Prediction Method for Mechanical Properties of Graphene-Reinforced Titanium-Based Composites with Reticulated Structure

Abstract

This invention discloses a method for predicting the mechanical properties of graphene-reinforced titanium matrix composites with a network structure, specifically comprising the following steps: Step 1, preparing the graphene-reinforced titanium matrix composite with a network structure using powder metallurgy, and obtaining its macroscopic stress-strain response and microscopic characteristics; Step 2, determining the design parameters of the network structure based on the microscopic characteristics of the graphene-reinforced titanium matrix composite obtained in Step 1; Step 3, determining the grain size of the metal matrix and the thickness of the graphene at the grain boundaries, and establishing representative volume elements of the graphene-reinforced titanium matrix composite with a network structure using Thiessen polygons; Step 4, based on Step 3, establishing a Johnson-Cook constitutive prediction model coupling plasticity and damage to predict the mechanical properties of the graphene-reinforced titanium matrix composite. This invention can determine the tensile strength and failure strain of graphene-reinforced titanium matrix composites with different grain sizes and graphene contents.

Description

Technical Field

[0001] This invention belongs to the field of metal-based nanocomposite materials technology, specifically relating to a method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure. Background Technology

[0002] Graphene, as a novel two-dimensional nanomaterial, has become an ideal reinforcing phase in the field of metal matrix composites due to its excellent mechanical properties. However, due to its large specific surface area, graphene is prone to aggregation, making its dispersion in the metal matrix difficult. This dispersion challenge, to some extent, restricts further improvement in the performance of composite materials. Therefore, research on the configuration design of graphene in metal matrices is particularly important. Among these, the most representative example is the network structure graphene-reinforced titanium-based composite material.

[0003] In graphene-reinforced titanium matrix composites with a network structure, the rigid graphene effectively enhances the composite's strength, while the network structure plays a positive role in regulating the composite's plasticity, effectively alleviating the contradiction between strength and plasticity. The network structure is mainly influenced by the grain size and number of the metal matrix, the thickness of the graphene at the grain boundaries, and interfacial products. However, the quantitative impact of the network structure and its influencing factors on the macroscopic mechanical properties of graphene-reinforced titanium matrix composites remains unclear. Therefore, providing a method for predicting the mechanical properties of graphene-reinforced titanium matrix composites with a network structure is of significant research importance. Summary of the Invention

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

[0005] The technical solution adopted in this invention is a method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure, specifically including the following steps:

[0006] Step 1: Prepare a network structure graphene-reinforced titanium-based composite material using powder metallurgy, and obtain its macroscopic stress-strain response and microscopic characteristics.

[0007] Step 2: Based on the microscopic characteristics of the network structure graphene-reinforced titanium-based composite material obtained in Step 1, determine the design parameters of the network structure.

[0008] Step 3: Based on the metal matrix grain size, grain number and grain boundary graphene thickness determined in Step 1 and Step 2, establish representative volume units of the network structure graphene-reinforced titanium matrix composite material using Thiessen polygons.

[0009] Step 4: Based on Step 3, establish a Johnson-Cook constitutive prediction model of plasticity and damage coupling to predict the mechanical properties of graphene-reinforced titanium-based composites.

[0010] The invention is further characterized in that,

[0011] In step 1, the graphene-reinforced titanium matrix composite material with a mesh structure is prepared by mixing high-purity graphite spheres and titanium alloy powder through three-dimensional vibration, followed by spark plasma sintering or selective laser melting.

[0012] In step 1, the macroscopic stress-strain response and microscopic characteristics of the graphene-reinforced titanium matrix composite material are obtained by using scanning and transmission electron microscopy to characterize the microscopic characteristics of the graphene-reinforced titanium matrix composite material with a mesh structure. The microscopic characteristics include grain size and graphene network thickness. The macroscopic stress-strain curve of the graphene-reinforced titanium matrix composite material with a mesh structure is measured by using an electronic universal testing machine. The macroscopic stress-strain curve includes tensile strength and failure strain.

[0013] Step 2 determines the design parameters of the network structure, specifically including the metal grain size. S Number of grains n Grain boundary graphene thickness N With stress concentration factor S cf .

[0014] Step 3, which utilizes Thiessen polygons to establish representative volumetric units of a mesh-structured graphene-reinforced titanium-based composite material, specifically includes the following steps:

[0015] Step 3.1, in two-dimensional space, place the point M Defined as P The set in the randomized source generates a crystal nucleus coordinate. M The nucleus point is defined as the zeta nucleus of the Thiessen polygon, as shown in the following equation:

[0016] ;

[0017] In the formula, p i ( x i , y i ) indicates the first i One crystal nucleation point, x i , y i Indicate its coordinates

[0018] Step 3.2, from each crystal nucleation point p iThe generated Thiessen polygons constitute a unit cell structure in two-dimensional space, and the set SV Depend on n One crystal nucleation point p i The composition is as shown in the following formula:

[0019] ;

[0020] Step 3.3: The Delaunay triangle of the Thiessen polygon is subdivided using the local transformation method to obtain the nucleation point. p i The corresponding Delaunay triangle T Among them, the iterative changes of the convex quadrilateral are determined by... Δp i p j p k In p r Point judgment, as shown in the following formula:

[0021] ;

[0022] In the formula, x r , y r Indicates the first r One crystal nucleation point p r The coordinates;

[0023] Step 3.4: Based on the nearest neighbor principle, connect the nucleus points in the Delaunay triangle network with line segments, and subdivide the space so that each point is associated with its nearest spatial region, forming a representative volume unit of the graphene-reinforced titanium-based composite material based on the Thiessen polygon mesh structure, as shown in the following equation:

[0024] ;

[0025] In the formula, E ( p,p i ) represents a two-dimensional region p arrive p i distance, Voronoi ( p i ) represents the Thiessen polygon.

[0026] In step 4, a constitutive prediction model of the coupling between plasticity and damage is established by Johnson-Cook.

[0027] The Johnson-Cook plastic constitutive model is shown in the following equation:

[0028] ;

[0029] In the plastic constitutive model, σ Represents flow stress, ε pl Represents effective plastic strain, while A , B , C , M and N These represent the matrix's yield strength, hardening modulus, strain rate coefficient, temperature coefficient, and hardening coefficient, respectively. C and M Both parameters are set to zero;

[0030] The Johnson-Cook damage constitutive model is shown in the following equation:

[0031] ;

[0032] In the formula, For failure strain, d1~d5 For material damage-related constants, p and q They are hydrostatic pressure and von- Mises Stress, where, d4 and d5 The value is zero.

[0033] In step 4, the prediction of the mechanical properties of graphene-reinforced titanium-based composites is specifically carried out by selecting the stress-strain data when the graphene volume fraction is zero based on the macroscopic stress-strain response data of the composites obtained in step 1, obtaining the plasticity and damage-related parameters in the constitutive model through data fitting, and substituting the microscopic parameters of graphene in the composites into the constitutive prediction model for solution.

[0034] The constitutive prediction model is solved using the ABAQUS explicit solver.

[0035] The beneficial effects of this invention are:

[0036] The present invention provides a method for predicting the mechanical properties of graphene-reinforced titanium-based composites with a mesh structure. Based on the microscopic characteristics of the metal matrix, such as grain size, grain number, and graphene thickness at grain boundaries, a mesh structure is constructed using Thiessen polygons. A Johnson-Cook plasticity-damage coupled constitutive prediction model is then established. This model can quantitatively correlate the microscopic characteristics and macroscopic mechanical properties of the composite material, predicting the mechanical properties of the graphene-reinforced titanium-based composites with a mesh structure. This provides theoretical guidance for optimization design and significantly reduces experimental costs and time. Attached Figure Description

[0037] Figure 1 This is a scanning electron microscope image of the network structure graphene-reinforced titanium-based composite material of the present invention;

[0038] Figure 2 This is a representative volumetric unit of the graphene-reinforced titanium-based composite material with a mesh structure based on Thiessen polygons, as described in this invention.

[0039] Figure 3 This is a comparison chart of the predicted stress-strain curves and experimental results of the mesh-structured graphene-reinforced titanium-based composite material of this invention;

[0040] Figure 4 This is the stress concentration factor-strain curve of the graphene network and titanium matrix of this invention. Detailed Implementation

[0041] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0042] Example 1

[0043] The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a mesh structure, as described in this invention, specifically includes the following steps:

[0044] Step 1: Prepare a network structure graphene-reinforced titanium-based composite material using powder metallurgy, and obtain its macroscopic stress-strain response and microscopic characteristics.

[0045] Step 2: Based on the microscopic characteristics of the network structure graphene-reinforced titanium-based composite material obtained in Step 1, determine the design parameters of the network structure.

[0046] Step 3: Based on the metal matrix grain size, grain number and grain boundary graphene thickness determined in Step 1 and Step 2, establish representative volume units of the network structure graphene-reinforced titanium matrix composite material using Thiessen polygons.

[0047] Step 4: Based on Step 3, establish a Johnson-Cook constitutive prediction model of plasticity and damage coupling to predict the mechanical properties of graphene-reinforced titanium-based composites.

[0048] Example 2

[0049] Based on the above Example 1, in step 1 of the method for predicting the mechanical properties of the graphene-reinforced titanium matrix composite material of the present invention, the graphene-reinforced titanium matrix composite material is prepared by mixing high-purity graphite spheres and titanium alloy powder through three-dimensional vibration, and then preparing the graphene-reinforced titanium matrix composite material by spark plasma sintering or selective laser melting.

[0050] Example 3

[0051] Based on Example 1 above, the method for predicting the mechanical properties of the graphene-reinforced titanium matrix composite material of the present invention, in step 1, specifically involves obtaining its macroscopic stress-strain response and microscopic characteristics. This is achieved by characterizing the microscopic characteristics of the graphene-reinforced titanium matrix composite material using scanning and transmission electron microscopy, including grain size and graphene network thickness. A universal testing machine is used to measure the macroscopic stress-strain curve of the graphene-reinforced titanium matrix composite material, which includes tensile strength (maximum stress) and failure strain (maximum strain). The specific method for obtaining the macroscopic stress-strain curve is existing technology.

[0052] Example 4

[0053] The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a mesh structure, as described in this invention, specifically includes the following steps:

[0054] Step 1: High-purity graphite spheres and titanium alloy powder are mixed by three-dimensional vibration, and then a network-structured graphene-reinforced titanium-based composite material is prepared by spark plasma sintering or selective laser melting. The microstructure of the network-structured graphene-reinforced titanium-based composite material is characterized using scanning and transmission electron microscopy, such as... Figure 1 The measurements included the grain size of the metal matrix and the thickness of the graphene network. The macroscopic stress-strain curves of the graphene-reinforced titanium matrix composite samples with a mesh structure were measured using an electronic universal testing machine, including tensile strength (maximum stress) and failure strain (maximum strain).

[0055] Step 2: Based on the microscopic characteristics of the network structure graphene-reinforced titanium-based composite material obtained in Step 1, determine the design parameters of the network structure.

[0056] The specific design parameters for the mesh structure include the metal grain size. S Number of grains nGrain boundary graphene thickness N With stress concentration factor S cf .

[0057] The relationship between the volume fraction of graphene and the volume fraction of the titanium matrix is ​​shown in the following formula (1):

[0058] (1);

[0059] in, H g It is the volume fraction of graphene. H m It is the volume fraction of the titanium matrix; the volume fraction of graphene in the network structure graphene / metal composite is determined by the number of metal matrix grains. n The thickness of graphene N and metal grain size S control.

[0060] H g The expression is shown in formula (2):

[0061] (2);

[0062] The volume fraction of the matrix phase is controlled by the number and size of the matrix grains. H m The expression is shown in formula (3):

[0063] (3);

[0064] Given a fixed model size, the design parameters for composite materials include the number of grains in the metal matrix. n The thickness of graphene N and metal grain size S And satisfy the following formula (4):

[0065] (4);

[0066] To describe the non-uniform stress distribution between graphene and the matrix, a stress concentration factor is used to quantitatively represent the load-bearing capacity of the network-structured graphene material. The equivalent stress of the composite material... σ E As shown in formula (5):

[0067] (5);

[0068] in, V m and V gThe volumes are those of the titanium matrix and graphene, respectively. V C This represents the total volume of the composite material. σ g and σ m It is the average stress of the graphene and titanium matrix, as shown in formula (6):

[0069] (6);

[0070] in, σ i This represents the stress in each unit cell of the graphene and titanium matrix. The stress concentration factor is shown in formula (7):

[0071] (7);

[0072] in, S cf(m) and S cf(g) These are the stress concentration factors of the matrix and graphene, respectively. Introducing the volume fraction into equation (5), the equivalent stress can be adjusted to equation (8):

[0073] (8);

[0074] Combining formulas (7) and (8), the volume fraction of the component phase H and stress concentration factor S cf The relationship between them can be expressed as shown in formula (9):

[0075] (9).

[0076] Step 3: Based on the metal matrix grain size, grain number, and grain boundary graphene thickness determined in Steps 1 and 2, representative volumetric units of the network structure graphene-reinforced titanium-based composite material are established using Thiessen polygons; for example... Figure 2 As shown, it should be noted that due to the pinning effect of the interface product TiC, the interface bonding force is strong, and the interface between graphene and titanium matrix can be regarded as an ideal interface.

[0077] Step 4: Based on Step 3, establish a Johnson-Cook constitutive prediction model of plasticity and damage coupling to predict the mechanical properties of graphene-reinforced titanium-based composites.

[0078] Specifically, based on the macroscopic mechanical properties of the composite material obtained in step 1, stress-strain data when the volume fraction of graphene is zero are selected, and plasticity and damage-related parameters in the constitutive model are obtained through data fitting; further, relevant microscopic parameters of graphene are obtained by consulting literature, and then all unknown constitutive parameters are substituted into the constitutive model and solved using the ABAQUS explicit solver to obtain the entire stress-strain curve of the network structure graphene-reinforced titanium-based composite material, where the maximum stress is the tensile strength and the maximum strain is the failure strain.

[0079] Example 5

[0080] Based on Example 4, step 3 of this embodiment, which utilizes Thiessen polygons to establish a representative volumetric unit of the graphene-reinforced titanium-based composite material with a mesh structure, specifically includes the following steps:

[0081] Step 3.1, in two-dimensional space, place the point M Defined as P The set in the randomized source generates a crystal nucleus coordinate. M The nucleus point of the Thiessen polygon is defined as shown in the following formula (10):

[0082] (10);

[0083] In the formula, p i ( x i , y i ) indicates the first i One crystal nucleation point, x i , y i Indicate its coordinates;

[0084] Step 3.2, from each crystal nucleation point p i The generated Thiessen polygons constitute a unit cell structure in two-dimensional space, and the set SV Depend on n One crystal nucleation point p i The composition is as shown in the following formula (11):

[0085] (11);

[0086] In the formula, Voronoi ( p i () represents a Thiessen polygon;

[0087] Step 3.3: The Delaunay triangle of the Thiessen polygon is subdivided using the local transformation method to obtain the nucleation point. pi The corresponding Delaunay triangle T Among them, the iterative changes of the convex quadrilateral are determined by... Δp i p j p k In p r Point judgment, as shown in the following formula (12):

[0088] (12);

[0089] In the formula, x r , y r Indicates the first r One crystal nucleation point p r The coordinates.

[0090] Step 3.4: Based on the nearest neighbor principle, connect the nucleus points in the Delaunay triangle network with line segments, and subdivide the space so that each point is associated with its nearest spatial region. Based on the metal matrix grain size, grain number and grain boundary graphene thickness determined in Step 1 and Step 2, form a representative volume unit of the Thiessen polygon-based mesh structure graphene-reinforced titanium matrix composite material, as shown in the following formula (13):

[0091] (13);

[0092] In the formula, E ( p,p i ) represents a two-dimensional region p arrive p i distance, Voronoi ( p i ) represents the Thiessen polygon.

[0093] Example 6

[0094] Based on Example 4, this embodiment establishes a Johnson-Cook plasticity and damage coupling constitutive prediction model in step 4. The Johnson-Cook plasticity constitutive model can be expressed as shown in formula (14):

[0095] (14);

[0096] In the plastic constitutive model, σ Represents flow stress, ε pl Represents effective plastic strain, while A , B , C , M and N These represent the matrix's yield strength, hardening modulus, strain rate coefficient, temperature coefficient, and hardening coefficient, respectively. Since this model does not consider the effects of temperature and strain rate, therefore... C and M Both parameters are set to zero.

[0097] The Johnson-Cook damage constitutive model of the present invention is shown in equation (15) below:

[0098] (15);

[0099] In the formula, For failure strain, d 1 ~d 5 represents the material damage-related constant. p and q They are hydrostatic pressure and von- Mises Stress, where, d 4 and d The value of 5 is zero.

[0100] Comparing the stress-strain curves of the composite material with graphene volume fractions of 0% and 2%, respectively, the model stress-strain calculation results are compared with the experimental results. Figure 3 As shown in the figure, the tensile strength and failure strain of the composite material predicted by the model are in good agreement with the macroscopic stress-strain response results obtained from the experiment in step 1, which verifies the reliability of the model. Figure 4 The stress concentration factor-strain curves of the graphene network and the matrix in the graphene-reinforced titanium matrix composite material with a mesh structure are shown. It can be seen from the figure that the stress concentration factor of graphene is much larger than that of the titanium matrix during loading, which shows that the mesh-distributed graphene has excellent load-bearing capacity.

[0101] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0102] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the mechanical properties of graphene-reinforced titanium-based composites with a network structure, characterized in that, Specifically, the following steps are included: Step 1: Prepare a network structure graphene-reinforced titanium-based composite material using powder metallurgy, and obtain its macroscopic stress-strain response and microscopic characteristics. Step 2: Based on the microscopic characteristics of the network structure graphene-reinforced titanium-based composite material obtained in Step 1, determine the design parameters of the network structure. Step 3: Based on the metal matrix grain size, grain number and grain boundary graphene thickness determined in Step 1 and Step 2, establish representative volume units of the network structure graphene-reinforced titanium matrix composite material using Thiessen polygons. Step 4: Based on Step 3, establish a Johnson-Cook constitutive prediction model of plasticity and damage coupling to predict the mechanical properties of graphene-reinforced titanium-based composites. Step 3, which involves establishing representative volumetric units of the graphene-reinforced titanium-based composite material using Thiessen polygons, specifically includes the following steps: Step 3.1, in two-dimensional space, place the point M Defined as P The set in the randomized source generates a crystal nucleus coordinate. M The nucleus point is defined as the zeta nucleus of the Thiessen polygon, as shown in the following equation: ； In the formula, p i ( x i , y i ) indicates the first i One crystal nucleation point, x i , y i Indicate its coordinates Step 3.2, from each crystal nucleation point p i The generated Thiessen polygons constitute a unit cell structure in two-dimensional space, and the set SV Depend on n One crystal nucleation point p i The composition is as shown in the following formula: ； Step 3.3: The Delaunay triangle of the Thiessen polygon is subdivided using the local transformation method to obtain the nucleation point. p i The corresponding Delaunay triangle T Among them, the iterative changes of the convex quadrilateral are determined by... Δp i p j p k In p r Point judgment, as shown in the following formula: ； In the formula, x r , y r Indicates the first r One crystal nucleation point p r The coordinates; Step 3.4: Based on the nearest neighbor principle, connect the nucleus points in the Delaunay triangle network with line segments, and subdivide the space so that each point is associated with its nearest spatial region, forming a representative volume unit of the network structure graphene-reinforced titanium-based composite material, as shown in the following equation: ； In the formula, E ( p,p i ) represents a two-dimensional region p arrive p i distance, Voronoi ( p i () represents a Thiessen polygon; In step 4, a Johnson-Cook constitutive prediction model coupling plasticity and damage is established. The Johnson-Cook plastic constitutive model is shown in the following equation: ； In the plastic constitutive model, σ Represents flow stress, ε pl Represents effective plastic strain, while A , B , C , M and N These represent the matrix's yield strength, hardening modulus, strain rate coefficient, temperature coefficient, and hardening coefficient, respectively. C and M Both parameters are set to zero; The Johnson-Cook damage constitutive model is shown in the following equation: ； In the formula, For failure strain, d1~d5 For material damage-related constants, p and q They are hydrostatic pressure and von-Mises Stress, where, d4 and d5 The value is zero.

2. The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure according to claim 1, characterized in that, In step 1, the graphene-reinforced titanium-based composite material with a mesh structure is prepared by mixing high-purity graphite spheres and titanium alloy powder through three-dimensional vibration, followed by spark plasma sintering or selective laser melting.

3. The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure according to claim 1, characterized in that, In step 1, obtaining the macroscopic stress-strain response and microscopic characteristics specifically involves characterizing the microscopic characteristics of the network-structured graphene-reinforced titanium-based composite material using scanning and transmission electron microscopy, including grain size and graphene network thickness; and measuring the macroscopic stress-strain curve of the network-structured graphene-reinforced titanium-based composite material using an electronic universal testing machine, including tensile strength and failure strain.

4. The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure according to claim 1, characterized in that, Step 2, which determines the design parameters of the mesh structure, specifically includes the metal grain size. S Number of grains n Grain boundary graphene thickness N With stress concentration factor S cf .

5. The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure according to claim 1, characterized in that, In step 4, the prediction of the mechanical properties of graphene-reinforced titanium-based composite material is specifically carried out 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 graphene in the composite material into the constitutive prediction model for solution.

6. The method for predicting the mechanical properties of graphene-reinforced titanium-based composite materials with a network structure according to claim 5, characterized in that, The constitutive prediction model is solved using the ABAQUS explicit solver.

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