Temperature-dependent constitutive relationship calculation method for additive manufacturing of titanium-aluminum alloys

Abstract

The application discloses a temperature-related additive manufacturing titanium-aluminum alloy constitutive relation calculation method, and creatively proposes a constitutive relation for the material according to the mechanical properties of the additive manufacturing titanium-aluminum alloy, considers temperature correlation, defines a temperature-related constitutive calculation process, and can predict and calculate the temperature-related mechanical properties of the additive manufacturing titanium-aluminum alloy at different temperatures, so that the calculation efficiency is improved, the process is streamlined and efficient, and the accuracy of a heat source model established in the process of laser additive manufacturing is maximized, thereby providing a theoretical basis and data support for material engineering service.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metal material constitutive relation, and particularly relates to a temperature-related constitutive relation calculation method for additive manufacturing titanium-aluminum alloy. BACKGROUND

[0002] Titanium-aluminum alloy has the comprehensive advantages of low density, high temperature resistance, high specific strength, etc., is widely used in the production of turbine blades of aerospace engines, and is the only candidate material for replacing traditional nickel-based high-temperature alloy turbine blades. Additive manufacturing, also known as 3D printing, can directly and conveniently manufacture complex-shaped parts by generating and utilizing digital models, layer-by-layer processing and layer-by-layer accumulation. The biggest feature of additive manufacturing is that it can break through the size limitation of solid objects, shorten the production cycle, improve production efficiency, and make product design more diversified and rich, thereby reducing manufacturing cost, so as to improve the disadvantages of traditional manufacturing of titanium-aluminum alloy complex structure parts. At present, the additive manufacturing technologies for titanium-aluminum alloy mainly include laser metal deposition, electron beam selective melting and selective laser melting.

[0003] Additive manufacturing of titanium-aluminum alloy is mainly applied to blade forming and related repair, and there are few reports on the development of constitutive model for additive manufacturing of titanium-aluminum alloy, especially the research on the influence of temperature on the constitutive relation is even rarer. SUMMARY

[0004] The purpose of the application is to provide a temperature-related constitutive relation calculation method for additive manufacturing of titanium-aluminum alloy, to construct a quasi-static constitutive model related to additive manufacturing of titanium-aluminum alloy and temperature, to realize finite element calculation of additive manufacturing of titanium-aluminum alloy based on a finite element software platform, to improve calculation accuracy and efficiency, and to expand the application conditions of material calculation.

[0005] The technical scheme of the application is as follows: a temperature-related constitutive relation calculation method for additive manufacturing of titanium-aluminum alloy, comprising the following steps:

[0006] S1, based on the stress-strain relation of additive manufacturing of titanium-aluminum alloy, an original constitutive model of additive manufacturing of titanium-aluminum alloy is constructed.

[0007] S2, based on the original constitutive model, quasi-static tensile test of titanium-aluminum alloy is simulated based on a finite element software platform to obtain the mechanical property curves of additive manufacturing of titanium-aluminum alloy related to temperature at different temperatures.

[0008] S3, quasi-static uniaxial tensile test of additive manufacturing of titanium-aluminum alloy is carried out at different temperatures to obtain test data.

[0009] S4, judge whether the fitting degree of the test data and the mechanical property curve is less than a preset threshold value, if yes, go to step S5, otherwise correct the material constants in the original constitutive model and return to step S2.

[0010] S5, solidify the material constants in the original constitutive model to obtain the constitutive model of the additive manufacturing titanium-aluminum alloy.

[0011] Further, the original constitutive model in step S1 is specifically:

[0012] σ = A + β1ε + K[1-exp(-β2ε)]

[0013] Wherein σ represents the true stress of the titanium-aluminum alloy, ε represents the equivalent strain of the titanium-aluminum alloy, A, K, β1, β2 are all temperature-dependent material constants.

[0014] Further, step S2 includes the following steps:

[0015] S21, define the temperature T, Poisson's ratio μ, elastic modulus E and yield stress σ of the titanium-aluminum alloy in the finite element software platform yield , and calculate the shear modulus G:

[0016]

[0017] S22, calculate the Mises equivalent stress σ e of the titanium-aluminum alloy:

[0018]

[0019] Wherein σ x represents the normal stress in the x direction, σ y represents the normal stress in the y direction, σ z represents the normal stress in the z direction, τ xy represents the shear force in the xy direction, τ yz represents the shear force in the yz direction, τ zx represents the shear force in the zx direction.

[0020] S23, judge whether the Mises equivalent stress σ e is greater than the yield stress σ yield , if yes, the titanium-aluminum alloy yields, go to step S25, otherwise the titanium-aluminum alloy does not yield, go to step S24.

[0021] S24, obtain the relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy based on the elastic stiffness matrix, and go to step S26.

[0022] S25, obtain the relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy based on the elastic stiffness matrix and the plastic strain, and go to step S26.

[0023] S26, the real stress σ of the titanium-aluminum alloy and the equivalent strain ε are related to each other, and the mechanical property curve of the titanium-aluminum alloy related to temperature under different temperatures is obtained through checking calculation.

[0024] Further, the step S24 comprises the following sub-steps:

[0025] S241, the elastic stiffness matrix D of the titanium-aluminum alloy is constructed e :

[0026]

[0027] S242, the relationship between the real stress σ of the titanium-aluminum alloy and the equivalent strain ε is obtained according to the elastic stiffness matrix D e :

[0028] dσ=D e dε

[0029] Wherein d represents the derivation operation.

[0030] Further, the step S25 comprises the following sub-steps:

[0031] S251, the tangent modulus H of the titanium-aluminum alloy is calculated:

[0032]

[0033] Wherein represents the equivalent plastic strain increment.

[0034] S252, the average plastic strain of the titanium-aluminum alloy is calculated according to the tangent modulus H :

[0035]

[0036] Wherein represents the average stress, σ x ′ represents the x-direction deviatoric stress, σ y ′ represents the y-direction deviatoric stress, σ z ′ represents the z-direction deviatoric stress.

[0037] S253, the plastic strain ε of the titanium-aluminum alloy is calculated according to the average plastic strain p :

[0038]

[0039] S254, the relationship between the real stress σ of the titanium-aluminum alloy and the equivalent strain ε is obtained according to the plastic strain ε p and the elastic stiffness matrix D e :

[0040] dσ=D e (dε-dε p )

[0041] Further, the material constants A, K, β1, β2 obtained by curing in step S5 are specifically:

[0042]

[0043]

[0044] β1=11230T 2 -1.799×10 7 +6.618×10 8

[0045] β2=15.0

[0046] The constitutive model of the additive manufacturing titanium-aluminum alloy is specifically:

[0047]

[0048] The present application has the beneficial effects that: the present application innovatively proposes the constitutive relationship for the material according to the mechanical properties of the additive manufacturing titanium-aluminum alloy, considers the temperature correlation, defines the temperature-related constitutive calculation process, can predict and calculate the temperature-related mechanical properties of the additive manufacturing titanium-aluminum alloy at different temperatures, not only can improve the calculation efficiency, but also has the advantages of process and high efficiency, and can maximize the accuracy of the heat source model established in the process temperature field numerical simulation of laser additive manufacturing, provides a theoretical basis and data support for material engineering service. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 The temperature-related constitutive relationship calculation method of the additive manufacturing titanium-aluminum alloy provided by the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0050] Exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the present application, and are not intended to limit the scope of the present application.

[0051] The embodiment of the present application provides a temperature-related constitutive relationship calculation method of additive manufacturing titanium-aluminum alloy, as shown in the figure, comprising the following steps S1-S5: Figure 1

[0052] ​S1, based on the stress-strain relationship of the additive manufacturing titanium-aluminum alloy, an original constitutive model of the additive manufacturing titanium-aluminum alloy is constructed. In the embodiment of the application, the original constitutive model is specifically:

[0053] σ=A+β1ε+K[1-exp(-β2ε)]

[0054] Wherein σ represents the true stress of the titanium-aluminum alloy, ε represents the equivalent strain of the titanium-aluminum alloy, A, K, β1, β2 are all temperature-dependent material constants.

[0055] S2, based on the original constitutive model, the quasi-static tensile test of the additive manufacturing titanium-aluminum alloy is simulated based on the finite element software platform, and the temperature-dependent mechanical property curve of the additive manufacturing titanium-aluminum alloy at different temperatures is obtained.

[0056] Step S2 includes the following steps S21-S26:

[0057] S21, the temperature T, Poisson's ratio μ, elastic modulus E and yield stress σ of the titanium-aluminum alloy are defined in the finite element software platform yield , and the shear modulus G is calculated:

[0058]

[0059] S22, the Mises equivalent stress σ e of the titanium-aluminum alloy is calculated:

[0060]

[0061] Wherein σ x represents the normal stress in the x direction, σ y represents the normal stress in the y direction, σ z represents the normal stress in the z direction, τ xy represents the shear force in the xy direction, τ yz represents the shear force in the yz direction, τ zx represents the shear force in the zx direction.

[0062] S23, it is judged whether the Mises equivalent stress σ e is greater than the yield stress σ yield , if yes, the titanium-aluminum alloy yields, and enters step S25, otherwise the titanium-aluminum alloy does not yield, and enters step S24.

[0063] S24, the relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy is obtained based on the elastic stiffness matrix, and step S26 is entered.

[0064] Step S24 includes the following steps S241-S242:

[0065] S241, the elastic stiffness matrix D of the titanium-aluminum alloy is constructede :

[0066]

[0067] S242、According to the elastic stiffness matrix D e The relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy is obtained:

[0068] dσ = D e dε

[0069] Wherein d represents the derivation operation.

[0070] S25, Based on the elastic stiffness matrix and the plastic strain, the relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy is obtained, and step S26 is entered.

[0071] Step S25 includes the following sub-steps S251-S254:

[0072] S251, Calculate the tangent modulus H of the titanium-aluminum alloy:

[0073]

[0074] Wherein represents the equivalent plastic strain increment.

[0075] S252, According to the tangent modulus H, the average plastic strain

[0076]

[0077] Wherein represents the average stress, σ x ' represents the x-direction deviatoric stress, σ y ' represents the y-direction deviatoric stress, σ z ' represents the z-direction deviatoric stress.

[0078] S253, According to the average plastic strain Calculate the plastic strain ε of the titanium-aluminum alloy p :

[0079]

[0080] S254, According to the plastic strain ε p and the elastic stiffness matrix D e The relationship between the true stress σ and the equivalent strain ε of the titanium-aluminum alloy is obtained:

[0081] dσ = D e (dε-dε p )

[0082] S26, according to the true stress σ of the titanium-aluminum alloy and the equivalent strain ε, a check calculation is performed to obtain a mechanical property curve of the additive manufacturing titanium-aluminum alloy related to temperature at different temperatures.

[0083] S3, a quasi-static uniaxial tensile test is performed on the additive manufacturing titanium-aluminum alloy at different temperatures to obtain test data.

[0084] S4, whether the fitting degree of the test data and the mechanical property curve is less than a preset threshold value is judged, if yes, step S5 is entered, otherwise, material constants in the original constitutive model are corrected, and step S2 is returned.

[0085] S5, the material constants in the original constitutive model are solidified to obtain a constitutive model of the additive manufacturing titanium-aluminum alloy.

[0086] In the embodiment of the application, the solidified material constants A, K, β1 and β2 are specifically as follows:

[0087]

[0088]

[0089] β1 = 11230T 2 -1.799 x 10 7 +6.618 x 10 8

[0090] β2 = 15.0

[0091] The constitutive model of the additive manufacturing titanium-aluminum alloy is specifically as follows:

[0092]

[0093] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of helping the reader to understand the principles of the application, and should be understood as not limiting the protection scope of the application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations according to the technical inspirations disclosed in the application, without departing from the essence of the application, and these modifications and combinations are still within the protection scope of the application.

Claims

1. A temperature-dependent additive manufacturing titanium-aluminum alloy constitutive relationship calculation method, characterized in that, The method comprises the following steps: S1, constructing an original constitutive model of the additive manufacturing titanium-aluminum alloy based on a stress-strain relationship of the additive manufacturing titanium-aluminum alloy; S2, simulating a quasi-static tensile test of the titanium-aluminum alloy based on a finite element software platform according to the original constitutive model, and obtaining a mechanical property curve of the additive manufacturing titanium-aluminum alloy related to temperature at different temperatures; S3, performing a quasi-static uniaxial tensile test on the additive manufacturing titanium-aluminum alloy at different temperatures, and obtaining test data; S4, judging whether the fitting degree of the test data and the mechanical property curve is less than a preset threshold value, if yes, entering step S5, otherwise, correcting material constants in the original constitutive model and returning to step S2; S5, solidifying the material constants in the original constitutive model, and obtaining a constitutive model of the additive manufacturing titanium-aluminum alloy; The original constitutive model in the step S1 is specifically: ； wherein denotes the true stress of the titanium-aluminum alloy, denotes the equivalent strain of the titanium-aluminum alloy, are temperature-dependent material constants; The step S2 comprises the following sub-steps: S21, define the temperature T, Poisson's ratio , elastic modulus E and yield stress of the titanium-aluminum alloy in the finite element software platform , and calculate the shear modulus G: ； S22, calculating the Mises equivalent stress of the titanium-aluminum alloy : ； wherein represents the x-direction normal stress, represents the y-direction normal stress, represents the z-direction normal stress, represents the xy-direction shear stress, represents the yz-direction shear stress, represents the zx-direction shear stress; S23, determining whether the Mises equivalent stress is greater than the yield stress If yes, the titanium-aluminum alloy yields and proceeds to step S25. If no, the titanium-aluminum alloy does not yield and proceeds to step S24.​ S24、Based on the elastic stiffness matrix to get the real stress of titanium aluminum alloy The relationship with the equivalent strain Enter step S26; S25, obtaining the real stress of the titanium-aluminum alloy based on the elastic stiffness matrix and the plastic strain and the relationship between the equivalent strain and the relationship between the equivalent strain and the relationship between the equivalent strain and the relationship between the equivalent strain and the relationship between the equivalent strain and the relationship between the equivalent strain and the relationship between the S26、According to the true stress of the titanium-aluminum alloy and the equivalent strain , the check calculation is performed to obtain the temperature-related mechanical property curve of the additive manufacturing titanium-aluminum alloy at different temperatures. The step S24 comprises the following sub-steps: S241. Constructing a stiffness matrix for a titanium-aluminum alloy : ； S242、According to the elastic stiffness matrix Real stress of the titanium-aluminum alloy is obtained Relationship with equivalent strain : ； wherein denotes a derivation operation; The step S25 comprises the following sub-steps: S251, calculating a tangent modulus H of the titanium-aluminum alloy: ； wherein represents the equivalent plastic strain increment; S252. Calculate the average plastic strain of the titanium-aluminum alloy from the tangent modulus H : ； wherein represents the average stress, represents the x-direction deviatoric stress, represents the y-direction deviatoric stress, represents the z-direction deviatoric stress; S253, according to the average plastic strain Calculating plastic strain of titanium-aluminum alloys : ； S254, the true stress of the titanium-aluminum alloy is obtained and the elastic stiffness matrix S254, the true stress of the titanium-aluminum alloy is obtained in relation to the equivalent strain S254, the true stress of the titanium-aluminum alloy is obtained 。 2. The method of calculating a constitutive relationship for additive manufactured titanium aluminide alloys of claim 1, wherein, The material constant obtained by the step S5 of solidification Specifically: ； ； ； ； The constitutive model of the additive manufacturing titanium-aluminum alloy is specifically: 。

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