Indentation as a Probe of Functionally Graded Materials

Functionally graded materials (FGMs), whose properties can be spatially tailored in a predefined way (Suresh, 2001), find multiple diverse applications in engineering. Indentation testing is widely used to characterise material stiffness, yet its ability to reveal spatial variations in graded material properties is still not fully understood. It is known that FGMs are known to exhibit a kind of size effect (see, e.g., Pourasghar and Chen, 2019), which in indentation testing is revealed most clearly in the fact that the material response to indentation depends on the indenter characteristic size (Argatov et al., 2019). However, despite being a topic of intensive study in the recent decade (Jana et al., 2026), FGMs still present a challenge for the material identification by means of indentation. In this seminar, an analytical framework (Argatov and Sabina, 2022), based on perturbation technique (Gao et al., 1992), is presented for interpreting indentation experiments on functionally graded materials, whose elastic properties vary with depth. The analysis shows that both the effective shear modulus obtained from indentation and the relative adhesive force are strongly influenced by the form of material gradation. These results demonstrate that indentation experiments can be used not only to measure an “effective” stiffness, but also as a sensitive probe of subsurface material structure, with important implications for material design and characterisation.

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