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Plastic bonded explosives are unique materials with complex properties. Research has deeply explored the reactive nature of these materials, but their mechanical performance has been largely neglected. Due to the aggregate composition of solid crystals covered in polymer binders which are heated and pressed into parts, the mechanical response of these materials is extremely complex. The primary objective of this thesis was to develop a unique fixture to allow for a smaller explosive specimen to be installed and tested under multiaxial loading conditions. The design was heavily dependent on set requirements as well as production and use preferences, and a thorough analysis was performed to verify the fixture correctly loaded the specimen without concerns of fixture damage or improper loading due to excessive strain across the fixture. Once fabricated, a test series was conducted on explosive specimens to validate the fixture’s capabilities and provide an initial look at the mechanical response of a complex aggregate material loaded in various combinations of stress states.Analytical methods were again relied on to convert load data to an expected stress state in the unique geometry to provide a first look at the material response.

Modern plasticity models contain numerous parameters that no longer correlate directly to measurements, leading to a lack of uniqueness during parameter identification. This problem is exacerbated when using only uniaxial test data to populate a three-dimensional model. Parameter identification typically is performed after all experiments are completed, and experiments using different loading conditions are seldom conducted for validation. Experimental techniques and computational methods for parameter identification are sufficiently advanced to permit real-time integration of these processes. This work develops a methodology for integrating multiaxial experimentation with constitutive parameter calibration and validation. The integrated strategy provides a closed-loop autonomous experimental approach to parameter identification. A continuous identification process guides the experiment to improve correlation across the entire axial-torsional test domain. Upon completion of the interactive test, constitutive parameters are available immediately for use in finite element simulations of more complex geometries. The autonomous methodology is demonstrated through both analytical and physical experiments on Ti-6Al-4V. The proposed approach defines a framework for parameter identification based on complete coverage of the stress and strain spaces of interest, thereby providing greater model fidelity for simulations involving multiaxial stress states and cyclic loading.

Trabecular bone is a major load-bearing tissue in the musculoskeletal system and is subjected to various multi-axial loads in vivo. For example, in the vertebral body, the trabecular bone is primarily subjected to uniaxial loads, in the proximal femur, trabecular bone is subjected to biaxial loads i.e. loads oriented at two mutually perpendicular directions, in distal radius, the trabecular bone can subjected to shear loads due to off-axis loading during a traumatic event. Understanding the multi-axial strength and underlying tissue-level failure mechanisms of human trabecular bone is of great clinical and scientific importance since age-related osteoporotic fractures primarily occur at trabecular bone sites, such as the hip, spine and wrist. With the onset of osteoporosis, there is an increase in porosity and deterioration of the microarchitecture of trabecular bone, which results in increased fragility and fracture susceptibility of trabecular bone.Using high-resolution, micro-CT based nonlinear finite element models, we investigated the strength of trabecular bone under compression, shear, biaxial and multiaxial loading conditions. Under uniaxial loading, it was shown that the variation in both compressive and shear strength was primarily attributed to the volume fraction of the trabecular bone, but the observed scatter in the ratio of the shear and compressive strength was attributed to heterogeneity and anisotropy of the trabecular microarchitecture. At the tissue-level, it was shown that shear loading leads to predominantly tensile tissue failure unlike compression loading that makes trabecular bone much weaker under shear loading. Under biaxial loading, it was shown that the yield strength varied with both volume fraction and anisotropy, and most of the variation in biaxial strength could be primarily attributed to similar variation of the uniaxial strengths with minor variations due to trabecular microarchitecture. Based on these results, the complete multi-axial yield strength behavior of trabecular bone was investigated for over 200 multi-axial load cases. A new yield strength criterion was then formulated in the six-dimensional strain space to mathematically characterize the multiaxial failure criterion of human trabecular bone.The research presented in this dissertation has provided considerable insight into the variation of both apparent-level strength and the tissue-level failure mechanisms of trabecular bone under various loading conditions. The role of bone volume fraction, anisotropy and microarchitecture on the uniaxial and multi-axial strength has been outlined. A multi-axial failure criterion has been formulated which can be used to noninvasively predict the strength of whole bones of osteoporotic patients using clinical CT scans.

In the combustion zone of industrial- and aero- gas turbines, thermomechanical fatigue (TMF) is the dominant damage mechanism. Thermomechanical fatigue is a coupling of independent creep, fatigue, and oxidation damage mechanisms that interact and accelerate microstructural degradation. A mixture of intergranular cracking due to creep, transgranular cracking due to fatigue, and surface embrittlement due to oxidation is often observed in gas turbine components removed from service. The current maintenance scheme for gas turbines is to remove components from service when any criteria (elongation, stress-rupture, crack length, etc.) exceed the designed maximum allowable. Experimental, theoretical, and numerical analyses are performed to determine the state of the component as it relates to each criterion (a time consuming process). While calculating these metrics individually has been successful in the past, a better approach would be to develop a unified mechanical modeling that incorporates the constitutive response, microstructural degradation, and rupture of the subject material via a damage variable used to predict the cumulative “damage state” within a component. This would allow for a priori predictions of microstructural degradation, crack propagation/arrest, and component-level lifing. In this study, a unified mechanical model for creep-fatigue (deformation, cracking, and rupture) is proposed. It is hypothesized that damage quantification techniques can be used to develop accurate creep, fatigue, and plastic/ductile cumulative- nonlinear- damage laws within the continuum damage mechanics principle. These damage laws when coupled with appropriate constitutive equations and a degrading stiffness tensor can be used to predict the mechanical state of a component. A series of monotonic, creep, fatigue, and tensile-hold creepfatigue tests are obtained from literature for 304 stainless steel at 600°C (1112°F) in an air. iv Cumulative- nonlinear- creep, fatigue, and a coupled creep-fatigue damage laws are developed. The individual damage variables are incorporated as an internal state variable within a novel unified viscoplasticity constitutive model (zero yield surface) and degrading stiffness tensor. These equations are implemented as a custom material model within a custom FORTRAN onedimensional finite element code. The radial return mapping technique is used with the updated stress vector solved by Newton-Raphson iteration. A consistent tangent stiffness matrix is derived based on the inelastic strain increment. All available experimental data is compared to finite element results to determine the ability of the unified mechanical model to predict deformation, damage evolution, crack growth, and rupture under a creep-fatigue environment.

Anisotropic tertiary creep damage formulations have become an increasingly important prediction technique for high temperature components due to drives in the gas turbine industry for increased combustion chamber exit pressures, temperature, and the use of anisotropic materials such as metal matrix composites and directionally-solidified (DS) Ni-base superalloys. Typically, isotropic creep damage formulations are implemented for simple cases involving a uniaxial state of stress; however, these formulations can be further developed for multiaxial states of stress where materials are found to exhibit induced anisotropy. In addition, anisotropic materials necessitate a fully-developed creep strain tensor. This thesis describes the development of a new anisotropic tertiary creep damage formulation implemented in a general-purpose finite element analysis (FEA) software. Creep deformation and rupture tests are conducted on L, T, and 45°-oriented specimen of subject alloy DS GTD-111. Using the Kachanov-Rabotnov isotropic creep damage formulation and the optimization software uSHARP, the damage constants associated with the creep tests are determined. The damage constants, secondary creep, and derived Hill Constants are applied directly into the improved formulation. Comparison between the isotropic and improved anisotropic creep damage formulations demonstrates modeling accuracy. An examination of the off-axis creep strain terms using the improved formulation is conducted. Integration of the isotropic creep damage formulation provides time to failure predictions which are compared with rupture tests. Integration of the improved anisotropic creep damage produces time to failure predictions at intermediate orientations and any state of stress. A parametric study examining various states of stress, and materials orientations is performed to verify the flexibility of the improved formulation. A parametric exercise of the time to failure predictions for various levels of uniaxial stress is conducted.

An accelerated method for determining the fatigue stress versus cycle life (S-N) behavior of isotropic materials is developed for prediction of axial (tension-compression), bending, shear, and multi-axial fatigue life at various stress ratios. The framework for this accelerated method was developed in accordance with a previous understanding of a strain energy and fatigue life correlation, which states: the total strain energy dissipated during a monotonic fracture and a cyclic process is the same material property, where each can be determined by measuring the area underneath the monotonic true stress-strain curve and the area within a hysteresis loop, respectively. The developed framework consists of the following six elements: (1) New experimental procedures used to acquire more sufficient uniaxial and multi-axial test results than conventional methods, (2) an analytical representation for the effect of the stress gradient through the fatigue zone, thus providing capability for bending fatigue prediction, (3) the effect of mean stress on fatigue life for tension/compression and bending, (4) development of an improved energy-based prediction criterion for shear loading at various stress ratios, (5) fatigue life prediction for materials experiencing the endurance limit phenomenon, and (6) the development of a multi-axial fatigue life prediction method. Validation of this accelerated fatigue life determination framework is achieved based on comparison with numerous experimental results acquired from Aluminum 6061-T6 and Titanium 6Al-4V. The results of the comparison are extremely encouraging, thus providing justification that the future direction for the strain-energy based fatigue life prediction method is very promising.

A novel method of predicting the multiaxial high-cycle fatigue strength of metallic components is proposed and verified for various steel, aluminium and cast iron alloys. The proposed Fatigue Damage Function shows superior multiaxial fatigue strength prediction compared to the established methods of Gough and Pollard, McDiarmid and Carpinteri and Spagnoli. A new material property, the Normal Stress Sensitivity Factor, is also introduced and its applicability is verified according to published test results of sixteen different structural alloys. To highlight the effectiveness of the proposed criterion, for industrial applications, a case study has been conducted on heat-treated and not heat-treated automatic transmission output shafts.