In composite structural design, a fundamental requirement is to furnish the designer with a set of elastic constants. For example, to design for a given temperature a laminate consisting of transversely isotropic fiber-reinforced laminae, we need five independent elastic constants of each lamina of interest, namely, E1, E2, ν12, G12, and ν23. At present, there exist seven tests, two of mechanical-lamina, two of thermal-expansion-lamina, and three of thermal-expansion-laminate types, to accomplish this task. It is known in the literature that the mechanical tests are capable of measuring E1, E2, and ν12, whereas the two thermal-expansion-lamina tests will measure α1 and α2, and the three thermal-expansion-laminate tests yield an over-determined system of three simultaneous equations of the remaining two unknown elastic constants, G12 and ν23. In this paper, we propose a new approach to determining those five elastic constants with uncertainty bounds using the extra information obtainable from an over-determined system. The approach takes advantage of the classical theory of error propagation for which variance formulas were derived to estimate standard deviations of some of our five elastic constants. To illustrate this approach, we apply it to a set of experimental data on PEEK/IM7 unidirectional lamina. The experiment consists of the following tests: Two tensile tests with four samples of unidirectional specimens to measure E1, E2 and ν12; two thermal-expansion-lamina tests for coefficients (α1 and α2) each using four [(0)32]T unidirectional specimens; and three thermal-expansion-laminate tests on four samples of [(+30/−30)8]s laminates. The results of our new approach are compared with those of a similar but more ad hoc approach that has appeared in the literature. The potential of applying this new methodology to the creation of a composite material elastic property database with uncertainty estimation and to the reliability analysis of composite structure is discussed.

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