On the structure of plastic and damage zones in different materials and at various scales

The regularities of the formation and structure of plastic and damage zones in structural materials of different types are considered. Our own experimental investigations of the plastic zone structure in metals and extensive literature data analysis are used as the basis for identifying general and particular features of the development of localised damage zones in various materials and at various length scales differing by several orders of magnitude. A single zone of severe deformation (the fracture process zone) is formed at the tip of a crack or a notch in a material in the brittle state. We show that the process of fracture in ductile and quasibrittle materials is accompanied by the formation of at least of two localised zones characterised by different degrees of deformation and damage: the inner fracture process zone (FPZ) of severe deformation, and the outer, plastic zone (PZ) or damage zone (DZ) where the degree of damage or deformation is lower. It is the presence of the outer zone of moderate deformation and damage (PZ or DZ) that gives rise to the appearance of the size effect. We consider the structure of crack tip zones (FPZ, and PZ or DZ) in materials other than metals, namely, in rubber toughened polymers, concrete, and rocks. We discuss that the fracture properties of different materials are determined by the mechanisms of damage accumulation in the crack tip zones and by the transition from low constraint (plane stress) to high constraint (plane strain) conditions near the crack tip. Although the mechanisms of damage accumulation in different materials may differ, we suggest that in all cases the disappearance of the outer zone (and hence the lack of size effect on strength) is a consequence of the presence of material hardening (as opposed to softening)

Defect population statistics near and far from a critical event

We consider the defect size distributions at different stages of damage evolution, from the initial stage of defect nucleation and accumulation, through the intermediate stage of defect propagation and into the final stage leading to the appearance of the major crack. Critical events considered in this context are related to (a) the formation of microcracks exceeding the structural threshold associated with the grain size, and (b) the formation of a major crack that corresponds to the attainment of the maximum load. The significance of these two critical events is that they are often used to define the boundary between micro- and macro-mechanical analyses, and used in order to establish scale and size effects on material strength. We consider the statistical distribution functions which are in widespread use for the description of cumulative defect size distributions, namely, the exponential, power law and the exponential-power law (also referred to as the Rosin-Rammler or Weibull) distributions. We note that the defect population statistics at different stages of evolution are best described by different statistical functions. We discuss of the relationship between defect size distributions and the statistics of material strength. We point out that Weibull strength statistics implies power law defect size distribution, and note the direct correspondence between the power law defect size distribution exponent and the Weibull modulus in the statistics of strength, giving the relationship between these parameters. We propose to use the transition between different distribution statistics as an indicator of the approach of a critical event. The effect of the structural size barrier associated with the grain size is to retard temporarily the crack growth beyond this critical size. This results in increasingly steep distribution curves, reflected in the increase of the Rosin-Rammler exponent parameter. Once crack growth proceeds beyond the structural barrier, a power law 'tail' of the crack size distribution appears. Microstructurally large defects evolve from the exponential towards power law cumulative size distributions. The appearance of the major crack is preceded by the decrease in the exponent of the power law 'tail'. Observations confirming these conclusions have been reported in materials science and seismology

Early tensile bond strengths of several enamel and dentin bonding systems.

Tensile bond strength tests are commonly used for the evaluation of adhesive dental materials. The majority of these tests are carried out after 24 h of storage in water. However, determination of the early tensile bond strength could be more important, especially in relation to gap formation between the cavity surface and the restorative material. This study investigated the tensile bond strengths of five enamel/dentin bonding systems and two experimental dentin bonding systems. Tensile bond strengths were obtained at one min, ten min, and 24 h after the resin composite was cured. Bond strengths at the early stages were always somewhat less than the 24-hour test results. For the enamel/dentin bonding systems, a significant difference was found between the enamel and dentin bond strengths at all time periods, except with Superbond D-liner and Liner Bond. The experimental group with glyceryl methacrylate as the primer produced a good 24-hour result (14.3 MPa), but the early bond strengths were no different from those in the non-primer-treated groups. It was concluded that this material may actually retard the polymerization of the bonding resin. Previous workers have suggested that a tensile bond strength in the order of 20 MPa is necessary for gap-free restorations to be obtained. Should this be the case, then all of the materials tested, from the aspect of early bond strength, lack the strength for prevention of gap formation, although Superbond D-liner and Liner Bond approached this hypothetical figure. These systems, Superbond D-liner and Liner Bond, also exhibit small differences between the enamel and dentin tensile bond strengths.link_to_subscribed_fulltex