Influences of rolling reduction on sheet metal formability

One common measure of sheet metal formability is the r value-the ratio between the width and thickness strains in a tensile test. The processing history imparted to a 2 mm, as-received aluminium sheet resulted in r values, at best, only a little greater than unity for the transverse orientations to the roll. This paper examines the effect on the initial r variation of a further 40 per cent cold reduction to the thickness in four passes. It is shown how an orthotropic yield function can explain the overall increase in r observed while retaining a similar dependence on sheet orientation. The influence of rolling reduction on the subsequent forming limit diagram is also examined theoretically when the principal stress axes are aligned with the material axes. The limiting strain is set by two contrasting conditions: diffuse and local instability. The influence of two important factors is established: (a) the average (r) over bar value in the plane of the sheet and (b) the effective prestrain history epsilon (0). It is shown how (a) and (b) influence the strains at the limit of formability as predicted by these criteria and thereby allow an understanding of the optimum condition for raising limit strains.