Date of Award

Fall 2021

Document Type

Open Access Dissertation


Mechanical Engineering

First Advisor

Michael Sutton


The efficient use of metals is important in various industries, including aerospace, automotive, and energy systems. In each case, the type and range of combined loading conditions can be quite different. The approaches to stress analysis of such complex engineering components and assemblies often are limited to elastic conditions. For those cases where components are relatively thin, elastic-plastic conditions are present; there is continuing interest in assessing the accuracy of analytic and computational models for combined loading conditions. In such cases, experiments performed with axial and shear loads (e.g., tension-torsion) provide baseline data regarding the relationship between applied stresses and specimen strains. Since stereo digital image correlation (StereoDIC) has been used extensively in recent years to measure full-field surface deformations, including both surface strains and displacements, the methodology provides quantitative data regarding the specimen's non-uniform deformation response. In particular, the full-field and non-contacting capabilities of StereoDIC are especially advantageous when applied to thin-walled tubular specimens subjected to multimodal loading. The first part of this work investigates the anisotropic behavior of two longitudinally extruded Al6061-T6 bars obtained from the same manufacturer. Since longitudinal extrusion is known to affect material isotropy, investigators performed a comprehensive series of mechanical characterization experiments, including torsion for cylindrical specimens and tension for flat dog-bone specimens extracted at different orientations from the rod materials. The Barlat Yld91 yield function, which requires six parameters for generally mixed-mode predictions, is employed in this study. The Newton-Raphson numerical method was used to solve the nonlinear set of Barlat equations to determine six anisotropic parameters from the yield stresses acquired from uniaxial and pure torsion testing. The results show the extruded Al6061-T6 bars have significant anisotropic behavior.

The second part of this work presents the effect of stress state and loading path on the elastic-plastic response and strain hardening of Al6061-T6 by performing combined tension-torsion, uniaxial tension, and pure torsion experiments on tubular specimens. Specialty grips and precision boring tools were developed and then manufactured for cylindrical specimen manufacturing and tension-torsion experiments. StereoDIC again is employed to measure reliable average surface strains while also providing full-field measurements to identify anomalies in material response due to machining imperfections and/or loading conditions. Mixed-mode loading experiments are performed in load-control mode using an electromechanical tension-torsion test frame. Results from proportional tension torsion experiments with stress ratio, β, defined as the ratio shear stress /normal stress in the range 0 ≤ β ≤ ∞ were obtained. By using plastic work/dissipation to determine equivalent strain from multiaxial stress states, measurements demonstrated that the yield stress defined by the Von Mises effective stress vs. equivalent strain response varied with β by up to 14%. Conversely, when using the Barlat Yld91 anisotropic yield function to define modified effective stress, direct comparison of the Barlat effective stress versus equivalent strain data for all mixed-mode loading experiments to the uniaxial tension data demonstrated that the Barlat Yld91 effective stress versus equivalent strain was within ±4% of the uniaxial data for all β, confirming that an anisotropic yield function should be employed to accurately predict plastic flow and strain hardening behavior in extrusions.

The third part of the work presents a combined theoretical and experimental material hardening behavior under only torsion loading for two new aluminum Al6061-T6 longitudinally extruded bars obtained from the same manufacturer as used previously. The theoretical elastic, plastic, and total shear strains due to applied shear stress are determined using incremental plasticity theory. A constitutive numerical model is developed for both isotropic (Von Mises) and anisotropic (Barlat'91) yield criteria. Assuming isotropic strain hardening formulations to describe the post-yield behavior for both yield criteria, the Von Mises isotropic model predictions are shown to either underestimate or overestimate the data by up to 25% for both extrusions. Conversely, the constitutive model using the anisotropic yield criteria is in excellent agreement, with deviations from the experimental measurements by less than 5%, again demonstrating that plastic anisotropy is essential for accurate prediction of the mechanical behavior of longitudinally extruded Al6061-T6 bars.

Finally, an experimental investigation of stress-strain was conducted to understand the effect of non-proportional tension-torsion loading on several specimens. The experimental measurements for selected non-proportional loading experimental are presented, and recommendations for further investigation of the stress-strain behavior under nonproportional tension-torsion loading are provided.