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An investigation of the microstructure-mechanical property relationships for gray cast iron and a vintage ASTM A7 steel are presented herein. Gray cast iron was shown to have a moderate sensitivity to strain rate and a large disparity in behavior between compression, tension, and torsion. ASTM A7 steel was shown to behave in a more complex manor with the strain rate sensitivity having a negative relationship in tension and positive relationship in compression and torsion, the tensile stress-state producing the highest stress response, and the material producing a higher stress response when exposed to elevated temperatures. The counterintuitive behavior observed in A7 steel was attributed to dynamic strain aging. The Mississippi State University Internal State Variable Plasticity-Damage model was updated to accurately capture negative strain rate sensitivity and DSA embrittlement by developing kinematic, thermodynamic, and kinetic constitutive relationships for dynamic strain aging. A parametric study was performed to elucidate the behavior of the new internal state variable for dynamic strain aging. Gray cast iron was successfully calibrated to a pre-DSA version of the plasticity-damage model and A7 steel was successfully calibrated to the updated plasticity-damage model.

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<div>The mechanical behaviors of different kinds of biological tissues, including muscle tissues, cortical bones, cancellous bones and skulls, were studied under various loading conditions to investigate their strain-rate sensitivities and loading-direction dependencies. Specifically, the compressive mechanical behaviors of porcine muscle were studied at quasi-static (<1/s) and intermediate (1/s─10^2/s) strain rates. Both the compressive and tensile mechanical behaviors of human muscle were investigated at quasi-static and intermediate strain rates. The effect of strain-rate and loading-direction on the compressive mechanical behaviors of human frontal skulls, with its entire sandwich structure intact, were also studied at quasi-static, intermediate and high (10^2/s─10^3/s) strain rates. The fracture behaviors of porcine cortical bone and cancellous bone were investigated at both quasi-static (0.01mm/s) and dynamic (~6.1 m/s) loading rates, with the entire failure process visualized, in real-time, using the phase contrast imaging technique. Research effort was also focused on studying the dynamic fracture behaviors, in terms of fracture initiation toughness and crack-growth resistance curve (R-curve), of porcine cortical bone in three loading directions: in-plane transverse, out-of-plane transverse and in-plane longitudinal. A hydraulic material testing system (MTS) was used to load all the biological tissues at quasi-static and intermediate loading rates. Experiments at high loading rates were performed on regular or modified Kolsky bars. Tomography of bone specimens was also performed to help understand their microstructures and obtain the basic material properties before mechanical characterizations. Experimental results found that both porcine muscle and human muscle exhibited non-linear and strain-rate dependent mechanical behaviors in the range from quasi-static (10^(-2)/s─1/s) to intermediate (1/s─10^2/s) loading rates. The porcine muscle showed no significant difference in the stress-strain curve between the along-fiber and transverse-to-fiber orientation, while it was found the human muscle was stiffer and stronger along fiber direction in tension than transverse-to fiber direction in compression. The human frontal skulls exhibited a highly loading-direction dependent mechanical behavior: higher ultimate strength, with an increasing ratio of 2, and higher elastic modulus, with an increasing ratio of 3, were found in tangential loading direction when compared with those in the radial direction. A transition from quasi-ductile to brittle compressive mechanical behaviors of human frontal skulls was also observed as loading rate increased from quasi-static to dynamic, as the elastic modulus was increased by factors of 4 and 2.5 in the radial and tangential loading directions, respectively. Experimental results also suggested that the strength in the radial direction was mainly depended on the diploë porosity while the diploë layer ratio played the predominant role in the tangential direction. For the fracture behaviors of bones, straight-through crack paths were observed in both the in-plane longitudinal cortical bone specimens and cancellous bone specimens, while the cracks were highly tortuous in the in-plane transverse cortical bone specimens. Although the extent of toughening mechanisms at dynamic loading rate was comparatively diminished, crack deflections and twists at osteon cement lines were still observed in the transversely oriented cortical bone specimens at not only quasi-static loading rate but also dynamic loading rate. The locations of fracture initiations were found statistical independent on the bone type, while the propagation direction of incipient crack was significantly dependent on the loading direction in cortical bone and largely varied among different types of bones (cortical bone and cancellous bone). In addition, the crack propagation velocities were dependent on crack extension over the entire crack path for all the three loading directions while the initial velocity for in-plane direction was lower than the other two directions. Both the cortical bone and cancellous bone exhibited higher fracture initiation toughness and steeper R-curves at the quasi-static loading rate than the dynamic loading rate. For cortical bone at a dynamic loading rate (5.4 m/s), the R-curves were steepest, and the crack surfaces were most tortuous in the in-plane transverse direction while highly smooth crack paths and slowly growing R-curves were found in the in-plane longitudinal direction, suggesting an overall transition from brittle to ductile-like fracture behaviors as the osteon orientation varies from in-plane longitudinal to out-of-plane transverse, and to in-plane transverse eventually.</div>