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This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their connection via tensors of elastic constants or compliances. Next the relationship between the elastic constants of individual crystallites to those of the polycrystal are developed by averaging according to micromechanical (Voigt, Reuss, Hill, Kröner self-consistent) and texture models. Different diffraction peaks respond differently to stress, and the strains measured from the peak positions are related to the stresses by a set of diffraction elastic constants. The later sections are devoted to practical applications: (i) in engineering where residual stress is estimated from the observed strains using known (or computed) diffraction elastic constants; and ii) in materials science where measurement of the diffraction elastic constants allows the single crystal elastic constants to be derived in favourable circumstances (e.g., ceria-tetragonal zirconia polycrystal, Ce-TZP).

This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.

Injection molding is one of the oldest polymer processing operations used to produce goods from thermoplastic polymers. Today, almost all commercial injection molding machines have a reciprocating single screw for softening (or melting) under heat a thermoplastic polymer, and polymer melt is then injected into an empty mold cavity, as schematically shown in Figure 8.1. In the injection molding operation, the mold is first closed and then a predetermined amount of polymer melt from the screw section is injected into an empty mold cavity. Pressure is maintained for some time after the mold cavity has been filled to permit the build-up of adequate pressure in the mold cavity. Cooling water is circulated through channels in the mold so as to keep the mold cavity walls at a temperature usually between room temperature and the softening (or melting) temperature of the polymer. Thus, the hot polymer begins to cool as it enters the mold cavity. When it is cooled to a state of sufficient rigidity, the mold is opened and the part is removed. Some of the important variables in the operation of an injection molding machine are: (1) pressure applied by the screw, (2) temperature profile of the screw section, (3) mold temperature, (4) the screw forward time, (5) the mold closed time, and (6) the mold open time. Relationships between these variables are very complicated. In general, one would like to know the pressure, temperature, and density of the polymer in the mold cavity as functions of time during and after the mold is filled. In principle, these quantities can be calculated, via a mathematical model, during the entire period of mold filling and subsequent cooling when information on the geometry of the mold cavity, the rheological properties of the polymer, the temperature at which the polymer enters the mold cavity, and the mold temperature is available. However, in practice it is not easy to develop a rigorous theory because of the geometrically complex shapes of mold cavities, the complex nature of mold filling patterns (i.e., jetting) at normal injection speeds of industrial practice, and the highly viscoelastic nature of polymer melts, which varies with temperature, pressure, and injection rate (i.e., shear rate in the runner).