Stress concentrations at cracks

The simplest approach to developing a fracture criterion would be to equate the highest tensile stress associated with a crack to the theoretical cleavage stress. For the geometry shown in Fig. 8.3, the crack could be considered to be an elliptical hole and the elastic solution discussed in Section 4.9 can be utilized, i.e.. 

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At room temperature, PP is a tough material with expanded plastic deformations in form of shear yielding. These processes are connected with drastic rearrangements on a lamellar and spherulitic level. However, a brittle fracture can be initiated in materials with large sphemlites and a reduced interspherulitic bonding 181- Lower temperatures, high strain rates, and high stress concentrations at crack tips favour the formation of crazes (overview in [9]). 

Figure 7.9 (a) x, y axis and stress components (b) schematic representation of stress concentration at crack tip (dashed line) and influence of a plastic zone (continuous line). 

Stress concentration at crack tip is sensibly reduced with craze initiation and not transferred to craze tip. 

One aspect of pressure vessel design which has received considerable attention in recent years is the design of threaded closures where, due to the high stress concentration at the root of the first active thread, a fatigue crack may quickly initiate and propagate in the radial—circumferential plane. Stress intensity factors for this type of crack are difficult to compute (112,113), and more geometries need to be examined before the factors can be used with confidence. 

Avoid surface discontinuities such as pits, slip marks (notches) and other damage that act as stress risers. Stresses concentrate at the tip of the notch. Therefore, stress-corrosion cracks usually originate from the base of a pit. 

Uniform microstractuie is cracial to the superior performance of advanced ceramics. In a cerantic material, atoms are held in place by strong chentical bonds that ate impervious to attack by corrosive materials or heat. At the same time, these bonds are not capable of much "give." When a ceramic material is subjected to mechanical stresses, these stresses concentrate at minute imperfections in the microstmcture, initiating a crack. The stresses at the top of the crack exceed the threshold for breaking the adjacent atomic bonds, and the crack propagates throughout the material causing a catastrophic brittle failure of the ceramic body. The rehability of a ceramic component is directly related to the number and type of imperfections in its microstmcture. 

Fig. 6.13. The Cook-Gordon (1964) mechanisms tensile debonding occurs at the weak interface ahead of crack tip as a result of lateral stress concentration and crack tip is effectively blunted.

It was proposed by Griffith in 1920 that microscopic cracks exist both within and on the surface of all real materials, which are deleterious to the strength of any material that does not possess ductility. The presence of cracks whose longest dimension is perpendicular to the direction of the applied tensile stress gives rise to especially large stress concentrations at the crack tip, where the real localized stress can approach the theoretical strength of the material due to a small area over which it is applied (see Figure 5.38). It can be shown that the maximum stress at the tip of a crack, is... 

For a given strain rate, e, the temperature domain can be divided into two regions. At low temperatures, the fracture is brittle with a nearly constant stress, chain mobility and the fracture occurs from stress concentration at the defects, leading to the formation of holes and then crack propagation. 

In any structure the entire structure responds to mechanical or thermal loads. It is also necessary to bear in mind that any structure will also experience localized stress concentrations at points of contact or separation in the structure. These points of contact or separation are sites susceptible to damage, cracking or failure initiation. Stress analysis using the finite element method in structures which are bolted, mating surfaces, vessels... 

Because of high stress concentration at the interface asperities, a scratched A1 surface significantly reduces the adhesion of the Si02 4.5 wt.% P film. Because the A1 plastic flow blunts the crack tips reaching the interface, it delays the loss of adhesion of the film from the... 

As in the case of electrical failure in random conductor-insulator networks in the earlier chapter, we first discuss here the concept of stress concentration in an otherwise perfect solid, which is stressed and contains a single crack inside. Here, the stresses concentrate at the sharp edges of the crack, where it can become much larger compared to the external force. As one increases the external force, the crack starts propagating from such... 

Usually the radius of curvature p at the sharp notch of the crack is determined by the atomic sizes and is very small. It is immediately evident that the stress concentration at the sharp notches of the microcracks can become extremely large due to the above stress intensity factor, and the fracture should start propagating from there. Although this analysis indicates clearly where the instabilities should occur, it is not sufficient to tell us when the instability does occur and the fracture propagation starts. This requires a detailed energy balance consideration. 

As mentioned above, the presence and occurrence of the rough crack surfaces (see Fig. 3.7) necessitates a change in the above Griffith estimate of the fracture strength or toughness (given by eqn (3.5)), where we had assumed a smooth crack surface. Let us express the stress concentration at the crack-tip generally by (3.7),... 

Fatigue progresses at the base of a notch in three stages (1) Stress concentration (2) Cracks initiate under repeated stresses ... 

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