A method for predicting cyclic creep deformation behavior based on unified viscoplasticity theory

Abstract

The application discloses a kind of based on the prediction method of cyclic creep deformation behavior of unified viscoplastic theory, specific implementation is at the same test temperature, carry out cyclic creep test under different conditions, obtain corresponding data;Unified viscoplastic constitutive model is established, including the establishment of main control equation, flow rule, movement hardening criterion, isotropic hardening criterion;A group of strain control creep-fatigue tests at the above temperature is carried out, and corresponding data is obtained, including each cycle hysteresis loop, each cycle peak stress, strain amplitude;The initial material parameters of the constitutive model are determined using the creep-fatigue test data, and the optimal material parameters are obtained by fitting a group of cyclic creep deformation curves through trial parameter method;The final constitutive model is determined using the obtained optimal material parameters, and the deformation behavior of the material under cyclic creep load is predicted by the constitutive model.The application has the advantages of strong applicability and high precision, and can predict the deformation behavior of the material under cyclic creep.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of constitutive model and cyclic deformation prediction, and particularly relates to a cyclic creep deformation behavior prediction method based on a unified viscoplasticity theory. BACKGROUND

[0002] Clean energy replacement action is an important measure to achieve the goal of "carbon neutralization", and high-temperature clean energy equipment such as nuclear energy and solar energy often bears a peak load with characteristics of low frequency and long holding time, which is called cyclic creep. The fatigue damage effect under cyclic creep is small, but the material hysteresis elastic deformation recovery phenomenon caused by this cyclic load leads to the increase of the creep rate and the decrease of the creep ductility of the structure in the subsequent cycle, which affects the service life of the high-temperature component. In order to accurately design the service life of the high-temperature component under cyclic creep load, it is necessary to develop a reasonable constitutive model to accurately simulate the deformation behavior of the high-temperature component under cyclic creep load. The widely used viscoplastic constitutive model has not yet been able to predict this deformation recovery behavior and its influence on the material creep behavior. SUMMARY

[0003] In view of the above problems of the prior art, the purpose of the present application is to provide a cyclic creep deformation behavior prediction method based on a unified viscoplasticity theory, which can realize the deformation behavior prediction of the material under cyclic creep load, and has the advantages of strong applicability, high precision and the like.

[0004] A cyclic creep deformation behavior prediction method based on a unified viscoplasticity theory, comprising the following steps:

[0005] S1: Under the same test temperature, cyclic creep tests under different conditions are carried out, the conditions including peak stress, valley stress, peak holding time, valley holding time, and corresponding data are obtained;

[0006] S2: A unified viscoplastic constitutive model is established, including the establishment of a master equation, a flow rule, a kinematic hardening criterion and an isotropic hardening criterion;

[0007] S3: A set of strain-controlled creep-fatigue tests are carried out at the temperature in step S1, and corresponding data are obtained, including each cycle hysteresis loop, each cycle peak stress and strain amplitude;

[0008] S4: The initial material parameters of the constitutive model in step S2 are determined by using the data in step S3, and the optimal material parameters are obtained by fitting a set of cyclic creep deformation curves in step S1 through trial parameter method;

[0009] S5: The final constitutive model is determined by using the optimal material parameters obtained in step S4, and the deformation behavior of the material under cyclic creep load is predicted by the constitutive model.

[0010] Further, step S2 specifically comprises the following steps:

[0011] S21: The unified viscoplastic theory decomposes the total strain rate into elastic strain rate and inelastic strain rate, and the master equation is shown in equation (1):

[0012]

[0013] In the equation, represents the total strain rate, represents the elastic strain rate, represents the inelastic strain rate, wherein According to Hooke's law, it is calculated from equation (2):

[0014]

[0015] In the equation, represents the stress rate, and E is the elastic modulus;

[0016] S22: Select the flow rule to establish the relationship between the inelastic strain rate and the stress, as shown in equation (3):

[0017]

[0018] In the equation, σ represents the applied stress, χ represents the back stress, R represents the drag stress, sign() is the sign function, A1, A2, n1, n2 are temperature-dependent material constants;

[0019] S23: According to the kinetic hardening criterion, the back stress χ in step S22 is decomposed into n nonlinear back stress components, as shown in equation (4):

[0020]

[0021] In the equation, χ i is the i-th back stress component, and the evolution rate equation of each back stress component is shown in equation (5):

[0022] In the equation, represents the i-th back stress component rate, represents the cumulative inelastic strain rate, C i represents the plastic modulus, γ i represents the dynamic recovery coefficient, q i is the static recovery coefficient, r i is the static recovery exponent, and the dynamic recovery coefficient is defined as a function related to the cumulative inelastic strain for better description of the cyclic creep deformation behavior, as shown in equation (6):

[0023] γ i = γ i,inf + ( γ i,ini - γ i,inf ) exp(- ω i | p | ) (6) i,inf , γ i,ini , ω i are temperature dependent material constants;

[0024] S24: According to the isotropic hardening criterion, the drag stress rate equation in S22 is shown in equation (7):

[0025]

[0026] where R is the drag stress rate, Q is the asymptotic value of the drag stress, b is the asymptotic rate, H is the linear term drag stress rate change, and the asymptotic rate b is related to the stress ratio in cyclic creep, as shown in equation (8):

[0027]

[0028] where σ p represents the peak stress in cyclic creep, σ v represents the valley stress in cyclic creep, b ini , b inf , b w are temperature dependent material constants.

[0029] Further, step S4 specifically includes the following steps:

[0030] S41: According to the initial uniaxial tensile data of the initial cyclic hysteresis loop in step S3, the elastic modulus E and the yield strength k of the material are fitted;

[0031] S42: Integrate equation (7) with respect to time to obtain equation (8):

[0032] R = Q (1 - e bp ) + H p + h (8) R is the difference between the peak stress of each cycle and the initial cyclic peak stress in step S3, and p is shown in equation (9):

[0033] where N is the number of cycles in the creep-fatigue test in step S3, ε is the strain amplitude in step S3, σ max is the peak stress in step S3, and Q, b, H are fitted according to the data of R and p.

[0034] ​S43: without considering the third term on the right side of formula (5), formula (5) is integrated with respect to time to obtain formula (10):

[0035]

[0036] In the formula, epsilon in is a non-elastic strain, and according to the Von-mises yield criterion, has:

[0037]

[0038] In the region controlled by the nth back stress, the influence of the first n-1 back stresses can be ignored, so:

[0039]

[0040] Formula (12) is differentiated with respect to epsilon in to obtain:

[0041]

[0042] In the double logarithmic coordinates, the parameter C n , gamma n can be obtained by fitting In the region controlled by the n-1th back stress, the influence of the first n-2 back stresses can be ignored, so:

[0043]

[0044] The parameters C n-1 , gamma n-1 are obtained, and in this way, the parameters C n-1 ,..., C1, gamma n-1 ,..., gamma1 can be obtained.

[0045] Further, in step S2, the creep acceleration phenomenon of cyclic creep and the stress range correlation are considered, and the kinematic hardening criterion and the isotropic hardening criterion are modified.

[0046] The present application has the beneficial effects that:

[0047] 1) The present application is based on the unified visco-plastic theory, and by modifying the kinematic hardening criterion and the isotropic hardening criterion, the creep acceleration phenomenon of cyclic creep and the stress range correlation can be accurately described, and the cyclic creep deformation prediction ability is high.

[0048] 2) A set of parameters of the present application can predict the cyclic creep behavior under different stress ratios and different holding times at the same temperature, and the application range is wide. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method for predicting cyclic creep deformation behavior according to the present invention;

[0050] Figure 2 This is a graph showing the fitting results of obtaining the parameters of the master control equation according to an embodiment of the present invention;

[0051] Figure 3 This is a graph showing the fitting results of obtaining the isotropic hardening criterion parameters according to an embodiment of the present invention;

[0052] Figure 4 This is a fitting result diagram of the motion hardening criterion parameters obtained by an embodiment of the present invention. 4a is the result of obtaining the second motion hardening parameter, and 4b is the result of obtaining the first motion hardening parameter.

[0053] Figure 5 This is the prediction result of cyclic creep deformation behavior in an embodiment of the present invention. Detailed Implementation

[0054] The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the following embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0055] Combination Figure 1 The present invention provides a method for predicting cyclic creep deformation behavior based on a unified viscoplasticity theory, comprising the following steps:

[0056] S1: Under the same test temperature, conduct cyclic creep tests under different conditions, including peak stress, valley stress, peak holding time, and valley holding time, and obtain the corresponding data. In this embodiment, AlCoCrFeNi... 2.1 High entropy alloy (EHEA) was subjected to four sets of cyclic creep tests at 800℃. The peak stress was 50MPa, and the valley stresses were 0MPa, 10MPa, 15MPa and 20MPa, respectively. The peak stress holding time was 20h and the valley stress holding time was 5h.

[0057] S2: Establish a unified viscoplastic constitutive model, including the establishment of the master equations, flow rules, kinematic hardening criteria, and isotropic hardening criteria.

[0058] S21: The unified viscoplastic theory decomposes the total strain rate into elastic strain rate and inelastic strain rate, and the master equation is shown in equation (1):

[0059]

[0060] In the formula, Indicates the total strain rate. represents the elastic strain rate, represents the inelastic strain rate, where According to Hooke's law, it can be calculated from equation (2):

[0061]

[0062] where, represents the stress rate, E is the elastic modulus,

[0063] S22: Select the flow rule to establish the relationship between the inelastic strain rate and the stress, as shown in equation (3):

[0064]

[0065] where, σ represents the applied stress, χ represents the back stress, R represents the drag stress, sign() is the sign function, A1, a2, n1, n2 are temperature-dependent material constants.

[0066] S23: According to the kinematic hardening criterion, the back stress χ in S22 is decomposed into n nonlinear back stress components, as shown in equation (4):

[0067]

[0068] where, χ i is the i-th back stress component. The evolution rate equation of each back stress component is shown in equation (5):

[0069]

[0070] where, represents the rate of the i-th back stress component, represents the cumulative inelastic strain rate, C i represents the plastic modulus, γ i represents the dynamic recovery coefficient, q i is the static recovery coefficient, r i is the static recovery exponent. In order to better describe the cyclic creep deformation behavior, the dynamic recovery coefficient is defined as a function related to the cumulative inelastic strain, as shown in equation (6):

[0071] γ i = γ i,inf + (γ i,ini - γ i,inf ) exp (-ω i |p|) (6)

[0072] where, p represents the cumulative inelastic strain, γ i,inf , γ i,ini , ω imaterial constants related to temperature, and the fitting results of the parameters of the kinematic hardening criterion.

[0073] S24: According to the isotropic hardening criterion, the drag stress rate equation in S22 is shown in equation (7):

[0074]

[0075] wherein, is the drag stress rate, Q is the asymptotic value of the drag stress, b is the asymptotic rate, and H is the linear term drag stress rate. In cyclic creep, the asymptotic rate b is related to the stress ratio, as shown in equation (8):

[0076]

[0077] wherein, σ p represents the peak stress in cyclic creep, σ v represents the valley stress in cyclic creep, b ini , b inf , b w are material constants related to temperature;

[0078] S3: A set of strain-controlled creep-fatigue tests are performed at the temperature described in S1, which is 800°C in the example, and the corresponding data are obtained, including each cycle hysteresis loop, each cycle peak stress, strain amplitude, and in the example, the strain amplitude is 0.4% and the holding time is 60s for the eutectic high-entropy alloy (EHEA) AlCoCrFeNi 2.1

[0079] S4: The initial material parameters of the constitutive model in S2 are determined using the data in S3, and the optimal material parameters are obtained by fitting a set of cyclic creep deformation curves in S1 through trial and error. In the example, the test with a valley stress of 0 MPa is selected as the calibration set to optimize the parameters.

[0080] S41: According to the initial uniaxial tensile data of the initial cyclic hysteresis loop described in S3, the elastic modulus E and the yield strength k of the material are fitted. As shown in equation (10), E is the slope of the linear segment, and k is the stress value corresponding to the beginning of the deviation from the linear stage. In the example, E = 50440 MPa and k = 191 MPa are obtained. Figure 2

[0081] S42: Equation (7) is integrated with respect to time to obtain equation (8):

[0082] R = Q (1 - e bp ) + Hp + h (8) R is the difference between each cycle peak stress and the initial cycle peak stress described in S3, and p is shown in equation (9): ​​

[0083] In the formula, N is the number of creep-fatigue test cycles described in S3, ε is the strain amplitude described in S3, and σ max This refers to the peak stress described in S3. Based on the data for R and p, Q, b, and G are fitted to obtain the values. Figure 3 As shown, through nonlinear fitting, in this embodiment, AlCoCrFeNi 2.1 EHEA is a cyclically softening material with Q = -19 MPa < 0, b = 9.5, and H = -49.

[0084] S43: Ignoring the third term on the right-hand side of equation (5), integrating equation (5) over time yields equation (10):

[0085]

[0086] According to the Von-Mises yield criterion, we have:

[0087] σ=χ+R+k+σ v (11) In the formula, σ v Let be viscous stress. In the region controlled by the nth back stress, the influence of the first n-1 back stresses is negligible, therefore:

[0088]

[0089] Apply equation (12) to ε in Differentiation yields:

[0090]

[0091] Fitting in log-log coordinates The parameter C can be obtained from the curve. n γ n In the region controlled by the (n-1)th back stress, the influence of the first (n-2)th back stress can be ignored, therefore:

[0092]

[0093] C can be obtained n-1 γ n-1 By analogy, C can be obtained. n-1 ,…,C1、γ n-1 ,…,γ1. For example Figure 4 As shown, fitting in double logarithmic coordinates The slope is γ n The intercept is In this embodiment, two back stresses are adopted, i.e. n = 2, C1 = 81240, C2 = 8413, γ1 = 8495, γ2 = 953 can be obtained. In order to describe the cyclic creep deformation characteristics, different static recovery parameters are adopted in the two back stresses. In the first back stress, the static recovery index r1 = 4.9 > 1, and the static recovery coefficient is taken as q1 = 10 -6 In the second back stress, the static recovery index r2 = 1, and the static recovery coefficient is taken as q2 = 0.03.

[0094] S44: A set of cyclic creep test data is selected as a calibration set to obtain optimal material parameters. Three sets of cyclic creep test data with different stress ratios are selected to obtain the relationship between the drag stress progressive rate b and the stress ratio. In the embodiment, the test with the valley stress of 0 MPa is selected as the calibration set to optimize the parameters, and the cyclic creep tests with the valley stress of 0 MPa, 10 MPa and 15 MPa are selected to calibrate the model parameters of the drag stress progressive rate b, and b ini = 8.17, b inf = 1.33, and b w = 15.74.

[0095] S5: The optimal material parameters obtained in S4 are used to determine the final constitutive model, and the deformation behavior of the material under the cyclic creep load is predicted by the constitutive model.

[0096] It can be seen from the results of Figure 5 that the cyclic creep deformation of the material can be well predicted by using the present application, and the present application has the outstanding advantages of few model parameters, simple operation and wide applicability.

Claims

1. A method for predicting cyclic creep deformation behavior based on a unified viscoplastic theory, characterized by Comprising the following steps: S1: performing cyclic creep tests under different conditions including peak stress, valley stress, peak holding time, valley holding time at the same test temperature, obtaining corresponding data; S2: establishing a unified visco-plastic constitutive model, including the establishment of master equation, flow rule, kinematic hardening criterion, isotropic hardening criterion; S3: performing a set of strain-controlled creep-fatigue tests at the temperature described in step S1, obtaining corresponding data, including each cycle hysteresis loop, each cycle peak stress, strain amplitude; S4: using the data in step S3, determining the initial material parameters of the constitutive model in step S2, and fitting the set of cyclic creep deformation curves in step S1 by trial method to obtain the optimal material parameters; S5: using the optimal material parameters obtained in step S4 to determine the final constitutive model, and predicting the deformation behavior of the material under cyclic creep load by the constitutive model; Step S2 specifically comprises the following steps: S21: the unified visco-plastic theory decomposes the total strain rate into elastic strain rate and inelastic strain rate, and the master equation is as shown in formula (1): （1）， wherein denotes the total strain rate, denotes the elastic strain rate, denotes the inelastic strain rate, wherein According to Hooke's law, calculated from equation (2): （2）， In the formula, represents the stress change rate, is the elastic modulus; S22: selecting flow rule, establishing the relationship between inelastic strain rate and stress, as shown in formula (3): （3）， wherein denotes the applied stress, denotes the back stress, denotes the drag stress, is a sign function, is a material constant depending on the temperature; S23: The back stress in step S22 is decomposed into individual non-linear back stress components according to the kinematic hardening criterion as shown in equation (4): S23: The back stress in step S22 is decomposed into individual non-linear back stress components according to the kinematic hardening criterion as shown in equation (4):​ （4）， wherein is the first back stress component, and each back stress component evolution rate equation is given by equation (5): （5）， wherein represents the first represents the cumulative inelastic strain rate, , represents the plastic modulus, represents the dynamic recovery coefficient, is the static recovery coefficient, is the static recovery exponent, for a better description of the cyclic creep deformation behavior, the dynamic recovery coefficient is defined as a function of the cumulative inelastic strain, as shown in equation (6):​ （6）， wherein represents the cumulative inelastic strain, is a temperature-dependent material constant; S24: according to the isotropic hardening criterion, the drag stress rate equation in S22 is as shown in formula (7): （7）， wherein is the rate of change of the drag stress, is the asymptotic value of the drag stress, is the asymptotic rate, is the rate of change of the linear term drag stress, in cyclic creep, the asymptotic rate is related to the stress ratio as shown in equation (8): （8）， wherein denotes the peak stress in the cyclic creep, denotes the valley stress in the cyclic creep, is a temperature-dependent material constant.

2. A method of predicting cyclic creep deformation behavior based on a unified viscoplastic theory according to claim 1, characterized in that Step S4 specifically comprises the following steps: S41: From the initial uniaxial tensile data of the hysteresis loop in step S3, the elastic modulus of the material is fitted and the yield strength ; S42: integrating formula (7) with respect to time to obtain formula (9): （9）， the difference between each cycle peak stress and the initial cycle peak stress in S3, as shown in equation (10): （10）， wherein is the number of cycles to failure in the creep-fatigue test described in S3, is the strain amplitude described in S3, is the peak stress described in S3, according to the and Data were fitted to obtain , S43: without considering the third term on the right side of formula (5), integrating formula (5) with respect to time to obtain formula (11): （11）， wherein is the non-elastic strain, according to the Von-mises yield criterion, has: （12）， In the first The influence of the back stress in the region of the second The influence of the back stress in the region of the second （13）， Substituting equation (13) into equation (12) gives Differentiating, we obtain: （14）， The parameters can be obtained by fitting the curves in a double logarithmic coordinate The parameters can be obtained by fitting the curves in a double logarithmic coordinate In the first In the region of the first back stress control, the influence of the second back stress can be neglected, and there is In the region of the first back stress control, the influence of the second back stress can be neglected, and there is （15）， are obtained and so on, and , S44: Select a set of cyclic creep test data as calibration set to obtain the optimal material parameters, and select three sets of cyclic creep test data with different stress ratios to obtain the drag stress progressive rate Relationship with stress ratio.

3. A method of predicting cyclic creep deformation behavior based on a unified viscoplastic theory according to claim 2, characterized in that In step S2, considering the creep acceleration phenomenon of cyclic creep and the stress range correlation, the kinematic hardening criterion and the isotropic hardening criterion are modified.

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