Tensile ligament

Metallurgical Considerations (Krafft s Tensile Ligament Instability Model [4])... 

Figure 5.3. Krafft s tensile-ligament instability model for fracture. Schematic of physical process (left), and model representation (right) [4].

The essence of Krafft s model involves the relationship between the onset of crack growth with that of plastic flow instability in these tensile ligaments ahead of the crack tip. Assuming that the strains within the crack tip plastic zone are constrained by the surrounding elastic material, the strain inside the plastic zone would follow a singularity as dictated by the surrounding elastic stress-strain field namely,... 

He proposed that crack growth instability, or fracture, would correspond to the onset of plastic flow instability (or necking) in the tensile ligament(s) at the crack tip or when e at r = dj. Thus,... 

Krafft [4] and Krafft and Mulherin [5] later extended the TLI model to describe stress corrosion crack growth. Crack growth was viewed in terms of the instability of tensile ligaments where their lateral contraction was augmented by uniform chemical dissolution of the tensile ligaments. For sustained-load crack growth in an inert environment, on the other hand, the reduction in the cross-sectional area of the ligaments would be associated with the creep rate (Landes and Wei [2], Yin et aL... 

Here, creep of the ligaments enhances the evolution of strain, and leads to earlier onset of tensile ligament instability hence, crack growth. 

Various crack advance theories have been proposed to relate crack propagation to oxidation rates and the stress-strain conditions at the crack tip, and these theories have been supported by a correlation between the average oxidation current density on a straining surface and the crack propagation rate for a number of systems [12,35]. There have been various hypotheses about the precise atom-atom rupture process at the crack tip—for example, the effect that the enviromnent has on the ductile fracture process (e g., the tensile ligament theory [36], the increase in the number of active sites for dissolution because of the strain concentration [37], the preferential dissolution of mobile dislocations because of the inherent chemical activity of the solute segregation in the dislocation core [38]). 

Collagens (see p. 344), of which there are at least 19 different varieties, form fibers, fibrils, networks, and ligaments. Their characteristic properties are tensile strength and flexibility. Elastin is a fiber protein with a high degree of elasticity. 

Dense or fibrous connective tissue this forms ligaments and tendons. Its densely packed collagen fibers have great tensile strength. 

Ligament Thickness. The ductile-to-brittle transition as measured in notched Izod, notched Charpy, and notched tensile impact tests is discontinuous and is dependent on both rubber concentration and particle size. These two parameters can be combined into a new morphological parameter that governs the ductile-to-brittle transition. The ligament thickness (interparticular distance), which is a function of rubber concentration and particle size,... 

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