Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

Abstract

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( : a ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar : a -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

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

“…However, the nonhomogeneity and transient specific parts of the higher order terms, that have A 0 , B 0 , C 0 and D 0 as the coefficients, are retained. The typical values of material properties and material thickness used in generating contours are as follows: Poisson's ratio = 0.3, shear modulus at the crack tip µ c = 1.5 GPa, density at the crack tip ρ c = 1200 kg/m 3 , and thickness t = 0.01 m. The nonhomogeneity parameter α for plotting these contours is obtained by fitting an exponential curve to the property variation profile of the laboratory-fabricated FGMs [Jain and Shukla 2006]. The nonhomogeneity parameter α for FGM fabricated in this study is 0.57.…”

“…The crack velocity used in generating all the contours is 650 ms −1 . This choice of velocity is made on the basis of available experimental data on velocities that are typically observed for this FGM [Jain and Shukla 2006].…”

“…Although the stationary crack problem in FGMs has received considerable attention, less is known about the behavior of a rapidly propagating crack in these materials. The problem of a crack moving with a constant velocity in FGMs has been presented by [Atkinson and List 1978;Wang and Meguid 1994;Nakagaki et al 1998;Parameswaran and Shukla 1998;Marur and Tippur 2000;Rousseau and Tippur 2001;Li and Weng 2002;Jain and Shukla 2006]. Recently, there has been some work on the fracture mechanics of anisotropic functionally graded materials.…”

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

“…Shukla and Jain [36,37] have studied experimentally the crack propagation in a FG elastic plate with material properties varying only in the anticipated horizontal direction of crack propagation as shown in Fig. 22.…”

“…Variations of the mass density, the shear modulus, and the static SIF (SSIF), K, along the x-direction obtained by fitting curves by the least squares method to the test data given in Jain and Shukla's paper [37] are given by The Poisson ratio ν = 0.34 is taken to be a constant.…”