The effects of heterogeneity and anisotropy on the size effect in cracked polycrystalline films (original) (raw)

Crack-tip parameters in polycrystalline plates with soft grain boundaries

2008

Two micromechanical models are used to calculate the statistical distributions of the stress intensity factor of a crack in a polycrystalline plate containing stiff grains and soft grain boundaries. The first is a finite-element method based Monte Carlo procedure where the microstructure is represented by a Poisson-Voronoi tessellation. The effective elastic moduli of the uncracked plate and the stress intensity factor of the cracked plate are calculated for selected values of the parameters that quantify the level of elastic mismatch between the grains and grain boundaries. It is shown that the stress intensity factor is independent of the expected number of grains, and that it can be estimated using an analytical model involving a long crack whose tip is contained within a circular inhomogeneity surrounded by an infinitely extended homogenized material. The stress intensity factor distributions of this auxiliary problem, obtained using the method of continuously distributed dislocations, are in excellent agreement with those corresponding to the polycrystalline microstructure, and are very sensitive to the position within the inhomogeneity of the crack tip. These results suggest that fracture toughness experiments on polycrystalline plates can be considered experiments on the single grain containing the crack tip, and in turn reflect the a / w effects typical of finite-geometry specimens.

Stress intensity factors of microstructurally small crack

International Journal of Fracture, 2000

The stress intensity factor (SIF) is widely used for evaluating integrity of cracked components. Averaging the anisotropy of each crystal, the macroscopic behavior of polycrystalline materials is isotropic and homogenous in terms of elastic deformation. However, the anisotropic and/or inhomogeneous property influences on the stress field around a crack if the crack size is small in comparison with the grain. Thus, the SIF of the microstructurally small crack may differ from that in the isotropic body. In present study, the effect of anisotropic/inhomogeneous elasticity on the SIF is investigated by using the finite element analysis (FEA). At first, the SIFs of semi-circular crack in a single crystal and a polycrystalline material are calculated. These reveal that the magnitude of SIF is dependent not only on the crystal orientation but also on the deformation constraint by the neighboring crystals. Then, the statistical scatter of SIF due to the random orientation of crystal orientation in a polycrystal is examined by a Monte Carlo simulation.

Influence of Crystal Grain on Stress Intensity Factor of Microstructurally Small Cracks

Journal of Solid Mechanics and Materials Engineering, 2007

If crack size is in the order of several grain diameters or smaller, the stress intensity factor (SIF), which brings about change in crack growth behavior, is affected by various factors caused by the grain. For example, kinks and bifurcations of cracks at grain boundary triple points vary the SIF when the crack runs along grain boundaries. The elastic anisotropy of crystals and inhomogeneous stress distribution at the microstructural level in a polycrystalline body also bring about changes in the SIF. In this paper, such influences of the crystal grain on the SIF are reviewed. Firstly, the SIF of kinked or branched cracks is outlined. Secondly, the SIF of cracks in an anisotropic body as well as inhomogeneous polycrystalline body is summarized. In particular, statistical changes in SIF are shown as a function of crack size. Finally, based on the results obtained, statistical changes in the SIF and their influence on the growth of the microstructurally-small-crack are discussed.

Crack tip stress fields and dislocation nucleation in anisotropic materials

Scripta Metallurgica, 1988

lntroduction Dislocation emission from the tip of a propagating crack has been shown to be an important factor in determining the fracture toughness and ductile to brittle transition temperature (DBTF) of many crystalline solids (Gilman et al [1], Burns & Webb [2], St.John [3], and Brede & Haasen [4]). Emitted dislocations reduce the stress intensity factor at the crack tip and slow its motion by crack tip blunting and dislocation shielding. However, many analyses to date, most notably that of Rice & Thomson [5], have considered only dislocation nucleation on slip planes which contain the crack front. Argon [6] has described the DBTT by analyzing dislocation emission on planes inclined to the crack front for isotropic materials. The purpose of this paper is to show that for some anisotropic materials of cubic symmetry under mode I crack loading, the resolved shear stress is greater on slip planes which are inclined 45 ° to the crack front rather than on planes which contain the crack front.

On the anisotropy of cracked solids

International Journal of Engineering Science, 2018

We consider the effective elastic properties of cracked solids, and verify the hypothesis that the effect of crack interactions on the overall anisotropy-its type and orientation-is negligible (even though the effect on the overall elastic constants may be strong), provided crack centers are located randomly. This hypothesis is confirmed by computational studies on large number of 2-D crack arrays of high crack density (up to 0.8) that are realizations of several orientation distributions. Therefore, the anisotropy can be accurately determined analytically in the non-interaction approximation (NIA). Since the effective elastic properties possess the orthotropic symmetry in the NIA (for any orientation distribution of cracks, including cases when, geometrically , the crack orientation pattern does not have this symmetry), the orthotropy of cracked solids is not affected by interactions.

On the Anisotropic Damaged Behavior of Polycrystals

Based on a well-established micromechanical model of damage initiation in low-cycle fatigue (LCF) already developed in , a new extension is proposed for describing the damage deactivation effect. With a small strain assumption, it is assumed that the local damage variables initiate at the crystallographic slip system level. It is considered that the damage is active only if micro-cracks (MC) are open, while damage affects differently the mechanical properties of polycrystals during its closure (inactive phase). The anisotropic damaged (activation and deactivation) behavior concept is adopted only at the macroscopic level. With a fourth-order damage tensor, the deactivation damage effect under multiaxial cyclic loadings is modeled describing the related phenomenon of the induced-oriented anisotropy. Several numerical simulations are conducted describing the overall damaged behavior of polycrystals in biaxial LCF. The responses of a given grains aggregate are recorded and then discussed. As a conclusion, the model describes fairly well the damage activation and deactivation effect in plastic fatigue, notably under multiaxial complex loading paths.

Monte-Carlo simulation of crack propagation in polycrystalline materials

Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2004

The paper deals with a model for transgranular crack propagation in a polycrystalline metals and alloys. According to experimental observations, the fracture surfaces (facets) remain perfectly flat within each individual grain, but the orientation of facets fluctuates from grain to grain. At the bigger length scales, this behaviour results in the roughness of fracture surface. The polycrystalline structure of simulated material is represented by pseudo-3D grain array. The “grain by grain” mode of crack propagation is simulated in terms of a “continuous time” kinetic Monte-Carlo (MC). The stochastic nature of the proposed model allows to estimate energy consumption during fracture and fracture surface topography, and provides a natural explanation for the experimentally observed scatter of macroscopic fracture characteristics.

Study of strain localizations in a polycrystalline medium in presence of a quasi-static crack

Numerical techniques have been widely applied in many recent works to investigate micro-scale behavior of materials. This work focuses on the analysis of strain localizations in a Nickel-based alloy, Haynes 230. Numerical models and experiments concern the study of the strain field generated around the crack tip inside a polycrystalline medium when the crack is quasi-static (not propagating). Experimentally, the tests were conducted in load control; one face of the specimens was monitored by high-resolution Digital Image Correlation (DIC) technique to evaluate the strain field ahead of the crack tip. The simulations were conducted adopting an open source finite element code, Warp3D, which implements a state of art Crystal Plasticity (CP) model. The models of the polycrystalline matrix were created considering the data obtained inspecting the specimen surface by the Electron Back-Scatter Diffraction (EBSD) technique, which allowed defining grains size and orientations. Experimental and numerical results were then compared in terms of strain localizations to evaluate the prediction capabilities of the models. The comparison focused on strain field extension and active grains.

Microscale characterization of granular deformation near a crack tip

Journal of Materials Science

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.

Three-dimensional local stress analysis on grain boundaries in polycrystalline material

International Journal of Solids and Structures, 2007

In order to understand the initiation behavior of microstructurally small cracks in a stress corrosion cracking condition, it is important to know the tensile normal stress acting on the grain boundary (normal GB stress). The local stress in a polycrystalline body is enhanced by the inhomogeneity which stems from the shape and orientation of each grain. The stress in a three-dimensional polycrystalline body consisting of 100 grains with random orientation, under a remote uniform tensile stress condition, is evaluated by the finite element method. It was revealed that the local stress on the polycrystalline body is inhomogeneous under uniform applied stress and becomes large at those grain boundaries that are perpendicular to the load axis, though there is large fluctuation. It was also shown that the normal GB stress tends to be large near the triple points due to the deformation constraint caused by adjacent grains. Finally, the maximum stress on the surface of a large component caused by the inhomogeneity was evaluated by using Gumbel statistics.