In recent years, great strides have been taken in the advancement of Shape Memory Alloy (SMA) modeling capabilities. The accompaniment of advanced constitutive models with standardized solution techniques have meant that we can dive deeper into the material and its thermomechanical response than ever before. The most widely modeled and produced SMA class in industry today is one which hosts Ni as a core component of its composition, and usually takes the form of NiTi. When these SMA materials are heat treated, particles form in the microstructure and the material response changes drastically. This work directly models aspects of the precipitated microstructure by creating a modeling framework based on the Finite Element Method (FEM). The framework is able to conduct micromechanical studies through the use of cubic Representative Volume Elements (RVEs) where the response of the SMA material matrix is driven by a currently developed SMA model with extended capabilities. The RVEs have Periodic Boundary Conditions (PBCs) applied to the cube faces, satisfying the assumption that the cube of material is an excerpt of a continuous material microstructure. Under these conditions, coherency stresses are introduced into the material through the introduction of elastic Eshelby-type stresses. The material has Ni depleted under the assumption of Fickian diffusion in accordance to the presence of precipitates, giving a heterogeneous distribution of Ni in the matrix, and the final conditioned microstructure is taken through a thermomechanical cycle. The final responses of the material are extracted as the volume average response of the microstructure during these cycles. The current work is broken down into two studies. The first study utilizes the newly developed framework in order to probe various changes in the microstructure which may come about during precipitation, and to determine effects of precipitate volume fraction on the material's macroscopic response. Of key interest in this study are the results of stresses arising from particle coherency with the matrix, changes due to Ni depletion arising from precipitation, and effects arising from purely structural interactions in the microstructure. The study shows that the presence of precipitates in SMAs smoothens their hysteretic behavior, decreases transformation strains, and shifts transformation temperatures to higher values. The subsequent study takes this modeling framework and applies it to predict responses of precipitated materials. It does this by estimating precipitate volume fractions in a heat treated material, and building and solving RVEs to predict the effective response of the precipitated material. The predicted RVE responses are then compared to experimental results. Excellent agreement is seen for low volume fractions of precipitates while trends are captured for higher estimated volume fractions. Using this modeling framework to understand the effects of various aspects of the aforementioned precipitation can help in the design of future materials and in the prediction of their energetic responses.
