A method for obtaining uniaxial stress-strain relationship of materials based on energy

Abstract

The present invention discloses a method for obtaining a uniaxial stress-strain relationship of a material based on energy, and constructs a plane indentation energy-displacement model; and performs quasi-static indentation on a predicted material through a plane indentation test to obtain a continuous load-displacement curve, and converts the load-displacement curve into an energy-displacement curve, and fits the energy-displacement curve to obtain a loading coefficient and a loading index of the energy-displacement curve, and brings the plane indentation energy-displacement model into the plane indentation energy-displacement model to calculate material model parameters according to the loading coefficient and the loading index, and then obtains the uniaxial stress-strain relationship of the material according to the material model parameters; the present invention overcomes the shortcomings of the prior art that the test needs to be combined with finite element analysis, and the solution is time-consuming and laborious, and proposes a simple, applicable, theoretically universal, single monotonic plane indentation test method, and realizes high-precision prediction of the uniaxial stress-strain relationship of the material by means of the energy-displacement indentation test relationship and the plane indentation energy-displacement model.

Description

Technical Field

[0001] The present invention relates to the technical field of uniaxial stress-strain relationship detection, and in particular to an energy-based material uniaxial stress-strain relationship acquisition method. Background Art

[0002] The uniaxial stress-strain curve of a material is the most basic relationship curve for determining material properties, and is also the basis for the correlation of various mechanical properties of a material (such as material hardness, strength, fracture performance, and fatigue life). The conventional approach to obtaining the stress-strain relationship of a material is to cut a portion of an engineering component or material to prepare a standard tensile specimen for a uniaxial tensile test. The preparation of a standard tensile specimen often requires larger raw materials. With the growing demand for non-destructive testing of the mechanical properties of small-sized materials and in-service structural materials, the standard uniaxial tensile test can no longer meet the relevant test requirements.

[0003] In recent years, the indentation test, which uses a spherical indenter (ball indentation) or a conical indenter (cone indentation) to obtain the mechanical properties of a material, has been studied and applied as a non-traditional test method. However, due to the long-term lack of theoretical models for the plane indentation test method, it has been difficult to gain attention in engineering applications. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides an energy-based method for obtaining the uniaxial stress-strain relationship of materials, proposes a plane indentation energy-displacement model, and based on this model proposes a plane indentation test method for obtaining the uniaxial stress-strain relationship of materials, thereby realizing micro-destructive detection of the uniaxial mechanical properties of small-sized materials and in-service structural materials.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for obtaining a uniaxial stress-strain relationship of a material based on energy comprises the following steps:

[0007] S1, constructing a plane indentation energy-displacement model;

[0008] S2, using a plane indentation test to perform quasi-static indentation on the predicted material to obtain a continuous load-displacement curve;

[0009] S3, converting the load-displacement curve into an energy-displacement curve;

[0010] S4, using a plane indentation energy-displacement model to calculate material model parameters according to an energy-displacement curve;

[0011] S5. Calculate the uniaxial stress-strain relationship of the material based on the material model parameters.

[0012] Preferably, the plane indentation energy-displacement model in step S1 includes a general energy formula and an iterative formula, and the general energy formula and the iterative formula are respectively expressed as:

[0013] Energy formula:

[0014]

[0015] Iterative:

[0016]

[0017] Where W is the deformation energy, C is the loading coefficient, m is the loading index, f(h), are the energy compensation functions, D is the cross-sectional diameter of the cylindrical plane indenter, E is the elastic modulus, n is the strain hardening exponent, σ y is the yield strength, n and σ y are the material model parameters, k1 and k2 are the effective volume constants of the deformed body, k3 and k4 are the equivalent strain constant and equivalent strain exponent of the energy density median point, respectively.

[0018] Preferably, step S2 specifically includes:

[0019] In the plane indentation test, a single monotonic quasi-static indentation loading is performed on the predicted material surface with a hard plane cylindrical indenter to obtain a continuous load-displacement curve.

[0020] Preferably, the conversion calculation formula of the energy-displacement curve in step S3 is expressed as:

[0021] W = ∫Pdh

[0022] Among them, W is the deformation energy, P is the load, and h is the displacement.

[0023] Preferably, step S4 specifically includes the following sub-steps:

[0024] S41, fitting the energy formula in the plane compression energy-displacement model according to the energy-displacement curve to obtain the loading coefficient and loading index;

[0025] S42. Calculate material model parameters iteratively based on loading coefficient and loading index using a plane indentation energy-displacement model; wherein the strain hardening exponent and yield strength are material model parameters.

[0026] Preferably, step S5 is specifically:

[0027] The uniaxial stress-strain relationship of the material is obtained based on the Hollomon law or Ramberg-Osgood law used to describe the material stress-strain curve combined with the material model parameters.

[0028] Preferably, the Hollomon law table in step S6 is:

[0029]

[0030] Where σ is stress, ε is strain, E is elastic modulus, n is strain hardening exponent, σ y is the yield strength.

[0031] Preferably, the Ramberg-Osgood law table in step S5 is:

[0032]

[0033] Where σ is stress, ε is strain, n is strain hardening exponent, σ y is the yield strength and K is the strain hardening coefficient.

[0034] The present invention has the following beneficial effects:

[0035] A plane indentation energy-displacement model is constructed; a quasi-static indentation is performed on the predicted material through a plane indentation test to obtain a continuous load-displacement curve, and the load-displacement curve is converted into an energy-displacement curve, and the energy-displacement curve is fitted to obtain the loading coefficient and loading index of the energy-displacement curve, and the material model parameters are calculated according to the loading coefficient and loading index by bringing the plane indentation energy-displacement model into the plane indentation energy-displacement model, and then the uniaxial stress-strain relationship of the material is obtained according to the material model parameters; the shortcomings of the prior art such as the need to combine experiments with finite element analysis and the time-consuming and laborious solution are overcome, and a simple, applicable, theoretically universal, single monotonic plane indentation test method is proposed, and the high-precision prediction of the uniaxial stress-strain relationship of the material is achieved by means of the energy-displacement indentation test relationship and the plane indentation energy-displacement model; the present invention is of great significance for the acquisition of uniaxial mechanical properties of small-sized materials and in-service structural materials, and can realize micro-damage detection of component materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of the steps of a method for obtaining a uniaxial stress-strain relationship of a material based on energy provided by the present invention;

[0037] Figure 2 It is a plane pressing finite element analysis model in an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of a plane indentation test in an embodiment of the present invention;

[0039] Figure 4 is a typical plane indentation test load-displacement curve in an embodiment of the present invention;

[0040] Figure 5The uniaxial stress-strain curve of material 1 in the embodiment of the present invention is obtained;

[0041] Figure 6 The uniaxial stress-strain curve of material 2 in the embodiment of the present invention is obtained. DETAILED DESCRIPTION

[0042] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0043] like Figure 1 As shown, an embodiment of the present invention provides an energy-based material uniaxial stress-strain relationship acquisition method, comprising the following steps:

[0044] S1, constructing a plane indentation energy-displacement model;

[0045] Preferably, the plane indentation energy-displacement model in step S1 includes a general energy formula and an iterative formula, and the general energy formula and the iterative formula are respectively expressed as:

[0046] Energy formula:

[0047]

[0048] Iterative:

[0049]

[0050] Where W is the deformation energy, C is the loading coefficient, m is the loading index, f(h), are the energy compensation functions, D is the cross-sectional diameter of the cylindrical plane indenter, E is the elastic modulus, n is the strain hardening exponent, σ y is the yield strength, n and σ y are the material model parameters, k1 and k2 are the effective volume constants of the deformed body, k3 and k4 are the equivalent strain constant and equivalent strain exponent of the energy density median point, respectively.

[0051] The relationship between the deformation energy W and the displacement h in the embodiment of the present invention is: the plane indentation energy-displacement model, which is expressed as: Among them, C and m are the loading coefficient and loading index of the energy-displacement curve, respectively, satisfying: m=φ(n,σ y / E,k1,k2,k3,k4); D is the cross-sectional diameter of the cylindrical plane indenter, E is the elastic modulus, n is the strain hardening exponent of the stress-strain relationship Hollomon law or Ramberg-Osgood law, σ y is the yield strength; k1 and k2 are the effective volume constants of the deformed body, k3 and k4 are the equivalent strain constant and exponent of the energy density midpoint, respectively. k1~k4 are obtained through finite element analysis. The plane is pressed into the finite element analysis model as shown in Figure 2 Its values ​​are shown in Table 1; f(h), are energy compensation functions respectively.

[0052] In the embodiment of the present invention, the compensation function f or There are many forms. As an example, the compensation function can be taken as 0, and the energy-displacement model is pressed into the plane, and the loading coefficient C and loading index m are obtained by fitting the energy-displacement test curve. There are many forms of φ function. As an example, φ can be taken as: Among them, b1~b4 are function constants, as shown in Table 1;

[0053] Table 1 Model parameters

[0054]

[0055] In the embodiment of the present invention, the elastic modulus is the most basic mechanical property of the material. When calculating the uniaxial stress-strain curve of the material, the elastic modulus needs to be known, and its calculation formula is expressed as:

[0056]

[0057] In the formula, E r is the reduced elastic modulus, ν is the Poisson's ratio of the material being tested, and ν i and E i are the Poisson’s ratio and elastic modulus of the indenter material, respectively; β is the indenter coefficient and is taken as 0.8511 for steel; D is the plane indenter diameter; and S is the unloading stiffness of the load-displacement curve.

[0058] S2, using a plane indentation test to perform quasi-static indentation on the predicted material to obtain a continuous load-displacement curve;

[0059] Preferably, step S2 specifically includes:

[0060] In the plane indentation test, a single monotonic quasi-static indentation loading is performed on the predicted material surface with a hard plane cylindrical indenter to obtain a continuous load-displacement curve.

[0061] In the embodiment of the present invention, Figure 3As shown in FIG. 1 , it is a simplified diagram of a plane indentation test. In the embodiment of the present invention, the uniaxial stress-strain relationship of the material is obtained based on the plane indentation load-displacement curve. Therefore, the first step in solving the problem is to obtain the plane indentation load-displacement curve. In order to make the load-displacement curve authentic and reliable, the surface of the tested sample is required to be smooth, with a roughness of less than 0.32 μm, and a dimensionless indentation displacement h / D (D is the indenter diameter) of not less than 0.2. Figure 4 The load-displacement curve of a typical plane compression test is shown in FIG.

[0062] S3, converting the load-displacement curve into an energy-displacement curve;

[0063] Preferably, the conversion calculation formula of the energy-displacement curve in step S3 is expressed as:

[0064] W = ∫Pdh

[0065] Among them, W is the deformation energy, P is the load, and h is the displacement.

[0066] Preferably, step S4 specifically includes the following sub-steps:

[0067] S41, fitting the energy formula in the plane compression energy-displacement model according to the energy-displacement curve to obtain the loading coefficient and loading index;

[0068] S42. Calculate material model parameters iteratively based on loading coefficient and loading index using a plane indentation energy-displacement model; wherein the strain hardening exponent and yield strength are material model parameters.

[0069] S5. Calculate the uniaxial stress-strain relationship of the material based on the material model parameters.

[0070] Preferably, step S5 is specifically:

[0071] The uniaxial stress-strain relationship of the material is obtained based on the Hollomon law or Ramberg-Osgood law used to describe the material stress-strain curve combined with the material model parameters.

[0072] Preferably, the Hollomon's law table in step S5 is:

[0073]

[0074] Where σ is stress, ε is strain, E is elastic modulus, n is strain hardening exponent, σ y is the yield strength.

[0075] Preferably, the Ramberg-Osgood law table in step S5 is:

[0076]

[0077] Where σ is stress, ε is strain, n is strain hardening exponent, σ y is the yield strength and K is the strain hardening coefficient.

[0078] In the embodiment of the present invention, Figure 5 , Figure 6 As shown, the stress-strain curves of two kinds of metal materials obtained by the technical solution of the present invention are compared with the results obtained by the traditional uniaxial tensile test; it can be seen from the figure that the stress-strain curves of the two kinds of metal materials obtained by the technical solution of the present invention are closely consistent with the results obtained by the traditional uniaxial tensile test. The technical solution of the present invention can accurately and effectively obtain the material stress-strain curve, and compared with the traditional uniaxial tensile test, this method saves time and labor, and can realize the performance test of small-sized materials or in-service structural materials.

[0079] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0080] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0081] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0082] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0083] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for obtaining a uniaxial stress-strain relationship of a material based on energy, characterized in that it comprises the following steps: S1. Construct a plane indentation energy-displacement model; the plane indentation energy-displacement model includes an energy general formula and an iterative formula, which are respectively expressed as: Energy formula: Iterative: Where W is the deformation energy, C is the loading coefficient, m is the loading index, f(h), are the energy compensation functions, D is the cross-sectional diameter of the cylindrical plane indenter, E is the elastic modulus, n is the strain hardening exponent, σ y is the yield strength, n and σ y are the material model parameters, k1 and k2 are the effective volume constants of the deformed body, k3 and k4 are the equivalent strain constant and equivalent strain index of the energy density median point, respectively; S2. A plane indentation test is used to perform quasi-static indentation on the predicted material to obtain a continuous load-displacement curve; specifically, in the plane indentation test, a hard plane cylindrical indenter is used to perform a single monotonic quasi-static indentation load on the surface of the predicted material to obtain a continuous load-displacement curve; S3. Convert the load-displacement curve into an energy-displacement curve; the conversion calculation formula of the energy-displacement curve is expressed as: W = ∫Pdh Where W is the deformation energy, P is the load, and h is the displacement; S4, using the plane indentation energy-displacement model to calculate the material model parameters according to the energy-displacement curve; specifically including the following sub-steps: S41, fitting the energy formula in the plane compression energy-displacement model according to the energy-displacement curve to obtain the loading coefficient and loading index; S42, calculating material model parameters according to the loading coefficient and the loading index by iterative formula in the plane indentation energy-displacement model; wherein the strain hardening index and the yield strength are the material model parameters; S5. Calculate the uniaxial stress-strain relationship of the material based on the material model parameters.

2. According to the method for obtaining the uniaxial stress-strain relationship of a material based on energy in claim 1, it is characterized in that step S5 specifically comprises: The uniaxial stress-strain relationship of the material is obtained based on the Hollomon law or Ramberg-Osgood law used to describe the material stress-strain curve combined with the material model parameters.

3. The method for obtaining the uniaxial stress-strain relationship of a material based on energy according to claim 2, characterized in that the Hollomon law table in step S5 is: in, σ is stress, ε is strain, E is elastic modulus, n is strain hardening exponent, σ y is the yield strength.

4. The method for obtaining the uniaxial stress-strain relationship of a material based on energy according to claim 2, characterized in that the Ramberg-Osgood law table in step S5 is: in, σ is stress, ε is strain, n is strain hardening exponent, σ y is the yield strength and K is the strain hardening coefficient.

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