Structural alloys used in energy system components exhibit complex thermomechanical behavior that is inherently time-dependent and hereditary, in the sense that current behavior depends not only on current conditions but on thermomechanical history. Recently, attention is being focused on new generations of alloys that possess strong directional characteristics, e.g., directionally solidified metals and metal-matrix composite materials. In high temperature applications these materials exhibit all the complexities of conventional alloys and further, their strong initial anisotropy adds additional complexities. Here a unified continuum theory is developed aimed at representing the high-temperature, time-dependent, hereditary deformation behavior of materials that are initially (locally) transversely isotropic.; This work begins with a review of Robinson's 1 isotropic theory for isothermal conditions. This theory is extended through the use of tensorial invariant theory in construction of a potential function similar to the yield function of classical plasticity theory. Once the potential is developed the unified theory is then derived. Next, the nature of the potential function is explored under conditions of constant inelastic state. Relationships between parameters associated with anisotropic strength are then derived. Following this an experimental procedure is developed wherein these relationships are used in obtaining the material constants characterizing viscoplasticity and transverse isotropy. Finally the theory is exercised with homogeneously stressed and strained elements.
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