Crack-tip parameters in polycrystalline plates with soft grain boundaries (original) (raw)
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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.
Brittle fracture in polycrystalline microstructures with the extended finite element method
International Journal for Numerical Methods in Engineering, 2003
A two-dimensional numerical model of microstructural e ects in brittle fracture is presented, with an aim towards the understanding of toughening mechanisms in polycrystalline materials such as ceramics. Quasi-static crack propagation is modelled using the extended ÿnite element method (X-FEM) and microstructures are simulated within the framework of the Potts model for grain growth. In the X-FEM, a discontinuous function and the two-dimensional asymptotic crack-tip displacement ÿelds are added to the ÿnite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by ÿnite elements with no explicit meshing of the crack surfaces. Hence, crack propagation can be simulated without any user-intervention or the need to remesh as the crack advances. The microstructural calculations are carried out on a regular lattice using a kinetic Monte Carlo algorithm for grain growth. We present a novel constrained Delaunay triangulation algorithm with grain boundary smoothing to create a ÿnite element mesh of the microstructure. The fracture properties of the microstructure are characterized by assuming that the critical fracture energy of the grain boundary (G gb c) is di erent from that of the grain interior (G i c). Numerical crack propagation simulations for varying toughness ratios G gb c =G i c are presented, to study the transition from the intergranular to the transgranular mode of crack growth. This study has demonstrated the capability of modelling crack propagation through a material microstructure within a ÿnite element framework, which opens-up exciting possibilities for the fracture analysis of functionally graded material systems. Copyright ? 2003 John Wiley & Sons, Ltd.
Discrete dislocation plasticity analysis of crack-tip fields in polycrystalline materials
Philosophical Magazine, 2005
Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation is inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.
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.
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.
Springer eBooks, 2008
Meso-and microscale analysis are promising disciplines to cover the crack initiation as well as the various crack propagation phenomena in engineering structures. On mesoscale it is observed that the crack propagation in polycrystalline metal materials occurs mainly along grain boundaries. Following this observation we present a two dimensional polycrystal meso model consisting of grains with an elastic orthotropic material law and cohesive interfaces along crystal boundaries, which is able to reproduce crack initiation and propagation in metallic materials. As an extension to classical Voronoi cell diagrams we apply an advanced algorithm to generate polycrystal material structures based on arbitrary distribution functions of grain size. Therewith we are more flexible to represent realistic grain size distributions. The polycrystal model is applied to analyze the crack initiation and propagation in statically loaded representative volume elements of aluminum on the mesoscale without the necessity of initial damage definition. Future research work is focused on the determination of constitutive relations for the cohesive interface law from mixed continuum atomistic simulations performed on a representative volume element on the microscale and homogenized to the mesoscale.
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.
The effects of heterogeneity and anisotropy on the size effect in cracked polycrystalline films
Fracture Scaling, 1999
A model is developed for quantifying the size effect due to heterogeneity and anisotropy in polycrystalline films. The Monte Carlo finite element calculations predict the average and standard deviation of the microscopic (local) stress intensity factors and energy release rate of a crack in a columnar aggregate of randomly orientated, perfectly bonded, orthotropic crystals (grains) under plane deformation. The boundary of the neartip region is subjected to displacement boundary conditions associated with a macroscopic (far field or nominal) Mode-I stress intensity factor and average elastic constants calculated for the uncracked film with a large number of grains. The average and standard deviation of the microscopic stress intensity factors and energy release rate, normalized with respect to the macroscopic parameters, are presented as functions of the number of grains within the near-tip region, and the parameters that quantify the level of crystalline anisotropy. It is shown that for a given level of anisotropy, as long as the crack tip is surrounded by at least ten grains, then the expected value and standard deviation of the crack tip parameters are insensitive to the number of crystals. For selected values of crystalline anisotropy, the probability distributions of Mode-I stress intensity factor and stress ahead of the crack are also presented. The results suggest that the size effect due to heterogeneity and anisotropy is weak; crack initiation load and direction are governed only by the details of the grains in the immediate vicinity of the crack tip.
Theoretical approach to the ductile fracture of polycrystalline solids
2018
It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing continuum of random deformable polyhedra, representing the grains, which fill the space without leaving voids. Adjacent grains slide with a relative velocity proportional to the local shear stress resolved on the plane of the shared grain boundary, when greater than a finite threshold. The polyhedral grains reshape continuously to preserve matter continuity, being the forces causing grain sliding dominant over those reshaping the grains. It has been shown in the past that this model does not conserve volume, causing a monotonic hydrostatic pressure variation with strain. This effect introduces a novel concept in the theory of plasticity because determines that any fine grained polycrystalline material will fail after a finite plastic strain. Here the ...