Elastic-plastic stress investigation on crack problems in composite materials - Zhuang, Jing (2015)
Defects in composite materials often have significant negative effects on structure’s reliability and lifespan. In the current study, we consider a composite structure where two dissimilar materials are bonded together with a straight interface. A defect in the form of a short crack either in Griffith or Zener-Stroh type is embedded near the interface so that the problem can be ideally simulated based on dislocation theory. Starting from the interaction between a single dislocation and the interface, we construct continuously distributed dislocations along the crack line that result in singular integral equations with Cauchy kernel. Those equations are then reduced into a set of linear simultaneous equations through Gauss-Chebyshev numerical technique. Solutions of the linear equations subjected to certain boundary condition illustrate that mixed mode stress intensity factors arise even only pure tensile loading is imposed along the crack faces. The major new contribution of the current thesis is that the above mentioned fracture mechanics problems are solved by taking small-scale plasticity zone corrections at the crack tips. This consideration makes the stress solution more reliable in failure analysis and prevention for composite structures with cracks. Various physical problems with different configurations have been resolved accordingly. A sub-interface Griffith crack subjected to pure tensile loading with plastic zone corrections is the first one solved. Either embedded in infinite bimaterial plate or in semi-infinite plane coated by a finite layer, this crack has been examined by the mixed mode Dugdale model ahead of the its tips, cancelling both normal and shear stress singularities along two long strips. Plastic zone size and crack tip opening displacement are obtained and discussed with respect to varied material mismatches, different loading conditions, crack depth under the interface, as well as the geometry of the whole structure. When we increase the complexity of the external loading, and include additional cases in plane strain condition, a generalized Irwin model is more appropriate for analyzing sub-interface crack embedded in a coating-substrate system, subjected to combined tension and shear loads. A two-dimensional plastic zone could better describe the real stress state at the crack tip when it is no longer mode I dominated. Another implementation of generalized Irwin model can be seen in our investigation of a displacement-loaded Zener-Stroh crack, where the combination of climb and glide dislocations entering its blunt tip accounts for the mode mixity. Within these two problems, in addition to discussing plastic zone size and crack tip opening displacement over a series of variables, we have also paid attention to the derivation of effective stress intensity factors, and see how this parameter has been improved due to plastic corrections. Based on the knowledge and insights I have gained throughout the PhD study, some future work is proposed at the end of the report. In aspect of theory development, we can continue the investigation of physical mechanism of crack initiation in nano composites. On the other hand, 3-D elastic-plastic fatigue analysis and failure prevention for offshore pipe lines is a pretty good example to implement our methodology into practical use.