Influence of specimen width on the elongation-to-fracture in cyclic-bending-under-tension of commercially pure titanium sheets

Abstract

In recent publications, we have shown that repeated bending and unbending during tension can significantly increase the percent elongation-to-fracture (ETF) of metallic sheets. A custom-built machine for cyclic bending under tension (CBT) testing was designed and used to test several sheet metals. In particular, the improvements in ETF using CBT were over 3× relative to simple tension (ST) for commercially pure titanium (cp-Ti) sheets. The present paper evaluates the influence of specimen width on the achieved ETF in CBT of cp-Ti sheets. To facilitate the study, the CBT machine was furnished with wide grips to enable processing of sheets in addition to testing narrow strips. The ETF was observed to reduce with the sheet width. To rationalize the observations, the strain rate-independent plasticity theory of von Mises (J2) with isotropic expansion of yield surfaces of cp-Ti was used in finite elements (FE) to perform a set of simulations. To facilitate the FE simulations of the CBT process stretching the sheets of cp-Ti far beyond the point of maximum uniform strain in ST, the post-necking hardening behavior was inferred along RD, TD, and 45 sheet directions using an established methodology combining ST tests, CBT tests, and modeling material behavior during CBT. Simulated geometries and mechanical fields were found to be in good agreement with corresponding measurements for every specimen width. While predicted axial strains were similar for every width, the strain path shifted from uniaxial tension for the narrow specimen toward plane-strain tension for the wider specimens. As such, as plane-strain tension was approached via progressively wider specimens, the width strains reduced, while the thinning strains increased. The increase in the thinning strain was established as the primary reason for the reduced ETF with increasing sheet width. Experimental and FE simulation results along with the insights into the influence of specimen width on the ETF in CBT of cp-Ti are presented and discussed.