Crack advance

When Plateau s rule is applied to solids, it may be said that a crack advances whenever the corresponding decrease d (SE)/dx in the strain energy is at least as great as the work necessary to extend the material (in front of the crack) to its maximum strain, that is, to rupture. Two semi-quantitative formulations of this idea are possible. 

The ubiquity of this power-law behaviour in SCG tests on PE has been the subject of considerable discussion, usually based on the assumption of a fibril creep failure mechanism [43, 45, 46, 47, 76, 79]. At high and intermediate K, after a certain induction period, steady-state crack advance is generally observed to occur by a stick-slip mechanism all or part of the fibrillar zone breaks down rapidly after an incubation time during which fibril creep takes place. The crack-tip then advances rapidly over a short distance and a new fibrillar zone stabilises, as sketched in Fig. 12. 

This behavior is characterized by a plateau region, which prevails above a definite threshold K. It is often referred to as stress-corrosion fatigue because SCC systems usually exhibit this behavior, and the most common theory assumes that the crack growth rate results from the addition of SCC, and pure fatigue crack advance. This is a type of... 

Fig. 13. Schematic picture of the pull-out process that takes place as the crack grows along the interface. As the crack advances, each connector is progressively stretched until it reaches its maximal length. At that point the connectors collapses onto the surface...

The temperature distribution during crack propagation is shown in Fig. 15. As the crack advances, the heat continues to diffuse along the normal to the craze surfaces but the size of the hot zone remains comparable to that of the craze thickness. The maximum temperature increase is located at the crack/craze interface, where the craze thickening and related heat flux into the bulk are maxima. At this location, the temperature reaches the glass transition temperature Tg but plasticity is not enhanced in the bulk, which remains primarily elastic during crack propagation. 

The temperature distribution at craze breakdown and during crack propagation is shown in Fig. 17. As the crack advances, the temperature reaches the glass transition temperature at the location of the crack-craze transition, where plastic dissipation caused by craze thickening is maximum. However, this remains confined to a small volume around the crack-craze surfaces (see Fig. 17) so that no plasticity on a larger scale is promoted. 

The factor of 2 arises from the fact that as the crack advances, the exposed surface area increases twice as rapidly as the area of the crack because each side of the crack is counted separately. The use of y is mainly historical and is significant only in the rare instance when the crack growth criterion is dominated by the energy required to create new surface. 

Under normal fatigue crack propagation (FCP) conditions, the crack advances on sach load cycle. Below a critical threshold value, no crack propagation occurs. This is denoted by the threshold value in Fig. 3. Unique to polymers, however, is a cumulative dama process at the fatigue crack tip which enables discontinuous crack growth (DCG), i.e., crack advance after a multiple number of load cycles This DCG process is sub-critical and appears below the threshold... 

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