The macroscopic residual stress distribution in γ-quenched and stress levelled U-0.8wt% Ti alloy tubes was studied using neutron diffraction techniques. Residual strains were evaluated from the difference in d-spacings measured in the tubes and in small reference samples machined from each tube. Residual stresses were calculated with the isotropic bulk values of the elastic constants for polycrystalline α-U. Quenching from the γ field resulted in a nearly equi-biaxial stress state at every point across the wall thickness of the tube. The magnitude of the radial stress was very small compared with that of the axial and hoop stresses which were compressive at the surfaces and tensile in the interior. Stress levelling relieved almost completely the hoop residual stress without affecting the radial stress. The axial residual stress becomes tensile through the wall thickness and remains constant at about 20% of its magnitude in the as-quenched condition.

The pressure ram forming (PRF™) process is simulated by implementing the mechanical threshold strength (MTS) model into ABAQUS finite element analysis software through a user material subroutine (UMAT). The predicted shape and thickness distribution of the PRF aluminium bottle and the force on the backing ram during forming are found to be in good agreement with measurements.

Finite element modelling of sheet-forming operations, such as pressure-ram-forming, (PRF™) requires knowledge of forming limits under biaxial strain conditions. In this work, elliptical bulge tests have been used to evaluate the forming limits of an aluminum bodystock alloy, X309, that is used for PRF™ applications. Limiting dome heights have been determined as a function of pressure-rate and temperature. All tests have been done with the rolling direction, RD, of the sheet aligned with the major axis of the bulge.

Uniaxial tension tests have been carried out along different angles from the rolling direction for both as-received and pre-strained sheet. By comparing the differences in the flow stress vs. orientation curves between the as-received and pre-strained sheets, the effect of pre-straining on material anisotropy is studied. It is demonstrated that the conventional methodology for determining material anisotropy would overestimate the pre-straining effect and would result in a completely erroneous yield surface.

Forming Limit Stress Diagrams (FLSDs) have been intensively studied and have been considered as being path-independent. This paper carries out a detailed study to examine the path-dependency of FLSDs based on different non-proportional loading histories, which are combinations of two linear strain paths. All simulations are based on crystal plasticity theory in conjunction with the M–K approach. It is confirmed that the Forming Limit Diagram (FLD) and the FLSD are two mathematically equivalent representations of forming limits in strain-space and stress-space, respectively. While the FLD is very sensitive to strain path changes, the FLSD is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The nature of the effect of a strain path change on forming limits is investigated in terms of the transition work hardening behaviour upon the path change, and the concept of the FLSD.

Time-dependent relaxation processes continue after forming of sheet metal components. Mechanical properties and even the shape of the part may evolve with time. Beverage can ends, made of an aluminum-magnesium alloy, provide one example of relaxation in a metal product. Ends are manufactured in a series of forming operations, and the can end buckle pressure plays an important role in the design. It has been established that buckle pressure decreases with time in service. In this work, we outline a simple bending test to study relaxation at stress levels well below the usual 0.2 percent offset yield stress. The evolution of stress and development of plastic strain with time are assessed through a simple analysis of springback. The microplastic processes that lead to permanent deformation of the bent beam are well characterized by a model developed by Garmestani and Hart.

The research by Prof. Paul Dawson has done much to further the use of constitutive models based on internal state variables toward applications of industrial relevance. Two particular models examined by Dawson are one based on the "mechanical threshold", developed by Kocks and co-workers and another based on the "hardness", advanced by Hart and co-workers The first of these is intended to describe bulk plastic flow, and is associated with the notion of percolation of dislocations. The second is a phenomenological model that includes anelasticity and gives reliable prediction of stress relaxation. In this work, we examine the time-dependent inelastic deformation of the aluminum alloy AA 5182-1119-during the manufacturing process, but also under in-service conditions. Assessment is made through evolution of both mechanical properties and geometry. A constitutive model based on two internal variables is proposed. One variable is the mechanical threshold stress, dominating for the bulk plastic flow; the other is due to the operation of dynamic pile-ups, providing microplasticity and based on a modification to Hart's model by H. Garmestani. These two state parameters are not directly related to distinct mechanisms of flow resistance in this solution-hardened alloy, but rather to long-range and short-range dislocation motions. As a result, this model can characterize both the large scale plastic flow and subsequent transient processes having very low strain rate, such as stress relaxation and time-dependent springback.

The dilatational plasticity theory of [J. Engng. Mater. Tech. 99 (1977) 2] is generalized in this paper for viscoplastic materials. A unit-cell model of a viscoplastic matrix containing a microvoid is adopted to establish the viscoplastic constitutive relations for voided, dilating materials. Approximate analytic constitutive relations are proposed, which not only have the correct asymptotic limits but also agree well with the unit-cell model.

A biaxial testing apparatus was used to investigate the elastic-plastic behaviour of an 1145 aluminum sheet alloy. Flat cruciform specimens were deformed up to effective strains of approximately 0.15 in biaxial stretching, along seven different proportional strain paths. A finite element analysis of each test was carried out using four different phenomenological models of anisotropic plasticity. An iterative procedure was coupled with the numerical analyses in order to determine the anisotropic parameters in the various yield functions and thus obtain best fits to these functions. This method of numerically analyzing cruciform specimens leads to fairly accurate biaxial flow curves, as well as plastic work contours. The results are also compared with crystal plasticity simulations using a Taylor-type model.

A mesoscopic approach for constructing a forming limit diagram (FLD) is developed. The approach is based on the concept of a unit cell. The unit cell is macroscopically infinitely small and thus represents a material point in the sheet, and is microscopically finitely large and thus contains a sufficiently large number of grains. The responses of the unit cell under biaxial tension are calculated using the finite element method. Each element of a mesh/unit cell represents an orientation and the constitutive response at an integration point is described by the single crystal plasticity theory. It is demonstrated that the limit strains are the natural outcomes of the mesoscopic approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach is not relevant in the mesoscopic approach. The effects of strain-rate sensitivity, single slip hardening and latent hardening, texture evolution, crystal elasticity and spatial orientation distribution on necking are discussed. Numerical results based on the mesoscopic approach are compared with experimental data.

Progress in computer simulation of sheet forming operations depends on accurate characterisation of the sheet strength. The strength exhibits anisotropy arising from its crystallographic texture. Approaches to incorporating representations for strength anisotropy in finite element formulations based on polycrystal plasticity and texture are reviewed. The approaches include ones that employ analytical (closed form) representations of the yield surface or plastic potential and others based on piecewise (numerical) representations. An approach based on directly embedding polycrystal plasticity without a macroscopic yield surface per se is summarised. Applications of the various approaches are presented, some related to forming operations such as deep drawing and others to formability tests such as the limiting dome height test.

A simplified method for analyzing the development of roping is proposed based on the observation that the initial texture and its spatial distribution are the predominant factors for roping. The method is validated by comparing its results with experimental observations, and with numerical results based on the finite element method.

The finite element method is used to numerically simulate the development of roping in an aluminium sheet AA6111 under stretching. The measured EBSD data are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. The effects of spatial orientation distribution, imposed deformation path, loading direction, and inhomogeneous deformation within individual grains on the roping are discussed. Correlation between roping and individual texture components is also explored.

The effect of the cube texture on the initiation of localized necking is studied numerically. The forming limit diagram (FLD) is constructed based on crystal plasticity theory in conjunction with the well-known M–K approach. It is found that, while the ideal cube texture decreases formability, a spread about cube significantly delays the initiation of localized necking when a sheet undergoes biaxial tension. The effect of the cube texture on the predicted FLDs is discussed in terms of the sharpness of the yield locus near equi-biaxial tension.

The anisotropic behaviour of some rolled aluminum alloys is investigated using the phenomenological approach via some of the recently proposed 3-D yield functions. The directional variations of the yield stress and the so-called R-values in the plane of the sheet are predicted using the 3-D yield functions and the results are compared to previously reported experimental measurements. The hardening properties of the alloys examined are extracted from the experimental uniaxial curves along the rolling direction (RD). The forming limit curves are produced using the Marciniak and Kuczynski (Marciniak, Z., Kuczynski, K., 1967 Limit strains in the process of stret-forming sheet metals. Int. J. Mech. Sci. 9, 609–620) approach and the predictions of different yield functions are compared to the experimental curves. In general, although the refinements incorporated to the yield function proposals in chronological order produced better agreement with the experimental observations (at the expense of some complexity in the formulation), the overall performance of each criteria examined could nevertheless vary with the type of the application, as can be anticipated from the phenomenological nature of the approach.