Subject stress intensity factor

Irwin [23] developed an expression for the mode I stress intensity factor around an elliptical crack embedded in an infinite elastic solid subjected to uniform tension. The most general formulation is given by ... 

A very wide sheet of grp which is known to contain intrinsic defects 1 mm long, is subjected to a fluctuating stress which varies from 0 to 80 MN/m. How many cycles would the sheet be expected to withstand if it is made from (a) chopped strand mat (CSM) and (b) woven roving (WR) reinforcement. The crack growth parameters C and n, and the critical stress intensity factors, Kc, for these materials are... 

Linear elastic fracture mechanics (LEFM) approach can be used to characterize the fracture behavior of random fiber composites. The methods of LEFM should be used with utmost care for obtaining meaningful fracture parameters. The analysis of load displacement records as recommended in method ASTM E 399-71 may be subject to some errors caused by the massive debonding that occurs prior to catastrophic failure of these composites. By using the R-curve concept, the fracture behavior of these materials can be more accurately characterized. The K-equa-tions developed for isotropic materials can be used to calculate stress intensity factor for these materials. 

Design parameters of structures containing defects can be established through the stress intensity factor, K. The failure criterion for structures that contain defects and are subjected to static or monotonically increasing loads is as follows ... 

Irwin (40) gave an alternative formulation to fracture by considering the distribution or field of stresses around a crack in an elastic material. He proposed that such a distribution could be expressed as a function of a parameter K, known as the stress intensity factor, and he established that the fracture would occur when K exceeds a critical value characteristic of each material. Figure 14.33 shows a sharp crack of length 2a in an infinite lamina subjected to a tensile stress ct. The equations defining the local stresses an, a22 < 12 are (42)... 

The crack length values obtained from the compliance method were finally compared with crack length measurements derived from a multispecimen procedure, in which a set of identical specimens was subjected to the same applied stress intensity factor (Kic = 0.48 MPa m ") for different times and then broken open in liquid nitrogen, and excellent agreement was found. 

EXAMPLE 2 - FOR SURFACE CRACK OR PART-THROUGH CRACK. In many applications, surface cracks or part-through cracks are of concern. The analysis procedure is identical to that used in Example 1. The stress intensity factor, K, for a semielliptical surface crack subjected to tensile loading perpendicular to the crack plane, as in Example 1, is given by [4] ... 

For certain simple specimen geometries and modes of loading, there are analytical solutions for the stress intensity factor. For a central crack of length la in an infinitely wide sheet, subjected to a distant tensile stress [Pg.270]

One of the simplest techniques to determine in a complex configuration is to use superposition to build up the solution from a set of simpler and known solutions. Clearly, the precision with which the superposed geometries replicate the final, more complex, structure will impact the accuracy of the final solution. Consider the situation shown in Fig. 8.24, in which cracks emanating from a circular hole is subjected to a biaxial stress. This solution can be broken down into two uniaxial stress solutions, and K. Thus, the total stress intensity factor is found by superposition, K=K, +K. A somewhat more complex configuration is shown in Fig. 8.25. The problem again involves a cracked circular hole but, in this case, it is being loaded along a semi-circular portion of the hole. The problem is asymmetric but, as shown, it can be found from the superposition of two symmetric solutions, i.e., K = K +K H. 

Superposition of K solutions is subjected to the same restrictions as those used for stresses and displacements. For example, the stress intensity factors must be associated with a single loading mode, often mode I, and the body geometry should be the same. An additional restriction is that the crack surfaces must be separated along their entire length in the final configuration. This can be a problem if one of the basic solutions involves compressive stresses that push the crack surfaces together. 

Two-dimensional problems concerning a crack of length L in an infinite body subjected to an arbitrary symmetrical loading stress o-(x) can be solved using a weight function approach. For this approach, the stress intensity factor K and the crack face displacements v (L, x) must be known for another symmetric case. The stress intensity factor fC for the unknown configuration is... 

Table 3. Fatigue Threshold Stress Intensity Factor and Paris Regime or UHMWPE Subjected to Different Processing Conditions ...

Rates of CF crack propagation are uniquely defined by the linear elastic fracture mechanics stress intensity factor range that combines the effects of applied load, crack size, and geometry 17,40. The similitude principle states that fatigue and CF cracks grow at equal rates when subjected to equal values of AK [6-S]. The dal N versus AK relationship may be complex however, an effective approach is based on a power (or Paris) relationship of the form [4/]... 

In the late 1950s Irwin developed the stress intensity factor approach (this is different to stress intensity used in pressure vessel stress analysis). Consider a structural component containing a sharp crack, subjected to a load applied in a direction normal to the crack surface (known as Mode I loading) as shown in Figure B.4. The normal stress in the y direction, Oy, at a point located at an angle 0 and at a distance r from the crack tip, can be expressed as... 

Determine the critical flaw size in a high strength steel plate subjected to a tensile stress of 1500 MPa and for which the critical stress intensity factor Kic = 50 MPa ym. Assume that the stress intensity factor for this geometry is Ki = 1.12... 

Crack velocity versus stress intensity factor (V-Kf) curves were obtained by two general tests, so called constant loading and relaxation tests [4. In the load relaxation method, the pre-cracked specimen was subjected to fast loading, followed by subsequent stopping of the crosshead at a certain displacement. Hence, the crack propagation resulted in a load relaxation and the load versus time curve allows the determination of the V-Kj curve with a single experiment, for crack rates down to 10 m/s [4]. The stress intensity factor can be calculated from expression (2) pro-... 

SIF), Ki/Kii, was varied by varying the distance of the precrack from the center plane, s, as shown in the figure. When the precrack was centered with respect to the loading point (.y = 0), the precrack was subjected to pure mode II loading. As s was increased, Ki/Kn also increased. The stress intensity factors, Ki and K, are expressed as... 

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