Energy perturbation finite element technique for damage tolerant design applications

Abstract

The application of the energy perturbation concept to damage tolerant design guidance, from the stress analyst's viewpoint, is provided in this paper. This application is accomplished by taking the physical interpretation of the explicit Bueckner's weight functions, h I( II) i j , for a crack and the explicit Green's functions, g ti j for a traction-free notch at i' s location with respect to j' s nodal perturbation location as the quantified attribution to the stress intensity factors ( K I( II) and to the tangential notch stress ( σ t ), respectively, with the unit traction application at the very same i' s nodal location. The use of the energy perturbation method for efficient finite element evaluations of the explicit weight functions for the entire structure of interest has been established by coupling the virtual crack extension technique with the singular elements. The extension from two dimensional (2-D) cracks to 2-D notches for the explicit Green's function evaluations with the energy perturbation concept will be discussed in this paper. Both the explicit weight functions for the cracks and the explicit Green's functions for the notches are independent of loading conditions for a given geometry but depend heavily on both geometry and constraint conditions. The method of obtaining the required stress intensity factor and the desired tangential notch stress of a given crack and notch geometry respectively for the specific constraint conditions, which are different from that of available explicit weight/Green's functions for the same geometry, is presented in this paper. This method is accomplished by combining either the predetermined explicit weight functions for the stress intensity factor calculations or the explicit Green's functions for the tangential notch stress evaluations with the self-equilibrium forces, which include not only the applied surface tractions but also the reaction forces that are induced by constraints at their application locations. The numerical examples shown in this paper are confined primarily to the simple 2-D crack/notch geometries for the illustration conveniences on using the energy perturbation technique for damage tolerant design applications. Since the explicit weight/Green's function evaluation for the entire structure of interest is based on the energy perturbation concept of finite element framework, the value of the proposed technique is its flexibility in applying the intended methodology to complex geometry and loading conditions for damage tolerant design applications.