Theoretical extension of elastic-perfectly plastic deformation length in roll forming of a channel section

In this paper, the Young’s modulus and the yield strength of the strip are considered in order to modify the deformation length analysis proposed by Bhattacharyya et al. New analytical equations are developed assuming an elastic-perfectly plastic material behaviour and the deformation length analysed for the simple case of roll forming a U-channel; the analytical results are verified by comparison with experimental data found in the literature. The proposed elastic-plastic deformation length is shorter than Bhattacharyya’s which is rigid-perfectly plastic. It is observed that the influence of elastic properties on the deformation length is not as significant as the plastic properties; however, the authors believe that the elastic effects become more important under conditions where a major area of the strip is under elastic deformation such as when the flange length is long.

Review of approximate analyses of sheet forming processes

Approximate models are often used for the following purposes: in on-line control systems of metal forming processes where calculation speed is critical; to obtain quick, quantitative information on the magnitude of the main variables in the early stages of process design; to illustrate the role of the major variables in the process; as an initial check on numerical modelling; and as a basis for quick calculations on processes in teaching and training packages. The models often share many similarities; for example, an arbitrary geometric assumption of deformation giving a simplified strain distribution, simple material property descriptions - such as an elastic, perfectly plastic law - and mathematical short cuts such as a linear approximation of a polynomial expression. In many cases, the output differs significantly from experiment and performance or efficiency factors are developed by experience to tune the models. In recent years, analytical models have been widely used at Deakin University in the design of experiments and equipment and as a pre-cursor to more detailed numerical analyses. Examples that are reviewed in this paper include deformation of sandwich material having a weak, elastic core, load prediction in deep drawing, bending of strip (particularly of ageing steel where kinking may occur), process analysis of low-pressure hydroforming of tubing, analysis of the rejection rates in stamping, and the determination of constitutive models by an inverse method applied to bending tests.

Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour

In the empirical methods for reinforcement design of underground excavations, an even distribution of rock bolts is generally recommended. This work proves that this design is not necessarily optimal and shows how the state-of-the-art reinforcement design could be improved through topology optimisation techniques. The Bidirectional Evolutionary Structural Optimisation (BESO) method has been extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr-Coulomb model is utilised for both original rock and reinforced rock. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome.

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 uniaxial tensile stage with tracking capabilities for micro X-ray diffraction applications

First results are presented for a uniaxial tensile stage designed to operate on a scanning micro X-ray diffraction synchrotron beamline. The new tensile stage allows experiments at typical loading cycles used in standard engineering stress–strain tests. Several key features have been implemented to support in situ loading experiments at the intragranular length scale. The physical size and weight of the load cell were minimized to maintain the correct working distance for the X-ray focusing optics and to avoid overloading the high-resolution raster scan translation stages. A high-magnification optical microscope and image correlation code were implemented to enable automated online tracking capabilities during macroscopic elongation of the sample. Preliminary in situ tensile loading experiments conducted on beamline 12.3.2 at the Advanced Light Source using a polycrystalline commercial-purity Ti test piece showed that the elastic–plastic response of individual grains could be measured with submicrometre spatial resolution. The experiments highlight the unique instrumentation capabilities of the tensile stage for direct measurement of deviatoric strain and observation of dislocation patterning on an intragranular length scale as a function of applied load.

Numerical models of plastic zones and associated deformations for elliptical inclusions in remote elastic loading-unloading with different R-ratios

Plastic zones and associated deformations ahead of a fatigue crack are well established nowadays. In-depth plane strain elasto-plastic finite element analysis is conducted in this investigation to understand the nature of cyclic plastic deformation and damage around soft and hard elliptical inclusions. Similar to fatigue crack tip, cyclic/reverse plastic zone and monotonic plastic zone are visible for soft elliptical inclusion. In the cyclic plastic zone, low cycle fatigue is the dominant cyclic deformation mode during symmetric load cycling, while ratcheting is dominant during asymmetric load cycling. The size of cyclic plastic zone depends upon the amplitude of remote stress while, the size of monotonic plastic zone depends upon the maximum remote stress. The size of monotonic plastic zone is equal to cyclic plastic zone during symmetric load cycling. The shape and size of plastic zones also depend upon the orientation of the soft inclusion. Cyclic plastic damage progression in the cyclic plastic zone for soft (MnS) inclusion is significant, while no cyclic plastic zone is visible for hard inclusion (Al2O3).

Determination of plastic yield stress from spherical indentation slope curve

The indentation slope curve from a spherical indentation on elastic-plastic materials is examined. By comparing it with that of an linear elastic material of the same elastic properties, we found that the start point of plastic yielding for an elastic-plastic material can be easily located from the indentation slope curve. Based on this analysis, a simple but effective method is proposed to measure the plastic yield stress of very small samples from a spherical nano-indentation slope curve.

Evolution of elastic modulus in roll forming

Roll forming is a continuous process in which a flat strip is incrementally bent to a desired profile. This process is increasingly used in automotive industry to form High Strength Steel (HSS) and Advanced High Strength Steel (AHSS) for structural components. Because of the large variety of applications of roll forming in the industry, Finite Element Analysis (FEA) is increasingly employed for roll forming process design. Formability and springback are two major concerns in the roll forming AHSS materials. Previous studies have shown that the elastic modulus (Young’s modulus) of AHSS materials can change when the material undergoes plastic deformation and the main goal of this study is to investigate the effect of a change in elastic modulus during forming on springback in roll forming. FEA has been applied for the roll forming simulation of a V-section using material data determined by experimental loading-unloading tests performed on mild, XF400, and DP780 steel. The results show that the reduction of the elastic modulus with pre-strain significantly influences springback in the roll forming of high strength steel while its effect is less when a softer steel is formed.