Numerical Simulations on the Indentation Behaviour of Shape Memory Alloys
Shape Memory Alloys (SMAs) are increasingly being used as micro actuators, sensors, as self expanding cardiovascular stents and in MEMs based devices because of their ability to recover large values of imposed strain. In light of the above applications, it is essential to be able to characterize the small volume mechanical properties of these materials. Instrumented indentation has emerged as a useful tool for this purpose. While the indentation tests are non- destructive and simple to conduct, the results obtained are difficult to interpret. This is because the stress state beneath the indenter is complex and non-homogeneous. Also, SMAs exhibit a complex deformation behaviour which is a combination of phase transformation and plastic yielding which makes the indentation analysis more difficult. Thus, it is essential to conduct numerical studies to better understand the response of these materials. In this thesis, the spherical indentation response of SMAs is investigated using the finite element method to understand the effect of various factors such as plastic slip, temperature etc. A constitutive model that allows for simultaneous development of plasticity and phase transformation is used for this purpose. It is found that the superelastic depth recovery ratio is independent of indentation strain and remains fairly constant in the absence of plasticity. Also, plastic yielding occurring concurrently with phase transformation is shown to retard the rate of evolution of phase transformation and inhibit strain recovery on unloading. FE simulations conducted over various temperatures revealed that the indention load and mean contact for a given indentation strain increased with an elevation in temperature. Also, the residual depth ratio obtained on unloading is found to be minimum near the A f similar to previously reported experimental observations. The expanding cavity model is developed and analytical solutions for the mean contact pressure and the size of the transformation zone obtained during indentation are derived. These solutions agree with the FE results for indentation strains in the range of 0.01 to 0.04. A method is proposed to evaluate the critical stress required to initiate phase transformation during uniaxial compression and the transformation strain based on the indentation stress strain curve. The effect of pressure sensitive transformation behaviour on the spherical indentation response is also studied. It is found that with increasing pressure sensitivity the mean contact pressure increases for a given indentation strain. At a constant load, the transformation zone size decreases with increase in the pressure sensitivity index.