Stress intensity factors of microstructurally small crack (original) (raw)
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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 path dependence on inhomogeneities of material microstructure
Crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. Several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sih criterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks.
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.
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.
Elastic solids with many cracks: A simple method of analysis
International Journal of Solids and Structures, 1987
A simple method of stress analysis in elastic solids with many cracks is proposed. It is based on the superposition technique and the ideas of selLconsistency applied to the average tractions on individual cracks. The method is applicable lo both two-and threedimensional crack arrays of arbitrary geometry. It yields approximate analytical solutions for the stress intensity factors (SIFs) accurate up to quite close distances between cracks. It is also suggested how a full stress field can be approximately constructed. Applications lo a configuration "crack-microcrack array" and lo a problem ol effective elastic properties of a solid with cracks are considered.
International Journal for Numerical Methods in Engineering
The realistic representation of material degradation at a fully evolved crack is still one of the main challenges of the phase-field method for fracture. An approach with realistic degradation behavior is only available for isotropic elasticity in the small deformation framework. In this paper, a variational framework is presented for the standard phase-field formulation, which allows to derive the kinematically consistent material degradation. For this purpose, the concept of representative crack elements (RCE) is introduced to analyze the fully degraded material state. The realistic material degradation is further tested using the self-consistency condition, where the behavior of the phase-field model is compared to a discrete crack model. The framework is applied to isotropic elasticity, anisotropic elasticity and thermo-elasticity, but not restricted to these constitutive formulations. K E Y W O R D S consistent material degradation, finite element method, homogenization, phase-field fracture 1 INTRODUCTION Realistic modeling of load and direction depending material degradation, crack opening, and closure are of fundamental importance for reliable predictions of crack kinematics and crack evolution. Thus, describing these features is still under development for the phase-field method. May et al, 1 Strobl and Seelig, 2 Schlüter, 3 and Steinke and Kaliske 4 have shown, that the well-known volumetric-deviatoric split (V-D) 5 and spectral split 6 approaches with tension/compression decomposition lead to misleading predictions for the force transfer through the crack. They have proposed and developed a model for the crack kinematics in case of isotropic, linear elastic material. The directional decomposition 4,7 overcomes the observed discrepancies of the V-D and spectral split by performing the following steps: • local crack orientation is determined from a chosen criterion, • crack coordinate system is introduced and applied to the stresses and strains, • stress tensor is decomposed with respect to the kinematic considerations of an equivalent discrete crack, and • corresponding material tangent is derived from the decomposed stress tensor. Also in Teichtmeister et al, 8 Bryant and Sun, 9 and Levitas et al., 10 considerations on the crack kinematics are used with the aim to obtain a consistent material degradation for the phase-field method. In those approaches, a crack orientation is explicitly introduced into the phase-field method. This step requires a few reconsiderations of the interpretation of the phase-field concept in the context of crack irreversibility. 6,11,12 [The copyright line for this article was changed on 10 December 2020 after original online publication.] This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Influence of the material substructure on crack propagation: a unified treatment
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
The influence of the material texture (substructure) on the force driving the crack tip in complex materials admitting Ginzburg-Landau-like energies is analyzed in a three-dimensional continuum setting. The theory proposed accounts for finite deformations and general coarse-grained order parameters. A modified expression of the J-integral is obtained together with other path-integrals which are necessary to treat cases where the process zone around the tip has finite size. The results can be applied to a wide class of material substructures. As examples, cracks in ferroelectrics and in materials with strain-gradient effects are discussed: in these cases the specializations of the general results fit reasonably experimental data.
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.
Stress intensity factors for interacting cracks
Engineering Fracture Mechanics, 1987
Experimental stress intensity factors (SIFs) for two interacting straight cracks in planehomogeneous regions were determined. Photoelastic data were collected from digitally sharpened isochromatic fringe patterns by using a digital image analysis system. SIFs were extracted by using the field equations derived from Williams' stress function. Numerical SIFs were also obtained by the boundary integral equation method. Good agreement was observed between experimental and numerical results. NOTATION crack tips as shown in Fig. 4 one-half crack length one-half horizontal distance between crack tips A and D one-half vertical distance between crack tips B and C one-half length of specimens specimen thickness one-half width of specimens orientation of crack AB with respect to the long direction of the specimens polar coordinates as shown in Fig. 9 applied far-field tensile stress stress intensity factor mode I SIF mode II SIF term used to normalize SIFs (= o/;;;; in this study) Young's Modulus Poisson's Ratio material fringe value