A simple relation for deviation of grey and nodular cast irons from Hookeʹs law

One of the features of graphite cast irons is the non-linear dependence between stress and strain far below the yield stress. All theoretical approaches to this non-linearity are based on many simplifying assumptions which are not fulfilled in real cast irons. Many phenomenological descriptions of the starting part of the stress–strain curve have been published but most are not applicable to very low stresses and strains. In the present work, a new simple rheological relation is proposed describing the deviation from Hookeʹs law. It was obtained using the derivatives of the starting parts of precisely measured stress–strain curves. The relation containing the deviation parameter is applied to grey and nodular cast irons but, in principle, it can also be applied to any other material with non-linear quasi-elastic behaviour under loading.