>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, σ_peakis the maximum far-field stress, and c is the short crack length.

In the process of obtaining the first cyclic crack tip opening displacement

$δ_{r}^{p}$

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

$δ ? = \frac{16 c (1 - v^{2}) σ_{y} \ln [\sec (\frac{π σ_{peak} (1 - R)}{4 σ_{y}})]}{π E};$

$? indicates text missing or illegible when filed$

wherein R is the load ratio.

In the process of obtaining the second monotonic crack tip opening displacement

$δ_{t}^{c}$

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

$δ ? \frac{8 c (1 - v^{2}) σ_{y} \ln [\sec (\frac{π σ_{peak}}{2 σ_{y}^{cr}})]}{π E};$

$? indicates text missing or illegible when filed$

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

$σ_{y}^{cr} = \frac{π σ_{peak}}{2 \arccos (\frac{c}{ρ^{cr} (t) + c})};$

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

In the process of obtaining the co-planar creep zone size related to the creep time ρ^cr(t), its expression is as follows:

$ρ^{cr} (t) = \frac{1}{2 π} {(\frac{K_{I}}{E})}^{2} {ψ_{cr} [\frac{{{WtE}^{m} (m + 1)}^{2}}{2 {mr}_{m}^{m + 1}}]}^{\frac{2}{m - 1}};$

wherein K₁is 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_mand ψ_crare correction parameters related to the creep stress index m.

When obtaining the correction parameter r_mrelated to the creep stress index m, its expression is as follows:

$r_{m} = {(\frac{π}{η_{m}} \frac{m + 1}{m})}^{\frac{1}{m + 1}};$

wherein η_mis the material parameter related to the creep stress index m.

When obtaining the correction parameter r_mrelated to the creep stress index m, its value is determined by using an interpolation method based on Table 1.

TABLE 1

m
3
5
9
13

r_m
3.86
3.41
3.03
2.87

When obtaining the correction parameter ψ_crrelated to the creep stress index m, its value is determined by using the interpolation method based on Table 2.

TABLE 2

m
3
5
13

ψ_cr
0.25
0.32
0.38

using the linear superposition method to obtain the total monotonic crack tip opening displacement δ_tand cyclic crack tip opening displacement δ_rof short cracks under the combined creep-fatigue action in step 4, its expression is as follows:

${\begin{matrix} δ_{t} = δ_{t}^{p} + δ_{t}^{c} \\ δ_{r} = δ_{r}^{p} + δ_{r}^{c} \end{matrix} .$

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.

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.

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.

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_mand ψ_crrelated to the creep stress index m are obtained as 1.01 and 0.3673, respectively.

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 σ_yof 164 MPa, Additionally, the Poisson's ratio v for the metallic material is 0.3.

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

$δ_{t}^{p}$

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

$δ_{r}^{p}$

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

δ
t
p

=

8
⁢
c
⁢

(

1
-

v
2

)

⁢

σ

y

⁢

ln

[

sec