On the HRR-field in power-law solids with microcracks (original) (raw)
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Interaction of microcracks with a macrocrack yielded in a narrow strip
Theoretical and Applied Fracture Mechanics, 2004
Plastic zone growth of collinear cracks has had a longstanding interest in ductile fracture. This work further considers yield zone growth in an isotropic, homogeneous elastic-perfectly plastic infinite plate containing a macrocrack with several neighboring microcracks. Normal loading is considered at distances far away from the cracks. The strip yield is adopted where the plastic zone is assumed to be confined to two narrow strips extending from the ends of a finite length crack while the microcracks are assumed to be elastic. The plastic zone length and crack opening displacement are found from asymptotic solution and compared with finite element solution.
We aim to derive a damage model for materials damaged by microcracks. The evolution of the cracks shall be governed by the maximum energy release rate, which was recently shown to be a direct consequence of the variational principle of a body with a crack (Arch. Appl. Mech. 69 (5) (1999) 337). From this, we get the path of the growing crack by introducing a series of thermodynamically equivalent straight cracks. The equivalence of the energy dissipated by microcrack growth and the damage dissipation leads to our damage evolution law. This evolution law will be embedded in a ÿnite deformation framework based on a multiplicative decomposition into elastic and damage parts. As a consequence of this, we can present the anisotropic damaged elasticity tensor with the help of push and pull operations. The connection of this approach to other well known damage theories will be shown and the advantages of a ÿnite element framework will be worked out. Numerical examples show the possibilities of the proposed model.
A new damage model for microcrack-weakened brittle solids
Acta Mechanica Sinica, 1993
In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given.
Dynamic propagation of a macrocrack interacting with parallel small cracks
AIMS Materials Science
In this study, the effect of small cracks on the dynamic propagation of a macrocrack is investigated by using a new continuum mechanics formulation, peridynamics. Various combinations of small cracks with different number, location and density are considered. Depending on the location, density and number of small cracks, the propagation speed of macrocrack differs. Some combinations of small cracks slows down the propagation of a macrocrack by 34%. Presented results show that this analysis can be useful for the design of new microstructurally toughened materials.
Numerical analysis of interaction and coalescence of numerous microcracks
Engineering Fracture Mechanics, 2005
The deformation and failure behaviors of brittle or quasi-brittle solids are closely related to interaction and propagation of stochastically distributed microcracks. The influence of microcrack interaction and evolution on the mechanical properties of materials presents a problem of considerable interest, which has been extensively argued but has not been resolved as yet. In the present paper, a novel numerical method is used to calculate the effective elastic moduli and the tensile strength, and to simulate the failure process of brittle specimens containing numerous microcracks. The influences of some crack distribution parameters reflecting the non-uniform spatial concentration, size and orientation distributions are examined. The effective elastic moduli and the tensile strength of brittle materials exhibit different dependences on microcrack interaction. For example, two microcrack distributions that lead to the identical effective elastic moduli may cause a pronounced difference in the tensile strengths and failure behaviors of materials. By introducing two criteria for microcrack growth and coalescence in terms of GriffithÕs energy release rate, the above numerical method is extended to simulate the coalescence process of microcracks that results in a fatal crack and the final rupture of a specimen.
Near-tip field of an anti-plane crack in a micro-cracked power-law solid
International Journal of Fracture, 1993
Asymptotic near-tip field is investigated for an anti-plane (mode III) crack in a power-law solid permeated by a distribution of micro-cracks. The micro-crack location is assumed to be random, while the micro-crack orientation is taken to be non-random. The anisotropic nature of this kind of damage gives rise to anisotropic constitutive equations for the overall macroscopic strains and stresses. The structure of the asymptotic field at a macro-crack tip is analyzed by solving a nonlinear eigenvalue problem. It is shown that under the assumptions made in this analysis the asymptotic crack tip field of the damaged solid has the same structure as the mode III HRR-field of the undamaged solid. Numerical results are presented for the angular functions, the contours of constant effective shear stress, the normalization constant arising in the near-tip field, and the crack opening displacement. By means of these results, the effects of the micro-crack density and orientation on the crack-tip field will be explored.
Damage evolution during microcracking of brittle solids
Acta Materialia, 2001
Microcracking due to thermal expansion and elastic anisotropy is examined via computer simulations with a microstructural-based finite element model. Random polycrystalline microstructures are generated via Monte Carlo Potts-model simulations. Microcrack formation and propagation due to thermal expansion anisotropy is investigated in these microstructures using a Griffith-type failure criterion in a microstructuralbased finite element model called OOF. Effects of the grain size distribution on the accumulation of microcrack damage, as well as on the threshold for microcrack initiation, are analysed. Damage evolution is rationalised by statistical considerations, i.e. damage accumulation is correlated with the statistical distributions of microstructural parameters.