Model for instrumented indentation of brittle open-cell foam

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Research Letter

Model for instrumented indentation of brittle open-cell foam Robert F. Cook, Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Address all correspondence to Robert F. Cook at [email protected] (Received 23 May 2018; accepted 5 July 2018)

Abstract A model is developed and implemented for load-controlled instrumented conical indentation of a brittle open-cell foam on a dense substrate. A survey of observations suggests that such indentations are typiﬁed by displacement excursions at small indentation loads, load-displacement variability, localized crushing, and a discrete to continuum transition at intermediate loads. The model includes all these effects as well as stiffening at large loads as the substrate is encountered. Direct quantitative comparison is made with measurements of a silica foam on a soda-lime glass substrate, strongly supporting the physical basis of the model.

Introduction The incorporation of porosity often confers advantages to the mechanical, thermal, optical, or chemical properties of materials and to the performance of components incorporating porous materials.[1–5] In particular, chemical properties of porous materials can be superior to those of their dense analogs if the chemical property is surface mediated and the pore surface is accessible for chemical reaction. Open-cell foam materials,[4] in which the entire interior pore surface of the material is accessible, thus have a great advantage for electrochemical, catalytic, separation, and other surface-based applications.[1–3] The structural (i.e., load-bearing) integrity of such materials is degraded, however, by the large porosity, φ. Typically, in open-cell foams φ ≈ 0.8 and hence the solid fraction (1–φ) ≈ 0.2. The signiﬁcant porosity leads to design trade-offs between chemical properties (enhanced by greater porosity) and mechanical properties (usually degraded by porosity). Similar trade-offs exist for thermal properties (insulating ability enhanced by porosity) or optical properties (refractive properties enhanced by porosity) versus mechanical properties.[1–3] The trade-off is especially acute for open-cell foams formed from ceramics and glasses as the mechanical properties are usually determined by the surface-defect controlled brittle fracture response of the base material rather than the less defectsensitive ductile response of metal foams. In developing an open-cell foam material or assessing its mechanical properties, instrumented indentation techniques are especially useful and have been used extensively: only small volumes of material are required for testing (relative to tension, compression, or bending specimens), the test surface requires minimal preparation, specimen gripping is not an issue, and the test can be performed locally to provide a map of the spatial distribution of properties. In such techniques, the indentation load and displacement are continuously

measured as a (usually) pyramidal or spherical probe is ﬁrst driven under

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