Failure initiation sites and instability of structural components with localized energy density

Abstract

When the surface or interior of a solid undergoes curvature and/or material change, there results localized fluctuation of the energy density field depending on the type of loading. These fluctuations are related to changes in the distortion and dilatation of material elements that could lead to failure by yielding and/or fracture should their magnitude become sufficiently large. According to the strain energy density criterion, failure is assumed to initiate at site of local maximum of minimum strain energy density denoted by [( dW/ dV) min max ] L and tends toward the global maximum of [( dW/ dV) min max ] G . The distance l between these two stationary values of dW/ dV at L and G provides an indication of failure instability. That is, large l corresponds to more wide spread failure while the opposite holds for small l. Specimens with three different geometries are analyzed; they consist of round shoulder, hole and edge notch. The loads are either bending or tension. As the severity of notch or hole curvature is varied, predicted failure path also altered from boundary to boundary or an interior point of the specimen. The narrowest section turns out to be most vulnerable. If the hole is filled with a material of higher modulus, it acts as a reinforcer such that failure site would be shifted away from the interface. In general, there prevails a trade off between l and [( dW/ dV) min max ] L . The undesirable combination would be for l and [( dW/ dV) min max ] L to increase simultaneously. Failure initiation and global instability would then likely occur in tandem. This corresponds to the bending of a specimen with round shoulders. A variety of other conditions are analyzed with results displayed graphically so that the ways with which load, geometry and material inhomogeneity affect the failure behavior of structural components with notches and holes could be better understood.