Effect of material nonhomogeneities on the HRR dominance |
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Authors: | Z. -H. Jin |
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Affiliation: | School of Aeronautics and Astronautics, Purdue University, 1282 Grissom Hall, West Lafayette, IN 47907-1282, USA |
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Abstract: | This work studies the asymptotic stress and displacement fields near the tip of a stationary crack in an elastic–plastic nonhomogeneous material with the emphasis on the effect of material nonhomogeneities on the dominance of the crack tip field. While the HRR singular field still prevails near the crack tip if the material properties are continuous and piecewise continuously differentiable, a simple asymptotic analysis shows that the size of the HRR dominance zone decreases with increasing magnitude of material property gradients. The HRR field dominates at points that satisfy |α−1 ∂α/∂xδ|1/r, |α−1 ∂2α/(∂xδ ∂xγ)|1/r2, |n−1 ∂n/∂xδ|1/[r|ln(r/A)|] and |n−1 ∂2n/(∂xδ ∂xγ)|1/[r2|ln(r/A)|], in addition to other general requirements for asymptotic solutions, where α is a material property in the Ramberg–Osgood model, n is the strain hardening exponent, r is the distance from the crack tip, xδ are Cartesian coordinates, and A is a length parameter. For linear hardening materials, the crack tip field dominates at points that satisfy |Etan−1 ∂Etan/∂xδ|1/r, |Etan−1 ∂2Etan/(∂xδ ∂xγ)|1/r2, |E−1 ∂E/∂xδ|1/r, and |E−1 ∂2E/(∂xδ ∂xγ)|1/r2, where Etan is the tangent modulus and E is Young’s modulus. |
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Keywords: | Nonhomogeneous material Functionally graded material Plasticity Crack tip field HRR-dominance |
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