Reassessing spherical indentation: Contact regimes and mechanical property extractions

Abstract

This work concerns systematic finite element simulations of spherical indentation experiments in solids with a vast combination of mechanical properties. The simulations are performed with large and small-strain implementations of the J 2-flow and J 2-deformation theories of plasticity for frictionless and frictional spherical and parabolic contacts. An in-depth comprehension is gained on the mechanics of the transition from the elasto-plastic to the fully-plastic indentation regimes, which allows us to (i) propose general correlations between hardness p ¯ , yield strength σ ys, power-law strain hardening coefficient n, and Young’s modulus E, enabling mechanical property extractions in polycrystalline metals from hardness measurements performed at different normalized penetrations a/ D, (ii) revisit prior conceptions about the contact regimes governing spherical indentation experiments, (iii) examine the validity of self-similarity analyses to fully-plastic indentation experiments, and (iv) find equivalencies between sharp and spherical hardness measurements. Strict analogies are first established between the transition from the elasto-plastic to the fully-plastic contact regimes in sharp and spherical indentations. This is accomplished by considering a constancy in the relationship between normalized hardness p ¯ / σ 0.1 and E/ σ 0.1 at different a/ D and n values, where σ 0.1 in the characteristic (representative) indentation strain in the spirit of Tabor’s analyses. A detailed discussion is then given on the mechanistic origin to the contact deformation regimes, addressing the role of large deformations and the validity of self-similarity assumptions upon the spherical indentation behavior. The analysis shows that the elasto-plastic regime has different mechanistic origins depending on the ranges of a/ D and n. Similarly, full-plasticity leads to three distinct indentation behaviors depending on the proximity of the strain hardening response to the perfectly-plastic model with n = 0, the assumed plasticity theory, and whether material pileup or sinking-in develop. The overall results are framed in the context of contact deformation maps, describing the evolution from the elasto-plastic to the fully-plastic regimes. The extraction of mechanical properties from the above general hardness relations is then confronted against numerous experiments performed in model polycrystalline metals, where guidelines are given to reduce the impact of frictional effects and to improve assessment of the actual σ ys in the material. Finally, a comprehensive discussion on the accuracy of flow vs. deformation plasticity theories in the modeling of indentation experiments is provided. It is suggested that while the flow theory reproduces the contact response in recrystallized polycrystals, deformation plasticity may be more relevant in predicting hardness values in work-hardened metals.