A simple approach to plane strain extrusion with dead metal zone using upper-bound theorem

This paper treats the upper-bound approach to the problem of rigid-plastic deformation in case where the configuration of the deformation zone is previously unknown. The plane strain forward extrusion process with the so-called dead metal zone is analysed by assuming a simple velocity field. The calculations are carried out for the material with or without strain hardening or strain rate sensitivity and for various reduction ratios. The numerical results show that the region of the dead metal zone becomes smaller with the increase in the reduction ratio. The calculated punch forces agree with the experimental ones fairly well. Furthermore, it is found that the dead metal zone becomes larger with increasing the strain hardening as well as the strain rate sensitivity of the material.     

An upper-bound analysis of a plastic flow joining process

This paper investigates the mechanics of the deformation process associated with the formation of a permanent joint between a metal disc and a shaft when material from the disc is plastically deformed and forced to flow into a groove cut on the surface of the shaft. Cold forged disc/shaft joints were sectioned and etched to reveal the internal flow patterns within the deforming disc. In addition an elastoplastic finite element analysis was performed using a simplified model of the deformation regions to provide further evidence of the internal flow patterns. Both of these techniques indicated the presence of a flow divide centered around a neutral radius within the disc and these observations enabled the selection of suitable velocity fields for the deformation regions of the disc. These velocity fields were then used in the derivation of a series of upper-bound expressions to account for the energy dissipated in plastic deformation and in overcoming surface frictional resistance along the contact surfaces. The derived upper-bound expressions were used to estimated the change in the mean forging pressure ratio throughout the forming operation. The results obtained using the derived upper-bound expressions compared very closely to those determined experimentally.     

A new upper-bound elemental technique approach to axisymmetric metal forming processes

A new upper-bound elemental technique (UBET) is proposed to improve the ineffectiveness of UBET for solving forging problems that are geometrically complex or need a forming simulation for predicting the profile of free boundary. This method combines the advantages of the stream function and the finite element method (FEM); specifically, the curve fitting property of FEM and the fluid incompressibility of the stream function. The formulated optimal design problems with constrained conditions are solved by the flexible tolerance method. Three forming problems (ring upsetting, closed-die, and backward-extrusion forging) are used to illustrate this method: the results of ring upsetting show a good ability of simulating for predicting the forming profile of a free boundary; the closed-die forging produces a lower upper-bound solution than UBET; and backward-extrusion forging demonstrates the flexible curve fitting property for a complex geometric boundary.     

An axisymmetric forging approach to preform design in ring rolling using a rigid–viscoplastic finite element method

In this paper, a new method for approximately predicting the deformation of material in ring rolling is presented. The plastic flow of material in ring rolling is assumed to be axisymmetric and thus the ring rolling process is considered as a sequence of consecutive forging processes. The problem, having tool velocity as well as material velocity field as unknown variables, is formulated by an axisymmetric rigid–viscoplastic finite element method. The unknown tool velocity is determined by making the circumferential stress on the ring cross-section exist in the range of user-specified values. The approach is applied to preform shape design in ring rolling of bearing races. The predicted results are compared with the experimental ones. It has been shown that the approximate approach presented is useful for engineering design of preform in ring rolling of bearing race-like rings.     

An approach to triangular induction heating in final precision forming of thick steel plates

An automatic high-frequency (HF) induction-heating (IH)-based triangular heating process was introduced in order to investigate the influence of designing heating patterns on the permanent deformation behavior of an SS400 thick plate. Temperature distribution and permanent plate deformation during triangular heating were predicted based on electromagnetic–thermal and thermal–structural analyses, respectively. Both analytical and experimental permanent deformation values obtained by zigzag-type triangular heating were significantly higher than those by fan-shaped triangular heating, presumably because of the different temperature gradient along the thickness. Proper design of triangular heating pattern appeared to be the most important factor in determining the final shape of the thick plate. All predicted results were in good agreement with the experimentally observed permanent deformation.     

A slip-line approach to visioplasticity in plane-strain extrusion by the finite flow-line regions technique

A numerical approach is proposed to establish a new procedure for the visioplasticity method. In this procedure, the finite flow-line regions are first produced by the least square's method and then the velocity field and strain-rate field are obtained for each region. From the calculated strain-rate field, the constructed model of the slip-line can then be developed to draw the slip-line field. Along these slip lines, the stress fields are found easily from Hencky's equations. Plane-strain extrusion through a cosine-curved die with 2:1 extrusion ratio is use to illustrated this new procedure. The results of this approach show more reasonable solutions compared with the traditional method by the integral equation, in this method the error of the integral of the finite-difference flow being avoided.     

An upper-bound cutting model for oblique cutting tools with a nose radius

The geometry of practical cutting tools is complex, and usually involves both non straight cutting edges and obliquity. It is of great practical importance to be able to predict cutting forces and chip flow directions for such tools. The authors demonstrate the use of a simplified geometry together with an upper bound model to predict the direction of chip flow. The model proposed includes a requirement for approximate force equilibrium as a method of estimating rake face contact area. A comparison of the results with those from earlier models and with experimental data is provided. Finally a proof of the Stabler chip flow hypothesis is given: it is shown that the hypothesis is only valid for the case of zero rake face friction.     

An experimental/analytical approach to study formability using a punch test

This study was carried out to upgrade tedious methods of obtaining strain distribution in punch stretching to a computerized, noninterrupted and fast testing system using optical sensing of deformation in previously imposed grid lines. An analytical model to compute the strain distribution and to relate it to the die load was also developed. Experimental and analytical studies were used to predict failure of products by determining critical values of strains of aluminum alloy and mild steel.     

转炉倾动力矩计算中几个问题的探讨

探讨了转炉倾动力矩计算模型的细化；总结出简单实用的计算程序框图；对炉液体积与液面线高度之间的规律进行了研究，提出了迭代步长的选取方法。     

带背压等径角挤压挤压力上限解析

等径角挤压过程中施加背压,可以有效地改善材料微观组织和力学性能。运用上限理论推导出了带背压等径角挤压的挤压力解析式,结合实验进行验证,分析了背压作用的影响因素及背压效果,为等径角挤压的工艺优化、背压施加方式、模具设计及设备选择,提供了可行的方法。     

Numerical modeling of embedded solid waveguides using SAFE-PML approach using a commercially available finite element package

Guided waves are attractive for long range inspections from a single generation position. However when the waveguide is embedded in another medium, the energy of the guided waves may leak into the surrounding material, causing significant reduction of the inspection distance. A number of analytical or numerical models were developed to understand the behavior of guided waves in embedded waveguides, among which one of the attractive methods was to combine the Semi-Analytical Finite Element (SAFE) method with Perfectly Matched Layer (PML). This paper presents a development to implement the SAFE-PML model in a commercially available Finite Element package. As no source code is required, the presented method will be attractive to a wide range of researchers in Non-Destructive Evaluation (NDE). The model is first demonstrated and validated in two cases with analytical solutions. Discussions have been carried out regarding the procedure to select proper modeling parameters. The potential of the model is also illustrated on an important application of guided waves along embedded pipelines.     

An approach to modelling erosion-corrosion of alloys using erosion-corrosion maps

A model has been developed to establish the boundaries on erosion-corrosion maps, where increases in erosion and corrosion are represented by increases in velocity and temperature respectively. The maps show the transitions through the regimes as functions of the main erosion-corrosion variables. The effects of additional parameters such as alloy corrosion resistance and particle flux on the transition boundaries on the maps are simulated in the model. This paper outlines the preliminary work which has been carried out on the mathematical algorithms used to calculate the transition boundaries. The variations in the location of the boundaries with target and particles properties are illustrated. Future development of the maps is discussed in terms of extension of the erosion-corrosion algorithms, and applications to in-service erosion-corrosion problems.     

正交异性幂强化材料的平面应力应变分析

在平面应力状态条件下,对Hill塑性屈服条件进行了研究.导出了正交异性材料屈服的参数方程,在同时考虑幂强化材料与正交异性指数的情况下,得到了轴对称平面应力满足平衡方程,协调方程及应力应变关系的解析解.研究表明,硬化指数n和R=H/G对应力应变影响较显著.而R90=H/F存在时,对应力应变影响较弱.     

A simplified triangular shell element with a necking criterion for 3-D sheet-forming analysis

A 3-node triangular shell element with only 3 translational degrees of freedom per node is presented, in which the out-of-plane displacement is the only d.o.f. considered for bending. The bending stiffness matrix of the element is derived by assuming constant curvature normal to the boundary with adjacent elements. An explicit dynamic time integration scheme is implemented for sheet forming analysis. The authors have incorporated in the numerical analysis their necking criterion based on the intrinsic Forming-Limit Stress Diagram.     

Experimental simulation of recrystallized microstructure in friction stir welded Al alloy using a plane-strain compression test

The effective strain rate during friction stir welding (FSW) of Al alloy 1050 was estimated experimentally by simulating the recrystallized grains of the stir zone through a combination of the plane-strain compression at various strain rates and the subsequent cooling tracing the cooling cycle of FSW. With the plane-strain compression test, it was possible to simulate the recrystallized grain structure of the friction stir welds, and the effective strain rate was estimated to be about 2–3 s⁻¹.     

An inverse analysis using a finite element model for identification of rheological parameters

In order to reduce the discrepency between experimental and numerical development, a parameter automatic identification procedure from rheological test is formulated as an inverse problem. The direct model which permits to simulate the large strain behaviour during the rheological test is a Finite Element Code. The inverse problem is formulated as finding a set of rheological parameters starting from a known constitutive equation. The goal is to compute the parameter vector which minimizes an objective function representing, in the least square sense, the difference between experimental and numerical data. The high nonlinearity of the problem to be solved, requires the use of an accurate evaluation of the sensitivity matrix by analytical differentiation of governing equations with respect to the parameters. Thus the optimisation algorithm is strongly coupled with the finite element simulation. This method, namely a Computer Aided Rheology (CAR) methodology is possible in principle for all tests able to be simulated. This paper concerns the thermoviscoplastic deformation during torsion and tension tests.     

Finite element method approach to forging process design

Forging processes in the past have primarily been developed based on empirical relationships or trial and error. The finite element approach to forging process development and design has been found to be practically feasible and economical. The rigid-viscoplastic finite element method (FEM) code “ALPID” developed by Battelle Columbus Laboratories, has been successfully utilized to simulate metal forming processes. In the following paper, the application of finite element simulation to study deformation mechanics in the forging of gear blanks and axle shafts is discussed. An underfill problem on the gear blank was overcome and tool life was improved on the axle shaft hot heading process.     

一种基于改善拟应变法的壳单元模型

基于Hu-washizu变分原理,推导了四节点六自由度壳单元的更新拉格朗日(U.L.)动力显式有限元列式。采用11参数改善拟应变(EAS)法,避免了剪切自锁,提高了计算精度。通过对标准算例计算,验证了该壳单元动力显式有限元模型用于计算弹塑性大变形问题的有效性和精确性。     

An analytical approach to asymmetrical cold strip rolling using the slab method

An analytical model for general asymmetrical cold rolling is proposed to investigate the behavior of sheet during asymmetrical rolling using the slab analysis. Neutral points between the upper and lower rolls and the strip, rolling pressure distribution along the contact interface of the roll and strip, and rolling forces, as well as rolling torque, can be calculated easily using this model. Rolling pressure distribution, rolling force, and rolling torque, which are affected by various rolling conditions such as roll speed ratio, thick-ness reduction, front and back tension, etc., are analyzed. Additionally, the limiting rolling conditions be-tween reduction and roll speed ratio, or front and back tension, under which the rolling process can be accomplished successfully, are discussed. By comparing analytical results and experimental measure-ments of rolling force, it is apparent that the proposed model can successfully provide useful knowledge for designing the pass schedule of the asymmetrical cold strip rolling process.