Crack propagation healing

Total interpenetration of chains (X approaches Rg) is not necessary to achieve complete strength when M > M and x < 7). However, a word of caution while complete strength may be obtained in terms of critical fracture measures such as G c and A lc, the durability, measured in sub-critical fracture terms, such as the fatigue crack propagation rate da/AN, may be very far from its fully healed state at r. We have shown that while the weld toughness A lc increases linearly with interdiffusion depth X as K f. X, the fatigue crack propagation behavior of partially healed welds behaves as [1]... 

An approach based on coordinative bonds was followed by Bielawski et al., who developed electrically conductive coordination polymers that can be healed after damage by thermal treatment [62]. Incidentally, one further successful approach does not rely on dynamic features within the material. It simply carries microencapsulated monomer within its matrix, a polymer, which contains a polymerization catalyst When a crack propagates through the polymer matrix, monomer is released and polymerized within the crack, restoring the initial material properties of the sample [63, 64]. 

Some kind of healing of the cracks is observed in particular conditions (cf. Section 9.7), but in principle cracking is an irrecoverable process, particularly in an advanced stage of crack propagation. After the discontinuity point, that is, after the first variation of the slope of the strain-stress (or load-deflection) curve, which is considered an indication of the first crack opening, the hypotheses of material continuity are no longer valid thus the notion of stress is applicable with serious restrictions. The question as to whether these hypotheses are applicable at all should be also formulated. 

A system of microcracks appears during the initial period of hardening of the cement paste. It is later subjected to the action of external loads and imposed deformations, which vary over time. Local stress concentrations contribute considerably to crack propagation also under relatively low to average stresses. In certain conditions, the microcracks may exhibit healing (cf. Section 9.7). In most cases, however, they remain and may develop into major cracks leading to disintegration of elements. 

So far, we have assumed that the threshold value Gq for vanishing crack speed is the Dupre energy of adhesion w for adherence, or twice the surface energy y for fracture of homogeneous bodies. Indeed, for adherence of glass on polyurethane, crack propagation was observed for G > w and crack healing for G < vi. (4,63,64)... 

At very low speeds of crack propagation through the adhesive joint, to the left of Fig. 34, the peeling and healing curves should coincide. However, it was found experimentally that there was always a gap between the curves, which was small for silicone rubbers but larger for less elastic materials. This gap was defined as the adhesive hysteresis. The equilibrium work of adhesion was somewhere within this gap, around 70 mJ m, but could not be found exactly in this experiment. 

In eqttilibrium conditions and at rest, dWg = 0 and G = 2y if G crosses this critical threshold, the crack propagates slowly as long as G < Gg (see section 11.1) and then in a catastrophic manner for G = Gg. Gg is the critical energy of tearing per unit of area. If G < 2y, the crack should close (dS < 0, dWg > 0). In reality, different irreversible processes, and particularly surface hydrolysis, oppose the healing of the crack. 

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