Asymptotic analysis and reflection photoelasticity for the study of transient crack propagation in graded materials

Abstract

The behavior of a rapidly moving transient crack in functionally graded materials (FGMs) is investigated theoretically and experimentally. First, a systematic theoretical analysis is presented for the development of the transient elastodynamic local stress, strain, and displacement field expansions near a growing mixed mode crack tip in FGMs. The crack propagation direction is assumed to be inclined to the direction of the property variation. The displacement potential approach in conjunction with asymptotic analysis is utilized to derive explicit expressions for stress, strain, and in-plane displacement fields. The transient crack growth is assumed to include processes in which both the crack tip speed and the dynamic stress intensity factor are differentiable functions of time. These stress fields are used to generate the contours of constant maximum shear stress (isochromatics fringes) and the effect of transient crack growth on these contours is discussed. To further understand the transient crack growth behavior, a series of dynamic fracture experiments are performed with functionally graded material fabricated inhouse. The phenomenon of transition from a static crack to a dynamic mode I crack is examined in these experiments. The full-field stress data around the crack is recorded using dynamic photoelasticity and high-speed digital photography. Due to opaqueness of FGMs, birefringent coatings are employed to obtain the full-field isochromatics around the crack tip. The stress field expansions developed in the first part of the study are used to interpret the experimental observations. The results of the experiments showed that the higher order transient expansion provides an accurate representation of crack tip fields under severe transient conditions.

A Review of Dynamic Fracture Studies in Functionally Graded Materials

“…Recently, Chalivendra and Shukla [15] and Chalivendra [16] developed the transient crack‐tip field expansions for straight and curved cracks propagating in an FGM. Most recently, Jain and Shukla investigated the transient behaviour of mixed‐mode cracks in FGMs, both analytically and experimentally [17].…”

Analysis and finite element simulations of the near-tip singular fields around a mode-3 stationary crack in plastically graded materials

“…Neartip fields were obtained recently by Chalivendra (2008Chalivendra ( , 2009) for stationary cracks embedded in inhomogeneous orthotropic medium under mode-1 loading and mixed-mode loading, respectively. Fracture analysis and experiments in inhomogeneous materials considering the dynamic effects (inertial effects of the medium) assuming linear elastic response of the medium have also received recent attention (Chalivendra, 2007;Jain and Shukla, 2007;Kulkarni et al, 2007;Kubair and Bhanu-Chandar, 2007;Lee et al, 2008;Kirugulige and Tippur, 2008;Kubair and Lakshmana, 2008;Shukla, 2008, 2010).…”