Slip-line model

Several researchers tried to replace the single-shear plane model by a shear zone model. Lee and Shaffer (1951) provided a slip-line solution by applying the theory of plasticity. In the slip-line model, the metal is assumed to flow along the line of maximum shear lines. The slip-line field solution cannot be applied easily to three-dimensional as well as strain-hardening cases. Sidjanin and Kovac (1997) applied the concept of fracture mechanics in chip formation process. Atkins (2003) demonstrated that the work for creation of new surfaces in metal cutting is significant. He also points out that Shaw (1954) has shown this work to be insignificant. However, when this work is included based on the modem ductile fracture mechanics, even the Merchant analysis provides reasonable results. 

The above results show close agreement between the experimental and theoretical friction factor (solid line) in the limiting case of the continuum flow regime. The Knudsen number was varied to determine the influence of rarefaction on the friction factor with ks/H and Ma kept low. The data shows that for Kn < 0.01, the measured friction factor is accurately predicted by the incompressible value. As Kn increased above 0.01, the friction factor was seen to decrease (up to a 50% X as Kn approached 0.15). The experimental friction factor showed agreement within 5% with the first-order slip velocity model. 

Figure 31 Slip-spring model results with CR (lines) and without it (points) for the standard parameters. The four panels show monomer mean-square displacement (a) and (c), end-to-end relaxation (b), and stress relaxation (d).

Earthquake Mechanism and Seafloor Deformation for Tsunami Generation, Fig. 6 Comparison of displacement profiles between imbedded crack (dashed line) and dislocation (solid line) models with same average slip (uniform slip for the dislocation model). See Fig. 5 for fault geometry... 

Figure 4.13 The slip-links model of Doi and Edwards, which hypothesizes that the primitive chain is defined by a line segment between slip-links and that it passes through small rings, where the slip-links are separated by a distance a.

Figure 9.23 Normalized dielectric constant o - s ( ), where Sq is the zero-frequency dielectric constant, and dielectric loss constant ( ) at 40 °C for a 6-arm polyisoprene star with = 459,000. Symbols are data ofWatanabeef a/. [66], and the lines are predictions of the slip link model. The parameters of the model = 4650 and Tq=42 s,are used for all calculations with the...

Slip-link model predictions of G ((u) (lines) compared to data (symbols) for model 1,4-poly-isoprene H-polymers with total molecular weights of 219,000 and 345,000 (McLeish etal. [24] samples H110B20A, with = 1.01 and = 1.13 and H160B40A,... 

Excellent agreement between experiment and onr calculations is obtained when considering the low temperature deformation in the hard orientation. Not only are the Peierls stresses almost exactly as large as the experimental critical resolved shear stresses at low temperatures, but the limiting role of the screw character can also be explained. Furthermore the transition from (111) to (110) slip at higher temperatures can be understood when combining the present results with a simple line tension model. 

Figure 10.16. NO conversion and ammonia slip as a function of the NH3/NO ratio in the presence of O2 and H2O over a V203/Ti02 catalyst at 623 K. The lines represent the model based on reactions (9)-(14) and the parameters in Tab. 10.7. [Adapted from).A. Dumesic, N.-Y. Topsoe, H. Topsoe, Y. Chen, and T. Slabiak, J. Catal. 163 (1996) 409.]...

The. Homogeneous Equilibrium Model (HEM) assumes uniform mixing of the phases across the. pipe diameter, no phase slip (mechanical equilibrium), thermal equilibrium between, the..phases and complete vapour/ liquid, equilibrium. "Homogenous" in the context of the HEM refers to the flow in the vent line. 

Fig. 2.17 Frequency dependence of dynamic shear moduli computed using a model for the linear viscoelasticity of a cubic phase based on slip planes, introduced by Jones and McLeish (1995). Dashed line G, solid line G".The bulk modulus is chosen to be G — 105 (arb. units). The calculation is for a slip plane density AT1 - 10 5 and a viscosity ratio rh = = 1, where rjs is the slip plane viscosity and t] is the bulk viscosity. The strain...

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