TY - JOUR
T1 - Analytical and numerical evaluation of crack-tip plasticity of an axisymmetrically loaded penny-shaped crack
AU - Chaiyat, Sumitra
AU - Jin, Xiaoqing
AU - Keer, Leon M.
AU - Kiattikomol, Kraiwood
N1 - Funding Information:
This work was supported by the Center for Surface Engineering and Technology at Northwestern University. The financial support from Thai government to S. Chaiyat through the King Mongkut’s institute of Technology north Bangkok is highly appreciated. The authors would like to thank Dr. Eugene L. Chez for valuable discussions.
PY - 2008/1
Y1 - 2008/1
N2 - Analytical and numerical approaches are used to solve an axisymmetric crack problem with a refined Barenblatt-Dugdale approach. The analytical method utilizes potential theory in classical linear elasticity, where a suitable potential is selected for the treatment of the mixed boundary problem. The closed-form solution for the problem with constant pressure applied near the tip of a penny-shaped crack is studied to illustrate the methodology of the analysis and also to provide a fundamental solution for the numerical approach. Taking advantage of the superposition principle, an exact solution is derived to predict the extent of the plastic zone where a Tresca yield condition is imposed, which also provides a useful benchmark for the numerical study presented in the second part. For an axisymmetric crack, the numerical discretization is required only in the radial direction, which renders the programming work efficient. Through an iterative scheme, the numerical method is able to determine the size of the crack tip plasticity, which is governed by the nonlinear von Mises criterion. The relationships between the applied load and the length of the plastic zone are compared for three different yielding conditions. To cite this article: S. Chaiyat et al., C. R. Mecanique 336 (2008).
AB - Analytical and numerical approaches are used to solve an axisymmetric crack problem with a refined Barenblatt-Dugdale approach. The analytical method utilizes potential theory in classical linear elasticity, where a suitable potential is selected for the treatment of the mixed boundary problem. The closed-form solution for the problem with constant pressure applied near the tip of a penny-shaped crack is studied to illustrate the methodology of the analysis and also to provide a fundamental solution for the numerical approach. Taking advantage of the superposition principle, an exact solution is derived to predict the extent of the plastic zone where a Tresca yield condition is imposed, which also provides a useful benchmark for the numerical study presented in the second part. For an axisymmetric crack, the numerical discretization is required only in the radial direction, which renders the programming work efficient. Through an iterative scheme, the numerical method is able to determine the size of the crack tip plasticity, which is governed by the nonlinear von Mises criterion. The relationships between the applied load and the length of the plastic zone are compared for three different yielding conditions. To cite this article: S. Chaiyat et al., C. R. Mecanique 336 (2008).
KW - Crack tip plasticity
KW - Dugdale approach
KW - Penny-shaped crack
KW - Tresca criterion
KW - Von Mises criterion
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U2 - 10.1016/j.crme.2007.10.015
DO - 10.1016/j.crme.2007.10.015
M3 - Short survey
AN - SCOPUS:38949192150
SN - 1631-0721
VL - 336
SP - 54
EP - 68
JO - Comptes Rendus - Mecanique
JF - Comptes Rendus - Mecanique
IS - 1-2
ER -