Date of Award


Degree Type


Degree Name

Master of Science in Mechanical Engineering and Applied Mechanics


Mechanical, Industrial and Systems Engineering

First Advisor

Hamouda Ghonem


A constitutive relationship for the dynamic flow stress in metallic alloys is derived as a function of strain, strain rate, temperature and microstructure parameters. The microstructural features of interest in this study are the secondary phase and the grain size in dual and single phase materials, respectively. The role of the secondary phase has been investigated in Carbon steels by determining the relative contribution of pearlite colonies to the evolving flow stress. In this regard, several steels have been studied including as-received A572 steel, composed of a-ferrite matrix phase and pearlite colonies, and a heat treated A572 comprised of carbide particles dispersed within a-ferrite matrix. In order to investigate the role of grain size being a strengthening mechanism on the flow stress, a fine and coarse grained Al6061 alloy have been investigated. An Equal Channel Angular Press is designed and built as a tool to refine the grain size of a coarse grained Al6061 material. Testing in the dynamic loading level is completed using a Split Hopkinson Pressure Bar at strain rates of 102 to 104s-1 at temperatures of 20, 300, 500 and 650°C for the carbon steel and 20, 50, 100 and 200°C for the aluminum alloy. Result of the experimental testing in the form of true stress-true strain curves are used to model the stress-strain relationship as the sum of two independent components; athermal and thermal. The athermal stress component, which is due to the interaction of dislocations with stress fields generated by long range barriers is described as a function of strain as well as relevant microstructural features. Sources of long range barriers include grain boundaries, large second phase particles, and dislocations on parallel slip planes. The thermal component of the flow stress is described as a function of strain rate and temperature and is the result of dislocation interactions with thermally activated barriers or short range barriers; dominant sources include Peierls-Nabarro barriers in BCC metals and forest dislocations in FCC metals. The presence of the dislocation forest as a short range barrier requires the inclusion of strain in the derivation of the thermal component of stress. These two stress components, thermal and athermal, are derived as explicit functions of loading and microstructure parameters. For the carbon steel it is determined that the thermal stress is a function of strain rate and temperature while the athermal component is dependent on the pearlite phase measured in terms of its volume fraction. For the single phase aluminum alloys, both the athermal and thermal stresses are shown to be grain size dependent. Upon reaching a critical grain size, the thermal component becomes increasingly sensitive to grain size refinement thus indicating a change in the deformation mechanism. This increased influence of the grain size on the thermal stress is accounted for by considering the evolution of the short range barrier source. This treatment, furthermore, provides knowledge of the different grain size scales encompassing, coarse, fine and ultra-fine each of which is defined by a deformation mechanism that reflects the specifics of dislocation/barrier interactions. These mechanisms are identified and numerically simulated.

A validation procedure of the final form of the proposed dynamic flow stress model which is derived as explicit function of loading and microstructure has been carried out though a numerical simulation using loading and material conditions that were not involved in the generation of the model parameters. A comparison of the simulation results and those experimentally obtained are described and discussed.



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