Significant scatter is observed in fatigue tests at specimen level despite the care taken to ensure that the specimens and the test conditions are identical. Heterogeneity in material microstructure is one of the major sources for this scatter. With the advancement in computing and experimental techniques, significant amount of work is being performed to develop computational frameworks that relate the material microstructure and fatigue life. These frameworks typically involve the use of crystal elasticity and plasticity based calculation of microstructural stress-strain fields, followed by the use of microstructure sensitive fatigue life models. One of the challenges in such frameworks is that simulations used to calculate microstructural scale stress-strain are computationally very expensive. So, to use such a framework to get predictive estimates of fatigue life, or to explore the vast space of possible microstructures, reductions in the computation time at the microstructural scale stress strain calculation step will be quite beneficial. In this research, we are investigating if techniques based on tensor decompositions and low rank approximation can achieve this reduction in the computation time.