Fracture, initiation

These weld defects not only substantially reduced the mechanical strength of the weld, the pores also formed stress-concentrating notches. Consequently, when the door frame was inadvertently struck during the scrap charging operation, a fracture initiated at the deficient weld and propagated rapidly through the %-in. (1.9-cm) plate, as revealed by the brittle appearance of the plate fracture and the directional chevron markings. 

Heavy equipment had passed over the site of failure initiation shortly before the rupture was discovered. It is probable that stresses associated with the heavy equipment initiated a fracture in the severely corroded pipe bottom. Once the fracture initiated, it propagated down the length of the line in response to stresses imposed by internal pressure. 

Evidence suggests that there is a threshold tensile stress at which void nucleation occurs and spall fracture initiates. Materials subject to transient internal tensions can support tensile stresses significantly in excess of this threshold level, however. Such behavior is a consequence of kinetics and inertia associated with the nucleation and growth of voids during spall. A fairly large body of experimental and theoretical literature on spall phenomena exists and many aspects of the effect are reasonably well understood. Review articles on spall (Curran et al., 1977 Davision and Graham, 1979 Curran, 1982 Meyer and Aimone, 1983 Novikov, 1981) provide access to most of the literature on the subject. 

There is considerable literature on material imperfections and their relation to the failure process. Typically, these theories are material dependent flaws are idealized as penny-shaped cracks, spherical pores, or other regular geometries, and their distribution in size, orientation, and spatial extent is specified. The tensile stress at which fracture initiates at a flaw depends on material properties and geometry of the flaw, and scales with the size of the flaw (Carroll and Holt, 1972a, b Curran et al., 1977 Davison et al., 1977). In thermally activated fracture processes, one or more specific mechanisms are considered, and the fracture activation rate at a specified tensile-stress level follows from the stress dependence of the Boltzmann factor (Zlatin and Ioffe, 1973). 

In a study where the uniform nucleation rate was varied over several values at a fixed strain rate of = 10 /s, the fragment number results shown in Fig. 8.21 were obtained. At lower nucleation rates nearly all fracture initiation sites grow to completion and provide the reduced number of fragments shown. 

Answer In the tensile test, the whole volume of the sample is subjected to a tensile stress of 230 MPa. In the bend test, only the lower half of the sample is subjected to a tensile stress. Furthermore, the average value of this tensile stress is considerably less than the peak value of 400 MPa (which is only reached at the underside of the sample beneath the central loading point). The probability of finding a fracture-initiating defect in the small volume subjected to the highest stresses is small. 

When a craze occurs around a rubber droplet the droplet is stressed not only in a direction parallel to the applied stress but also in the plane of the craze perpendicular to the applied stress (see Figure 3.9). Such a triaxial stress leading to dilation of the particle would be resisted by the high bulk modulus of the rubber, which would thus become load bearing. The fracture initiation stress of a polyblend should not therefore be substantially different from that of a glass. 

As usual, ph represents the mean arithmetical number of intermolecular bonds, ph being the total amount of bonds in both parts of fractured initial molecules ... 

Mechanical treatment alone may be sufficient to induce significant decomposition such processes are termed mechanochemical or tribo-chemical reactions and the topic has been reviewed [385,386]. In some brittle crystalline solids, for example sodium and lead azides [387], fracture can result in some chemical change of the substance. An extreme case of such behaviour is detonation by impact [232,388]. Fox [389] has provided evidence of a fracture initiation mechanism in the explosions of lead and thallium azide crystals, rather than the participation of a liquid or gas phase intermediate. The processes occurring in solids during the action of powerful shock waves have been reviewed by Dremin and Breusov [390]. 

Knowledge of the stresses in a reservoir is essential to get information about the pressure at which initialization of a fracture can take place. The upper bound of the fracture initialization pressure can be estimated using a formula given... 

Three modes are clearly defined for crack propagation from a very thin (radius of the order of 10 gm) notch-machined in the specimen (Fig. 12.3). This notch induces a stress concentration effect, higher than those produced by all the other defects already present in the specimen, which governs the fracture initiation. For isotropic materials, mode I (the most severe) is generally used and gives the lowest value of toughness. In the case of adhesives and laminates, modes II and III are also performed. 

Hasselman, D.P.H. (1969), Unified theory of thermal shock fracture initiation and crack propagation in brittle ceramics , J. Am. Ceram. Soc., 52, 600-604. 

J. Vlachopoulos and T. W. Chan, A Comparison of Melt Fracture Initiation Conditions in Capillaries and Slits, J. Appl. Polym. Set also, J. Vlachopoulos, M. Horie, and S. Lidorikis, An Evaluation of Expressions Predicting Die Swell, Trans. Soc. Rheol., 16, 669 (1972). 

The general principles involved in the failure analysis of ceramic materials are similar to the failure analysis of metals and alloys. Because of the brittle behavior of ceramic materials, failure may result in many pieces of the sample, which have to be reassembled in order to obtain information on the form of loading and the point of fracture initiation. The utmost care should be exercised in the reassembly of the fractured pieces so that the features of the fracture are preserved. 

Figure 7.79 Fracture surface shows convergent chevron patterns as the fracture initiation site.1 (Reprinted with the permission of M. Zamanzadeh, ATCO Associates, Pittsburgh, USA)...

The fracture surface profile is shown in Figure 7.80. The presence of a circumferential ridge and depression in the cylindrical surface is to be noted in the case of both the broken and reference pins. By comparing the cylindrical parts of the broken pin with the reference pin it was concluded that the fracture of the broken pin initiated at the circumferential depression. Macroetching with 50% hydrochloric acid for 30 s enabled the identification of fracture initiation site in Figure 7.80. 

A transverse cross-section through the fracture initiation site was examined by metallography. The fracture surface profile was found to be relatively flat and there was no crack branching. The microstructure showed dark-etching-tempered martensite. Further no plastic deformation was observed at the fracture initiation site. 

It is concluded that the pin failed due to fatigue initiated at the outside cylindrical surface where wear and pitting corrosion occurred. The fracture initiated at a shallow circumferential groove and corrosion of the fracture occurred after the rupture. There was no evidence of stress-corrosion cracking. 

Table 3.1 Room temperature dynamic and quasi-static fracture initiation toughness values of the ceramic materials tested in the present study...

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... 

Failure Mechanisms. BPF polycarbonate develops crazes at ascending stresses and fractures in a pseudo-brittle manner similar to polystyrene or PMMA. At room temperature the block polymers develop few separate crazes. As the yield is approached, shear bands grow from the edges. Fracture initiates at an edge from a point where the two shear bands initiated. When a neck forms, the plastic strain in the neck is ca. 80% however fracture occurs shortly after the neck is formed so that the ultimate elongation of the specimen is only 10 or 12%. The shear bands and necks show some stress whitening (Figure 9). 

In fact, the first quantitative attempt to incorporate the dynamics of the crack into the Griffith energy balance concept was given by Mott (1948). He suggested that unlike the Griffith case of fracture initiation or nucleation... 

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