Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials

Ortiz, Michael; Suresh, S.

doi:10.1115/1.2900782

Cited by 123 publications

(54 citation statements)

References 10 publications

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“…This creates severe restrictions in the critical time step size in intrinsic CZM methods, a problem that is avoided in the discontinuous Galerkin method where the only penalty in the critical time step size is a factor of √ β s , as discussed above (13). In practice, 1 < β s < 10 is enough to ensure numerical stability (35), implying a minimal impact on the stable time step size.…”

Section: Dg/cz Weak Formulationmentioning

confidence: 99%

A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method

Radovitzky

Seagraves

Tupek

et al. 2011

Computer Methods in Applied Mechanics and Engineering

134

110

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A scalable algorithm for modeling dynamic fracture and fragmentation of solids in three dimensions is presented. The method is based on a combination of a discontinuous Galerkin (DG) formulation of the continuum problem and Cohesive Zone Models (CZM) of fracture. Prior to fracture, the flux and stabilization terms arising from the DG formulation at interelement boundaries are enforced via interface elements, much like in the conventional intrinsic cohesive element approach, albeit in a way that guarantees consistency and stability. Upon the onset of fracture, the traction-separation law (TSL) governing the fracture process becomes operative without the need to insert a new cohesive element. Upon crack closure, the reinstatement of the DG terms guarantee the proper description of compressive waves across closed crack surfaces.The main advantage of the method is that it avoids the need to propagate topological changes in the mesh as cracks and fragments develop, which enables the Preprint submitted to Elsevier Science 16 August 2010indistinctive treatment of crack propagation across processor boundaries and, thus, the scalability in parallel computations. Another advantage of the method is that it preserves consistency and stability in the uncracked interfaces, thus avoiding issues with wave propagation typical of intrinsic cohesive element approaches.A simple problem of wave propagation in a bar leading to spall at its center is used to show that the method does not affect wave characteristics and as a consequence properly captures the spall process. We also demonstrate the ability of the method to capture intricate patterns of radial and conical cracks arising in the impact of ceramic plates which propagate in the mesh impassive to the presence of processor boundaries.

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Section: Dg/cz Weak Formulationmentioning

confidence: 99%

A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method

Radovitzky

Seagraves

Tupek

et al. 2011

Computer Methods in Applied Mechanics and Engineering

134

110

View full text Add to dashboard Cite

show abstract

“…The surface-like cohesive formulation is adopted in this work (e.g. see Willam et al 1989;Ortiz and Suresh 1993;Xu and Needleman 1993;Ortiz and Pandolfi 1999). In this formulation, a cohesive element consists of two surface elements which coincide in the reference configuration.…”

Section: A Appendix: Finite Element Formulation Of the Interface Elementmentioning

confidence: 99%

A theoretical and computational framework for studying creep crack growth

Elmukashfi

Cocks

2017

Int J Fract

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In this study, crack growth under steady state creep conditions is analysed. A theoretical framework is introduced in which the constitutive behaviour of the bulk material is described by power-law creep. A new class of damage zone models is proposed to model the fracture process ahead of a crack tip, such that the constitutive relation is described by a traction-separation rate law. In particular, simple critical displacement, empirical Kachanov type damage and micromechanical based interface models are used. Using the path independency property of the C * -integral and dimensional analysis, analytical models are developed for pure mode-I steady-state crack growth in a double cantilever beam specimen (DCB) subjected to constant pure bending moment. A computational framework is then implemented using the Finite Element method. The analytical models are calibrated against detailed Finite Element models. The theoretical framework gives the fundamental form of the model and only a single quantityĈ k needs to be determined from the Finite Element analysis in terms of a dimensionless quantity φ 0 , which is the ratio of geometric and material length scales. Further, the validity of the framework is examined by investigating the crack

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“…Because the auxiliary equations may be activated by problem-specific conditions, various physical phenomena that may arise at different points along the loading path may be simulated using this approach. This is similar to the on-demand insertion of interface elements within the finite-element framework proposed by Ortiz and Suresh (1993) which the present framework enables naturally.…”

Section: Discussionsupporting

confidence: 60%

CZM-based Finite-Volume Homogenization and Optimization of Periodic Composites

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Statistical Properties of Residual Stresses and Intergranular Fracture in Ceramic Materials

Cited by 123 publications

References 10 publications

A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method

A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method

A theoretical and computational framework for studying creep crack growth

CZM-based Finite-Volume Homogenization and Optimization of Periodic Composites

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