Revisiting the fracture forming limits of bulk forming under biaxial tension

Abstract

The formability limits of bulk metal forming in principal strain space and in the effective strain vs. stress-triaxiality space are characterized by an uncertainty region in which cracks may be triggered by tension (mode I of fracture mechanics) or by out-of-plane shear (mode III). The problem in obtaining experimental data in this region has been known for a long time and the main objective of this paper is to present a new upset formability test geometry that can effectively contribute to the characterization of the formability limits of bulk metal forming parts subjected to biaxial tension. Alongside with this objective, this paper also presents an analytical expression for converting the fracture forming limit line corresponding to crack opening by mode III in principal strain space into a hyperbolic fracture limit curve in the effective strain vs. stress-triaxiality space. The overall methodology employed by the authors combines experimentation along with analytical and numerical modelling, and the contents of the paper is a step towards diminishing the actual lack of knowledge regarding failure by fracture in bulk metal forming parts subject to stress-triaxiality values beyond uniaxial tension. Results show that a new uncoupled ductile fracture criterion built upon combination of the integrands of the Cockcroft-Latham and McClintock criteria can be successfully used to model the physics of the bulk metal forming limits for the entire range of stress-triaxiality values corresponding to cracking on free surfaces.

On the utilization of radial extrusion to characterize fracture forming limits. Part II: testing and modelling

“…Competition between cracking opening modes by tension (mode I) and by out-of-plane shearing (mode III) in conventional bulk formability tests give rise to an 'uncertainty region' in principal strain space, as it was recently observed by Sampaio et al [1]. Although research on formability and crack opening modes has been taking the competition between crack opening modes into account, there are aspects related to material flow transitions in regions of bulk metal forming parts subjected to extensive plastic material flow that are not commonly taken into consideration.…”

On the utilization of radial extrusion to characterize fracture forming limits. Part I – methodology and tooling

“…1) within which failure occurs by mixed modes resulting from competition between cracking by tension (mode I) and by out-of-plane shearing (mode III). This was recently confirmed by Sampaio et al [7], who designed a new test specimen to investigate the morphology of the cracks in the 'uncertainty region' of principal strain space and concluded that fracture was triggered by out-ofplane shearing (mode III) and propagate radially by tension (mode I). Transitions from crack opening by mode I to propagation by mode III at the leftmost corner of the 'uncertainty region' were previously observed by the authors during upset compression of cylindrical flanged test specimens made from aluminum AA2030-T4 [8].…”

“…In view of the above, Sampaio et al [7] proposed a new ductile damage criterion based on combination of the Cockcroft and Latham Although research on formability and crack opening modes has been directly, or indirectly, associated with stress triaxiality and, sometimes, also with the Lode parameter [11], there are aspects related to material flow transitions that are not commonly taken into consideration. Accountability of these aspects means, in practical terms, to include the three-dimensional to plane stress material flow transitions (i.e., bulk-to-sheet evolutions) in the list of parameters that are responsible for the competition between the different crack opening modes.…”

A complete characterization of THE fracture forming limits in bulk forming by means of an upset geometry sequence

“…The results of Sampaio et al 14 with the new barreled ring test specimen also underlined the existence of an “uncertainty region” (refer to the orange-shaded region in Figure 1(b)) in which cracks may open by mixed modes resulting from combination of modes I (by tension) and III (by out-of-plane shear).…”

“…Modeling the fracture forming limits in bulk forming resulting from cylindrical, tapered, flanged, and barreled ring formability tests with the ductile fracture criterion (adapted from Sampaio et al 14 ).…”