Rate and Time-Dependent Failure: Mechanisms and Predictive Models

No text on polymer science and viscoelasticity is complete without a discussion of time-dependent failure and just as with other structural materials, failure must be defined. In this chapter, only failure by a creep to yield or a creep to rupture (separation) will be considered. We will address both the mechanisms of deformation that often precede these types of failures as well as modeling to describe this behavior. The primary focus will be on one-dimensional models but many of the models discussed have been or can be extended to three-dimensions. The procedures to be discussed are not new and are relatively easy to use by the design engineer to make estimates of the time for either yielding or rupture to occur. While no discussion of either viscoelastic fracture mechanics or fatigue crack growth will be given these are very important topics and the reader is referred to Knauss (1973, 2003) for the former and to Kinloch and Young (1983) for the latter for an in-depth discussion of these topics. Fracture based approaches for prediction of time to failure work best when a crack of a known size exists. The same is true for fatigue as a relation between crack growth rates and time to failure can be established. Newer approaches provided by damage mechanics (Krajcinovic, (1983)) and viscoplasticity (Lubliner, (1990)) provide a more rational but highly mathematical approach to damage and/or failure evolution for three-dimensional stress states and are perhaps best suited for numerical procedures such as the finite element method. Here we restrict ourselves to simpler, analytic approaches to introduce the fundamental issues. Failure is a defined quantity that must be established in the initial design stages. Typically, structural failure is defined as excessive deflection, yielding, or rupture. Excessive deflection may occur while materials of a structure are linear elastic or viscoelastic without yielding and for such circumstances can be predicted and prevented by elastic or viscoelastic stress, strain and deflection analysis as described in earlier chapters. The focus in this chapter will be on excessive deformation due to time-dependent yielding and/or progressive damage accumulation leading to rupture.