A method and system for obtaining microscopic strength criteria of brittle materials

Abstract

The present invention discloses a method and system for obtaining a mesoscopic strength criterion for brittle materials, and relates to the technical field of material mesoscopic strength analysis, including: processing a brittle material into a sample; arranging artificial speckles on the surface of the sample; performing a compression test on the sample, and simultaneously monitoring the displacement field and the strain field to obtain the final strain data points of the observation points of the sample under different working conditions; using the generalized Hooke's law to convert the final strain data points to the principal stress space, and draw a principal stress space data point diagram; fitting the principal stress space data point diagram to obtain the mesoscopic strength criterion of the brittle material. The present invention can efficiently and quickly obtain the constitutive relationship of the mesoscopic strength of brittle materials, and has broad application prospects and value in the analysis of the failure process of brittle materials and the numerical calculation of constitutive models.

Description

Technical Field

[0001] The present invention relates to the technical field of material microscopic strength analysis, and more particularly to a method and system for obtaining microscopic strength criteria for brittle materials. Background Art

[0002] The macroscopic shear failure constitutive model is not suitable for simulating the material fracture process, because the theoretical and numerical analysis requires the unit-level crack initiation criterion, which is independent of the shape and size of the material. However, the study found that there is a difference between the macroscopic strength and the microscopic strength of the material under the same loading conditions. The peak load or peak stress of the specimen determined under a specific specimen shape, size and loading conditions can only be regarded as an apparent equivalent strength, which cannot be used to describe the crack initiation and failure phenomenon of the local unit.

[0003] The strength of existing brittle materials such as rocks measured through mechanical tests (such as uniaxial and triaxial compression tests) belongs to macroscopic strength. The macroscopic strength of materials cannot be directly used in the analysis of microscopic damage and fracture of materials. It has obvious size effect and shape effect, and the macroscopic failure mode of materials is often caused by micro-scale fracture initiation and penetration.

[0004] Therefore, how to provide a method and system for obtaining the mesoscopic strength criterion of brittle materials and efficiently and quickly obtain the constitutive relationship of the mesoscopic strength of brittle materials is an urgent problem to be solved by technical personnel in this field. Summary of the invention

[0005] In view of this, the present invention provides a method and system for obtaining the mesoscopic strength criterion of brittle materials, which can efficiently and quickly obtain the constitutive relationship of the mesoscopic strength of brittle materials, and has broad application prospects and value in the failure process analysis of brittle materials and numerical calculation of constitutive models.

[0006] In order to achieve the above object, the present invention adopts the following technical solution: a method for obtaining a mesoscopic strength criterion for brittle materials, comprising:

[0007] Processing brittle materials into test specimens;

[0008] Arrange artificial speckles on the surface of the sample;

[0009] Performing a compression test on the sample, and monitoring the displacement field and the strain field at the same time, to obtain the final strain data points of the observation points of the sample under different working conditions;

[0010] The final strain data points are converted into principal stress space by using generalized Hooke's law, and a principal stress space data point diagram is drawn;

[0011] The principal stress space data point diagram is fitted to obtain the microscopic strength criterion of the brittle material.

[0012] Preferably, the compression test includes: a uniaxial compression test, a biaxial compression test or a triaxial compression test.

[0013] Preferably, the displacement field calculation formula of the sample is as follows:

[0014]

[0015] In the formula, x i ,y i 、x i ',y i ' is the coordinate component of each point in the speckle pattern.

[0016] Preferably, the displacement field data is smoothed, and then the strain component is calculated using the Green-Lagrange strain:

[0017]

[0018] In the formula, ε xx , ε yy They respectively represent the strain components in two mutually perpendicular directions on the two-dimensional plane of the speckle on the sample surface.

[0019] Preferably, the different working conditions represent different forces applied during the compression test.

[0020] Preferably, the conversion formula for converting the final strain data point to the principal stress space using the generalized Hooke's law is expressed as:

[0021]

[0022] Among them, σ1 and σ2 represent the maximum principal stress and intermediate principal stress of the observation point selected during the test loading process, respectively; ε1 and ε2 represent the maximum principal strain and intermediate principal strain of the observation point recorded during the test loading process, respectively; E represents the strength modulus; ν represents the Poisson's ratio of the experimental material.

[0023] Preferably, the number of samples is increased and / or the test state of the samples is changed to obtain the maximum principal strain and intermediate principal strain data when the observation point is ruptured.

[0024] Preferably, a system for obtaining a microscopic strength criterion for brittle materials comprises:

[0025] A specimen processing module is used to process brittle materials into specimens;

[0026] A speckle arrangement module is used to arrange artificial speckles on the surface of the sample;

[0027] A test module is used to perform a compression test on the sample, monitor the displacement field and the strain field at the same time, and obtain the final strain data points of the observation points of the sample under different working conditions;

[0028] A conversion module, used to convert the final strain data points into principal stress space by using generalized Hooke's law, and draw a principal stress space data point graph;

[0029] The fitting module is used to fit the principal stress space data point diagram to obtain the mesoscopic strength criterion of the brittle material.

[0030] It can be known from the above technical scheme that, compared with the prior art, the present invention discloses a method and system for obtaining the microscopic strength criterion of brittle materials, including: processing the brittle material into a sample; arranging artificial speckles on the surface of the sample; performing a compression test on the sample, and simultaneously monitoring the displacement field and the strain field to obtain the final strain data points of the observation points of the sample under different working conditions; using the generalized Hooke's law to convert the final strain data points to the principal stress space, and draw a principal stress space data point diagram; fitting the principal stress space data point diagram to obtain the microscopic strength criterion of the brittle material. The present invention can efficiently and quickly obtain the constitutive relationship of the microscopic strength of brittle materials, and has broad application prospects and value in the analysis of the failure process of brittle materials and the numerical calculation of constitutive models. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0032] Figure 1 A schematic flow chart of a method for obtaining a mesoscopic strength criterion for brittle materials provided by the present invention.

[0033] Figure 2 A schematic diagram of the structure of a system for obtaining a microscopic strength criterion for brittle materials provided by the present invention.

[0034] Figure 3 A schematic diagram of final strain data points provided by an embodiment of the present invention.

[0035] Figure 4 A schematic diagram of principal stress space data points provided by an embodiment of the present invention.

[0036] FIG. 5( a ) is a schematic diagram of the reference image principle for displacement monitoring using digital image correlation provided by an embodiment of the present invention.

[0037] FIG. 5( b ) is a schematic diagram of the principle of deformation images for displacement monitoring using digital image correlation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] Generally, mechanical tests of brittle materials obtain macroscopic strength criteria, which are difficult to apply to microscopic damage and fracture analysis of materials. The embodiment of the present invention discloses a method and system for obtaining microscopic strength criteria for brittle materials, which can efficiently and quickly obtain the constitutive relationship of the microscopic strength of brittle materials, and has broad application prospects and value in the analysis of the failure process of brittle materials and the numerical calculation of constitutive models.

[0040] Example 1

[0041] The embodiment of the present invention discloses a method for obtaining a mesoscopic strength criterion for brittle materials, such as Figure 1 As shown, including:

[0042] Processing brittle materials into test specimens;

[0043] Arrange artificial speckles on the surface of the sample;

[0044] Performing a compression test on the sample, and monitoring the displacement field and the strain field at the same time, to obtain the final strain data points of the observation points of the sample under different working conditions;

[0045] The final strain data points are converted into principal stress space by using generalized Hooke's law, and a principal stress space data point diagram is drawn;

[0046] The principal stress space data point diagram is fitted to obtain the microscopic strength criterion of the brittle material.

[0047] Specifically, the compression test includes: a uniaxial compression test, a biaxial compression test or a triaxial compression test.

[0048] Specifically, processing the brittle material into a specimen includes: processing any brittle experimental material required to test the microscopic strength into any specimen suitable for mechanical experiments and placing it on a mechanical testing machine to prepare for the experiment.

[0049] Specifically, the embodiment of the present invention selects a biaxial compression test, which is convenient for photographing samples and changing the test state of the samples (the ratio of the horizontal and vertical load loading rates of the biaxial press); a digital camera is used to photograph and record the fracture process of brittle material samples such as rocks in the biaxial compression mechanics test, and the displacement field data of the surface of the thin plate sample is obtained in combination with the digital image correlation DIC method, and then the displacement data of the particles (observation points) near the fracture path of the sample are selected for differentiation to obtain the evolution path of the intermediate principal strain and the maximum principal strain (ε2, ε1), and the intermediate principal strain and the maximum principal strain (ε2, ε1) data at the time of particle fracture are obtained by increasing the number of samples and changing the test state of the sample (the ratio of the horizontal and vertical load loading rates of the biaxial compressor) The data are statistically analyzed and fitted using mathematical methods to obtain the equation of the failure envelope in the principal stress space, and then the microscopic strength criterion of the test material sample is obtained.

[0050] In the embodiment of the present invention, the digital image correlation (DIC) technology is a non-contact modern optical measurement test technology. The basic principle is to track the displacement change of the same pixel point in different deformed images, so as to inversely calculate the displacement field. In the selected speckle image, a sub-image centered at the point to be measured (x0, y0) is tracked, and the position of the previously selected sub-image in the deformed image and the displacement component (u, v) of the sub-image are found by minimizing or maximizing the correlation coefficient. The above process is repeated to obtain the full-field displacement of the calculation area. The calculation principle is shown in Figures 5(a) and 5(b).

[0051] DIC is a complete and mature application tool used in many fields for displacement and strain monitoring.

[0052] Specifically, a digital camera and a digital image correlation (DIC) method are used to synchronously monitor the displacement field and the strain field, and the displacement evolution process of the sample during the experiment is obtained, as shown in FIG5(a) and FIG5(b), where FIG5(a) is a diagram before deformation and FIG5(b) is a diagram after deformation; the displacement data is first obtained, and then the displacement data is differentiated to obtain the strain.

[0053] Specifically, the displacement field calculation formula of the sample is as follows:

[0054]

[0055] In the formula, x i ,y i 、x i ',y i' is the coordinate component of each point in the speckle pattern; (x0, y0) represents the two-dimensional coordinate of the observation point; the embodiment of the present invention selects a square area centered at the point (x0, y0); (u0, v0) are the displacements of the observation point in the x and y directions respectively (that is, (u, v) in Figure 5(b)); u and v represent the distance of the two-dimensional graph; x and y represent the direction of the two-dimensional graph.

[0056] Specifically, the strain calculation process is relatively complicated. Before calculating the strain, the displacement field data needs to be smoothed, and then the Green-Lagrange strain is used to calculate the strain component:

[0057]

[0058] In the formula, ε xx , ε yy They respectively represent the strain components in two mutually perpendicular directions on the two-dimensional plane of the speckle on the sample surface.

[0059] like Figure 3 As shown, it is a data point diagram of maximum principal strain ε1-intermediate principal strain ε2 of an embodiment of the present invention. By fitting a series of data points in the ε1-ε2 diagram using an appropriate mathematical function, the mesoscopic strength criterion function form of the tested material can be obtained.

[0060] Specifically, the different working conditions indicate that different forces are applied during the compression test.

[0061] Specifically, the conversion formula between principal strain and principal stress is obtained through the generalized Hooke's law.

[0062] Specifically, the generalized Hooke's law is used to convert the final strain data point into the principal stress space using the conversion formula expressed as:

[0063]

[0064] Among them, σ1 and σ2 represent the maximum principal stress and intermediate principal stress of the observation point selected during the test loading process, respectively; ε1 and ε2 represent the maximum principal strain and intermediate principal strain ((ε2, ε1) data point) of the observation point (particle) recorded by DIC during the test loading process, respectively; E represents the strength modulus; ν represents the Poisson’s ratio of the experimental material.

[0065] The embodiment of the present invention uses the generalized Hooke's law to transfer the mesoscopic strength criterion to the principal stress space (σ2, σ1) and plots it into a graph, as shown in FIG. Figure 4 As shown; after observing the morphology of the mesoscopic strength envelope, the corresponding function is selected to fit the failure envelope of the sample, and finally the mesoscopic strength criterion is obtained.

[0066] Among them, the shapes of the ε1-ε2 curves obtained from experiments on different brittle materials are different, so the function forms used for fitting are also different (cannot be determined), and the general form can be expressed as:

[0067]

[0068] where F T and F S They represent the microscopic tensile strength and microscopic shear failure of the material respectively; a, b, c, d, e, and h are all constants, f represents a function, σ1 and σ2 represent the maximum principal stress and intermediate principal stress of the observation points selected during the test loading process respectively.

[0069] Specifically, the maximum principal strain and intermediate principal strain data at the time of rupture of the observation point are obtained by increasing the number of specimens and / or changing the specimen test state (horizontal and vertical load rate ratio of the biaxial press).

[0070] Specifically, the brittle material includes rock, ceramic, gypsum, concrete, glass or cast iron.

[0071] Specifically, the embodiments of the present invention can be applied to the development and application of finite element constitutive models.

[0072] In general numerical simulation programs, it is necessary to specify a specific constitutive relation for the simulation object. When the model unit does not yield, it can be regarded as a completely elastic body, and its stress and strain obey the isotropic linear elastic constitutive relation. The unit damage can be handled by constructing a damage indicator function with the help of the experimentally obtained microscopic strength criterion to determine whether the unit has entered the yield state.

[0073] Specifically, the mesoscopic strength criterion finally obtained by the embodiment of the present invention is a stress function, which is plotted as a curve with two principal stresses as horizontal and vertical coordinates. When the principal stress coordinate of a point in the specimen unit is located above the mesoscopic strength criterion curve during loading, it means that the stress at this point on the specimen is greater than the maximum stress that the material can withstand, and then this point or this unit will enter a yield state.

[0074] The constitutive model corresponding to the material can be obtained by degrading the elastic modulus of the post-yield unit and combining it with the corresponding plastic flow law. Subsequently, the corresponding numerical simulation work can be carried out by introducing this constitutive model into the program.

[0075] The computer numerical simulation process itself has the step of inputting the elastic modulus of the material unit. It is only necessary to edit the program (computer language, the specific code varies according to the programming language used and the numerical simulation software) so that after the unit yield is found, the value of the material elastic modulus is reduced, and the parameters that need to be input in the numerical simulation process are automatically modified according to the formulas and laws of fluid plasticity, so as to obtain a reasonable mesoscopic constitutive model of the material.

[0076] The embodiment of the present invention is based on a method for obtaining a mesoscopic strength criterion for brittle materials based on mechanical testing combined with DIC strain measurement. The material mesoscopic strength criterion is coupled to a numerical simulation calculation through secondary development of a programming language, and the mesoscopic strength criterion is used to predict and analyze the material fracture process. The mesoscopic strength criterion specifies / maps out the maximum stress state that a certain material can withstand. Once the stress of a material unit recorded during the experiment exceeds this specified value, its elastic modulus will "degrade", that is, it will become soft and no longer hard. At the same time, the strain will begin to increase. When it increases to a certain extent, cracks will occur and the specimen will begin to rupture. Therefore, the mesoscopic strength criterion can be used to predict and analyze the material's mesoscopic fracture process.

[0077] Example 2

[0078] The embodiment of the present invention discloses a method for obtaining a mesoscopic strength criterion for brittle materials. The embodiment of the present invention takes gypsum material as an example, processes the gypsum material into several 50mm×50mm×50mm specimens, places them on a biaxial testing machine, arranges artificial speckles on the surface of the specimens, and performs a biaxial compression test. At the same time, a digital camera and a digital image correlation DIC method are used to synchronously monitor the full-field displacement and strain field. After the experiment, the DIC image processing algorithm is used to count the final strain data points (ε2, ε1) of the selected particles on the surface of the specimen and plot them in the ε1-ε2 diagram. The force applied by the biaxial testing machine is changed (the working condition is changed) to obtain the final strain data points (ε2, ε1) of the particles of the gypsum specimen under different working conditions. Finally, the data points (ε2, ε1) are transferred to the principal stress space (σ2, σ1) using the generalized Hooke's law and plotted into a graph. After observing the morphology of the mesoscopic strength envelope, the corresponding function is selected to fit the failure envelope of the specimen, and the mesoscopic strength criterion is finally obtained.

[0079] Example 3

[0080] The embodiment of the present invention discloses a system for obtaining a microscopic strength criterion for brittle materials, such as Figure 2 As shown, including:

[0081] A specimen processing module is used to process brittle materials into specimens;

[0082] A speckle arrangement module is used to arrange artificial speckles on the surface of the sample;

[0083] A test module is used to perform a compression test on the sample, monitor the displacement field and the strain field at the same time, and obtain the final strain data points of the observation points of the sample under different working conditions;

[0084] A conversion module, used to convert the final strain data points into principal stress space by using generalized Hooke's law, and draw a principal stress space data point graph;

[0085] The fitting module is used to fit the principal stress space data point diagram to obtain the mesoscopic strength criterion of the brittle material.

[0086] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0087] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for obtaining a mesoscopic strength criterion for brittle materials, characterized in that: include: Processing brittle materials into test specimens; Arrange artificial speckles on the surface of the sample; Performing a compression test on the sample, and monitoring the displacement field and the strain field at the same time, to obtain the final strain data points of the observation points of the sample under different working conditions; The final strain data points are converted into principal stress space by using generalized Hooke's law, and a principal stress space data point diagram is drawn; Fitting the principal stress space data point diagram to obtain the mesoscopic strength criterion of the brittle material; The displacement field calculation formula of the sample is as follows: In the formula, x i ,y i 、x i ',y i ' is the coordinate component of each point in the speckle pattern; The displacement field data is smoothed, and then the strain component is calculated using the Green-Lagrange strain: In the formula, ε xx , ε yy They represent the strain components in two mutually perpendicular directions on the two-dimensional plane of the speckle on the sample surface; The conversion formula for converting the final strain data point to the principal stress space using the generalized Hooke's law is expressed as: Among them, σ1 and σ2 represent the maximum principal stress and intermediate principal stress of the observation point selected during the test loading process; ε1 and ε2 represent the maximum principal strain and intermediate principal strain of the observation point recorded during the test loading process; E represents the strength modulus; ν represents the Poisson's ratio of the experimental material; Among them, the mesoscopic strength criterion is a stress function, and the two principal stresses are a curve graph with the horizontal and vertical coordinates respectively. When the principal stress coordinate of a point in the specimen unit during loading is above the mesoscopic strength criterion curve, it means that the stress at this point on the specimen is greater than the maximum stress that the material can withstand, then this point or this unit will enter a yield state; the mesoscopic strength criterion stipulates / draws out the maximum stress state that a certain material can withstand.

2. A method for obtaining a mesoscopic strength criterion for brittle materials according to claim 1, characterized in that: The compression test includes: a uniaxial compression test, a biaxial compression test or a triaxial compression test.

3. The method for obtaining a mesoscopic strength criterion for brittle materials according to claim 1, characterized in that: The different conditions indicate that different forces are applied during the compression test.

4. The method for obtaining a mesoscopic strength criterion for brittle materials according to claim 1, characterized in that: Increase the number of specimens and / or change the specimen testing state to obtain the maximum principal strain and intermediate principal strain data when the observation point is ruptured.

5. A system for obtaining a mesoscopic strength criterion for brittle materials, using a method for obtaining a mesoscopic strength criterion for brittle materials as claimed in any one of claims 1 to 4, characterized in that: include: A specimen processing module is used to process brittle materials into specimens; A speckle arrangement module is used to arrange artificial speckles on the surface of the sample; A test module is used to perform a compression test on the sample, monitor the displacement field and the strain field at the same time, and obtain the final strain data points of the observation points of the sample under different working conditions; A conversion module, used to convert the final strain data points into principal stress space by using generalized Hooke's law, and draw a principal stress space data point graph; The fitting module is used to fit the principal stress space data point diagram to obtain the mesoscopic strength criterion of the brittle material.

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