A radial compression test for plastic flow studies

Abstract

ABSTRACT--A hydraulic experimental setup and related instrumentation were developed for testing constitutive models of ideal plastic behavior at large deformations using slow, radial compression of short, hollow cylinders at constant height. At this preliminary stage of development, plasticine rings with initial inner diameters of 25.4 mm were reduced to a final diameter of 9 mm or less. Further development is needed to test first lead and then harder metals.KEY WORDS--Plastic flow, radial compression, plasticine, metal forming Ductile metals undergo a continuous, fluid-like deformation when a sufficient pressure difference is applied to some parts of their boundary under kinematic conditions allowing freedom of shape. The accurate prediction of ductile behavior is important in many engineering applications, notably in metal-forming processes. Analyses of the mechanical aspects of such processes use constitutive relations that mathematically model ductile metals as a plastic material, with a yield function, or as a viscoplastic material, in which case a yield stress appears in the stress-strain rate relation, but there is no yield function.A new, all-encompassing class of ideal ductile materials with a yield function was first defined in Ref. 1, and exact solutions for slow frictionless ring-forming problems are presented in Refs. 9 and 10.Briefly, we call a material "ideal ductile" when (i) it is incompressible, (ii) it has a material constant K with dimension of stress, called the shear flow stress, and (iii) it has a stress deviator, sij, that depends quasi-linearly on the strain rate, eij. 1Thus, an ideal ductile material, as defined here, has a constitutive equation ( K, el, e2, e3) 24, 1997. Final manuscript received: September 7, 1999 such that the stress rate of strain relation is of the form Sij = KF(el, e2, e3)and furthermore that there exists a yield criterion, using the same function F, of the following form:(3) K For illustration purposes, the following four specific models are presented for the function F:In the above, the principal strain rates el and e3 in F2 are the largest and the smallest strain rates, respectively, whereas el in F4 denotes the principal strain rate with the largest absolute value.Of the models above, the first three--associated with the works ofTresca, 2 Saint-V6nant 3 and yon Mises4--are of significant historical importance, whereas the fourth is of relatively recent vintage. 5 Traditionally, no distinction is made between the Tresca and Saint-V6nant models, but this is historically incorrect, as explained in Ref. 1.The second and third models are the most common in metal-forming practice, but the fourth model was recently claimed to better fit experimental data for mild steel. 5What is remarkable with ideal ductile materials is that for a limited class of problems that have a high degree of symmetry, there exist closed-form solutions that are identical regardless of the choice of model. The radial deformation of a constant-height circular ring between frictionless platen i...