Modeling a sample size-dependency of martensitic phase transformation using a mesoscale framework

Abstract

Listen

Translate article

Predicting a sample size-dependency of the constitutive response of any material system when it is being used in nano- and micro-scale devices, such as NEMS and MEMS, is very crucial for their design process. This also includes the shape memory alloys (SMAs), where predicting a sample size-dependency of the phase transformation process is the key aspect. Many experimental studies with micropillar compression tests showed an increase in critical stress to transformation and an increase in transformation hardening as the sample size decreases below a critical size. In this work, we have employed and extended a recently developed mesoscale framework to model such size effects in SMAs. A plane strain tensile SMA strip of finite width is analyzed within a small deformation framework. The martensitic transformation regions are modeled as Eshelby inclusions in an austenite phase matrix. Circular potential nucleation sites are considered with a square packing for their spatial locations and with nucleation stress assigned to each site from a Gaussian distribution. The combination of the Gaussian distribution of nucleation stress and the size of the nucleation site represents the underlying SMA material microstructure. Our numerical analysis, with varying values of the aspect ratio between the strip width and the nucleation site size, provides a critical value of the aspect ratio characterizing a transitioning length scale between a bulk vs. a sample size-dependent phase transformation behavior. At the transition, the critical stress to phase transformation and the transformation hardening increase drastically as the aspect ratio decreases below its critical value. The limitations of these predictions are discussed with existing literature on experimental observations, and some perspectives to improve the model are stated.