Strength-size relationships in two porous biological materials

According to the Weibull theory for brittle materials, the mean experimental strength decreases with test specimen size. For the brittle parts of an organism this would mean that becoming larger in size results automatically in reducing strength. This unfavorable relationship was investigated for two porous, biological materials that are promising concept generators for crack deflective and energy dissipative applications in compressive overloading: the quasi-brittle coconut endocarp and the brittle spines of the sea urchin Heterocentrotus mamillatus. Segments in different volumes were prepared and tested in uniaxial compression experiments. Failure of both materials is Weibull distributed underlining that it is caused by statistically distributed flaws in the structure. However, the coconut endocarp has a much higher Weibull modulus (m = 14.1-16.5) than the spines (m = 5). The more predictable failure of the endocarp is probably attributed to a rather homogeneous microstructural design and water bound in the structure. In terms of the spines it was found that the Weibull modulus is structure dependent: More homogeneous spines feature a higher Weibull modulus than spines with a heterogeneous structure. Whereas the nearly dense endocarp exhibited, although less pronounced, the expected decrease in strength with increase in size, the spines showed a failure independently of size. This remarkable behavior may be explained with their highly porous internal structure. Small and large spines consist of struts of similar size, which constitute the porous internal structure, potentially limiting the flaw size to the size of the strut regardless of the spine size.

Scaling is an important aspect of the biomimetic work process, since biological role models and structures have rarely the same size as their technical implementations. The algorithms of Weibull are a standard tool in material sciences to describe scaling effects in materials whose critical strength depends on statistically distributed flaws. The challenge is to apply this theory (developed for homogeneous, isotropic technical materials) to brittle and quasi-brittle biological materials with hierarchical structuring. This study is a first approach to verify whether the Weibull theory can be applied to the coconut endocarp and to sea urchin spines in order to model their size/volume/property-relations.