  Finding an accurate stress-strain relation, able to describe the mechanical
behavior of metals during {forming} and machining processes, is an important
challenge in several fields of mechanics, with significant repercussions in the
technological field. Indeed, in order to predict the real mechanical behavior
of materials, constitutive laws must be able to take into account elastic,
viscous and plastic phenomena. Most constitutive models are based on empirical
evidence and/or theoretical approaches, and provide a good prediction of the
mechanical behavior of several materials.
  Here we present a non linear stress-strain relation based on fractional
operators. The proposed constitutive law is based on integral formulation, and
takes into account the viscoelastic behavior of the material and the inelastic
phenomenon that appears when the stress reaches a particular yielding value. A
specific case of the proposed constitutive law for imposed strain history is
used to fit experimental data obtained from tensile tests on two kind of metal
alloys. A best-fitting procedure demonstrates the accuracy of the proposed
stress-strain relation and its results are compared to those obtained with some
classical models. We conclude that the proposed model provides the best results
in predicting the mechanical behavior for low and high values of stress/strain.
