web service Code 128 Code Set A Flow and fracture of a crystalline material in .NET Creator 3 of 9 in .NET Flow and fracture of a crystalline material

Flow and fracture of a crystalline material use none none integrated tocompose none for code 128 generator Figure 4.18. Variation in none none B with water content of the ice.

(Data reported by Duval, 1977.). Visual Studio Development Tools and Languages the latter, while in the expected direction, is probably unreasonable in magnitude. Finally, we return to the effect of the water content on the creep rate. This was studied by Duval (1977) in a pioneering set of sophisticated experiments.

His results, expressed in terms of the decrease in B with increasing water content, are shown in Figure 4.18. With an increase in water content from 0.

01% to 0.8%, B decreases from 0.24 to 0.

16 MPa a1/3 . Lliboutry (1983) reports that the water content of basal ice of temperate glaciers typically varies between 0.6% and 0.

95%. Based on the line in Figure 4.18, this corresponds to a variation in B from 0.

177 to 0.170, and hence in of 12%. The individual data points in Figure 4.

18 suggest an even greater sensitivity. Lower water contents, and hence higher values of B, are likely in temperate ice of polythermal glaciers..

Fracture At suf ciently high stres ses, ice fractures (Figure 4.16). Crevassing, resulting from high tensile stresses, is the type of fracturing with which people are most familiar.

However, fracturing near the base of the subaerial part of a calving face may be largely a consequence of crushing (compression). Owing to the importance of fracture in design of structures ranging from buildings to airplanes, the study of linear elastic fracture mechanics is well developed, and we will only skim the surface of this eld. Basically, aws or microcracks exist in most if not all crystalline.

Fracture Crack Crack tip Figure 4.19. Stress eld on an in nitesimal element located a distance r from a crack tip.

(Modi ed from Kenneally, 2003.). sxx sxz szx szz materials, and any far- e ld stresses on the material are ampli ed at the tips of these cracks. Thus, cracks may propagate at stresses far below the strength of an un awed specimen of the material. The elastic stress eld around the tip of a vertical crack in the surface of a solid of in nite horizontal extent, subjected to a far- eld tensile stress, , that is normal to the crack, is given by:.

3 KI cos 1 + sin sin none none x = 2 2 2 2 r 3 KI cos 1 sin sin z = 2 2 2 2 r 3 KI x z = sin cos cos 2 2 2 2 r (4.11). (see, for example, Lawn, 1993, p. 25). Here, r is the distance from the crack tip measured along a line making an angle with the crack axis (Figure 4.

19), and KI is a parameter known as the stress intensity factor. In general, K I = a, where a is the crack length. Thus, KI increases as either the far- eld stress or crack length increase.

The is a geometrical parameter that, in our case, depends upon factors such as the spacing of crevasses, the ice thickness, and the far eld stress. Thus, KI , and particularly , describe how the far- eld stresses are ampli ed or intensi ed around a crack tip. Clearly, high values of KI translate into high stresses around the crack tip and, if the stresses become high enough, the crack will propagate.

Rather than express this critical value in terms of the stresses themselves,. Flow and fracture of a crystalline material Critical stress intensity factor, KIc, kPa m1/2. Figure 4.20. Variation of none none KIc with density.

Based on laboratory measurements. (After Rist et al., 1999.

Reproduced with permission of the authors and the American Geophysical Union.). Porosity 0.4 180 160 140 120 100 8 none for none 0 60 40 500 600 700 800 900 0.3 0.

2 0.1 0.0.

Ice density, r, kg the standard procedure is none for none to express it in terms of a value of K called the fracture toughness, KIc . KIc is a material property of the medium. If KI exceeds KIc , the fracture will propagate unstably.

Rist et al. (1999) have summarized their own measurements of KIc on ice cores from Antarctica and other workers measurements on other types of samples and nd that it increases approximately linearly with density (Figure 4.20).

The scatter in the data is large, however. Stress intensity factors are complicated and often tedious to derive, but they can be obtained from handbooks such as Sih (1973). Conveniently, they obey the principal of superposition; thus, in problems with a complex stress con guration, if one can obtain stress intensity factors for each of the stresses separately, they can be added to obtain the stress intensity factor for the whole problem (Kanninen and Popelar, 1985, p.

27). We will illustrate this below. The alert reader may have noticed that the stresses in Equations (4.

11) become in nite as r 0. However, deformation in a region immediately around the crack tip is plastic, and this keeps the stresses nite. To estimate the radius, rp , of this plastic region, take = 0 in the rst or second of Equations (4.

11), assume that plastic behavior will occur once the stress exceeds 0.1 MPa (a commonly cited plastic yield strength for ice), adopt a value for KIc of 0.16 MPa m 1/2 , and solve for rp .

The result is rp 0.4 m. The principles of linear elastic fracture mechanics only apply if rp is small compared with a.

As we are concerned principally.
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