A constitutive model construction method and system for predicting nickel-titanium alloy welding deformation

Abstract

The present invention discloses a constitutive model construction method and system for predicting nickel-titanium alloy welding deformation, which relates to the field of material science and technology. The method is based on the stress-strain relationship of nickel-titanium alloy materials during ideal elastic deformation and linear elastic deformation, and further considers the high temperature difference and large deformation during resistance welding. The total strain equation of the nickel-titanium alloy material is constructed as a linear superposition of the linear elastic constitutive equation of austenite strain and martensite strain and the phase transformation strain equation. At this time, the constitutive model of the nickel-titanium alloy material during superelastic deformation is represented by the total strain equation, which is used for the simulation of the nickel-titanium alloy welding process. The method can use more advanced simulation calculation methods and means to improve the accuracy and reliability of simulation calculations, so as to optimize resistance welding technology and improve the quality of welded joints.

Description

Technical Field

[0001] The present application relates to the field of material science and technology, and in particular to a constitutive model construction method and system for predicting nickel-titanium alloy welding deformation. Background Art

[0002] In modern industrial manufacturing, resistance butt welding technology is widely used in the connection of metal materials due to its advantages such as high welding efficiency, simple operation and low cost. Especially for alloy materials such as nickel-titanium alloy with excellent physical and chemical properties, resistance butt welding technology plays a vital role. However, resistance butt welding is a multi-field coupled nonlinear process involving the interaction of multiple physical fields such as heat, electricity, and force, making the welding process complex and difficult to control. Therefore, in-depth understanding and exploration of the thermal field, deformation field and phase change process during resistance butt welding is of great significance to improving the welding process level and joint quality.

[0003] At present, resistance welding technology has made certain research progress. During the welding process, by applying current, the workpiece's own resistance is used to generate heat, so that the contact surface of the workpiece melts and forms a welded joint. In this process, the welding time is short, the temperature changes greatly, and the contact resistance is uncertain, which is affected by many factors such as the workpiece material, surface state, electrode shape, etc. In addition, external interference such as ambient temperature and humidity will also affect the welding process. In order to deeply understand and explore the resistance welding process, simulation calculation methods are used in the prior art. By simulating and calculating the thermal field and deformation field during the welding process, the change process and distribution trend of material properties and microstructure during the welding process can be evaluated. This method can effectively predict the quality of the welded joint and provide a theoretical basis for the optimization of the welding process.

[0004] Although the existing technology has achieved certain results, there are still problems with the accuracy of simulation calculations: although the simulation calculation method can evaluate the change process and distribution trend of material properties and microstructures during welding, can more deeply understand and explore the heat, deformation and phase change process of welding, and has a guiding role in improving welding technology and joint quality, its accuracy is affected by many factors. For example, the accuracy of the simulation model and the selection of the calculation method will affect the reliability of the simulation results.

[0005] Therefore, in order to solve the problems existing in the prior art, it is necessary to further optimize the resistance welding technology and improve the quality of the welded joints. This requires a more in-depth study and exploration of the thermal field, deformation field and phase change process during resistance welding, and the use of more advanced simulation calculation methods and means to improve the accuracy and reliability of simulation calculations. Summary of the invention

[0006] Based on this, the present application proposes a constitutive model construction method and system for predicting nickel-titanium alloy welding deformation, aiming to adopt more advanced simulation calculation methods and means to improve the accuracy and reliability of simulation calculations, so as to optimize resistance butt welding technology and improve the quality of welded joints.

[0007] The first aspect of the present application provides a constitutive model construction method for predicting nickel-titanium alloy welding deformation, the method comprising:

[0008] According to the stress tensor in nickel-titanium alloy material during ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant;

[0009] According to the stress in the nickel-titanium alloy material during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space;

[0010] The shear stress at the starting point of the martensitic transformation is obtained by calculating the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T ;

[0011] According to the strain generated by stress on martensite and austenite in the nickel-titanium alloy material during superelastic deformation, the total strain equation of the nickel-titanium alloy material is constructed as the linear superposition of the linear elastic constitutive equation of austenite strain and martensite strain and the phase transformation strain equation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows: ,in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents phase change strain;

[0012] According to the stress of nickel-titanium alloy material Conditional relationship with temperature T The austenite content is obtained and martensite content ;

[0013] According to the deformation amount and martensite content caused by martensitic transformation The phase change strain is obtained ;

[0014] According to the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

[0015] Compared with the prior art, the present application provides a constitutive model construction method for predicting the welding deformation of nickel-titanium alloy. The method is based on the constitutive equation of nickel-titanium alloy material during linear elastic deformation in three-dimensional space, and further considers the influence of yield effect, strain hardening, phase transformation deformation, temperature effect, etc. in material deformation, so it is suitable for predicting the resistance resistance of nickel-titanium alloy with high temperature difference and large deformation. Since martensite and austenite will coexist in the material after a certain degree of phase transformation, the two phases will also produce strain when subjected to stress, so the linear superposition of austenite strain, martensite strain and phase transformation strain is performed. On the one hand, the accuracy of the model can be improved: during the resistance welding process, metal materials such as nickel-titanium alloy may undergo complex phase transformation and deformation. The linear superposition of austenite strain, martensite strain and phase transformation strain can more comprehensively reflect the actual deformation of the material during the welding process; during the welding process of nickel-titanium alloy, due to temperature changes, a phase transformation from austenite to martensite may occur. This phase transformation will cause the redistribution of internal stress and the generation of strain in the material. Incorporating phase transformation strain into the constitutive equation can more accurately predict the deformation behavior of the material. On the other hand, the welding process can be optimized: by constructing a constitutive equation including austenite strain, martensite strain and phase transformation strain, the deformation of the material under different welding process parameters can be simulated, which helps engineers select the optimal welding process parameters to reduce welding deformation and improve welding quality; defects that may occur during the welding process, such as cracks and deformation, are often closely related to the deformation behavior of the material. By predicting the deformation of the material through the constitutive equation, potential welding defects can be discovered and prevented in time.

[0016] Therefore, this application proposes a constitutive model construction method for predicting nickel-titanium alloy welding deformation. This method can use more advanced simulation calculation methods and means to improve the accuracy and reliability of simulation calculations, so as to optimize resistance butt welding technology and improve the quality of welded joints.

[0017] As an optional implementation of the first aspect, according to the stress tensor in the nickel-titanium alloy material during ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor The steps include:

[0018] Stress tensor in nickel-titanium alloy material when constructing ideal elastic deformation and the strain tensor The linear relationship expression is:

[0019] ,

[0020] ,

[0021] in, is the stress tensor, is the strain tensor, is the stiffness tensor, S is the flexibility tensor;

[0022] Fourth-order stiffness tensor It is expressed as:

[0023] ,

[0024] in, is called the Lamé constant, is the Kronecker representation of the i-th row and j-th column, is the Kronecker representation of the kth row and lth column, is the Kronecker representation of the i-th row and k-th column, is the Kronecker representation of the jth row and lth column, is the Kronecker representation of the ith row and lth column, is the Kronecker representation of the kth row and jth column;

[0025] According to the generalized Hooke's law, the Lame constant is related to the elastic modulus E and Poisson's ratio of the nickel-titanium alloy material. , and the conversion relationship of the flexibility tensor of nickel-titanium alloy materials, the fourth-order flexibility tensor is obtained The expression is:

[0026] ,

[0027] ,

[0028] ,

[0029] ;

[0030] .

[0031] As an optional implementation of the first aspect, according to the stress in the nickel-titanium alloy material during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , the steps of obtaining the Lamé constant include:

[0032] Constructing the stress in the NiTi alloy material during linear elastic deformation and strain The relational expression is:

[0033] ,

[0034] Among them, A is the yield strength, B is the material strain hardening modulus, n is the hardening index, and m is the temperature softening index. is the dimensionless strain rate, is the dimensionless temperature;

[0035] Divide both sides of the above relationship by the strain The function formula of equal Young's modulus is obtained:

[0036] ;

[0037] Obtain the Poisson's ratio v of the nickel-titanium alloy material in the plastic deformation stage 1 and the Poisson's ratio v in the elastic deformation stage 2 According to the Poisson's ratio in the plastic deformation stage and the Poisson's ratio in the elastic deformation stage, the transverse strain formula of the nickel-titanium alloy material is obtained:

[0038] ,

[0039] in, is the axial strain, is the lateral strain;

[0040] Dividing both sides of the above transverse strain formula by the axial strain gives the equivalent Poisson's ratio function:

[0041] ;

[0042] The above-obtained E, Substitute the Lame constant and the elastic constant E of the nickel-titanium alloy material, The conversion relationship is obtained from and .

[0043] As an optional implementation of the first aspect, the step of obtaining the constitutive equation of the nickel-titanium alloy material during linear elastic deformation in three-dimensional space includes:

[0044] Will and Respectively Substituting the fourth-order stiffness tensor into the form of

[0045] ,

[0046] The constitutive equation of the nickel-titanium alloy material when reconstructing the linear elastic deformation in three-dimensional space is: .

[0047] As an optional implementation of the first aspect, the strain-induced martensitic transformation conditions of the nickel-titanium alloy material are calculated according to the Tresca yield criterion form to obtain the shear stress at the starting point of the induced martensitic transformation. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T The steps include:

[0048] The starting and ending conditions of strain-induced martensite in nickel-titanium alloy are calculated according to the Tresca yield criterion:

[0049] ,

[0050] ,

[0051] in, represents the maximum shear stress;

[0052] The relationship between the temperature required for the transformation of martensite to austenite and the corresponding shear stress is expressed by the equation:

[0053] ,

[0054] ,

[0055] in, They represent the temperatures required for the nickel-titanium alloy material to start and completely transform from martensite to austenite under no stress. and represent the shear stress required for the nickel-titanium alloy material to transform from martensite to austenite at room temperature respectively;

[0056] According to the temperature T and corresponding shear stress required for the transformation of martensite to austenite The relationship equation between the shear stress and Conditional relationship with temperature T , and then according to the transformation relationship between shear stress and stress, we can get stress Conditional relationship with temperature T .

[0057] As an optional implementation of the first aspect, according to the stress of the nickel-titanium alloy material Conditional relationship with temperature T The austenite content is obtained and martensite content The steps include:

[0058] Building conditional relationships and martensite content The relationship is: ,

[0059] Reconstruction of austenite content and martensite content The relationship is: ;

[0060] in, ,

[0061] In particular, ,

[0062] The conversion relationship between shear stress and stress is: .

[0063] As an optional implementation of the first aspect, according to the deformation amount and martensite content caused by the martensitic transformation The phase change strain is obtained The steps include:

[0064] Constructing the deformation and martensite content produced by the martensitic transformation The phase change strain The relationship is:

[0065] ,

[0066] in, Represents the amount of deformation produced by the martensitic phase transformation, measured by a tensile test.

[0067] A second aspect of an embodiment of the present application provides a constitutive model construction system for predicting nickel-titanium alloy welding deformation, the system comprising:

[0068] Rational elastic model building block for stress tensors in NiTi alloy materials according to ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant;

[0069] Linear elastic model building module for stress in NiTi alloy materials during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space;

[0070] The induced martensitic transformation module is used to calculate the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion form, and obtain the shear stress at the starting point of the induced martensitic transformation. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T ;

[0071] A superelastic model building module is used to construct a total strain equation of the nickel-titanium alloy material as a linear superposition of a linear elastic constitutive equation of austenite strain and martensite strain and a phase transformation strain equation according to the strain generated by stress on martensite and austenite in the nickel-titanium alloy material during superelastic deformation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows: ,in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents phase change strain;

[0072] The hyperelastic model building module includes phase change strain solving unit, flexibility tensor solving unit and phase change content solving unit, among which:

[0073] Phase transformation strain solver is used to calculate the stress of nickel-titanium alloy materials Conditional relationship with temperature T The austenite content is obtained and martensite content ;

[0074] Compliance tensor solver for the amount of deformation and martensite content due to martensitic transformation The phase change strain is obtained ;

[0075] Phase change content solver is used to calculate the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

[0076] A third aspect of an embodiment of the present application provides a computer device, comprising a memory, a processor, and a processing program stored on the memory and executable on the processor, wherein when the processing program is executed by the processor, the above-mentioned method for constructing a constitutive model for predicting welding deformation of nickel-titanium alloy is implemented.

[0077] A fourth aspect of an embodiment of the present application provides a computer-readable storage medium, on which a processing program is stored. When the processing program is executed by a processor, the above-mentioned constitutive model construction method for predicting nickel-titanium alloy welding deformation is executed.

[0078] Additional aspects and advantages of the present application will be given in part in the following description, and in part will become apparent from the following description, or will be understood through the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 A flowchart of a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the first embodiment of the present application;

[0080] Figure 2 A nickel-titanium alloy stress-temperature phase diagram in a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the first embodiment of the present application;

[0081] Figure 3 A finite element model diagram of resistance butt welding in a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the second embodiment of the present application;

[0082] Figure 4 A temperature distribution diagram of nickel-titanium alloy resistance welding 0.2 seconds after starting welding in a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the second embodiment of the present application;

[0083] Figure 5 A diagram showing deformation simulation results of a nickel-titanium alloy wire welding process in a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the second embodiment of the present application;

[0084] Figure 6 This is a schematic structural diagram of a constitutive model building system for predicting nickel-titanium alloy welding deformation proposed in the third embodiment of the present application.

[0085] The following specific implementation methods will further illustrate the present application in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0086] In order to facilitate understanding of the present application, the present application will be described more fully below with reference to the relevant drawings. Several embodiments of the present application are provided in the drawings. However, the present application can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive.

[0087] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0088] In order to illustrate the technical solution described in this application, a specific embodiment is provided below for illustration.

[0089] It should be noted that in the following embodiments, it is first necessary to clarify the materials and their physical properties, as well as to model and assume conditions.

[0090] When clarifying the materials and their physical properties, it should be noted that the temperature field and deformation process of nickel-titanium alloy resistance welding need to be simulated. Therefore, some basic physical performance parameters of the material are first clarified. The thermophysical performance parameters of the material are less affected by temperature when the temperature is lower than the melting point, while the mechanical performance parameters are more sensitive to temperature changes. Therefore, the thermophysical properties of the material will be calculated and simulated using some fixed parameters. For example, Table 1 lists some physical performance parameters of nickel-titanium alloy used in this numerical simulation. The electrode material is the copper material provided by the software for calculation.

[0091] Table 1 Thermophysical properties of nickel-titanium alloy

[0092]

[0093] When modeling and assuming conditions, it should be noted that in the process of resistance welding, the electrode, base material, circuit, etc. form a series circuit, and its energy conversion conforms to Joule's law. That is to say, the greater the resistance, the greater the resistance thermal power. During the entire welding process, the largest resistance comes from the contact resistance between the end faces of the two wire sections. There is currently no accurate or feasible calculation formula for the contact resistance here. Therefore, some assumptions are used in the simulation calculation. These assumptions will make the calculation results somewhat inconsistent with the actual situation, but it can still qualitatively analyze the distribution of temperature and deformation, which has certain guiding significance for the research and analysis of nickel-titanium alloy wire resistance welding. For example:

[0094] (1) Since the contact resistance is much larger than the resistance between the copper electrode and the material itself, it is assumed that all the energy comes from the contact end surface of the wire and the heat source is evenly distributed on the contact end surface.

[0095] (2) Since the contact resistance here cannot be accurately calculated or evaluated, the actual power cannot be effectively calculated during the welding process. It is assumed here that the highest temperature at the joint during the welding process is close to the melting point of the material, and the melting point of nickel-titanium alloy is about 1310°C.

[0096] (3) The initial ambient temperature is set to 25°C.

[0097] (4) The nickel-titanium alloy wire is set as a cylindrical support, that is, its axis remains unchanged.

[0098] (5) Since the copper electrode is much larger than the nickel-titanium wire and dissipates heat quickly, in order to simplify the calculation, only a part of the copper electrode was modeled and it was assumed that the surface temperature of the copper electrode was the same as room temperature.

[0099] See also Figure 1 , is a flow chart of a constitutive model construction method for predicting nickel-titanium alloy welding deformation proposed in the first embodiment of the present application, the method steps comprising:

[0100] S01: Stress tensor in nickel-titanium alloy material during ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant.

[0101] It should be noted that the constitutive relationship of metal materials reflects the law of macroscopic stress variation with strain under certain deformation conditions. Nickel-titanium alloy is very different from other materials due to its superelasticity and shape memory. In this regard, many scholars have studied the material constitutive equation of nickel-titanium alloy, but they are mainly concentrated in the field of engineering applications. However, there is no data on the constitutive equation of nickel-titanium alloy suitable for high temperature difference and large deformation of welding. This embodiment will combine the existing theory with the summary of the superelastic deformation behavior of nickel-titanium alloy to construct a new constitutive equation of nickel-titanium alloy for the simulation of the welding process of nickel-titanium alloy.

[0102] For an ideal elastic material, the stress and strain of the material are in a linear relationship, and the stress tensor in the nickel-titanium alloy material during ideal elastic deformation can be obtained. and the strain tensor The linear relationship expression of is shown in formula (1) and formula (2):

[0103] (1)

[0104] (2)

[0105] in, is the stress tensor, is the strain tensor, is the stiffness tensor, S is the flexibility tensor;

[0106] For isotropic materials, since stress and strain are symmetric tensors, C and S are isotropic symmetric tensors, and the fourth-order stiffness tensor is The general form is:

[0107] (3)

[0108] in, is called the Lamé constant, is the Kronecker representation of the i-th row and j-th column, is the Kronecker representation of the kth row and lth column, is the Kronecker representation of the i-th row and k-th column, is the Kronecker representation of the jth row and lth column, is the Kronecker representation of the ith row and lth column, is the Kronecker representation of the kth row and jth column;

[0109] According to the generalized Hooke's law, the Lame constant is related to the elastic modulus E and Poisson's ratio of the nickel-titanium alloy material. , and the conversion relationship of the flexibility tensor of nickel-titanium alloy materials, the fourth-order flexibility tensor is obtained The expression is:

[0110] (4)

[0111] (5)

[0112] (6)

[0113] (7)

[0114] (8)

[0115] S02: Stress in NiTi alloy material during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space.

[0116] It should be noted that the constitutive equation of nickel-titanium alloy materials under linear elastic deformation (JC constitutive equation) is a commonly used mechanical model in material mechanics, which is used to describe the relationship between stress and strain of materials. The JC constitutive equation is an extension of the linear elastic theory and can better describe the deformation behavior of materials under high stress. This constitutive equation takes into account the influence of the material's yield effect, strain hardening, and temperature effect on the stress-strain relationship. It is often used for the elastic-plastic behavior of metals under large strain, high strain rate, and large temperature difference.

[0117] Stress in NiTi alloy during linear elastic deformation and strain The relational expression is:

[0118] (9)

[0119] Among them, A is the yield strength, B is the material strain hardening modulus, n is the hardening index, and m is the temperature softening index. is the dimensionless strain rate, is the dimensionless temperature; this equation can better describe the more realistic deformation of materials in more environments, but this equation only describes the deformation behavior of materials in one-dimensional space.

[0120] Dividing both sides of formula (9) by strain gives the equivalent Young's modulus function:

[0121] (10)

[0122] Obtain the Poisson's ratio v of the nickel-titanium alloy material in the plastic deformation stage 1 and the Poisson's ratio v in the elastic deformation stage 2 According to the Poisson's ratio in the plastic deformation stage and the Poisson's ratio in the elastic deformation stage, the transverse strain formula of the nickel-titanium alloy material is obtained:

[0123] (11)

[0124] in, is the axial strain, is the lateral strain;

[0125] Dividing both sides of formula (11) by the axial strain yields the equivalent Poisson's ratio function:

[0126] (12)

[0127] The E obtained by combining formula (10) and formula (12) Substitute the Lame constant and the elastic constant E of the nickel-titanium alloy material, The conversion relationship is obtained from and .

[0128] Will and Respectively Substituting the fourth-order stiffness tensor into the form of

[0129] (13)

[0130] Martensite and austenite have different properties, and two different equivalent stiffness tensors can be obtained.

[0131] The constitutive equation of the nickel-titanium alloy material when reconstructing the linear elastic deformation in three-dimensional space is:

[0132] (14)

[0133] S03: Calculate the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion form, and obtain the shear stress at the starting point of the induced martensitic transformation and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T .

[0134] It should be noted that the stress-induced martensite condition of the material can be set with reference to the yield condition of the material yield. The Tresca yield criterion believes that when the maximum shear stress in the material reaches a certain critical value, the material will begin to yield.

[0135] The starting and ending conditions of strain-induced martensite in nickel-titanium alloy are calculated according to the Tresca yield criterion:

[0136] (15)

[0137] (16)

[0138] in, represents the maximum shear stress;

[0139] For example, Figure 2 As shown in the figure, it is a stress-temperature phase diagram of nickel-titanium alloy. The martensitic phase transformation condition in the figure can be assumed to be a straight line. The equation of the straight line is as follows, that is, the relationship equation between the temperature required for the transformation of martensite to austenite and the corresponding shear stress:

[0140] (17)

[0141] (18)

[0142] in, They represent the temperatures required for the nickel-titanium alloy material to start and completely transform from martensite to austenite under no stress, which need to be measured by differential scanning calorimetry DSC; and represent the shear stress required for the nickel-titanium alloy material to start and completely transform from martensite to austenite at room temperature, respectively, which can be measured by tensile test;

[0143] According to the temperature T and corresponding shear stress required for the transformation of martensite to austenite The relationship equation between the shear stress and Conditional relationship with temperature T , and then according to the transformation relationship between shear stress and stress, we can get stress Conditional relationship with temperature T .

[0144] S04: According to the strain generated by the stress on martensite and austenite in the nickel-titanium alloy material during superelastic deformation, the total strain equation of the nickel-titanium alloy material is constructed as the linear superposition of the linear elastic constitutive equation of austenite strain and martensite strain and the phase transformation strain equation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows:

[0145] (19)

[0146] in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents the phase change strain.

[0147] It should be noted that nickel-titanium alloy will undergo martensitic phase transformation during the stress process, and the martensite content in the material during the phase transformation process is related to the stress and temperature of the material. Nickel-titanium alloy exists in the form of austenite at room temperature, and will undergo a phase transformation into martensite when subjected to stress. This phase transformation process is accompanied by a certain deformation, which is recorded as phase transformation strain. After a certain degree of phase transformation, martensite and austenite will coexist in the material, and the two phases will also produce strain when subjected to stress. Therefore, the total strain of the material is the linear superposition of austenite strain, martensite strain, and phase transformation strain.

[0148] Specifically, the S04 includes S041, S042 and S043, wherein:

[0149] S041: Based on the stress of nickel-titanium alloy material Conditional relationship with temperature T The austenite content is obtained and martensite content .

[0150] Building conditional relationships and martensite content The relationship is:

[0151] (20)

[0152] Reconstruction of austenite content and martensite content The relationship is:

[0153] (twenty one)

[0154] According to the material stress state The maximum shear stress in the material can be calculated using the following formula

[0155] (twenty two)

[0156] The martensite content in the material can then be calculated based on the phase diagram

[0157] (twenty three)

[0158] Special

[0159] (twenty four)

[0160] S042: Based on the deformation and martensite content caused by martensitic transformation The phase change strain is obtained .

[0161] It should be noted that during the phase change process, the material exhibits superelastic deformation, and the amount of superelastic deformation is related to the martensite content in the material.

[0162] Deformation and martensite content caused by martensitic transformation The phase change strain The relationship is:

[0163] (25)

[0164] in, Represents the amount of deformation produced by the martensitic phase transformation, measured by a tensile test.

[0165] S043: According to the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

[0166] Specifically, and Substituting into formula (8), we can obtain the equivalent flexibility tensor of austenite and martensite: and .

[0167] At this point, the calculation process of all the values ​​in formula (19) has been obtained, and the superelastic temperature-dependent constitutive equation of nickel-titanium alloy can be calculated. Since this constitutive equation is based on the JC constitutive equation, takes into account the martensitic phase transformation, and adopts a tensor form, this constitutive equation can be applied to large strains, large temperature differences, high strain rates, etc. Welding meets these characteristics, so the constitutive equation is more suitable for the numerical simulation of nickel-titanium alloy welding.

[0168] In the second embodiment, based on the constitutive model of the nickel-titanium alloy material during superelastic deformation obtained in the first embodiment, a comparative analysis of the resistance butt welding finite element model is performed.

[0169] like Figure 3 As shown in the figure, it is a finite element model diagram of resistance butt welding. The nickel-titanium alloy wire is wrapped in a circle of copper electrodes, and the models on both sides are symmetrical. For the mechanical boundary conditions, the contact end faces of the two wires are set as frictionless support, that is, the contact plane of the two wires never changes. A force of 7N is loaded on each of the other two ends of the two wires. For the thermal boundary conditions, there is a heat flux plane heat source on the contact end face, and a convection heat dissipation boundary condition on the surface of the nickel-titanium alloy, with a convection coefficient of 12W / m2℃ and a radiation coefficient of 0.6. Triangular meshing is used, and the mesh on the nickel-titanium alloy is encrypted. The constitutive equation of the nickel-titanium alloy material is used to calculate the stress-strain curves at various temperatures and input them into the material properties in sections for subsequent stress field simulations.

[0170] It should be noted that in the solution, the total time is set to 0.2s, the initial time step is 0.001s, the minimum time step is 0.001s, and the maximum time step is 0.005s. Figure 4 This is the temperature distribution diagram of the nickel-titanium alloy resistance welding 0.2 seconds after the welding is started. The maximum temperature is 1305.5 degrees Celsius, which is close to the melting point of nickel-titanium alloy. It can be seen that the isotherms are relatively dense in the part where the nickel-titanium alloy contacts the copper electrode. In other words, the temperature gradient is large when welding here, and the hardness of the nickel-titanium alloy welded joint changes drastically here. From the tensile test results, the fracture position of the nickel-titanium alloy wire when stretched is also approximately here. These phenomena indicate that due to the heat dissipation of the copper electrode, this place has become the boundary of the nickel-titanium alloy affected by heat. On one side is the base material that is not affected by heat, and on the other side is the nickel-titanium alloy that has recovered from the heat. Due to the large temperature gradient, the welded joint has brittle fracture here.

[0171] However, the above temperature field data plus the force load were used to calculate the welding deformation field of NiTi alloy using the constructed NiTi alloy constitutive equation. Figure 5This is the deformation simulation result diagram of the nickel-titanium alloy wire welding process. Using the nickel-titanium alloy constitutive equation constructed above, the simulation can simulate the situation in which the material is squeezed out to form protrusions when it is subjected to force and heat at the same time, which is consistent with the actual welding situation.

[0172] In summary, the present application provides a constitutive model construction method for predicting the welding deformation of nickel-titanium alloys. This method combines the existing material plasticity theory, modern tensor theory and the phase change behavior of nickel-titanium alloys to summarize and calculate, and constructs a new superelastic constitutive equation for nickel-titanium alloys. This constitutive equation takes into account the effects of yield effect, strain hardening, phase change deformation, temperature effect, etc. in material deformation, so it is also applicable under high temperature difference and large deformation conditions. The temperature field and deformation of nickel-titanium alloy resistance welding were simulated and calculated using the above constitutive equation. The temperature field shows that the material temperature will drop rapidly near the contact area between the nickel-titanium alloy wire and the copper electrode, and the temperature gradient is large, which confirms that the analysis of the cause of the brittle fracture of the nickel-titanium alloy resistance welding joint is correct. The deformation field simulation of nickel-titanium alloy using the new constitutive equation is consistent with the morphology of the nickel-titanium alloy resistance welding joint produced by actual welding, which also shows the practicality of the constitutive equation in nickel-titanium alloy welding simulation.

[0173] See also Figure 6 , shown is a structural schematic diagram of a constitutive model building system for predicting nickel-titanium alloy welding deformation in the third embodiment of the present application, the system comprising:

[0174] Rational elastic model building module 10, for stress tensor in nickel-titanium alloy material according to ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant;

[0175] The linear elastic model building module 20 is used to construct a linear elastic model according to the stress in the nickel-titanium alloy material during linear elastic deformation. and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space;

[0176] The induced martensitic transformation module 30 is used to calculate the strain-induced martensitic transformation conditions of the nickel-titanium alloy material according to the Tresca yield criterion form, and obtain the shear stress at the starting point of the induced martensitic transformation. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T ;

[0177] The superelastic model construction module 40 is used to construct the total strain equation of the nickel-titanium alloy material as the linear superposition of the linear elastic constitutive equation of the austenite strain and the martensite strain and the phase transformation strain equation according to the strain generated by the stress on the martensite and the austenite in the nickel-titanium alloy material during superelastic deformation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows: ,in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents phase change strain;

[0178] The hyperelastic model building module 40 includes a phase change strain solving unit 401, a flexibility tensor solving unit 402 and a phase change content solving unit 403, wherein:

[0179] Phase transformation strain solving unit 401 is used to calculate the phase transformation strain according to the stress of nickel-titanium alloy material. Conditional relationship with temperature T The austenite content is obtained and martensite content ;

[0180] The flexibility tensor solving unit 402 is used to calculate the deformation amount and martensite content of the martensite phase transformation according to the deformation amount and martensite content of the martensite phase transformation. The phase change strain is obtained ;

[0181] Phase change content solving unit 403 is used to calculate the phase change content according to the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

[0182] On the other hand, the present application also proposes a computer device, which includes a memory, a processor, and a processing program stored in the memory and executable on the processor. When the processing program is executed by the processor, the above-mentioned constitutive model construction method for predicting nickel-titanium alloy welding deformation is implemented.

[0183] On the other hand, the present application further proposes a computer-readable storage medium, on which a processing program is stored. When the processing program is run by a processor, the above-mentioned constitutive model construction method for predicting nickel-titanium alloy welding deformation is executed.

[0184] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0185] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A constitutive model construction method for predicting nickel-titanium alloy welding deformation, characterized in that: The method comprises: According to the stress tensor in nickel-titanium alloy material during ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant; According to the stress in the nickel-titanium alloy material during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space; The shear stress at the starting point of the martensitic transformation is obtained by calculating the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T ; According to the strain generated by stress on martensite and austenite in the nickel-titanium alloy material during superelastic deformation, the total strain equation of the nickel-titanium alloy material is constructed as the linear superposition of the linear elastic constitutive equation of austenite strain and martensite strain and the phase transformation strain equation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows: ,in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents phase change strain; According to the stress of nickel-titanium alloy Conditional relationship with temperature T The austenite content is obtained and martensite content , specifically including: Building conditional relationships and martensite content The relationship is: , Reconstruction of austenite content and martensite content The relationship is: ; in, , In particular, , The conversion relationship between shear stress and stress is: ; According to the deformation amount and martensite content caused by martensitic transformation The phase change strain is obtained , specifically including: constructing the deformation amount and martensite content produced by martensitic transformation The phase change strain The relationship is: ， in, It represents the amount of deformation produced by the martensitic phase transformation, measured by a tensile test; According to the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

2. A constitutive model construction method for predicting nickel-titanium alloy welding deformation according to claim 1, characterized in that: According to the stress tensor in nickel-titanium alloy material during ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor The steps include: Stress tensor in nickel-titanium alloy material when constructing ideal elastic deformation and the strain tensor The linear relationship expression is: ， ， in, is the stress tensor, is the strain tensor, is the stiffness tensor, S is the flexibility tensor; Fourth-order stiffness tensor It is expressed as: ， in, is called the Lamé constant, is the Kronecker representation of the i-th row and j-th column, is the Kronecker representation of the kth row and lth column, is the Kronecker representation of the i-th row and k-th column, is the Kronecker representation of the jth row and lth column, is the Kronecker representation of the ith row and lth column, is the Kronecker representation of the kth row and jth column; According to the generalized Hooke's law, the Lame constant is related to the elastic modulus E and Poisson's ratio of the nickel-titanium alloy material. , and the conversion relationship of the flexibility tensor of nickel-titanium alloy materials, the fourth-order flexibility tensor is obtained The expression is: ， ， ， ； 。 3. A constitutive model construction method for predicting nickel-titanium alloy welding deformation according to claim 2, characterized in that: According to the stress in the nickel-titanium alloy material during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , the steps of obtaining the Lamé constant include: Constructing the stress in the NiTi alloy material during linear elastic deformation and strain The relational expression is: ， Among them, A is the yield strength, B is the material strain hardening modulus, n is the hardening index, and m is the temperature softening index. is the dimensionless strain rate, is the dimensionless temperature; Divide both sides of the above relationship by the strain The function formula of equal Young's modulus is obtained: ； The Poisson's ratio v1 of the nickel-titanium alloy material in the plastic deformation stage and the Poisson's ratio v2 of the elastic deformation stage are obtained, and the transverse strain formula of the nickel-titanium alloy material is obtained according to the Poisson's ratio of the plastic deformation stage and the Poisson's ratio of the elastic deformation stage: ， in, is the axial strain, is the lateral strain; Dividing both sides of the above transverse strain formula by the axial strain gives the equivalent Poisson's ratio function: ； The above-obtained E, Substitute the Lame constant and the elastic constant E of the nickel-titanium alloy material, The conversion relationship is obtained from and .

4. A constitutive model construction method for predicting nickel-titanium alloy welding deformation according to claim 3, characterized in that: The steps of obtaining the constitutive equation of the nickel-titanium alloy material during linear elastic deformation in three-dimensional space include: Will and Respectively Substituting the fourth-order stiffness tensor into the form of ， The constitutive equation of the nickel-titanium alloy material when reconstructing the linear elastic deformation in three-dimensional space is: .

5. A constitutive model construction method for predicting welding deformation of nickel-titanium alloy according to claim 4, characterized in that: The shear stress at the starting point of the martensitic transformation is obtained by calculating the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T The steps include: The starting and ending conditions of strain-induced martensite in nickel-titanium alloy are calculated according to the Tresca yield criterion: ， ， in, represents the maximum shear stress; The relationship between the temperature required for the transformation of martensite to austenite and the corresponding shear stress is expressed by the equation: ， ， in, They represent the temperatures required for the nickel-titanium alloy material to start and completely transform from martensite to austenite under no stress. and represent the shear stress required for the nickel-titanium alloy material to transform from martensite to austenite at room temperature respectively; According to the temperature T and corresponding shear stress required for the transformation of martensite to austenite The relationship equation between the shear stress and Conditional relationship with temperature T , and then according to the transformation relationship between shear stress and stress, we can get stress Conditional relationship with temperature T .

6. A constitutive model construction system for predicting nickel-titanium alloy welding deformation, characterized in that: The system comprises: Rational elastic model building block for stress tensors in NiTi alloy materials according to ideal elastic deformation and the strain tensor The linear relationship between and the fourth-order flexibility tensor , where the fourth-order stiffness tensor and the fourth-order flexibility tensor Introducing the Lamé constant; Linear elastic model building module for stress in NiTi alloy materials during linear elastic deformation and strain Obtain the elastic modulus E and Poisson's ratio of nickel-titanium alloy materials , to obtain the Lame constant, substitute the Lame constant into the fourth-order stiffness tensor , in order to obtain the constitutive equation of nickel-titanium alloy material under linear elastic deformation in three-dimensional space; The induced martensitic transformation module is used to calculate the strain-induced martensitic transformation conditions of nickel-titanium alloy materials according to the Tresca yield criterion form, and obtain the shear stress at the starting point of the induced martensitic transformation. and shear stress that induces martensite finish point , and then get the stress Conditional relationship with temperature T ; A superelastic model building module is used to construct a total strain equation of the nickel-titanium alloy material as a linear superposition of a linear elastic constitutive equation of austenite strain and martensite strain and a phase transformation strain equation according to the strain generated by stress on martensite and austenite in the nickel-titanium alloy material during superelastic deformation. The constitutive model of the nickel-titanium alloy material during superelastic deformation is expressed by the total strain equation as follows: ,in, and denote the flexibility tensor and content of austenite, respectively. and denote the flexibility tensor and content of martensite, respectively. represents phase change strain; The hyperelastic model building module includes phase change strain solving unit, flexibility tensor solving unit and phase change content solving unit, among which: Phase transformation strain solver is used to calculate the stress of nickel-titanium alloy materials Conditional relationship with temperature T The austenite content is obtained and martensite content , specifically including: Building conditional relationships and martensite content The relationship is: , Reconstruction of austenite content and martensite content The relationship is: ; in, , In particular, , The conversion relationship between shear stress and stress is: ; Compliance tensor solver for the amount of deformation and martensite content due to martensitic transformation The phase change strain is obtained , specifically including: constructing the deformation amount and martensite content produced by martensitic transformation The phase change strain The relationship is: ， in, It represents the amount of deformation produced by the martensitic phase transformation, measured by a tensile test; Phase change content solver is used to calculate the fourth-order flexibility tensor The austenite flexibility tensor is obtained and the flexibility tensor of martensite .

7. A computer device, characterized in that: The computer device includes a memory, a processor, and a processing program stored in the memory and executable on the processor. When the processing program is executed by the processor, a constitutive model construction method for predicting nickel-titanium alloy welding deformation is implemented as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a processing program, and when the processing program is executed by a processor, the method for constructing a constitutive model for predicting welding deformation of nickel-titanium alloy as described in any one of claims 1 to 5 is implemented.

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