Nanovoid induced multivariant martensitic growth under negative pressure: Effect of misfit strain and temperature on PT threshold stress and phase evolution

Abstract

In the present work, the effect of a pre-existing nanovoid on multivariant martensitic growth and in particular, on the phase transformation (PT) threshold stress, is investigated using the phase field approach. In order to create a pre-existing nanovoid in the model, a single nanovoid has been stabilized in the center of the computational domain using a phase field approach. The coupled Ginzburg-Landau and elasticity equations are solved to capture the evolution of martensitic nanostructure. The above systems of equations are solved using the finite element approach and the COMSOL code. Nanovoid-induced two variant martensitic growth under negative pressure is studied in detail. The PT threshold stress is found for different nanovoid misfit strain constants and different temperatures. The PT threshold stress increases linearly by increasing the temperature for any misfit strain which rate of increase is found the same for any misfit strain. For any temperature, the PT threshold stress nonlinearly decreases as the misfit strain constant increases. Under the applied negative pressure, both the first and the second variants grow from the nanovoid surface which evolutions are explained based on the distributions of the stress and transformation work. The martensitic growth is more pronounced for larger misfit strains due to higher stress concentrations. The martensitic nanostructure, stress distribution and the PT threshold stress are also found in the presence of a nano-hole for different temperatures and are compared to those of the nanovoid. The martensitic growth is also studied for different temperatures. As the temperature increases, the growth is slower and this is explained using the phase concentration for both the first and the second variants which increases nonlinearly and its growth rate nonlinearly varied vs time for any temperature. For larger temperatures, the phase concentration decreases and the growth rate decreases at the same phase concentration. A larger negative pressure is required for the martensitic growth at larger temperatures. The effect of sample size on the PT threshold stress was also investigated. The effect of mechanical driving force on the nanovoid-induced martensitic growth is studied by applying different negative pressures. As the negative pressure increases the growth exceedingly increases. The phase concentration evolution reveals the dependence of the growth on the loading magnitude so that for any loading, the phase concentration increases nonlinearly with a nonlinearly variable growth rate. As the loading increases, the phase concentration increases and the growth rate increases at the same phase concentration. Applying uniaxial loading results in nanovoid-induced single variant martensitic growth for which the PT threshold stress almost linearly decreases as the misfit strain constant increases. Comparing the results of the uniaxial loading and negative pressure shows that the PT threshold stress under uniaxial loading is approximately 1.6 times smaller than that under negative pressure for any misfit strain. The presented model and the obtained results will help to develop an interaction model between nanovoids and multiphase structure at the nanoscale.