On the relationship between indenation hardness and modulus, and the damage resistance of biological materials

Abstract

The remarkable mechanical performance of biological materials is based on intricate structure-function relationships. Nanoindentation has become the primary tool for characterising biological materials, as it allows to relate structural changes to variations in mechanical properties on small scales. However, the respective theoretical background and associated interpretation of the parameters measured via indentation derives largely from research on 'traditional' engineering materials such as metals or ceramics. Here, we discuss the functional relevance of indentation hardness in biological materials by presenting a meta-analysis of its relationship with indentation modulus. Across seven orders of magnitude, indentation hardness was directly proportional to indentation modulus, illustrating that hardness is not an independent material property. Using a lumped parameter model to deconvolute indentation hardness into components arising from reversible and irreversible deformation, we establish criteria which allow to interpret differences in indentation hardness across or within biological materials. The ratio between hardness and modulus arises as a key parameter, which is a proxy for the ratio between irreversible and reversible deformation during indentation, and the material's yield strength. Indentation hardness generally increases upon material dehydration, however to a larger extend than expected from accompanying changes in indentation modulus, indicating that water acts as a 'plasticiser'. A detailed discussion of the role of indentation hardness, modulus and toughness in damage control during sharp or blunt indentation yields comprehensive guidelines for a performance-based ranking of biological materials, and suggests that quasi-plastic deformation is a frequent yet poorly understood damage mode, highlighting an important area of future research.

Lacunar-canalicular bone remodeling: Impacts on bone quality and tools for assessment

“…Because elasticity is not neglected, nanoindentation hardness differs from conventional hardness testing for materials that are not perfectly plastic. 160 Measurement of time-dependent material properties through either performing creep or stress-relaxation tests or using dynamic nanoindentation are also welldeveloped for bone. 83,155,161,162 Most nanoindentation systems are capable of time-efficient twodimensional mapping.…”

Hardness and Elastic Modulus of Al-Based Composite Developed from Aluminium Piston Scraps Using Alumina and Snail shell as Reinforcements

“…According to Labonte et al (2017), true resistance to plastic deformation, H, depends on the ratio of indentation hardness to indentation modulus. Indentation hardness is proportional to indentation modulus with a proportionality constant of 0.05.…”

“…Where Hi, H, Ei and β represent indentation hardness, true hardness, indentation modulus, equivalent cone angle of indenter (usually 19.7 o ), respectively (Sakai 1999;Labonte et al, 2017;Olawuni et al, 2020).…”

“…The ratio of these properties is a measure of material toughness, an important consideration in engineering material. Hardness is a pointer to strength and in combination with toughness of brittle material (Tabor, 2000;Sakai, 1993;Sakai, 1999;Sakai et al, 1999;Cheng & Cheng 1998;Labonte et al, 2017). Furthermore, the relationship between hardness and elastic modulus of composites can be modelled for predictive purposes.…”

Mechanical and elemental characterization of ant mandibles: consequences for bite mechanics

“…Among several mechanical parameters that characterize a material, hardness (H) and Young's modulus (E) provide relevant information on its behavior under loading (Arzt et al 2002;Enders et al 2004;Barbakadse et al 2006;Labonte et al 2017). Young's modulus measures the material resistance to elastic deformation under compressive or tensile forces, while H reflects the material resistance to plastic deformation (Berthaume 2016).…”