The increasing use of alpha/beta Ti-Al alloys in critical aircraft gas turbine engine and airframe applications necessitates the further development of physically-based constitutive models that account for their complex microdeformation mechanisms. Alpha/beta Ti-Al alloys are dual-phase in nature consisting of a mixture of hcp (alpha) and bcc (beta) crystal structures, which through variation in alloying elements and/or processing techniques can be produced in a wide range of microstructural compositions and morphologies. A constitutive model for these materials should address the various sources of material anisotropy and heterogeneity at both the micro and macroscales. The main sources of anisotropy in these materials are the low symmetry of the hcp phase, the texture, the relative strengths of different slip systems, non-planar dislocation core structures, phase distributions, and dislocation substructure evolution. The focus of this work is the development of a 3-D crystal plasticity model for duplex Ti-6Al-4V (Ti-64), an (alpha+beta) alloy. The model is used to study the process of attachment fatigue. Attachment fatigue is a boundary layer phenomenon in which most of the plastic deformation and damage accumulation occurs at depths on the order of tens of microns and encompasses regions of only a few grains into the depth of the material. The use of computational micromechanics-based crystal plasticity models to study attachment fatigue is a relatively new approach. This approach has the potential to offer additional insight to classical homogeneous plasticity models, since the length scales over which relative slip and crack initiation occur during this process is on the order of microstructural dimensions. Emphasis is placed on understanding the effects that texture, slip strength anisotropy, and phase distribution have on the surface and subsurface deformation fields during attachment fatigue. The deformation fields are quantified in terms of cumulative effective plastic strain distributions, plastic strain maps, and plastic strain-based critical plane multiaxial fatigue parameters.