Stable and Unstable Crack Growth in Viscoelastic Media

Abstract

The failure of load-bearing structures by fracture is generally important in all phases of our society. It may concern small household items as well as expensive structures of civil or space applications and accordingly may cause varying degrees of economic distress. While the state of failure is usually easily determined as either "not failed" or "completely failed," the estimation of how close to either state a structure is, poses a much more difficult problem. It is important to recognize, however, that from an engineering point of view, the latter problem is the important one because it would allow, in principle, the prediction of the conditions leading to fracture and thus to a close estimate of the service life of a structure. Inasmuch as failures by fracture involve the growth of cracks it appears that keeping track of the size of a crack in a particular structure provides a means of assessing *quantitatively* the strength prior to complete failure. If one agrees that the description of structural strength is rationalized in terms of the size of the defects, it foll0ws that one must attempt to understand the laws that govern the growth of such defects in order to predict complete failure. Fracture of materials is a complicated process which encompasses atomistic aspects, as well as microscopic and large-scale continuum mechanical considerations. Although one of these aspects should not be considered without the other we shall be concerned with the continuum-mechanical formulation of the problem of fracture growth in viscoelastic materials. From this viewpoint the prediction of failure comprises three phases: first an examination of the physical situation presented by a static or growing defect in a material, second the translation of this physically observable situation into a mathematical model which is amenable to analysis by currently available or extendable tools of mathematics, third the theoretical exploitation of the mathematical model in an attempt to predict the behavior of defects under load and the comparison of these results with experimentally observable phenomena to assess the validity of the modelling process as given from phase one and phase two. While there are many important details that have bearing on such a development we shall be concerned more with the principles of the analysis and show how the various considerations of the three phases enter into the overall structure of the crack propagation problem. In keeping analytic work as simple as possible it is intended to emphasize what type of results may be obtained with the aid of continuum mechanics and where continuum mechanics requires support by microscopic considerations.

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