Starting with specific constitutive equations, methods of evaluating material properties from experimental data are outlined and then illustrated for some polymeric materials; these equations have been derived from thermodynamic principles, and are very similar to the Boltzmann superposition integral form of linear theory. The experimental basis for two equations under uniaxial loading and the influence of environmental factors on the properties are first examined. It is then shown that creep and recovery data can be conveiently used to evaluate properties in one equation, while two‐step relaxation data serve the same purpose for the second equation. Methods of reducing data to accomplish this characterization and to determine the accuracy of the theory are illustrated using existing data on nitrocellulose film, fiber‐reinforced phenolic resin, and polyisobutylene. Finally, a set of three‐dimensional constitutive equations is proposed which is consistent with nonlinear behavior of some metals and plastics, and which enables all properties to be evaluated from uniaxial creep and recovery data.

Bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity. Inequalities between certain approximate and exact forms of the potential and complementary energy functionals are first estab lished. These inequalities are then used in conjunction with a new method for minimizing the difference between upper and lower bounds in order to derive volumetric and linear thermal expansion coefficients. Application is made to two- and three-phase isotropic composites and a fiber-reinforced material. It is found for some important cases that the solutions are exact, and take a very simple form. We also show conditions under which the rule-of-mixtures and Turner's equation can be used for thermal expansion coeffi cients. Finally, simple methods for extending all results to viscoelastic composites are indicated.

A B S T R A C T A theory is developed for predicting the time-dependent size and shape of cracks in linearly viscoelastic, isotropic media. First, the effect of a narrow zone of disintegrating material at the crack tip off opening displacement and on a finite stress distribution ahead of the tip is examined for elastic materials. Extension to viscoelastic media is then made. Although the undamaged portion of the continuum is assumed linear, no significant restrictions are placed on the nature of the zone of failing material at the crack tip and, therefore, this material may be highly nonlinear, rate-dependent, and even discontinuous. Finally, formulation of the problem is completed by introducing a local energy criterion of failure at the tip which is applicable to both constant and transient tip velocities. Parts II-IV, to appear in succeeding issues, will cover approximate methods of analysis and several applications of the theory.Int. Journ. ofFracture, 11 (1975) 141-159

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