New approaches to detect the onset of localised necking in sheets under through-thickness strain gradients

• Two local methodologies to detect the onset of necking under significant through thickness strain gradients are proposed.
• A time-dependent method and a time-position-dependent method are analyzed and validated for stretch-bending tests.
• Both methods satisfactorily estimate the limit strains with and without bending effects for AA7075-O.

The standard ISO 12004-2:2008 provides a position-dependent methodology to estimate the limit strains in Nakazima- and Marciniak-type tests. However, this method is not applicable, at least in its current formulation, when there are significant strain gradients across the sheet thickness, such as when using relatively small punch radii or in stretch-bending operations very commonly in industrial practice. This paper analyses two physically-based methodologies, a time-dependent method and a time-position-dependent method (called here flat-valley method), to detect the onset of necking and to evaluate the limit strains under significant strain gradients through the sheet thickness. The digital image correlation (DIC) technique is used to compute the displacement and strain evolutions at the outer surface of the tested specimens using the commercial software ARAMIS®. A detailed analysis and validation of both methodologies, and comparison with other local methods recently published in the literature, are carried out in the light of a series of Nakazima tests and stretch-bending tests for different cylindrical punch radii in AA7075-O.