Crack-tip fields in anisotropic shells

Abstract

Asymptotic crack-tip fields including the effect of transverse shear deformation in an anisotropic shell are presented. The material anisotropy is defined here as a monoclinic material with a plane symmetry at x3 = 0. In general, the shell geometry near the local crack tip region can be considered as a shallow shell. Based on Reissner shallow shell theory, an asymptotic analysis is conducted in this local area. It can be verified that, up to the second order of the crack tip fields in anisotropic shells, the governing equations for bending, transverse shear and membrane deformation are mutually uncoupled. The forms of the solution for the first two terms are identical to those given by respectively the plane stress deformation and the antiplane deformation of anisotropic elasticity. Thus Stroh formalism can be used to characterize the crack tip fields in shells up to the second term and the energy release rate can be expressed in a very compact form in terms of stress intensity factors and Barnett- Lothe tensor L. The first two order terms of the crack-tip stress and displacement fields are derived. Several methods are proposed to determine the stress intensity factors and 'T-stresses'. Three numerical examples of two circular cylindrical panels and a circular cylinder under symmetrical loading have demonstrated the validity of the approach. The application of a fail-safe design philosophy can be greatly enhanced by a thorough under- standing of the resistance of structures and structural materials to failure in the presence of a discontinuity. Shell-like structural components comprise major load-carrying components in aircraft and space vehicles such as aircraft fuselage, reusable launch vehicles, solid propellant rocket motors, and spacecraft use propellant tanks, etc. Depending on their structural details that a variety of failure modes may occur, the failure behavior and resulting residual strength present formidable challenges to the design of these structures and in service structures beyond their original life goal. Motivated by the role of the curvature on the crack tip behavior of shell-like structures, the stress analysis of a crack in isotropic shells based on ordinary linear elastic fracture mechanics has been attracted considerable attention since 1960s. The presence of the curvature causes the coupling between membrane and bending stresses or a combination of in plane and out of plane displacements. Under the small strain and small deformation assumptions, solutions based on linearized classical shell theory can be found (e.g., Folias, 1965, 1967; Copley and Sanders, 1969; Erdogan and Kibler, 1969; Simmonds et al., 1978). Since Kirchhoff assump- tion only enables the satisfaction of two boundary conditions along the crack surfaces, the Kirchhoff boundary condition for transverse shear resultant yields the angular distribution of the leading singular stress term near the crack tip depending on the Poisson's ratio. The