Critical review of some theories in fracture mechanics

Abstract

Several theories in fracture mechanics apparently approach the problem of crack extension from different points of view but lead to the same main result. Thus, in the case of brittle cracks, an equivalence exists between the Griffith energy criterion, the Barenblatt cohesion modulus theory, and the assumption of a critical mean stress at an end-region of fixed size. It is shown that the feature common to these theories is the adoption (explicitly stated or not) of an autonomous end-region, and that this assumption alone is sufficient for arriving at the principal results.In the case of brittle materials, the end-region acts as an instability kernel. This region develops into an instable region at a certain load, and crack extension takes place. The instability is clearly associated with the atomic force-distance relations. The interatomic distance thus provides the characteristic length needed to assure the existence of an autonomous end-region.It is suggested that similar instable end-regions may develop also in non-brittle materials. The characteristic length is here given by different kinds of imperfections.If no other characteristic length than the dimensions of the crack can be found, then a conclusion must be that the fracture stress is independent of the size of the crack.In fracture mechanics there are several theories which aim at a rather general description of the fracture process without going much into detail as concems material properties and surrounding conditions. Since the Griffith theory(i) (1920) those theories almost invariably start from the Kolosov-Inglis solution of the stress-strain field surrounding a crack in an elastic medium. In some theories the corresponding dynamic solution is used.The big difficulty in fracture mechanics is that the fracture process takes place in a small region near the crack-tip and the characteristics of this region cannot be determined by the Kolosov(2)-Inglis(3) solutfton at all. In fact one could, albeit somewhat roughly, define this endregion where the fracture process takes place as the region where the Kolosov-Inglis solution is not applicable. The Kolosov-Inglis solution is therefore useful for the determination of the boundary conditions of the end-region, but a description of the properties of this end-region is necessary for an understanding of the fracture process.In the Griffith theory the properties of the end-region are described only by ascribing to it a certain energy-absorbing capacity. This is the Griffith energy criterion. This criterion has been extended by Orowan(11) for the case of non-brittle fractures. In another theory the end-region is ascribed a certain stress-carrying capacity and a certain size. In the Barenblatt(4) theory the end-region is ascribed a cohesion modulus. The size of the end-region is assumed to be small compared to the dimensions of the crack in all these theories. Barenblatt assumed that the size of the end-region, although it does not need to be specified as in the stress criterion, is autonomous, i.e. not depending ...

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