Quasi-brittle fracture

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. 

Fracture Stress and Strain. Yielding and plastic deformation in the schematic representation of tensile deformation were associated with microfibrillation at the interface and stretching of the microfibrils. Because this representation was assumed to apply to both the core-shell and interconnected-interface models of compatibilization, the constrained-yielding approach was used without specific reference to the microstructure of the interface. In extending the discussion to fracture, however, it is useful to consider the interfacial-deformation mechanisms. Tensile deformation culminated in catastrophic fracture when the microfibrillated interface failed. This was inferred from the quasi-brittle fracture behavior of the uncompatibilized blend with VPS of 0.5, which indicated that the reduced load-bearing cross section after interfacial debonding could not support plastic deformation. Accordingly, the ultimate properties of the compatibilized blend depended on interfacial char-... 

The concept of quasi-brittle fracture implies that some materials that exhibit the characteristics of plastic materials at standard test, collapse in tests of the sample with a crack due to the quasi-brittle mechanism, that is, plastic deformation is concentrated in a narrow layer near the tip of a crack. For such materials, Griffith s criterion is relevant instead of the value of the surface energy to introduce the work of plastic deformation at the crack tip. 

Shilang Xu, H.W. Reinhardt. 1999. Determination of double-K criterion for crack propagation in quasi-brittle fracture. Part II Analytical evaluating and practical measuring methods for three-point bending notched beams. International Journal of Fracture. (98) 151-177. 

This is simply the equation of the surface with its points of critical combinations of studied factors, log V jci, T X2, and lo Xs, that result in brittle or quasi-brittle fracture without subcritical crack growth. Therefore, choosing the values of any two factors (e.g., /o and V), one can determine critical values of the third factor (T) with which brittle fracture will occur without stable crack growth. 

Quasi-brittle fracture. See fracture. Quasi-brittle fracture is characterized by some toughening mechanism which increases the fracture energy to a range from 0.1 kJm-2 (in concrete) to several kJm-2 in fibre-reinforced materials. 

FRACTURE TOUGHNESS STRESS INTENSITY factor CRACK BRIDGING QUASI-BRITTLE FRACTURE STRAIN... 

Shear yielding in the form of a quasi-homogeneous,bulk process can contribute substantially to the crack resistance of a polymeric solid. On the other hand, however, localized shear yielding in the form of shear micro-bands is befleved to be a precursor of brittle fracture in many semicrystalline and glassy thermoplas-... 

LEFM methods are applicable to characterize the rate dependent fracture behavior of engineering polymers in the regime of quasi-brittle failure, yielding material specific fracture toughness values independent of specimen configuration. 

In the regime of quasi-brittle failure, there is a clear tendency for a decrease in fracture toughness with increasing impact rate for all materials investigated. However, the ra e sensitivity of fracture toughness values strongly depends on the specific polymer type. 

Also included in Table I are the true fracture stress (of) calculated from the cross section of the fractured specimen, and the fracture strain (ef). The fracture stress dropped significantly, from 171 MPa for LLDPE to 100 MPa and 35 MPa for 10% and 25% PS, respectively. The fracture stress of the 37.5% PS blend was even lower, 8.5 MPa, but was still higher than the oy value of 5.9 MPa, so the blend deformed in a ductile manner. The blend with 50% PS fractured in a quasi-brittle manner at a stress of 7.0 MPa, which was slightly lower than cry for this composition. The large decrease in Of with increasing PS concentration was consistent with debonded PS particles that were not load-bearing during plastic deformation. 

Ductile-to-Quasi-Britde Transition. The transition from Type I to Type II and Type III stress-strain behavior was accompanied by a sharp drop in f. The large decrease in fracture strain with a relatively small change in composition has been called a ductile-to-quasi-brittle transition rather than a ductile-to-brittle transition, because even when the fracture strain is low,... 

The ductile-to-quasi-brittle transition occurs because the true fracture stress, as determined by P, decreases with increasing PS more rapidly than the yield stress, determined by P (Figure 9). The critical PS content (Vf>s) at the ductile-to-quasi-brittle transition can be determined from the condition that the true yield stress is equal to the true fracture stress. From equations 8 and 13,... 

Figure 9. Schematic of the effect of PS content on yield stress (atJ) and true fracture stress (ef) to give the ductile-to-quasi-brittle transition.

Tensile deformation of the uncompatibilized blend with 50% PS was characterized by the appearance of several regions of localized stress-whitening in the gauge section without global necking. Fracture occurred at one of these regions at a relatively low strain, about 3.2%. This behavior is characterized as quasi-brittle rather than brittle, because some level of plastic deformation precedes fracture even though the fracture strain is low (Chapter 21). 

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

In our concluding remarks we can emphasize that depending on the nature of interactions between the components that constitute the medium and the solid, as well as on a combination of external conditions, one may observe the effects of various types and intensity. These include the facilitation of plastic flow of solids, or, alternatively, brittle fracture due to the action of lowered stresses mechanochemical phenomena in the zone of contact mechanically activated corrosion (the stress corrosion) the processes that are close to the spontaneous dispersion (the so-called quasi-spontaneous dispersion), and the true spontaneous dispersion, leading to the formation of thermodynamically stable lyophilic system. A great variety of types of interactions that exist between the stressed solids and the medium in contact with it requires careful and thorough examination of conditions under which... 

S.P. Shah, S.E. Swartz, Ch. Ouyang, Fracture Mechanics of Concrete Applications of Fracture mechanics to concrete, rock, and other quasi-brittle materials . John Wiley Sons. Inc., New York, NY, USA, and Toronto, Ont., Canada (1995). 

B.62 Fracture Mechanics of Concrete Applications of fracture mechanics to concrete, rock, and other quasi-brittle materials. 

The close-up of dimpled areas is shown in Figure 5.61. The dimples are shallow and inclined characteristic of ductile fracture. No sign of cleavage or quasi-cleavage is observed. The absence of river pattern excludes the possibility of brittle fracture. 

Figure 12.1 Load-extension curves for a typical polymer tested at four temperatures showing different regions of mechanical behaviour (a) brittle fracture (b) ductile failure (c) necking and cold-drawing (d) homogeneous deformation (quasi-ruhher-like behaviour)...

---