Elastic-plastic fracture mechanics EPFM

The utility of K or any elastic plastic fracture mechanics (EPFM) parameter to describe the mechanical driving force for crack growth is based on the ability of that parameter to characterize the stress-strain conditions at the crack tip in a maimer which accounts for a variety of crack lengths, component geometries and loading conditions. Equal values of K should correspond to equal crack tip stress-strain conditions and, consequently, to equivalent crack growth behavior. In such a case we have mechanical similitude. Mechanical similitude implies equivalent crack tip inelastic zones and equivalent elastic stress fields. Fracture mechanics is... 

In the case of thin sections the measure of toughness is given by plane-stress fracture toughness, Kc and elastic-plastic fracture mechanics (EPFM) are used. It is also necessary to bear in mind that plane-stress fracture toughness Kc is higher than plane-strain fracture toughness Xlc. 

The deformation characteristic of more ductile polymer materials at ambient temperatures like most thermoplastics or all elastomers is highly non-linear, e.g., either mostly viscoelastic or entropy-elastic or a combination of both. Compared to concepts of LEFM relatively rarely used for polymer materials different concepts of non-linear elastic firacture mechanics such as elastic-plastic fracture mechanics (EPFM) or post-yield fracture mechanics (PYFM) are somewhat widely applied, therefore. One of the most important concepts of EPFM is the J integral concept. Notwithstanding the J integral is primarily defined to be valid... 

In the previous sections, it was frequently stressed that linear-elastic fracture mechanics can only be used if the plastic zone near the crack tip is sufficiently small. If this is not the case, we enter the domain of elastic-plastic fracture mechanics (epfm) which can deal with a large plastic zone. The method, however, cannot be used for arbitrarily large plastic zones - plastic behaviour must stiU be restricted to the region around the crack tip and must be mainly determined by the surrounding elastic stress field. 

Fig. 5.10. Failure-assessment diagram (after [21]) in standardised form for Y = const. The arrows show how the state of the loaded component changes when the corresponding parameter is raised. Thus, increasing the limiting stress criimit or the initial crack length a increases the tendency for failure by crack propagation, whereas increasing the fracture toughness Kic decreases it. Within the region marked with EPFM, elastic-plastic fracture mechanics has to be used because the plastic zone near the crack tip is not small. This theory is the topic of section 5.3...

Figure 3 shows the load (P) - load line displacement (5) records obtained from fracture tests at room temperature and at quasi-static conditions (low loading rates) of propylene homopolymer, PPO, and thee controlled-rheology PPs. The mechanical response for all the materials presented clearly elastic-plastic behaviour and this justifies the use of the EPFM multiple specimen method to evaluate the fracture behaviour. In addition, all the curves deviated from linearity and at a certain deflection level, sudden instability occurred and the specimen broke in two halves. The difference in stiffness is due to the different initial crack lengths. 

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