The standard practice in the literature for modeling materials processing in which changes in temperature induce significant volume changes is based on the a posteriori substitution of a temperature-dependent expression for density into the governing equations for an incompressible material. In this paper we show this ad hoc approach misses important terms in the equations, and by example show the ad hoc equations fail to capture important physical effects. First we derive the three-dimensional equations which govern the deformation and heat transfer of materials with prescribed temperature-dependent density. Specification of density as a function of temperature translates to a thermomechanical constraint, in contrast to the purely mechanical incompressibility constraint, so that the constraint response function (“pressure”) enters into the energy equation as well as the momentum equation. Then we demonstrate the effect of the correct constraint response by comparing solutions of our thermomechanical theory with solutions of the ad hoc theory in plane Poiseuille flow. The differences are significant, both quantitatively and qualitatively. In particular, the observed phenomenon of expansion cooling is captured by the thermomechanically constrained theory, but not by the ad hoc theory.

Cao et al. previously derived a thermomechanically constrained theory for materials with temperature-dependent density and applied it to the illustrative problem of plane Poiseuille flow between isothermal walls. Here the theory is applied to geometries and thermal boundary conditions of practical importance in polymer processing: flows through planar, circular and annular dies with heat loss through the die walls. How geometry and thermal boundary conditions combine with material propehes, especially thermal expansivity, to effect velocity and temperature profiles, and mass and volume flow rates is explored. A comparison is made with predictions that follow i f temperaturedependence of density is either ignored or handled (as is the standard practice) by a posteriori insertion of a temperature-dependent expression for density into equations derived for constant density.

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Highly localized tribological contacts can modify the surface texture of rolling element bearing surfaces. The evolution of the surface texture generates modified subsurface stress fields within the contact and subsequently may alter the bearing rolling contact fatigue (RCF) life. In this present study, relationships between bearing surface topography and subsurface stress states are examined for their effects on bearing RCF life in the limiting case of boundary or dry contact. Results show that seemingly minor changes to surface topography may influence the stress distribution enough to affect RCF life under heavily loaded conditions.

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