Stress-strain relation estimation method

Abstract

A stress-strain relationship estimation method according to the present invention comprises: a step (S1) for performing a torsion test on a first round bar test piece (10) to obtain a relationship between a torsion torque and a torsion angle; a step (S3) in which a torsion test is performed on a second round bar test piece (10) having a parallel section (11) having a smaller radius than the first round bar test piece (10), and the relationship between the torsion torque and the torsion angle is obtained; a step (S5) in which the relationship between the shear stress and the surface shear strain is obtained on the basis of the relationship between the torsion torque and the torsion angle obtained by the respective torsion tests of the first round bar test piece (10) and the second round bar test piece (10); and a step (S7) in which the shear stress and the surface shear strain are converted into uniaxial tensile stress and strain, and the relationship between the stress and the strain is estimated.

Description

Technical Field

[0001] This invention relates to a method for estimating stress-strain curves, and particularly to a method for estimating stress-strain curves that can accurately estimate the relationship between stress and strain in a high-strain region (strainport larger than uniform elongation) of metallic materials. Background Technology

[0002] In the press forming of thin metal sheets, there are cases where the material is subjected to deformation exceeding the uniform elongation under uniaxial tension. In the implementation of press forming analysis based on high-precision FEM (finite element analysis), understanding the work-hardening property (stress-strain relationship) after the uniform elongation during uniaxial tension is crucial. In particular, the uniform elongation of ultra-high tension materials is very small (e.g., the uniform elongation of 1180 MPa steel is 6-7%), therefore, understanding the stress-strain relationship after the uniform elongation (e.g., when the elongation reaches approximately 20%) is important.

[0003] To date, methods for obtaining stress-strain relationships have been proposed using hydraulic bulging tests (Non-Patent Document 1), compression tests (Non-Patent Document 2), and shearing tests (Non-Patent Document 3, Patent Document 1). These testing methods, compared to conventional uniaxial tensile tests, are less prone to causing necking and can impart large deformation states, thus enabling the determination of stress-strain relationships after uniform elongation in uniaxial tension. Furthermore, methods have been proposed for estimating stress-strain relationships in high-strain regions after necking occurs using uniaxial tensile tests (Non-Patent Document 4, Patent Document 2). This method uses strain distribution measured by methods such as Digital Image Correlation (DIC) to theoretically calculate the tensile load acting on the tensile test specimen.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Patent No. 5910803

[0007] Patent Document 2: Japanese Patent No. 6669290

[0008] Non-patent literature

[0009] Non-patent literature 1: Nasser, A. et al.: J. Mater. Proc. Technol., 210 (2010), 429-436.

[0010] Non-patent literature 2: Iwata et al.: Plasticity and Processing, 54-632 (2013), 836-840.

[0011] Non-patent literature 3: Chengchuan et al.: Plasticity and Processing, 62-727 (2021), 103-108.

[0012] Non-patent literature 4: Shirakami et al.: Iron and Steel, 103-10 (2017), 589-595. Summary of the Invention

[0013] The problem that the invention aims to solve

[0014] However, the hydraulic bulging test in Non-Patent Document 1 yields the stress-strain relationship under an equi-biaxial tensile stress state (a state applied isotropically in-plane), while the compression test in Non-Patent Document 2 yields the stress-strain relationship under compression. To use the results obtained from these tests in FEM-based stamping analysis, a transformation to a stress-strain relationship equivalent to uniaxial tension is required. Depending on the anisotropic yield function used in this transformation, errors may arise.

[0015] Furthermore, in hydraulic bulging tests, it is often assumed that the strain and stress at the apex of the specimen are equal regardless of direction. In recent years, strain has been measured using DIC (Diverterless Induction Coefficient), which, while considering the influence of strain direction, still relies on the hydraulic pressure to estimate stress as a constant stress, independent of direction. Therefore, the estimated stress is considered to contain errors, and the obtained stress-strain relationship cannot be considered sufficiently accurate. Moreover, the aforementioned hydraulic bulging test requires a specialized testing machine, making it impractical in terms of versatility. Furthermore, hydraulic bulging tests ultimately result in necking and fracture of the specimen, making it impossible to obtain the stress-strain relationship up to the high-strain region where necking occurs.

[0016] On the other hand, in the compression test of Non-Patent Document 2, even if the strain applied to the test piece increases, necking does not occur. However, the friction between the test piece and the clamps and the influence of the clamps are significant, requiring correction using FEM analysis. Furthermore, in order to apply compression tests to thin steel sheets, from the perspective of measuring strain in the thickness direction, it is necessary to stack the thin steel sheets, and it is believed that errors caused by stacking also exist.

[0017] Furthermore, the methods in Non-Patent Literature 3 and Patent Literature 1 require assumptions about the theoretical calculations of the load acting on the tensile test specimen (e.g., the associated flow rule, the formula representing the relationship between the plastic strain increment and the stress state, anisotropic yield functions, etc.). Moreover, when necking occurs in the tensile test specimen, the strain ratio distribution in the width direction differs, significantly affecting the accuracy of the pre-assumed yield function, potentially leading to errors if the assumptions deviate from reality. In particular, after necking occurs in the thickness direction of the tensile test specimen, it is affected by shearing in the thickness direction, but the yield function does not consider shearing in the thickness direction, thus sometimes further increasing the error. Additionally, this method uses a camera to measure strain, making it unsuitable for continuously acquiring data from the start of the tensile load until the strain region exceeds uniform elongation, provided that a regression curve of the stress-strain relationship is derived from discrete time-series strain data.

[0018] Furthermore, in the shear tests of Non-Patent Document 4 and Patent Document 2, due to the applied shear deformation, the test piece does not experience necking, and it has the advantage of being able to determine the stress-strain relationship up to fracture. However, a large-scale, specialized testing machine is needed to clamp and fix the front and back surfaces of the rectangular test piece on both sides in the width direction with a chuck, move the chuck in opposite directions, and induce in-plane shear deformation in the test piece. In addition, since the ends of the test piece undergo tensile deformation, it is not pure shear deformation, resulting in a greater reduction in plate thickness at the ends of the test piece, which introduces errors.

[0019] The present invention was made to solve the above-mentioned problems, and its purpose is to provide a stress-strain relationship estimation method that can directly and accurately estimate the stress-strain relationship in the high strain region of a metallic material without producing a necking deformation.

[0020] Methods for solving problems

[0021] The stress-strain relationship estimation method of the present invention estimates the stress-strain relationship of metallic materials, comprising the following steps: a first torsion test step, wherein a first torsion test is performed to obtain the relationship between torsional torque T1 and torsion angle Φ1, wherein the first torsion test is performed by applying a torsional torque T1 around the axis of a first round-bar specimen having a reduced section of a round bar with a first radius R1, thereby causing the reduced section to undergo shear deformation; a second torsion test step, wherein a second torsion test is performed. The relationship between torsional torque T2 and torsion angle Φ2 is obtained by applying a torsional torque T2 around the axis of a second round bar test piece having a second radius R2 smaller than the first radius R1, causing the parallel portion to shear deform. The shear stress-surface shear strain relationship is obtained by using the relationship between torsional torque T1 and torsion angle Φ1 obtained in the first torsion test step and the relationship between torsional torque T2 and torsion angle Φ2 obtained in the second torsion test step to determine the shear stress and shear strain of the surface of the parallel portion of the first round bar test piece. The relationship between the shear stress and surface shear strain (SST) is as follows: The shear stress τ and surface shear strain γ obtained in the shear stress-surface shear strain relationship acquisition step are transformed into uniaxial tensile stress σ and strain ε. The relationship between the uniaxial tensile stress σ and strain ε is estimated. In the shear stress-surface shear strain relationship acquisition step, the shear stress τ is obtained using the torsional torque T1 at the torsional angle Φ1 obtained in the first torsional test step and the torsional torque T2' when the torsional angle Φ2 obtained in the second torsional test step is consistent with the torsional angle Φ1 obtained in the first torsional test step. The surface shear strain γ is obtained using the torsional angle Φ1 obtained in the first torsional test step.

[0022] Alternatively, in the process of obtaining the shear stress-surface shear strain relationship, the shear stress τ is calculated using equation (1), and the surface shear strain γ is calculated using equation (2).

[0023] [Mathematical Expression 1]

[0024]

[0025] τ is the shear stress (Pa).

[0026] γ represents the surface shear strain (-).

[0027] T1 is the first torsional torque (Nm).

[0028] T2' is the second torsional torque (Nm).

[0029] R1 is the radius (m) of the parallel part of the first round bar test piece.

[0030] R2 is the radius (m) of the parallel portion of the second round bar test piece.

[0031] θ1 is the unit angle of twist (=Φ1 / L) (rad / m).

[0032] Φ1 is the first twist angle (rad).

[0033] L is the length (m) of the parallel portion of the first torsion test piece.

[0034] Alternatively, the first and second round bar test pieces may have clamping portions extending outward in the length direction from both ends of the parallel portion via a gradual change portion. The torsion angle Φ1 obtained in the first torsion test and the torsion angle Φ2 obtained in the second torsion test are set in the elastic region to be the same as the measured value T of the torsional torque. e The angle of twist Φ is estimated proportionally. e In the elastoplastic deformation portion, the measured value Φ0 and the estimated value Φ of the torsion angle at the elastic limit, the boundary between the elastic and elastoplastic regions, are used. s The difference (=Φ0-Φ) s The torsion angle Θ(T) of the transition portion of the first or second round bar test piece and the torsion angle Θ(T) at the elastic critical point. s The change in Θ(T) - Θ(T) s To correct the measured value of the torsion angle φ a The torsion angle φ obtained from (Φ1 or Φ2) t (=φ) a -(Φ0-Φ s )-(Θ(T)-Θ(T s ))).

[0035] Alternatively, in the first torsion test step and the second torsion test step, when the clamping portions of the two ends of each test piece in the length direction are held by the test piece holder in order to apply torsional torque to the first round bar test piece and the second round bar test piece, a gap is provided between the clamping portion and the test piece holder.

[0036] Invention Effects

[0037] According to the present invention, the stress-strain relationship in the high-strain region exceeding uniform elongation during uniaxial tensile testing of metallic materials can be obtained directly and with high precision. Furthermore, large testing equipment as in conventional hydraulic bulging, compression, or shear tests is not required; a smaller, more compact testing machine can be used to continuously obtain the stress-strain relationship in the high-strain region. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the processing flow in the stress-strain relationship estimation method according to embodiments of the present invention.

[0039] Figure 2 This is a diagram illustrating an example of a round bar test piece used in a torsion test that undergoes shear deformation under a torsional torque, as described in the stress-strain relationship estimation method according to an embodiment of the present invention.

[0040] Figure 3 This is a diagram illustrating the torsion test machine for micro round lod used in the stress-strain relationship estimation method according to an embodiment of the present invention.

[0041] Figure 4 This is a graph showing the relationship between the torsion angle and the torsional torque obtained by using torsion tests on round bar test pieces with different radii of parallel portions in the stress-strain relationship estimation method of the embodiments of the present invention. It is a graph illustrating the relationship between the torsion angle and the torsional torque with or without correction based on the torsion angle.

[0042] Figure 5 The graphs show the results of the stress-strain relationship under uniaxial tension obtained by torsion testing using a round bar test piece made of steel plate with a tensile strength of 980 MPa and a thickness of 1.2 mm in the embodiments (Example 1, Example 2) and the stress-strain relationship obtained by conventional hydraulic bulging test (Example 1) ((a) without correction of torsion angle (Example 1), (b) with correction of torsion angle (Example 2)).

[0043] Figure 6 The graph shows the results of the stress-strain relationship under uniaxial tension obtained by torsion testing using a round bar test piece made of steel plate with a tensile strength of 590 MPa and a thickness of 1.2 mm in the embodiment (Example 3 of the invention), and the stress-strain relationship obtained by conventional hydraulic bulging test (Example 2 of the prior art). Detailed Implementation

[0044] Before describing the stress-strain relationship estimation method of the embodiments of the present invention, the process of obtaining the invention and the round bar test piece and the micro-round bar torsion testing machine used in the implementation of the present invention will be described.

[0045] <The Invention Process>

[0046] As a deformation mode that is less prone to necking and can impart large deformation in a high strain region with elongation exceeding uniformity compared to the tensile deformation of a typical uniaxial tensile test, the inventors focused on the shear deformation of a torsion test using a round bar specimen. However, the shear strain of a round bar specimen increases linearly from the center (axis) of the cross-section outward in the radial direction and is distributed concentrically from the axis, resulting in non-uniform shear strain within the cross-section.

[0047] Therefore, the inventors conducted in-depth research on a method for determining shear stress and shear strain using torsion tests on round bar specimens. As a result, focusing on torsion tests on small round bar specimens with slightly different diameters (e.g., 1 mm and 1.1 mm), it was possible to assume that the shear stress τ generated on the surface of the round bar specimen did not differ significantly due to the small diameter difference. If this assumption is made, it was found that the shear stress τ acting on the surface of the round bar specimen can be calculated based on the difference in torsional torque in the torsion tests of each round bar specimen.

[0048] Furthermore, regarding the shear strain of the circular bar specimen after shear deformation, it was conceived to approximate it using the average value of the surface shear strain generated by torsion tests on circular bar specimens with slightly different diameters. Therefore, it was conceived to determine the relationship between shear stress and surface shear strain by conducting torsion tests on two types of circular bar specimens with slightly different diameters.

[0049] Furthermore, it was conceived that by assuming the isotropy of the material, the anisotropy of the actual metallic material could be corrected based on the results of uniaxial tensile tests, thereby transforming the stress and strain of uniaxial tension into shear stress and surface shear strain obtained through torsion tests of two round bar specimens with different diameters. From this, the following insight was gained: the relationship between stress and strain in uniaxial tension in high-strain regions exceeding uniform elongation can be estimated.

[0050] <Round Bar Test Piece>

[0051] The round bar test piece 10 is manufactured by cutting a tiny metal sheet (e.g., a steel plate with a thickness of 1.2 mm) cut from a metal plate while rotating it along a rotation axis in the length direction. For example... Figure 2 As shown, the round bar test piece 10 has a parallel portion 11 in the shape of a round bar and a clamping portion 15 extending outward in the length direction from both ends of the parallel portion 11 via a gradient portion 13.

[0052] The parallel portion 11 is machined into a cylindrical shape with a specified diameter smaller than the thickness of the metal plate. From the viewpoint of shear deformation, it is preferable that the diameter of the parallel portion 11 is as small as possible, but from the viewpoint of dimensional accuracy, it is preferably about 1 mm. Furthermore, the length of the parallel portion 11 in the longitudinal direction is not particularly limited, and can be appropriately set, for example, it can be about 2 to 3 mm. The gradient portion 13 is formed between the parallel portion 11 and the clamping portion 15, and is a section where the diameter changes gradually. The clamping portion 15 is a flat plate-shaped section (fixed area) held and fixed by the test piece holders 111 and 113 of the micro cylindrical bar torsion testing machine 100, described later. The thickness of the clamping portion 15 can, for example, be the same as the thickness of the metal plate supplied to the cylindrical bar test piece 10.

[0053] <Micro-bar Torsion Testing Machine>

[0054] Figure 3 This illustrates an example of a micro-round bar torsion testing machine 100 used for torsion tests employing round bar test pieces 10. For example... Figure 3 As shown, the micro-bar torsion testing machine 100 includes a step motor 101, a reduction gear 103, a rotation side torsion axis 105, a coupling 107, a fixed side torsion axis 109, test piece holders 111 and 113, a torque meter 115, and an amplifier 117.

[0055] The rotating-side torsion shaft 105 is connected to the stepper motor 101 via a coupling 107 and a reducer 103. On the other hand, the fixed-side torsion shaft 109 is connected to a torque meter 115, and an amplifier 117 is connected to the torque meter 115. The command value of the stepper motor 101 and the output from the amplifier 117 are then collected by a measurement recorder (not shown). Furthermore, test piece holders 111 and 113, which hold the two ends of the round bar test piece 10 in the longitudinal direction, are respectively provided on the rotating-side torsion shaft 105 and the fixed-side torsion shaft 109 to apply torsional torque to the round bar test piece 10.

[0056] When performing a torsion test on a round bar test piece 10 using a micro round bar torsion testing machine 100, the clamping part 15 of the round bar test piece 10 is first held by the test piece holder 111 on the rotating side torsion shaft 105 and the test piece holder 113 on the fixed side torsion shaft 109.

[0057] Furthermore, by inputting a specified command value to the stepper motor 101, a torsional torque T is applied to the clamping portion 15 of the round bar test piece 10 via the reducer 103, coupling 107, rotating torsion shaft 105, and test piece holder 111, causing the parallel portion 11 to undergo shear deformation. The torsion angle Φ of the round bar test piece 10 with the applied torsional torque can be estimated based on the command value of the stepper motor 101 and the reduction ratio of the reducer 103, or it can be directly measured by using a potentiometer or similar device capable of measuring the rotation angle of the reducer 103's rotating shaft.

[0058] In the micro-bar torsion testing machine 100, the alignment of the cores of the rotating torsion shaft 105 and the fixed torsion shaft 109 is important for the accuracy of torsional torque measurement. Therefore, it is preferable to provide a centering adjustment mechanism between the test piece holders 111 and 113 on both sides in the micro-bar torsion testing machine 100.

[0059] <Methods for Estimating Stress-Strain Relationships>

[0060] The stress-strain relationship estimation method of the embodiments of the present invention obtains the stress-strain relationship of metallic materials. Furthermore, as... Figure 1 As shown, the stress-strain relationship estimation method includes a first torsion test procedure S1, a second torsion test procedure S3, a shear stress-surface shear strain relationship acquisition procedure S5, and a stress-strain relationship estimation procedure S7. Hereinafter, the following will be used... Figure 3 The stress-strain relationship estimation method of this embodiment is implemented using the micro-bar torsion testing machine 100 shown, and the above-described steps are explained.

[0061] First Torsion Test Procedure

[0062] In the first torsion test step S1, a first torsion test is performed by applying a torsional torque T1 around the axis of a first round bar test piece 10 having a first radius R1 parallel section 11, causing shear deformation of the parallel section 11. Then, the relationship between the torsional torque T1 applied to the first round bar test piece in the first torsion test and the torsion angle Φ1 of the first round bar test piece 10 is obtained. In the first torsion test step S1, the relationship between the torsional torque T1 and the torsion angle Φ1 up to the maximum torsion angle at which a crack occurs in the parallel section 11 of the first round bar test piece 10 is obtained.

[0063] Second Torsion Test Procedure

[0064] In the second torsion test step S3, a second torsion test is performed by applying a torsional torque T2 to the core of a second round bar test piece 10, which has a second radius R2 smaller than the first radius R1, causing shear deformation of the parallel portion 11. Then, the relationship between the torsional torque T2 applied to the second round bar test piece 10 in the second torsion test and the torsion angle Φ2 of the second round bar test piece 10 is obtained.

[0065] In the second torsion test step S3, the relationship between the torsional torque T2 and the torsion angle Φ2 is obtained up to the maximum torsion angle until a crack occurs in the parallel portion 11 of the second round bar test piece 10.

[0066] Procedure for Obtaining the Shear Stress-Surface Shear Strain Relationship

[0067] In the step S5 of obtaining the shear stress-surface shear strain relationship, the relationship between the shear stress τ and the surface shear strain γ on the surface of the parallel portion 11 of the first round bar test piece 10 is determined. Furthermore, in order to determine the relationship between the shear stress τ and the surface shear strain γ, the relationship between the torsional torque T1 and the torsion angle Φ1 obtained in the first torsion test step S1, and the relationship between the torsional torque T2 and the torsion angle Φ2 obtained in the second torsion test step S3 are used.

[0068] The shear stress τ is determined using the torsional torque T1 at the torsion angle Φ1 obtained in the first torsion test step S1 and the torsional torque T2' when the torsion angle Φ2 obtained in the second torsion test step S3 is the same as the torsion angle Φ1. On the other hand, the surface shear strain γ is determined using the torsion angle Φ1 obtained in the first torsion test step S1.

[0069] The shear stress τ and the surface shear strain γ can be obtained by the following equations (1) and (2), respectively.

[0070] [Mathematical Expression 2]

[0071]

[0072] τ is the shear stress (Pa).

[0073] γ represents the surface shear strain (-).

[0074] T1 is the first torsional torque (Nm).

[0075] T2' is the second torsional torque (Nm).

[0076] R1 is the radius (m) of the parallel part of the first round bar test piece.

[0077] R2 is the radius (m) of the parallel portion of the second round bar test piece.

[0078] θ1 is the unit angle of twist (=Φ1 / L) (rad / m).

[0079] Φ1 is the first twist angle (rad).

[0080] L is the length (m) of the parallel portion of the first torsion test piece.

[0081] The shear stress τ shown in equation (1) is derived as follows. In the parallel section 11 of the cylindrical rod ( Figure 2 In the first circular bar test piece 10 (radius R1) and the second circular bar test piece (radius R2, R1 > R2) with different radii, under the condition that the torsion angle per unit length is equal, the shear strain distribution from the axis center to R2 in the radial cross section of the parallel portion 11 is equal. As a result, the stress distribution that generates torque in the first and second circular bar test pieces 10 is also equal. Therefore, the difference (T1 - T2') between the torque T1 of the first circular bar test piece 10 and the torque T2' of the second circular bar test piece 10 becomes the torque generated in the "ring portion (ring portion) of the first circular bar test piece 10 from radius R2 to the outer radius R1". Furthermore, if we consider that the shear strain generated in the parallel portion 11 is proportional to the distance from the axis center, then under the condition that the difference (R1-R2) between the radii of the first round bar test piece 10 and the second round bar test piece 10 is very small, we can assume that the torque and shear strain of the annular portion of the first round bar test piece 10 are constant. Based on this assumption, the shear stress τ on the surface of the parallel portion 11 can be expressed by equation (1). In addition, the surface shear strain γ shown in equation (2) is approximated by the average value of the shear strain generated on the surface of the parallel portion 11 through the torsion tests of the first and second round bar test pieces 10 respectively.

[0082] Stress-Strain Relationship Estimation Process

[0083] In the stress-strain relationship estimation step S7, the shear stress τ and surface shear strain γ obtained in the shear stress-surface shear strain relationship acquisition step S5 are transformed into uniaxial tensile stress σ and strain ε, respectively, and the relationship between stress σ and strain ε in uniaxial tension is estimated.

[0084] The stress σ and strain ε of uniaxial tension can be transformed using the following equations (3) and (4), respectively. Equation (3) is derived by using the shear strain γ and shear stress τ to obtain the strain ε of uniaxial tension under the assumption of equivalent plastic work in isotropic steel sheet (Mises material). In this derivation, the relationships between strain and shear strain and stress and shear stress in uniaxial tension in the plastic region, the relationship between stress and strain in uniaxial tension using the longitudinal elastic coefficient E in the elastic region, and the relationship between shear stress and shear strain using the transverse elastic coefficient G are used. Furthermore, in the derivation of equation (3), the definitions of the relationship between "elastoplastic strain", "elastic strain" and "plastic strain" in uniaxial tension, and the definitions of the relationship between "elastoplastic shear strain", "elastic shear strain" and "plastic shear strain" in shear are used. In addition, Equation (4) is obtained by modifying the relationship between stress σ and shear stress τ in uniaxial tension under the assumption of isotropic material (Mises material) under the isoplastic strain state, taking into account the anisotropy of metallic materials.

[0085] [Mathematical Expression 3]

[0086]

[0087] In equations (3) and (4), A is a correction factor considering the anisotropy of the metallic material. In the case where the metallic material is not anisotropic (isotropic), A is set to 1. Conversely, in the case where the metallic material is anisotropic, a value for A is assigned based on the stress-strain curve up to uniform elongation in a uniaxial tensile test. As the case of anisotropic metallic materials, it is known that rolled metallic materials exhibit characteristic variations in the rolling direction (L direction), its perpendicular direction to the rolling direction (C direction), and the 45° direction (D direction). Therefore, for example, when collecting tensile test specimens from the metallic material, multiple tensile test specimens can be collected along their length direction corresponding to the anisotropy of the metallic material, and a uniaxial tensile test can be performed to determine the value of A. Furthermore, in equation (3), E is the Young's modulus, which can be the value determined by a uniaxial tensile test of the metallic material. Furthermore, G is the shearing modulus, which can be calculated based on the longitudinal modulus E determined by uniaxial tensile testing and the Poisson's ratio of the metallic material (a value of 0.28-0.30 when the metallic material is steel plate).

[0088] According to the stress-strain relationship estimation method of this embodiment, the stress-strain relationship in the high-strain region exceeding the uniform elongation during uniaxial tension of a metallic material can be estimated. Furthermore, in the stress-strain relationship estimation method of this embodiment, a torsion test is performed using a round bar test piece with a diameter of approximately 1 mm. Therefore, large equipment such as conventional hydraulic bulging tests, compression tests, or shear tests is not required; by using a relatively small and compact micro-round bar torsion testing machine 100, the stress-strain relationship in the high-strain region can be estimated.

[0089] In the stress-strain relationship estimation method of this embodiment, as described above, the shear stress τ acting on the surface of the parallel portion 11 of the first and second round bar test pieces 10 is calculated assuming that there is no large difference due to the different diameters of the parallel portion 11 (refer to formula (1)). Therefore, the smaller the difference between the first radius R1 of the parallel portion 11 of the first round bar test piece 10 and the second radius R2 of the parallel portion 11 of the second round bar test piece 10, the more accurately the shear stress τ can be estimated. However, due to the limitation of the processing accuracy of the round bar test piece 10, the difference between the first radius R1 and the second radius R2 is preferably about 0.1 mm, and more preferably about 0.05 mm.

[0090] Furthermore, in the above description, in the first torsion test step S1 and the second torsion test step S3, a micro-bar torsion testing machine 100 is used to perform torsion tests and obtain the relationship between the torsional torque and torsion angle of two types of bar test pieces 10 with different diameters. However, there is a mechanical backlash in the micro-bar torsion testing machine 100 (backlash of the reducer 103, and the gap between the clamping parts of the test piece holders 111 and 113 and the clamping part 15 of the bar test piece 10). Therefore, the error in the torsion angle obtained in the elastic region after the torsional torque is initially applied around the shaft of the bar test piece 10 is large.

[0091] Therefore, it is preferable to modify the torsion angles (Φ1 and Φ2) obtained in the first torsion test step S1 and the second torsion test step S3 as follows.

[0092] First, in the torsion test, it is determined whether the shear deformation of the round bar test piece 10 is in the elastic region or the elastoplastic region. The elastic region and the elastoplastic region can be determined, for example, based on the following equation (5).

[0093] [Mathematical Expression 4]

[0094]

[0095] T eT is the measured value (T1 or T2) of the torsional torque applied to the first and second round bar test pieces 10. s It is the torsional torque at the boundary (elastic critical point) between the elastic and elastoplastic regions. Additionally, R is the radius (R1 or R2) of the parallel portion 11 of the round bar test piece 10, and Y... s It is the uniaxial yield stress of the metallic material used in the round bar test piece 10. And, A is a correction factor that takes into account the anisotropy of the metallic material, which is the same as that in equation (3) and equation (4).

[0096] Then, the measured value T of the torsional torque in the torsion test. e T s In the case of small values, the shear deformation of the parallel portion 11 of the round bar test piece 10 is determined to be an elastic region. In contrast, at the measured value T of the torsional torque... e For T s Under the above circumstances, the shear deformation of the parallel portion 11 of the round bar test piece 10 is determined to be an elastoplastic region.

[0097] When the region is determined to be elastic, the measured values ​​T of the torsion angle and torsional torque of the round bar test piece 10 are... e Proportional, let the torsion angle Φ be derived by the following equation (6). e .

[0098] [Mathematical Expression 5]

[0099]

[0100] G is the transverse elastic modulus (MPa) of the round bar test piece, and R is the radius (mm) of the parallel portion 11 of the round bar test piece 10.

[0101] On the other hand, when it is determined to be an elastoplastic region, the measured value Φ0 of the torsion angle at the elastic critical point is compared with the estimated value Φ of the torsion angle. s The difference (=Φ0-Φ) s The offset is used to correct the torsion angle obtained through torsion testing. Φ s The measured value T of the torsional torque in equation (6) e The torsional torque T at the elastic critical point s The estimated angle of twist at that time.

[0102] Furthermore, in the round bar test piece 10, the radius of the transition section 13 from the clamping part 15 to the parallel part 11 varies along the length direction. Therefore, based on the torsion angle Θ of the transition section 13 given by equation (7), the change in the torsion angle Θ of the transition section 13 relative to the elastic critical point (=Θ(T)-Θ(T)) is used. sThe torsion angle of the round bar test piece 10 is further corrected. Θ(T) is the torsion angle of the gradient section 13 under the torsional torque T. s The elastic critical point (torsional torque T) is the point where the elasticity is critical. s The twist angle of the gradient section 13 at ().

[0103] [Mathematical Expression 6]

[0104]

[0105] That is, in the case where it is determined to be an elastoplastic region, the measured value of the torsion angle φ will be corrected using the following formula (8). a The obtained value φ t The torsion angle of the round bar test piece 10.

[0106] [Mathematical Expression 7]

[0107]

[0108] Figure 4 The graph shows the relationship between the torsional angle per unit length in axial direction and the torsional torque in a torsion test using two round bar test pieces 10 with different diameters and parallel sections 11. Figure 4 The charts shown present results using round bar test pieces 10 made from steel plates with a tensile strength of 980 MPa and a thickness of 1.2 mm. The diameter of the parallel portion 11 of the first round bar test piece 10 is 1.1 mm, and the diameter of the parallel portion 11 of the second round bar test piece 10 is 1 mm. Furthermore, Figure 4 The horizontal axis is the unit torsion angle θ1 and θ2 obtained by dividing the torsion angles Φ1 and Φ2 of the first and second round bar test pieces 10 by the length L of the parallel part 11 in the length direction.

[0109] like Figure 4 As shown, in the region with a small torsion angle, as mentioned earlier, due to the mechanical clearance of the micro-round bar torsion testing machine 100, the error of the torsion angle is large. Therefore, depending on whether the torsion angle correction is present or not, the torsion torque will vary.

[0110] In a typical round bar torsion testing machine, the clamping part 15 of the round bar test piece 10 is usually fully clamped by the test piece holders 111 and 113. However, in a micro round bar torsion testing machine 100 that uses a round bar test piece 10 with a diameter of about φ1mm in the parallel part 11, a very small misalignment between the rotational torsion shaft 105 and the fixed torsion shaft 109 of the micro round bar torsion testing machine 100 can affect the accuracy of the torsional torque measurement.

[0111] Therefore, in the first torsion test step S1 and the second torsion test step S3, when the clamping portions 15 at both ends of each round bar test piece 10 in the longitudinal direction are held by the test piece holders 111 and 113, a gap can be provided between the clamping portions 15 and the test piece holders 111 and 113. Moreover, this gap is preferably about 10 μm to 20 μm. As a result, when the torsional torque of each round bar test piece 10 is applied, the clamping portions 15 can move freely without being fixed by the test piece holders 111 and 113. As a result, abnormalities such as the fluctuation of torque generated in the round bar test piece 10 due to the offset of the axis of the rotating torsion shaft 105 and the fixed torsion shaft 109 can be mitigated, and the accuracy of the torsional torque measurement can be improved.

[0112] [Example]

[0113] An experiment was conducted to verify the effectiveness of the stress-strain relationship estimation method of the present invention, and therefore it will be described below.

[0114] In this embodiment, the stress-strain relationship of steel plates with tensile strengths of 980 MPa and 590 MPa, which are metallic materials, is estimated by using the method of the aforementioned implementation method.

[0115] First, it is made of steel plate with a thickness of 1.2mm. Figure 3 The first and second round bar test pieces 10 are shown with different diameters of the parallel portion 11. The diameter of the parallel portion 11 of the first round bar test piece 10 is 1.1 mm, and the diameter of the parallel portion 11 of the second round bar test piece 10 is 1.0 mm.

[0116] Next, the first and second round bar test pieces 10 were prepared using... Figure 2 The micro-round bar torsion testing machine 100 shown is used to perform torsion tests to obtain the relationship between the torsional torque applied to each round bar test piece 10 and the torsion angle of each round bar test piece 10.

[0117] Then, based on the relationship between the torsional torque and the torsional angle obtained from the first and second round bar test pieces 10 respectively, the shear stress and surface shear strain acting on the surface of the parallel portion 11 of the first round bar test piece 10 are calculated. The calculation of shear stress and surface shear strain uses the aforementioned equations (1) and (2).

[0118] Next, the shear stress and surface shear strain calculated by the aforementioned equations (3) and (4) are transformed into uniaxial tensile stress (equivalent stress) and strain (equivalent strain), and the relationship between stress and strain is estimated.

[0119] Furthermore, in this embodiment, as described in the implementation, the stress and strain are also estimated for the case where the torsion angle obtained in the respective torsion tests of the first and second round bar test pieces 10 is corrected to calculate the shear stress and surface shear strain. In the correction of the torsion angle, the uniaxial yield stress Ys and the transverse elastic modulus G are values ​​determined by uniaxial tensile tests of steel plates of each tensile strength.

[0120] In addition, in this embodiment, the stress-strain relationship was obtained through a hydraulic bulging test as a comparison. In the hydraulic bulging test, test pieces made of steel plates with tensile strengths of 980 MPa and 590 MPa and a thickness of 1.2 mm were also used as test materials.

[0121] exist Figure 5 The diagram shows graphs comparing the results of estimating the stress-strain relationship (equivalent stress and equivalent strain) under uniaxial tension using the method of this invention for 980 MPa grade steel sheets, and the results of obtaining the equivalent stress-strain relationship through hydraulic bulging tests. The uniform elongation of the 980 MPa grade steel sheet in the uniaxial tensile test was 7.0% (true strain 0.068).

[0122] exist Figure 5 In the middle are the stress-strain curves of the estimated N number = 2 for the fabrication of the round bar test piece 10 and the implementation of the stress-strain relationship in Examples 1 and 2 of the invention. Figure 5 Example 1 of the invention shown in (a) is the result without correction of the torsion angle Φ. Figure 5 Example 2 of the invention shown in (b) is the result of a correction to the torsion angle Φ. In addition, the stress-strain curve of the prior art 1 is obtained by a hydraulic bulging test.

[0123] like Figure 5 As shown, Invention Example 1 is well consistent with Prior Art Example 1. In Invention Example 1, a high-strain region that is 35% wider than that in Prior Art Example 1 can be estimated. Furthermore, regarding... Figure 5 Invention Example 1 of (a) and Figure 5 When compared with Invention Example 2 of (b), it is shown that by correcting the torsion angle Φ obtained by the torsion test, the deviation of the elastic region can be reduced in particular.

[0124] Figure 6The diagram shows graphs comparing the results of estimating the stress-strain relationship (equivalent stress and equivalent strain) under uniaxial tension using the method of the present invention for 590 MPa grade steel sheets (Example 3 of the invention) and the results of obtaining the equivalent stress-strain relationship through a hydraulic bulging test (Example 2 of the prior art). The uniform elongation of the 590 MPa grade steel sheet in the uniaxial tensile test was 15.1% (true strain 0.141). Figure 6 In the present invention, Example 3 is a stress-strain curve obtained by fabricating a round bar test piece 10 and performing an estimated stress-strain relationship test with an N number of times = 1. In the present invention, Example 2 is a stress-strain curve obtained through a hydraulic bulging test. Furthermore, Example 3 is a result of correcting the torsion angle obtained through a torsion test.

[0125] like Figure 6 As shown, in Invention Example 3, which estimates the tensile strength of a steel plate of 590 MPa, it is possible to estimate the stress-strain relationship in a high-strain region that is more than four times that of the conventional Example 2, which was tested by hydraulic bulging.

[0126] [Potential for Industrial Applications]

[0127] According to the present invention, a stress-strain relationship estimation method is provided that can directly and accurately estimate the stress-strain relationship in the high-strain region of a metallic material without producing a necking deformation.

[0128] [Explanation of reference numerals in the attached figures]

[0129] 10 round bar test pieces

[0130] 11 Parallel Department

[0131] 13 Gradient Section

[0132] 15 clamping parts

[0133] 100 Micro Round Bar Torsion Testing Machine

[0134] 101 stepper motor

[0135] 103 reducer

[0136] 105 Rotary Side Torsion Shaft

[0137] 107 Coupling

[0138] 109 Fixed-side torsion shaft

[0139] 111 Test Piece Holder

[0140] 113 Test Piece Holder

[0141] 115 torque meter

[0142] 117 amplifier.

Claims

1. A method for estimating stress-strain relationship, wherein, The process includes the following steps: The first torsion test procedure involves conducting a first torsion test to obtain the relationship between the torsional torque T1 and the torsion angle Φ1. The first torsion test involves applying a torsional torque T1 around the axis of a first round bar test piece with a parallel part of a round bar having a first radius R1, thereby causing the parallel part to undergo shear deformation. The second torsion test procedure involves conducting a second torsion test to obtain the relationship between the torsional torque T2 and the torsion angle Φ2. The second torsion test involves applying a torsional torque T2 around the axis of a second round bar test piece having a second radius R2 that is smaller than the first radius R1, causing the parallel portion to undergo shear deformation. The shear stress-surface shear strain relationship acquisition process uses the relationship between the torsional torque T1 and the torsional angle Φ1 obtained in the first torsional test process and the relationship between the torsional torque T2 and the torsional angle Φ2 obtained in the second torsional test process to determine the relationship between the shear stress τ and the surface shear strain γ of the surface of the parallel portion of the first round bar test piece. and The stress-strain relationship estimation step transforms the shear stress τ and surface shear strain γ obtained in the shear stress-surface shear strain relationship acquisition step into uniaxial tensile stress σ and strain ε, and estimates the relationship between the uniaxial tensile stress σ and strain ε. In the process of obtaining the shear stress-surface shear strain relationship, The shear stress τ is calculated using the torsional torque T1 at the torsion angle Φ1 obtained in the first torsion test procedure and the torsional torque T2' at which the torsion angle Φ2 obtained in the second torsion test procedure is the same as the torsion angle Φ1 obtained in the first torsion test procedure. The surface shear strain γ is determined using the torsion angle Φ1 obtained in the first torsion test procedure.

2. The method for estimating the stress-strain relationship according to claim 1, wherein, In the process of obtaining the shear stress-surface shear strain relationship, the shear stress τ is calculated using equation (1), and the surface shear strain γ is calculated using equation (2). [Mathematical Expression 1] τ is the shear stress (Pa). γ represents the surface shear strain (-). T1 is the first torsional torque (Nm). T2' is the second torsional torque (Nm). R1 is the radius (m) of the parallel part of the first round bar test piece. R2 is the radius (m) of the parallel portion of the second round bar test piece. θ1 is the unit angle of twist (=Φ1 / L) (rad / m). Φ1 is the first twist angle (rad). L is the length (m) of the parallel portion of the first torsion test piece.

3. The method for estimating the stress-strain relationship according to claim 1 or 2, wherein, The first and second round bar test pieces have clamping portions that extend outward in the length direction from both ends of the parallel portion via a gradient portion. For the torsion angle Φ1 obtained in the first torsion test procedure and the torsion angle Φ2 obtained in the second torsion test procedure, In the elastic region, set to the measured value T of the torsional torque. e The angle of twist Φ is estimated proportionally. e , In the elastoplastic region, the measured value Φ0 and the estimated value Φ at the boundary between the elastic region and the elastoplastic region, i.e., the elastic critical point, are used. s The difference (=Φ0-Φ) s The torsion angle Θ(T) of the transition portion of the first or second round bar test piece and the torsion angle Θ(T) at the elastic critical point. s The change in Θ(T) - Θ(T) s To correct the measured value of the torsion angle φ a The torsion angle φ obtained from (Φ1 or Φ2) t (=φ) a -(Φ0-Φ s )-(Θ(T)-Θ(T s ))).

4. The method for estimating the stress-strain relationship according to claim 1 or 2, wherein, In the first torsion test step and the second torsion test step, when the clamping portions of the two ends of each test piece in the length direction are held by the test piece holder in order to apply torsional torque to the first round bar test piece and the second round bar test piece, a gap is provided between the clamping portion and the test piece holder.

Images