NONLINEAR FRACTURE MECHANICS THE （非线性断裂力学）.pdf

NONLINEAR FRACTURE MECHANICS THE COHESIVE CRACK MODEL (Dugdale, D.S.: Yielding of steel sheets containing slits, J. Mechanics Physics Solids 8 (1960), 100-104 Barenblatt, G.I.: The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks, J. Applied Mathematics and Mechanics 23 (1959), 622-636. Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture, in H.L. Dryden and T. von Karman (eds.), Advanced in Applied Mechanics, Academic Press, New York, 1962, pp. 55-129.) ductile materials ⇒ Dugdale’s model purely brittle materials ⇒ Barenblatt’s model quasi brittle materials ⇒ Hillerborg’s Fictitious (e.g. concrete) Crack Model brittle matrix composites ⇒ Bridged crack model quasi brittle matrix composites ⇒ Cohesive crack model cohesive crack model 1 Dugdale’s Model for ductile fracture Fracture of elasto-plastic materials Assumptions: - Mode I crack in an infinite sheet under uniform tensile stress - the material is ductile and the plastic deformations localized in a thin zone coplanar with the crack - the plastic zone is modeled through a fictitious crack (of unknown length) and a uniform distribution of cohesive tractions σP = yield stress Length of the cohesive zone The length of the cohesive zone aP is calculated by imposing the condition of smooth closure of the crack faces: KI KIσ + KIσ P 0 where: KIσ σ π (a + aP ) cohesive crack model 2 The SIF due to the plastic stresses is calculated using the SIFs d