Stress/strain conditions, linear elastic fracture mechanics

Substantial work on the appHcation of fracture mechanics techniques to plastics has occurred siace the 1970s (215—222). This is based on earlier work on inorganic glasses, which showed that failure stress is proportional to the square root of the energy required to create the new surfaces as a crack grows and iaversely with the square root of the crack size (223). For the use of linear elastic fracture mechanics ia plastics, certaia assumptioas must be met (224) (/) the material is linearly elastic (2) the flaws within the material are sharp and (J) plane strain conditions apply ia the crack froat regioa. 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

Several cautions are, however, in order. Polymers are notorious for their time dependent behavior. Slow but persistent relaxation processes can result in glass transition type behavior (under stress) at temperatures well below the commonly quoted dilatometric or DTA glass transition temperature. Under such a condition the polymer is ductile, not brittle. Thus, the question of a brittle-ductile transition arises, a subject which this writer has discussed on occasion. It is then necessary to compare the propensity of a sample to fail by brittle crack propagation versus its tendency to fail (in service) by excessive creep. The use of linear elastic fracture mechanics addresses the first failure mode and not the second. If the brittle-ductile transition is kinetic in origin then at some stress a time always exists at which large strains will develop, provided that brittle failure does not intervene. 

Now, consider the stress concentration produced by cracks. The stress field around a crack tip can be determined by linear elastic fracture mechanics (common solutions for this are available in standard text books [51, 53]). Here, a material is treated as a linear elastic continuum, and a crack is assumed to be a mathematical section through it (having a crack tip radius of zero). Under plane strain conditions, the components of the local stress field on a volume element, o,j, in a region near the crack tip is space dependent and can be expressed as (polar coordinates r and 0 origin at the crack tip) [51, 53] ... 

The stress condition in linear elastic fracture mechanics in which there is zero strain in a direction normal to both the axis of applied tensile stress and the direction of crack growth (that is, parallel to the crack front) most nearly achieved in loading thick plates along a direction parallel to the plate surface. Under plane-strain conditions, the plane of fracture instability is normal to the axis of the principal tensile stress. 

When specimens rupture in tensile experiments, the failure typically initiates at an identifiable crack or flaw within the specimen. A method to obtain estimations of the material toughness from this result is based on the inspection of fracture surfaces and the appUcation of the linear elastic fracture mechanics, hmnediately prior to material frachire, and provided plane-strain conditions hold, the stress intensity factor reaches a critical value, which is considered a measure of the fracture toughness, K, ... 

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