Inertia Effects on the Ductile Failure of Thin Rings

Abstract

The introduction of inertia terms into a theoretical model of thin ring expansion shows that classical plastic instability concepts, defined in terms of the local strain in the necking region, no longer apply. By introducing the role of void growth in triggering local necking, through a recently proposed constitutive equation for porous plastic materials, it is possible to overcome this difficulty. A criterion based on a critical void volume fraction provides the alternative means to predict failure. This theory was applied to a thin ring configuration, and the results were found to compare favorably with experimental values obtained from statically and dynamically loaded rings. The experimental techniques developed to handle the thin ring configuration are also described. IntroductionDuctile failure as a phenomenon associated with plastic instability dates back to the time of Considere [1] who identified the point of instability as the onset of localized necking brought about when the increment of strain hardening became equal to the geometric softening, at the point of maximum load in a simple tension test. Marciniak and Kuczynski [2] considered this phenomenon in metal sheets under biaxial tension, and developed a mathematical model (M-K model) to construct forming limit diagrams. This model is based on an initial geometric imperfection, which is a localized thickness reduction in the sheet lying perpendicular to the major principal strain direction. By this method they predicted that the strain in the uniform region reaches a limiting value at which point the local strain in the defective region becomes unstable. In recent studies by Hutchinson and Neale [3] and Ghosh [4] the analysis was extended to include the effect of strain rate and different viscoplastic constitutive laws on localized necking. The results of this analysis, in its application to the case of uniaxial tension under quasi-static loading, predicted that the strain at necking increases with an increase in the strain-rate sensitivity and the strain-hardening parameter. These results were verified experimentally for different materials by Ghosh [4]. This analysis also predicted, depending on the constitutive equation, either no effect on or minor reduction of uniform strain at necking due to an increase in strain rate. These theoretical results were in agreement with the experiments of Sagat and Taplin [5] for superplastic materials under quasi-static loading conditions.In the high strain-rate loading regime, where the quasistatic loading assumption no longer applies, considerable evidence exists, Wilson [6], that an increase in strain rate can

Numerical Study of Damage Evolution and Failure in an Electromagnetic Corner Fill Operation

“…Rajendran and Fyfe [12] explained the increased ductility of an electromagnetically expanded ring, by proposing that the inertial effects resulted in compressive forces, which could lead to retardation of void growth and a delay in necking. Recently the current authors studied EM free formed and conical (34q side angle) parts [13].…”

Identification of the critical wavelength responsible for the fragmentation of ductile rings expanding at very high strain rates

“…Meanwhile, Rajendran and Fyfe (1982) glimpsed the stabilizing effect of inertia in the growth of necks represented by geometrical imperfections. Fressengeas and Molinari (1985) developed a stability analysis within the theoretical framework of a 1-D model for uni-axial tension.…”

Void-containing nonlinear materials subject to high-rate loading

“…The Gurson model has widely been used in analyzing ductile fracture and localization failure problems. 55 The Gurson theory has also been used to model the process of dynamic ductile fracture 8,62,63 and dynamic ductile crack growth. 64,65 However, theoretically speaking, the Gurson model is only suitable for a quasistatic situation since the inertial effects are not included.…”