Bursting failure prediction in tube hydroforming processes by using rigid–plastic FEM combined with ductile fracture criterion

The most common failure in tube hydroforming is the bursting failure due to excessive thinning of large deformation. To evaluate the forming limit of hydroforming processes, the Oyane's ductile fracture integral I was introduced and calculated from the histories of stress and strain according to every element by using the rigid–plastic finite element method. The region of fracture initiation and the forming limit for three hydroforming processes, such as a tee extrusion, an automobile rear axle housing, and a lower arm under different forming conditions are predicted in this study. Also it is shown that the material parameters used in the ductile failure can be obtained from the experimental forming limit diagram. From the results, the prediction of the bursting failure and the plastic deformation for the three hydroforming examples demonstrates to be reasonable so that this approach can be extended to a wide range of practical tube hydroforming processes.     

Tensile plastic instability and ductile fracture criteria in uniaxial compression tests

Experimental measurements of the free surface strain increment components on high-carbon steel compression specimens were used to estimate the point at which tensile plastic instability occurred at the equatorial free surface. A number of compression tests, with various combinations of specimen geometry and platen friction conditions, were carried out to the point of macroscopic fracture on the barrelled surface, thus giving a wide variation in the history of the stress components and the strain increments at the equator. In these tests the equatorial strain to instability varied widely but the strain from instability to fracture varied only slightly. Metallographic examination of the equatorial free surface showed that there was no evidence of fracture damage in specimens prior to instability, but specimens compressed just beyond the point of instability showed abundant evidence of microscopic fracture damage. It was concluded that the start of tensile plastic instability marks the point where internal microscopic cavities begin the process of growth and coalescence by internal necking. A criterion for ductile fracture in metal-working operations is proposed which is based on an estimate of the point where tensile plastic instability begins.A number of suggested criteria for ductile fracture were examined and found to be unsatisfactory when applied to the present results. There was no evidence of local necking on the free surface of the compression specimens after instability had occurred.     

A new mechanism of plastic flow

When ductile materials are tested in simple shear, with moderate amounts of compressive stress on the shear plane, what appears to be negative strain hardening occurs at relatively large strains. These results are in apparent contradiction to the commonly held views that metals strain harden without saturation to the highest values of strain and that compressive stress on the shear plane does not influence flow stress.A new mechanism of plastic flow is presented that involves the formation and rewelding or microcracks of limited extent on shear surfaces. Possible applications of the new theory to metal cutting and geological events are briefly discussed.     

Dynamics of glass-reinforced plastic and combined rod columns

A model and program have been developed which make it possible to perform the dynamic calculations of rod columns assembled from steel and glass-reinforced plastic rods and located in curved wells under an arbitrary cycled movement of a polished stick. A practical problem is solved from stimulated vibrations of the deep pumping facility rod column with the glass-reinforced plastic rods; an analysis is made of the influence of the loading mode on its dynamic performance. The area of the polished stick strokes is detected for which the efficient performance of the pumping facility is possible.     

Finite-element calculation of plastic flow at various temperatures and speeds

A method is proposed for calculating plastic strain from plastic-flow theory at different deformation speeds and temperatures, on the basis of the finite-element method.     

On the plane-stress essential fracture work in plastic failure of ductile materials

In plane-stress ductile fracture, the irreversible work dissipated inside the fracture process zone (FPZ) is a material constant for a given sheet thickness and is called the specific essential fracture work (w_e). However, work dissipated elsewhere in the outer plastic zone is nonessential and is dependent on specimen geometry and size. In this paper, a theoretical basis for the essential fracture work is given and a simple but elegant experimental method is presented to separate the essential work from the total fracture work. In-plane mode I (opening) and mixed mode I/II (opening/sliding) as well as out-of-plane tearing mode III fractures are analysed. Experiments are conducted on a range of ductile engineering materials including metals, polymers and papers to illustrate the working principles of the theory.     

Effect of lubricant fluid on plastic metal flow in sliding contact

Plastic metal flow in surface layers, especially “abnormal metal flow”, in which the direction of metal flow in the inner surface layer is different from that in the layer nearer the surface, in sliding contacts between a pin of cemented carbide and a ring of steel under lubrication is discussed in this paper. Low viscosity mineral oil is used as a base oil. Sulphide and chloride extreme pressure additives are also mixed with the base oil. Such a lubricant has a great influence on the plastic metal flow of a ring.While base oil produces severe plastic metal flow, the sulphide additive causes the plastic metal flow to be very mild. In contrast, a lubricant containing a chloride additive causes abnormal metal flow, where cracks can be seen. Conditions for and causes of abnormal metal flow are investigated.     

Force, torque and plastic flow analysis in rotary upsetting of ring shaped billets

The orbital upsetting of rings has been analysed for a Mises material by using an upper bound approach. Forging forces, rocking die torques and ring profiles are calculated at each step of the process. Experiments are described in which rings made of 1045 mild steel, 52100 chromium alloyed steel and 316 stainless steel are upset at room temperature on a 1.6 MN rotary press. The main parameters are: orbital oscillation angle, 2°, upper die oscillations, 200 min⁻¹ and lower die speed, 4.10 mm s⁻¹. An experimental rocking die placed on a conventional testing machine has been used for the rotary upsetting of rings made of Plasticine as model material. The simulation parameters are: oscillation, 2°, upper die oscillations, 40 min⁻¹, speed, 98.4 mm min⁻¹. The theoretical values of forging forces, rocking torques, and ring profiles are in keeping with the experiments. So the proposed upper bound approach may be considered as a good model for rotary upsetting.     

Post-critical deformation pattern in plane strain plastic flow with yield-surface vertex effect

This work is concerned with the formation of multiple macroscopic shear bands viewed as a mechanism of large plastic deformation of polycrystalline metals. The plastic deformation pattern in a time-independent material with a yield-surface vertex effect is investigated numerically in plane strain beyond the critical instant of ellipticity loss under quasi-static loading. The energy criterion of path instability applied to a family of post-critical solutions eliminates unstable paths and enables the overall deformation pattern to be determined, although the solutions remain locally indeterminate due to the absence of an internal length scale. In particular, the volume fraction of incipient shear bands is found to have a well-defined value irrespective of the mesh size in finite element calculations. As an apparently novel qualitative result, the formation of coarse, differently aligned secondary bands is observed at later stages of simulation.     

Study of fracture of specimens made of fiberglass plastic using acoustic-emission and strain measurements

The crack resistance of specimens made of a fiberglass plastic composite material has been studied. All specimens had approximately the same geometric dimensions. At the center of the specimens, there were 25-mm-long notches on both sides. The specimens were loaded with a static or cyclic load at a frequency f = 5 Hz. The tests were performed using acoustic-emission (AE) and strain gage measurements. The AE technique allowed stable localization of a flaw at an early stage of growth and made it possible to automate the measurement process. The strain gage measuring system was used to find deformations in the zones of localization of AE signals.     

Scaling laws for wall shear stress through stenoses under steady and pulsatile flow conditions.

Most patients with atherosclerosis exhibit isolated stenoses of one or more epicardial coronary arteries. The wall shear stresses produced in high-grade stenosis are important in the understanding of atheromatous plaque rupture and thrombosis. This study is designed to establish a method which can be used to scale the different wall shear stresses obtained under different flow conditions to be normalized and subsequently collapsed on to a single general curve. The simulations include both steady and pulsatile flow. The reduced area percentages of the stenoses studied are 50, 75 and 90 per cent. Scaling laws for steady and pulsatile flow conditions are proposed and presented. It can be found from the results that the scaling analysis for pulsatile flow conditions is more complicated than for steady flow conditions and is restricted to, and only valid at, certain time intervals.     

Effect of surface contour on the role of plastic flow in metal friction

Unlubricated friction between steel and three soft metals, aluminum, silver and copper, was studied under conditions designed to observe effects of macroscopic surface contour upon localized contacts between microscopic surface asperities. The contours of the specimens were interchanged between plane for the steel with cylinder for the softer metal, and the reverse, other variables being the same. Results show two different friction regimes. When the softer metal was cylindrical, friction coefficients were lower and static friction was less than kinetic by factors ranging from two to four. Wear was also less. These results are interpreted on the hypothesis that deformation of microscopic surface contacts at small loads is principally elastic with this configuration, but is plastic when the harder surface is cylindrical and the softer is plane.     

Spatial and temporal variation of turbulence characteristics in combined sewer flow

Flow unsteadiness is a typical feature of both combined and storm sewer flow. The following study therefore deals with both theoretical and experimental investigations of the steady uniform and transient turbulent open-channel flows in a circular conduit with smooth walls as well as over rough sediment deposits. The aim of the study is to define the relationship between flow unsteadiness and selected flow/turbulence characteristics estimated in a circular tube running partially full using the ultrasonic velocity profiler (UVP) method. The temporal/spatial turbulence intensities and the Reynolds stress distribution were identified in the mid-vertical of the pipe. Generally, the absolute values of turbulent characteristics are larger in the rising branch of the hydrograph than in the descending one for the same flow depths. This difference in absolute values is related to the flow equilibrium parameter. Furthermore, the influence of the sediment bed on selected flow/turbulence variables was studied. The results show a strong impact of cross-section geometry on local values of friction velocity, i.e. bottom shear stress, along the wetted perimeter of the channel cross-section. Interestingly, their relative values decreased along with an increase in flow depth.     

Bulk plastic flow and the frictional properties of titanium carbide at high temperature

In this study it has been shown that dislocations are mobile in titanium carbide crystals at 20°C and that, although bulk stresses are relieved by cleavage, the asperities are likely to be deformed in a plastic manner during sliding. Consequently, when the temperature is increased—thus allowing extensive bulk plastic flow and reducing the hardness by a factor of five—the magnitude of the coefficient of friction is not significantly influenced. An epitaxial titanium oxide film is formed on the surface of titanium carbide at temperatures above 1200°C and in a vacuum of 10⁻⁴ mm Hg. This effectively lubricates the surfaces and prevents the increase in friction usually observed with other transition metal compounds above 0.48 Tm. The magnitude of friction above this temperature for tungsten carbide specimens, where a surface film is not formed, is dependent on both the temperature and time of contact. It is suggested that this is due to growth and strengthening of the contact area by volume diffusion.     

Micromechanical simulations of biaxial yield, hardening and plastic flow in short glass fiber reinforced polyamide

Mean-field homogenization (MFH) is used to predict the biaxial yield behavior, hardening and plastic flow of composite materials made of an elasto-plastic matrix reinforced with misaligned short fibers. The procedure is applied to short glass fiber reinforced polyamide, which represents an important industrial application of those composites. First, MFH is verified against full-field accurate finite element simulations of representative volume elements with multiple fibers. Next, a parametric study is carried out with MFH in order to predict the biaxial plastic behavior of numerous microstructures corresponding to various values of volume fraction, aspect ratio and second-rank orientation tensor components of the glass fibers. Results demonstrate the loss of both isotropic hardening and plastic flow normality, except for 2D random orientation. For illustration, a fit of Hill's orthotropic plasticity criterion is conducted for several orientation tensors.     

Effect of strength mismatch on fully plastic fields in dissimilar joints under combined loading

Via detailed finite clement limit analyses, plastic limit loads, rotation factors, and crack-tip stress field are investigated for a combined tension and bending of a plance strain single-edge-cracked bimaterial specimen. Limiting bimaterial specimens are considered, consisting of an clastic/perfectly plastic material bonded to an elastic material having the same elastic properties. The limit loads of bimaterial specimens are shown to be very close to those of homogeneous specimens, so that limit load information for homogeneous specimens can be used even for bimaterial specimens. A tractable, approximate elliptical yield locus is proposed, which first the FE. results within 1% for all ranges of tension-to-bending ratios. The plastic rotation factor of bimaterial specimens can be higher than that of homogeneous specimens as much as 25%, when the specimen is subject to small tensile forces. Results from the present analysis is applied to the analysis of typical fracture testing specimens such as compact tension specimens. For both homogeneous and bimaterial specimens, larger tensile forces are associated with substantial loss of crack-tip constrait. Bimaterial specimens have as much as 2 times higher constraint than homogenous specimens, due to plastic strength mismatch. Tractable closed form approximations for crack-tip stresses are proposed in terms of tension-to-bending ratio.     

Statistical evaluation of forming limit in hydroforming process using plastic instability combined with FORM

Deviation of raw material parameters, such as work hardening, anisotropy, yield stress, etc., leads to an uncertainty to the position of the forming limit curve (FLC). This paper presents a novel approach to statistically evaluate the forming limit in hydroforming processes when taking into account the variations in the material parameters. First, plastic instability based on the Hill’s quadratic plastic potential is employed to construct the deterministic FLC. Then, with using the assumption that all material parameters are normally distributed random variables, stochastic modeling of the FLC with a confidence level is carried out, and statistical evaluation of the FLC is performed. In this work, a first-order reliability method is adopted for the reliability assessment of the FLC, and this is verified with the Monte-Carlo simulation method.     

Further investigation into extrusion of trocoidal gear sections considering three-dimensional plastic flow

In the present study, theoretical development proposed in previous work carried out in extrusion of clover sections in relation to a generalized die design method is presented in the extended scope for three-dimensional extrusion of trocoidal gear sections from round billets with experimental verification. Computations are carried out for clover and trocoidal gear sections. The CAD/CAM of the suggested dies is introduced for the experiments. Experiments are carried out for a clover section and a trocoidal gear section with eight teeth. Al 2024 aluminum billets were used as the working material. Half-cut specimens are used for flow visualization of the extrusion process. The theoretical predictions are in good agreement with the experimental results in extrusion load and metal flow.     

Kinematic shakedown analysis under a general yield condition with non-associated plastic flow

A nonlinear, purely kinematic approach with the finite element implementation is developed to perform shakedown analysis for materials obeying a general yield condition with non-associated plastic flow. The adopted material model can be used for both isotropic materials (e.g. von Mises's, Mohr-Coulomb and Drucker-Prager criteria) and anisotropic materials (e.g. Hill's and Tsai-Wu criteria) with both associated and non-associated plastic flow. Nonlinear yield criterion is directly introduced into the kinematic shakedown theorem without linearization and instead a nonlinear, purely kinematic formulation is obtained. By means of mathematical programming techniques, the finite element model of shakedown analysis is formulated as a nonlinear programming problem subject to only a small number of equality constraints. The objective function corresponds to plastic dissipation power which is to be minimized and an upper bound to the shakedown load of a structure can then be obtained by solving the minimum optimization problem. A direct, iterative algorithm is proposed to solve the resulting nonlinear programming problem, where a penalty factor based on the calculation of the plastic dissipation power is used to overcome the numerical difficulty caused by the non-differentiability of the objective function in elastic areas. The calculation is entirely based on a purely kinematical velocity field without calculation of stresses. Meanwhile, only a small number of equality constraints are introduced into the nonlinear programming problem. So the computational effort is very modest. Numerical applications prove that the developed algorithm has a very good numerical stability and computational efficiency. The proposed approach can capture different plastic behaviours of materials and therefore has a very wide applicability.     

Modeling and simulation of polymer melts flow in the extrusion process of plastic profile with metal insert

The extrusion technology of plastic profile with metal insert is recently an advanced plastic processing method whose products keeps rising today for their excellent performance. However, the related fundamental research on polymer forming mechanism in the extrusion process of plastic profile with metal insert is lagging behind. With the development of computational fluid dynamics (CFD) theory, numerical method becomes an effective way to investigate such complex material forming problems as in the polymer extrusion process. In the present study, the mathematical model for three-dimensional non-isothermal viscous flow of the polymer melts obeying a Carreau model is developed based on the CFD theory. The Williams–Landel–Ferry equation is employed to involve the temperature dependence of material parameters. A decoupled numerical algorithm based on the penalty finite element method is conducted to predict the rheological behaviors of polymer melts within the complex flow channel. The streamline upwind/Petrov–Galerkin scheme is employed to improve the computational stability for the calculation of temperature field. Based on the theoretical model, the essential flow characteristics of polymer melts in the extrusion process of plastic profile with metal insert is investigated. The distributions of principal field variables like flow velocity, melt temperature, flow stress and pressure drop are predicted. The effects of die structure parameters including the intake angle and the distribution section length upon the melts flow patterns are further discussed. The variations of melt rheological properties versus different processing conditions like the volume flow rate and the metal insert moving velocity are also investigated. Some advice on practical processing operations of the extrusion process of plastic profile with metal insert is accordingly put forward based on the numerical results.