Numerical Investigation on Crack Propagation for a Central Cracked Brazilian Disk Concerning Friction
Abstract
:1. Introduction
2. Integral and Crack Propagation Criteria
2.1. Two-Dimensional Interaction Integral with MFEM
2.2. Criteria for Crack Propagation
3. The WFM Concerning Frictional Contact
4. Results and Discussion
4.1. SIFs and T-Stress Concerning Frictional Contact
4.2. Crack Initiation and Propagation Concerning Frictional Contact
4.2.1. Crack Initiation
4.2.2. Crack Propagation Trajectory
5. Conclusions
- (1)
- The friction has a significant effect on the mode II SIF after the crack is closed, but has no influence on the stress intensity factor of mode I and T-stress. When the crack is closed, the mode II SIF decreases obviously as increasing the friction.
- (2)
- There are significant effects on the crack propagation angle and crack propagation trajectory due to the change of the friction after the crack is closed with the appropriate relative crack length and loading angle.
- (3)
- When T-stress is positive, the influence of friction becomes obvious and the crack propagation angle increases with a lager friction coefficient.
- (4)
- After the crack is closed, as increasing the friction, the amount of the deviation increases and the curvature of the path decreases. Furthermore, the crack type is easier to change with the increase of friction.
- (5)
- The effects of friction on the mode II SIF and the propagation path are more obvious with the larger the relative crack length and loading angle.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
W | interacting strain energy density |
, , | stresses, displacements and strains of the actual fields |
, , | stresses, displacements and strains of the auxiliary fields |
, C, C+, C- | different integral contours |
E*, E | elastic modulus |
v | Poisson’s ratio |
, | stress intensity factors of the auxiliary fields |
, | stress intensity factors of the actual fields |
T-stress | |
P | radial force |
B | thickness of the CCBD |
R | radius of the CCBD |
a | half the length of the crack |
, , | dimensionless forms of stress intensity factors and T-stress |
f | a line load |
polar co-ordinates | |
β | loading angle |
θ0 | crack propagation angle |
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Categories | Values | |
---|---|---|
Geometry characters | R (mm) | 50 |
B (mm) | 30 | |
Material properties | Compressive strength σc (MPa) | 28 |
Tensile strength σt (MPa) | 3.81 | |
Poisson’s ratio v | 0.21 | |
Young’s modulus E (GPa) | 15 |
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Huang, J.; Pan, X.; Li, J.; Dong, S.; Hua, W. Numerical Investigation on Crack Propagation for a Central Cracked Brazilian Disk Concerning Friction. Appl. Sci. 2021, 11, 2839. https://doi.org/10.3390/app11062839
Huang J, Pan X, Li J, Dong S, Hua W. Numerical Investigation on Crack Propagation for a Central Cracked Brazilian Disk Concerning Friction. Applied Sciences. 2021; 11(6):2839. https://doi.org/10.3390/app11062839
Chicago/Turabian StyleHuang, Jiuzhou, Xin Pan, Jianxiong Li, Shiming Dong, and Wen Hua. 2021. "Numerical Investigation on Crack Propagation for a Central Cracked Brazilian Disk Concerning Friction" Applied Sciences 11, no. 6: 2839. https://doi.org/10.3390/app11062839
APA StyleHuang, J., Pan, X., Li, J., Dong, S., & Hua, W. (2021). Numerical Investigation on Crack Propagation for a Central Cracked Brazilian Disk Concerning Friction. Applied Sciences, 11(6), 2839. https://doi.org/10.3390/app11062839