A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

Abstract

This study aimed to develop a method to build a 'bridge' between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

Thermal wave: from nonlocal continuum to molecular dynamics

“…Thanking to the gradation of microstructure morphology, porosity, and chemical/material ingredients in functionally graded materials (FGMs), FGMs have a unique potential as materials resistant to the contact damage, cracking, deection, thermal stresses, and heat ow. [69][70][71][72][73][74][75] FGMs also enable the engineering of advanced materials with tuned multiphysics properties to satisfy mechanical, hygrothermal, electrical, and biological requirements for a wide range of applications in thermal barriers, bone tissues and implants, and thermoelectric generators and energy harvesters. Advances in powder metallurgy, 76 laser cutting, 57 and additive manufacturing/3D printing 77 have also facilitated the arbitrary variation of material gradient and micro-architecture of functionally graded solid and porous materials in order to reach optimum multiphysical properties.…”

Thermal fracture model for a functionally graded material with general thermomechanical properties and collinear cracks

“…But the real material properties may be not approached accurately by such homogeneous multilayered method. Some nonhomogeneous multilayered methods can be found in other signi cant researches [3,18,22,[26][27][28][29]. Of them, the piecewise exponential model (PE model) proposed by Guo et al [3], Guo and Noda [26], and Bai et al [27] was perfectly applied to solve the crack problem of FGMs with general properties.…”

“…Since the PE model is based on the analytical model of a single layer with exponential properties, many analytical models published in the past decades on the crack problems of FGMs assuming exponential properties can be uni ed with the concept of the PE model as they form a strong base for establishing a general analytical model for FGMs. Then, the PE model was expanded to the crack problems of FGMs with stochastic properties [28] and mixed mode crack problems [29]. However, the PE method for FGMs with general thermomechanical properties and collinear cracks has not been studied previously.…”

An analytical model for collinear cracks in functionally graded materials with general mechanical properties

“…Following this work, Guo and Noda [15] proposed an analytical thought combining the piecewise-exponential model and a perturbation method to investigate the thermal shock crack problems of FGMs with general thermomechanical properties. Guo et al [16] developed an analytical fracture mechanics model to predict the stress intensity factors in FGMs with stochastic uncertainties in phase volume fractions. Wang et al [17] considered the anti-plane crack problem in a functionally graded material strip.…”