Method for calculating service life of material under action of thermal shock load

Abstract

The present disclosure discloses a method for calculating the service life of a material under the action of a thermal shock load. The method includes steps of obtaining test results at different thermal shock temperatures and a thermal shock cycle number according to a thermal shock test, and calculating a temperature rise rate to temperature drop rate ratio R.sub.v; calculating a corresponding stress intensity factor ΔK according to a crack length a measured in the test; calculating a thermal stress σ at the notch and a notch stress concentration coefficient k.sub.t of the test specimen; calculating a stress intensity factor threshold ΔK.sub.th according to the crack length a measured in the test; and substituting the obtained the stress intensity factor ΔK, stress intensity factor threshold ΔK.sub.th and temperature rise rate to temperature drop rate ratio R.sub.v into a thermal fatigue crack growth model.

Claims

1. A method for calculating the service life of a material under the action of a thermal shock load, wherein a thermal shock life calculation model based on crack growth is established by associating a thermal shock crack length a with a thermal shock temperature T, a thermal shock rate ratio R.sub.v and a thermal shock cycle number N: $(\frac{d a}{d N}) = C {(\frac{4 \sqrt{2}}{{(1 - R R_{v})}^{n} E^{'} (1 - 2 v) σ_{y s}})}^{m} (Δ K^{2 m} - Δ K_{t h}^{2 m})$ where da/dN is a thermal shock crack growth rate; C, n and m are material constants related to a thermal shock temperature; R is a thermal stress ratio; v is a Poisson’s ratio of the material; R.sub.v is a temperature rise rate to temperature drop rate ratio in a thermal shock process; E′ is an elastic modulus, $E^{'} = E / (1 - v^{2})$ is a yield stress of the material; ΔK is a stress intensity factor related to the thermal shock temperature; ΔK.sub.th is a stress intensity factor threshold; formula (1) is integrated to obtain a thermal fatigue life change calculation model with respect to crack growth: $\int_{N_{1}}^{\begin{array}{l} N \end{array}} d N = \int_{a_{1}}^{a} \frac{1}{C {(\frac{4 \sqrt{2}}{{(1 - R R_{v})}^{n} E^{'} (1 - 2 v) σ_{y s}})}^{m} (Δ K^{2 m} - Δ K_{t h}^{2 m})} d a$ where a.sub.i is an initiation size of a crack; N.sub.i is an initiation life of the crack; the method for calculating the service life of the material under the action of the thermal shock load comprises the following steps: S1 carrying out a thermal shock test on a standard thermal fatigue test specimen under different test conditions, and establishing an a-N relational graph according to test results obtained in the thermal shock test at different thermal shock temperatures and a thermal shock cycle number; S2 calculating the temperature rise rate to temperature drop rate ratio R.sub.v according to a change in the temperature at a notch of the test specimen in the thermal shock test process in step (1); S3 establishing a relationship between the stress intensity factor ΔK and the crack length a according to the a-N relationship in step (1): $Δ K = \frac{σ_{\max} - k_{t} c_{c l}}{\sqrt{1 + 4.5 (a / ρ)}} \sqrt{π \frac{a^{a} {(a_{s} - a)}^{(1 - α)}}{Q}} F (\frac{c}{t}, \frac{c}{a}, \frac{a}{b}, Φ)$ where k.sub.t is a stress concentration coefficient at the notch of the test specimen; σ.sub.max is a maximum thermal stress in a test area of the test specimen; σ.sub.cl is the closure stress of a thermal shock crack; ρ is a radius of the root of the notch of the test specimen; Q is a shape correction factor; α is a thermal fatigue crack growth influence factor; as is a crack arrest size of the thermal shock crack; F is a boundary condition; c is a depth of the thermal shock crack; t is a thickness of the test specimen; b is a width of the test specimen; Φ is an angular function of an elliptical crack tip; S4 calculating anotch thermal stress σ and a notch stress concentration coefficient k.sub.t of the test specimen under thermal shock test conditions by using finite element software; S5 calculating a relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a according to the test results in step (1): $Δ K_{t h} = {(\frac{a}{a - d})}^{1 / 2} Δ σ_{e R} \sqrt{π d}$ where d is a microscopic crack size limit of the material; σ.sub.eR is an ordinary fatigue limit of the material; and S6 substituting formulas (3) and (4) into formula (2) for integration to obtain a thermal fatigue life calculation model based on crack growth.

2. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in formula (1), the temperature rise rate to temperature drop rate ratio R.sub.v in the thermal shock process on the right side of the equal sign is closely related to the test conditions in the thermal shock process, and the size of R.sub.v reflects the severity of thermal shock.

3. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in formula(1), the stress intensity factor AK on the right of the equal sign reflects the magnitude of a driving force for fatigue crack growth in the thermal shock process, and is closely related to the temperature in the thermal shock process, a crack length, and a shape of the test specimen.

4. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in formula (1), the stress intensity factor threshold ΔK.sub.th on the right side of the equal sign reflects the size of an obstacle to be overcome in the thermal shock crack growth process, and is related to the fatigue crack length and properties of the material.

5. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (1), a relationship among temperature rise and drop time of the test specimen under different thermal shock conditions, a change in the temperature at the notch of the test specimen, the thermal shock crack length a, and the thermal shock cycle number N is determined by means of carrying out thermal shock tests under different test conditions.

6. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (2), the temperature rise rate to temperature drop rate ratio R.sub.v is calculated according to the temperature at the notch of the test specimen in the thermal shock test process in step (1), and an expression is as follows: $R_{v} = \frac{v_{H}}{v_{C}}$ where v.sub.H is a temperature rise rate, and vc is a temperature drop rate.

7. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (3), in the relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a, the closure stress σ.sub.cl, the crack arrest size as of the crack and the depth c of the crack are determined according to the test results in step(1), and expressions of the shape correction factor Q and the boundary condition F are as follows: $Q = 1 + 1.46 {(\frac{2 c}{a})}^{1.65}$ $F = (1.04 + 0.2 {(\frac{a}{2 t})}^{2} - 0.106 {(\frac{a}{2 t})}^{4}) (1.1 + 0.35 {(\frac{a}{2 t})}^{2})$ .

8. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (4), the same test conditions are set in the finite element analysis according to a temperature change and thermal shock time of a test area in the thermal shock test process in step (1), so as to ensure that an obtained thermal stress change and temperature change are consistent with those in a real test; transient thermal-mechanical coupling analysis is performed, on the basis of a transient thermal module and a transient structural module in the NASYS software, on the standard fatigue test specimen model used in step (1), thus determining the change in the thermal stress at the notch of the test specimen and the notch stress concentration coefficient k.sub.t; and an expression is as follows: $k_{t} = \frac{σ_{\max}}{σ_{0}}$ where σ.sub.max is the maximum stress at a stress concentration portion; and σ.sub.0 is a nominal stress.

9. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (5), in the relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a, the microscopic crack size limit d of the material is obtained according to a grain size of the material or a micro defect size of the material and the ordinary fatigue limit σ.sub.eR of the material through an S-N curve of the material or obtained by carrying out a fatigue test.

10. The method for calculating the service life of the material under the action of the thermal shock load according to claim 1, wherein in step (6), the stress intensity factor ΔK in formula (3), the stress intensity factor threshold ΔK.sub.th in formula (4), and the temperature rise rate to temperature drop rate ratio R.sub.v calculated in step (2) are substituted into formula (2) for integration, thus obtaining the thermal shop fatigue life calculation model based on crack growth.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 is a flow chart of a specific implementation according to the present disclosure;

[0027] FIG. 2 is a diagram of a change of a temperature at a notch in a thermal shock process;

[0028] FIG. 3 is a diagram of changes in a temperature rise rate and a temperature drop rate at a notch in a thermal shock process; and

[0029] FIG. 4 is a schematic diagram of stress concentration at a notch of a test specimen.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The present disclosure is further described below in combination with the accompanying drawings and embodiments.

[0031] As shown in FIG. 1, a method for calculating the service life of a material under the action of a thermal shock load is provided. A thermal shock life calculation model based on crack growth is established by associating a thermal shock crack length a with a thermal shock temperature T, a thermal shock rate ratio R.sub.v and a thermal shock cycle number N:

$(\frac{d a}{d N}) = C {(\frac{4 \sqrt{2}}{{(1 - R R_{v})}^{n} E^{'} (1 - 2 v) σ_{y s}})}^{m} (Δ K^{2 m} - {Δ K}_{t h}^{2 m})$

[0032] where da/dN is a thermal shock crack growth rate; C, n and m are material constants related to a thermal shock temperature; R is a thermal stress ratio; v is a Poisson’s ratio of the material; R.sub.v is a temperature rise rate to temperature drop rate ratio in a thermal shock process; E′ is an elastic modulus, E′=E/(1-v.sup.2); σ.sub.ys is a yield stress of the material; ΔK is a stress intensity factor related to the thermal shock temperature; ΔK.sub.th is a stress intensity factor threshold;

[0033] formula (1) is integrated to obtain a thermal fatigue life change calculation model with respect to crack growth:

$\int_{N_{1}}^{N} d N = \int_{a 1}^{a} \frac{1}{C {(\frac{4 \sqrt{2}}{{(1 - R R_{v})}^{n} E^{'} (1 - 2 v) σ_{y s}})}^{m} (Δ K^{2 m} - Δ K_{t h}^{2 m})} d a$

[0034] where a.sub.i is an initiation size of a crack; N.sub.i is an initiation life of the crack.

[0035] In formula (1), the temperature rise rate to temperature drop rate ratio R.sub.v in the thermal shock process on the right side of the equal sign is closely related to the test conditions in the thermal shock process, and the size of R.sub.v reflects the severity of thermal shock; the stress intensity factor ΔK on the right of the equal sign reflects the magnitude of a driving force for fatigue crack growth in the thermal shock process, and is closely related to the temperature in the thermal shock process, a crack length, and a shape of the test specimen;the stress intensity factor threshold ΔK.sub.th on the right side of the equal sign reflects the size of an obstacle to be overcome in the thermal shock crack growth process, and is related to the fatigue crack length and properties of the material.

[0036] The method for calculating the service life of a material under the action of a thermal shock load includes the following steps: [0037] (1) a thermal shock test is carried out on a standard thermal fatigue test specimen under different test conditions, and an a-N relational graph is established according to test results obtained in the thermal shock test at different thermal shock temperatures and a thermal shock cycle number; [0038] (2) the temperature rise rate to temperature drop rate ratio Rv is calculated according to a change in the temperature at a notch of the test specimen in the thermal shock test process in step (1); [0039] (3) a relationship between the stress intensity factor ΔK and the crack length a is established according to the a-N relationship in step (1): $Δ K = \frac{σ_{\max} - k_{t} c_{c l}}{\sqrt{1 + 4.5 (a / p)}} \sqrt{π \frac{a^{a} {(a_{s} - a)}^{(1 - a)}}{Q} F (\frac{c}{t}, \frac{c}{a}, \frac{a}{b}, Φ)}$ where k.sub.t is a stress concentration coefficient at the notch of the test specimen; σ.sub.max is a maximum thermal stress in a test area of the test specimen; σ.sub.cl is the closure stress of a thermal shock crack; p is a radius of the root of the notch of the test specimen; Q is a shape correction factor; α is a thermal fatigue crack growth influence factor; a.sub.s is a crack arrest size of the thermal shock crack; F is a boundary condition; c is a depth of the thermal shock crack; t is a thickness of the test specimen; b is a width of the test specimen; Φ is an angular function of an elliptical crack tip; [0040] (4) a notch thermal stress σ and a notch stress concentration coefficient k.sub.t of the test specimen under thermal shock test conditions are calculated by using finite element software; [0041] (5) a relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a is calculated according to the test results in step (1): $Δ K_{t h} = {(\frac{a}{a - d})}^{1 / 2} Δ σ_{e R} \sqrt{π d}$ where d is a microscopic crack size limit of the material; σe.sub.R is an ordinary fatigue limit of the material; and [0042] (6) formulas (3) and (4) are substituted into formula (2) for integration to obtain a thermal fatigue life calculation model based on crack growth.

[0043] In step (1), a relationship among temperature rise and drop time of the test specimen under different thermal shock conditions, a change in the temperature at the notch of the test specimen, the thermal shock crack length a, and the thermal shock cycle number N is determined by means of carrying out thermal shock tests under different test conditions.

[0044] In step (2), the temperature rise rate to temperature drop rate ratio R.sub.v is calculated according to the temperature at the notch of the test specimen in the thermal shock test process in step (1), and an expression is as follows:

$R_{v} = \frac{v_{H}}{v_{C}}$

[0045] where v.sub.H is a temperature rise rate, and v.sub.c is a temperature drop rate.

[0046] In step (3), in the relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a, the closure stress σc.sub.l, the crack arrest size as of the crack and the depth c of the crack are determined according to the test results in step (1), and expressions of the shape correction factor Q and the boundary condition F are as follows:

$Q = 1 + 1.46 {(\frac{2 c}{a})}^{1.65}$

$F = (1.04 + 0.2 {(\frac{a}{2 t})}^{2} - 0.106 {(\frac{a}{2 t})}^{4}) (1.1 + 0.35 {(\frac{a}{2 t})}^{2})$

[0047] In step (4), the same test conditions are set in the finite element analysis according to a temperature change and thermal shock time of a test area in the thermal shock test process in step (1), so as to ensure that an obtained thermal stress change and temperature change are consistent with those in a real test; transient thermal-mechanical coupling analysis is performed, on the basis of a transient thermal module and a transient structural module in the NASYS software, on the standard fatigue test specimen model used in step (1), thus determining the change in the thermal stress at the notch of the test specimen and the notch stress concentration coefficient k.sub.t; and an expression is as follows:

$k_{t} = \frac{σ_{\max}}{σ_{0}}$

[0048] where σ.sub.max is the maximum stress at a stress concentration portion; and σ.sub.0 is a nominal stress.

[0049] In step (5), in the relationship between the stress intensity factor threshold ΔK.sub.th and the crack length a, the microscopic crack size limit d of the material is obtained according to a grain size of the material or a micro defect size of the material and the ordinary fatigue limit σ.sub.eR of the material through an S-N curve of the material or obtained by carrying out a fatigue test.

[0050] In step (6), the stress intensity factor ΔK in formula (3), the stress intensity factor threshold ΔK.sub.th in formula (4), and the temperature rise rate to temperature drop rate ratio R.sub.v calculated in step (5) are substituted into formula (2) for integration, thus obtaining the thermal shop fatigue life calculation model based on crack growth.

[0051] The present disclosure is further described below in combination with specific embodiments.

Embodiment

[0052] In this embodiment, calculation of a thermal shock fatigue life of a GH4169 high-temperature alloy material is taken as an example, including the following steps:

[0053] Step (1), a thermal shock test was carried out on a standard GH4169 thermal fatigue test specimen at 600° C., 650° C. and 700° C.; the test specimen was ground and polished using sand paper of 2000 meshes respectively when thermal shock cycle numbers are 100, 500, 1000, 2000, 3000, 5000, 7000, and 9000; and a thermal fatigue crack length a was then measured under an optical microscope to obtain a-N curves at different thermal shock temperatures, and the a-N curves were treated to obtain a curve

$\frac{d a}{d N} - a .$

[0054] Step (2), in the thermal shock test process, a change of the temperature at a notch of the test specimen was obtained as shown in FIG. 2; the temperature data in FIG. 2 was processed to obtain a diagram of a temperature rise rate and a temperature drop rate at the notch of the test specimen, as shown in FIG. 3; and a temperature rise rate to temperature drop rate ratio R.sub.v in the thermal shock process was calculated according to formula (5).

[0055] Step (3), the same test conditions were set in the finite element analysis according to a temperature change and thermal shock time of a test area in the thermal shock test process in step (1), so as to ensure that an obtained thermal stress change and temperature change were consistent with those in a real test; transient thermal-mechanical coupling analysis was performed, on the basis of a transient thermal module and a transient structural module in the NASYS software, on the standard fatigue test specimen model used in step (1), thus determining the change in the thermal stress at the notch of the test specimen and the notch stress concentration coefficient k.sub.t.

[0056] Step (4), the thermal shock crack length a, the depth c of the crack, and the width b and thickness t of the thermal shock test specimen which were obtained in step (1) weresubstituted into formulas (6) and (7) to obtain a shape correction factor Q and a boundary condition F.

[0057] Step (5), the thermal stress at the notch of the test specimen and the stress concentration coefficient kt obtained in step (3), the shape correction factor Q and boundary condition F obtained in step (4), and the crack length a measured in step (1) were substituted into formula (3) to obtain a relationship curve between the stress intensity factor ΔK and the crack length a

[0058] Step (6), the microscopic crack size limit d of the material was the grain size of the material, and an ordinary fatigue limit σ.sub.eR was obtained from the S-N curve of the material; and a relationship curve between the stress intensity factor threshold ΔK.sub.th and the crack length a is obtained according to the thermal fatigue crack length a measured in step (1).

[0059] Step (7), the temperature rise rate to temperature drop rate ratio R.sub.v obtained in step (2), the stress intensity factor ΔK obtained in step (5) and the stress intensity factor threshold ΔK.sub.th obtained in step (6) are substituted into formula (2) for integration, thus obtaining a thermal shock fatigue crack life calculation model based on crack growth.

[0060] The above describes only the preferred embodiments of the present disclosure. It should be noted that those of ordinary skill in the art can further make several improvements and retouches without departing from the principles of the present disclosure. These improvements and retouches shall all fall within the protection scope of the present disclosure.

Method for calculating service life of material under action of thermal shock load

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Abstract

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