On the ability of nanoindentation to measure anisotropic elastic constants of pyrolytic carbon

Abstract

We used cube corner, Berkovich, cono-spherical, and Vickers indenters to measure the indentation modulus of highly oriented bulk pyrolytic carbon both normal to and parallel to the plane of elastic isotropy. We compared the measurements with elastic constants previously obtained using strain gage methods and ultrasound phase spectroscopy. While no method currently exists to extract the anisotropic elastic constants from the indentation modulus, the method of Delafargue and Ulm (DU) [17] was used to predict the indentation modulus from the known elastic constants. The indentation modulus normal to the plane of isotropy was ∼ 20% higher than the DU predictions and was independent of indenter type. The indentation modulus parallel to the plane of isotropy was 2-3 times lower than DU predictions, was depth dependent, and was lowest for the cube corner indenter. We attribute the low indentation modulus to nanobuckling of the graphite-like planes and the indenter type dependence to the impact of differing degree of transverse stress on the tendency toward nanobuckling.

Nanoscale elasticity of highly anisotropic pyrocarbons

“…The latter include results from tensile tests performed on low modulus carbon fibers coated by RL and ReL PyCs, as-prepared and after heat treatment at 1600° [10], as well as tensile (TT) and compressive tests (CT) [11], ultrasound phase spectroscopy (US) [7] and three point bending tests (TPB) [9] on a commercial high textured PyC. Existing results from nanoindentation [34,35,8,12] were not included because of serious questions raised in the literature regarding the ability of these methods to separate in-plane and out-of-plane properties [8,12].…”

“…Indeed, C 11 constants obtained using acoustic methods are in the range 40-50 GPa [6,7]; indentation moduli are around 10-30 GPa, i.e. lower or equal to the transverse values [8,12]; longitudinal moduli from tensile/compression tests show values ranging from around 20 GPa [11] as-prepared PyCs [10] and up to 400 GPa when heat treated at high temperature (2200°C) [10].…”

“…Elastic constants (in GPa) of pyrocarbon models obtained from constrained tensile (C T 01] for tensile, compressive and shear tests, respectively; numbers in parentheses are the standard deviations on the last digit obtained from independent simulations (tensile tests in x and y for C T 11 for instance); proportions (in %) with respect to the corresponding values for graphite(Table 2) are given in square brackets bleow the absolute values) 12. values.…”

An orthotropic material model for steel fibre reinforced concrete based on the orientation distribution of fibres

“…(17), (18). In the following, the ODF is calculated using the 2 nd order alignment tensor, A ij , which defines the main material symmetry axes of one meso-volume element of SFRC.…”

“…The development of artificial composites is often motivated by the need to increase material strength in an efficient and economically reasonable way. The aim of adding fibres to the matrix is the improvement of specific mechanical properties leading, however, often to anisotropic behaviour, which can be observed in reinforced rubber-like materials [28], in fibre-reinforced polymers [11,27,35], in carbonreinforced composites [17], and paper [10]. The present research focuses on a cementitious composite formed by the mixing of concrete matrix with steel fibres, SFRC.…”