Crack size, critical

Therefore, the crack critical size in the rubber is significantly larger than the critical size in the bitumen a a... 

Eor an impact strength of 34 J (25 ft-lbf) the equivalent fracture toughness (150) is approximately 120 MPay. The fracture toughness dictates the critical size of crack above which fast fracture intervenes, so the smaller its value the smaller the critical crack and hence the greater significance of the transverse impact requirement specified by Manning. 

The left-hand side of our equation says that fast fracture will occur when, in a material subjected to a stress a, a crack reaches some critical size a or, alternatively, when material containing cracks of size a is subjected to some critical stress cr. The right-hand side of our result depends on material properties only E is obviously a material constant, and G, the energy required to generate unit area of crack, again must depend only on the basic properties of our material. Thus, the important point about the equation is that the critical combination of stress and crack length at which fast fracture commences is a material constant. 

First, the pressure vessel must be safe from plastic collapse that is, the stresses must everywhere be below general yield. Second, it must not fail by fast fracture if the largest cracks it could contain have length 2a (Fig. 16.4), then the stress intensity K CTV must everywhere be less than K. Finally, it must not fail by fatigue the slow growth of a crack to the critical size at which it runs. 

During fatigue the stress amplitude usually remains constant and brittle failure occurs as a result of crack growth from a sub-critical to a critical size. Clearly the rate at which these cracks grow is the determining factor in the life of the component. It has been shown quite conclusively for many polymeric materials that the rate at which cracks grow is related to the stress intensity factor by a relation of the form... 

Assuming that the geometry function, Y, does not change as the crack grows then this equation may be integrated to give the number of cycles, N/, which are necessary for the crack to grow from its initial size (2n,) to its critical size at fracture (lOc). 

During cyclic loading, any cracks in the material will propagate until they reach this critical size. If the article is to have an endurance of at least 10 cycles then equation (2.119) may be used to determine the size of the smallest flaw which can be present in the material before cycling commences. 

While ideally structures should be designed and fabricated so that environment-sensitive cracking is avoided, in practice it is sometimes necessary to live with the problem. This implies an ability to detect and measure the size of cracks before they reach the critical size that may result in catastrophic failure. Such inspection has important implications for plant design, which should be such as to allow inspection at relevant locations. The latter are regions of high residual stress (welded, bolted or riveted joints) and regions of geometrical discontinuity (notches, crevices, etc.) where stress or environment concentration may occur. 

Figure 14.31 Dependence of the total energy change, AC/, on a at constant a. (la = crack length = critical size.)...

If NDI techniques can detect initial cracks as small as 10 in., then using Ui = 10 in., the estimated resulting fatigue life would be about 5 x 10 cycles. If, on the other hand, the initial crack size must be estimated from proof testing, say at 150 ksi, the assumed initial crack size for use in the fatigue analysis must be equal to the critical size for the proof stress (cr r), Eqn. (7.14). 

Under the conditions when transition to plastic flow takes place, the development of a crack in solid is accompanied by substantial deformation of the latter. The relationship between the body strength and the critical size of primary crack, /cr, can in this case be described by the equation similar to the Griffits expression, namely [37] ... 

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