Inclusion shapes

EinaHy, hydrogen in relatively small amounts can lead to cracking, especially as the strength increases. If the presence of hydrogen caimot be adequately lowered by the ladle treatment, combinations of low carbon and siHcon, inclusion shape control, and more than 0.25% copper can be helpful in minimizingloss of toughness. 

Replacement of rare earth elements for sulfide inclusion shape oontrpl 1 extreme steel desulfurization with the aid of calcium. 

In an elastically homogeneous system, the elastic strain energy per unit volume of the inclusion Age is independent of inclusion shape and is given by... 

The average strain in the inclusion is given by i = AJ and in the matrix by l2 = A2 , where e is the average overall strain and denotes the average over all orientations and inclusion shapes. (The corresponding stresses are BJ a and B2o respectively) Then... 

Szecsody, J.E. et al., Influence of iron oxide inclusion shape on CoII/IIIEDTA reactive transport through spatially heterogeneous sediment, Water Resour. Res., 34, 2501, 1998b. 

Two concepts from fibre-reinforcement theory are of general use in polymer mechanics. The first is the effect of inclusion shape on the anisotropic elastic moduli of a composite. Two rules control the effects of fibre reinforcement ... 

INPUT VALUES -Updated 6 j and e/ -Sub-phases config. e.g. interface vectors and inclusion shapes. OPERATION... 

In most cases, the removal of burr and cold-worked metal from the edge of the punched hole increases the hole expansion considerably. The hole expansion also increases with the increase in er and r, values and decreases with the increase in tensile strength. Inclusion shape control also improves hole-expansion performance. 

Lauritzen SI, Hoffman JD (1960) Theory of formation of polymer crystals with folded chains in dilute solution. J Res Natl Bur Stand 64A 73-102 Le Meins J-F, Moldenaers P, Mewis J (2003) Suspensions of monodisperse spheres in polymer melts particle size effects in extensional flow. Rheol Acta 42 184—190 Lee BJ, Meat ME (1991) Effect of inclusion shape on the stiffness of nonlinear two-phase composites. J Mech Phys Solids 39 627-649... 

To date, results have been obtained for minimum-energy type simulations of elastic deformations of a nearest-neighbor face-centered cubic (fee) crystal of argon [20] with different inclusion shapes (cubic, orthorhombic, spherical, and biaxially ellipsoidal). On bisphenol-A-polycarbonate, elastic constant calculations were also performed [20] as finite deformation simulations to plastic unit events (see [21]). The first molecular dynamics results on a nearest-neighbor fee crystal of argon have also become available [42]. The consistency of the method with thermodynamics and statistical mechanics has been tested to a satisfactory extent [20] e.g., the calculations with different inclusion shapes all yield identical results the results are independent of the method employed to calculate the elastic properties of the system and its constituents (constant-strain and constant-stress simulations give practically identical values). 

The constraint matrix T depicts the effect of the constraining matrix on the inclusion and is a function of matrix material properties and ellipsoidal inclusion shape. It represents the piezoelectric analog to Eshelby s tensor in the elastic case, see Dunn and Taya [66]. Expressions for cylindrical inclusions to model fibrous composites are provided by Dunn and Taya [67] (this reference uses a different notation, T is called S). Equating Eqs. (5.12) and (5.13) and making use of Eq. (5.14) to replace the eigenfields Z and Eq. (5.11) to eliminate the perturbation fields Z after some manipulations, leads to... 

Both Voigt and Reuss models provide initial estimates of the upper and lower bounds of elasticity of multiphase composites with the only consideration of the inclusion volmne fraction but irrespective of inclusion shape/geometry, orientation and spatial arrangement. 

All carbon steel products should be fully killed and fine-grain treated and should be supplied in normalized, normalized and tempered, or quenched and tempered condition. Production should be by a low-sulfur and low-phosphorus refining process (e.g. electric furnace with double deslagging or in the basic oxygen converter). The heat should be vacuum degassed and inclusion shape control treated, preferably by calcium. 

Calame [16] has proposed a numerical simulation method to solve an equation of the similar form as Hanai equation with power of w-th fraction, as shown in equation 9.29, and has described a method of empirically determining the value of n using least-squares fitting. Equation of the same form as equation 9.29 has also been discussed by Tuncer et al. [17] in context of effect of inclusion shape factor on the permittivity of the mixture. 

Recently, extensive studies have been done on the utilization of rare earth metals and Ca in the ingot-making and continuous casting processes, with the objective of high-grade steel production. Rare earths and Ca control not only the inclusion shape (Luyckx et al. 1970), but also the solidification structure itself (Sakuraya et al. 1976, Chistyakov et al. 1966). It is well known that the addition of rare earths results in the grain refinement of steels. 

Describes fractured and (low) porous rooks, implements inclusion shape (aspect ratio), and orientation random orientation (isotropic) aligned orientation (anisotropio) ... 

The generalization of the inclusion shape from a sphere to an ellipsoid creates different properties of the composite with respect to the field direction related to the ellipsoid axis. A single ellipsoid or a set of ellipsoids with identical or preferred orientation originates an anisotropy effect. If the inclusions are randomly oriented, then isotropy results (see Section 11.1.4). In this section these two cases are discussed. 

The generalization of the inclusion shape from a sphere to an ellipsoid creates different properties of the composite with respect to the field direction related to the ellipsoid axis system. 

Table 11.2 shows expressions of the parameter R" for some inclusion shapes. 

---