Stress-Strain data for metals in bar and sheet form: strain rate, thickness and temperature influences

Abstract

Over the past few decades various models of different formats have been developed to correctly evaluate and predict the strength of materials. However, these models are limited in certain environmental conditions in implementing the effect of material's thickness into their models. As such an there was a need to consider the basics of mechanical engineering and to try and define the trend, thickness has upon the behaviour of materials with respect to environmental conditions. The work consisted of a representation of tensile testing testing of common engineering alloys across a wide range of temperature, strain rate and thickness. Acquisition of high strain rate data and extended strain data (split-hopkinson, bulge forming and plane strain compression). A review of existing graphical techniques and limited applications using strength reduction factors, as well as applying the accepted empirical formulae, Johnson-Cook, Armstrong-Zerrili, Ramberg-Osgood and Hollomon. Later, recognising a need for a new approach as with a universal (quartic) polynomial fit to all plastic flow curves in which coefficients are T, ε̇ and t̄ dependant. Adoptation of a common numerical procedure for strain intercept ε0 and cut-off instability co-ordinates (σi, εi)- each as the solution to the roots of a quartic. Therefore, a proposal of the flow curve tables allowing interpolation and extrapolation, a numerical representation of any previous "Atlas of Curves". Subsequently, leading to reconstruction of the full stress-strain curve with the addition of elastic strain calculated from the modulus applicable to the specific test condition by further testing of these data from literature; both improving the existing and producing new empirical and simulation based models to analyse the materials, which will be subjected to dynamic loading as well as temperature and strain rates variations. The main objective of the work, was involved in creating a polynomial fit to describe the three physical conditions in terms of coefficients and to verify the findings in a FEA package, ABAQUS. A new process in reading the stress-strain data. By means of such development an instability study of strain limits based on Considére criteria was developed which illustrated the ways to prolong the instability limit. A secondary study of this work relates to creating a bridge between the micro-structure and macro-structure of the tested materials. A series of correlations and trends were developed to further signify the shift in micro-structural restructuring, whilst the material is under load. Another important aspect of the work consists, of carrying out an analytical study on Ramberg-Osgood equation. Ramberg-Osgood equation has been at the forefront of many engineering advancement. However it can yet be improved and reformatted by means of defining a set value for its variable constants. As such a fix ƞt value based on a best-fit approach was developed which was analytically tested.