The application of fractal and quantum geometry to brittle fracture

Estimation of fracture energy from the work of fracture and fracture surface area: I. Stable crack growth

“…The estimated size of the region was represented by a radius, a 0 . West et al (1999) also estimated this region using a different approach. a 0 was determined to be approximately 1.2 nm.…”

“…The only fact of importance to the present paper is that the surface is not smooth at the atomic scale, a fact on which all the investigators agree. The fact that fracture is fractal implies that there are self-affine, scale invariant geometric constructs from the atomic length scale magnified to greater length scales (Mecholsky et al 1989;West et al 1999). A non-smooth fracture surface presents a question with respect to the assumption of the cross-sectional area accounting for all of the energy absorbing mechanisms in the creation of the fracture surface.…”

“…Thus, the size of the free volume in the amorphous structure is important to the fracture process in glass and to the created structure of the fracture surface. In addition, West et al (1999), using molecular orbital calculations, have predicted that the fracture process is not a simple breaking of individual bonds, but rather a reconfiguration of an ensemble of bond groups at the tip of a crack that propagates in a manner to form the rough fracture surface observed. Thus, entropy is an essential element of the fracture process.…”

Transmission Welding of Glass by Femtosecond Laser: Mechanism and Fracture Strength

“…Due to the presence of micro cracks at sufficiently higher laser pulse energies as mentioned earlier in this section, it can be seen that the fracture strength does not monotonically increase with laser pulse energy, rather there is an optimum pulse energy beyond which the resultant fracture strength will decrease. However, the detrimental effect of the micro cracks is smaller than the beneficial effect of the compact ring structure (three-member rings) which has the highest barrier to fracture of all ring configurations [36]; therefore, the fracture strengths in welded regions for all laser pulse energy conditions in this study are still higher than the reference region.…”

Fractografia quantitativa

“…Sendo a 0 uma dimensão característica relacionada à escala do processo e determinada experimentalmente (WEST et al, 1999). O modelo de Mecholsky limitase a fraturas com comportamento absolutamente frágil, com aspecto "espelho + névoa + crista de galo", com rugosidade progressiva a partir da nucleação de acordo com o crescimento da velocidade de propagação da trinca (PLANGSANGMAS;…”