Aspect Ratio Evolution in Embedded, Surface, and Corner Cracks in Finite-Thickness Plates under Tensile Fatigue Loading
Abstract
:1. Introduction
2. Numerical Modelling
2.1. Stress Intensity Factor (SIF)
- For ,
- For ,
2.2. Crack Front Evolution
3. Numerical Results
4. Discussion
5. Conclusions
- (i)
- Those paths associated with embedded cracks exhibit aspect ratios higher than 1 and increase with the crack depth, while they are lower than 1 and diminish with the crack depth in the case of surface and corner cracks.
- (ii)
- Any increase of the Paris exponent of the material leads to a decrease of the aspect ratio in the case of surface and corner cracks and, on the other hand, to an increase of it in the case of embedded flaws.
- (iii)
- Both the crack propagation rate and the maximum stress intensity factor (SIF) are higher for the case of corner cracks than for surface ones, and higher for the latter than for the embedded defects.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
a | crack depth |
a0 | initial crack depth |
af | final crack depth |
a/b | crack aspect ratio |
(a/b)0 | initial crack aspect ratio |
a/t | relative crack depth |
(a/t)0 | initial relative crack depth |
Δai | crack advance at the point i |
Δa(max) | maximum crack advance in the iterations |
b | second dimension of the crack (modeled as an ellipse) |
C | Paris constant |
da/dN | crack growth rate |
F | parameter to obtain K |
Fi | parameter F to obtain K at the point i |
F(max) | maximum parameter F over the crack front |
ϕ | angle characterizing a point at the crack front |
K | stress intensity factor (SIF) |
ΔK | stress intensity factor range |
m | Paris exponent |
n | dimensionless number of cycles required for fatigue crack propagation |
N | number of cycles required for fatigue crack propagation |
p | point over the crack front |
Q | shape factor |
σ | remote tensile stress |
Δσ | remote tensile stress range |
t | plate thickness |
w | plate width |
z | number of parts in which each ellipse (crack front) is divided |
Appendix A
- fϕ is given by Equation (A5).
- fϕ is given by Equation (A5).
- M2, M3, and g are given by Equations (A2)–(A4).
- fϕ is given by Equation (A17).
- g and fϕ are given by Equations (A13) and (A17).
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Parameters | Configuration | ||
---|---|---|---|
Embedded Crack | Surface Crack | Corner Crack | |
a/b | 0 to ∞ | 0 to 2 | 0.2 to 2 |
a/t | <1.25 (a/b + 0.6) if 0 ≤ a/b ≤ 0.2 <1 if a/b > 0.2 | <1 | |
ϕ | −π to π | 0 to π | 0 to π/2 |
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Toribio, J.; Matos, J.-C.; González, B. Aspect Ratio Evolution in Embedded, Surface, and Corner Cracks in Finite-Thickness Plates under Tensile Fatigue Loading. Appl. Sci. 2017, 7, 746. https://doi.org/10.3390/app7070746
Toribio J, Matos J-C, González B. Aspect Ratio Evolution in Embedded, Surface, and Corner Cracks in Finite-Thickness Plates under Tensile Fatigue Loading. Applied Sciences. 2017; 7(7):746. https://doi.org/10.3390/app7070746
Chicago/Turabian StyleToribio, Jesús, Juan-Carlos Matos, and Beatriz González. 2017. "Aspect Ratio Evolution in Embedded, Surface, and Corner Cracks in Finite-Thickness Plates under Tensile Fatigue Loading" Applied Sciences 7, no. 7: 746. https://doi.org/10.3390/app7070746