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

Stress rupture (sometimes called creep-rupture) is a time-dependent failure mode occurring in unidirectional fiber composites under high tensile loads sustained over long times (e. g., many years), resulting in highly variable lifetimes and where failure has catastrophic consequences. Stress-rupture is of particular concern in such structures as composite overwrapped pressure vessels (COPVs), tension members in infrastructure applications (suspended roofs, post-tensioned bridge cables) and high angular velocity rotors (e.g., flywheels, centrifuges, and propellers). At the micromechanical level, stress rupture begins with the failure of some individual fibers at random flaws, followed by local load-transfer to neighboring intact fibers through shear stresses in the matrix. Over time, the matrix between the fibers creeps in shear, which causes lengthening of local fiber overload zones around previous fiber breaks, resulting in even more fiber breaks, and eventually, formation clusters of fiber breaks of various sizes, one of which eventually grows to a catastrophically unstable size. Most previous models are direct extension of classic stochastic breakdown models for a single fiber, and do not reflect the micromechanical detail, particularly in terms of the creep behavior of the matrix. These models may be adequate for interpreting experimental, composite stress rupture data under a constant load in service; however, they are of highly questionable accuracy under more complex loading profiles, especially ones that initially include a brief “proof test” at a “proof load” of up to 1.5 times the chosen service load. Such models typically predict an improved reliability for proof-test survivors that is higher than the reliability without such a proof test. In our previous work relevant to carbon fiber/epoxy composite structures we showed that damage occurs in the form of a large number of fiber breaks that would not otherwise occur, and in many important circumstances the net effect is reduced reliability over time, if the proof stress is too high. The current paper continues our previous work by revising the model for matrix creep 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, thus, 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 reminiscent of a yield stress in the plastic limit, which the model also admits. The new model predicts very similar behavior to that seen in the previous model under linear viscoelastic behavior of the matrix, except that it allows for a threshold shear stress. This threshold allows 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. Derivations of length-scales resulting from non-linear matrix creep are provided as Appendices in the Supplementary Material.