A failure criteria for unidirectional fiber reinforced composites based on micromechanics by asymptotic homogenization

Resumo

This work presents a successful methodology for obtaining failure envelopes of unidirectional fiber reinforced composites based on micromechanical analysis by the asymptotic homogenization [1] method. Given a structure (in this case a composite material lamina) and external loads, plus having its material heterogeneity geometrically represented by a periodic unit cell of microstructure, the asymptotic homogenization method is able to predict its micromechanical stresses. Such stresses may be evaluated by failure criteria of the composite's constituents for several loading conditions, and this way it is possible to assess the composite's failure envelope. In the methodology developed, a periodic unit cell of the composite microstructure is isolated, consisting of a parallelepiped of polymeric matrix reinforced by cilindrical fibers oriented in one direction, and its behaviour is evaluated by an appropriate finite elements model. At first, the unit cell is tested in several directions to find strengths for the matrix and fiber and also matrix/fiber interface, thus evaluating failure characteristics of the composite constituents. The tests are carried out considering several possible orientations for the unit cell inside the related macroscopic media, which take into account the possible relative positions of the chosen unit cell inside the material heterogeneity of the composite. Then, the strengths of the constituents are used to predict the failure envelope for the fiber reinforced material, according to failure criteria devoted to the constituents. In this prediction, it is possible to say which is the constituent that fails first for each of the test loads. The results obtained are in good agreement with experimental data for carbon/epoxi and glass/epoxi composites. Moreover, the envelopes obtained are similar to the Puck & Schürmann [2] criterion, widely used to predict failure of such composites. This way, the present methodology renders good failure envelopes for fiber reinforced composites and gives information on the strengths of the constituents and material phase of failure, benefits from an incorporated micromechanical analysis.

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