Method and program for analyzing the strength properties of metallic materials

Abstract

Provided is a technique that can contribute to suppressing the amount of data required for formulating the strain rate dependence of the yield point and facilitating the desired analysis to be easily performed. 【Solution means】In a molded body formed by molding a metal material to be analyzed, a strength test is performed in which a load is applied and deformed at three different load rates, so that the strain rate ε when deformed · 1, ε · 2, ε · 3 and the yield point σ y,1 , σ y,2 , σ y,3 are measured. Then, in the relational expression of the strain rate ε dependence of the yield point σ of the metal material formulated using three material parameters A, B, and C based on the thermoactivation process theory, (σ y ε · ) = (σ y, ε · ) = (σ y,1 , ε · 1)(σ y,2 , ε · 2)(σ y,3 , ε · 3) is assumed to hold, and the three material parameters A, B, and C are derived by calculating the simultaneous equations of the three material parameters A, B, and C.

Description

[Technical Field]

[0001] This invention relates to a technology that facilitates the formulation of the strength characteristics of metal materials applied to various devices such as motors, inverters, and power receiving and transforming equipment, and that can contribute to the analysis of said strength characteristics. [Background technology]

[0002] In various types of equipment such as motors, inverters, and power receiving and transforming equipment (electrical equipment, electronic equipment, etc.), there is a desire for higher performance (e.g., high rotational speed, high frequency, shock resistance, explosion resistance, etc.), miniaturization, and weight reduction. However, this also means that loads with high strain rates may be applied. Therefore, it is desirable to rationally design the strength of these devices while considering such high strain rate loads.

[0003] For example, the strength properties of metallic materials used in the components of the aforementioned equipment are strain rate dependent, and in the case of steel materials in particular, it is known that strength increases with increasing strain rate.

[0004] Therefore, when aiming to improve the performance of equipment, it is considered effective to consider the strain rate due to the loads that may act on the components of the equipment, conduct strength tests on the metal materials applied to those components, analyze the strength characteristics of the metal materials based on the test results (static strength, fatigue strength, etc.), and then perform strength design.

[0005] Strength testing is a known method in which a molded body (test specimen, etc.) made by appropriately shaping a metal material to be tested (analyzed) is subjected to a load under arbitrary loading conditions (e.g., loading speed, temperature, etc.) to cause deformation, and the strength characteristics are formulated and analyzed from the relationship between the load (force during deformation) and the amount of deformation. Furthermore, strength testing machines capable of applying loads under a wide range of diverse loading conditions (e.g., tensile testing machines, fatigue testing machines, etc.) are commercially available.

[0006] Non-patent document 1 discloses that the yield behavior of a body-centered cubic lattice metallic material can be expressed by a relational equation including a frequency coefficient, which is a material parameter, as shown in equation (1) below, based on the theory of thermal activation processes. Furthermore, it is disclosed that equation (1) can be transformed into equation (2) below, and that by using a set of yield point data obtained from strength tests under various loading conditions to perform calculations (identify material parameters), it can be organized into a single characteristic curve. Note that in equations (1) and (2) below, ε · Let be the strain rate, A be the frequency coefficient, H be the apparent activation energy, R be the gas constant, and T be the temperature (absolute temperature).

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[0009] Non-patent document 2 focuses on the fact that the relationship between the yield point and temperature can be expressed by an Arrhenius-type relation, and discloses that the relationship between temperature and strain rate with respect to the yield point (dependence of the yield point on the strain rate) can be formulated using equation (2). Specifically, first, the following equation (3), obtained by dividing both sides of equation (2) by the gas constant R, is used as the relation for the parameter H' (strain rate - temperature parameter H') that shows the strain rate characteristics with respect to temperature. Then, it is disclosed that the relationship between temperature and strain rate with respect to the yield point can be expressed by a relation including two material constants, which are material parameters, as shown in equation (4) below. Note that in equation (4) below, σ y is the yield point, and B and C are material parameters.

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Prior Art Documents

Non-Patent Documents

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Summary of the Invention

Problems to be Solved by the Invention

[0013] In Non-Patent Document 2, a large number of strength tests were carried out under a wide range of loading conditions (strain rate, temperature) to obtain a large group of yield point data, and by performing calculations based on the least squares method on the data group, the material parameters (A, B, C) in equations (3) and (4) were specified.

[0014] Therefore, when simply analyzing the strength characteristics of a metal material based on Non-Patent Documents 1, 2, etc., for example, a strength testing machine capable of obtaining a large amount of data as described above (for example, a high-performance and high-cost strength testing machine) is required, and there is also a possibility that the calculation of the data group will become difficult. As a result, the types of applicable strength testing machines are restricted (for example, general-purpose products cannot be used and are excluded), and it becomes difficult to simply (for example, easily) perform the desired analysis. Even if the analysis can be performed, there is a risk of increased costs and the like.

[0015] The present invention has been made in view of the above-described technical problems, and an object thereof is to provide a technique that can contribute to suppressing the amount of data required for formulating the strain rate dependence of the yield point and making it easier to simply perform the desired analysis.

Means for Solving the Problems

[0016] One aspect of the method for analyzing the strength characteristics of a metal material according to this invention is a method for analyzing the strength characteristics of a metal material by calculation using a computer. In this method, when a load is applied to a molded body formed by molding the metal material at three different load rates and deformed, the strain rates ε · 1, ε · 2, ε · 3 and the yield points σ · 1, σ · 2, σ · 3 corresponding to the strain rates ε y,1 , σ y,2 , σ y,3 are substituted into the following simultaneous equations (6) to (10) and calculated to derive A, B, and C in the first calculation step, and A, B, and C derived in the first calculation step are substituted into the following equations (3) and (4) and calculated to derive σ y , H´ in the second calculation step. It is characterized by having these. The metal material may be characterized by having a body-centered cubic lattice structure.

[0017] Among the symbols in the following equations (3), (4), (6) to (10), ε · is the strain rate, σ yε is the yield point, T is the temperature (absolute temperature), R is the gas constant, H is the apparent activation energy, and H' is the strain rate ε with respect to temperature T. · The parameters A, B, and C, which describe the characteristics, are material parameters.

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[0025] One embodiment of the program may be characterized by causing the computer to perform the first and second steps of the method for analyzing the strength properties of the metallic material. [Effects of the Invention]

[0026] As described above, the present invention can reduce the amount of data required to formulate the strain rate dependence of the yield point, thereby contributing to making it easier to perform the desired analysis. [Brief explanation of the drawing]

[0027] [Figure 1] A schematic diagram illustrating test specimen 1 to be used in the strength test according to the example (dimensions in mm). [Figure 2] A schematic diagram illustrating the tensile testing machine 2 used in the strength test according to the embodiment (a partial cross-sectional view showing the inside of the piston rod 26). [Figure 3] A diagram showing stress-strain curves for each load condition, illustrating the measurement results of the strength tests conducted in the examples. [Figure 4] This figure shows a magnified view of the region where the yield point occurred in each stress-strain curve of Figure 3. [Figure 5] A diagram showing the stress-time curve and strain-time curve separated from the stress-strain curve at a loading rate of 1 mm / s. [Figure 6] Figure 4 shows the relationship between the yield point and strain rate in each stress-strain curve. [Figure 7] This figure shows an example of a yield point-strain rate curve formulated by the first calculation step S1 and the second calculation step S2. [Modes for carrying out the invention]

[0028] The method and program for analyzing the strength properties of a metallic material according to the embodiment of the present invention are completely different from the conventional configuration (hereinafter referred to as the conventional configuration) which uses a large dataset of yield points obtained by conducting numerous strength tests under a wide range of loading conditions, as shown in equations (3) and (4) based on the thermal activation process theory in Non-Patent Documents 1 and 2.

[0029] In other words, this embodiment focuses on the fact that there are three material parameters (A, B, C) in equations (3) and (4), and has found that by using yield point data with respect to strain rate obtained from strength tests under three different loading conditions, these three material parameters can be identified, and the strain rate dependence of the yield point can be formulated.

[0030] Specifically, the strain rate ε in equation (3) · (4) Yield point σ y Assuming that the solution to equation (5) below holds, the material parameters in equations (3) and (4) can be formulated by a system of equations (6) to (10) below.

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[0037] In equations (5) to (10), T is the temperature (absolute temperature), R is the gas constant, H is the apparent activation energy, and H' is the strain rate ε with respect to temperature T. ·The parameters A, B, and C, which describe the characteristics, are assumed to be material parameters.

[0038] The solution to equation (5) is obtained by conducting strength tests on a molded body made by shaping the metal material being analyzed, applying loads at three different load rates to deform it, and determining the strain rate (ε) for each deformation. · 1,ε · 2,ε · 3) and yield point (σ y,1 ,σ y,2 ,σ y,3 It can be found as a combination of )

[0039] Then, by appropriately performing the following two steps (hereinafter referred to as the first calculation step S1 and the second calculation step S2, respectively) using computer calculations, for example, it becomes possible to formulate the strain rate dependence of the yield point.

[0040] First, in the first calculation step S1, the solution to equation (5) obtained in the strength test (strain rate ε) · 1,ε · 2,ε · 3 and the yield point σ y,1 ,σ y,2 ,σ y,3 By substituting ) into the system of equations (6) to (10) and performing the calculation, A, B, and C are derived. Then, in the second calculation step S2, by substituting A, B, and C derived in the first calculation step S1 into equations (3) and (4) and performing the calculation, σ y Derive H'.

[0041] In the analysis method having the first calculation step S1 and the second calculation step S2 as described above, the first calculation step S1 and the second calculation step S2 can be made into a program that causes a computer to execute them. This program can be distributed, for example, via a network or stored on a recording medium and distributed.

[0042] Furthermore, the metallic material to be analyzed only needs to have a strain rate dependence of its yield point. One example of such a material is one with a body-centered cubic lattice structure. Specific examples include electromagnetic soft iron, but the analysis is not limited to this.

[0043] Furthermore, a strength test only requires that a load be applied to a molded body made by shaping the metal material to be analyzed under arbitrary loading conditions (e.g., loading speed, temperature, etc.) to deform it, and the strain of the molded body under that load be measured. Examples of such methods include, but are not limited to, the use of a tensile testing machine or a fatigue testing machine.

[0044] According to this embodiment, compared to conventional configurations, it is possible to reduce the amount of data required for analyzing the strength properties of metal materials. As a result, for example, the types of strength testing machines that can be applied to obtain such data can be increased (for example, general-purpose machines can be used), making it easier to perform the desired analysis simply (for example, easily), and contributing to cost reduction of the analysis.

[0045] The method and program for analyzing the strength properties of a metallic material in this embodiment only needs to be configured to identify three material parameters using yield point data for strain rates obtained from strength tests under three different loading conditions, and thereby formulate the strain rate dependence of the yield point, allowing for a variety of design modifications. In other words, it is possible to appropriately apply common technical knowledge from various fields (for example, the field of metallic materials, the field of strength analysis, the field of computers and programs applicable to strength analysis, etc.) and modify the design by appropriately referring to prior art documents as needed. One example of this is shown in the following embodiment.

[0046] Examples In this example, electromagnetic soft iron (a metallic material corresponding to JIS-SUY-0) was used as the test material (subject of analysis), and a test piece 1 was obtained by forming the electromagnetic soft iron into a thin plate shape as shown in Figure 1. Strength tests were then conducted on three different loading conditions (load speeds of 1 mm / s, 2 m / s, and 10 m / s). Using the yield point data with respect to strain rate obtained from these strength tests, the first calculation step S1 and the second calculation step S2 were appropriately performed to attempt to formulate the strain rate dependence of the yield point in the electromagnetic soft iron.

[0047] <Composition of Test Specimen 1> Test specimen 1 was obtained by shaping the electromagnetic soft iron (the material to be analyzed) into a thin plate (thickness t=2 mm) as shown in Figure 1, and then performing heat treatment (annealing) at a temperature of 850°C for 6 hours. After the heat treatment, the microstructure of the cross-section of the central part of test specimen 1 was observed after etching with Nital, and the grain size was measured. The average grain size was found to be 101 μm.

[0048] In the test specimen 1 shown in Figure 1, a constricted portion 11 is provided at a position offset to one side in the longitudinal direction (left-right direction in Figure 1; hereinafter simply referred to as the longitudinal direction) from the center of the test specimen 1, and the diameter is reduced in the short direction (up-down direction in Figure 1; hereinafter simply referred to as the short direction), thus forming a shape similar to a so-called dumbbell-shaped test specimen. As a result, the gripping portion 12, which is one end in the longitudinal direction of the test specimen 1, is smaller in shape than the gripping portion 13, which is the other end in the longitudinal direction of the test specimen 1.

[0049] On one flat surface 15 in the thickness direction of the test specimen 1, thin strain gauges 17a and 17b are attached to the central part of the constricted portion 11 and the central part of the gripped portion 13, respectively. On the flat surface 16, which is the back side of the flat surface 15 of the test specimen 1, a random pattern colored area (not shown) made of black ink applied for measurement by digital image correlation is provided in the central part of the constricted portion 11, and a strain gauge 17b (not shown) is attached to the central part of the gripped portion 13.

[0050] <Method of Tensile Testing> The tensile test was performed using a hydraulic servo-type tensile testing machine 2 (HITS-T10 manufactured by Shimadzu Corporation) equipped with a run-up mechanism as shown in Figure 2. The tensile testing machine 2 shown in Figure 2 mainly comprises gripping parts (gripping devices) 21 and 22 that grip the gripped parts 12 and 13 of the test piece 1 in a position where it is extended vertically (hereinafter simply referred to as the vertical direction as appropriate), a load cell 23 connected to the gripping part 21 located on the lower vertical side, and a movable part 24 that can move the gripping part 22 located on the upper vertical side by pulling it vertically upward.

[0051] The movable part 24 has a rod-shaped run-up rod 25 connected to the gripping part 22, and a cylindrical piston rod 26 that can house the run-up rod 25 so that it can reciprocate vertically and is movable vertically by the drive of a hydraulic servo (hydraulic cylinder) (not shown). An inlet / outlet 20 is provided on the vertically lower side of the piston rod 26, through which the run-up rod 25 can be moved in and out.

[0052] On the upper vertical side of the outer circumferential surface of the run-up rod 25, a tapered portion 25a is formed, which is inclined to increase in diameter toward the upper vertical side. On the other hand, on the lower vertical side of the inner circumferential surface of the piston rod 26, a tapered portion 26a is formed, which is inclined to decrease in diameter toward the lower vertical side (inclined at approximately the same angle as the tapered portion 25a).

[0053] For example, in the moving section 24 as shown in Figure 2, when the piston rod 26 is moved vertically upward (for example, at a high loading speed, as indicated by the white arrow in the figure), in the run-up section 27 until the tapered portion 25a of the run-up rod 25 and the tapered portion 26a of the piston rod 26 come into contact (surface contact), the run-up rod 25 protrudes from the entrance / exit 20 of the piston rod 26 as the movement progresses. Then, after the piston rod 26 has moved further through the run-up section 27, the run-up rod 25 moves vertically upward together with the piston rod 26 (for example, at an initial speed of a high loading speed). As a result, a tensile load is applied to the test piece 1.

[0054] <Measurement of load and strain> In this embodiment, the testing machine 2 was placed in a room temperature atmosphere (at T=293K) as shown in Figure 2, and the test specimen 1 was loaded under loading conditions of loading speeds of 1 mm / s, 2 m / s, and 10 m / s, and the load (nominal stress σ) under these conditions was measured. n (Mpa) and strain (nominal strain ε) n The (%) values ​​were measured as shown below. In this example, two measurements were taken for each load condition (using two test pieces 1), and the average value from these two measurements was adopted as the respective measured value.

[0055] First, the load was measured using either a strain gauge 17b or a load cell 23. In this embodiment, when the test specimen 1 was loaded at a load rate of 1 mm / s, the correlation between the measured values ​​of the strain gauge 17b and the measured values ​​of the load cell 23 was investigated, and it was found that there was a linear relationship. Therefore, when loading was performed at relatively fast load rates (e.g., 2 m / s, 10 m / s), a converted value derived based on this linear relationship and the measured values ​​of the strain gauge 17b was appropriately applied as the measured value at that load.

[0056] Strain was measured using either a strain gauge 17a or a digital image correlation method via the colored portion of the constricted section 11. In this embodiment, if the nominal strain of the test piece 1 was less than 2%, the measurement taken with the strain gauge 17a was used as the measured value. If the nominal strain was 2% or more, the average value of the measurement taken using the digital image correlation method on the colored portion of the constricted section 11 in the longitudinal direction region of 8 mm was used as the measured value.

[0057] <Measurement results from tensile testing> Figure 3 shows the measurement results of the tensile test for each loading condition as stress-strain curves. According to Figure 3, it can be seen that as the loading rate increases, the stress-strain curve tends to shift towards the high-stress side. From this, it can be inferred that the mechanical properties of the electromagnetic soft iron applied to test specimen 1 exhibit a strain rate dependence.

[0058] Figure 4 is an enlarged view of the region where the yield point occurs in each stress-strain curve of Figure 3. According to Figure 4, in each stress-strain curve, the points where the maximum value occurs (indicated by symbols 41 to 43 in the figure) are the upper yield points, indicating that yield stress has been generated.

[0059] In each stress-strain curve in Figure 4, the strain rate at the yield point can be derived by performing calculations using the central difference method based on the strain value at the respective yield point. In other words, a value corresponding to the solution of equation (5) can be derived for each.

[0060] For example, if we change the stress-strain curve for a load condition of a load rate of 1 mm / s to data for change over time, we can separate it into a stress-time curve and a strain-time curve, as shown in Figure 5. In the strain-time curve, the slope of the tangent line at the point indicated by reference numeral 51 in Figure 5 corresponds to the strain rate.

[0061] Figure 6 shows the relationship between the yield point and strain rate in each stress-strain curve in Figure 4. According to Figure 6, it can be inferred that the electromagnetic soft iron applied to test specimen 1 has the characteristic that the yield point increases as the strain rate increases.

[0062] <Formulation of the strain rate characteristics at the yield point> In the first calculation step S1, the yield point and strain rate for each stress-strain curve in Figure 4 were substituted into the simultaneous equations (6) to (10) to derive the material parameters A, B, and C, which were found to be A = 5.88 × 10⁻⁶. 15 / s, B=8.32MPa, C=3.82×10 4 It became K.

[0063] Then, in the second calculation step S2, by substituting A, B, and C derived in the first calculation step S1 into equations (3) and (4) and performing the calculation, σ y We were able to derive H'. The yield point-strain rate curve in Figure 7 is derived from σ as described above. y This shows the curve formulated by H'. According to Figure 7, it can be seen that the electromagnetic soft iron applied to test piece 1 has a strain rate dependence of the yield point, and that it is possible to analyze the strength characteristics.

[0064] Although the present invention has been described in detail only with respect to the specific examples described above, it will be obvious to those skilled in the art that a wide variety of modifications are possible within the scope of the technical concept of the present invention, and it is natural that such modifications fall within the scope of the claims. [Explanation of Symbols]

[0065] 1…Test piece 2…Tensile testing machine

Claims

1. A method for analyzing the strength properties of a metallic material using computer calculations, The strain rate ε when a load is applied to a molded body formed by molding the metal material at three different load rates and deformed by performing a strength test on the molded body ・ １ , ε ・ ２ , ε ・ ３ and, the yield points σ ・ １ , σ ・ ２ , σ ・ ３ with respect to the strain rate ε ｙ,１ , σ ｙ,２ , σ ｙ,３ are substituted into the simultaneous equations of the following equations (6) to (10) and calculated to derive A, B, and C in a first calculation step, By substituting A, B, and C derived in the first calculation step into equations (3) and (4) below and performing the calculation, σ ｙ The second operation step is to derive H', A method for analyzing the strength properties of a metallic material, characterized by having [a certain characteristic]. Note that among the symbols in equations (3), (4), (6) to (10) below, ε ・ σ is the strain rate. ｙ ε is the yield point, T is the temperature (absolute temperature), R is the gas constant, H is the apparent activation energy, and H' is the strain rate ε with respect to temperature T. ・ The parameters A, B, and C, which describe the characteristics, are material parameters. [Math 3] [Math 4] [Math 6] [Number 7] [Number 8] [Number 9] [Number 10]

2. The method for analyzing the strength properties of a metallic material according to claim 1, characterized in that the metallic material has a body-centered cubic lattice structure.

3. A program characterized by causing the computer to perform the first and second steps of the method for analyzing the strength properties of a metallic material according to claim 1 or 2.

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