The mechanical and functional responses of shape memory alloys (SMAs), which are often used in small volume applications, can be evaluated using instrumented indentation tests. However, deciphering the indentation test results in SMAs can be complicated due to the combined effects of the non-uniform state of stress underneath the indenter and stress-induced phase transformation. To address this issue, an expanding cavity model (ECM) applicable to spherical indentation of SMAs is developed in this work based on an analytical solution for an internally pressurized hollow sphere. Analytical expressions for key indentation parameters such as the mean contact pressure and size of the transforming zone are obtained, whose validity is evaluated by recourse to finite element simulations and published experimental data for a Ni–Ti alloy. It is shown that the ECM predicts the above parameters reasonably well for indentation strains varying from 0.01 to 0.04. Also, a method is proposed to determine the critical stress required to initiate phase transformation under uniaxial compression based on the application of the ECM to interpret the indentation stress–strain response.

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Instrumented indentation is particularly useful for characterizing the mechanical behavior of shape memory alloys (SMAs), which are often used as 'small volume' elements such as thin films or wires. Deciphering the measured indentation response, which is as such difficult for elastic-plastic materials due to the inhomogeneous state of stress underneath the indenter, becomes more complex for SMAs owing to the simultaneous occurrence of stress induced martensite transformation (SIMT) in conjunction with plastic deformation. In this work, a constitutive model that is able to capture the coupled nature of phase transformation and plastic deformation is employed to study, through finite element analyses, the spherical indentation behavior of SMAs at a temperature above the austenite finish temperature, A f. It is found that the concurrent development of plastic yielding and SIMT leads to slower evolution of martensite volume and a smaller transformed zone size. Also, in the absence of plastic yielding, the proportion of depth recovered by superelasticity is fairly constant. It is also observed, from a systematic comparison with a conventional elastic-plastic material, that the presence of the transformed zone significantly alters the stress distribution beneath the indenter.

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Instrumented indentation has proved to be an invaluable tool to determine the small volume mechanical behaviour of shape memory alloys (SMAs). Multi-axial experiments show that SMAs can exhibit pressure sensitive martensite phase transformation, which manifests in terms of tension-compression asymmetry of the associated stress and strain. Since high magnitude of pressure can prevail during indentation, the spherical indentation response of SMAs is investigated in this work by using a constitutive model that captures the above behaviour. Finite element (FE) simulations are first performed at two temperatures (close to A s and above A f ) and corresponding to different values of pressure sensitivity parameter γ 1 for a Ni-Ti SMA. It is found that the indentation load and mean contact pressure enhance at a given depth, while the residual depth at complete unloading (for temperature below A f ) reduces with increase in γ 1. Further, the transformation zone size at a fixed load drops dramatically with increase in pressure sensitivity index. An expanding cavity model (ECM) is also developed to predict the mean contact pressure for a pressure sensitive SMA and validated against FE simulations as well as available experimental data.