An Asymptotic Analysis of Static and Dynamic Crack Extension Along a Ductile Bimaterial Interface/Anti-Plane Case

In this paper is presented the new approach to asymptotic analysis of the stress and strain fields around a crack tip that is propagating dynamically along a bimaterial interface. Through asymptotic analysis the problem is being reduced to solving the Riemann-Hilbert's problem, what yields the strain potential that is used for determination of the strain field around a crack tip. The considered field is that of a dynamically propagating crack with a speed that is between zero and shear wave speed of the less stiffer of the two materials, bound along the interface. Using the new approach in asymptotic analysis of the strain field around a tip of a dynamically propagating crack and possibilities offered by the Mathematica programming package, the results are obtained that are compared to both experimental and numerical results on the dynamic interfacial fracture known from the literature. This comparison showed that it is necessary to apply the complete expression obtained by asymptotic analysis of optical data and not only its first term as it was done in previous analyses.

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Dynamic crack propagation in a 2D elastic body. The out-of plane case

PAMM ◽

10.1002/pamm.200700241 ◽

2007 ◽

Vol 7 (1) ◽

pp. 1090801-1090802

Author(s):

A.-M. SÃ¤ndig ◽

A. Lalegname ◽

S. Nicaise

Keyword(s):

Crack Propagation ◽

Elastic Body ◽

Dynamic Crack Propagation ◽

Dynamic Crack ◽

Plane Case ◽

Out Of Plane

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Validity of the Finite Fracture Mechanics Based Asymptotic Analysis for Predictions of Crack Deflection in Thin Layers of Ceramic Laminates

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.627.237 ◽

2014 ◽

Vol 627 ◽

pp. 237-240 ◽

Cited By ~ 1

Author(s):

Oldřich Ševeček ◽

Dominique Leguillon ◽

Tomáš Profant ◽

Michal Kotoul

Keyword(s):

Potential Energy ◽

Asymptotic Solution ◽

Asymptotic Analysis ◽

Crack Extension ◽

Crack Deflection ◽

Thin Layers ◽

Reference Solution ◽

Finite Fracture Mechanics ◽

Higher Order Terms ◽

Good Agreement

The work studies and compares different approaches suitable for predictions of the crack deflection (bifurcation) in ceramic laminates containing thin layers under high residual stresses and discuss a suitability and limits of using of the asymptotic analysis for such problems. The thickness of the thin compressive layers where the crack deflection occurs is only one order higher than the crack extension lengths considered within the solution. A purely FEM based calculation of the energy and stress conditions, necessary for the crack propagation, serves as the reference solution to the problem. The asymptotic analysis is used after for calculations of the same quantities (especially of energy release rate – ERR). This concept enables semi-analytical calculations of ERR or changes in potential energy induced by the crack extensions of different lengths and directions. Such approach can save a large amount of simulations and time compared with the pure FEM based calculations. It was found that the asymptotic analysis provides a good agreement for investigations of the crack increments enough far from the adjacent interfaces but for longer extensions (of length above 1/5-1/10 of the distance from the interface) starts more significantly to deviate from the correct solution. Involvement of the higher order terms in the asymptotic solution or other improvement of the model is thus advisable.

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