Assessing the Damage Tolerance and Modeling of Fiber Reinforced Polymers and Elastomers

Expert Analysis

In general, polymers exhibit time dependence. If the forces and/or displacements are small such that the polymer behaves elastically (i.e., when unloaded, the load and displacement is zero if given enough time to recover), then it is said that the material has not suffered any permanent damage. For a viscoelastic material, this means that the stress can be accurately predicted by linear viscoelasticity.

Figure 1 shows the calculation of the linear viscoelastic stress given an arbitrary strain history.

The viscoelastic relaxation modulus E(t) is a fundamental property of the polymer network. It can be shown that the relaxation modulus can be computed given the cross-link density, the monomeric friction coefficient and other fundamental chain properties. The time dependence of the polymer network in a linear viscoelastic material is unaffected by the presence of reinforcing fibers.

Figure 2 shows the grow discrepancy between the linear viscoelastic stress prediction and the actual behavior of the polymer.

As the composite experiences increasing levels of stress, other time dependent phenomena begin to emerge as illustrated in Figure 2. Agreement between the linear viscoelastic predictions and actual begin to diverge. At this point, it is necessary to incorporate a more thorough understanding of the mechanism for damage. Void formation, entropic factors such as chain stretching become more important in determination of the stress response. This consultant has over 20 year of experience in the analysis of viscoelastic materials including the formulation and design of time dependent polymer and composites.

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