1. A method for evaluating a small sample of a low cycle fatigue life curve of a material, comprising:

acquiring low cycle fatigue test data, and fitting the relation between the total strain amplitude and the load reversal times through a three-parameter power function curve;

deforming the three-parameter power function formula to obtain a linear expression under a logarithmic coordinate system, and expressing two parameters in the linear expression as an expression of fatigue limit parameters;

solving the relation between the other two parameters and the fatigue limit parameter in the three-parameter power function formula, and deducing the function expression of the total strain amplitude relative to the load reversal times and the fatigue limit parameter;

establishing a total residual error square sum expression of the low cycle fatigue life curve by combining the test data;

and solving the optimal fatigue parameter value through an efficient optimization algorithm, and solving the result of the target parameter in the three-parameter power function expression, thereby determining the expression of the low-cycle fatigue life curve.

2. The method of claim 1, wherein obtaining low cycle fatigue test data and fitting the relationship between total strain amplitude and load reversal times with a three parameter power function curve comprises:

obtaining small sample data of low cycle fatigue test of materialIncluding total strain magnitudeAnd corresponding load reversal times at failure of 2N_fAnd using a three parameter power function curveTo fit the relationship between the total strain amplitude and the number of load reversals, where α, β andare all undetermined parameters, andis a fatigue limit parameter.

3. The evaluation method according to claim 2, wherein transforming the three-parameter power function formula to obtain a linear expression in a logarithmic coordinate system, and expressing two parameters in the linear expression as an expression of the fatigue limit parameter comprises:

for a three-parameter power function formulaA transformation is performed to express it as a linear expression in logarithmic coordinates:and expressing two coefficients A and B in the linear expression as fatigue limit parametersAre respectively asAnd

4. the method of claim 3, wherein solving the relationship between the remaining two parameters and the fatigue limit parameter in the three-parameter power function formula and deriving a functional representation of the total strain amplitude with respect to the number of load reversals and the fatigue limit parameter comprises:

by two coefficients in a linear expressionAndthe results of calculating the parameters alpha and beta in the original three-parameter power function expression are recorded asAndand deforming the three-parameter power function expression to obtain a function of the total strain amplitude on the reverse times of the load:

wherein the content of the first and second substances,indicating total strain amplitudeAs fatigue limit parameterAnd number of load reversals 2N_fAs a function of (c).

5. The method of claim 4, wherein the step of establishing a sum of squares of total residuals of the low cycle fatigue life curve in combination with the test data comprises:

binding to test dataBuilding the sum of squares of the total residuals of the epsilon-N curvesExpression:

wherein the content of the first and second substances,representing the sum of squares of the total residuals Mse as a fatigue limit parameterAs a function of (c).

6. The evaluation method according to claim 5, wherein the determining the expression of the low cycle fatigue life curve by solving the optimal fatigue parameter values through an efficient optimization algorithm and solving the results of the target parameters in a three-parameter power function expression comprises:

solving for the sum of squares of the total residuals by an efficient optimization algorithmMinimum fatigue limit parameterAs a result, the result is optimal for the value of the fatigue parameter;

by substituting the value of the optimum fatigue parameter intoAndand obtaining results of other parameters of the three-parameter power function expression, and determining an epsilon-N curve.

7. The assessment method according to claim 3, characterized by passing fatigue limit parametersTo express two coefficients in the transformed linear expression asAndthe specific substeps are as follows:

for a three-parameter power function formulaThe simultaneous logarithms on both sides gave the following expression:

let a ═ lg α and B ═ β, then the above formula is:

combining the data of the small sample of the low cycle fatigue test of the obtained material And the least square principle, and expresses two coefficients A and B in the above formula as fatigue limit parametersIs recorded asAndthen:

8. the assessment method of claim 4, wherein the total strain amplitude is expressed as a function of the number of load reversals and the fatigue limit parameter, comprising:

obtaining fatigue limit parameters of alpha and beta according to the relation between two parameters A and B in the linear expression and alpha and beta in the original three-parameter power function expressionExpression (2)Andrespectively as follows:

substituting the two expressions into a three-parameter power function expression and deforming the expression to obtain a total strain amplitude2N for load reversal times_fAnd fatigue limit parameterThe function of (a) expresses:

9. the method of claim 5, wherein the sum of squares of total residuals from the epsilon-N curveWith respect to fatigue limit parametersThe function expression of (2) determines the quality of the epsilon-N curve.

10. The method of claim 6, wherein the optimal fatigue parameter values are solved by an efficient optimization algorithm such as genetic algorithm or sequential quadratic programming

Background

Considering that the high-temperature low-cycle strain fatigue test has high difficulty, long test period and high test cost, the high-temperature low-cycle strain fatigue performance is necessary performance data for the engineering application of some materials, and the performance data without high-temperature low-cycle strain can influence the engineering application of the materials.

Therefore, how to provide a curve capable of better reflecting the real strain fatigue life relation under the small subsample test data is very important.

It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present invention and therefore may include information that does not constitute prior art known to a person of ordinary skill in the art.

Disclosure of Invention

The embodiment of the invention aims to provide a sample evaluation method for a material low-cycle fatigue life curve, which can provide an epsilon-N curve result with the minimum sum of squares of total residuals.

According to an aspect of an embodiment of the present invention, there is provided a small subsample evaluation method of a material low cycle fatigue life curve, the evaluation method including:

acquiring low cycle fatigue test data, and fitting the relation between the total strain amplitude and the load reversal times through a three-parameter power function curve;

deforming the three-parameter power function formula to obtain a linear expression under a logarithmic coordinate system, and expressing two parameters in the linear expression as an expression of fatigue limit parameters;

solving the relation between the other two parameters and the fatigue limit parameter in the three-parameter power function formula, and deducing the function expression of the total strain amplitude relative to the load reversal times and the fatigue limit parameter;

establishing a total residual error square sum expression of the low cycle fatigue life curve by combining the test data;

and solving the optimal fatigue parameter value through an efficient optimization algorithm, and solving the result of the target parameter in the three-parameter power function expression, thereby determining the expression of the low-cycle fatigue life curve.

In an exemplary embodiment of the present disclosure, obtaining low cycle fatigue test data, fitting a relationship between total strain amplitude and load reversal times by a three-parameter power function curve, comprises:

obtaining small sample data of low cycle fatigue test of materialIncluding total strain magnitudeAnd corresponding load reversal times at failure of 2N_fAnd using a three parameter power function curveTo fit the relationship between the total strain amplitude and the number of load reversals, where α, β andare all undetermined parameters, andis a fatigue limit parameter.

In an exemplary embodiment of the present disclosure, transforming a three-parameter power function formula to obtain a linear expression in a logarithmic coordinate system, and expressing two parameters in the linear expression as an expression of a fatigue limit parameter, includes:

for a three-parameter power function formulaA transformation is performed to express it as a linear expression in logarithmic coordinates:and expressing two coefficients A and B in the linear expression as fatigue limit parametersAre respectively asAnd

in an exemplary embodiment of the present disclosure, solving the relation between the remaining two parameters in the three-parameter power function formula and the fatigue limit parameter, and deriving a functional expression of the total strain amplitude with respect to the number of load reversals and the fatigue limit parameter, includes:

by two coefficients in a linear expressionAndthe results of calculating the parameters alpha and beta in the original three-parameter power function expression are recorded asAndand deforming the three-parameter power function expression to obtain a function of the total strain amplitude on the reverse times of the load:

wherein the content of the first and second substances,indicating total strain amplitudeAs fatigue limit parameterAnd number of load reversals 2N_fAs a function of (c).

In an exemplary embodiment of the present disclosure, in combination with experimental data, an overall residual sum of squares expression for the low cycle fatigue life curve is established, comprising:

binding to test dataBuilding the sum of squares of the total residuals of the epsilon-N curvesExpression:

wherein the content of the first and second substances,representing the sum of squares of the total residuals Mse as a fatigue limit parameterAs a function of (c).

In an exemplary embodiment of the present disclosure, the determining the expression of the low cycle fatigue life curve by solving the optimal fatigue parameter value through an efficient optimization algorithm and solving the result of the target parameter in a three-parameter power function expression includes:

solving for the sum of squares of the total residuals by an efficient optimization algorithmMinimum fatigue limit parameterAs a result, the result is a value of the optimal fatigue parameter;

by substituting the value of the optimum fatigue parameter intoAndand obtaining results of other parameters of the three-parameter power function expression, and determining an epsilon-N curve.

In an exemplary embodiment of the present disclosure, the fatigue limit parameter is passedTo express two coefficients in the transformed linear expression asAndthe specific substeps are as follows:

for a three-parameter power function formulaThe simultaneous logarithms on both sides gave the following expression:

let a ═ lg α and B ═ β, then the above formula is:

combining the data of the small sample of the low cycle fatigue test of the obtained material And the least square principle, and expresses two coefficients A and B in the above formula as fatigue limit parametersIs recorded asAndthen:

in an exemplary embodiment of the present disclosure, the total strain amplitude is expressed as a function of the number of load reversals and the fatigue limit parameter, the basic idea being as follows:

obtaining fatigue limit parameters of alpha and beta according to the relation between two parameters A and B in the linear expression and alpha and beta in the original three-parameter power function expressionExpression (2)Andrespectively as follows:

substituting the two expressions into a three-parameter power function expression and deforming the expression to obtain a total strain amplitude2N for load reversal times_fAnd fatigue limit parameterThe function of (a) expresses:

in an exemplary embodiment of the present disclosure, the sum of squares of the total residuals according to the epsilon-N curveWith respect to fatigue limit parametersThe function expression of (2) determines the quality of the epsilon-N curve.

In an exemplary embodiment of the present disclosure, the optimal fatigue parameter value is solved by an efficient optimization algorithm such as a genetic algorithm or a sequential quadratic programming

Currently, the Manson-coefficient formula is used more often in describing the epsilon-N curve. The Manson-coffee formula can give a better fitting result under the condition that the elastic line and the plastic line are both straight lines. While the Manson-coffee formula is widely used in engineering, it also exposes its own drawbacks. The defect is mainly reflected in that the fatigue limit of the material cannot be reflected, which is inconsistent with the actual situation. Meanwhile, elastic lines and plastic lines of many materials decomposed according to the Manson-coffee formula are not straight lines in a log-log coordinate system, but are curves slightly bending downwards. And, the total strain life curve obtained by using the Manson-coffee formula is the sum of two straight lines, and the sum of the squares of the total residual errors is not the minimum. The method based on the traditional three-parameter power function can overcome the defects of the Manson-coffee formula to a certain extent, but the method calculates the fatigue parameter value by maximizing the absolute value of a linear correlation coefficient, and under the result, the total residual square sum of the epsilon-N curve is not minimum. Therefore, the fatigue parameter value is calculated by minimizing the sum of squares of the residual errors based on the three-parameter power function expression, the epsilon-N curve of the low-cycle fatigue life of the turbine part material is further obtained, the defects of the Manson-coffee formula can be effectively overcome, and the epsilon-N curve result with the minimum sum of squares of the total residual errors is given.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:

fig. 1 is a schematic flow chart of a sample evaluation method for a low cycle fatigue life curve of a material according to an embodiment of the present disclosure.

Fig. 2 is a schematic view of a low cycle fatigue curve of a GH4169 material at 650 ℃.

Fig. 3 is a schematic view of a low cycle fatigue curve of a GH4169 material at 550 ℃ according to an embodiment of the disclosure.

Fig. 4 is a schematic view of a low cycle fatigue curve of a GH4169 material at 360 ℃ according to an embodiment of the disclosure.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art.

Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the inventive aspects may be practiced without one or more of the specific details, or with other methods, steps, and so forth. In other instances, well-known methods, step implementations, or operations are not shown or described in detail to avoid obscuring aspects of the invention.

The flow charts shown in the drawings are merely illustrative and do not necessarily include all of the contents and steps, nor do they necessarily have to be performed in the order described. For example, some steps may be decomposed, and some steps may be combined or partially combined, so that the actual execution sequence may be changed according to the actual situation.

The present disclosure provides a small subsample evaluation method of a material low cycle fatigue life curve, as shown in fig. 1, the evaluation method includes:

s100, acquiring low cycle fatigue test data, and fitting the relation between the total strain amplitude and the load reversal times through a three-parameter power function curve;

s200, deforming the three-parameter power function formula to obtain a linear expression under a logarithmic coordinate system, and expressing two parameters in the linear expression as an expression of the fatigue limit parameter;

step S300, solving a relational expression between the other two parameters and the fatigue limit parameter in the three-parameter power function formula, and deducing a function expression of the total strain amplitude relative to the load reversal times and the fatigue limit parameter;

s400, establishing a total residual error square sum expression of the low cycle fatigue life curve by combining test data;

and S500, solving the optimal fatigue parameter value through an efficient optimization algorithm, and solving the result of the target parameter in the three-parameter power function expression, thereby determining the expression of the low-cycle fatigue life curve.

Currently, the Manson-coefficient formula is used more often in describing the epsilon-N curve. The Manson-coffee formula can give a better fitting result under the condition that the elastic line and the plastic line are both straight lines. While the Manson-coffee formula is widely used in engineering, it also exposes its own drawbacks. The defect is mainly reflected in that the fatigue limit of the material cannot be reflected, which is inconsistent with the actual situation. Meanwhile, elastic lines and plastic lines of many materials decomposed according to the Manson-coffee formula are not straight lines in a log-log coordinate system, but are curves slightly bending downwards. And, the total strain life curve obtained by using the Manson-coffee formula is the sum of two straight lines, and the sum of the squares of the total residual errors is not the minimum. The method based on the traditional three-parameter power function can overcome the defects of the Manson-coffee formula to a certain extent, but the method calculates the fatigue parameter value by maximizing the absolute value of a linear correlation coefficient, and under the result, the total residual square sum of the epsilon-N curve is not minimum.

Therefore, the fatigue parameter value is calculated by minimizing the sum of squares of the residual errors based on the three-parameter power function expression, the epsilon-N curve of the low-cycle fatigue life of the turbine part material is further obtained, the defects of the Manson-coffee formula can be effectively overcome, and the epsilon-N curve result with the minimum sum of squares of the total residual errors is given.

Hereinafter, each step in a sample evaluation method of a material low cycle fatigue life curve provided by the present disclosure will be described in detail.

In step S100, low cycle fatigue test data is acquired, and the relationship between the total strain amplitude and the load reversal number is fitted by a three-parameter power function curve.

Specifically, obtaining sample data of a low cycle fatigue test of a material Including total strain magnitudeAnd corresponding loads at which failure occursNumber of inversions 2N_fAnd using a three parameter power function curveTo fit the relationship between the total strain amplitude and the number of load reversals, where α, β andare all undetermined parameters, andis a fatigue limit parameter.

TABLE 1 Low cycle fatigue test data for turbine component GH4169 materials at different temperatures

In step S200, the three-parameter power function formula is transformed to obtain a linear expression in a logarithmic coordinate system, and two parameters in the linear expression are expressed as an expression of the fatigue limit parameter.

In particular, for a three parameter power function formulaA transformation is performed to express it as a linear expression in logarithmic coordinates: and expressing two coefficients A and B in the linear expression as fatigue limit parametersExpression ofAre respectively shown asAnd

wherein the fatigue limit parameter is passedTo express two coefficients in the transformed linear expression asAndthe specific substeps are as follows:

step S210, for a three-parameter power function formulaThe simultaneous logarithms on both sides gave the following expression:

step S220, let a ═ lg α and B ═ β, then the above formula is:

step S230, combining the small sample data of the low cycle fatigue test of the obtained materialAnd the least square principle, and expresses two coefficients A and B in the above formula as fatigue limit parametersIs recorded asAndthen:

then the following can be obtained at 650 ℃:

at 550 ℃:

at 360 ℃:

in step S300, the relation between the remaining two parameters in the three-parameter power function formula and the fatigue limit parameter is solved, and a functional expression of the total strain amplitude with respect to the number of load reversals and the fatigue limit parameter is derived.

In particular, by two coefficients in a linear expressionAndthe results of calculating the parameters alpha and beta in the original three-parameter power function expression are recorded asAndand transforming the three-parameter power function expression to obtainTo the function of the total strain amplitude with respect to the number of load reversals:

wherein the content of the first and second substances,indicating total strain amplitudeAs fatigue limit parameterAnd number of load reversals 2N_fAs a function of (c).

Wherein the total strain amplitude is expressed as a function of the number of load reversals and the fatigue limit parameter, comprising the steps of:

step S310, obtaining fatigue limit parameters of alpha and beta according to the relation between two parameters A and B in the linear expression and alpha and beta in the original three-parameter power function expressionExpression (2)Andrespectively as follows:

then at 650 deg.C:

at 550 ℃:

at 360 ℃:

step S320, obtaining the temperature differenceAndsubstituting into the three-parameter power function expression and deforming the expression to obtain the total strain amplitude2N for load reversal times_fAnd fatigue limit parameterThe function of (a) expresses:

in step S400, an expression of the sum of squares of the total residuals of the low cycle fatigue life curve is established in combination with the test data.

In particular, binding assay dataBuilding the sum of squares of the total residuals of the epsilon-N curvesExpression:

wherein the content of the first and second substances,representing the sum of squares of the total residuals Mse as a fatigue limit parameterAs a function of (c).

Wherein the sum of squares of the total residuals according to the epsilon-N curveWith respect to fatigue limit parametersThe function expression of (2) determines the quality of the epsilon-N curve.

At 650 ℃:

at 550 ℃:

at 360 ℃:

in step S500, the optimal fatigue parameter value is solved through the high efficiency optimization algorithm, and the result of the target parameter in the three-parameter power function expression is solved, thereby determining the expression of the low cycle fatigue life curve.

Specifically, solving for the sum of squares of the total residuals by an efficient optimization algorithmMinimum fatigue limit parameterAs a result, the result is a value of the optimal fatigue parameter; by substituting the value of the optimum fatigue parameter intoAndand obtaining results of other parameters of the three-parameter power function expression, and determining an epsilon-N curve.

Step S510, solving the optimal fatigue parameter value through efficient optimization algorithms such as genetic algorithm or sequence quadratic programming

Then at 650 deg.C:

at 550 ℃:

at 360 ℃:

step S520, optimizing fatigue parametersAndthe result of substituting the three-parameter power function expression back into the epsilon-N curve is as follows:

at 650 ℃:

the corresponding low cycle fatigue epsilon-N curve is:

at 550 ℃:

the corresponding low cycle fatigue epsilon-N curve is:

at 360 ℃:

the corresponding low cycle fatigue epsilon-N curve is:

in the related art, the low cycle fatigue epsilon-N curve of the GH4169 material calculated by various methods at 650 ℃, 550 ℃ and 360 ℃ can also be calculated based on the Manson-coffee formula and the conventional three-parameter power function method, and the results of the residual square sum of the methods are shown in Table 2 in FIGS. 2, 3 and 4.

Table 2 residual sum of squares results for each method

As can be seen from Table 2, the residual square sum of the low cycle fatigue epsilon-N curves of the GH4169 material at different temperatures calculated by the method of the present disclosure is the minimum of the three methods, which illustrates the effectiveness and superiority of the method of the present disclosure. Meanwhile, the epsilon-N curve results shown in FIG. 2, FIG. 3 and FIG. 4 show that the low cycle fatigue life curve calculated by the method of the present disclosure can be well matched with the test data.

Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.