Bradley Dodd

Convexity restrictions on non-quadratic anisotropic yield criteria

Abstract Examination of Hills 1979 anisotropic yield criterion [ Math. Proc. Camb. Phil. Soc. 85, 179 (1979)] shows that for Cases I, II and III, there are combinations of m and R for which the yield loci are outwardly concave or even unbounded. For Case I, all loci are concave unless m = 2. For Cases II and III, the combinations of m and R which lead to concavity and unboundedness have been established. Case IV and Hosfords criterion have no problem regions as long as m ⩾ 1.

On the anomalous behaviour of anisotropic sheet metals

Abstract Using Hills 1948 criterion [1] for anisotropic yielding and the strain ratio, r , it has been shown that the ratio of the balanced biaxial yield stress, σ b , to the uniaxial tensile yield stress, σ u , should be > 1 if r > 1 and r r σ b to σ u was always > 1 in that study. This was termed anomalous behaviour. Hill has proposed a new criterion[3] that not only appears to provide greater flexibility than does his earlier version but can also encompass anomalous behaviour which the earlier version cannot. Four simplified cases of the 1979 criterion have been proposed[3] and to date only one has been subjected to experimental assessment. However, the goals of those studies were not concerned with anomalous behaviour per se. In this paper, all four cases are analysed to determine the interrelationships of the parameters r and m (exponent in Hills new criterion) required to encompass anomalous behaviour. It is found that for each of the four cases anomalous behaviour is predicted for a range of ( m , r ) combinations which are presented graphically in this paper.

Limitations on isotropic yield criteria

Abstract A number of isotropic yield criteria are examined from the viewpoint of concavity limitations. Also, for some criteria the inner and outer bounds of the loci are defined. Except for Druckers yield criterion, it is shown that all the others considered are special cases of Hills 1979 criterion assuming isotropy.

On tangential velocity discontinuities being coincident with stress discontinuities

Abstract Whether or not in a slip-line field a stress discontinuity can be simultaneously a velocity discontinuity has been discussed since the late 1940s. According to the usual “jump” conditions it is not impossible to have a tangential velocity component across a stress discontinuity. However, Hill[1] demonstrated the impossibility of there being a simultaneous stress and velocity discontinuity in an elastic-plastic material. This note briefly reviews the historical arguments surrounding this subject and then, based on a discussion of the state within the transition region, shows that the possibility of a simultaneous stress and velocity discontinuity depends on suppositions concerning material behavior within it.

Workability and CAD/CAM

The objective of this report is to highlight the need to include process simulation in forming CAD/CAM systems, and furthermore to suggest that such simulation packages should include an assessment of damage accumulation in the form of an appropriate workability criterion

Forming-limit diagrams for Al 2124 and AlLi 8090 through fracture mechanics and perturbation analysis

Abstract A parallel comparative ‘fracture mechanics and perturbation analysis’ study for the construction of ‘forming-limit diagrams’ is presented in this work. The first is based on the notions of a recently introduced generalization of the T-criterion of fracture for the case of uncracked specimens. According to this generalization the failure of a material is described by a set of two material constants, i.e. its maximum ability to absorb dilatitional and/or distortional strain energy. On the other hand the perturbation analysis is based on the introduction of a disturbance added to the homogeneous solution satisfying the set of governing differential equations of the problem. Both approaches are applied for the case of two conventional alloys, e.e. Al 2124 and AlLi 8090, and their predictions are then compared with each other and also with the experimental results obtained from a series of in-plane and out-of-plane metal-forming processes.

A slip-line field solution for plane-strain indentation by an obtuse-angle wedge

Abstract A slip-line field solution with lines of stress discontinuity is proposed which is shown to be admissible for obtuse-angled wedges with interfacial friction. The dead metal cap solution which is used conventionally when θ − λ ⩾ π 4 has a lower load than the corresponding non-dead metal cap solution. This result is referred to as Haddows paradox. Using the new solution it is shown that, at the point of transition, corresponding to θ − λ = π 4 , the load coincides with that of the non-dead metal case. Thus Haddows paradox is inoperative.

On possible branching conditions in plane stress

Abstract A new condition is described which allows for the possibility of. localized necking in the tension-tension quadrant where Hills characteristic necking [ J. Mech. Phys. Solids 1 , 19–30 (1952)] is suppressed. A link is recognized between this condition and the more general conditions for constitutive branching recently described by Hill [ Math. Proc. Camb. Phil. Soc. (1983)].

The effect of plastic potential on Lode's strain variable

Abstract A general expression for the Lode strain variable is derived using a special case of the non-quadratic yield criterion recently proposed by Hill. A number of plots of the Lode variables for different strain ratios and criterion exponents are presented. The Lode variables obtained experimentally for materials can be fitted by a judicious choice of strain ratio and yield criterion exponent.

Flow localization and fracture in materials exhibiting structural superplasticity

For a superplastic material which does not cavitate, fracture by rupture is expected. For superplastics which do cavitate, two modes of fracture are described depending on whether deformation remains in region II or III. If grain coarsening occurs, thermoplastic shear instabilities occur between cavities when there is a transition in mode of deformation from II to III. If deformation is stabilized in region II, shear instability is suppressed and fracture occurs by the growing together of voids according to McClintocks model.