Shape distortion in sintering results from nonhomogeneous temperature activating a long-range mass transport.

Sintering theory predicts no long-range mass transport or distortion for uniformly heated particles during particle coalescence. However, in sintering-based manufacturing processes, permanent part distortion is often observed. The driving forces and mechanisms leading to this phenomenon are not understood, and efforts to reduce distortion are largely limited to a trial-and-error approach. In this paper, we demonstrate that distortion during sintering results from mass-transport driven by nonhomogeneous temperature distribution. We then show that hitherto unknown mass transport mechanisms, working in the direction opposite to temperature gradient are the likely cause of distortion. The experimental setup, designed for this purpose, enables the quantification of distortion during sintering. Two possible mass transport mechanisms are defined, and the continuum model applicable to both is formulated. The model accurately predicts the transient and permanent distortion observed during experiments, including their size dependence. Methods to control distortion that can give rise to 4D printing are discussed.

Lattice continuum and diffusional creep.

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.

Size-dependent energy in crystal plasticity and continuum dislocation models.

In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nye's dislocation density tensor, be justified from the point of view of dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physical expressions is possible, but only if the multiplicity of characteristic lengths associated with different slip systems, is sacrificed. Finally, we discuss the consequences of the assumption that a single length scale governs the plasticity of a crystal, and note that the plastic dissipation at interfaces has a strong dependence on the length scale embedded in the energy expression.