Michael J. Worswick

Void growth and constitutive softening in a periodically voided solid

Abstract A three-dimensional finite element model of a periodically voided elastic-plastic solid is used to predict void growth and constitutive softening under tensile plastic deformation. The analysis considers an infinite block of material containing a three-dimensional periodic array of voids, subjected to a remote deformation or stress field. The predicted initial dilatational and extensional void growth rate, as a function of stress triaxiality and material work-hardening rate, agrees well with the analytical results of Budiansky et al . ( Mechanics of Solids, The Rodney Hill 60th Anniversary Volume , edited by H.G. H opkins and M.J. Sewell , p. 13, Pergamon Press, Oxford, 1982) for an isolated void in a viscous solid. Increased initial void volume fraction (⨍) has little effect on the dilatational growth rate, but strongly affects the extensional growth rate at high levels of triaxiality. The effect of void aspect ratio on void growth rate was seen during uniaxial tensile deformation, during which extensive void elongation caused a reduction in the final or asymptotic void growth rates. Constitutive softening is shown to be primarily a function of porosity and stress triaxiality.

The Effect of Tool–Sheet Interaction on Damage Evolution in Electromagnetic Forming of Aluminum Alloy Sheet

A study of the effect of tool-sheet interaction on damage evolution in electromagnetic forming is presented. Free form and conical die experiments were carried out on 1 mm AA5754 sheet. Safe strains beyond the conventional forming limit diagram (FLD) were observed in a narrow, region in the free form experiments, and over a significant region of the part in the conical die experiments. A parametric numerical study was undertaken, that showed that tool-sheet interaction had a significant effect on damage evolution. Metallographic analysis was carried out to quantify damage in the parts and to confirm the numerical results.

Introduction of an Electromagnetism Module in LS-DYNA for Coupled Mechanical-Thermal-Electromagnetic Simulations

A new electromagnetism module is being developed in LS-DYNA for coupled mechanical/thermal/electromagnetic simulations. One of the main applications of this module is Electromagnetic Metal Forming. The electromagnetic fields are solved using a Finite Element Method for the conductors coupled with a Boundary Element Method for the surrounding air/insulators. Both methods use elements based on discrete differential forms for improved accuracy. The physics, numerical methods and capabilities of this new module are presented in detail as well as its coupling with the mechanical and thermal solvers of LS-DYNA. This module is then illustrated on two Electromagnetic Metal Forming cases, the forming of an aluminum sheet on a conical die using a spiral coil, and the forming of an aluminum sheet on a v-shaped die using a “double pancake” coil. The experimental setups are presented as well as comparisons between experimental and numerical results.

Void coalescence within periodic clusters of particles

Abstract The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modelled using a unit cell approach. Three discrete particles are introduced into each unit cell while a secondary population of small particles within the surrounding matrix is represented using the Gurson–Tvergaard–Needleman (GTN) constitutive equations. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined. The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence failure strains. Coalescence of voids within a first-order particle cluster (consisting of three particles) is a stable event while collapse of inter-cluster ligaments leads to imminent material collapse through void-sheeting.

The numerical simulation of stretch flange forming

Abstract Simulations of stretch flange forming operations are undertaken using explicit dynamic finite element calculations utilizing various quadratic and non-quadratic yield criteria. Both circular and square cut-out blanks are investigated with corresponding circular and square punches. Simple stretch flanges are considered, utilizing a single punch to expand the cut-out, as well as z-flanges, which employ a back-up punch to form the second bend needed in the z-flange profile. Results from a model of an automotive inner component incorporating a cut-out with stretch flange corner features are also presented. Predictions utilizing the Barlat-89 criterion are shown to accurately capture the effect of yield anisotropy ( R -value). The predicted strains from the corner regions of square cut-out stretch flange laboratory specimens are shown to be similar to those within the automotive inner panel, supporting the use of laboratory-scale stretch flange experiments to simulate the larger panels. Measured limit strains from the stretch flange formability experiments are compared to forming limit diagram (FLD) data from dome specimens. Stretch flange formability is shown to exceed allowable levels predicted using a classical FLD approach, particularly for simple stretch flanges, indicating that the FLD approach is overly conservative.

Electromagnetic impact welding of Mg to Al sheets

Abstract Magnesium (Mg) and aluminium (Al) alloys have been lap welded using an electromagnetic impact welding technique. Metallographic examination of the welds has revealed sound and defect free interfaces. Complete metal continuity has been observed with a characteristic wavy interface. X-ray diffraction analysis has shown no intermetallic phases and suggested that this electromagnetic technique is a solid state welding process. All the shear strength samples welded with discharge energy of 6·7 kJ failed away from weld either in the plastically deformed zone or in the base metal. Optimum discharge energy has been determined as 6·7 kJ based on the shear strength results of the welds.

Rate sensitivity and tension-compression asymmetry in AZ31B magnesium alloy sheet.

The constitutive response of a commercial magnesium alloy rolled sheet (AZ31B-O) is studied based on room temperature tensile and compressive tests at strain rates ranging from 10−3 to 103 s−1. Because of its strong basal texture, this alloy exhibits a significant tension–compression asymmetry (strength differential) that is manifest further in terms of rather different strain rate sensitivity under tensile versus compressive loading. Under tensile loading, this alloy exhibits conventional positive strain rate sensitivity. Under compressive loading, the flow stress is initially rate insensitive until twinning is exhausted after which slip processes are activated, and conventional rate sensitivity is recovered. The material exhibits rather mild in-plane anisotropy in terms of strength, but strong transverse anisotropy (r-value), and a high degree of variation in the measured r-values along the different sheet orientations which is indicative of a higher degree of anisotropy than that observed based solely upon the variation in stresses. This rather complex behaviour is attributed to the strong basal texture, and the different deformation mechanisms being activated as the orientation and sign of applied loading are varied. A new constitutive equation is proposed to model the measured compressive behaviour that captures the rate sensitivity of the sigmoidal stress–strain response. The measured tensile stress–strain response is fit to the Zerilli–Armstrong hcp material model.

Influence of material properties on the ballistic performance of ceramics for personal body armour

In support of improved personal armour development, depth of penetration tests have been conducted on four different ceramic materials including alumina, modified alumina, silicon carbide and boron carbide. These experiments consisted of impacting ceramic tiles bonded to aluminum cylinders with 0.50 caliber armour piercing projectiles. The results are presented in terms of ballistic efficiency, and the validity of using ballistic efficiency as a measure of ceramic performance was examined. In addition, the correlation between ballistic performance and ceramic material properties, such as elastic modulus, hardness, spall strength and Hugoniot Elastic Limit, has been considered.

Modeling void nucleation and growth within periodic clusters of particles

Abstract The effect of particle clustering on void damage rates in a ductile material under triaxial loading conditions is examined using three-dimensional finite element analysis. An infinite material containing a regular distribution of clustered particles is modeled using a unit cell approach. Deformation strain states characteristic of sheet metal forming are considered; that is, deep drawing, plane strain and biaxial stretching. Uniaxial tensile stress states with varying levels of superimposed hydrostatic tension are also examined. The orientation of a particle cluster with respect to the direction of major principal loading is shown to significantly influence void damage rates.Early in the bulk deformation process, a particle cluster that is aligned with the direction of major principal strain experiences a more rapid accumulation of plastic strain, resulting in premature void nucleation. After void nucleation, however, the plastic strains within a cluster oriented transverse to the major principal strain quickly overcome those of the aligned case, leading to higher overall void damage rates.

Prediction of Necking in Tubular Hydroforming Using an Extended Stress-Based Forming Limit Curve

This paper presents an extended stress-based forming limit curve (XSFLC) that can be used to predict the onset of necking in sheet metal loaded under non-proportional load paths, as well as under three-dimensional stress states. The conventional strain-based eFLC is transformed into the stress-based FLC advanced by Stoughton (1999, Int. J. Mech. Sci., 42, pp. 1-27). This, in turn, is converted into the XSFLC, which is characterized by the two invariants, mean stress and equivalent stress. Assuming that the stress states at the onset of necking under plane stress loading are equivalent to those under three-dimensional loading, the XSFLC is used in conjunction with finite element computations to predict the onset of necking during tubular hydroforming. Hydroforming of straight and pre-bent tubes of EN-AW 5018 aluminum alloy and DP 600 steel are considered. Experiments carried out with these geometries and alloys are described and modeled using finite element computations. These computations, in conjunction with the XSFLC, allow quantitative predictions of necking pressures; and these predictions are found to agree to within 10% of the experimentally obtained necking pressures. The computations also provide a prediction of final failure location with remarkable accuracy. In some cases, the predictions using the XSFLC show some discrepancies when compared with the experimental results, and this paper addresses potential causes for these discrepancies. Potential improvements to the framework of the XSFLC are also discussed.