Dynamic response of interfacial finite cracks in orthotropic materials subjected to concentrated loads |
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Authors: | C Rubio-Gonzalez E Lira-Vergara |
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Affiliation: | (1) Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140, USA;(2) Vehicle Design and R&A Department, Ford Motor Company, Dearborn, MI 48121, USA; |
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Abstract: | A cohesive zone model has been proposed to model crack growth with a part-through process zone in a thin solid. With the solid
being modeled in Kirchhoff’s plate theory, the crack with a relatively long, inclined front is modeled as a line discontinuity
with a finite cohesive zone within the plate. A cohesive force law is adopted to capture the effect of residual strength and
residual rigidity of a plate cross-section gradually cracking through the thickness. It is derived by a plane-strain elasticity
analysis of a cross section normal to the part-through crack. It is then applied in the plate formulation of a line crack
to simulate its propagation within the plate plane. This model essentially resolves the originally three-dimensional crack
problem in two hierarchical steps, i.e., in the thickness and in the in-plane directions. In the present study, the bending
case is considered. A boundary element method is applied to numerically derive the cohesive force law and simulate the crack
growth in a thin titanium-alloy plate. The computational efficiency of the model is demonstrated. The plate is shown to fracture
in a nominally brittle or ductile manner depending on its thickness. |
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