A general methodology for bearing design in non-symmetric T-shaped sections in extrusion process

In this study, a general methodology has been developed to design the proper bearing in order to eliminate the curvature of the final product in extrusion process. Three smooth curved (advanced-surface) dies with non-symmetric T-shaped sections and different off-centricities have been studied. For each die, the proper bearing has been designed and physical and numerical modeling have been performed to validate the design. The design procedure is as follows: A formulation, based on Bezier curves, has been used to determine the exit velocity profile. Since the result of Bezier method is different from the actual velocity profile, the Chitkara corrective function has been modified and applied to improve the velocity field. A deviation function has been developed to measure the curvature of the final product in terms of the exit velocity field. Considering the obtained velocity field, the friction effects, and the geometry of the dies, the proper bearing for each die has been designed. Finally, numerical and physical modeling have been performed on the die-bearing combination. According to the results, the curvature of the final product was eliminated to a great extent.     

Parameters affecting the free‐radical melt grafting of maleic anhydride onto linear low‐density polyethylene in an internal mixer

Our main objective of this study was to study the parameters affecting the free‐radical melt grafting of maleic anhydride (MA) onto linear low‐density polyethylene (LLDPE) with dicumyl peroxide (DCP) in an internal mixer. The degree of grafting (DG) was measured with titrometry and Fourier transform infrared spectroscopy. The extent of chain‐branching/crosslinking was evaluated with gel content and melt flow index measurements. The flow behavior and melt viscoelastic properties of the grafted samples were measured by using rheometric mechanical spectrometry. Feeding order, DCP and MA concentration, reaction temperature, rotor speed, and grade of LLDPE were among parameters studied. The results show that the reactant concentration (MA and DCP) played a major role in the determination of the grafting yield and the extent of the chain‐branching/crosslinking as competitive side reactions. The order of feeding also had an appreciable effect on the DG and the side reactions. Increasing the rotor speed increased the grafting yield and reduced side reactions by means of intensification of the mixing of reactants into the polyethylene (PE) melt. Chain‐branching dominated the side reactions for lower molecular weight PE, whereas for higher molecular weight PE, chain‐branching led to crosslinking and gel formation. The results of the melt viscoelastic measurements on the grafted samples provided great insight into the understanding of the role of influential parameters on the extent of side reactions and resulting changes in the molecular structure of the grafted samples. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 141–149, 2006     

Coupled continuum damage mechanics and crystal plasticity model and its application in damage evolution in polycrystalline aggregates

In the present study, damage initiation and growth in a polycrystalline aggregate are investigated. In this regard, an anisotropic continuum damage mechanics coupled with rate-dependent crystal plasticity theory is employed. Using a thermodynamically consistent procedure, a finite deformation formulation is derived. For this purpose, the damage tensor is incorporated in the crystal plasticity formulation for a cubic single crystal. The damage evolution is considered to be dependent on the history of damage, equivalent plastic strain, stress triaxiality, and Lode parameters. This material model is implemented in the commercial finite-element code Abaqus/Standard by developing a user material subroutine (UMAT). Using the available experimental tests of 316L single crystal in the literature, the crystal plasticity hardening and damage parameters are calibrated considering the stress–strain curve before and after necking, respectively. The damage sites in a single-phase polycrystalline aggregate are also considered using a polycrystalline model consisting of grains with random sizes and orientations. The results show that the damage arises at the grain boundaries and triple junctions. Moreover, growth of the damage mostly occurs in the grains with higher Schmid factor compared to the neighboring grains. The presented model manifests capacity for determination of damage initiation sites and damage evolution in polycrystalline models.

     

Implementation of a Robust Algorithm for Prediction of Forming Limit Diagrams

In this article, a robust algorithm for prediction of forming limit diagrams (FLD) has been presented. The presented model is based on the “Marciniak and Kuczynski” (M-K) theory. Solution to the system of equations has been obtained by applying the Newton’s method. Since the Newton’s method usually has nonconverging problem, a particular backtracking algorithm has been developed and applied. In this algorithm, a technique for step length selection in the frame of gradient descent method has been implemented. Also for the convergence criterion the so-called “Armijo” condition has been used. For verification of the results, BBC2000 yield function and Swift hardening law for AK steel metal have been used. To obtain the necking angle, the effect of groove orientation on the left- and right-hand sides of FLD has been considered. Finally, the predicted FLD has been compared with the published experimental results.     

The Effect of the Imposed Boundary Rate on the Formability of Strain Rate Sensitive Sheets Using the M-K Method

In spite of the fact that the experimental results indicate the significant effect of strain rate on forming limits of sheets, this effect is neglected in all theoretical methods of prediction of Forming Limit Diagrams (FLDs). The purpose of this paper is to modify the most renowned theoretical method of determination of FLDs (e.g., M-K model) so as to enable it to take into account the effect of strain rate. To achieve this aim, the traditional assumption of preexistence of an initial geometrical inhomogeneity in the sheet has been replaced with the assumption of a preexisting “material” inhomogeneity. It has been shown that using this assumption, the strain rate would not be omitted from equations; thus, it is possible to demonstrate its effect on FLDs. To validate the results, they are compared with some published experimental data. The good agreement between the theoretical and experimental results shows capabilities of the proposed method in predicting the effect of the imposed rate at the boundary (which is physically the effect of the punch speed difference in sheet forming) on FLDs.     

Second order stress gradient plasticity with an application to thin foil bending

The continuum theory of dislocations is applied to formulate the problem of a double ended dislocation pileup under quadratic applied stress. Accordingly, a second order stress gradient plasticity model is presented to address the contribution of the first and the second stress gradients in the effect interpretation. The model is employed to predict the initial strengthening and subsequent hardening in curved and straight thin foils under pure bending within the continuum framework. It is shown that the so-called stress gradient plasticity model that ignores the second stress gradient may not give sound interpretations of the size effects. The plastic response of thin foils is affected by both the first and second stress gradients, yet their interaction strongly depends upon the length scale parameter. The larger the length scale parameter, the quadratic term contribution would be important and the predictions of the first and second order models deviate significantly from each other.     

Electron transfer kinetics during the reduction and turnover of the cytochrome caa3 complex from Bacillus subtilis

The cytochrome caa3 complex from Bacillus subtilis is a member of the cytochrome oxidase superfamily of respiratory enzyme complexes. The key difference in the cytochrome caa3 complex lies in the addition of a domain, homologous with mitochondrial cytochrome c, that is fused to the C-terminal end of its subunit II. Measurements of steady-state and transient reduction kinetics have been carried out on the cytochrome caa3 complex. Reduction of the cyanide-bound enzyme with ascorbate and N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) supports a sequence of electron transfer in which cytochromec is reduced initially, and this is followed by rapid internal electron transfer from cytochrome c to CuA and from CuA to cytochrome a. Steady-state kinetics with exogenous cytochrome c as the substrate demonstrates the capability of the cytochrome caa3 complex to act as a cytochrome c oxidase. The cytochrome c from B. subtilis is the most efficient cytochrome c of those tested. Steady-state kinetics with ascorbate-TMPD as the reductant, in the absence of exogenous cytochrome c, reveals a biphasic pattern even though only a single, covalent cytochrome c interaction site is present. The two-phase kinetics are characterized by a low activity phase associated with a high apparent affinity for TMPD and a high activity phase with a low affinity for TMPD. This pattern is observed over a wide range of ionic strengths and enzyme concentrations, and with both purified and membrane extract forms of cytochrome caa3. It is proposed that the biphasic steady-state kinetics of this oxidase, and other members of the cytochrome oxidase superfamily, do not result directly from different interactions with cytochrome c but are due to a change in the redox kinetics within the centers of the conventional oxidase unit itself. Our results will be related to models that account for the biphasic steady-state kinetics exhibited by cytochrome oxidase.     

Finite element and analytical fluid-structure interaction analysis of the pneumatically actuated diaphragm microvalves

In this paper, the fluid flow and the diaphragm deflection are studied in the pneumatically actuated diaphragm microvalve by performing finite element and analytical fluid-structure interaction simulations. The results of these approaches are compared and their validity is discussed. An analytical relation is obtained for the critical diaphragm deflection which leads to unstable response of the microvalve. This relation shows that the critical deflection is only a function of the microvalve geometry, namely its inlet height and outlet radius. The phenomenon of the diaphragm deflection jump is justified in the microvalve behavior. The effect of different fluid flow and diaphragm parameters on the microvalve response is investigated that can be used to improve the microvalve design.     

An improved strain gradient approach for determination of deformation localization and forming limit diagrams

The purpose of this study is to develop a methodology for prediction of the deformation localization and forming limit diagrams (FLD). The strain gradient approach is incorporated into the M–K method for deformation localization analysis and the prediction of forming limit diagram in sheet metal forming. This approach introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation inhomogeneity and material softening. To solve the non-linear second order boundary value problem collocation method has been used. In this solution, the neck evolution structure has been presented. Compared to the “Shooting Method” used by other researchers in the present work, the convergence and accuracy of solution is guaranteed with better speed. It thus overcomes the imperfection sensitivity encountered in the conventional M–K method and the neck evolution structure presented. Also the post-localization behavior of sheet metal presented. The comparison between the experimental and theoretical results for FLDs as predicted by different methods indicates that the present approach is quite successful.     

Some improvements on the unfolding inverse finite element method for simulation of deep drawing process

The linear unfolding inverse finite element method (IFEM) has been modified and enhanced by implementing large deformation relations. The method is helpful to predict forming severity of the part that should be deep drawn as well as its blank shape and strain distribution in preliminary design stage. The approach deals with minimization of potential energy and large deformation relations with membrane elements. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as 2D problem. Moreover, the nonlinear stress-strain relationship of plastic material properties has been considered to increase the accuracy of the results. An experiment set up has been prepared to form a rectangular cup. Then, the obtained cup has been analyzed by linear unfolding IFEM and the proposed method. Comparisons of the measured thickness strains and the blank shape show that the proposed method predicts the strain distribution more accurately than the linear method.