtaining an adjustment coefficient K based on the sensitivity constant α and the stress triaxiality η of the material, The adjustment coefficient K and the nominal fracture elongation ε of the material. f,nom Based on the above, the fracture strain ε of the material f A fracture strain estimation step that estimates the fracture strain, A fracture strain estimation method having [a certain characteristic].

2. The fracture strain estimation method according to claim 1, wherein the sensitivity constant acquisition step is to acquire the sensitivity constant α based on whether the crystal structure is a body-centered cubic lattice structure, a face-centered cubic lattice structure, or a hexagonal close-packed structure.

3. The aforementioned sensitivity constant acquisition step involves determining whether the crystal structure is a body-centered cubic lattice structure, a face-centered cubic lattice structure, or a hexagonal close-packed structure, and then determining the crystal structure constant α 0 Obtain the crystal structure constant α 0 The fracture strain estimation method according to claim 2, wherein the sensitivity constant α is obtained based on the above.

4. The aforementioned sensitivity constant acquisition step is performed when the crystal structure is the body-centered cubic lattice structure, the crystal structure constant α 0 The crystal structure constant α is set to a value between 0.5 and 1.5, and when the crystal structure is the face-centered cubic lattice structure, the crystal structure constant α 0 The crystal structure constant α is set to a value between 1.0 and 2.0, and when the crystal structure is the hexagonal close-packed structure, 0 The fracture strain estimation method according to claim 3, wherein the value is set to a value of 0.0 or more and 1.0 or less.

5. The sensitivity constant acquisition step acquires the sensitivity constant α based on the yield stress σ of the material y and the tensile strength σ u of the material. The fracture strain estimation method according to claim 1

6. The above susceptibility constant acquisition step is the yield stress σ y and the aforementioned tensile strength σ u The work hardening constant σ is the ratio of to y / σ u The fracture strain estimation method according to claim 5, wherein the sensitivity constant α is obtained based on the above.

7. The aforementioned sensitivity constant acquisition step involves determining whether the crystal structure is a body-centered cubic lattice structure, a face-centered cubic lattice structure, or a hexagonal close-packed structure, and then determining the crystal structure constant α 0 Obtain the crystal structure constant α 0 and the work hardening constant σ y / σ u The fracture strain estimation method according to claim 6, wherein the sensitivity constant α is obtained based on the sum of the following.

8. The aforementioned step of obtaining the sensitivity constant is α = α 0 + σ y / σ u The fracture strain estimation method according to claim 7, wherein the sensitivity constant α is obtained by calculation using the formula as follows.

9. The yield stress of the aforementioned yield stress y , the tensile strength σ u and the nominal elongation at break ε f,nom It has a public information acquisition step that obtains information from publicly available information, The aforementioned step of obtaining the susceptibility constant involves obtaining the yield stress σ from the publicly available information. y and the tensile strength σ u Using The fracture strain estimation step involves the nominal fracture elongation ε obtained from the publicly available information. f,nom A fracture strain estimation method according to claim 5, using [the specified method].

10. The yield stress of the aforementioned yield stress y , the tensile strength σ u and the nominal elongation at break ε f,nom It has an examination step to obtain through an examination, The susceptibility constant acquisition step involves the yield stress σ obtained by the test. y and the tensile strength σ u Using The fracture strain estimation step involves the nominal fracture elongation ε obtained by the test. f,nom A fracture strain estimation method according to claim 5, using [the specified method].

11. The fracture strain estimation method according to claim 10, wherein the test is a uniaxial tensile test.

12. The fracture strain estimation method according to claim 1, wherein the adjustment coefficient acquisition step is to acquire the adjustment coefficient K based on the product of the sensitivity constant α and the stress triaxiality η.

13. The fracture strain estimation method according to claim 12, wherein the adjustment coefficient acquisition step is to acquire the adjustment coefficient K by calculation using the formula K = exp[-α(η - 1 / 3)].

14. The fracture strain estimation step involves the adjustment coefficient K and the nominal fracture elongation ε of the material. f,nom Based on the product of the above, the fracture strain ε f A method for estimating fracture strain according to claim 1, which estimates the fracture strain.

15. The fracture strain estimation step is ε f = Kε f,nom The fracture strain ε is calculated using the formula shown above. f A method for estimating fracture strain according to claim 14, which estimates the fracture strain.

16. A CAE fracture estimation method using the fracture strain estimation method described in any one of claims 1 to 15, A stress triaxiality η calculation step in which a computer calculates the stress state of each element of the material and calculates the stress triaxiality η of each element, The computer performs the adjustment coefficient acquisition step for each of the elements and calculates the adjustment coefficient K in the adjustment coefficient calculation step, The computer performs the fracture strain estimation step for each element and calculates the fracture strain ε f A fracture strain calculation step to calculate the fracture strain, The computer calculates the equivalent plastic strain ε for each of the elements. peq A step to calculate the equivalent plastic strain, The computer calculates the equivalent plastic strain ε for each of the elements. peq and the fracture strain ε f A fracture estimation step that estimates the likelihood of fracture based on the above, A CAE fracture estimation method having the following characteristics.

17. A fracture estimation program, which is a computer program that causes the computer to execute the CAE fracture estimation method described in claim 16.

18. A design step of designing a product by the CAE fracture estimation method described in claim 16, A production step for producing the product designed in the above design step, A method for producing a product having [a certain characteristic].

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