Rapid prediction method for high-temperature yield strength of orthotropic metal material

Abstract

The invention provides a rapid prediction method for high-temperature yield strength of an orthotropic metal material. The method comprises the following steps: establishing an expression of material distortion energy density based on an equivalent energy method; deducing a specific expression of distortion energy density based on a stress-strain component by considering a uniaxial tensile stress state and orthoanisotropy of the material; calculating to obtain a key constant value under a uniaxial tensile stress state and a material melting temperature; and finally, deriving a high-temperature yield strength expression of the material in different directions. According to the method, a small number of parameters such as the elastic constant and the specific heat capacity which can be quickly obtained through table look-up are used as input, the yield strength values of the orthotropic material at different temperatures can be quickly predicted, and high cost caused by high-temperature tests of a large number of materials can be avoided; and a fast and efficient yield strength prediction mode is provided for material high-temperature performance prediction and structure high-temperature strength check in practical engineering.

Description

Technical Field

[0001] This invention belongs to the field of yield strength prediction technology, specifically relating to a rapid method for predicting the high-temperature yield strength of orthotropic metallic materials for additive manufacturing. Background Technology

[0002] Additive manufacturing is a widely used forming process in engineering. This process enables the flexible and rapid forming of metal structures by laying molten metal wires along a predetermined trajectory. The highly nonlinear changes in the temperature field during additive manufacturing affect the solidification process, leading to the formation of non-equilibrium microstructures and residual stresses. Macroscopically, this manifests as orthotropic anisotropy in the mechanical properties of the material.

[0003] For structures subjected to high-temperature loads, the high-temperature yield strength of additively manufactured metal structures needs to be considered during the design process. However, the experimental measurement of the high-temperature yield strength of orthotropic materials is costly and difficult, and there is an urgent need to propose a rapid prediction method for the high-temperature yield strength of orthotropic materials. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] This invention proposes a rapid prediction method for the high-temperature yield strength of orthotropic metallic materials, in order to solve the technical problems of how to reduce the test measurement cost, reduce the test difficulty, and improve the prediction speed of orthotropic materials at high temperatures.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention proposes a rapid prediction method for the high-temperature yield strength of orthotropic metallic materials. This rapid prediction method specifically includes the following steps:

[0008] S1. Based on the maximum energy density W at the initial yield point of the material. total With distortion energy density W d (T) and thermal energy density W T Based on the relationship between (T), establish the expression for the material distortion energy density:

[0009] W total =W d (T)+KW T (T)

[0010] Among them, W total W is a constant that depends only on the type of material and its microstructure. d(T) represents the strain energy density stored per unit volume of material under stress at temperature T; the constant K is a dimensionless proportionality coefficient related to elastic deformation energy and thermal energy, reflecting the conversion relationship between elastic deformation energy and thermal energy; W T (T) is the thermal energy density of a unit volume of material at temperature T, calculated using the following formula:

[0011]

[0012] Among them, C P (T) represents the specific heat capacity of the material at temperature T and pressure P; ρ is the density of the material, which is a constant at different temperatures T.

[0013] S2. Expressing the stress and strain tensors as the sum of their respective spherical and deviatoric tensors, we obtain the distortion energy density expression based on the stress and strain tensor components.

[0014] σ and ε are the material stress tensor and strain tensor, respectively. σ is expanded to represent the stress sphere tensor σ. v and stress deviator σ d In the form of ε, the expansion is expressed as the strain sphere tensor ε v and strain deviator tensor ε d Substituting the following forms into the material deformation energy W and distortion energy W... d Volumetric strain energy W v Relationship:

[0015]

[0016] The distortion energy density expression based on stress and strain tensor components is obtained:

[0017]

[0018] Where, σ i and ε i These are the diagonal components of the stress tensor and the strain tensor, respectively, i = 1, 2, 3; σ 12 σ 23 σ 31 Let ε be the off-diagonal component of the stress tensor. 12 ε 23 ε 31 For the off-diagonal components of the strain tensor;

[0019] S3. Assuming the material is under uniaxial tensile stress, and combining this with the generalized Hooke's law for orthotropic materials, the expression for the distortion energy density under uniaxial tension is derived.

[0020] Under uniaxial tensile stress, the material stress state is as follows:

[0021] σ1≠0, σ2=σ3=σ 12 =σ 23 =σ 31 =0

[0022] The strain state of the material is:

[0023] ε 12 =ε 23 =ε 31 =0

[0024] Substituting the material's stress-strain state into the distortion energy density expression, we obtain:

[0025]

[0026] Set σ s1 σ s2 Let σ be the yield strength of the material in the principal stress directions 1 and 2. The material is approximately in a linear elastic state before yielding. Then, the yield strength σ under uniaxial tension along direction 1 is... s1 Similarly, satisfying the above distortion energy density expression, the material's elastic constant at temperature T is expressed as the elastic modulus E1(T) in direction 1 and the Poisson's ratio ν, representing the Poisson effect in direction 2 when stretched in direction 1. 12 (T), the yield strength of the material at temperature T is expressed as σ. s1 (T), then the expression for the material distortion energy density under uniaxial tension along direction 1 is:

[0027]

[0028] Under biaxial uniaxial tension, the elastic constants of the material at temperature T are expressed as the elastic modulus E2(T) in the two directions and the Poisson's ratio ν, which represents the Poisson effect in the one direction under biaxial tension. 21 (T), the yield strength of the material at temperature T is expressed as σ. s2 (T), then the expression for the material distortion energy density under uniaxial tension along direction 2 is:

[0029]

[0030] S4. Calculate the constant K under the special condition that the distortion energy density is 0 during material melting.

[0031] At melting temperature T m Material distortion energy density W d (T m Calculate K under the condition that ) = 0:

[0032]

[0033] Under uniaxial tensile stress in one direction, substituting the expression for the distortion energy density and the arbitrary reference temperature T = T0 into the maximum energy density W... total With distortion energy density W d (T) and thermal energy density W T The formula for the relationship between (T):

[0034]

[0035] After simplification, the expression for the constant K is obtained as follows:

[0036]

[0037] S5. Due to the law of conservation of energy, W total If it remains unchanged under any condition, then under uniaxial tension in one direction and at any temperature T, we have:

[0038]

[0039] In the joint step S4, W total The expression:

[0040]

[0041] Substituting K into the result of step S4:

[0042]

[0043] The expression for the high-temperature yield strength of the material in different directions is derived, and the results are correlated with temperature T, elastic modulus E, Poisson's ratio ν, and specific heat capacity C of the material. p Related;

[0044] The expression for the high-temperature yield strength of orthotropic materials in the 1-direction is:

[0045]

[0046] Similarly, under uniaxial tension in two directions and at any temperature T, we have:

[0047]

[0048] In the joint step S4, W total The expression:

[0049]

[0050] Substituting K into the result of step S4, the expression for the high-temperature yield strength in direction 2 is obtained as follows:

[0051]

[0052] S6. Using the high-temperature yield strength expressions of the two orthotropic materials obtained in step S5, and given the elastic model and Poisson's ratio of the material at high temperature, the specific heat capacity of the material is obtained by looking up the table, and the high-temperature yield strength of the orthotropic material in different directions is directly predicted.

[0053] (III) Beneficial Effects

[0054] This invention proposes a rapid method for predicting the high-temperature yield strength of orthotropic metallic materials. Based on the equivalent energy method, an expression for the material's distortion energy density is established. Considering the uniaxial tensile stress state and orthotropic anisotropy, a specific expression for the distortion energy density based on stress-strain components is derived. Key constant values ​​are calculated under uniaxial tensile stress state and the material's melting temperature. Finally, expressions for the high-temperature yield strength of the material in different directions are derived. This method uses only a few parameters, such as elastic constants and specific heat capacity, which can be quickly obtained by looking up tables, as input. It can quickly predict the yield strength values ​​of orthotropic materials at different temperatures, avoiding the high costs associated with numerous high-temperature material tests. This provides a fast and efficient yield strength prediction method for predicting the high-temperature performance of materials and verifying the high-temperature strength of structures in practical engineering. Attached Figure Description

[0055] Figure 1 This is a flowchart of the rapid prediction method for high-temperature yield strength of orthogonal anisotropic metallic materials according to the present invention.

[0056] Figure 2 This is a schematic diagram of the fitted curve of the specific heat capacity of titanium alloy TC4 with respect to temperature.

[0057] Figure 3 This is a schematic diagram of the interpolation curve and error curve between the predicted and experimental values ​​of the high-temperature yield strength of titanium alloy TC4. Detailed Implementation

[0058] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0059] This embodiment proposes a rapid prediction method for the high-temperature yield strength of orthotropic metallic materials. Taking additive manufacturing of titanium alloy TC4 as an example, the main process is as follows: Figure 1 As shown, the specific steps include the following:

[0060] Step 1: Establish the expression for specific heat capacity with respect to temperature, providing model input for the calculation of the specific heat capacity integral in yield strength.

[0061] 1.1) Obtain the specific heat capacity data of the material by consulting relevant documents or handbooks. The melting point T of titanium alloy TC4 was found in Volume IV of the Chinese Aeronautical Materials Handbook. mThe specific heat capacity parameters of the material at 1630-1650℃ and at different temperatures are shown in Table 1. When the temperature exceeds 500℃, the specific heat capacity remains almost unchanged, and the specific heat capacity is about 723 J / (kg·℃).

[0062] Table 1. Specific heat capacity parameters of titanium alloy TC4

[0063]

[0064] 1.2) Establish a fitting function for specific heat capacity with respect to temperature. A second-order polynomial is used for fitting, and the fitted curve is shown below. Figure 2 As shown, the correlation coefficient R 2 =0.996, the fitted function expression is as follows:

[0065] C p (T)=-1.513e -4 T 2 +0.279T+602.607(20℃≤T≤500℃)

[0066] C p (T) = 723 (T ≥ 500℃)

[0067] Step 2: Obtain the high-temperature elastic parameters and room-temperature yield strength values ​​of the material through literature search or material testing. The elastic parameters of additively manufactured titanium alloy TC4 at different temperatures are shown in Table 2.

[0068] Table 2 Elastic parameters of additively manufactured titanium alloy TC4 at different temperatures

[0069]

[0070] Step 3: Substitute the above results into the high-temperature yield strength expression to calculate the material yield strength value at the corresponding temperature and compare it with the experimental results for verification.

[0071] 3.1) Select T0 = 20℃, T m =1630℃. Calculate the integral value of specific heat capacity with respect to temperature at different temperatures. The results are shown in Table 3.

[0072] Table 3. Integral values ​​of specific heat capacity with respect to temperature

[0073]

[0074]

[0075] 3.2) The elastic parameters and specific heat capacity integrals of the material at different temperatures were substituted into the high-temperature yield strength expression of orthogonal anisotropic materials in different directions to predict the yield strength. The results are shown in Table 4 below.

[0076] Table 4. Prediction results of high-temperature yield strength of additively manufactured titanium alloy TC4

[0077]

[0078] 3.3) To verify the accuracy of the prediction results, the predicted values ​​were compared with the high-temperature test results. The interpolation curves of the predicted and test values ​​are shown below. Figure 3 As shown in Table 5, the errors are as follows. From the error results, except for the yield strength prediction error of 5.27% in direction 1 at 600℃, the errors of the other results are all less than 5%, indicating that the prediction results have high accuracy and fully meet the engineering design requirements.

[0079] Table 5 Comparison of Predicted and Tested High-Temperature Yield Strength Results of Additively Manufactured Titanium Alloy TC4

[0080]

[0081] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for rapid prediction of high-temperature yield strength of orthotropic metallic materials, characterized in that, The rapid prediction method for high-temperature yield strength includes the following steps: S1. Based on the relationship between the maximum energy density at the initial yield of the material and the distortion energy density and thermal energy density, establish an expression for the material distortion energy density; S2. Express the stress and strain tensors as the sum of their respective spherical and partial tensors to obtain the distortion energy density expression based on the stress and strain tensor components; S3. Assuming the material is under uniaxial tensile stress, and combining the generalized Hooke's law for orthotropic materials, the expression for the distortion energy density under uniaxial tensile stress is derived. S4. Calculate the constant K under the special condition that the distortion energy density is 0 when the material melts; S5. Based on the constant K, the high-temperature yield strength expression of orthogonal anisotropic materials in two directions is obtained; S6. Using the high-temperature yield strength expressions of the two orthotropic materials obtained in step S5, and given the elastic model and Poisson's ratio of the material at high temperature, the specific heat capacity of the material is obtained by looking up the table, and the high-temperature yield strength of the orthotropic material in different directions is directly predicted.

2. The method for rapid prediction of high-temperature yield strength of orthotropic metallic materials as described in claim 1, characterized in that, In step S1, based on the maximum energy density W at the initial yield of the material... total With distortion energy density W d (T) and thermal energy density W T Based on the relationship between (T), establish the expression for the material distortion energy density: W total =W d (T)+KW T (T) Among them, W total W is a constant that depends only on the type of material and its microstructure. d (T) represents the strain energy density stored per unit volume of material under stress at temperature T; the constant K is a dimensionless proportionality coefficient related to elastic deformation energy and thermal energy, reflecting the conversion relationship between elastic deformation energy and thermal energy; W T (T) is the thermal energy density of a unit volume of material at temperature T, calculated using the following formula: Among them, C P (T) represents the specific heat capacity of the material at temperature T and pressure P; ρ represents the density of the material, which is a constant at different temperatures T.

3. The method for rapid prediction of high-temperature yield strength of orthotropic metallic materials as described in claim 2, characterized in that, In step S2, σ and ε are the material stress tensor and strain tensor, respectively, and σ is expanded to represent the stress sphere tensor σ. v and stress deviator σ d In the form of ε, the expansion is expressed as the strain sphere tensor ε v and strain deviator tensor ε d Substituting the following forms into the material deformation energy W and distortion energy W... d Volumetric strain energy W v Relationship: The distortion energy density expression based on stress and strain tensor components is obtained: Where, σ i and ε i These are the diagonal components of the stress tensor and the strain tensor, respectively, i = 1, 2, 3; σ 12 σ 23 σ 31 For the off-diagonal components of the stress tensor, ε 12 ε 23 ε 31 For the off-diagonal components of the strain tensor.

4. The method for rapid prediction of high-temperature yield strength of orthotropic metallic materials as described in claim 3, characterized in that, In step S3, Under uniaxial tensile stress, the material stress state is as follows: σ1≠0,σ2=σ3=σ 12 =s 23 =s 31 =0 The strain state of the material is: Substituting the material's stress-strain state into the distortion energy density expression, we obtain: Set σ s1 σ s2 Let σ be the yield strength of the material in the principal stress directions 1 and 2. The material is approximately in a linear elastic state before yielding. Then, the yield strength σ under uniaxial tension along direction 1 is... s1 Similarly, satisfying the above distortion energy density expression, the material's elastic constant at temperature T is expressed as the elastic modulus E1(T) in direction 1 and the Poisson's ratio ν, representing the Poisson effect in direction 2 when stretched in direction 1. 12 (T), the yield strength of the material at temperature T is expressed as σ. s1 (T), then the expression for the material distortion energy density under uniaxial tension along direction 1 is: Under biaxial uniaxial tension, the elastic constants of the material at temperature T are expressed as the elastic modulus E2(T) in the two directions and the Poisson's ratio ν, which represents the Poisson effect in the one direction under biaxial tension. 21 (T), the yield strength of the material at temperature T is expressed as σ. s2 (T), then the expression for the material distortion energy density under uniaxial tension along direction 2 is:

5. The method for rapid prediction of high-temperature yield strength of orthotropic metallic materials as described in claim 4, characterized in that, In step S4, At melting temperature T m Material distortion energy density W d (T m Calculate K under the condition that ) = 0: Under uniaxial tensile stress in one direction, substituting the expression for the distortion energy density and the arbitrary reference temperature T = T0 into the maximum energy density W... total With distortion energy density W d (T) and thermal energy density W T The formula for the relationship between (T): After simplification, the expression for the constant K is obtained as follows:

6. The method for rapid prediction of high-temperature yield strength of orthotropic metallic materials as described in claim 5, characterized in that, In step S5, W total If it remains unchanged under any condition, then under uniaxial tension in one direction and at any temperature T, we have: In the joint step S4, W total The expression: Substituting K into the result of step S4: The expression for the high-temperature yield strength of orthotropic materials in the 1-direction is: Similarly, under uniaxial tension in two directions and at any temperature T, we have: In the joint step S4, W total The expression: Substituting K into the result of step S4, the expression for the high-temperature yield strength in direction 2 is obtained as follows:

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