Micromechanical modelling for onset of distortional matrix damage of fiber reinforced composite materials

A new multi-scale modelling approach is applied to specimen testing to define the critical strain invariants for the damage onset theory proposed by Gosse, Christensen and Hart-Smith. The onset theory is a micromechanics theory that uses critical strain invariants to predict the onset of damage within fiber polymer composites. To obtain the critical strain invariants for the matrix, finite element analyses are required of unidirectional off-axis specimens that have been tested to failure. The strains remain linear to failure and critical strain invariants can be determined from a linear finite element analysis but the use of continuum models to obtain the critical values requires strain enhancement factors. In this paper a new micromechanics-based modelling approach is proposed. A finite element analysis of the composite specimen is implemented with a square fiber array embedded within the polymeric matrix. Failure initiation sights are identified to obtain the critical values directly without the need for the strain enhancement factors. Numerical examples of the modelling process are provided including a 10° off-axis coupon with rectangular tabs. The results are compared to different modelling approaches. The tests and modelling are repeated for a 20° off-axis coupon but with oblique as well as rectangular tabs.