Micromechanics of Fatigue Damage in Unidirectional Polymer Composites

Abstract

A work in progress is described that so far includes a finite element (FE) micromechanics modeling capability that generates random distributions of fibers in a periodic unit cell to predict fatigue damage in the matrix. The FE micromechanics model has automated features that facilitate parametric studies. This includes the ability to simulate any three-dimensional macroscopically uniform state of stress and to generate new fiber distributions within random-periodic unit cells that can have variable numbers of fibers. A damage evolution variable driven by the kinetic theory of fracture was implemented numerically in the FE computations. The spatial evolution of damage in the micromechanics model causes the deformation at some point to become unstable and define macroscopic failure of the composite. The effects of element size, time increment size, failed element residual properties, and fiber distribution were explored. Nomenclatureh = Planck's constant k = Boltzmann constant K b = molecular bond rupture rate T = absolute temperature U = activation energy γ = activation volume σ = effective stress σ 1 , σ 2 , σ 3 = ordered principal stresses ξ = hydrostatic stress η = second deviatoric stress invariant ξ 0 , η ∞ = constants in isotropic failure criterion ξ p , η p = stress point coordinates ξ f , η f = stress point coordinates on failure surface θ = orientation in the pi-plane

Random Fiber Micromechanics of Fatigue Damage

“…Different from the work reported previously [4], here we used the theory of yielding and failure for isotropic materials described by Christensen [7]. To date, we have restricted use to the form previously described by Raghava et al [8] as shown in Eq.…”

“…Study of fatigue at the micro-stress level will help to understand how to formulate composite level fatigue models for application in full scale structural analysis. Micromechanics of random fiber distributions also permit study of the effect of fiber distribution and other material parameters at the micro-scale on fatigue damage evolution and fatigue life [4].…”

“…The micromechanical model was described previously [4] and allows for either uniform hexagonal fiber packing or a "random-periodic" fiber packing as shown in Figure 1. The full details of the model were described by Anderson [5].…”

“…  (4) The above gives some fraction of the stress magnitude S according to how close the state of stress is to the failure surface and is applied in Eq. (1).…”

“…Note that η can be negative when the deviatoric part of Equation (3) is small compared to the hydrostatic part. For η < 0, then η was set to zero in Equation (4).…”