Conformal Map on Rough Boundaries Application to Fracture

1996 ◽  
Vol 463 ◽  
Author(s):  
Stéphane Roux ◽  
Damien Vandembroucq
Keyword(s):  
Glass Fibers ◽  
Interfacial Crack ◽  
Mapping Technique ◽  
Local Mode ◽  
Rough Boundary ◽  
Conformal Map ◽  
Mode Iii ◽  
Infinite Domains ◽  
Conformai Mapping ◽  
Roughness Amplitude

ABSTRACTA conformai mapping technique is presented which allows to solve efficiently harmonic and bi-harmonic problems in semi-infinite domains limited by a rough boundary. This technique is applied to obtain the statistical distribution of flux and elastic stress in the vicinity of a self-affine boundary. This computation justifies the occurence of Weibull statistics for the strength of glass fibers, with Weibull modulus depending on the roughness amplitude. Another application concerns the determination of the local mode III stress intensity factor ahead of a rough crack. Extension of the method to surface stress-corrosion, and interfacial crack propagation are discussed.

Dynamic mode-III interfacial crack in ferroelectric materials

2000 ◽  
Vol 11 (4) ◽  
pp. 211-222 ◽  
Author(s):  
Shengping Shen ◽  
Zhen-Bang Kuang ◽  
Toshihisa Nishioka
Keyword(s):  
Interfacial Crack ◽  
Ferroelectric Materials ◽  
Dynamic Mode ◽  
Mode Iii

Singularities, interfaces and cracks in dissimilar anisotropic media

1990 ◽  
Vol 427 (1873) ◽  
pp. 331-358 ◽  
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Elastic Anisotropy ◽  
Homogeneous Medium ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Mode Iii ◽  
Crack Problems

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

Elastic Green's function for a composite solid with a planar crack in the interface

1989 ◽  
Vol 4 (1) ◽  
pp. 124-136 ◽  
Author(s):  
V. K. Tewary ◽  
R. H. Wagoner ◽  
J. P. Hirth
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Interfacial Crack ◽  
Mode I ◽  
Mode Iii ◽  
Line Load ◽  
Planar Crack ◽  
Composite Solid

The elastic Green's functions for displacements and stresses have been calculated for a composite solid containing a planar crack in a planar interface using the Green's function derived in a previous paper for a line load parallel to the composite interface. The resulting functions can be used to calculate the stress or displacement at any point in the composite for a variety of elastic singularities. As specific applications, the Mode I stress intensity factor of an interfacial crack was calculated as were the Green's functions for the semi-infinite antiplane strain case. The Mode I case shows the near-crack tip oscillations reported by other authors while the Mode III case does not. The newly devised Green's functions are shown to reproduce the results of other authors in the isotropic limit.

Mode-III interfacial crack propagation in heterogeneous media

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Camille Jestin ◽  
Olivier Lengliné ◽  
Jean Schmittbuhl
Keyword(s):  
Crack Propagation ◽  
Heterogeneous Media ◽  
Interfacial Crack ◽  
Mode Iii

Interaction of a Screw Dislocation with an Interfacial Crack in Two Dissimilar Piezoelectric Layers

2004 ◽  
Vol 261-263 ◽  
pp. 141-146
Author(s):  
Jin Xi Liu ◽  
Ai Ping Liu ◽  
Z.Q. Jiang ◽  
Ai Kah Soh
Keyword(s):  
Conformal Mapping ◽  
Screw Dislocation ◽  
Complex Variable ◽  
Piezoelectric Effect ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Mapping Technique ◽  
Intensity Factors ◽  
Piezoelectric Layers ◽  
Crack Tip Shielding

A screw dislocation interacting with a semi-infinite interfacial crack in two dissimilar piezoelectric layers is studied. The complex variable method and the conformal mapping technique are employed to obtain the solution of the problem. The stress and electric displacement intensity factors are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electro-elastic material constants. Numerical example shows that the influence of piezoelectric effect on the crack tip shielding is significant.

scholarly journals Fracture of Thin-Walled Polyoxymethylene Bulk Specimens in Modes I and III

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5096
Author(s):  
Peer Schrader ◽  
Anja Gosch ◽  
Michael Berer ◽  
Stephan Marzi
Keyword(s):  
Fracture Surface ◽  
Crack Growth ◽  
Cantilever Beam ◽  
Double Cantilever Beam ◽  
Polymeric Materials ◽  
Local Mode ◽  
Mode I ◽  
Mode Iii ◽  
Thin Walled ◽  
Twisting Angle

Thin-walled polymeric components are used in many applications. Hence, knowledge about their fracture behavior in bulk is beneficial in practice. Within this study, the double cantilever beam (DCB) and out-of-plane double cantilever beam (ODCB) tests are enhanced to enable the testing of such bulk specimens in mode I and mode III on the basis of the J-integral. This paper then presents and discusses the experimental results following the investigation of a semicrystalline polymer (polyoxymethylen) under quasi-static load conditions. From the experiments, fracture energies of similar magnitude in both mode I and mode III were determined. In mode III, pop-in fracture was observed. Furthermore, the fracture surfaces were investigated regarding the mode I and mode III dominant crack growth mechanisms, based on the morphology of the tested material. For specimens tested in mode I, no signs of plastic deformation were observed, and the fracture surface appears flat. In mode III, some samples display a twisted fracture surface (twisting angle close to 45°), which indicates local mode I crack growth. A transfer of the presented methodology to other (more ductile) polymeric materials is deemed possible without further restrictions. In addition, the presented setup potentially enables an investigation of polymeric bulk specimens in mixed mode I+III.

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