  The stress-strain curves of most metallic alloys are often described using
the relatively simple Ramberg-Osgood relationship. Whilst this description
captures the overall stress-strain curve under monotonic tensile loading with
reasonable overall accuracy, it often presents significant errors in the
immediate post-yield region where the interplay between the elastic and plastic
strains is particularly significant. This study proposes and develops a new
approach to the description of the tensile stress-strain curve based on the
Yield Volume Fraction (YVF) function. The YVF description provides an excellent
match to experimental stress-strain curves based on a physically meaningful
parameter that corresponds to the cumulative volume fraction of the polycrystal
that undergoes yielding during monotonic deformation. The statistical nature of
the polycrystal yield phenomenon is highlighted by the fact that the YVF model
achieves good agreement with observations when the lognormal and extreme value
distributions are employed to express the cumulative density function for the
total yield volume fraction, and the probability density function for the
incremental yield volume fraction, respectively. This proposed approach is
compared with crystal plasticity finite element (CPFE) simulations and the
Ramberg-Osgood model, along with experimental observations. The results
highlight the potential of more extensive use of statistical methods in the
description of material deformation response for improved design.
