Abstract
This paper deals with an infinite slab with a semi-infinite crack, which is subjected to the anti-plane sheark III field at infinity. The slab is made of an elasto-damaged material. Analytical solution is obtained by use of conformal mapping. The shape of damaged-zone, the dissipative energy, the shear opening displacement on the crack surface and several stress distribution curves are given. The far field condition is checked, The asymptotic behavior near the crack-tip is given.
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Abbreviations
- k III :
-
Mode-III stress intensity factor
- \(\tilde G\) :
-
elastic shear modulus
- \(\tilde \tau _D \) :
-
the damaged shear stress of material
- \(\{ \tilde x,\tilde y\} \) :
-
Cartesian coordinates with origin at the crack-tip
- \(\{ x,y\} = \{ \tilde x,\tilde y\} /\frac{{k_{III}^2 }}{{\tilde G\tilde \tau _D }}\) :
-
non-dimensional coordinates
- \(\frac{z}{z}\begin{array}{*{20}c} { = x + iy = re^{i\theta } } \\ { = x - iy = re^{ - i\theta } } \\ \end{array} \) :
-
non-dimensional complex variable in the physical-plane
- \(\{ \tilde \tau _x ,\tilde \tau _y \} \) :
-
the components of shear stress
- \(\{ \tau _x ,\tau _y \} = \{ \tilde \tau _x ,\tilde \tau _y \} /\tilde G\) :
-
non-dimensional shear stress components
- \(\tilde \tau = \frac{1}{2}(\tilde \tau _x^2 + \tilde \tau _y^2 )^{1/2} \) :
-
resultant shear stress
- \(\tau = \tilde \tau /\tilde G\) :
-
non-dimensional resultant shear stress
- \(\tilde w\) :
-
out-plane displacement
- \(w = \tilde w/\frac{{k_{III}^2 }}{{\tilde G\tilde \tau _D }}\) :
-
non-dimensional out-plane displacement
References
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The project supported by National Natural Science Foundation of China
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Tianhu, H., Xiaoti, Z. & Kehchih, H. The anti-plane shear field in an infinite slab of elasto-damaged material with a semi-infinite crack. Acta Mech Sinica 7, 351–359 (1991). https://doi.org/10.1007/BF02486744
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DOI: https://doi.org/10.1007/BF02486744