Brittle fracture flaws

This result indicates that the stress necessary to cause brittle fracture is lower, the longer the existing crack and the smaller the energy, P, expended in plastic deformation. The quantity Of represents the smallest tensile stress that would be able to propagate the crack of length 2 L. The term Of (tt L)°5 is generally denoted by the symbol K and is known as the stress-intensity factor (for a sharp elastic crack in an infinitely wide plate). Fracture occurs when the product of the nominal applied stress and the stress concentration factor of a flaw attains a value equal to that of the cohesive stress. 

An otherwise well-made pipe will sustain steady pressures up to 2.19 MPa (318 psi) without failing by brittle fracture if it contains initial flaws as large as 1 mm. Similar calculations show that initial flaws or inclusions smaller than 4.5 mm permit steady operation at 150 psi (1.03 MPa). 

A well-made PVC pipe has outside diameter 150 mm and wall thickness 15 mm. Measurements on this pipe give K c = 2.4 MPa m / and yield stress, ay = 50 MN Assume that the largest flaws are 100-/im cracks and that the calibration factor for the specimens used to measure fracture toughness is 1.12. The pipe is subjected to a test in which the internal pressure is gradually raised until the pipe fails. Will the pipe fail by yielding or brittle fracture in this burst test At what pressure will the pipe rupture ... 

The brittle-ductile transition temperature depends on the characteristics of the sample such as thickness, surface defects, and the presence of flaws or notches. Increasing the thickness of the sample favors brittle fracture a typical example is polycarbonate at room temperature. The presence of surface defects (scratches) or the introduction of flaws and notches in the sample increases Tg. A polymer that displays ductile behavior at a particular temperature can break in the brittle mode if a notch is made in it examples are PVC and nylon. This type of behavior is explained by analyzing the distribution of stresses in the zone of the notch. When a sample is subjected to a uniaxial tension, a complex state of stresses is created at the tip of the notch and the yield stress brittle behavior known as notch brittleness. Brittle behavior is favored by sharp notches and thick samples where plane strain deformation prevails over plane stress deformation. 

During the last twenty years, there has been an increasing awareness of the danger of brittle fracture of steel vessels at ambient temperatures, largely as a result of the work of Pellini and Puzak at the Naval Research Laboratory and their investigations of failures of World War II ships. Their "Fracture-Analysis Diagram" (Figure 3-1) shows that a small flaw can initiate brittle fracture at tern-... 

Finally, another important ramification of the stochastic nature of brittle fracture is the effect of the stress distribution during testing on the results. When a batch of ceramics is tested in tension, the entire volume and surface are subjected to the stress. Thus a critical flaw anywhere in the sample will propagate with equal probability. In three- or four-point flexure tests, however, only one-half the sample is in tension, and the other one-half is in compression. In other words, the effective volume tested is, in essence, reduced. It can be shown that the ratio of the tensile to flexural strength for an equal probability of survival is... 

Metals that fracture with a relatively small or negligible amount of plastic strain exhibit brittle fracture. Cracks propagate rapidly. Brittle failure results from cleavage (splitting along definite planes). Ductile fracture is better than brittle fracture, because ductile fracture occurs over a period of time, where as brittle fracture is fast, and can occur (with flaws) at lower stress levels than a ductile fracture. Figure 1 shows the basic types of fracture. 

The tensile properties of brittle materials depend to a considerable extent on the cracks and other flaws inherent in the material. As we shall see later, for a material in tension, brittle fracture occurs through the propagation of one of these cracks. Since load cannot be transmitted through free surfaces, the presence of cracks essentially creates concentrations of stress intensity. When this tensile stress exceeds the fracture strength of the material, fracture occurs. It is apparent, therefore, that in contrast to tensile stresses, which open cracks, compressive stresses tend to close them. This could conceivably enhance the tensile strength. 

Brittle fracture—Can occur at low or intermediate tem-j)eratures. Brittle fractures bave occurred in vessels made of low carbon steel in the 40°-50 F range during hydrotest where minor flaws exist. 

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