The crack-tip process zone

The crack-tip environment with its stress and plastic-strain concentration furnishes the means and driving forces for local fracturing of material, making the crack propagate to final fracture. The material separation in crack extension can occur by a variety of mechanisms in which a number of factors can play important roles, such as the structural constitution of the polymer, i.e., whether it is in unoriented or oriented glassy form or in semi-crystalline form, with a variety of morphologies. We consider first a selection of prominent forms of fracture in polymers and end with a short section on the fracture toughnesses of some prominent polymers. 

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The second physical quantity of interest is, r t = 90 pm, the critical crack tip stress field dimension. Irwin s analysis of the crack tip process zone dimension for an elastic-perfectly plastic material began with the perfectly elastic crack tip stress field solution of Eq. 1 and allowed for stress redistribution to account for the fact that the near crack tip field would be limited to Oj . The net result of this analysis is that the crack tip inelastic zone was nearly twice that predicted by Eq. 3, such that... 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

In a subsequent series of experiments, Landes and Wei [2] demonstrated that the phenomenon is real, and modeled the crack growth response in terms of creep deformation rate within the crack-tip process zone. The effort has been further substantiated by the work of Yin et al. [3]. The results and model development from these studies are briefly summarized, and extension to probabihstic considerations is reviewed. It is hoped that this effort will be extended to understand the behavior of other systems, and affirm a mechanistic basis for understanding and design against creep-dominated failures. The author relies principally on the earher works of Li et aL [1], Landes and Wei [2], Yin et al. [3], Krafft [4] and Krafft and Mulherin [5]. The findings rely principally on the laborious experimental measurements by Landes and Wei [2], and the conceptual modeling framework by Kraftt... 

As mentioned at the start of this section, the J-integral concept was originally applied to metals, in which the linear elasticity concept might include the plastic observations, i.e., plastic flow in the close vicinity of the tip. Reservations regarding the use of the J-integral in brittle materials, such as ceramics, are a consequence of the presence of microcracks or rather subcritical crack growth before fracture sets in, making it not strictly applicable. However, in ceramics, in which extensive inelastic processes are active in the crack-tip process zone, the use of J is not more restrictive than the use of the Kic criterion in linear elastic firacture mechanics. 

Thus, the above discussion on the J-integral shows that its measurement in various refractories yields Jic values which exceed Gjc- With regard to Jic, these measurements appear promising as a technique for quantitatively describing the inelastic energy consumption in the crack-tip process zone during fracture initiation in refractory ceramics. 

The test specimen size-effect on Kc and Rc is examined in the present work for a polycrystalline graphite. In particular, the excess energy consumption, Rc — K jE, will be related to the size of test specimen as well as to the test conditions. It will be concluded that this excess energy is intimately related to the processes and mechanisms of microcracking and slippage of graphite basal planes that occur in the locations away of the crack-tip process zone. 

During the DCG process, a single craze forms the crack tip plastic zone (CTPZ). The craze progressively weakens during each successive load cycle, while the... 

It appears that the toughening effect near a crack tip occurs as follows after initial deformation, cavitation occurs within or aroimd the soft phase in a zone surrounding the crack tip. This zone is known as the process zone. The newly created surface around these cavities in the process zone allows the latter to grow plastically, thus absorbing some energy. Localized shear deformations, often referred to as shear bands, may also grow from these cavities. If the volume fraction... 

Another approach to the fracture of ductile polymers stems from the recognition that for such materials the crack tip deformation zone has two components, as shown in Figure 12.21. There is an inner zone where the fracture process occurs -which could involve a combination of shear yielding and crazing - and an outer zone where extensive yielding and plastic deformation occur. This approach was originally proposed by Broberg [70], and has been developed by Mai and Cottrell [71], Hashemi and Williams [72], Mai [73] and others. 

The elastic stress cannot exceed the yield stress of the material, implying a region of local yielding at the crack tip. Nevertheless, to apply the simple framework of hnear elastic fracture mechanics, Irwin [J. Applied Mechanics, 24, 361 (1957)] proposed that this process zone size / be treated as an effective increase in crack length be. Fracture toughness is then given by... 

Rather than bearing an infinite stress at the crack tip, yielding occurs resulting in a volume of inelastically deformed material along the crack front called the process zone, as shown in Fig. 2. The size of the inelastic zone, r j , under a monotonic tensile stress, o , can be approximated by substituting o = Oj into eq. 2 for the horizontal plane, 0 = 0... 

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