Hierarchical microcrack model for materials exemplified at enamel

This article investigates the mechanical properties of a material with hierarchically arranged microcracks.

Hierarchically structured biomaterials such as enamel exhibit superior mechanical properties as being stiff and damage tolerant at the same time. The common mechanical explanation for this behavior is based on the hierarchically structured arrangement of hard minerals and soft organics and their cooperative deformation mechanisms. In situ mechanical experiments with mm-sized bovine enamel bending bars an scanning electron microscope reveal that enamel is able to withstand mechanical loading even if it contains microcracks on different lengths scales. To clarify this issue an analytical hierarchical microcrack model of non-interacting cracks is presented.

The model predicts a decrease of the elastic modulus and the fracture strength with increasing levels of hierarchy. The fracture strain on the other hand may decrease or increase with the number of hierarchical levels, depending on the microcrack density. This simple hierarchical microcrack model is able to explain already published experiments with focused ion beam prepared μm-sized enamel cantilevers on different hierarchical levels. In addition it is shown that microcracking during loading in hierarchical materials may lead to substantial pseudoplastic behavior.