On the Displacement Field for Unidirectional Off-Axis Composites in 3-Point Flexure — Part 1: Analytical Approach

Abstract

The displacement field of a unidirectional off-axis specimen in 3-point flexure test is obtained in a new way, by applying the Second Castigliano's theorem and the unitarial load method. The displacement field is calculated for two cases: in the first one, lift-off between specimen and fixture support occurs caused by bending-twisting coupling, and specimen is supposed to contact with the test fixture support at two diagonally opposite points. In the second case, lift-off does not occur and specimen is supposed to contact with the fixture support at four corners. The limit between two cases is established by the calculation of the critical value of the span-to-width ratio for lift-off to occur. The displacement field calculated includes shear effects and satisfies displacements compatibility and equilibrium conditions, except in the vicinity of point reactions and applied load. Neither displacement field solutions for composite plates with point boundary conditions, nor solutions based on the Second Castigliano's theorem concerning composite plates have been encountered in the literature survey.