Mechanics of crack propagation in materials with initial (residual) stresses (review) |
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Authors: | A N Guz |
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Institution: | 1.S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine,Kyiv,Ukraine |
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Abstract: | Major results on the mechanics of crack propagation in materials with initial (residual) stresses are analyzed. The case of
straight cracks of constant width that propagate at a constant speed in a material with initial (residual) stresses acting
along the cracks is examined. The results were obtained, based on linearized solid mechanics, in a universal form for isotropic
and orthotropic, compressible and incompressible elastic materials with an arbitrary elastic potential in the cases of finite
(large) and small initial strains. The stresses and displacements in the linearized theory are expressed in terms of analytical
functions of complex variables when solving dynamic plane and antiplane problems. These complex variables depend on the crack
propagation rate and the material properties. The exact solutions analyzed were obtained for growing (mode I, II, III) cracks
and the case of wedging by using methods of complex variable theory, such as Riemann–Hilbert problem methods and the Keldysh–Sedov
formula. As the initial (residual) stresses tend to zero, these exact solutions of linearized solid mechanics transform into
the respective exact solutions of classical linear solid mechanics based on the Muskhelishvili, Lekhnitskii, and Galin complex
representations. New mechanical effects in the dynamic problems under consideration are analyzed. The influence of initial
(residual) stresses and crack propagation rate is established. In addition, the following two related problems are briefly
analyzed within the framework of linearized solid mechanics: growing cracks at the interface of two materials with initial
(residual) stresses and brittle fracture under compression along cracks |
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