Investigation of the large deformations of composite plane with interface crack loaded by uniform pressure
DOI:
https://doi.org/10.21638/11701/spbu01.2020.114Abstract
The analytical solution to a nonlinear problem of elasticity for the composite plane formed by connection of two half-planes from different materials with an interface crack is obtained. The elastic properties of half-planes are modeled by semi-linear harmonic material. External loading is uniform pressure, which is orthogonal to the deformed surfaces of a crack coasts, the stresses at infinity are absent. For the solution to a nonlinear plane problem methods of the theory of the complex variable functions are used. An existence of critical values of pressure at the coasts of a crack which excess conducts to loss of stability of a material and to large post-critical displacements, deformations and stresses in a vicinity of a crack is established. The critical pressures have the order of the shear modules of the materials and are really possible for low-modules rubber-like materials (elastomers). For the rigid materials with the large module of shear, in particular metals, the critical pressures really are not achieved. The formulas for disclosing of the crack coasts depending on value of pressure and parameters of materials are obtained, the plots of displacements of the crack surfaces for different values of pressure are presented. On the base of a common solution the asymptotic expansions are constructed for nominal (Piola) and Cauchy stresses in vicinities of a crack ends. The nominal stresses have the root singularities, the Cauchy stresses have no singularities at the tips of crack.
Keywords:
nonlinear plane problem, composite plane, interface crack, semi-linear material, complex-variable methods
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