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.     

Necking of an anisotropic plastic material

The two conditions for stable necking, treated as a bifurcation of stress path, are derived. The anisotropic material considered is one for which the plastic work increment = $\overline{\sigma }d\overline{e}$, where both the generalized yield stress $\overline{\sigma }$ and generalized plastic strain increment $d\overline{e}$ are invariant functions. The method is applied to the necking of a thin cylinder under internal pressure.     

Dynamics of an elastic capsule in moderate Reynolds number Poiseuille flow

The dynamic motions and lateral equilibrium positions of a two-dimensional elastic capsule in a Poiseuille flow were explored at moderate Reynolds number (10 ⩽ Re ⩽ 100) as a function of the initial lateral position (y₀), Re, aspect ratio (ɛ), size ratio ($\lambda$), membrane stretching coefficient (φ) and bending coefficient (γ). The transition between tank-treading (TT) and swinging (SW) to tumbling (TU) motions was observed and the lateral equilibrium positions of the capsules varied according to the conditions. The initial behavior of the elastic capsule was influenced by variation in the initial lateral position (y₀), but the equilibrium position and dynamic motion of the capsule were not affected by such variation. The capsules had a stronger tendency toward TU motion at higher values of Re, φ and γ, whereas the capsules underwent TT or SW motion as the values of ɛ and $\lambda$ increased. Under moderate Re Poiseuille flows, capsules tended to migrate across streamlines to a specific equilibrium position. The lateral equilibrium position shifted toward the centerline at larger $\lambda$ and migrated toward the wall at larger $\epsilon \text{,}\varphi \text{and}\gamma$. As Re increased, the equilibrium position first shifted toward the bottom wall, then toward the channel center. However, different equilibrium position trends were obtained around the SW–TU transition. The capsule undergoing TU motion tended to migrate downward toward the bottom wall more than the capsule undergoing SW motion, all other conditions being similar.     

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.     

Effect of heating rate on steam pressure induced in crack-like cavities in moisture saturated polymer matrix composites

When moisture saturated composites are rapidly heated, the steam pressure inside cavities can cause the composite to delaminate. We study the effect of heating rate on the steam pressure inside an isolated long thin “crack-like” cavity of thickness h assuming that the chemical potential of water is continuous across the cavity/polymer interface. For such a cavity in an infinite plate, we show there is sufficient moisture for the steam pressure to reach the saturated steam pressure, irrespective of the heating rate. However, for a plate of thickness L exposed to dry air, the cavity pressure reaches a maximum value, which depends only on the normalized plate thickness, α = L/h and normalized heating rate, $\beta =\dot{T}{h}^2/T_{0}D(T_0)$ where $\dot{T}$ is the heating rate, D(T₀) is the moisture diffusivity at the initial temperature T₀, before it decays to zero because of the dry air outside. For this case, the maximum steam pressure can be significantly less than the saturation pressure. The results in this work can also be used to study ‘popcorning’ observed in electronic packages.