Methods of determining stress intensity factors

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. 

One superposition technique that is used extensively is shown in Fig. 8.26. The K solution on the left is found by superposing the two configurations on the right. In the final configuration, the crack surfaces must be free of stress. For the uncracked configuration A =0, but there is a stress concentration that occurs over the superposed location of the crack. This stress is then removed by the crack surface tractions applied to the cracked body without an external load and, thus, the superposed K=K.  

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. 

Elastic solutions are often available for notches with small flank angles and small root radii. In the limit of zero root radius, the notch will be equivalent to a crack, i.e.. 

This approach often utilizes analytical or numerical solutions for o- but one can also use experimental data. 

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D. P. Rooke, F. I. Baratta and D. J. Cartwright, Simple methods of determining stress intensity factors, Engg. Frac. Mech., 14(1981) 397 25. 

In the Fracture mechanics approach, subcritical debonding rate is determined, often as a function of a fracmre parameter such as the applied energy release rate, G. Paris was the first to use this method, and noted that the crack growth rate per cycle was related to the energy release rate (by way of the stress intensity factor) through a power law relationship of the form... 

The fundamental postulate of Linear Elastic Fracture Mechanics (LEFM) is that the behaviour of cracks is determined solely by the value of the Stress Intensity Factors (SIFs). The stress field in the vicinity of the crack tip is characterized by the SIFs Kj, K[i and Km. In the present paper the displacement extrapolation method for evaluating SIFs is employed [6]... 

All expressions show a linear variation of the stress intensity factor K with the applied force F. Interestingly on loading the specimens, the crack propagation can be measiu-ed in a domain where K < K, that is, before catastrophic feiliu-e. This domain is referred to as the subcritical domain. Subcritical crack growth has important implications on the ageing of glass, that is, its behavioiu- with time. This issue is addressed extensively in Chapter 9. It should also be noted that an indentation method may be employed to determine toughness when small quantities of material are available. This issue is discussed in more detail in Chapter 8. 

Since the importance of the stress intensity factors was demonstrated in determining crack-tip stress fields in two-dimensional problems [24], many different methods have been devised for obtaining SIF [25]. 

The stress and displacement distribution has been calculated for CT-specimen and DCB-specimen using the finite element method [ll]. The stress intensity factors of the two media and w.ere determined, from eq.(5) using the cartesian... 

Standard Test Method for Determining Threshold Stress Intensity Factor for Environment-Assisted Cracking of Metallic Materials, Standard E 1681-03, ASTM International, West Conshohocken, PA, 2003. 

The crack opening can be determined (p = 1), if the fringe order n is known. This method has been used in investigations of stationary cracks to determine static and dynamic stress intensity factors, the latter being induced by a shock wave. 

A third method which recently provided considerable insight into the role of crazes in deformation and fracture of amorphous polymers is the optical interference measurement of crazes (preceding a crack). Since the pioneer work of Kambour, this method has been widely used to determine characteristic craze dimensions and critical displacements. W. Doll gives an overview on recent results and on their interpretation in terms of fracture mechanics parameters (stress intensity factor, plastic zone sizes, fracture surface morphology, fracture energy). 

The concept of crack growth resistance curves (1 -curves) for determining critical stress intensity factors (Kc) is relatively new. A proposed standard method for -curve determination has been developed [ ]. The mechanics of i -curve testing with a crack-line-wedge-loaded (CLWL) specimen and the detailed pro-... 

VI.40. The calculated applied stress intensity factor should be shown to be less than the material fracture toughness value in Eq. (VI.3), with appropriate allowance for plasticity effects and factors of safety. The method for determining the material fracture toughness should be selected from three options, all of which are illustrated... 

The controlled surface flaw method was used for the fracture toughness determination. A Vicker s diamond point indent which was oriented orthogonally to the test bar was made at the midpoint of the inner span on the tensile surface. An indentation load of either 15 or 25 kg was used. The critical stress intensity factor, Kic, was then calculated after fracture u.sing Chantickul s equation ... 

This test method can be used to measure the relative susceptibility of materials by "Determining the Threshold Stress Intensity Factor for Environment-Assisted Cracking EAC of Metallic Materials. Constant load specimens, both the fatigue precracked single edge beam SE(B) and precracked compact specimens are tested in bending. The SE(B) was originally referred to as the Cantilever Beam Test. 

In the crack tip opening displacement method (or CTOD-method for short), it is assumed that crack propagation is not determined by the stress intensity factor, but by the amount of plastic deformation near the crack tip. This can be measured by the opening 5t of the crack tip. If this reaches a critical value Jc, the crack propagates. 

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