In this work, we present an anisotropic multi-phase phase field model with fully variational evolution to treat the large boundary energy differences characteristic of nanotwinned structures in face centered cubic materials. This model formulation is first verified and validated against MD simulation, theory, and experiment. Using the model, we study the processes of grain boundary detachment and subsequent detwinning of nanotwins with thicknesses ranging from 1 nm to 15 nm under annealing temperatures at and below 700K.