AUTHOR=Engelbrecht-Wiggans Amy , Phoenix Stuart Leigh 

TITLE=A Stochastic Model Based on Fiber Breakage and Matrix Creep for the Stress-Rupture Failure of Unidirectional Continuous Fiber Composites 2. Non-linear Matrix Creep Effects

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.644815

DOI=10.3389/fphy.2021.644815

ISSN=2296-424X

ABSTRACT=Stress rupture is a time-dependent failure mode occurring in unidirectional fiber composites under high tensile loads sustained over long times, resulting in highly variable lifetimes and explosive consequences. Stress-rupture is of particular concern in composite overwrapped pressure vessels (COPVs), tension members in infrastructure applications and high angular velocity rotors.  Stress rupture begins with the failure of individual fibers at random flaws, followed by local load-transfer to intact neighbors through shear stresses in the matrix.  Over time, the matrix between the fibers creeps in shear, lengthening the overload zones around previous fiber breaks, resulting in more fiber breaks, and eventually, formation clusters of fiber breaks, one of which eventually becomes catastrophically unstable. 
Most previous models are extensions of stochastic breakdown models for single fibers, and do not reflect micromechanical detail, particularly the creep behavior of the matrix. These models may be adequate for modeling composite stress rupture under a constant load; however, they are of highly questionable accuracy under more complex loading profiles. Of particular interest is a constant load in service that follows a brief ‘proof test’ at a load level up to 1.5 times this service load. Such models frequently predict an improved reliability for proof-test survivors. In our previous work we showed that damage occurs in the form of a large number of fiber breaks, and the net effect is reduced reliability over time. 
The current paper revises the previous model to include non-linear creep whereby power-law creep behavior occurs not only in time but also in shear stress level and with differing exponents. This model admits two additional parameters, one determining the sensitivity of shear creep rate to shear stress level, and another that acts as a threshold shear stress level. The new model predicts very similar behavior to the previous model, except that it allows for a threshold shear stress allowing consideration of behavior under near plastic matrix yielding or even matrix shear failure, the consequence of which is a large increase in the length-scale of load transfer around fiber breaks, and thus, a significant reduction in composite strength and increase in variability.