METHOD AND SYSTEM FOR EVALUATING THE PERFORMANCE OF METALLIC MATERIALS BASED ON CREEP-FATIGUE INTERACTION

Abstract

A method and system for evaluating the performance of metallic materials based on creep-fatigue interaction, comprising: based on elastic-plastic property data and creep property data of metallic materials, calculating the monotonic crack tip opening displacement and cyclic crack tip opening displacement caused by plasticity or creep of short cracks under maximum far-field stress and far-field cyclic stress, respectively; using the linear superposition method to obtain the total monotonic crack tip opening displacement and cyclic crack tip opening displacement of short cracks under the combined creep-fatigue action; by calculating the short crack growth rate of the metallic material under creep-fatigue interaction, the performance of the metallic material is evaluated. The invention solves the problems of traditional methods, such as relying on a large amount of crack growth experimental data and insufficient consideration of creep-fatigue short crack effects.

Claims

1. (canceled)

2. (canceled)

3. (canceled)

4. A computer-implemented method for evaluating performance of metallic materials under creep-fatigue interaction, the method executed by a processor and comprising: (a) obtaining elastic-plastic property data from a uniaxial tensile test of a metallic material specimen, including yield strength (.sub.y), elastic modulus (E), Poisson's ratio (v); (b) obtaining creep property data from a uniaxial creep test of the specimen, including a creep stress index (m); (c) calculating, based on the elastic-plastic property data and evolution laws of a plastic zone at a crack tip: (i) a first monotonic crack tip opening displacement $\left({}_t^c\right)$ caused by plasticity under maximum far-field stress (.sub.peak) acting on short cracks of length (c), using: ${}_r^p=\frac{8c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y}\right)\right]}{E}$ (ii) a first cyclic crack tip opening displacement $\left({}_r^p\right)$ caused by plasticity under far-field cyclic stress, using: ${}_r^p=\frac{16c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}\left(1-R\right)}{4{}_y}\right)\right]}{E}$ where R is a load ratio; (d) calculating, based on the creep property data, evolution laws of a creep zone at the crack tip, and a dislocation model: (i) a co-planar creep zone size (.sup.cr(t)) related to creep time (t), specimen thickness (W), and correction parameters (r.sub.m, .sub.cr) tied to the creep stress index (m), using: ${}^{\mathrm{cr}}\left(t\right)=\frac{1}{2}{\left(\frac{K_I}{E}\right)}^2{{}_{\mathrm{cr}}\left[\frac{{{\mathrm{WtE}}^m\left(m+1\right)}^2}{2{\mathrm{mr}}_m^{m+1}}\right]}^{\frac{2}{m-1}}$ wherein K.sub.I is a Mode I stress intensity factor; (ii) an equivalent creep yield strength $\left({}_y^{\mathrm{cr}}\right),$ using: ${}_y^{\mathrm{cr}}=\frac{{}_{\mathrm{peak}}}{2\arccos \left(\frac{c}{{}^{\mathrm{cr}}\left(t\right)+c}\right)}$ (iii) a second monotonic crack tip opening displacement $\left({}_t^c\right)$ caused by creep under .sub.peak, using: ${}_t^c=\frac{8c\left(1-v^2\right){}_y^{\mathrm{cr}}\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y^{\mathrm{cr}}}\right)\right]}{E}$ (iv) a second cyclic crack tip opening displacement $\left({}_r^c\right)$ caused by creep under far-field cyclic stress, using: ${}_r^c=\frac{16c\left(1-v^2\right){}_y^{\mathrm{cr}}\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}\left(1-R\right)}{4{}_y^{\mathrm{cr}}}\right)\right]}{E}$ (e) applying linear superposition to calculate a total monotonic crack tip opening displacement (.sub.t) and cyclic crack tip opening displacement (.sub.r) under combined creep-fatigue action: $\{\begin{array}{c}{}_t={}_t^p+{}_t^c\\ {}_r={}_r^p+{}_r^c\end{array}$ (f) calculating a short crack growth rate ((dc).sub.cycle) to evaluate material performance, using: ${\left(\mathrm{dc}\right)}_{\mathrm{cycle}}=\left({}_t{}_r\right).$ where and are model fitting parameters derived from physical test data; (g) outputting the short crack growth rate to a display or storage medium for structural integrity assessment of energy equipment components operating at 500-700 C.

5. The method of claim 4, wherein obtaining the correction parameter (r.sub.m) comprises: retrieving a material parameter (.sub.m) associated with the creep stress index (m); calculating r.sub.m using: $r_m={\left(\frac{}{{}_m}\frac{m+1}{m}\right)}^{\frac{1}{m+1}}$ wherein .sub.m is determined via interpolation from empirical data mapping m to .sub.m.

6. The method of claim 4, wherein the correction parameters (r.sub.m, .sub.cr) are obtained by interpolating values from predefined tables based on the creep stress index (m): r.sub.m values: $\begin{array}{c}m=3.fwdarw.r_m=3.86\\ m=5.fwdarw.r_m=3.41\\ m=9.fwdarw.r_m=3.03\\ m=13.fwdarw.r_m=2.87\end{array}$ .sub.cr values: $\begin{array}{c}m=3.fwdarw.{}_{\mathrm{cr}}=0.25\\ m=5.fwdarw.{}_{\mathrm{cr}}=0.32\\ m=13.fwdarw.{}_{\mathrm{cr}}=0.38.\end{array}$

Description

4. BRIEF DESCRIPTION OF ACCOMPANYING DRAWINGS

[0026] In order to explain the technical schemes in the embodiments of the invention or prior art more clearly, the accompanying drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings in the following description are only are some embodiments of the invention. For those of ordinary skill in the art, other accompanying drawings can be obtained based on these accompanying drawings without exerting creative efforts.

[0027] FIG. 1 is a flowchart of the method of the invention;

[0028] FIG. 2 is a schematic diagram of the parameter fitting of uniaxial creep test data in the invention.

[0029] FIG. 3 is a schematic diagram of the parameter fitting of uniaxial tensile test data in the invention.

[0030] FIG. 4 is a graph of the creep-fatigue short crack growth rate calculation results in the invention.

[0031] FIG. 5 is a graph of the creep-fatigue short crack growth rate calculation results based on test data by using the traditional method in the invention.

5. SPECIFIC EMBODIMENT OF THE INVENTION

[0032] In order to make the objects, technical schemes and advantages of the embodiments of the invention clearer, the technical schemes in the embodiments of the invention will be clearly and completely described below in combination with the accompanying drawings in the embodiments of the invention, obviously, the described embodiments are some, but not all embodiments of the invention. The components of the embodiments of the invention generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the invention to be protected, but merely represents selected embodiments of the invention. Based on the embodiments of the invention, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the invention.

[0033] As shown in FIG. 1 to FIG. 5, In order to address the above problem, the invention provides a method and system for evaluating the performance of metallic materials based on creep-fatigue interaction; by calculating the short cracks of metallic materials under creep-fatigue interaction, the creep-fatigue performance of metallic materials is evaluated in a simple and efficient manner, including the following step: constructing a short crack growth rate calculation model under creep-fatigue interaction. The prediction model utilizes creep performance data based on uniaxial creep tests and elastic-plastic property data based on uniaxial tensile tests to calculate the creep-fatigue short crack growth rate of the material; by using elastic-plastic property data from uniaxial tensile tests, combined with the evolution law of the plastic zone at crack tip, and applying the dislocation model, the first monotonic crack tip opening displacement

[00001]${}^p\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by plasticity under maximum far-field stress acting on short cracks and the first cyclic crack tip opening displacement

[00002]${}^p\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by plasticity under far-field cyclic stress are obtained; by utilizing creep performance data based on uniaxial creep tests and combined with the evolution law of the creep zone at crack tip, and applying the dislocation model, the second monotonic crack tip opening displacement

[00003]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by creep under maximum far-field stress acting on short cracks and the second cyclic crack tip opening displacement

[00004]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by creep under far-field cyclic stress are obtained; based on the monotonic/cyclic crack tip opening displacement caused by creep/fatigue, the total monotonic crack tip opening displacement .sub.t and cyclic crack tip opening displacement .sub.r of short cracks under the combined creep-fatigue action are calculated; based on the obtained .sub.t and .sub.r, the creep-fatigue short crack growth rate of the material is calculated by using the crack growth rate model under the creep-fatigue interaction. The invention solves the problems of traditional methods, such as relying on a large amount of crack growth experimental data and insufficient consideration of creep-fatigue short crack effects.

[0034] The invention provides a method for calculating short cracks in metallic materials under creep-fatigue interaction, comprising the following steps: [0035] step 1: constructing a short crack growth rate calculation model under the creep-fatigue interaction. This prediction model uses creep property data from uniaxial creep tests and elastic-plastic property data from uniaxial tensile tests to calculate the creep-fatigue short crack growth rate of the material; [0036] step 2: by utilizing the elastic-plastic property data based on uniaxial tensile tests and combined with evolution law of the plastic zone at crack tip, and applying the dislocation model, the first monotonic crack tip opening displacement

[00005]${}^p\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by plasticity under maximum far-field stress acting on short cracks and the first cyclic crack tip opening displacement

[00006]${}^p\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by plasticity under far-field cyclic stress are obtained; [0037] step 3: by utilizing creep performance data based on uniaxial creep tests and combined with the evolution law of the creep zone at crack tip, and applying the dislocation model, the second monotonic crack tip opening displacement

[00007]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by creep under maximum far-field stress acting on short cracks and the second cyclic crack tip opening displacement

[00008]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by creep under far-field cyclic stress are obtained; [0038] step 4: based on the monotonic/cyclic crack tip opening displacement caused by creep/fatigue, the total monotonic crack tip opening displacement .sub.t and cyclic crack tip opening displacement .sub.r of short cracks under the combined creep-fatigue action are calculated; [0039] step 5: based on the obtained .sub.t and .sub.r, the creep-fatigue short crack growth rate of the material is calculated by using the crack growth rate model under the creep-fatigue interaction.

[0040] When constructing the short crack growth rate calculation model under the creep-fatigue interaction in step 1, the crack growth rate is expressed as the crack growth per cycle: (dc).sub.cycle.

[0041] The formula used in constructing the short crack growth rate calculation model under the creep-fatigue interaction in step 1:

[00009]${\left(dc\right)}_{\mathrm{cycle}}=B\left({}_t{}_r\right)a;$

wherein and are fitting parameters of the model.

[0042] In the process of obtaining the first monotonic crack tip opening displacement

[00010]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

caused by plasticity under maximum far-field stress acting on short cracks in step 2, its expression is as follows:

[00011]$\text{?}=\frac{8c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y}\right)\right]}{E};$$\text{?}\text{indicates text missing or illegible when filed}$

wherein .sub.y is the yield strength of the material, E is the elastic modulus of the material, v is the Poisso's ratio of the material, .sub.peak is the maximum far-field stress, and c is the short crack length.

[0043] In the process of obtaining the first cyclic crack tip opening displacement

[00012]${}_r^p$

caused by plasticity under far-field cyclic stress in step 2, its expression is as follows:

[00013]$\text{?}=\frac{16c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}\left(1-R\right)}{4{}_y}\right)\right]}{E};$$\text{?}\text{indicates text missing or illegible when filed}$

wherein R is the load ratio.

[0044] In the process of obtaining the second monotonic crack tip opening displacement

[00014]${}_t^c$

caused by creep under maximum far-field stress acting on short cracks in step 3, its expression is as follows:

[00015]$\text{?}\frac{8c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y^{\mathrm{cr}}}\right)\right]}{E};$$\text{?}\text{indicates text missing or illegible when filed}$

[0045] Preferably, when obtaining the material' s equivalent creep yield strength, its expression is as follows:

[00016]${}_y^{\mathrm{cr}}=\frac{{}_{\mathrm{peak}}}{2\arccos \left(\frac{c}{{}^{\mathrm{cr}}\left(t\right)+c}\right)};$

wherein .sup.cr(t) is the co-planar creep zone size related to the creep time.

[0046] In the process of obtaining the co-planar creep zone size related to the creep time .sup.cr(t), its expression is as follows:

[00017]${}^{\mathrm{cr}}\left(t\right)=\frac{1}{2}{\left(\frac{K_I}{E}\right)}^2{{}_{\mathrm{cr}}\left[\frac{{{\mathrm{WtE}}^m\left(m+1\right)}^2}{2{\mathrm{mr}}_m^{m+1}}\right]}^{\frac{2}{m-1}};$

wherein K.sub.1 is the stress intensity factor for Mode I cracks, m is the creep stress index of the material, W is the specimen thickness, t is the creep time, and r.sub.m and .sub.cr are correction parameters related to the creep stress index m.

[0047] When obtaining the correction parameter r.sub.m related to the creep stress index m, its expression is as follows:

[00018]$r_m={\left(\frac{}{{}_m}\frac{m+1}{m}\right)}^{\frac{1}{m+1}};$

wherein .sub.m is the material parameter related to the creep stress index m.

[0048] When obtaining the correction parameter r.sub.m related to the creep stress index m, its value is determined by using an interpolation method based on Table 1.

TABLE-US-00001 TABLE 1 m 3 5 9 13 r.sub.m 3.86 3.41 3.03 2.87

[0049] When obtaining the correction parameter .sub.cr related to the creep stress index m, its value is determined by using the interpolation method based on Table 2.

TABLE-US-00002 TABLE 2 m 3 5 13 .sub.cr 0.25 0.32 0.38
using the linear superposition method to obtain the total monotonic crack tip opening displacement .sub.t and cyclic crack tip opening displacement .sub.r of short cracks under the combined creep-fatigue action in step 4, its expression is as follows:

[00019]$\{\begin{array}{c}{}_t={}_t^p+{}_t^c\\ {}_r={}_r^p+{}_r^c\end{array}.$

[0050] When predicting the creep-fatigue short crack growth rate for high-temperature components of energy equipment, the materials are heat-resistant martensitic steel and austenitic steel, with a service temperature range of 500-700 C.

[0051] Embodiment 1: please refer to FIG. 1, the method for calculating short cracks in metallic materials under creep-fatigue interaction provided by the invention comprises short crack growth rate calculation method under creep-fatigue interaction on creep performance data based on uniaxial creep tests and on the elastic-plastic property data based on uniaxial tensile tests.

[0052] In order to better illustrate the method of the invention for calculating short cracks in metallic materials under creep-fatigue interaction, a single-edge notch specimen will be used for validation. The material used for validation is 316H heat-resistant steel, and uniaxial creep, uniaxial tensile, and creep-fatigue short crack growth tests are conducted under conditions of 550 C. The predicted creep-fatigue short crack growth rate is tested by using a load control method, maintaining the peak load, with a trapezoidal waveform.

[0053] Step (1): based on the steady-state creep rate at different stress levels obtained from uniaxial creep tests, a nonlinear fitting method is used, as shown in FIG. 2, the creep stress index m under 550 C. conditions is 11.31. Further, the correction parameters r.sub.m and .sub.cr related to the creep stress index m are obtained as 1.01 and 0.3673, respectively.

[0054] Step (2): based on a tensile curve obtained from uniaxial tensile tests, as shown in FIG. 3, the elastic-plastic property under 550 C. conditions is obtained, including: the elastic modulus E of 180 GPa and the yield stress .sub.y of 164 MPa, Additionally, the Poisson's ratio v for the metallic material is 0.3.

[0055] Step (3): based on the obtained elastic-plastic property, the obtaining the first monotonic crack tip opening displacement

[00020]${}_t^p$

caused by plasticity under maximum far-field stress acting on short cracks and the first cyclic crack tip opening displacement

[00021]${}_r^p$

caused by plasticity under far-field cyclic stress are obtained. Their expressions are as follows:

[00022]${}_t^p=\frac{8c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y}\right)\right]}{E};{}_r^p=\frac{16c\left(1-v^2\right){}_y\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}\left(1-R\right)}{4{}_y}\right)\right]}{E}.$

[0056] Step (4): based on the obtained creep property, the co-planar creep zone size .sup.cr(t) related to the creep time and the material' s equivalent creep yield strength are obtained. The expressions are as follows:

[00023]${}^{\mathrm{cr}}\left(t\right)=\frac{1}{2}{\left(\frac{K_I}{E}\right)}^2{{}_{\mathrm{cr}}\left[\frac{{{\mathrm{WtE}}^m\left(m+1\right)}^2}{2{\mathrm{mr}}_m^{m+1}}\right]}^{\frac{2}{m-1}};{}_y^{\mathrm{cr}}=\frac{{}_{\mathrm{peak}}}{2\arccos \left(\frac{c}{{}^{\mathrm{cr}}\left(t\right)+c}\right)};$

[0057] Step (5): by using the results obtained in step (4); the second monotonic crack tip opening displacement

[00024]${}_t^c$

caused by creep under maximum far-field stress acting on short cracks and the second cyclic crack tip opening displacement

[00025]${}_r^c$

caused by creep under far-field cyclic stress are obtained, the expressions are as follows:

[00026]${}_t^c=\frac{8c\left(1-v^2\right){}_y^{\mathrm{cr}}\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}}{2{}_y^{\mathrm{cr}}}\right)\right]}{E};{}_r^c=\frac{16c\left(1-v^2\right){}_y^{\mathrm{cr}}\ln \left[\sec \left(\frac{{}_{\mathrm{peak}}\left(1-R\right)}{4{}_y^{\mathrm{cr}}}\right)\right]}{E}.$

[0058] Step (6): by using the monotonic/cyclic crack tip opening displacement caused by creep/fatigue determined in step (4), the total monotonic crack tip opening displacement .sub.t and cyclic crack tip opening displacement .sub.r of short cracks under the combined creep-fatigue action are calculated, its expression is as follows:

[00027]$\{\begin{array}{c}{}_t={}_t^p+{}_t^c\\ {}_r={}_r^p+{}_r^c\end{array}.$

[0059] Step (7): based on the obtained .sub.t and .sub.r, the creep-fatigue short crack growth rate of the material is calculated by using the crack growth rate model under the creep-fatigue interaction, its expression is as follows

[00028]${\left(\mathrm{dc}\right)}_{cycle}=\left({}_t{}_r\right).$

[0060] To verify the method for calculating short cracks in metallic materials under creep-fatigue interaction proposed in this invention, the creep-fatigue short crack growth rate under 550 C. conditions calculated by using this method is shown in FIG. 4. For comparison, the results of the traditional method for calculating short crack growth rate based on experimental data under creep-fatigue interaction are shown in FIG. 5. It can be seen that the method for calculating short cracks in metallic materials under creep-fatigue interaction in this invention provides good predictions of creep-fatigue short crack growth rates under different hold times, addressing the limitations of traditional methods, which cannot accurately describe short crack growth behavior and have dwell time-dependent prediction results.

[0061] The invention is described with reference to flowcharts and/or block diagrams of methods, devices (systems), and computer program products according to embodiments of the invention. It should be understood that each flow and/or block in the flowchart and/or block diagram, and a combination of flows and/or blocks in the flowchart and/or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in one or more processes in the flowchart and/or one or more blocks in the block diagram.

[0062] In addition, the terms first and second are only used for descriptive purposes, and should not be understood as indicating or implying relative importance or implying the number of indicated technical features. Therefore, the features defined with first or second may expressly or implicitly include one or more of the features, and in the description of the invention, the meaning of multiple is two or more, unless otherwise expressly limited.

[0063] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Therefore, if these modifications and variations of the invention fall within the scope of the claims of the invention and their equivalents, the invention is also intended to include these modifications and variations.