An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature
Abstract
:1. Introduction
2. Theory and Methods
3. The Finite Element Model
3.1. Geometry Model
3.2. Material Properties
3.3. The Finite Element Model
4. Results
4.1. Equivalent Plastic Strain and its Gradient
4.2. Characterization of Composite Constraint
4.3. Correlation of Dp between Composite Constraint
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
a | Crack length |
APEEQ | Area surrounded by the equivalent plastic strain isoline |
Ap | A new constraint parameter |
A2 | A constraint parameter |
B | Specimen thickness |
DP | Normalized parameter of the equivalent plastic strain gradient |
DPEEQ | Equivalent plastic strain gradient |
Dref | Average gradient of equivalent plastic strain at r0 of a reference standard specimen |
E | Young’s modulus |
F | Faraday’s constant |
h | Stress triaxiality |
J | J integral |
Jc | Average of calculated J integrals |
Jref | Average of calculated J integrals for a reference standard specimen |
KJc | Measured fracture toughness |
Kref | Fracture toughness of a reference standard specimen |
Mmol | Molecular weight of the metal atomic |
m | Oxidation current decay curve |
N | Hardening exponent in the Ramberg–Osgood equation |
Q | A constraint parameter |
r | Distance along the crack front |
r0 | Characteristic distance |
Tt | Test temperature |
Tstress | Intensity of the crack tip’s stress field |
Time before the current decay onset | |
W | Specimen width |
z | Thickness coordinate at the crack front |
zc | Charge change caused by oxidation process |
α | Offset coefficient of the material |
σ0 | Yield stress |
dεp/dr | Equivalent plastic strain gradient at a fixed distance ahead of the crack tip |
ε0 | Yield strain |
εf | Oxide film’s degradation strain |
Strain rate at a fixed distance ahead of the crack tip | |
εp | Equivalent plastic strain |
Constant of oxidation rate | |
ρ | Density of the metal |
ν | Poisson’s ratio |
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Name | Type | Tt (°C) | Number | W (mm) | B (mm) | a/W |
---|---|---|---|---|---|---|
C(T)25 | C(T) | −60 | 10 | 50 | 25 | 0.5162 |
C(T)50 | C(T) | −60 | 5 | 100 | 50 | 0.5104 |
SE(B)10 × 10d | SE(B) | −67/−70 | 15 | 10 | 10 | 0.5245 |
Young’s Modulus E (MPa) | Poison’s Ratio ν | Yield Stress σ0 (MPa) | Hardening Exponent n | Offset Coefficient α |
---|---|---|---|---|
215 000 | 0.3 | 517 | 3.7 | 6.2 |
Specimen Types | KJc (MPa m1/2) | Jc (kJ/m2) | DPEEQ | Dp |
---|---|---|---|---|
C(T)25 | 68.5 | 19.86022 | 0.02210 | 0.67100 |
74.4 | 23.42873 | 0.02451 | 0.74417 | |
75.2 | 23.93529 | 0.02484 | 0.75419 | |
84.2 | 30.00731 | 0.02877 | 0.87351 | |
93.1 | 36.68616 | 0.03287 | 0.99800 | |
93.9 | 37.31935 | 0.03325 | 1.00953 | |
94.8 | 38.03817 | 0.03367 | 1.02229 | |
99.7 | 42.07201 | 0.03601 | 1.09333 | |
102 | 44.03553 | 0.03711 | 1.12673 | |
105 | 46.66395 | 0.03856 | 1.17076 | |
C(T)50 | 81.6 | 28.18274 | 0.02600 | 0.78941 |
91.2 | 35.20405 | 0.03009 | 0.91359 | |
101.6 | 43.69084 | 0.03447 | 1.04658 | |
105.8 | 47.37773 | 0.03617 | 1.09819 | |
109.3 | 50.56421 | 0.03755 | 1.14009 | |
SE(B)10 × 10d | 79.9 | 27.02069 | 0.02685 | 0.81522 |
83.7 | 29.65199 | 0.02839 | 0.86197 | |
98.5 | 41.06534 | 0.03489 | 1.05963 | |
101.1 | 43.26187 | 0.03612 | 1.09667 | |
105.7 | 47.28821 | 0.03832 | 1.16347 | |
105.9 | 47.46734 | 0.03841 | 1.16620 | |
120.4 | 61.35584 | 0.04571 | 1.38784 | |
120.5 | 61.4578 | 0.04576 | 1.38936 | |
123.4 | 64.45153 | 0.04727 | 1.43521 | |
131.4 | 73.07918 | 0.05151 | 1.56394 | |
132.7 | 74.53234 | 0.05221 | 1.58519 | |
133.5 | 75.43371 | 0.05264 | 1.59825 | |
141.0 | 84.14749 | 0.05669 | 1.72152 | |
143.5 | 87.1579 | 0.05806 | 1.76281 | |
159.6 | 107.8124 | 0.06681 | 2.02848 |
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Zhao, L.; Shi, Z.; Wang, Z.; Yang, F. An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature. Materials 2022, 15, 881. https://doi.org/10.3390/ma15030881
Zhao L, Shi Z, Wang Z, Yang F. An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature. Materials. 2022; 15(3):881. https://doi.org/10.3390/ma15030881
Chicago/Turabian StyleZhao, Lingyan, Zheren Shi, Zheng Wang, and Fuqiang Yang. 2022. "An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature" Materials 15, no. 3: 881. https://doi.org/10.3390/ma15030881
APA StyleZhao, L., Shi, Z., Wang, Z., & Yang, F. (2022). An Investigation of a New Parameter Based on the Plastic Strain Gradient to Characterize Composite Constraint around the Crack Front at a Low Temperature. Materials, 15(3), 881. https://doi.org/10.3390/ma15030881