Pyramidal indentation load–depth curve of viscoelastic materials

Abstract

The indentation load P versus depth h curves are examined to investigate the time-dependent surface deformation of viscoelastic materials. The viscoelastic P–h curves significantly depend on the temperature of measurement and the penetration rate of indentation. Sneddon's elastic solution of a conical indentation is extended to a viscoelastic one for a conical or a pyramidal indentation in terms of the hereditary integral. Several types of viscoelastic problems are discussed in relation to the test techniques and analyses for determining the relaxation modulus E(t) and the creep compliance D(t). The superposition rules of time–temperature, penetration depth–temperature, and penetration depth–penetration rate are examined. The viscoelastic indentation tests (constant rate penetration test and constant load creep test) of amorphous Se are conducted at temperatures from 10 to 42 °C. The theoretical considerations and the test results encourage pyramidal indentation as an efficient microprobe for the viscoelastic characterization, in particular, of extremely small-size test specimens and ceramic, metal, and polymer thin films coated on substrate.