Interfaces in composites are expected to be non-planar. What attempts have been made to provide expressions for the displacement and stress fields due to dislocations and cracks that lie on a non-planar interface in three dimensions?
We are investigating the problem of the propagation of a crack on a non-planar interface with a sinusoidal shape in planes perpendicular to the direction of fracture propagation. In this study it is found that a basic ingredient is the displacement and stress fields due to sinusoidal dislocations (screws and edges on average) lying on the non-planar interface. This is a direct extension of our study (see our contributions in Research Gate) of non-planar crack propagation in homogeneous solids . Work is in progress.
Unfortunately no experimental work at present, just theory using elasticity and dislocations in solids. Clearly our study needs to be confronted with experiments. No software in the analysis.
We are involved in a research project entitled " NON-PLANAR INTERFACE CRACK UNDER GENERAL LOADING". The study's objective is to analyze the conditions of propagation of an oscillatory front crack along a non-planar interface, under mixed mode I + II + III loading. The crack model consists of a continuous distribution of three families of non-straight dislocations having the shape of the crack front: families 1 and 2 are edges (on average) and family 3 is screw. The associated Burgers vectors bj (j= I, II and III) are directed along the applied tension and shears x2, x1 , and x3 directions, respectively. The dislocations are directed along the x3- direction and spread in x2x3- planes in a small oscillating form e(x1,x3) at average elevation h(x1) .
At present, the displacement and stress fields of interface dislocations with bI and bIII are available (part I of this work). Results are displayed, that make easily accessible stress terms with singularities 1/x1 and Dirac delta function, involved in the crack analysis to come (Part II).
Expressions for crack-tip stresses and crack extension force are now available for a model of non-planar interface crack in bi-elastic solids with oscillatory front ξ= ξ (x1, x3) spreading in x2x3-plane perpendicular to fracture propagation x1-direction. The average crack plane is Ox1x3, perpendicular to the applied tension x2- direction. The shearing stresses are applied in the x1 and x3 directions, parallel to Ox1x3. Also considered are induced shearing and normal stresses that originate from Poisson contractions in the media. Please see “Non-planar interface crack under general loading III. Dislocation, crack-tip stress and crack extension force” in our contributions in ResearchGate. Contributions are welcome to improve the current dislocation theory of brittle fracture
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