Shear inhomogeneous

The orientational relationships between the martensite and austenite lattice which we observe are partially in accordance with experimental results In experiments a Nishiyama-Wasserman relationship is found for those systems which we have simulated. We think that the additional rotation of the (lll)f< c planes in the simulations is an effect of boundary conditions. Experimentally bcc and fee structure coexist and the plane of contact, the habit plane, is undistorted. In our simulations we have no coexistence of these structures. But the periodic boundary conditions play a similar role like the habit plane in the real crystals. Under these considerations the fact that we find the same invariant direction as it is observed experimentally shows, that our calculations simulate the same transition process as it takes place in experiments. The same is true for the inhomogeneous shear system which we see in our simulations. 

Inelastic deformation of any solid material is heterogeneous. That is, it always involves the propagation of localized (inhomogeneous) shear. The elements of this localized shear do not occur at random places but are correlated in a solid. This means that the shears are associated with lines rather than points. The lines may delineate linear shear (dislocation lines), or they may delineate rotational shear (disclination lines). The existence of correlation means that when shear occurs between a pair of atoms, the probability is high that an additional shear event will occur adjacent to the initial pair because stress concentrations will lie adjacent to it. This is not the case in a liquid where the two shear events are likely to be uncorrelated. 

Transformation Twinning of Z 2(CsCl)-Type Structure Based on an Inhomogeneous Shear Model Frederick E. Wang... 

Fig. 21. The first paper of Wang published in 1971, in which an inhomogeneous shear modelproposed as the mechanism leading to a twining of B2-type structure. J. Appl. Pliys. Vol. 43, p.92 (1972).

Twin and antiphase boundary formations in TiNi through inhomogeneous shear mechanism... 

The atomic mechanism, based on the previously proposed inhomogeneous shear, leading to the formation of twinning and antiphase boundaries in TiNi with the CsCl-type structure is described. The twinning mechanism described herein explains the electrical resistivity anomaly due to incomplete thermal cyclings observed previously in TiNi. This explanation is in keeping, in a qualitative manner, with the "memory effects observed in relation to the electrical resistivity anomaly. 

Fig. 22. Showing how the inhomogeneous shear proposed (Fig. 21) in 1972 to apply in TiNi in the formation of twin and antiphase boundaries. This paper was published in 1973, more than 10 years before Goo et al claimed to have observed for the first time twining in B2 structure of TiNi (see Fig. 23). J.Appl.Phys. vol 44, p.3013 (1973).

Particle dynamics wall effects inertial effects inhomogeneous shear fields Brownian motion. 

When the imposed deformation consists of an inhomogeneous shear, as in torsion, the normal forces generated (corresponding to the stresses t2i in Figures 1.15 and 1.16) vary from point to point over the cross-section (Figure 1.17). The exact way in which they are distributed depends on the particular form of strain energy function obeyed by the rubber that is, on the values of Wi and W2, which obtain under the imposed deformation state (Rivlin, 1947). 

Next, we consider a steady, inhomogeneous shearing flow between identical bumpy boundaries, in which the working of the slip velocity through the shear stress at the boundary is not balanced by the rate of collisional dissipation. The thickness of the shearing flow, the relative velocity of the boundaries, and the shear and normal stress must be related in order for a steady flow solution to exist. Two different types of solutions are found, depending upon whether the boundaries provide or remove fluctuation energy to or from the flow. 

A few additional comments about when and under what conditions one must use a nonlinear viscoelastic constitutive equation are discussed here. At this time it seems that whenever the flow is unsteady in either a Lagrangian DvIDt 0) or a Eulerian (9v/9r 0) sense, then viscoelastic effects become important. In the former case one finds flows of this nature whenever inhomogeneous shear-free flows arise (e.g., flow through a contraction) and in the latter case in the startup of flows. However, even in simple flows, such as in capillaries or slit dies, viscoelastic effects can be important, especially if the residence time of the fluid in the die is less than the longest relaxation time of the fluid. Then factors such as stress overshoot could lead to an apparent viscosity that is higher than the steady-state viscosity. In line with these ideas one defines a dimensionless group referred to as the Deborah number ... 

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