This paper presents two micromechanical models to study the statistics of the local stress intensity factor of a cracked polycrystalline plate. The first is a finite element model based Monte Carlo procedure where the plate’s microstructure, which includes a finite number of crystals (or grains) separated by a finite thickness interphase, is approximated as a Poisson-Voronoi tessellation (Fig. 1). The statistics of the effective elastic moduli of the uncracked plate are calculated as well as the local stress intensity factors of the corresponding cracked plate (Fig. 2). This is done for selected values of the parameters that quantify the ratio of elastic mismatch between the crystals and the grain boundaries, and the expected number of grains in the plate. The results indicate that the average values and standard deviations of the local stress intensity factors are independent of the number of grains in the plate. The results of the Monte Carlo model suggest that the crack tip parameters of cracked polycrystalline plates could be calculated using an efficient alternative analytical model involving a long crack penetrating a circular inhomogeneity (Fig. 3). This problem is solved using the method of continuously distributed dislocations and by expressing the traction-free condition along the crack surfaces as a system of singular integral equations, which are solved numerically. The results demonstrate that as long as the elastic mismatch between the inhomogeneity and the surrounding material is interpreted correctly, then the approximate analytical model is associated with averaged stress intensity factors that are in excellent agreement with those of the polycrystalline microstructure. An attempt is made to apply the developed models to interpret experimental data obtained from warm lake ice. It is concluded that proper interpretation of data obtained from polycrystalline plates with compliant grain boundaries necessitates stress analyses that incorporate explicitly the stochastic microstructure.
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- Crack-Tip Parameters in Polycrystalline Plates with Compliant Grain Boundaries
- Springer Netherlands
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