Fracture stress concentration factors

Fracture is caused by higher stresses around flaws or cracks than in the surrounding material. However, fracture mechanics is much more than the study of stress concentration factors. Such factors are useful in determining the influence of relatively large holes in bodies (see Section 6.3, Holes in Laminates), but are not particularly helpful when the body has sharp notches or crack-like flaws. For composite materials, fracture has a new dimension as opposed to homogeneous isotropic materials because of the presence of two or more constituents. Fracture can be a fracture of the individual constituents or a separation of the interface between the constituents. 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

This result indicates that the stress necessary to cause brittle fracture is lower, the longer the existing crack and the smaller the energy, P, expended in plastic deformation. The quantity Of represents the smallest tensile stress that would be able to propagate the crack of length 2 L. The term Of (tt L)°5 is generally denoted by the symbol K and is known as the stress-intensity factor (for a sharp elastic crack in an infinitely wide plate). Fracture occurs when the product of the nominal applied stress and the stress concentration factor of a flaw attains a value equal to that of the cohesive stress. 

In the blends, the maximum stress at low rates decreases, as expected, with increasing rubber concentration. At high rates, the 15 and 20% blends show an unexpectedly strong upswing in the maximum stress. The maximum stress before fracture can increase if the stress-concentration factor ahead of the notch is lowered. 

Figure 5-15 should be used if the vessel is in brittle (low temperature) or fatigue service. For brittle fracture the maximum tensile stress is governing. The stress concentration factor is applied to the stresses which are perpendicular to the change in section,... 

The report of the inquiry [111] criticised the design and fabrication of the alterations made to the original pontoon. The actual cause of the accident was the failure of some tie bars in the detail around the jacking points. The failure was due to brittle fracture which initiated from severe notches such as a small radius curve at the fillet between the spade end and the shank of the tie bar. Weld defects and fatigue cracks were also present in tie bars subsequently recovered from the sea bed. The tie bars had been flame cut to shape and had weld repairs visible to the eye. There had been no post welding heat treatment of the steel. The steel complied with the original specification but tests showed low Charpy V notch impact values. Photo elastic tests indicated a stress concentration factor of 7 at the fillet between the spade end and the shank. The fracture was initiated in the opinion of the inquiry tribunal by the low ambient temperature of around 3°C. 

As the last variable in this list of materials, the tear strength has to be mentioned. First the basic task for this test has to be defined A membrane has a tear-type damage of a defined length. Required is the load at which the tear will be subject to unstable spread so that the membrane finally fails. The theory here is that of fracture mechanics, in which the stress concentration factor is defined as the decisive variable. This material variable is defined on the basis of the linear theory of elasticity and can be applied to anisotropic materials without any problems. It shows that this theory is also valid as a good approximation for coated fabrics. 

The evaluation should be done according to linear-elastic fracture mechanics where a stress concentration factor Kc is defined as follows ... 

Using stress concentration factor, ATi, and the following equation, one can evaluate the fracture stress (Or) at the stress concentration feature ... 

Many investigations have been made on the low-temperature properties of aluminum alloys [1-4] however, in addition to the determination of tensile and elastic properties as a function of temperature, notched tensile properties and notched/unnotched tensile ratios were determined. The notched/unnotched ratios were determined as a function of temperature in order to evaluate the toughness, which is often referred to in terms of resistance to brittle fracture, or notch sensitivity [5-7]. A notched specimen with a stress concentration factor K oi 6.3 was selected for use in this investigation because previous axial fatigue tests of complex welded joints, and fatigue and burst tests of pressure vessels made of 301 extra full hard stainless steel exhibited excellent correlation with notched/unnotched tensile ratios obtained with this value of over a range of temperatures... 

For very small notch radii, the calculation of the stress concentration factor is problematic and the methods of fracture mechanics are more precise. Nevertheless, the fact that there is a singularity at the crack tip is reflected correctly by K. ... 

Stress Concentration Factor and Fracture Energy. The critical stress-concentration factor K c defines the critical tensile stress CTc necessary to start the propagation of a crack of length ao in a specimen ... 

When the stress concentration factor becomes high (K, > 5) fracture mechanics must be used, but this is beyond the scope of this paper. 

If contact with a rough surface is poor, whether as a result of thermodynamic or kinetic factors, voids at the interface are likely to mean that practical adhesion is low. Voids can act as stress concentrators which, especially with a brittle adhesive, lead to low energy dissipation, i/f, and low fracture energy, F. However, it must be recognised that there are circumstances where the stress concentrations resulting from interfacial voids can lead to enhanced plastic deformation of a ductile adhesive and increase fracture energy by an increase in [44]. 

As always, of course, to alleviate fracture problems it is essential to avoid the factors which are likely to cause brittleness. These include stress concentrations and low temperatures and the effects of these will be considered in the following sections. 

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