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Constraint effects on crack-tip fields in elastic-perfectly plastic materials. (English) Zbl 0997.74052

The authors consider a stationary crack in the constitutive framework of Prandtl-Reuss elasto-perfect plastic materials, with von Mises yield condition, under plane strain state. Motivated by numerical calculations performed by different authors, the material is assumed to be incompressible, and all stress components are non-singular functions depending on the polar angle, but not on the distance from crack tip. The asymptotic solutions of the governing differential equations and plastic sectors depend on the polar angle. The authors require the continuity of all components, and formulate appropriate boundary conditions on the crack plane for problems under I, II and mixed-mode loadings. Two constraint parameters to quantify the constraint level are put into evidence. The angular variations of stress components found in the paper are comapared with finite element results and with other solutions existing in the literature.

MSC:

74R20 Anelastic fracture and damage
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74G70 Stress concentrations, singularities in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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