Linear elastic fracture mechanics behavior

Linear Elastic Fracture Mechanics Behavior of Graphite... 

Karger-Kocsis recorded the different fracture behaviors of non-nucleated and -modified PP (MFR 0.8 dg min 1) tested in a three-point bending configuration at 1 ms-1 at 23 °C, a-PP was semi-ductile and /3-PP ductile with a plastic hinge at - 40 °C a-PP was brittle, /i-PP ductile [72], The descriptors from the linear elastic fracture mechanics (LEFM), Kq, the stress intensity factor, and Gc, the energy release rate, used to quantify the toughness correlated well with the fracture picture. This conclusion is also valid for... 

Linear elastic fracture mechanics (LEFM) approach can be used to characterize the fracture behavior of random fiber composites. The methods of LEFM should be used with utmost care for obtaining meaningful fracture parameters. The analysis of load displacement records as recommended in method ASTM E 399-71 may be subject to some errors caused by the massive debonding that occurs prior to catastrophic failure of these composites. By using the R-curve concept, the fracture behavior of these materials can be more accurately characterized. The K-equa-tions developed for isotropic materials can be used to calculate stress intensity factor for these materials. 

The fact that thermosets are typically brittle and generally exhibit linear elastic stress-strain behavior suggests that linear elastic fracture mechanics (LEFM) and test methods may be applicable. In fact, these approaches have proven very popular, as is evidenced by the successful use of a number of LEFM-based fracture... 

Polymers which yield extensively under stress exhibit nonlinear stress-strain behavior. This invalidates the application of linear elastic fracture mechanics. It is usually assumed that the LEFM approach can be used if the size of the plastic zone is small compared to the dimensions of the object. Alternative concepts have been proposed for rating the fracture resistance of tougher polymers, like polyolelins, but empirical pendulum impact or dart drop tests are deeply entrenched forjudging such behavior. 

For many engineering applications, impact fracture behavior is of prime practical importance. While impact properties of plastics are usually characterized in terms of notched or un-notched impact fracture energies, there has been an increasing tendency to also apply fracture mechanics techniques over the last decade [1, 2 and 3]. For quasi-brittle fracture, a linear elastic fracture mechanics (LEFM) approach with a force based analysis (FBA) is frequently applied to determine fracture toughness values at moderate loading rates. 

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. 

In Chapters 2 and 3, the restrictions in the use of linear elastic fracture mechanics (LEFM) were discussed in terms of the dimensions of the crack and the body (specimen, component, or structure) relative to the size of the crack-tip plastic zone. Simple estimates of the plastic zone sizes were given in Section 3.6. A more detailed examination of the role of constraint (plane strain versus plane stress) and the variations in plastic zone size from the surface to the interior of a body would help in understanding fracture behavior and the design of practical specimens for measurements of fracture toughness. Note that the plastic zone size in actual materials... 

Our discussion thus far has focused in a rather superficial way on the general evolution of the important area of fracture mechanics. The basic objective of fracture mechanics is to provide a useful parameter that is characteristic of the given material and independent of test specimen geometry. We wUl now consider how such a parameter, such as G (, is derived for polymers. In doing so we confine our discussion to the concepts of linear elastic fracture mechanics (LEFM). As the name suggests, LEFM apphes to materials that exhibit Hookean behavior. 

The equivalence of K and (7, which strictly holds for elastic materials with linear load-deflection characteristics, is referred to as linear-elastic fracture mechanics (LEFM). Subsequently this basic concept has been modified to describe also the behavior of ductile materials. For instance. Wells [3] considered the plastic strain at the crack tip as the crack... 

Newman and Williams (1978) carried out sharp-notch Charpy tests for ABS at 193 < T(K) < 333 and showed that linear elastic fracture mechanics was applicable only up to 233 K. Above 273 K, the energy absorbed in impact was proportional to the fi"acture area and correlated well with the volume of the whitened zone. Mixed behavior occurred at the intermediate temperatures. More detailed study of the notched Izod impact behavior of ABS was carried out using instrumented... 

The figure also shows a schematic diagram of load vs displacement plots describing the procedure for determination of the critical load in a linear-elastic fracture mechanics (LEFM) test (see Fig. 10.1c). The determination of Ki is dependent on testing the material under conditions in which it exhibits essentially linear-elastic behavior indicative of a plastic zone that is very small relative to flaw size and specimen dimensions, the domain of LEFM. The equations for the compact specimen and three-point bend specimen are as follows ... 

A critical research gap in corrosion science is the absence of the corrosion equivalent for the stress intensity factor (K) that has been the mainstay of structural mechanics for the past several decades. The stress intensity factor was developed to predict the behavior of pre-existing flaws in structural materials and the eventual life of a component under conditions in which the flaw develops into stable cracks. The power of K is in the concept of similitude well-defined cracks and crack tips that are different in size or shape but possess the same K (as determined by geometry, loading, and the theories of linear-elastic fracture mechanics) will experience the same mechanical driving force for crack growth. Thus, similitude allows small, well-defined samples to be tested in the laboratory to determine the conditions of crack growth and fracture and the results to be quantitatively extended to more complicated real-world structures containing cracks. Virtually... 

---