Crack friction

Microcracking-induced hysteresis may be seen in Fig. 7.34, where surface-crack friction and sliding occur. A comparison is made between such a case and one without crack friction and sliding. 

Substances in this category include Krypton, sodium chloride, and diamond, as examples, and it is not surprising that differences in detail as to frictional behavior do occur. The softer solids tend to obey Amontons law with /i values in the normal range of 0.5-1.0, provided they are not too near their melting points. Ionic crystals, such as sodium chloride, tend to show irreversible surface damage, in the form of cracks, owing to their brittleness, but still tend to obey Amontons law. This suggests that the area of contact is mainly determined by plastic flow rather than by elastic deformation. 

Submitting the main topic, we deal with models of solids with cracks. These models of mechanics and geophysics describe the stationary and quasi-stationary deformation of elastic and inelastic solid bodies having cracks and cuts. The corresponding mathematical models are reduced to boundary value problems for domains with singular boundaries. We shall use, if it is possible, a variational formulation of the problems to apply methods of convex analysis. It is of importance to note the significance of restrictions stated a priori at the crack surfaces. We assume that nonpenetration conditions of inequality type at the crack surfaces are fulfilled, which improves the accuracy of these models for contact problems. We also include the modelling of problems with friction between the crack surfaces. 

We consider the model of a plate with a crack describing the plate vertical displacements with a given friction between the crack surfaces. The results of this section are published in (Kovtunenko, 1998). 

For wear resistance and low friction, coatings of PTFE or M0S2 generally have been satisfactory. Use of low thermal expansion filler in PTFE helps minimise cracking and loss of adhesion from metal substrates with their lower coefficients of expansion. 

The material in use as of the mid-1990s in these components is HDPE, a linear polymer which is tough, resiUent, ductile, wear resistant, and has low friction (see Olefin polymers, polyethylene). Polymers are prone to both creep and fatigue (stress) cracking. Moreover, HDPE has a modulus of elasticity that is only one-tenth that of the bone, thus it increases the level of stress transmitted to the cement, thereby increasing the potential for cement mantle failure. When the acetabular HDPE cup is backed by metal, it stiffens the HDPE cup. This results in function similar to that of natural subchondral bone. Metal backing has become standard on acetabular cups. 

Hard plating is noted for its excellent hardness, wear resistance, and low coefficient of friction. Decorative plating retains its brilliance because air exposure immediately forms a thin, invisible protective oxide film. The chromium is not appHed directiy to the surface of the base metal but rather over a nickel (see Nickel and nickel alloys) plate, which in turn is laid over a copper (qv) plate. Because the chromium plate is not free of cracks, pores, and similar imperfections, the intermediate nickel layer must provide the basic protection. Indeed, optimum performance is obtained when a controlled but high density (40—80 microcrack intersections per linear millimeter) of microcracks is achieved in the chromium lea ding to reduced local galvanic current density at the imperfections and increased cathode polarization. A duplex nickel layer containing small amounts of sulfur is generally used. In addition to... 

Toughening for whisker-reinforced composites has been shown to arise from two separate mechanisms frictional bridging of intact whiskers, and pullout of fractured whiskers, both of which are crack-wake phenomena. These bridging processes are shown schematically in Figure 13. The mechanics of whisker bridging have been addressed (52). The appHed stress intensity factor is given by ... 

The pullout regime assumes a linearly decreasing constitutive relationship as the crack opens up, and the whiskers pull out of the matrix with increasing ease. One solution (52) for frictional pullout alone is... 

Modtilus Measurements Another SCC test technique is the use of changes of modulus as a measure of the damping capacity of a metal. It is known that a sample of a given test material containing cracks will have a lower effec tive modulus than does a sample of identical material free of cracks. The technique provides a rapid and reliable evaluation of the susceptibility of a sample material to SCC in a specific environment. The so-called internal friction test concept can also be used to detect and probe nucleation and progress of cracking and the mechanisms controlling it. 

In compression, of course, the strength is greater. Most ceramics are about fifteen times stronger in compression than in tension, for the reasons given in Chapter 17. For ice the factor is smaller, typically six, probably because the coefficient of friction across the crack faces (which rub together when the ceramic is loaded in compression) is exceptionally low. At stresses below 6 MPa, ice loaded in compression deforms by creep at 6 MPa it crushes, and this is the maximum stress it can carry. 

Slip membrane serves to reduce friction between the slab and sub-base to minimize subsequent slab cracking. This is normally a polyethylene sheet. It may also serve as a damp-proof membrane ... 

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