The failure of ceramic materials is caused by the extension of small flaws. Therefore, linear-elastic fracture mechanics can be applied to describe the failure behaviour. The main problem in the application of the simple fracture mechanics relation is the existence of a rising crack growth resistance curve, which is caused by crack bridging forces behind the advancing crack tip or by transformations in front of the crack tip. The increasing crack growth resistance leads to problems in the transformation of results from specimens with macrocracks to components with natural cracks.

Fracture Mechanics of Ceramics

An empirical stress-intensity factor equation for the surface crack

: An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

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Virtual crack closure technique: History, approach, and applications

The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single-mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed-mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non-linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.

Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues

An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

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Extended finite element method for three-dimensional crack modelling

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Calculation of strain-energy release rates with higher order and singular finite elements

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

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Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

https://ntrs.nasa.gov/api/citations/19870011944/downloads/19870011944.pdf

Ivatury S. Raju

Papers

An empirical stress-intensity factor equation for the surface crack

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Calculation of strain-energy release rates with higher order and singular finite elements

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Convergence of strain energy release rate components for Edge-Delaminated composite laminates