Cracks growth

When a is the gross applied stress, E is Young s modulus, and a is half the crack length, Griffith showed that the critical point is defined by the relation 

A more general equation was derived by Orowan (43), who replaced Ys with the term Ys + Yp, where Yp accounts for the energy involved in plastic deformation. Irwin (44) considered the fracture of solids from a thermodynamic point of view and arrived at the equation 

At the critical conditions of crack spreading, the critical stress intensity factor, K is given by 

Similarly the work done per unit area of new crack surface is given by It must be remembered that a crack will spread only if the total energy of the system is decreased. A more general case may be written 

The stress intensity factor forms the central part of a great deal of the fracture and fatigue literature. Once the stress intensity factor is known, it is possible to determine the minimum stress value that would cause failure. This 

Chapter 6 dealt with residual stresses that occur when products are cooled rapidly from both the sides. There are biaxial compressive stresses in the surface layers and biaxial tensile stresses in the interior. If a hole is drilled through such a product, it cuts through the tensile stress region, and acts as a stress-concentrating feature with a q value of 2. If there is ingress of a stress cracking fluid, radial cracks may form from the bore of the hole, perpendicular to the residual circumferential stresses. These cracks will be at the mid-thickness of the product. 

Residual stresses can also arise if a hole is drilled, with a blunt bit, through a product that is initially stress-free. The drilling operation generates enough heat to melt a thin annulus of plastic surrovmding the hole. When this cools down, it contracts, so has a residual tensile circiunferential stress (the effect is the converse of shrink-fitting a metal rim on a wooden wagon wheel). Consequently, cracks may start in a radial direction, but they will turn to follow the boundary of the overheated layer. These two examples show that the crack patterns can reveal the type of residual stress field in a product. 

Cracks tend to initiate on the surface of products for a munber of reasons— bending or torsion loading causing high surface stresses, surface scratches causing stress concentrations or surface degradation. However, in some circumstances (yield stress concentrations at a notch or weak interfaces) 

1 Fracture mechanics The stress intensity factor of a crack tip stress field 

Once a sharp crack has formed, it is possible to analyse its growth, using the concepts of fracture mechanics. The subject was developed for the failure of large metal structures. Linear elastic fracture mechanics, the simplest theory, considers the stress and strain fields around the crack tip in elastic materials. In the majority of cases, the crack faces move directly apart (mode I deformation in the jargon) rather than sliding over each other in 

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The application of load in materials produces internal modifications such as crack growth, local plastic deformation, corrosion and phase changes, which are accompanied by the emission of acoustic waves in materials. These waves therefore contain information on the internal behaviour of the material and can be analysed to obtain this information. The waves are detected by the use of suitable sensors, that converts the surface movements of the material into electric signal. These signals are processed, analysed and recorded by an appropriate instrumentation. 

Elastic energy release due to subcritical crack growth is one recognized source of structure-related AE within its acknowledged lunitations, AEBIL provides a viable means of early on-line deteetion and localization of stable crack propagation. 

BE-74E3 Creep crack growth in carbon- manganese steel at 300 420 Mr. R. Maskel BABCOCK ENERGY Ltd... 

SMT-2070 Development of creep crack growth testing and data analyses procedures for Dr. Bilal Dogan GKSS... 

Rice J.R., Drucker D. (1967) Energy changes in stressed bodies due to void and crack growth. Int. J. Eracture Mech. 3 (1), 19-27. 

Fig. 3. The effect of crack growth on potential energy in a loaded body where (a) is a cracked body of arbitrary shape with a load P appHed, and (b) is the change in potential energy in the body owing to incremental crack growth, Sa. Other terms are defined in text.

An attempt has been made to define a single critical value, like for brittle fracture, from these curves (5). However, the amount of crack growth which is used to define this critical value is inevitably rather arbitrary. A more recent approach (6) is to fit a power law curve of the form... 

Eig. 9. Schematic fatigue crack growth data showing the regions of growth rate. 

Eracture mechanics concepts can also be appHed to fatigue crack growth under a constant static load, but in this case the material behavior is nonlinear and time-dependent (29,30). Slow, stable crack growth data can be presented in terms of the crack growth rate per unit of time against the appHed R or J, if the nonlinearity is not too great. Eor extensive nonlinearity a viscoelastic analysis can become very complex (11) and a number of schemes based on the time rate of change of/have been proposed (31,32). 

The use of fatigue data and crack length measurements to predict the remaining service life of a stmcture under cyclic loading is possibly the most common application of fracture mechanics for performance prediction. In complex stmctures the growth of cracks is routinely monitored at intervals, and from data about crack growth rates and the applied loadings at that point in the stmcture, a decision is made about whether the stmcmre can continue to operate safely until the next scheduled inspection. 

ASTM E647-93, "Measurement of Fatigue Crack Growth Rates," Annual Book of ASTM Standards, ASTM Puhhcations, Philadelphia, 1993. 

Fig. 5. Comparison of crack growth rates of titanium aluminides, composites, and IN-100 tests at 650°C, R = 0.1, v = 0.2 Hz except for the composite...

Fig. 15. Crack growth vs cyclic iatensity factor for particulate MMCs.

Stress corrosion cracking, prevalent where boiling occurs, concentrates corrosion products and impurity chemicals, namely in the deep tubesheet crevices on the hot side of the steam generator and under deposits above the tubesheet. The cracking growth rates increase rapidly at both high and low pH. Either of these environments can exist depending on the type of chemical species present. 

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