Prediction method for mechanical property of graphene reinforced titanium-based composite material with net-shaped structure

Abstract

The invention discloses a method for predicting the mechanical property of a reticular structure graphene reinforced titanium-based composite material, and the method specifically comprises the following steps: 1, preparing the reticular structure graphene reinforced titanium-based composite material by using a powder metallurgy method, and obtaining the macroscopic stress-strain response and microscopic characteristics of the reticular structure graphene reinforced titanium-based composite material; step 2, determining design parameters of the net structure according to the microscopic characteristics of the graphene reinforced titanium-based composite material of the net structure obtained in the step 1; 3, the grain size of a metal matrix and the thickness of grain boundary graphene are determined, and a representative volume unit of the graphene-reinforced titanium-based composite material of the net-shaped structure is established through a Thiessen polygon; and 4, on the basis of the step 3, a constitutive prediction model of Johnson-Cook plasticity and damage coupling is established, and the mechanical property of the graphene reinforced titanium-based composite material is predicted. According to the method, the tensile strength and failure strain of the graphene-reinforced titanium-based composite material with the net-shaped structure under different grain sizes and graphene contents can be determined.

Description

Technical Field

[0001] The present invention belongs to the technical field of metal matrix nanocomposites, and particularly relates to a method for predicting the mechanical properties of a reticulated structure graphene-reinforced titanium matrix composite material. Background Art

[0002] As a new type of two-dimensional nanomaterial, graphene has become an ideal reinforcing phase in the field of metal matrix composites due to its excellent mechanical properties. Because graphene has a large specific surface area, it is prone to agglomeration, which makes it difficult to disperse in the metal matrix. This dispersion problem restricts the further improvement of the properties of the composite material to a certain extent. Therefore, it is particularly important to study the configuration design of graphene in the metal matrix. Among them, the most representative is the reticulated structure graphene-reinforced titanium matrix composite material.

[0003] In the reticulated structure graphene-reinforced titanium matrix composite material, the hard graphene can effectively enhance the strength of the composite material, and the network structure has a positive regulatory effect on maintaining the plasticity of the composite material, effectively alleviating the contradiction between the strength and plasticity of the composite material. The reticulated structure is mainly affected by the grain size of the metal matrix, the number of grains, the thickness of the graphene at the grain boundary, the interfacial products, etc. However, the quantitative influence of the reticulated structure and its influencing factors on the macroscopic mechanical properties of the graphene-reinforced titanium matrix composite material is still unclear. Therefore, it is of great research significance to provide a method for predicting the mechanical properties of the reticulated structure graphene-reinforced titanium matrix composite material. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the mechanical properties of a reticulated structure graphene-reinforced titanium matrix composite material, which can determine the tensile strength and failure strain of the reticulated structure graphene-reinforced titanium matrix composite material under different grain sizes and graphene contents.

[0005] The technical solution adopted by the present invention is a method for predicting the mechanical properties of a reticulated structure graphene-reinforced titanium matrix composite material, which specifically includes the following steps: Step 1, preparing a reticulated structure graphene-reinforced titanium matrix composite material by powder metallurgy method, and obtaining its macroscopic stress-strain response and microscopic characteristics; Step 2, determining the design parameters of the reticulated structure according to the microscopic characteristics of the reticulated structure graphene-reinforced titanium matrix composite material obtained in Step 1; Step 3, establishing a representative volume element of the reticulated structure graphene-reinforced titanium matrix composite material by using the Thiessen polygon according to the grain size of the metal matrix, the number of grains and the thickness of the graphene at the grain boundary determined in Step 1 and Step 2; Step 4, based on Step 3, establish a constitutive prediction model for Johnson-Cook plasticity and damage coupling to predict the mechanical properties of graphene-reinforced titanium matrix composites.

[0006] The features of the present invention also lie in that In Step 1, to prepare the reticulated graphene-reinforced titanium matrix composite, high-purity graphite balls and titanium alloy powders are subjected to three-dimensional vibration powder mixing and then the reticulated graphene-reinforced titanium matrix composite is prepared by spark plasma sintering or selective laser melting.

[0007] The specific method for obtaining its macroscopic stress-strain response and microscopic characteristics in Step 1 is to use scanning and transmission electron microscopes to characterize the microscopic characteristics of the reticulated graphene-reinforced titanium matrix composite, and the microscopic characteristics include grain size and graphene network thickness; use an electronic universal testing machine to measure the macroscopic stress-strain curve of the reticulated graphene-reinforced titanium matrix composite, and the macroscopic stress-strain curve includes tensile strength and failure strain.

[0008] The design parameters for determining the reticulated structure in Step 2 specifically include the metal grain size S , the number of grains n , the thickness of grain boundary graphene N and the stress concentration factor S cf .

[0009] The specific steps for establishing the representative volume element of the reticulated graphene-reinforced titanium matrix composite using the Thiessen polygon in Step 3 are as follows: Step 3.1, in two-dimensional space, define the point M as a set in P , randomly generate a coordinate of a crystal nucleus, M define it as the crystal nucleus point of the Thiessen polygon, as shown in the following formula: ; In the formula, p i ( x i , y i ) represents the i th crystal nucleus point, x i , y i represents its coordinate Step 3.2, the cell structure in two-dimensional space is composed of Thiessen polygons generated by each crystal nucleus point p i , and the set SV is composed of n crystal nucleus points p iComposed as shown in the following formula: ; Step 3.3: Subdivide the Delaunay triangles of the Voronoi polygons using the local transformation method to obtain the nucleation points p i The corresponding Delaunay triangles T , where the changing sides of the convex quadrilateral iteration are determined by the Δp i p j p k points in p r as shown in the following formula: ; In the formula, x r , y r represents the r th nucleation point p r coordinates; Step 3.4: According to the nearest neighbor principle, connect the nucleation points in the Delaunay triangle network with line segments and subdivide the space so that each point is associated with the nearest spatial region it is in, forming a representative volume element of graphene-reinforced titanium matrix composite based on Voronoi polygons, as shown in the following formula: ; In the formula, E ( p, p i ) represents the distance from p to p i in the two-dimensional region, Voronoi ( p i ) represents the Voronoi polygon.

[0010] In Step 4, establish the constitutive prediction model of Johnson-Cook plasticity and damage coupling; The Johnson-Cook plastic constitutive model is shown in the following formula: ; Among them, in the plastic constitutive model, σ represents the flow stress, ε pl represents the effective plastic strain, while A , B , C , M and Nrespectively represent the yield strength, hardening modulus, strain rate coefficient, temperature coefficient, and hardening coefficient of the matrix; C and M both parameters are set to zero; The Johnson-Cook damage constitutive model is shown as follows: ; In the formula, is the failure strain, d1~d5 is the material damage-related constant, p and q are the hydrostatic pressure and von- Mises stress respectively, where d4 and d5 have values of zero.

[0011] Specifically, in step 4, the mechanical properties of the graphene-reinforced titanium matrix composite are predicted. According to the macroscopic stress-strain response data of the composite obtained in step 1, the stress-strain data when the graphene volume fraction is zero are selected, and the plastic and damage-related parameters in the constitutive model are obtained through data fitting. Based on the microscopic parameters of graphene in the composite, they are substituted into the constructed constitutive prediction model for solution.

[0012] The constitutive prediction model is solved using the ABAQUS explicit solver.

[0013] The beneficial effects of the present invention are: The prediction method for the mechanical properties of the reticulated structure graphene-reinforced titanium matrix composite of the present invention constructs a reticulated structure using the Thiessen polygon according to the microscopic characteristics such as the grain size, grain number, and grain boundary graphene thickness of the metal matrix, and then establishes a Johnson-Cook plastic and damage coupling constitutive prediction model. The model can quantitatively correlate the microscopic characteristics of the composite with the macroscopic mechanical properties, predict the mechanical properties of the reticulated structure graphene-reinforced titanium matrix composite, and thus can provide theoretical guidance for the optimization design, significantly reducing the experimental cost and experimental period. Description of the Drawings

[0014] Figure 1 is the scanning electron microscope morphology diagram of the reticulated structure graphene-reinforced titanium matrix composite of the present invention; Figure 2 is the representative volume element of the reticulated structure graphene-reinforced titanium matrix composite established based on the Thiessen polygon of the present invention; Figure 3 is the comparison diagram of the stress-strain curve prediction result and the experimental result of the reticulated structure graphene-reinforced titanium matrix composite of the present invention; Figure 4 is the stress concentration factor-strain curve of the graphene network and the titanium matrix of the present invention. Detailed implementation manners

[0015] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0016] Embodiment 1 The prediction method for the mechanical properties of the reticulated graphene-reinforced titanium matrix composite of the present invention specifically includes the following steps: Step 1: Prepare the reticulated graphene-reinforced titanium matrix composite by powder metallurgy method, and obtain its macroscopic stress-strain response and microscopic characteristics; Step 2: Determine the design parameters of the reticulated structure according to the microscopic characteristics of the reticulated graphene-reinforced titanium matrix composite obtained in Step 1; Step 3: Establish a representative volume element of the reticulated graphene-reinforced titanium matrix composite by using the Thiessen polygon according to the grain size, grain number and grain boundary graphene thickness of the metal matrix determined in Steps 1 and 2; Step 4: On the basis of Step 3, establish a constitutive prediction model coupling Johnson-Cook plasticity and damage to predict the mechanical properties of the graphene-reinforced titanium matrix composite.

[0017] Embodiment 2 On the basis of the above Embodiment 1, in Step 1 of the prediction method for the mechanical properties of the reticulated graphene-reinforced titanium matrix composite of the present invention, the reticulated graphene-reinforced titanium matrix composite is prepared by subjecting high-purity graphite balls and titanium alloy powder to three-dimensional vibration powder mixing and then preparing the reticulated graphene-reinforced titanium matrix composite by spark plasma sintering or selective laser melting.

[0018] Embodiment 3 On the basis of the above Embodiment 1, the obtaining of the macroscopic stress-strain response and microscopic characteristics in Step 1 of the prediction method for the mechanical properties of the reticulated graphene-reinforced titanium matrix composite of the present invention specifically means using a scanning and transmission electron microscope to characterize the microscopic characteristics of the reticulated graphene-reinforced titanium matrix composite, and the microscopic characteristics include grain size and graphene network thickness; using an electronic universal testing machine to measure the macroscopic stress-strain curve of the reticulated graphene-reinforced titanium matrix composite, and the macroscopic stress-strain curve includes the tensile strength (maximum stress) and the failure strain (maximum strain). The specific obtaining method of the macroscopic stress-strain curve is the prior art.

[0019] Embodiment 4 Prediction method for mechanical properties of reticulated structure graphene reinforced titanium matrix composite material, specifically comprising the following steps: Step 1, after three-dimensional vibration mixing of high-purity graphite balls and titanium alloy powders, prepare a reticulated structure graphene reinforced titanium matrix composite material by spark plasma sintering or selective laser melting; use scanning and transmission electron microscopes to characterize the microscopic features of the reticulated structure graphene reinforced titanium matrix composite material, such as Figure 1 , including the grain size of the metal matrix, the thickness of the graphene network, etc.; use an electronic universal testing machine to measure the macroscopic stress-strain curve of the reticulated structure graphene reinforced titanium matrix composite material sample, including the tensile strength (maximum stress) and the failure strain (maximum strain); Step 2, determine the design parameters of the reticulated structure according to the microscopic features of the reticulated structure graphene reinforced titanium matrix composite material obtained in Step 1; The design parameters of the reticulated structure specifically include the metal grain size S , the number of grains n , the thickness of the grain boundary graphene N and the stress concentration factor S cf .

[0020] The relationship between the volume fraction of graphene and the volume fraction of the titanium matrix is as shown in the following formula (1): (1); Among them, H g is the volume fraction of graphene, H m is the volume fraction of the titanium matrix; the volume fraction of graphene in the reticulated structure graphene / metal composite material is controlled by the number of metal matrix grains n , the thickness of graphene N and the metal grain size S .

[0021] H g The expression of (2); The volume fraction of the matrix phase is controlled by the number of matrix grains and the size of the grains, H m The expression of (3); When the model size is certain, the design parameters of the composite material include the number of metal matrix grains n , the thickness of graphene N and the metal grain size S , and satisfy the following formula (4): (4); To describe the non-uniform distribution of stress between graphene and the matrix, the stress concentration factor is used to quantitatively represent the load-bearing capacity of the reticulated graphene material. The equivalent stress of the composite material σ E As shown in formula (5): (5); Wherein, V m and V g are the volumes of the titanium matrix and graphene respectively, V C is the total volume of the composite material. σ g and σ m are the average stresses of graphene and the titanium matrix, as shown in formula (6): (6); Wherein, σ i is the stress of each unit in graphene and the titanium matrix. The stress concentration factor is as shown in formula (7): (7); Wherein, S cf(m) and S cf(g) are the stress concentration factors of the matrix and graphene respectively. By introducing the volume fraction into equation (5), the equivalent stress can be adjusted to formula (8): (8); Combining formula (7) and formula (8), the relationship between the volume fraction H of the component phase and the stress concentration factor S cf can be expressed as shown in formula (9): (9).

[0022] Step 3: According to the grain size, grain number and grain boundary graphene thickness of the metal matrix determined in Step 1 and Step 2, a representative volume element of the reticulated graphene-reinforced titanium matrix composite is established using the Thiessen polygon; as Figure 2 shown, it should be noted that due to the pinning effect of the interfacial product TiC, the interfacial bonding force is strong, and the interface between graphene and the titanium matrix can be regarded as an ideal interface.

[0023] Step 4, based on Step 3, establish a constitutive prediction model for the coupling of Johnson-Cook plasticity and damage to predict the mechanical properties of graphene-reinforced titanium matrix composites.

[0024] Specifically, according to the macroscopic mechanical properties of the composite material obtained in Step 1, select the stress-strain data when the volume fraction of graphene is zero, and obtain the plasticity and damage-related parameters in the constitutive model through data fitting; further obtain the relevant microscopic parameters of graphene by referring to the literature, and then substitute all the unknown constitutive parameters into the constitutive model and use the ABAQUS explicit solver for solution to obtain the entire stress-strain curve of the reticulated graphene-reinforced titanium matrix composite, where the maximum value of the stress is the tensile strength and the maximum value of the strain is the failure strain.

[0025] Example 5 Based on Example 4, the specific steps for using the Thiessen polygon to establish a representative volume element of the reticulated graphene-reinforced titanium matrix composite in Step 3 are as follows: Step 3.1, in a two-dimensional space, define the point M as the set in P , randomly generate a crystal nucleus coordinate, M define it as the crystal nucleus point of the Thiessen polygon, as shown in the following formula (10): (10); In the formula, p i ( x i , y i ) represents the i th crystal nucleus point, x i , y i represents its coordinates; Step 3.2, the Thiessen polygons generated by each crystal nucleus point p i constitute the unit cell structure in the two-dimensional space, and the set SV is composed of n crystal nucleus points p i , as shown in the following formula (11): (11); In the formula, Voronoi ( p i ) represents the Thiessen polygon; Step 3.3, use the local transformation method to subdivide the Delaunay triangles of the Thiessen polygon to obtain the crystal nucleus points piThe corresponding Delaunay triangle T , where the changing side of the convex quadrilateral iteration is determined by Δp i p j p k in p r point judgment, as shown in the following formula (12): (12); In the formula,[[]] x r , y r represents the r th crystal nucleus point p r coordinates.[[]]

[0026] Step 3.4, according to the nearest neighbor principle, connect the crystal nucleus points in the Delaunay triangle network with line segments, and subdivide the space so that each point is associated with the nearest spatial region it is in. According to the metal matrix grain size, grain number, and grain boundary graphene thickness determined in Step 1 and Step 2, a representative volume element of the graphene-reinforced titanium matrix composite with a reticular structure based on Voronoi polygons is formed, as shown in the following formula (13): (13); In the formula,[[]] E ([[]] p, p i ) represents the distance from p to p i in the two-dimensional region,[[]] Voronoi ([[]] p i ) represents the Voronoi polygon.[[]]

[0027] Example 6 Based on Example 4, in this example, in Step 4, a constitutive prediction model of Johnson-Cook plasticity and damage coupling is established. The Johnson-Cook plasticity constitutive model can be expressed as formula (14): (14); Among them, in the plasticity constitutive model,[[]] σ represents the flow stress,[[]] ε pl represents the effective plastic strain, while A , B , C , M and NThey represent the yield strength, hardening modulus, strain rate coefficient, temperature coefficient, and hardening coefficient of the matrix, respectively. Given that the influence of temperature and strain rate is not considered in this model, C and M both parameters are set to zero.

[0028] The Johnson-Cook damage constitutive model of the present invention is shown in the following formula (15): (15); In the formula, is the failure strain, d 1 ~d 5 are material damage-related constants, p and q are the hydrostatic pressure and von- Mises stress respectively, where, d 4 and d 5 have values of zero.

[0029] The entire stress-strain curves of the composites with graphene volume fractions of 0% and 2% are compared respectively. The comparison between the model stress-strain calculation results and the experimental results is as Figure 3 shown. It can be seen from the figure that the predicted tensile strength and failure strain of the composites by the model are in good agreement with the macroscopic stress-strain response results obtained from the experiments in step 1, verifying the reliability of this model. Figure 4 shows the stress concentration factor-strain curves of the graphene network and the matrix in the reticulated graphene-reinforced titanium matrix composite. It can be seen from the figure that during the loading process, the stress concentration factor of graphene is much larger than that of the titanium matrix, thus reflecting the excellent load-bearing capacity of the reticulated graphene.

[0030] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.

[0031] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the mechanical properties of a network-structured graphene-reinforced titanium-based composite material, characterized in that: The specific steps include: Step 1, preparing a network-structured graphene-reinforced titanium-based composite material by a powder metallurgy method, and obtaining its macroscopic stress-strain response and microscopic characteristics; Step 2, determining the design parameters of the network structure according to the microscopic characteristics of the network structure graphene reinforced titanium-based composite material obtained in step 1; Step 3, according to the metal matrix grain size, grain number and grain boundary graphene thickness determined in Step 1 and Step 2, a representative volume unit of the mesh structure graphene reinforced titanium matrix composite material is established using Thiessen polygons; Step 4: Based on step 3, a Johnson-Cook plasticity and damage coupling constitutive prediction model is established to predict the mechanical properties of graphene reinforced titanium-based composites.

2. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 1, characterized in that: In the step 1, the network-structured graphene-reinforced titanium-based composite material is prepared by subjecting high-purity graphite balls and titanium alloy powder to three-dimensional vibration mixing, and then preparing the network-structured graphene-reinforced titanium-based composite material by spark plasma sintering or selective laser melting.

3. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 1, characterized in that: The macroscopic stress-strain response and microscopic characteristics of the titanium-based composite material are obtained in step 1 by using scanning and transmission electron microscopes to characterize the microscopic characteristics of the network-structured graphene-reinforced titanium-based composite material, wherein the microscopic characteristics include grain size and graphene network thickness; and the macroscopic stress-strain curve of the network-structured graphene-reinforced titanium-based composite material is measured by an electronic universal testing machine, wherein the macroscopic stress-strain curve includes tensile strength and failure strain.

4. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 1, characterized in that: The step 2 determines the design parameters of the mesh structure, specifically including the metal grain size S , number of grains n , graphene thickness at grain boundaries N and stress concentration factor S cf .

5. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 1, characterized in that: The step 3 of establishing a representative volume unit of a mesh-structured graphene-reinforced titanium-based composite material using Thiessen polygons specifically includes the following steps: Step 3.1, in two-dimensional space, point M Defined as P A collection in the random nucleus coordinates is generated. M The crystal nucleus point defined as the Thiessen polygon is as shown below: ； In the formula, p i ( x i , y i ) indicates the i Nucleus point, x i , y i Indicates its coordinates Step 3.2, each nucleus point p i The generated Thiessen polygons form a unit cell structure in two-dimensional space. SV Depend on n Nucleus p i The composition is shown in the following formula: ； Step 3.3, use the local transformation method to subdivide the Delaunay triangle of the Thiessen polygon to obtain the crystal nucleus point p i The corresponding Delaunay triangle T , where the changing sides of the convex quadrilateral iteration are given by Δp i p j p k In p r Point judgment, as shown below: ； In the formula, x r , y r Indicates r Nucleus p r The coordinates of Step 3.4, according to the nearest neighbor principle, the crystal nucleus points in the Delaunay triangle network are connected with line segments, and the space is subdivided so that each point is associated with the nearest spatial region where it is located, forming a representative volume unit of the mesh structure graphene reinforced titanium-based composite material, as shown in the following formula: ； In the formula, E ( p,p i ) represents the two-dimensional region p arrive p i The distance Voronoi ( p i ) represents Thiessen polygons.

6. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 1, characterized in that: In the step 4, a Johnson-Cook plasticity and damage coupling constitutive prediction model is established; The Johnson-Cook plastic constitutive model is shown as follows: ； Among them, in the plastic constitutive model, σ represents the flow stress, ε pl represents the effective plastic strain, and A , B , C , M and N They represent the yield strength, hardening modulus, strain rate coefficient, temperature coefficient and hardening coefficient of the matrix respectively; C and M Both parameters were set to zero; The Johnson-Cook damage constitutive model is shown as follows: ； In the formula, is the failure strain, d1~d5 is the material damage related constant, p and q are the hydrostatic pressure and von-Mises Stress, where d4 and d5 The value of is zero.

7. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 6, characterized in that: The mechanical properties of the graphene-reinforced titanium-based composite material are predicted in step 4 by selecting the stress-strain data when the graphene volume fraction is zero based on the macroscopic stress-strain response data of the composite material obtained in step 1, obtaining the plasticity and damage-related parameters in the constitutive model through data fitting, and substituting the microscopic parameters of the graphene in the composite material into the constitutive prediction model for solving the problem.

8. The method for predicting mechanical properties of a network-structured graphene-reinforced titanium-based composite material according to claim 7, characterized in that: The constitutive prediction model is solved using the ABAQUS explicit solver.

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