Fracture initiation stress

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. 

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). 

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. 

Tests in a Clj + Oj mixture at 427°C have shown that the worst elements for promoting susceptibility are Al, Sn, Cu, V, Cr, Mn, Fe and Ni, while the least harmful are Zr, Ta and Mo. a-phase alloys are generally more susceptible than )3-phase alloys. Heat treatment has not been examined extensively, but some heat treatments render some a-alloys more susceptible or change the mode of fracture. The general effect will depend upon the alloy and the heat-treatment cycle. Subsequent cold work can sometimes considerably lower susceptibility. Failure times decrease as either the testing temperature or initial stress value is raised. 

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. 

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. 

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). 

Fig. 25. Variation of craze initiation-stress, craze intensification stress, and tensile fracture stress, Oj, with AN content...

Fracture initiated in the tensile tested ABS samples, as noted also by Truss and Chadwick from either surface flaws or from internal flaws. Figure 33a shows an SEM picture of the tensile fracture surface of a sample broken at a comparatively high deformation rate of 12.7 cm/min. The fracture surface is unlike that of SAN (Fig. 27 a) or that of rubber modified polystyrene (Fig. 3 a). Fracture, for this specimen, has developed from both a surface source and from an internal source and fine radial flow lines emanate from both sources. The slow growth region adjacent to the source tends to develop a conical shape as has been noted This is probably a result of localized shear formation. In ABS specimens subject to creep deformation at low values of stress, the creep strain is found to be due almost entirely to shear but, at higher stresses, shear is accompanied by crazing Crazes can also be induced... 

Fig. 34. Influence of morphology (f, = content of coarsespherulites) on band initiation stress, and strain at fracture,...

Inspite of a high band initiation stress Og, the resistance of PS to subsequent crack growth and final fracture is relatively low. The K -values of the crystalline polymers are much higher. A similar connection has also been established recently for various polymers under tensile test conditions... 

Fig. 38, Mode Il-fracture toughness, vs. band initiation stress, Cj, for various polymers at T = —80 °C (open symbols fine spherulitic, dark symbols coarse spherulitic morphology)...

Fig. 30a-c. Optical micrographs of PS film squares during a "fragility test illustrating a craze initiation, b local fibril breakdown and c catastrophic fracture. Tensile stress lies along the horizontal direction (From Ref. courtesy Macromolecules (ACS))... 

However, a critical value is found for the applied stress intensity factor, K ic, below which the environmental stress-cracking agent accelerates fracture initiation below this transition value, the slope of the stress intensity factor vs. initiation time plot is higher but still similar for the two materials. 

Zehnder, A.T. and Rosakis, A.J. (1990). Dynamic Fracture Initiation and Propagation in 4340 Steel under Impact Loading, International Journal of Fracture, 43, pp. 271-285. Kalthoff, J.F., Beinert, J. and Winkler, S. (1977). Measurements of Dynamic Stress Intensity Factors for Fast Running and Arresting Cracks in Double-Cantilever-Beam Specimens. n Fast Fracture and Crack Arrest, ASTMSTP 627, pp. 161-176, Hahn, G.T. and Kanninen, M.F. (Eds.). American Society for Testing and Materials. 

The critical stress intensity factor, Kc, at fracture initiation was measured by single-edge notched three-point bending tests carried out at low (lOmm/min) and high (Im/s) load point displacement rate under different environmental conditions (temperature and moisture). 

Fracture toughness, expressed in term of the critical stress intensity factor Kc, was determined at fracture initiation and that point was identified from the load diagram. Although linearity requirements as set out in the protocol were generally satisfied, the identification of the point of fracture initiation from the load diagram was often uncertain because of the difficulty to distinguish small, residual fluctuations in the load signal due to dynamic effects from a pop-in effect. When in doubt about that the test was discarded. 

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