			Home About us Contact

Griffith Criterion (griffith + criterion)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Aspects of cleavage fracture initiation , relative influence of stress and strain

FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 9-10 2006
K. WALLIN
ABSTRACT Cleavage fracture initiation has generally been assumed to be controlled mainly by matrix stress. Recently, several different cleavage fracture models have been proposed, where also strain is included in the failure criterion. However, the proposals have been rather crude and unable to provide clearly improved fracture estimates. Here, the first two steps of cleavage fracture (particle failure and grain fracture) are examined in more detail. It is shown that both stress and strain are important for cleavage fracture initiation, but that strain mainly affects particle failure, whereas grain fracture is controlled by a pure Griffith criterion. The findings are important for the development of new cleavage fracture models and to the proper way of accounting for constraint. [source]

A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007
C. Miehe
Abstract The paper considers a variational formulation of brittle fracture in elastic solids and proposes a numerical implementation by a finite element method. On the theoretical side, we outline a consistent thermodynamic framework for crack propagation in an elastic solid. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius,Planck inequality in the sense of Coleman's method. Here, the canonical direction of the crack propagation associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip and minimizes the incremental energy release. On the numerical side, we exploit this variational structure in terms of crack-driving configurational forces. First, a standard finite element discretization in space yields a discrete formulation of the global dissipation in terms configurational nodal forces. As a consequence, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface segments of the mesh. Critical for the success of this procedure is its embedding into an r-adaptive crack-segment reorientation procedure with configurational-force-based directional indicator. Here, successive crack releases appear in discrete steps associated with the given space discretization. These are performed by a staggered loading,release algorithm of energy minimization at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive-definite discrete subproblems with successively decreasing overall stiffness, providing an extremely robust algorithmic setting in the postcritical range. We demonstrate the performance of the formulation by means of representative numerical simulations. Copyright © 2007 John Wiley & Sons, Ltd. [source]

On rate independent models for crack propagation

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
Dorothee Knees
We model the evolution of a single crack as a rate,independent process based on the Griffith criterion. Three approaches are presented, namely a model based on global energy minimization, a model based on a local description involving the energy release rate and a refined local model which is the limit problem of regularized, viscous models. Finally we present an example which sheds light on the different predictions of the models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Epsilon-stable quasi-static brittle fracture evolution

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2010
Christopher J. Larsen
We introduce a new definition of stability, ,-stability, that implies local minimality and is robust enough for passing from discrete-time to continuous-time quasi-static evolutions, even with very irregular energies. We use this to give the first existence result for quasi-static crack evolutions that both predicts crack paths and produces states that are local minimizers at every time, but not necessarily global minimizers. The key ingredient in our model is the physically reasonable property, absent in global minimization models, that whenever there is a jump in time from one state to another, there must be a continuous path from the earlier state to the later along which the energy is almost decreasing. It follows that these evolutions are much closer to satisfying Griffith's criterion for crack growth than are solutions based on global minimization, and initiation is more physical than in global minimization models. © 2009 Wiley Periodicals, Inc. [source]