JP2019174270A - Deformation resistance measuring method of elastic-plastic material - Google Patents

Abstract

To measure a deformation resistance of an elastic-plastic material with higher accuracy.SOLUTION: The deformation resistance measuring method of the elastic-plastic material includes: a step for calculating a relational expression of a coefficient group of an approximated curve of a plastic load curve and a coefficient group of a hardening rule of an elastic-plastic material by extracting a plastic load curve from a load curve and an unload curve contained in the load-displacement curve at the time of a hardness test of an elastic-plastic material; and a step for determining the coefficient group of the hardening rule of a measuring object elastic-plastic material based on the coefficient group and the relational expression of the approximated curve of the plastic load curve by extracting a plastic load curve from the load curve and unload curve contained in the load-displacement curve at the time of the hardness test of the measuring object elastic-plastic material.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a method for measuring deformation resistance of an elastic-plastic material.

  In order to measure the deformation resistance, it is necessary to cut and test a tensile test piece or a compression test piece from the material, and therefore it is not easy to measure the deformation resistance in a minute region. On the other hand, a method for estimating the deformation resistance using a nanoindenter has also been tried, but the indenter is extremely small, so although the deformation resistance of each structure such as ferrite, pearlite, and martensite can be known, In order to derive a macro deformation resistance as an average value, it is necessary to average the measurement values at a large number of measurement points, which is not easy. Further, when a nanoindenter is used, the estimated deformation resistance is up to several percent strain, so the deformation resistance in large deformation such as forging or wire drawing cannot be estimated.

On the other hand, for example, Patent Document 1 proposes a method for obtaining a material constant of an elastic-plastic material using a hardness tester. Specifically, in Patent Document 1, a curve composed of a, b, and c when a formula of a load P-displacement δ curve generated when a hardness test is performed on an elastoplastic material is P = aδ ² + bδ + c. The relationship between the constant set and the material constant set consisting of the yield stress σ _y , work hardening index n and work hardening coefficient A in a certain elastic-plastic material is stored in a database in advance, and the load obtained by the hardness test of the material to be investigated A method is described in which an actual curve constant set is obtained from a displacement curve, and the material constant set of the material to be investigated is determined by collating this curve constant set with a database.

JP-A-9-288050

  However, when the deformation resistance is estimated using a loading curve which is a combined deformation of elastic deformation and plastic deformation as in the technique described in Patent Document 1, for example, the elastic modulus of the test piece at the time of creating the database and the investigation target When the elastic modulus of the test piece is different, there is a problem that sufficient accuracy cannot be obtained.

  Therefore, an object of the present invention is to provide a novel and improved method for measuring deformation resistance of an elastic-plastic material, which can measure the deformation resistance of an elastic-plastic material with higher accuracy.

According to an aspect of the present invention, a plastic loading curve is extracted from a loading curve and an unloading curve included in a load-displacement curve at the time of a hardness test of an elastoplastic material, and a coefficient set and an elastic group of an approximate curve of the plastic loading curve are extracted. A step of calculating a relational expression with a coefficient set of a hardening law of a plastic material, and extracting a plastic load curve from a load curve and an unload curve included in a load-displacement curve at the time of a hardness test of an elastic plastic material to be measured, A method for measuring a deformation resistance of an elastoplastic material, comprising: determining a coefficient set of a hardening rule of an elastoplastic material to be measured based on a coefficient set of an approximate curve of a plastic loading curve and a relational expression.
According to the above configuration, since the coefficient set of the hardening rule of the elastoplastic material to be measured is determined based on the plastic loading curve indicating the plastic displacement generated in the loading process, the deformation resistance of the elastoplastic material can be determined with higher accuracy. Can be measured.

  In the above method for measuring deformation resistance of an elastoplastic material, the approximate curve of the plastic loading curve is a cubic curve passing through the origin, and the hardening law of the elastoplastic material and the elastoplastic material to be measured is the Ludwick hardening law. Good.

It is a flowchart which shows the schematic step of the deformation resistance measuring method which concerns on the 1st Embodiment of this invention. It is a figure for demonstrating the method to acquire the load-displacement curve at the time of the hardness test of an elastic-plastic material in the example of FIG. It is an enlarged view of FIG. 2A. It is a graph which shows the example of the load-displacement curve in the 1st Embodiment of this invention. It is a graph which shows the example of the approximate curve of the plastic loading curve in the 1st Embodiment of this invention. It is a stress-plastic strain graph which shows the plastic strain computed from the material constant group determined by the Example and the comparative example about the SUJ2-QT material, and the measured value of the plastic strain in a tension test. It is a stress-plastic strain graph which shows the plastic strain computed from the material constant group determined by the Example and the comparative example about the SCr420 normal material, and the measured value of the plastic strain in a tension test. It is a stress-plastic strain graph which shows the plastic strain computed from the material constant group determined by the Example and the comparative example, and the measured value of the plastic strain in a tensile test about S10C normal material.

  Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the present specification and drawings, components having substantially the same functional configuration are denoted by the same reference numerals, and redundant description is omitted.

(First embodiment)
FIG. 1 is a flowchart showing schematic steps of a deformation resistance measuring method according to the first embodiment of the present invention. In the present embodiment, the deformation resistance measuring method extracts a plastic loading curve from a load-displacement curve at the time of a hardness test of an elastic-plastic material having a known hardening rule coefficient set (hereinafter also referred to as a material constant set). Step S10 for calculating a relational expression between a coefficient set of an approximate curve of a plastic loading curve (hereinafter also referred to as a curve constant set) and a material constant set of an elastoplastic material, and an elastoplastic material to be measured whose material constant set is unknown Step S20 for extracting a plastic loading curve from a load-displacement curve at the time of a hardness test and determining a material constant set of an elastic-plastic material to be measured based on a curve constant set of an approximate curve of the plastic loading curve and the above relational expression. Including. Here, since the hardening rule is a mathematical expression of the deformation resistance of the elastoplastic material, determining the material constant set of the hardening rule is equivalent to measuring the deformation resistance of the elastoplastic material.

  2A and 2B are diagrams for explaining a method for obtaining a load-displacement curve in the hardness test of the elastic-plastic material in the example of FIG. 2B is an enlarged view of FIG. 2A. When the material constant set of the hardening rule of the elastoplastic material is known, the load against the indentation amount during the hardness test, that is, the load-displacement curve can be predicted with high accuracy by using the finite element method (FEM). it can. 2A and 2B show an example of a two-dimensional axisymmetric model used to obtain a load-displacement curve in this way. In the illustrated example, the indenter 1 is an elastic body assuming a diamond having an elastic modulus of 1050 GPa and a Poisson's ratio of 0.1, and the radius of curvature of the tip spherical surface is 1/16 inch≈1.6 mm. The pushing amount of the indenter 1 was 20 μm. The test body 2 is an elastic-plastic body having a diameter of 20 mm and a height of 25 mm, and has an elastic modulus of 190 GPa and a Poisson's ratio of 0.3.

  In the model as described above, the larger the radius of curvature of the tip spherical surface of the indenter 1 is, the smaller the influence of friction is, so that the estimation accuracy of the material constant group is improved. On the other hand, if the radius of curvature of the tip spherical surface of the indenter 1 is increased, the reaction force at the time of pushing increases, and the testing machine becomes larger in order to increase the rigidity of the hardness testing machine. From these viewpoints, the radius of curvature of the tip spherical surface of the indenter 1 is desirably 10 mm to 0.25 mm. Further, the tip shape of the indenter 1 is not limited to a spherical surface, but can be a quadrangular pyramid (Vickers) or a triangular pyramid (Berkovic), but the model can be two-dimensional axisymmetric. Thus, an axisymmetric shape such as a spherical surface or a cone is advantageous.

Here, the elastic-plastic material constituting the specimen 2, Ludwik curing law _{(σ = Y 0 + Kε p} n) of the material constants set _(Y 0, K, n) are known. In step S10 shown in FIG. 1, a load-displacement curve at the time of a hardness test is acquired for a plurality of elastic-plastic materials having different material constant pairs of hardening rules, and the plastic loading curve extracted from each load-displacement curve is obtained. By calculating the relational expression between the curve constant group of the approximate curve and the material constant group of the elastoplastic material, a relational expression capable of accurately determining the material constant group of the elastoplastic material to be measured can be obtained. In the example described below, Y ₀ (500 MPa, 1000 MPa, 2000 MPa), K (2000 MPa, 4000 MPa, 8000 MPa), and n (0.1, 0.2, 0.4) are set for the material constant group of the Ludwick curing rule. The relational expression is calculated using 3 × 3 × 3 = 27 elasto-plastic materials, each of which has three values set.

FIG. 3 is a graph showing an example of a load-displacement curve in the first embodiment of the present invention. In the illustrated example, an elastic-plastic material in which the material constant set of the Ludwick hardening rule is Y ₀ = 2000 MPa, K = 4000 MPa, and n = 0.2 is determined by the method described above with reference to FIGS. 2A and 2B. The acquired load-displacement curve is shown. The load-displacement curve indicates a loading curve indicating the displacement when the indenter 1 is pushed into the test body 2 with a predetermined load (loading process), and the displacement when the indenter 1 is subsequently released (unloading process). Including unloading curve. Since the plastic displacement is not restored in the unloading process, the residual plastic displacement δ ₀ remains in the unloading curve. The shift unloading curve obtained by shifting the unloading curve by the residual plastic displacement δ ₀ and passing through the origin corresponds to the elastic displacement generated in the loading process. Therefore, by extracting the displacement (elastic displacement) of the shift unloading curve from the displacement (elastic displacement + plastic displacement) of the loading curve included in the load-displacement curve, the plastic loading curve indicating the plastic displacement generated in the loading process is extracted. can do.

FIG. 4 is a graph showing an example of an approximate curve of a plastic loading curve in the first embodiment of the present invention. In the illustrated example, the range of 33% to 100% of the displacement of the plastic loading curve illustrated in FIG. 3 is approximated by a cubic curve (P = aδ ³ + bδ ² + cδ) passing through the origin. Here, the reason why the approximate range is limited to the range of 33% to 100% of the displacement is that in the region where the displacement is small, there is a possibility that the accuracy of approximation may be reduced due to disturbance due to yield elongation or the like. The reason why the approximate curve is a cubic curve that passes through the origin is that the plastic loading curve passes through the origin, and the material constant set (Y ₀ , K, n) of the Ludwick hardening rule includes three elements. Table 1 below shows the material constant sets (Y ₀ , K, n) of the 27 types of elastoplastic materials described above and the curve constant sets (a, b, c) of the approximate curves of the plastic loading curve.

From the relationship between the material constant group and the curve constant group shown in Table 1, a relational expression represented by the following formula (1) and the coefficients in Table 2 can be calculated. In the equation (1), by setting coefficients d _{1 to} d ₂₇ as shown in the following Table 2 for each of the curve constant pairs (a, b, c), all ₂₇ types of elastic-plastic materials The curve constant set (a, b, c) can be calculated from the constant set (Y ₀ , K, n). In the formula (1), α represents any one of a, b, and c.

A set of curve constants of approximate curves of plastic loading curves (a , B, c), the material constant set (Y ₀ , K, n) of the hardening rule of the elasto-plastic material to be measured can be determined. Specifically, a set of curve constants (a, b, c) calculated for the elastoplastic material to be measured and a set of curve constants (a , B, c) can be determined as a material constant set (Y ₀ , K, n) that matches within a predetermined error range.

(Second Embodiment)
As a second embodiment of the present invention, in a deformation resistance measuring method for determining a material constant set of an elastic-plastic material to be measured in the same steps as in the first embodiment, a Ludwick hardening rule is used as a hardening rule for an elastic-plastic material. it may be used n-th power hardening law (σ = Kε _p ⁿ⁾ instead. In this case, the plastic loading curve extracted from the load-displacement curve at the time of the hardness test of the elastoplastic material by the same method as in the first embodiment is a quadratic curve (P = aδ ² + bδ) passing through the origin. Approximate. In the example described below, with respect to the material constant group of the n-th power hardening rule, there are four values for K (500 MPa, 1000 MPa, 2000 MPa, 8000 MPa) and three values for n (0.1, 0.2, 0.4). The relational expression is calculated using 4 × 3 = 12 types of elastoplastic materials. Table 3 below shows the material constant groups (K, n) of 12 kinds of elastoplastic materials and the curve constant groups (a, b) of the approximate curve in the range of 33% to 100% of the displacement of the plastic loading curve. .

From the relationship between the material constant group and the curve constant group shown in Table 3, a relational expression represented by the following equation (2) and the coefficient in Table 4 can be calculated. In equation (2), by setting coefficients d _{1 to} d ₁₂ as shown in the following Table 4 for each of the curve constant groups (a, b), the material constant groups are obtained for all twelve elastoplastic materials. The curve constant set (a, b) can be calculated from (K, n). In the formula (2), α represents one of a and b.

  A set of curve constants (a) of the approximate curve of the plastic loading curve extracted from the load-displacement curve at the time of the hardness test of the elastoplastic material to be measured by the relational expression represented by the above formula (2) and the coefficient in Table 4. , B), the material constant set (K, n) of the hardening rule of the elasto-plastic material to be measured can be determined. Specifically, the curve constant set (a, b) calculated for the measurement target elasto-plastic material and the relational expression expressed by the formulas (2) and the coefficients in Table 4 (a, b). ) Can be determined as a material constant pair (K, n) that matches within a predetermined error range.

(Comparative example)
As a comparative example, while using the n-th power hardening law as curing law elastoplastic material as in the second embodiment described above the (σ = Kε _{p ^n),} load at hardness test elastoplastic material - displacement curve An example in which the included loading curve (see FIG. 3, which is different from the plastic loading curve) is used as an approximation target will be described. In the example described below, as in the second embodiment described above, the material constant set of the n-th power hardening rule is set by using 12 types of elastoplastic materials in which K is set to 4 and n is set to 3 types. The relational expression was calculated. A set of material constants (K, n) of 12 elasto-plastic materials and a set of curve constants (a, b) of a quadratic curve passing through the approximated origin in the range of 33% to 100% of the displacement of the loading curve The results of determining the relationship are shown in Table 5 below.

From the relationship between the material constant group and the curve constant group shown in Table 5, the relational expression represented by the equation (2) and the coefficient in Table 6 used in the second embodiment can be calculated. In the equation (2), by setting coefficients d _{1 to} d ₁₂ as shown in the following Table 6 for each of the curve constant groups (a, b), the material constant groups are set for all twelve elastoplastic materials. The curve constant set (a, b) can be calculated from (K, n).

  Also in this comparative example, the curve constant of the approximate curve of the load curve included in the load-displacement curve at the time of the hardness test of the elasto-plastic material to be measured is obtained by the relational expression represented by the above formula (2) and the coefficient of Table 6. From the set (a, b), the material constant set (K, n) of the hardening rule of the elasto-plastic material to be measured can be determined. Specifically, a set of curve constants (a, b) calculated from the loading curve for the elastoplastic material to be measured, and a set of curve constants calculated by the relational expressions represented by the coefficients in Formula (2) and Table 6 ( The material constant set of the elasto-plastic material to be measured can be determined as a material constant set (K, n) that matches a, b) within a predetermined error range.

(Verification)
Verification was performed for the first embodiment (Example 1), the second embodiment (Example 2), and the comparative example of the present invention described above. Specifically, a JIS No. 4 sub-size tensile test piece was cut out from each of the SUJ2-QT material, the SCr420 normal material, and the S10C normal material, a tensile test was performed, and the deformation resistance was obtained from the stress-strain curve. The elastic modulus was 190 GPa for the SUJ2-QT material, 200 GPa for the SCr420 normal material, and 224 GPa for the S10C normal material. Using this deformation resistance and elastic modulus, a load-displacement curve at the time of the hardness test was obtained by the method described with reference to FIGS. 2A and 2B. For this load-displacement curve, Example 1 (approximate the plastic loading curve with a cubic curve passing through the origin), Example 2 (approximate the plastic loading curve with a quadratic function passing through the origin), and Comparative Example Table 7 shows the results obtained for each curve constant set (approximate the loading curve with a quadratic function passing through the origin).

Here, in Example 1, the curve constant set (a, b, c) calculated for each of the SUJ2-QT material, the SCr420 normal material, and the S10C normal material, and the coefficients of the above formula (1) and Table 2 were used. In order to match the curve constant set (a, b, c) calculated by the relational expression expressed by the following formula within an error range of 1.0% or less, Excel (registered trademark) The material constant set (Y ₀ , K, n) of the Ludwick hardening rule was determined using the solver function. Similarly, in Example 2, the curve constant set (a, b) and the curve constant set (a, b) calculated by the relational expression represented by the above-described equation (2) and the coefficients in Table 4 are 1. The material constant pair (K, n) of the n-th power hardening rule was determined so as to match within a range of error of 0 or less. Similarly, in the comparative example, the curve constant set (a, b) and the curve constant set (a, b) calculated by the relational expression represented by the coefficients shown in the above formula (2) and Table 6 are 1. The material constant pair (K, n) of the n-th power hardening rule was determined so as to match within a range of error of 0 or less. Table 8 shows the material constant groups determined in Example 1, Example 2, and Comparative Example.

  5, FIG. 6 and FIG. 7 respectively show the plastic strain calculated from the material constant set determined in Examples and Comparative Examples and the tensile test for SUJ2-QT material, SCr420 normal material, and S10C normal material. It is a stress-plastic strain graph which shows the measured value of plastic strain. For each of the SUJ2-QT material, the SCr420 normal material, and the S10C normal material, Example 1 (Ludwick hardening law + plastic loading curve) reproduces the measured value with the highest accuracy. Further, Example 2 (n-th power hardening law + plastic loading curve) also reproduces the measured values with higher accuracy than the comparative example (n-th power hardening law + loading curve). The elastic modulus of the SCr420 normal material and the S10C normal material is different from the elastic modulus (190 GPa) of the test body 2 in the finite element method (FEM) model described with reference to FIGS. 2A and 2B. In Example 2, even in such a case, the actual measurement value could be reproduced with high accuracy.

  From the results of the above verification, the embodiment of the present invention using a plastic loading curve extracted from a load-displacement curve at the time of a hardness test in order to determine a material constant set of an elastic-plastic material to be measured has a wide range of strengths. Even if the elastic modulus of the steel material of the level is different from that at the time of calculating the relational expression, it is shown that it is effective for accurately measuring the deformation resistance of the elasto-plastic material to be measured. Further, in the embodiment of the present invention, it was also shown that the accuracy is further improved when the Ludwick curing rule is used as the curing rule and the approximate curve is a cubic curve passing through the origin.

  Although exemplary embodiments of the present invention have been described above, the technical scope of the present invention is not limited to these embodiments, and the present invention is within the scope of the technical idea described in the claims. Including embodiments that have been changed or modified in accordance with what can be conceived by those having ordinary skill in the art.

  1 ... indenter, 2 ... specimen.

Claims (2)

The plastic loading curve is extracted from the loading curve and unloading curve included in the load-displacement curve at the time of the hardness test of the elastoplastic material, and the coefficient set of the approximate curve of the plastic loading curve and the coefficient of the hardening law of the elastoplastic material Calculating a relational expression with the pair;
The plastic loading curve is extracted from the loading curve and unloading curve included in the load-displacement curve at the time of the hardness test of the elastoplastic material to be measured, and based on the coefficient set of the approximate curve of the plastic loading curve and the relational expression Determining a coefficient group of a hardening rule of the elastoplastic material to be measured, and measuring a deformation resistance of the elastoplastic material. The approximate curve of the plastic loading curve is a cubic curve passing through the origin,
The method for measuring deformation resistance of an elastoplastic material according to claim 1, wherein a hardening rule of the elastoplastic material and the elastoplastic material to be measured is a Ludwick hardening rule.

Images