Failure criteria fracture

The decrease in with crack depth for fracture of IG-11 graphite presents an interesting dilemma. The utihty of fracture mechanics is that equivalent values of K should represent an equivalent crack tip mechanical state and a singular critical value of K should define the failure criterion. Recall Eq. 2 where K is defined as the first term of the series solution for the crack tip stress field, Oy, normal to the crack plane. It was noted that this solution must be modified at the crack tip and at the far field. The maximum value of a. should be limited to and that the far... 

The decreasing value of K with decreasing flaw size for fracture of IG-11 graphite suggests that the near crack tip failure criterion would be better expressed by combining the near crack tip stress intensification estimated by K with the far field applied stress, Sfraa(Eq. 28). Using simple superposition of the stress perpendicular... 

In the maximum stress failure criterion, each and every one of the stresses in principal material coordinates must be less than the respective strengths otherwise, fracture is said to have occurred. That is, for tensile stresses,... 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

Hence, the ratio Klc/Klcs may be directly and quantitatively related to the crack tip radius, g, at the onset of crack growth by assuming a failure criterion based upon the attainment of a critical stress acting at a certain distance ahead of the tip. A brief examination of Eq. (12) shows that it exhibits the same general trends with regard to rate and temperature dependence that were used successfully in the yield stress discussion to explain in a qualitative way the observed fracture behaviour. 

To summarise, the fracture data and type of crack growth over a wide range of rates and temperatures may all be rationalised by the concept of a critical stress acting over a critical distance and this two-parameter model provides a unique failure criterion for thermosetting polymers. 

Before starting this analysis a clear formulation of a failure criterion for a given object is needed. In some cases, the criterion is self-evident, e.g. when failure occurs by fracture in a pipe whereas in other cases it requires significant experimental study and analysis. 

The results of the experiments were analysed according to continuum mechanics as v/ell as fracture mechanics principles. The evaluation of the stress at failure as well as the energy released are used to evaluate the validity of, respectively, a maximum stress criterion energy approach as a failure criterion. 

The maximum principal strain criterion for failure simply states that failure (by yielding or by fracture) would occur when the maximum principal strain reaches a critical value (ie., the material s yield strain or fracture strain, e/). Again taking the maximum principal strain (corresponding to the maximum principal stress) to be 1, the failure criterion is then given by Eqn. (2.4). 

Several things immediately become obvious from Eqns. (7.10) and (7.11) (i) A specific, independent failure criterion is used, and the crack size for failure, Uf, is a function of the fracture toughness and the maximum applied stress,... 

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