Deformation processing of metal powders: Part I—Cold isostatic pressing

Analytical and numerical techniques are used to analyze in detail the stage I Cold Isostatic Pressing (CIPing) of metal powders. Plastic yielding is considered to be the only densification mechanism and the constitutive model developed recently by Fleck, Kuhn and McMeeking [(J. Mech. Phys. Solids40, 1139 (1992)] is used to describe the elastoplastic behavior of the metal powder. It is shown that, for the case of powder consolidation in a long cylindrical tube, a change in length is not possible, unless it is accompanied by some distortion (“shape change”) of the CIPed specimen. The numerical implementation of the constitutive elastoplastic equations in a finite element program is discussed. The finite element method is used to analyze the CIPing of titanium powder. The predictions of the finite element solution agree well with available experimental data.     

Substepping algorithms with stress correction for the simulation of sheet metal forming process

The finite element analysis of the sheet metal forming process involves various nonlinearities. To predict accurately the final geometry of the sheet blank and the distribution of strain and stress and control various forming defects, such as thinning, wrinkling and springback, etc., the accurate integration of the constitutive laws over the strain path is essential. Our objective in this paper is to develop an effective and accurate stress integration scheme for the analysis of three-dimensional sheet metal forming problems. The proposed algorithm is based on the explicit “substepping” schemes incorporating with the stress correction scheme. The proposed algorithms have been implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform. The algorithms are then employed to analyze a typical deep-cup drawing process and the accuracy of these algorithms has been compared with the implicit “return” algorithm and explicit forward algorithm. The results indicate that the explicit schemes with local truncation error control, together with a subsequent check of the consistency conditions, can achieve the same or even better level of accuracy as “return” algorithm does for integrating large plastic problems like sheet metal forming process.     

Collision between a ring and a beam

With car–parapet collision accidents in mind, a normal collision between a free-flying half ring and a simply supported beam with/without axial constraints is studied, in which an elastic–plastic half ring with an attached mass and the elastic–plastic beam are taken as the simplest models of a car and a parapet, respectively. Particular attention is paid to the energy partitioning between the two structures and the evolution of the contact regions during collision. A mass–spring finite difference (MS–FD) model is employed whilst the large deflection and axial stretching/compression are incorporated. The numerical results show that the less stiff (i.e. softer) structure will dissipate more energy and the contact regions will move away from the initial contact points. With the increase of the relative thickness of the beam to the ring, the final deformation of the half ring will transform from a “U” shape to a “W” shape.     

Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings

In this paper the crushing behavior of thin-walled tubes under static and dynamic loading is investigated. First, a finite element (FE) model for empty thin-walled tube was constructed and validated by available experimental and numerical data. The comparison between the FE results and the existing numerical solutions as well as the available experimental results showed good agreements. Next, a model for the foam was adopted and implemented in an in-house FE code. The implemented isotropic foam model was then used to simulate the behavior of foam-filled tubes under both static and dynamic loadings. Good agreement was observed between the results from the model with those obtained by analytical relations and experimental test data. The validated FE model was then used to conduct a series of parametric studies on foam-filled tapered tubes under static and dynamic loadings. The parametric studies were carried out to determine the effect of different parameters such as the number of oblique sides, foam density and boundary conditions on crushing behavior of rectangular tubes. The characteristic included deformed shapes, load–displacement, fold length and specific energy absorptions.     

Experimental analysis and numerical simulation of sintered micro-fluidic devices using powder hot embossing process

For the past 2 years, interest in manufacturing technologies based on micro-fluidic systems has been continuously increasing. Today, micro-fluidic systems are used in numerous biomedical and pharmaceutical applications. Micro-fluidics cannot be thought about separately without advances in micro- and nano-fabrication. Investigations based on experiments, finite element modelling and simulations of powder hot embossing process (PHE) were performed to optimise the sintering step and processing parameters of micro-fluidic components. The model pertaining to thermo-elasto-viscoplastic behaviour was identified for 316L stainless steel powders. In this regard, different material properties such as sintering stress, bulk, and shearing viscosities were identified by inverse analysis from present dilatometer measurements using beam-bending and free sintering tests. The identification of materials was performed for various powder volume loadings and kinetic rates for different 316L elaborated feedstock, and the parameters were obtained as functions of relative density. The initial inhomogeneity due to the PHE process has been taken into account in the sintering simulation, as it affects the final shrinkage of the sintered components. The solid-state sintering simulations were investigated for various final sintering temperatures and kinetic rates to obtain high and homogeneous relative density distributions, achieve isotropic shrinkage and optimise the sintering process parameters. The numerical simulations were realised based on the identified parameters on a 3D micro-structured specimen with an associated rectangular plate support elaborated by PHE; this allowed a comparison between the numerical predictions and the experimental results for the sintering stage. The finite element simulation results of the sintering stage with a micro-fluidic structured component at a high final temperature (1360 °C) are in excellent agreement with the results of the experiments. The comparison of the simulation and experimental results validated the identified and implemented physical model and proposed methodologies.     

The boundary element method in elasticity

This paper describes the application of the boundary element method in elasticity starting by discussing the basic weighted residual expressions. Boundary elements of different orders are presented and discussed, together with the numerical integration schemes. The relationships are presented for three dimensional elasticity and specialized to the two dimensional case. Results are presented and discussed, specially in relation to finite elements and other “domain” type techniques.     

Calculation of design sensitivity for large-size transient dynamic problems using Krylov subspace-based model order reduction

Nowadays, transient dynamic responses of a large-size finite element (FE) model can be solved within a reasonable computation time owing to rapid improvement in both numerical schemes and computing resources. However, increasing demands for accurate simulation and complicated modeling have led to larger and more complex finite element models, which consequently result in considerably high computational cost. In addition, when structural optimizations include transient responses such as displacement, velocity, and acceleration, the optimizations often do not end within a reasonable process time because the large-size simulation must be repeated many times. In order to reduce the computational cost in this respect, model order reduction (MOR) for the original full-order model (FOM) can be used for the transient response simulation. In this paper, a transient dynamic response analysis using Krylov subspace-based MOR and its design sensitivity analysis with respect to sizing design variables is suggested as an approach to the handling of large-size finite element models. Large-size finite element models can incur the problem of a long computation time in gradient-based optimization iterations because of the need for repeated simulation of transient responses. In the suggested method, the reduced order models (ROMs) generated from the original FOMs using implicit moment-matching via the Arnoldi process are used to calculate the transient response and its design sensitivity. As a result, the speed of numerical computation for the transient response and its design sensitivity is maximized. Newmark’s time integration method is employed to calculate transient responses and their design sensitivities. In the case of the transient sensitivity analysis, we apply a temporal discretization scheme to the design sensitivity equation derived by directly differentiating the governing equation with respect to design variables. This methodology has been programmed on the MATLAB with the FE information extracted from the FE package ANSYS. Two application examples are provided to demonstrate the numerical accuracy and efficiency of the suggested approach. The relative errors of transient response and design sensitivity between the FOMs and ROMs are also compared according to the orders of the reduced model. Calculation of transient dynamic responses and their sensitivities using Krylov subspacebased MOR shows a sizeable reduction in computation time and a good agreement with those provided by the FOM.     

有限元逆算法与板料成形工艺的评价

依据理想形变理论，研究开发了冲压成形过程模拟的有限元逆算法，根据变形体的整体塑性功取相对极值的条件，导出了塑算法有限元方程。提出了求逆算法初始解以及求解与给定形状的毛坯相对应的冲压件形状的迭代计算方法。采用有限元塑算法预测了与冲压件形状相对应的冲压件毛坯的展开形状，根据给定的板坯形状计算了冲压件最终构形及应变分布。分析计算实例表明，逆算法可用于对板料成形工艺方案进行快速评价，对冲压工艺参数进行优化。     

Buckling phenomena related to rolling and levelling of sheet metal

The paper deals with analytical and numerical considerations of buckling phenomena in thin plates or strips under in-plane loads which typically appear during rolling and levelling, i.e. straightening by stretching, of sheet metal. Buckling due to self-equilibrating residual stresses, caused by the rolling process, in eventual conjunction with global tensile stresses (denoted as “rolling buckling”) as well as buckling during the levelling process (denoted as “stretching buckling” or “towel buckling”) are considered. Analytical estimates are derived and compared against results of numerical simulations and field observations. Mode jumping by varying the global strip tension is explained on the basis of the derived analytical solutions. It is shown how from the waves, i.e. height and length, observed on the strip sliding over or lying on a rigid plane one can provide information about the distribution of the differences in the plastic strains over the width of the strip which lead to the buckled configuration. And, vice versa, knowledge of the plastic strain distribution can be used for estimating the expected wave heights representing a measure for the geometrical quality of the rolled product. The influence of the dead weight of the strip on the post-buckling pattern is also discussed on the basis of non-linear analyses.     

Surface geometry of slide bearings after percussive burnishing

A review of literature about the effect of oil pockets on improvement of sliding elements tribological performance as well as about the changes of surface topography during “zero-wear” process is shown. The paper presents also the results of experimental investigations done in the Department of Manufacturing Processes and Production Organisation of Rzeszow University of Technology, connected with the creation of oil pockets on sliding surfaces. In order to simulate a deterministic surface a program for the visualisation of pits was written. The procedures for assessment of the oil pocket size of specific shape and oil pockets coverage are presented. The tendencies of changes of surface topography and oil pockets dimensions during “zero-wear” process are also described.     

Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure

The dynamic plastic collapse of energy-absorbing structures is more difficult to understand than the corresponding quasi-static collapse, on account of two effects which may be described as the “strain-rate factor” and the “inertia factor” respectively. The first of these is a material property whereby the yield stress is raised, while the second can affect the collapse mode, etc. It has recently been discovered [6,7]that structures whose load-deflection curve falls sharply after an initial “peak” are much more “velocity sensitive” than structures whose load-deflection curve is “flat-topped” (Fig. 1a); that is, when a given amount of energy is delivered by a moving mass, the final deflection depends more strongly on the impact velocity. In this paper we investigate strain-rate and inertia effects in these two types of structure by means of some simple experiments performed in a “drop hammer” testing machine, together with some simple analysis which enables us to give a satisfactory account of the experimental observations. The work is motivated partly by difficulties which occur in small-scale model testing of energy-absorbing structures, on account of the fact that the “strain-rate” and “inertia” factors not only scale differently in general, but also affect the two distinct types of structure differently.     

The stability of plastic deformation in tension

Different concepts of the term “stability” are discussed and the resulting stability conditions in tension are derived. Particular importance is given to the relation between stability and the type of heterogeneities that may occur in tensile specimens. It is shown that a general instantaneous criterion of stability, in terms of the deformation properties of the material, cannot be formulated. However, if finite deformations are considered it is possible to derive general necessary criteria, which depend, of course, on the definition of stability adopted.The results obtained can explain the experimental observations concerning the phenomenon of necking in tensile tests, particularly its “weak” relation to the point of maximum load.     

On the dimensional accuracy of deep drawing products by hydroforming processes

In the hydroforming process the punch deforms the blank to its final shape by moving against a controllable fluid-pressure in a pre-determined path. The present work exhibits the fact that the final geometry of the product (mainly the wall thickness variations) depends on the overall history by which the fluid pressure-path is operated during the drawing process. In addition, other phenomena akin to hydroforming processes have been observed, e.g. the shift in the location of the rupture site (if it occurs) from near the bottom of the product to near its lip and the (slight) variation in the final length of the product. In order to explain these occurrences a detailed numerical stress analysis is offered, featured by an ad-hoc “finite difference” scheme. It differs from previous solutions by admitting changes in the thickness of the blank and still accounting for the blank/tool interfacial friction and the out-of-plane curvature of the product. The material behavior of the blank includes exponential strain hardening, normal anisotropy and initial strain. The experiments shown here were carried out on aluminum sheets with a specially built hydroforming machine.     

Understanding simultaneous double-disk grinding: operation principle and material removal kinematics in silicon wafer planarization

Simultaneous double-disk grinding (DDG) is a novel and powerful technology for precision-machining mono-crystalline silicon slices (“wafers”). With DDG the extreme degrees of planarity can be achieved, which the fabrication of micro-electronic devices with minimum lateral feature dimensions of 90 nm and below demands. In DDG, both sides of the wafer are ground simultaneously between two opposite grinding wheels on collinear spindle axes. It is a chuck-less process, in which the workpiece is machined in “free-floating” fashion. Machining kinematics, removal mechanism, and resulting wafer shape differ from those known from (chuck-mounted) single-side grinding or double-sided batch lapping, which are conventionally used in mechanical wafer shaping. This article explains the kinematics of DDG and derives the basic, method-inherent features always observed on DDG-ground wafers from simple kinematic considerations without further model assumptions: global wafer shape, center dip (“navel”), edge thickness roll-off, and symmetries. The expected results are compared with experimental data.     

Modelling one-dimensional unsteady flows in ducts: Symmetric finite difference schemes versus galerkin discontinuous finite element methods

The Euler equations for one-dimensional unsteady flows in ducts have been solved resorting to classical symmetric shock-capturing methods with second-order accuracy and to the recent discontinuous Galerkin finite-element method, with second- and third-order accuracy. In particular, the finite difference techniques adopted are the two-step Lax—Wendroff method and the MacCormack predictor—corrector method, with the addition of the flux corrected transport (FCT) or of the Davis nonupwind TVD scheme to suppress the spurious oscillations in the vicinity of discontinuous solutions. The finite-element method adopted is based on the weak formulation of the Euler equations, which are solved by introducing a discontinuous finite-element space discretization. A dissipative mechanism has been considered to supplement the FEM with a “discontinuity capturing” operator, adding a “viscous like” term to damp minor numerical overshoots arising in proximity of steep gradients of the solution. The numerical tests chosen to carry out a comparison between these schemes are the shock-tube problem and the shock—turbulence interaction problem. Both the test cases considered show the superiority of third-order FEM calculations, whereas the comparison between the computer run times points out the greater computational effort required.     

Finite element analysis of ball burnishing process: comparisons between numerical results and experiments

Ball burnishing is a surface enhancement process where a residual compressive stress is created in the surface layers of the workpiece. Several studies have been conducted on this process, but they are more concerned with the experimental aspect. So, there is still a real need for reliable numerical models that enable us to understand the mechanical behaviour of the workpiece during the process. These models also serve to optimise the studied process. Two-dimensional and three-dimensional finite element (FE) ball burnishing modelling is presented in this paper, where an elastic–plastic material model is assumed in the framework of the FE analysis. The pertinence of these models to predict residual stresses created by the process is discussed by drawing comparisons between simulation results and experimental data. The obtained results show that the three-dimensional FE model predicts the residual stresses and provides useful information on the effect of the process parameters.     

Experimental study and finite element analysis of simple X- and T-branch tube hydroforming processes

The tube hydroforming process is a relatively complex manufacturing process; the performance of this process depends on various factors and requires proper combination of part design, material selection and boundary conditions. Due to the complex nature of the process, the best method to study the behaviour of the process is by using numerical techniques and advanced explicit finite element (FE) codes. In this work, X- and T-branch components were formed using a tube hydroforming machine and experimental load paths (forming pressure and axial feed) were obtained for the processes via a data acquisition system integrated with the machine. Subsequently, the processes were simulated using LS-DYNA3D explicit FE code using the same experimental boundary, loading conditions and the simulation results were compared with the experimental results. It was found that the developed branch height and the wall thickness distribution along different planes were in good agreement with the experimental results.     

Polynomial solutions for thin plates

A least-squares approach is used to obtain polynomial solutions for the deflected shape of thin plates in flexure. The method corresponds to the finite element method with an energy basis, except that a single “macro” element is used. Satisfactory results are obtained for both triangular and rectangular plates and the method is clearly widely applicable.     

Investigations of friction stir welding process using finite element method

The aim of this study is to investigate the process of friction stir welding (FSW) by using finite element method (FEM). Currently, the materials that are difficult to be joined with conventional fusion methods can now be easily joined with the method of friction stir welding. In this paper, the welding capability of many different materials with this method has been investigated by using analytical and numeric methods. In this study, a finite element (FE) model was developed for welding process with friction stir welding of AZ31 magnesium alloy. This model was performed by the software of DEFORM 3D finite element in 960, 1,964, and 2,880 rpm rotational speeds and in 10 and 20 mm?min^?1 transverse speeds. The temperature values taken from experiments and the temperature values with FEM are compared, and according to these results, it can be stated that the FE model gives reasonable results with experimental results based on temperatures values. Hence, the FE model can be used to predict other parameters of FSW process in future studies.     

An upper bound analysis for the reshaping of thick tubes with experimental verification

Reshaping process based on the cold roll forming technology is a process in which noncircular pipes can be produced from circular pipes. A generalized upper bound solution for the deformation of thick tubes between four flat rolls has been formulated. The deforming zone has been divided into two areas namely the “contact region” and the “free region”. Owing to the different physical character of these deforming zones two different kinds of admissible velocity fields have been obtained for each of the deforming zones. To formulate the stream lines and stream surfaces in the deforming zones use has been made of the Bezier curves which have been utilized to define stream lines in such a way that could be manipulated easily to obtain the optimum shape for the upper bound solution to be optimized. This new formulation was used to predict the upper bound on power. Using the theory presented here, the influence of process parameters such as radius of rolls, initial pipe dimensions; amount of roll gap reduction and the roll speed on the final rolled product were investigated. In order to verify the theoretical results, an experimental rolling rig was designed and built which comprised of four flat rolls. Using this rig Al 6101 round pipes were rolled and the variations in the above-mentioned parameters were investigated. Quantities such as energy, wall thickness, and corner radius of the tube were observed and measured. Comparison of theoretical and experimental results showed good agreement and hence demonstrated the capabilities of the new formulation presented here.