Although 3D printing has the potential to transform manufacturing processes, the strength of printed parts often does not rival that of traditionally-manufactured parts. The fused-filament fabrication method involves melting a thermoplastic, followed by layer-by-layer extrusion of the molten viscoelastic material to fabricate a three-dimensional object. The strength of the welds between layers is controlled by interdiffusion and entanglement of the melt across the interface. However, diffusion slows down as the printed layer cools towards the glass transition temperature. Diffusion is also affected by high shear rates in the nozzle, which significantly deform and disentangle the polymer microstructure prior to welding. In this paper, we model non-isothermal polymer relaxation, entanglement recovery, and diffusion processes that occur post-extrusion to investigate the effects that typical printing conditions and amorphous (non-crystalline) polymer rheology have on the ultimate weld structure. Although we find the weld thickness to be of the order of the polymer size, the structure of the weld is anisotropic and relatively disentangled; reduced mechanical strength at the weld is attributed to this lower degree of entanglement. (C) 2017 Elsevier Ltd. All rights reserved.