Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

COMPRESSION BEHAVIOR AT HIGH STRAIN RATE FOR AN ULTRA HIGH PERFORMANCE CONCRETE

The need for a stronger and more durable building material is becoming more important as the structural engineering field expands and challenges the behavioral limits of current materials. One of the demands for stronger material is rooted in the effects that dynamic loading has on a structure. High strain rates on the order of 101 s-1 to 103 s-1, though a small part of the overall types of loading that occur anywhere between 10-8 s-1 to 104 s-1 and at any point in a structures life, have very important effects when considering dynamic loading on a structure. High strain rates such as these can cause the material and structure to behave differently than at slower strain rates, which necessitates the need for the testing of materials under such loading to understand its behavior. Ultra high performance concrete (UHPC), a relatively new material in the U.S. construction industry, exhibits many enhanced strength and durability properties compared to the standard normal strength concrete. However, the use of this material for high strain rate applications requires an understanding of UHPC’s dynamic properties under corresponding loads. One such dynamic property is the increase in compressive strength under high strain rate load conditions, quantified as the dynamic increase factor (DIF). This factor allows a designer to relate the dynamic compressive strength back to the static compressive strength, which generally is a well-established property. Previous research establishes the relationships for the concept of DIF in design. The generally accepted methodology for obtaining high strain rates to study the enhanced behavior of compressive material strength is the split Hopkinson pressure bar (SHPB). In this research, 83 Cor-Tuf UHPC specimens were tested in dynamic compression using a SHPB at Michigan Technological University. The specimens were separated into two categories: ambient cured and thermally treated, with aspect ratios of 0.5:1, 1:1, and 2:1 within each category. There was statistically no significant difference in mean DIF for the aspect ratios and cure regimes that were considered in this study. DIF’s ranged from 1.85 to 2.09. Failure modes were observed to be mostly Type 2, Type 4, or combinations thereof for all specimen aspect ratios when classified according to ASTM C39 fracture pattern guidelines. The Comite Euro-International du Beton (CEB) model for DIF versus strain rate does not accurately predict the DIF for UHPC data gathered in this study. Additionally, a measurement system analysis was conducted to observe variance within the measurement system and a general linear model analysis was performed to examine the interaction and main effects that aspect ratio, cannon pressure, and cure method have on the maximum dynamic stress.

Influence of traumatic impaction and pathological loading on knee menisci

Nearly half of the US population faces the risk of developing knee osteoarthritis (OA). Both in vitro and in vivo studies can aid in a better understanding of the etiology, progression, and advancement of this debilitating disorder. The knee menisci are fibrocartilagenous structures that aid in the distribution of load, attenuation of shock, alignment and lubrication of the knee. Little is known about the biochemical and morphological changes associated with knee menisci following altered loading and traumatic impaction, and investigations are needed to further elucidate how degradation of this soft tissue advances over time. The biochemical response of porcine meniscal explants was investigated following a single bout of dynamic compression with and without the treatment of the pharmaceutical drug, anakinra (IL-1RA). Dynamic loading led to a strain-dependent response in both anabolic and catabolic gene expression of meniscal explants. By inhibiting the Interleukin-1 pathway with IL-1RA, a marked decrease in several catabolic molecules was found. From these studies, future developments in OA treatments may be developed. The implementation of an in vivo animal model contributes to the understanding of how the knee joint behaves as a whole. A novel closed-joint in vivo model that induces anterior cruciate ligament (ACL) rupture has been developed to better understand how traumatic injury leads to OA. The menisci of knees from three different groups (healthy, ACL transected, and traumatically impacted) were characterized using histomorphometry. The acute and chronic changes within the knee following traumatic impaction were investigated. The works presented in this dissertation have focused on the characterization, implementation, and development of mechanically-induced changes to the knee menisci.

AN ASSESSMENT OF BALLAST SOURCE'S QUALITY AND LOCATIONS WITH RESPECT TO MDOT'S UPGRADE OF THE WOLVERINE RAILROAD LINE FOR HIGH SPEED RAIL USEAGE

The Michigan Department of Transportation is evaluating upgrading their portion of the Wolverine Line between Chicago and Detroit to accommodate high speed rail. This will entail upgrading the track to allow trains to run at speeds in excess of 110 miles per hour (mph). An important component of this upgrade will be to assess the requirement for ballast material for high speed rail. In the event that the existing ballast materials do not meet specifications for higher speed train, additional ballast will be required. The purpose of this study, therefore, is to investigate the current MDOT railroad ballast quality specifications and compare them to both the national and international specifications for use on high speed rail lines. The study found that while MDOT has quality specifications for railroad ballast it does not have any for high speed rail. In addition, the American Railway Engineering and Maintenance-of-Way Association (AREMA), while also having specifications for railroad ballast, does not have specific specifications for high speed rail lines. The AREMA aggregate specifications for ballast include the following tests: (1) LA Abrasion, (2) Percent Moisture Absorption, (3) Flat and Elongated Particles, (4) Sulfate Soundness test. Internationally, some countries do require a highly standard for high speed rail such as the Los Angeles (LA) Abrasion test, which is uses a higher standard performance and the Micro Duval test, which is used to determine the maximum speed that a high speed can operate at. Since there are no existing MDOT ballast specification for high speed rail, it is assumed that aggregate ballast specifications for the Wolverine Line will use the higher international specifications. The Wolverine line, however, is located in southern Michigan is a region of sedimentary rocks which generally do not meet the existing MDOT ballast specifications. The investigation found that there were only 12 quarries in the Michigan that meet the MDOT specification. Of these 12 quarries, six were igneous or metamorphic rock quarries, while six were carbonate quarries. Of the six carbonate quarries four were locate in the Lower Peninsula and two in the Upper Peninsula. Two of the carbonate quarries were located in near proximity to the Wolverine Line, while the remaining quarries were at a significant haulage distance. In either case, the cost of haulage becomes an important consideration. In this regard, four of the quarries were located with lake terminals allowing water transportation to down state ports. The Upper Peninsula also has a significant amount of metal based mining in both igneous and metamorphic rock that generate significant amount of waste rock that could be used as a ballast material. The main drawback, however, is the distance to the Wolverine rail line. One potential source is the Cliffs Natural Resources that operates two large surface mines in the Marquette area with rail and water transportation to both Lake Superior and Lake Michigan. Both mines mine rock with a very high compressive strength far in excess of most ballast materials used in the United States and would make an excellent ballast materials. Discussions with Cliffs, however, indicated that due to environmental concerns that they would most likely not be interested in producing a ballast material. In the United States carbonate aggregates, while used for ballast, many times don't meet the ballast specifications in addition to the problem of particle degradation that can lead to fouling and cementation issues. Thus, many carbonate aggregate quarries in close proximity to railroads are not used. Since Michigan has a significant amount of carbonate quarries, the research also investigated using the dynamic properties of aggregate as a possible additional test for aggregate ballast quality. The dynamic strength of a material can be assessed using a split Hopkinson Pressure Bar (SHPB). The SHPB has been traditionally used to assess the dynamic properties of metal but over the past 20 years it is now being used to assess the dynamic properties of brittle materials such as ceramics and rock. In addition, the wear properties of metals have been related to their dynamic properties. Wear or breakdown of railroad ballast materials is one of the main problems with ballast material due to the dynamic loading generated by trains and which will be significantly higher for high speed rails. Previous research has indicated that the Port Inland quarry along Lake Michigan in the Southern Upper Peninsula has significant dynamic properties that might make it potentially useable as an aggregate for high speed rail. The dynamic strength testing conducted in this research indicate that the Port Inland limestone in fact has a dynamic strength close to igneous rocks and much higher than other carbonate rocks in the Great Lakes region. It is recommended that further research be conducted to investigate the Port Inland limestone as a high speed ballast material.

Finite element study on fracture patterns in human scaphoid wrist bone due to free fall

Scaphoid is one of the 8 carpal bones found adjacent to the thumb supported proximally by Radius bone. During the free fall, on outstretched hand, the impact load gets transferred to the scaphoid at its free anterior end. Unique arrangement of other carpal bones in the palm is also one of the reasons for the load to get transferred to scaphoid. About half of the total load acting upon carpal bone gets transferred to scaphoid at its distal pole. There are about 10 to 12 clinically observed fracture pattern in the scaphoid due to free fall. The aim of the study is to determine the orientation of the load, magnitude of the load and the corresponding fracture pattern. This study includes both static and dynamic finite element models validated by experiments. The scaphoid model has been prepared from CT scans of a 27 year old person. The 2D slices of the CT scans have been converted to 3D model by using MIMICS software. There are four cases of loading studied which are considered to occur clinically more frequently. In case (i) the load is applied at the posterior end at distal pole whereas in case (ii), (iii) and (iv), the load is applied at anterior end at different directions. The model is given a fixed boundary condition at the region which is supported by Radius bone during the impact. Same loading and boundary conditions have been used in both static and dynamic explicit finite element analysis. The site of fracture initiation and path of fracture propagation have been identified by using max principal stress / gradient and max principal strain / gradient criterion respectively in static and dynamic explicit finite element analysis. Static and dynamic impact experiments were performed on the polyurethane foam specimens to validate the finite element results. Experimental results such as load at fracture, site of fracture initiation and path of fracture propagation have been compared with the results of finite element analysis. Four different types of fracture patterns observed in clinical studies have been identified in this study.

Synthesis of computations and experiments for obtaining pulsatile gas flow rates from dynamic pressure difference measurements across an orifice-plate meter

The use of conventional orifice-plate meter is typically restricted to measurements of steady flows. This study proposes a new and effective computational-experimental approach for measuring the time-varying (but steady-in-the-mean) nature of turbulent pulsatile gas flows. Low Mach number (effectively constant density) steady-in-the-mean gas flows with large amplitude fluctuations (whose highest significant frequency is characterized by the value fF) are termed pulsatile if the fluctuations have a direct correlation with the time-varying signature of the imposed dynamic pressure difference and, furthermore, they have fluctuation amplitudes that are significantly larger than those associated with turbulence or random acoustic wave signatures. The experimental aspect of the proposed calibration approach is based on use of Coriolis-meters (whose oscillating arm frequency fcoriolis >> fF) which are capable of effectively measuring the mean flow rate of the pulsatile flows. Together with the experimental measurements of the mean mass flow rate of these pulsatile flows, the computational approach presented here is shown to be effective in converting the dynamic pressure difference signal into the desired dynamic flow rate signal. The proposed approach is reliable because the time-varying flow rate predictions obtained for two different orifice-plate meters exhibit the approximately same qualitative, dominant features of the pulsatile flow.

Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

Dynamic properties of wood using the Split-Hopkinson Pressure Bar

Strain rate significantly affects the strength of a material. The Split-Hopkinson Pressure Bar (SHPB) was initially used to study the effects of high strain rate (~103 1/s) testing of metals. Later modifications to the original technique allowed for the study of brittle materials such as ceramics, concrete, and rock. While material properties of wood for static and creep strain rates are readily available, data on the dynamic properties of wood are sparse. Previous work using the SHPB technique with wood has been limited in scope to variability of only a few conditions and tests of the applicability of the SHPB theory on wood have not been performed. Tests were conducted using a large diameter (3.0 inch (75 mm)) SHPB. The strain rate and total strain applied to a specimen are dependent on the striker bar length and velocity at impact. Pulse shapers are used to further modify the strain rate and change the shape of the strain pulse. A series of tests were used to determine test conditions necessary to produce a strain rate, total strain, and pulse shape appropriate for testing wood specimens. Hard maple, consisting of sugar maple (Acer saccharum) and black maple (Acer nigrum), and eastern white pine (Pinus strobus) specimens were used to represent a dense hardwood and a low-density soft wood. Specimens were machined to diameters of 2.5 and 3.0 inches and an assortment of lengths were tested to determine the appropriate specimen dimensions. Longitudinal specimens of 1.5 inch length and radial and tangential specimens of 0.5 inch length were found to be most applicable to SHPB testing. Stress/strain curves were generated from the SHPB data and validated with 6061-T6 aluminum and wood specimens. Stress was indirectly corroborated with gaged aluminum specimens. Specimen strain was assessed with strain gages, digital image analysis, and measurement of residual strain to confirm the strain calculated from SHPB data. The SHPB was found to be a useful tool in accurately assessing the material properties of wood under high strain rates (70 to 340 1/s) and short load durations (70 to 150 μs to compressive failure).