Stress-based predictions of formability and failure in incremental sheet forming

 This research investigates the deformation mechanism in incremental sheet forming (ISF) with relation to necking and failure. A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is strictly valid only when the strain path is linear throughout the deformation process. Where the strain path in ISF is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is used to model the necking and fracture limits. Simulation model is evaluated for a single point incremental forming using AA 6022-T4E32 and checked the accuracy against experiments.

Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.

Path independent limiting criteria in sheet metal forming

The Forming Limit Diagram (FLD) is a conventional failure diagram to estimate necking limits of sheet metal for proportional loading conditions. Previous studies reveal that the FLD is not suitable for predicting the influence of nonlinear strain paths. This paper presents methodical comparison among all common available strain path independent strain/stress based limiting criteria. All the strain path independent strain based limiting criteria (Traditional Failure Diagram (TFD), Extended Forming Limit Diagram (XFLD), Extended Stress Ratio Based Forming Limit Diagram (ESRFLD), and Polar Effective Plastic StrainDiagram (PEPSD)) and stress based limiting criteria (Traditional Stress based Failure Diagram (TFSD), Stress Based Forming Limit Diagram (FLSD), Stress Ratio and Stress Based Forming Limit Diagram (SRFLSD), Extended Stress Based Forming Limit Diagram (XFLSD), and Polar Effective Stress Diagram (PESSD)) are approximately path-independent for smaller amount of pre-straining and path dependent for large pre-straining conditions. From advance image correlation technique precisely determination of local strains near necked area is possible today. However direct determination of local stresses near necked area is not possible. Therefore, local stresses and equivalent stress are determined by employing both yield criterion and strain-hardening law. Similarly equivalent strain is calculated by the use of yield criterion. Therefore, the choice of yield criterion has an impact on the results for TFD, XFLD, ESRFLD and PEPSD. However, selections of both yield criterion and strain-hardening law have substantial influence on the results for TFSD, FLSD, SRFLSD, XFLSD and PESSD. The inherent calculation error can be minimized by generation of experimental data for each material and then selection of representable yield criterion and strain-hardening law. Improvement of experimental techniques and generation of rigorous material data bank in various strain paths may help researchers to diagnose and resolve the issue. TFD, TFSD and XFLSD have inherent variables to take care the effect of through thickness stress, however rigorous experimental verification is needed before the field application.

`I feel enlightened now, but...`: the limits to the pedagogic translation of critical social discourses in physical education

The emancipatory goal that underpins critical theories of teaching and learning is built on a theory of rational self-determination. In the context of physical education, critical educators believe that through a process of enlightenment teachers can recognize and transform elements of injustice and inequality that exist, albeit unwittingly, in their practice. However, despite the broad appeal of this orientation there are relatively few empirical accounts of how theories of enlightenment manifest themselves in the practice of emancipation. Propelled by the lacuna that clearly exists between critical theory and critical practice, this paper reports on the introduction of critical social discourses to a preservice PE program. It uses a case study methodology to report on two student-teachers' engagement with a range of critical social discourses during a year-long PE unit. The paper discusses some of the ways these students engaged with the theory and practice of a critical orientation for teaching and learning in physical education. Aspects of their experiences are then interpreted through Fay's (1987) critical but postmodern "limits to change" thesis. The paper concludes with tempered optimism about the potential for critical social discourses to guide preservice teachers in practical ways.

Limits to problem solving in science

Popper, Polanyi and Duncker represent the widely held position that theoretical and experimental scientific research are motivated by problems to which discoveries are solutions. According to the argument here, their views are unsupported and - in light of counter-instances, anomalous chance discoveries, and the force of curiosity - over-generalized.

Characterisation of a synthesised fluorescent ligand (4-acridinol-1-sulphonic acid) using nuclear magnetic resonance spectroscopy

The synthesis and complete characterisation of the fluorescent ligand, 4-acridinol-1-sulphonic acid (the acridine analogue of 8-quinolinol-5-sulfonic acid) is described. Using a judicious array of nuclear magnetic resonance spectroscopy experiments, the structural elucidation and full assignment of all proton and carbon chemical shifts were afforded. The 4-acridinol-1-sulphonic acid was found to behave in a similar manner to 8-quinolinol-5-sulphonic acid, forming fluorescent complexes with magnesium(II) and zinc(II). The uncorrected emission maxima for the metal–acridinol complexes were found to be at around 620 nm compared to 505 nm for the respective quinolinol complexes. Unfortunately, preliminary spectrofluorimetric analytical figures of merit revealed that the detection limits of the new acridinol metal complexes were one and a half orders of magnitude poorer than those attained with the corresponding quinolinol ligand. However, in contrast to 8-quinolinol-5-sulphonic acid, the 4-acridinol-1-sulphonic acid ligand showed considerable selectivity for magnesium(II) and zinc(II) over aluminium(III).

Effect of membrane stress on surface roughness changes in sheet forming

Friction plays an important role in sheet metal forming (SMF) and the roughness of the surface of the sheet is a major factor that influences friction. In finite element method (FEM) models of metal forming, the roughness has usually been assumed to be constant; even though it is commonly observed that sheet drawn under tension over a tool radius results in the surface becoming shiny, indicating a major change in surface morphology. An elastic–plastic FEM model for micro-contact between a flat surface and a single roughness peak has been developed. The model was used to investigate the effect of the membrane stress in the sheet on the deformation of an artificial roughness peak. From the simulation results, the change in asperity, or deformation of the local peak, for a given nominal tool contact stress is significantly influenced by the local substrate stress. The height of the asperity decreases with increasing substrate stress and the local pressure is much higher than the nominal pressure. In addition, the local contact stress decreases with an increase in the substrate stress levels.

A finite element simulation of micro-mechanical frictional behaviour in metal forming

Friction is a critical factor for sheet metal forming (SMF). The Coulomb friction model is usually used in most finite element (FE) simulation for SMF. However, friction is a function of the local contact deformation conditions, such as local pressure, roughness and relative velocity. Frictional behaviour between contact surfaces can be based on three cases: boundary, hydrodynamic and mixed lubrication. In our microscopic friction model based on the finite element method (FEM), the case of dry contact between sheet and tool has been considered. In the view of microscopic geometry, roughness depends upon amplitude and wavelength of surface asperities of sheet and tool. The mean pressure applied on the surface differs from the pressure over the actual contact area. The effect of roughness (microscopic geometric condition) and relative speed of contact surfaces on friction coefficient was examined in the FE model for the microscopic friction behaviour. The analysis was performed using an explicit FE formulation. In this study, it was found that the roughness of deformable sheet decreases during sliding and the coefficient of friction increases with increasing roughness of contact surfaces. Also, the coefficient of friction increases with the increase of relative velocity and adhesive friction coefficient between contact surfaces.

A shape error metric for sheet metal forming and its application to springback

There are many variations within sheet metal forming, some of which are manifest in the final geometry of the formed component. It is important that this geometric variation be quantified and measured for use in a process or quality control system. The contribution of this paper is to propose a novel way of measuring the geometric difference between the desired shape and an actual formed "U" channel. The metric is based upon measuring errors in terms of the significant manufacturing variations. The metric accords with the manually measured errors of the channel set. The shape error metric is then extended to develop a simple empirical, whole-component, springback error measure. The springback error measure combines into one value all the angle springback and side wall curl geometric errors for a single channel. Two trends were observed: combined springback decreases when the blank holder force is increased; and the combined springback marginally decreases when the die radii is increased.