Effect of the kinematic hardening on the plastic anisotropy parameters for metallic sheets

The initial plastic anisotropy parameters are conventionally determined from the Lankford strain ratios defined by $r^{\psi }=\frac{{\epsilon }_{22}^{\mathrm{p}\psi }}{{\epsilon }_{33}^{\mathrm{p}\psi }}$ (ψ being the direction of the loading path). They are usually considered as constant parameters that are determined at a given value of the plastic strain far from the early stage of the plastic flow (i.e. equivalent plastic strain of ${\epsilon }_{\mathrm{eq}}^{\mathrm{p}}=0.2\text{\%}$) and typically at an equivalent plastic strain in between 20% and 50% of plastic strain failure (or material ductility). What prompts to question about the relevance of this determination, considering that this ratio does not remain constant, but changes with plastic strain. Accordingly, when the nonlinear evolution of the kinematic hardening is accounted for, the Lankford strain ratios are expected to evolve significantly during the plastic flow.In this work, a parametric study is performed to investigate the effect of the nonlinear kinematic hardening evolution of the Lankford strain ratios for different values of the kinematic hardening parameters. For the sake of clarity, this nonlinear kinematic hardening is formulated together with nonlinear isotropic hardening in the framework of anisotropic Hill-type (1948) yield criterion. Extension to other quadratic or non-quadratic yield criteria can be made without any difficulty. This parametric study is completed by studying the effect of these parameters on simulations of sheet metal forming by large plastic strains.     

A priori study for the modelling of velocity–interface correlations in the stratified air–water flows

This work concerns the modelling of stratified two-phase turbulent flows with interfaces. We consider an equation for an intermittency function $\alpha (\mathbf{x}\text{,}t)$ which denotes the probability of finding an interface at a given time t and a given point $\mathbf{x}$. In Wacławczyk and Oberlack (2011) a model for the unclosed terms in this equation was proposed. Here, we investigate the performance of this model by a priori tests, and finally, based on the a priori data discuss its possible modification and improvements.     

Effect of notch depth on strain-concentration factor of rectangular bars with a single-edge notch under pure bending

The FEM is employed to study the effect of notch depth on a new strain-concentration factor (SNCF) for rectangular bars with a single-edge notch under pure bending. The new SNCF $K_{\epsilon }^{\mathrm{new}}$ is defined under the triaxial stress state at the net section. The elastic SNCF increases as the net-to-gross thickness ratio h₀/H₀ increases and reaches a maximum at h₀/H₀ = 0.8. Beyond this value of h₀/H₀ it rapidly decreases to the unity with h₀/H₀. Three notch depths were selected to discuss the effect of notch depth on the elastic–plastic SNCF; they are the extremely deep notch (h₀/H₀ = 0.20), the deep notch (h₀/H₀ = 0.60) and the shallow notch (h₀/H₀ = 0.95). The new SNCF increases from its elastic value to the maximum as plastic deformation develops from the notch root. The maximum $K_{\epsilon }^{\mathrm{new}}$ of the shallow notch is considerably greater than that of the deep notch. The elastic $K_{\epsilon }^{\mathrm{new}}$ of the shallow notch is however less than that of the deep notch. Plastic deformation therefore has a strong effect on the increase in $K_{\epsilon }^{\mathrm{new}}$ of the shallow notch. The variation in $K_{\epsilon }^{\mathrm{new}}$ with M/M_Y, the ratio of bending moment to that at yielding at the notch root, is slightly dependent up to the maximum $K_{\epsilon }^{\mathrm{new}}$ for the shallow notch. This dependence is remarkable beyond the maximum $K_{\epsilon }^{\mathrm{new}}$. On the other hand, the variation in $K_{\epsilon }^{\mathrm{new}}$ with M/M_Y is independent of the stress–strain curve for the deep and extremely deep notches.     

The effect of different inlet conditions of air in a rectangular channel on convection heat transfer: Turbulence flow

Theoretical and empirical correlations for duct flow are given for hydrodynamically and thermally developed flow in most of previous studies. However, this is commonly not a realistic inlet configuration for heat exchanger, in which coolant flow generally turns through a serpentine shaped passage before entering heat sinks. Accordingly, an experimental investigation was carried out to determine average heat transfer coefficients in uniformly heated rectangular channel with 45° and 90° turned flow, and with wall mounted a baffle. The channel was heated through bottom side with the baffle. In present work, a detailed study was conducted for three different height of entry channel (named as the ratio of the height of entry channel to the height of test section (${\overline{H}}_{\text{c}}=h_{\text{c}}/H$)) by varying Reynolds number (${\mathit{Re}}_{\text{Dh}}$). Another variable parameter was the ratio of the baffle height to the channel height (${\overline{H}}_{\text{b}}=h_{\text{b}}/H$). Only one baffle was attached on the bottom (heating) surface. The experimental procedure was validated by comparing the data for the straight channel with no baffle. Reynolds number $({\mathit{Re}}_{\text{Dh}})$ was varied from 2800 to 30,000, so the flow was considered as only turbulent regime. All experiments were conduced with air accordingly; Prandtl number (Pr) was approximately fixed at 0.71. The results showed that average Nusselt number for θ = 45° and θ = 90° were 9% and 30% higher, respectively, than that of the straight channel without baffle. Likewise, the pressure drop increased up to 4.4 to 5.3 times compare to the straight channel.