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Crack opening

Rubin Y 1997 Organic approaches to endohedral metallofullerenes cracking open or zipping up carbon shells Chem. Eur. J. 3 1009-16... [Pg.2436]

We shall investigate the problem of controlling the external forces with an objective functional describing the crack opening... [Pg.130]

We note that if the crack opening is zero on F,, i.e. [%] = 0, the value of the objective functional Js u) is zero. We also assume that near F, the punch does not interact with the shell. It turns out that in this case the solution X = (IF, w) of problem (2.188) is infinitely differentiable in a neighbourhood of points of the crack. This property is local, so that a zero opening of the crack near the fixed point guarantees infinite differentiability of the solution in some neighbourhood of this point. Here it is undoubtedly necessary to require appropriate regularity of the curvatures % and the external forces u. The aim of the following discussion is to justify this fact. At this point the external force u is taken to be fixed. [Pg.131]

An existence theorem to the equilibrium problem of the plate is proved. A complete system of equations and inequalities fulfilled at the crack faces is found. The solvability of the optimal control problem with a cost functional characterizing an opening of the crack is established. The solution is shown to belong to the space C °° near crack points provided the crack opening is equal to zero. The results of this section are published in (Khludnev, 1996c). [Pg.171]

Further, in Section 3.1.4, an optimal control problem is analysed. The external forces u serve as a control. The solution existence of the optimal control problem with a cost functional describing the crack opening is proved. Finally, in Section 3.1.5, we prove C°°-regularity of the solution near crack points having a zero opening. [Pg.173]

This functional characterizes an opening of the crack. As before, x,0 is the solution of (3.48) corresponding to f,g)- At the first step we prove the existence of the optimal control problem. The next step is to prove the C°°-regularity of the solution provided that the crack opening is zero. We fixed the parameter c in this subsection the passage to the limit, as c —> 0, is analysed in Section 3.2.4. [Pg.192]

As it turns out, the solution of (3.48) is infinitely differentiable provided that f,gG C°°, the crack opening is equal to zero and a contact between plates is absent in the vicinity of the considered point. We prove this assertion in the neighbourhood of a point x, G F n The case x F n F, is simpler (see Remark after the proof of Theorem 3.7). [Pg.193]

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... [Pg.56]

But it does not usually do this. We have already seen that, if the length of the fibres is less than 2x, they will not fracture. And if they do not fracture they must instead pull out as the crack opens (Fig. 25.6). This gives a major new contribution to the toughness. If the matrix shear strength is tr (as before), then the work done in pulling a fibre out of the fracture surface is given approximately by... [Pg.269]

Crack extension is often observed to vary significantly at the same nominal value of AK (= Y AOpos Tta) for different values of R-ratio. Elber [26] was the first to explain this observation for metals in terms of the crack closure phenomenon. He determined, by measuring specimen compliance, that fatigue cracks open and close at the crack tip at positive values of stress due to contact between crack surfaces behind the crack tip. For elastic fatigue conditions it is generally found that P p = P, and Kop = K, where P is the applied load. [Pg.493]

In the traditional Dugdale model [56], a = Oy and the familiar result is obtained, Gic = cTySc- In the EPZ model, cr exceeds critical crack opening displacement <5c is proportional to the maximum stresses cr in the deformation zone... [Pg.385]

Pressurized air can do the same type of damage as pressurized water. Treat all operations on compressed air systems with the same care taken on liquid systems. Closed valves should be slowly cracked open and both sides allowed to equalize prior to opening the valve further. [Pg.631]

Fig. 8.35 Reduction in area versus applied potential for 316 stainless steel, in 5 ppm chloride content water at 250°C. Horizontal arrows indicate RA% for tests in argon gas open-annealed, filled-sensitised. Vertical downward pointing arrows on the annealed curve indicate cracking-non-cracking boundaries. Full downward pointing arrow on the sensitised curve indicates commencement of cracking. Open upward pointing arrow on the sensitised curve indicates transition from transgranular to intergranular cracking... Fig. 8.35 Reduction in area versus applied potential for 316 stainless steel, in 5 ppm chloride content water at 250°C. Horizontal arrows indicate RA% for tests in argon gas open-annealed, filled-sensitised. Vertical downward pointing arrows on the annealed curve indicate cracking-non-cracking boundaries. Full downward pointing arrow on the sensitised curve indicates commencement of cracking. Open upward pointing arrow on the sensitised curve indicates transition from transgranular to intergranular cracking...
The above discussion has assumed that the crack is loaded in mode 1 (the crack opening mode, with a tensile stress normal to the plane of the crack). Hydrogen has relatively little effect in modes II or III, as these generate shear stresses at the crack tip, rather than tensile stresses, and the shear behaviour of steels is relatively little affected by hydrogen, presumably because dilation of the lattice at the crack tip (which does not occur in modes II and III) is required for hydrogen accumulation. [Pg.1250]

Asian restaurants, with the help of people like Ms. Kim, who is Korean, are creating Asian cocktails as specialty drinks that showcase the house style, starting at the bar. The popularity of Asian accents in international cooking is cracking open cocktail menus, too. [Pg.142]

Effective molecular mass between crosslinks tvtc/kg mol 1 Tensile yield strength cry/MPa Energy release rate Gic/Jm 2 Half crack opening displacement w = 6/2 = Gic/2cry w/pm Chain contour length (Eq. 7.9) lc/nm... [Pg.334]

The boundary of the proposed deformation zone is shown in Fig. 7.3 according to Eq. (7.2). The displacement at the crack tip at x = 0 is called crack opening displacement 5 or critical crack opening displacement 8C if the crack is going to propagate. [Pg.343]


See other pages where Crack opening is mentioned: [Pg.421]    [Pg.128]    [Pg.134]    [Pg.168]    [Pg.182]    [Pg.189]    [Pg.90]    [Pg.544]    [Pg.549]    [Pg.549]    [Pg.53]    [Pg.53]    [Pg.55]    [Pg.291]    [Pg.494]    [Pg.352]    [Pg.355]    [Pg.384]    [Pg.439]    [Pg.449]    [Pg.1083]    [Pg.343]    [Pg.152]    [Pg.667]    [Pg.1294]    [Pg.1302]    [Pg.1374]    [Pg.1374]    [Pg.727]    [Pg.313]    [Pg.315]    [Pg.316]    [Pg.316]   
See also in sourсe #XX -- [ Pg.149 ]

See also in sourсe #XX -- [ Pg.134 , Pg.137 ]




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Crack Mouth Opening Displacement

Crack Mouth Opening Displacement CMOD)

Crack Opening Displacement (COD

Crack mouth opening

Crack opening displacement

Crack opening stretch

Crack tip opening displacement

Crack tip opening displacement CTOD)

Cracking ring-opening

Cracks of minimal opening

Cracks of zero opening

Critical crack opening displacement

Existence of minimal opening cracks

Fatigue crack opening

Fracture crack opening displacement

Fracture toughness crack opening displacement

Fully Open Cracks that are Stationary or Growing

Ratio of Crack Opening Dependency

Ratio of Crack Opening Dependency RCOD)

Tough polymers crack opening displacement

Wide-opened crack

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