Cracking energy density

Due to the plane-specific namre of crack nucleation under multiaxial tests. Mars and Fatemi proposed the cracking energy density as an equivalence parameter that represents the portion of strain energy density available to be released as crack growth on a specific material plane. The form of the cracking energy density Wc is... 

Based on comparison of three traditional equivalence parameters with cracking energy density, the maximum principal strain corresponded the closest to the cracking energy density. Thus, Mars and Fatemi judged that the maximum principal strain is the most robust and meaningful of the traditional parameters considered in their work. 

Cincinnati, Oh., 17th.-19th. Oct. 2000, paper 67 CRACKING ENERGY DENSITY AS A PREDICTOR OF FATIGUE LIFE UNDER MULTIAXIAL CONDITIONS... 

An alternative energy approach to the fracture of polymers has also been developed on the basis of non-linear elasticity. This assumes that a material without any cracks will have a uniform strain energy density (strain energy per unit volume). Let this be IIq. When there is a crack in the material this strain energy density will reduce to zero over an area as shown shaded in Fig. 2.65. This area will be given by ka where )k is a proportionality constant. Thus the loss of elastic energy due to the presence of the crack is given by... 

FIGURE 1.5 Energy release rate Gc versus length c of a bond line crack. U is the strain energy density. Block thickness H—2 mm, length L — 20 mm. (From Gent, A.N., Suh, J.B., and Kelly, III, S.G., Int. J. Non-Linear Mech., 42, 241, 2007. With permission.)... 

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

The parameters governing crack propagation have been proposed by Sih and Madenci [8] with the strain energy density theory. The strain energy density function, d Wld V, in front of the crack tip has been expressed in the form... 

Analogous results have been found for other polymers. Crazing at crack tips exhibits exactly the same behavior. In order to evaluate the acceleration of crazing by action of a solvent, the interaction between the polymer and the solvent can be quantified by means of the solubility parameter, 5, defined as the cohesive energy density where AHy is the vaporization... 

To and the crack faces. The curve T is shrunk onto the crack tip to give J. ni is a unit vector that is normal to T or To and that points away from the crack tip. ni is the component of n, into xi direction. U is the strain energy density and u is the displacement vector. The material density is p. The advantage of a far-field integral such as Equation (4) is that J can be evaluated along any curve surrounding the crack tip and the singularity at the crack tip, which is problematic in numerical models, can be avoided. 

Figure 9,14 Normalized largest fragment mass versus energy density for water ice at low temperature (77K) and 255 K. For the comparison, basalt and pyrophyllite data is also plotted [46], The data at 81 K by Lange and Ahrens [47] shows rather weaker strength than the present data because there might be initial cracks in the target before the shot. (Figure from Kato et al. [35].)...

Here, is again the surface work, S is the surface energy as previously defined and is the loss function dependent on crack speed, temperature and the strain, eo, applied to the specimen. The theory gives explicitly in terms of the energy density distribution in the specimen and the plastic or visco-elastic hysteresis of the material. 

The physical requirement that strain energy in the elastic body be finite (or bounded) suggests that the order of singularity of stresses at the crack tip can be represented at most by (The basic reasoning is that, with stress and strain proportional to strain energy density would be proportional to The strain... 

The main advantage of liquid fuels over their gaseous fuel alternatives is the extremely high energy density (thermal energy/volume ratio). Typically they would have a GCV of 40 MJ/kg, which in volumetric terms is equivalent to 33,000 MJ/Nm compared with natural gas at about 34 MJ/Nm. Heavy fuel oils are blended products based on the residues from various refinery distillation and cracking processes. 

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