Fracture dimensions

Figure 2. Typical fracture dimensions. (Reproduced with permission from ref. 2. Copyright 1983 Society of Petroleum Engineers.)...

Fig. 6. (A) Location of the mapped foreshore transect (see Fig. 5) the Main Limestone is exposed above in a 15-20 m cliff section 175 m south of the foreshore. (B) Map of dolomite-cemented fractures on a 100 m x 20 m transect some fractures extend landward of the transect. (C) Summary of fracture orientations measured across the transect. (D) Summary of fracture dimensions measured across the transect.

The permeability in the x, y and z directions, is strongly affected by the fracture distribution and fracture dimensions. Since the fracture apertures depend on pressure in the fluid and normal and shear stresses (see equations (3) and (4)), the permeability of the reservoir (defined by its components AT,), should be treated as a... 

FIGURE 10.14 The dependence of impact toughness on fracture dimension for HOPE samples in tests with varied sharp notch length a (1) and testing temperature T(2) [47],... 

In an ideal situation we would like to have a balanced combination between evaluation of the welder s performance on one hand, and a fracture mechanics basis on the other hand in tenns of "being certain that a defect with dimensions exceeding a certain critical value is not present". The second aspect could be regarded as a safety net with a balanced conservatism. 

The parameters for the model were originally evaluated for oil shale, a material for which substantial fracture stress and fragment size data depending on strain rate were available (see Fig. 8.11). In the case of a less well-characterized brittle material, the parameters may be inferred from the shear-wave velocity and a dynamic fracture or spall stress at a known strain rate. In particular, is approximately one-third the shear-wave velocity, m has been shown to be about 6 for various brittle materials (Grady and Lipkin, 1980), and k can then be determined from a known dynamic fracture stress using an analytic solution of (8.65), (8.66) and (8.68) in one dimension for constant strain rate. 

If we then introduce a flaw into the system, by poking a pin into the inflated balloon, the balloon will explode, and all this energy will be released. The membrane fails by fast fracture, even though well below its yield strength. But if we introduce a flaw of the same dimensions into a system with less energy in it, as when we poke our pin into a partially inflated balloon, the flaw is stable and fast fracture does not occur. Finally, if we blow up the punctured balloon progressively, we eventually reach a pressure at which it suddenly bursts. In other words, we have arrived at a critical balloon pressure at which our pin-sized flaw is just unstable, and fast fracture just occurs. Why is this ... 

Two wooden beams are butt-jointed using an epoxy adhesive (Fig. A1.3). The adhesive was stirred before application, entraining air bubbles which, under pressure in forming the joint, deform to flat, penny-shaped discs of diameter 2fl = 2 mm. If the beam has the dimensions shown, and epoxy has a fracture toughness of 0.5 MN mT , calculate the maximum load F that the beam can support. Assume K = cT Tra for the disc-shaped bubbles. 

One way of measuring thermal shoek resistanee is to drop a piece of the ceramic, heated to progressively higher temperatures, into cold water. The maximum temperature drop AT (in K) which it can survive is a measure of its thermal shock resistance. If its coefficient of expansion is a then the quenched surface layer suffers a shrinkage strain of a AT. But it is part of a much larger body which is still hot, and this constrains it to its original dimensions it then carries an elastic tensile stress EaAT. If this tensile stress exceeds that for tensile fracture, <7js, the surface of the component will crack and ultimately spall off. So the maximum temperature drop AT is given by... 

Material properties for ice are listed in Table 28.3. The fracture toughness is low (0.12 MPa m ). The tensile strength of ice is simply the stress required to propagate a crack of dimensions equal to the grain size d, with... 

The narrow molecular weight distribution means that the melts are more Newtonian (see Section 8.2.5) and therefore have a higher melt viscosity at high shear rates than a more pseudoplastic material of similar molecular dimensions. In turn this may require more powerful extruders. They are also more subject to melt irregularities such as sharkskin and melt fracture. This is one of the factors that has led to current interest in metallocene-polymerised polypropylenes with a bimodal molecular weight distribution. 

The basic assumptions of fracture mechanics are (1) that the material behaves as a linear elastic isotropic continuum and (2) the crack tip inelastic zone size is small with respect to all other dimensions. Here we will consider the limitations of using the term K = YOpos Ttato describe the mechanical driving force for crack extension of small cracks at values of stress that are high with respect to the elastic limit. 

The variability in fracture stress when small artificial flaws were controlling strength was particularly pronounced for H-451 graphite, as can be seen in Fig. 12. Here the crack dimensions and crack trip process zone dimensions are comparable to the microstructural dimensions. Consequently, local variations in microstmeture... 

If we take the nominal fracture toughness of IG-11 graphite to be 1 MPayin and the maximum stress in the process zone to be = 60.2 MPa according to the above analysis, we find that rj, = 88 pm. This value is virtually identical to r<, , = 90pm, the process zone dimension determined using Eq. 3. To summarize, the above analysis strongly supports a hypothesis that the maximum critical stress... 

The first detailed book to describe the practice and theory of stereology was assembled by two Americans, DeHoff and Rhines (1968) both these men were famous practitioners in their day. There has been a steady stream of books since then a fine, concise and very clear overview is that by Exner (1996). In the last few years, a specialised form of microstructural analysis, entirely dependent on computerised image analysis, has emerged - fractal analysis, a form of measurement of roughness in two or three dimensions. Most of the voluminous literature of fractals, initiated by a mathematician, Benoit Mandelbrot at IBM, is irrelevant to materials science, but there is a sub-parepisteme of fractal analysis which relates the fractal dimension to fracture toughness one example of this has been analysed, together with an explanation of the meaning of fractal dimension , by Cahn (1989). 

The aim of this chapter is to describe the micro-mechanical processes that occur close to an interface during adhesive or cohesive failure of polymers. Emphasis will be placed on both the nature of the processes that occur and the micromechanical models that have been proposed to describe these processes. The main concern will be processes that occur at size scales ranging from nanometres (molecular dimensions) to a few micrometres. Failure is most commonly controlled by mechanical process that occur within this size range as it is these small scale processes that apply stress on the chain and cause the chain scission or pull-out that is often the basic process of fracture. The situation for elastomeric adhesives on substrates such as skin, glassy polymers or steel is different and will not be considered here but is described in a chapter on tack . Multiphase materials, such as rubber-toughened or semi-crystalline polymers, will not be considered much here as they show a whole range of different micro-mechanical processes initiated by the modulus mismatch between the phases. 

When fracture is confined to a single plane of the lattice, the net solution collapses to the nail solution. Consider an atomically thin slab of dimension V = AL, where A is unit area and L is a bond length, the strain energy stored is U = a AL/lE and the energy dissipated is U = DoE p — / c). The VP model then predicts that Gic o- such that... 

Resistance to Fracture - The ion or ionized complexes that the resins are required to fix are of varied dimensions and weights. The swelling and contraction of the resin bead that this causes must obviously not cause the grains to burst. 

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. 

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

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