Shear rupture nucleation and dynamic propagation is a challenging, non- linear, highly interactive process with important practical implications. Here we focus on two aspects of this problem: propagation speeds and shock front radiation from the dynamic crack tip as well as nucleation of dynamic rupture due to fluid injection.
Spontaneously propagating cracks in solids emit pressure and shear waves and are, in part, driven by energy transfer due to them. When a shear crack propagates faster than the shear wave speed of the material, the coalescence of the shear wavelets emitted by the near-crack-tip region forms a shock front that significantly concentrates particle motion. The equivalent scenario involving a pressure shock front should not be possible, since cracks should not be able to exceed the pressure wave speed, at least in an isotropic linear-elastic solid. Here we present full-field experimental evidence of dynamic shear cracks in viscoelastic polymers that result in the formation of a pressure shock front, in addition to the shear one. In that sense, the crack appears to be supersonic. The apparent violation of classic theories is explained by the strain-rate-dependent material behavior of polymers: the increased wave speeds within the highly- strained region around the crack tip allow for supersonic crack propagation with respect to the (lower) wave speeds at short distances away from the interface, resulting in the formation of the pressure shock front. The crack speed remains below the pressure wave speed prevailing locally, about its tip, in agreement with basic physics and energy considerations of linear-elastic theories.
We find that the shock fronts emitted by the shear cracks in the viscoelastic materials are curved and propose a novel method to quantify the viscoelastic wave speeds of the solids in the dynamic range of strain rates based on the curvature. Only kinematic relationships are used in the method, without the need for the constitutive relationship of the material. Measuring or inferring the material properties at elevated strain rates in viscoelastic solids is a difficult task, because of practical limitations of obtaining accurate measurements in that regime. Under the quasi-elastic solid approximation, in which the strain-rate history is neglected, we use the pressure-wave speed measurements to infer the associated value of the Young’s modulus, estimated by assuming a constant value of the Poisson’s ratio. We complement these results with the characterization of the Young’s modulus at lower strain rates via canonical compressive tests. Our results not only confirm previous findings that the Young’s modulus dependence on the strain rate in PMMA is significant but also demonstrate that its variation is more pronounced in the dynamic strain-rate range, with important consequences for the design of structures employing viscoelastic materials that are required to withstand elevated strain rates.
The second part of the study concentrates on the nucleation of shear dynamic rupture due to fluid injection or, more broadly, on the interaction of frictional faulting with fluids. Fluid overpressure is recognized to play a fundamental role in promoting fault motion. A large number of observations has shed light on the interplay between fluids and faulting, both in natural events and in earth-quakes induced by human activities, such as wastewater disposal associated with oil and gas extraction. Fluids can induce a variety of earthquake source behaviors ranging from unstable, dynamic motions to stable, quasi-static ones, which a number of field studies suggests that can coexist on the same fault areas at different times, depending on the local conditions. In fact, a higher pore pres-sure plays the dual role of reducing the frictional strength of the fault and of increasing the nucleation size, e.g., the critical length for a shear crack to transition from quasi-static to dynamic motions. However, due to the complexity of the frictional problem at the fault interface, the understanding of which of these two effects prevails remains elusive. The assumption of a critical nucleation length represents a powerful, yet simplified concept, which currently does not include the dependence on the rate of the pore pressure increase.
Here, we explore the effect of the rate of the pore pressure increase on the rupture nucleation. We find that elevated injection rates induce triggering of the rupture at lower pressure values and minimal volumes of the injected fluid, if compared to slow injection rates. For the slow injection rates, we experimentally observe a much larger portion of interface wetted by the fluid and a phase of accelerated slip prior to the dynamic event (quasi-dynamic nucleation process). In some cases, we record much smaller foreshock-like events at the injection site. These findings suggest the presence of a prominent quasi-static nucleation process over the interface. In cases of rapid pore pressure increase, the nucleation process is much shorter in time and much more compact in space, being highly concentrated around the injection location. The dynamic events, once initiated, are qualitatively similar across different injection rates, but quantitatively different, with the slow-injection ones experiencing higher stress drops and higher slips, perhaps due to the effect of fluids on the friction properties. These findings suggest the need to develop nucleation size estimates that include the rate of the pore pressure increase and motivate further investigation of how friction properties depend on the presence of fluids. The details of the obtained experimental findings, once analyzed through numerical modeling, will place important constrains on the forms of the acceptable friction laws, including the effects of pore fluid pressure and its rate of change.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/Z9J96497, author = {Gabuchian, Vahe}, title = {Experimental Investigation of Thrust Fault Rupture Mechanics}, school = {California Institute of Technology}, year = {2015}, doi = {10.7907/Z9J96497}, url = {https://resolver.caltech.edu/CaltechTHESIS:04222014-195027916}, abstract = {Thrust fault earthquakes are investigated in the laboratory by generating dynamic shear ruptures along pre-existing frictional faults in rectangular plates. A considerable body of evidence suggests that dip-slip earthquakes exhibit enhanced ground motions in the acute hanging wall wedge as an outcome of broken symmetry between hanging and foot wall plates with respect to the earth surface. To understand the physical behavior of thrust fault earthquakes, particularly ground motions near the earth surface, ruptures are nucleated in analog laboratory experiments and guided up-dip towards the simulated earth surface. The transient slip event and emitted radiation mimic a natural thrust earthquake. High-speed photography and laser velocimeters capture the rupture evolution, outputting a full-field view of photo-elastic fringe contours proportional to maximum shearing stresses as well as continuous ground motion velocity records at discrete points on the specimen. Earth surface-normal measurements validate selective enhancement of hanging wall ground motions for both sub-Rayleigh and super-shear rupture speeds. The earth surface breaks upon rupture tip arrival to the fault trace, generating prominent Rayleigh surface waves. A rupture wave is sensed in the hanging wall but is, however, absent from the foot wall plate: a direct consequence of proximity from fault to seismometer. Signatures in earth surface-normal records attenuate with distance from the fault trace. Super-shear earthquakes feature greater amplitudes of ground shaking profiles, as expected from the increased tectonic pressures required to induce super-shear transition. Paired stations measure fault parallel and fault normal ground motions at various depths, which yield slip and opening rates through direct subtraction of like components. Peak fault slip and opening rates associated with the rupture tip increase with proximity to the fault trace, a result of selective ground motion amplification in the hanging wall. Fault opening rates indicate that the hanging and foot walls detach near the earth surface, a phenomenon promoted by a decrease in magnitude of far-field tectonic loads. Subsequent shutting of the fault sends an opening pulse back down-dip. In case of a sub-Rayleigh earthquake, feedback from the reflected S wave re-ruptures the locked fault at super-shear speeds, providing another mechanism of super-shear transition.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/V3A7-7686, author = {Mihaly, Jonathan Michael}, title = {Investigation of Hypervelocity Impact Phenomena Using Real-time Concurrent Diagnostics}, school = {California Institute of Technology}, year = {2013}, doi = {10.7907/V3A7-7686}, url = {https://resolver.caltech.edu/CaltechTHESIS:06072013-143355354}, abstract = {Hypervelocity impact of meteoroids and orbital debris poses a serious and growing threat to spacecraft. To study hypervelocity impact phenomena, a comprehensive ensemble of real-time concurrently operated diagnostics has been developed and implemented in the Small Particle Hypervelocity Impact Range (SPHIR) facility. This suite of simultaneously operated instrumentation provides multiple complementary measurements that facilitate the characterization of many impact phenomena in a single experiment. The investigation of hypervelocity impact phenomena described in this work focuses on normal impacts of 1.8 mm nylon 6/6 cylinder projectiles and variable thickness aluminum targets. The SPHIR facility two-stage light-gas gun is capable of routinely launching 5.5 mg nylon impactors to speeds of 5 to 7 km/s. Refinement of legacy SPHIR operation procedures and the investigation of first-stage pressure have improved the velocity performance of the facility, resulting in an increase in average impact velocity of at least 0.57 km/s. Results for the perforation area indicate the considered range of target thicknesses represent multiple regimes describing the non-monotonic scaling of target perforation with decreasing target thickness. The laser side-lighting (LSL) system has been developed to provide ultra-high-speed shadowgraph images of the impact event. This novel optical technique is demonstrated to characterize the propagation velocity and two-dimensional optical density of impact-generated debris clouds. Additionally, a debris capture system is located behind the target during every experiment to provide complementary information regarding the trajectory distribution and penetration depth of individual debris particles. The utilization of a coherent, collimated illumination source in the LSL system facilitates the simultaneous measurement of impact phenomena with near-IR and UV-vis spectrograph systems. Comparison of LSL images to concurrent IR results indicates two distinctly different phenomena. A high-speed, pressure-dependent IR-emitting cloud is observed in experiments to expand at velocities much higher than the debris and ejecta phenomena observed using the LSL system. In double-plate target configurations, this phenomena is observed to interact with the rear-wall several micro-seconds before the subsequent arrival of the debris cloud. Additionally, dimensional analysis presented by Whitham for blast waves is shown to describe the pressure-dependent radial expansion of the observed IR-emitting phenomena. Although this work focuses on a single hypervelocity impact configuration, the diagnostic capabilities and techniques described can be used with a wide variety of impactors, materials, and geometries to investigate any number of engineering and scientific problems.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/DJDD-2487, author = {Mello, Michael}, title = {Identifying the Unique Ground Motion Signatures of Supershear Earthquakes: Theory and Experiments}, school = {California Institute of Technology}, year = {2012}, doi = {10.7907/DJDD-2487}, url = {https://resolver.caltech.edu/CaltechTHESIS:06072012-032023169}, abstract = {The near-field ground motion signatures associated with sub-Rayleigh and supershear ruptures are investigated using the laboratory earthquake experiment originally developed by Rosakis and co-workers (Xia et al., 2004, 2005a; Lu et al., 2007; Rosakis et al., 2007). Heterodyne laser interferometers enable continuous, high-bandwidth measurements of fault-normal (FN), fault-parallel (FP), and vertical (V) particle velocity ``ground motion" records at discrete locations on the surface of a Homalite-100 test specimen as a sub-Rayleigh or a supershear rupture sweeps along the frictional fault. Photoelastic interference fringes, acquired using high-speed digital photography, provide a synchronized, spatially resolved, whole field view of the advancing rupture tip and surrounding maximum shear stress field.
The first phase of experimental investigations examine and verify the ground motion signatures of supershear ruptures. Experimental results demonstrate that a shear Mach front produced by a stable supershear rupture is characterized by a dominant FP velocity component. The situation is shown to reverse in the sub-Rayleigh rupture speed regime whereby the FN particle velocity component dominates the ground motion record. Additional distinguishing particle velocity signatures, consistent with theoretical and numerical predictions, and repeatedly observed in experimental records are, (1) a pronounced peak in the FP velocity record induced by the leading dilatational field, which sweeps the measurement station in advance of the shear Mach front, and (2) a pronounced velocity swing in the FN record associated with the arrival of a trailing Rayleigh sub-Rayleigh (secondary) rupture, which follows the arrival of the shear Mach front. Analysis of the particle velocity records also confirms 2D steady-state theoretical predictions pertaining to the separation, attenuation, and radiation partitioning of the shear and dilatational portions of the rupture velocity field components.
The second phase of our experimental investigations re-examine the 2002, Mw7.9, Denali fault earthquake and the remarkable set of near-source ground motion records obtained at (PS10), located approximately 85 km east of the epicenter and just 3 km north of the fault along the Alaska pipeline. Motivated by the analysis and interpretation of these records by (Ellsworth et al., 2004; Dunham and Archuleta, 2004, 2005), we attempt to mimic the Denali strike-slip rupture scenario and replicate the PS10 ground motion signatures using a laboratory earthquake experiment. The experiments feature a left-to-right (west-to-east) propagating right lateral rupture within a Homalite-100 test specimen with particle velocity data collected at a near-field station situated just above (north of) the fault. Both sub-Rayleigh and supershear laboratory earthquake experiments are conducted using the Denali PS10 configuration in order to compare and contrast the resulting particle velocity signatures. Supershear laboratory records capture all of the prominent features displayed within the PS10 ground motion records. Noted velocity signatures are correlated to the location of the rupture fronts and their noted arrival times in the synchronized photoelastic image sequence. Scaling relationships are also presented which transform the laboratory records through six orders of magnitude in time, to match the scale of the PS10 ground motion records. The strong correlation between the scaled experimental records and the actual PS10 ground motion records support the hypothesis that the Denali strike-slip fault exhibited a supershear burst.
Finally, we present a 2D steady state, stress-velocity formulation that relates the FP and FN particle velocity records measured close to the fault, to the evolution of the stress tensor at the same location. A locally steady-state condition is assumed within a restricted time interval in order to invoke these relationships and estimate the dynamic stresses, σxx(t) and τ(t), at the near-fault station. Dynamic stress measurements enable a new class of friction investigations using the laboratory earthquake configuration. Experimental findings are presented, which capture the temporal and spatial distributions of σxx and τ, evolution of the dynamic friction coefficient, and velocity weakening behavior of a supershear slip-pulse.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/AQJH-3D60, author = {Lamberson, Leslie Elise}, title = {Dynamic Optical Investigations of Hypervelocity Impact Damage}, school = {California Institute of Technology}, year = {2010}, doi = {10.7907/AQJH-3D60}, url = {https://resolver.caltech.edu/CaltechTHESIS:05282010-183132978}, abstract = {One of the prominent threats in the endeavor to develop next-generation space assets is the risk of space debris impact in earth’s orbit and micrometeoroid impact damage in near-earth orbit and deep space. To date, there is no study available which concentrates on the analysis of dynamic crack growth from hypervelocity impacts on such structures, resulting in their eventual catastrophic degradation. Experiments conducted using a unique two-stage light-gas gun facility have examined the in situ dynamic fracture of brittle polymers subjected to this high-energy-density event. Optical techniques of caustics and photoelasticity, combined with high-speed photography up to 100 million frames per second, analyze crack growth behavior of Mylar and Homalite 100 thin plates after impact by a 1.8 mm diameter nylon 6-6 right cylindrical slug at velocities ranging from 3 to 7 km/s (7000–15500 mph). Crack speeds in both polymers averaged between 0.2 and 0.47 cR, the Rayleigh wave speed (450–1000 mph). Shadow spots and surrounding caustics reveal time histories of the dynamic stress intensity factor, as well as the energy release rate ahead of the mode-I, or opening, crack tips. Results indicate that even under extreme impact conditions of out of-plane loading, highly localized heating, and energetic impact phenomena involving plasma formation and ejecta, the dynamic fracture process occurs during a deformation regime dominated by in-plane loading. These findings imply that the reliability of impacted, thin-walled, plate and shell space structures, idealized by the experimental configuration investigated, can be predicted by the well defined principles of classical dynamic fracture mechanics.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/BGGT-MC04, author = {Lu, Xiao}, title = {Combined Experimental and Numerical Study of Spontaneous Dynamic Rupture on Frictional Interfaces}, school = {California Institute of Technology}, year = {2009}, doi = {10.7907/BGGT-MC04}, url = {https://resolver.caltech.edu/CaltechETD:etd-10242008-070701}, abstract = {The process of spontaneous dynamic frictional sliding along the interface of two elastic solids is of great interest to a number of disciplines in engineering and sciences. Applications include frictional rupture processes in earthquakes, delamination of layered composite materials, and sliding between soft membranes in biological systems. The transient nature of rupture dynamics presents an array of fascinating yet challenging questions, including the nucleation process, the mechanism of interface failure, and the speed and mode of rupture propagation.
This thesis presents such a combined experimental and theoretical study aimed at understanding the conditions for selecting pulse-like vs. crack-like rupture modes and subshear vs. supershear rupture speeds. There are two major contributions in this work. The first one is high-resolution experimental study of the rupture modes on a frictional interface. The study presents first experimental observations of spontaneous pulse-like ruptures in a homogeneous linear-elastic setting that mimics crustal earthquakes, reveals how different rupture modes are selected based on the level of fault prestress, demonstrates that both rupture modes can transition to supershear speeds, and advocates, based on comparison with theoretical studies, importance of velocity-weakening friction for earthquake dynamics. The second major contribution is the numerical modeling of the rupture experiments that reveal the importance of the rupture nucleation mechanism and friction formulations. The modeling of sub-Rayleigh to supershear transition has demonstrated the influence of rupture nucleation mechanism on supershear transition distance, as well as on the mechanism of supershear transition. The modeling of pulse-like to crack-like rupture mode transition has confirmed the necessity of velocity weakening friction for producing pulse-like rupture to match the experimental observations.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Lapusta, Nadia and Rosakis, Ares J.}, } @phdthesis{10.7907/9GD9-A088, author = {Brown, Michal Amaris}, title = {Measuring Stress in Thin-Film - Substrate Systems Featuring Spatial Nonuniformities of Film Thickness and/or Misfit Strain}, school = {California Institute of Technology}, year = {2007}, doi = {10.7907/9GD9-A088}, url = {https://resolver.caltech.edu/CaltechETD:etd-06042007-171342}, abstract = {
It is very important to be able to accurately determine the film stress distribution in a thin film structure, since stress can lead directly to failure and as such is intimately related to reliability and process yield. The most common way of inferring film stress caused by a given process is by measuring system curvature before and after the process; the change in curvature is directly related to the stress caused by that process, usually through the Stoney formula. This formula was derived based on a number of restrictive assumptions. Two of these are the assumptions of a spatially uniform film thickness and a spatially uniform misfit strain; taken together, these assumptions imply constant curvature and film stress over the entire wafer. In practice, these conditions are rarely met, and yet the Stoney formula is still the film stress measurement standard.
Recently, extensions to this formula were derived which allow for spatial non-uniformities in film thickness and misfit strain. The resulting Stoney-like relations which relate film stress and wafer curvature, known as the HR relations, require knowledge of not only the curvature at a single point, but also full-field curvature information. In this work, the HR relations are verified by comparison with X-ray microdiffraction. Two independent XRD measurements are used; one measures substrate curvature and the other determines film stress. Since these measurements are independent, the substrate curvature data are used as an input to the Stoney and HR stress/curvature relations. The resulting film stresses are then compared with XRD film stress data. From this, it is established that the HR relations result in substantially more accurate film stress predictions than does the Stoney analysis.
Next, a full-field curvature measurement technique, Coherent Gradient Sensing, is introduced as an ideally suited measurement tool for inferring film stress through the HR analysis. CGS measurements are taken of several progressively more interesting test wafers and the curvature is used through the HR relations to determine film stress.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/0CCJ-5S66, author = {Lykotrafitis, Georgios C.}, title = {Experimental Study of Dynamic Frictional Sliding Modes along Incoherent Interfaces}, school = {California Institute of Technology}, year = {2006}, doi = {10.7907/0CCJ-5S66}, url = {https://resolver.caltech.edu/CaltechETD:etd-01162006-005552}, abstract = {Dynamic sliding along incoherent (frictional) interfaces is investigated experimentally in a microsecond time scale. A bimaterial system comprised of Homalite and steel plates and a homogeneous system consisting of two Homalite plates are considered. The plates are held together by a uniform compressive stress while dynamic sliding is initiated by an impact-induced shear loading. The evolution of maximum shear stress contours is recorded by high-speed photography in conjunction with dynamic photoelasticity. Simultaneously with photoelasticity, a newly-developed technique based on laser interferometry is employed to locally measure the sliding speed at the interface.
The response of the Homalite-steel bimaterial system differs according to whether the impact loading is applied to the Homalite plate or to the steel plate. In the first case, a disturbance traveling along the interface at a constant speed close to the Rayleigh wave speed of steel generates a shear Mach line crossing the P-wave front. Sliding initiates behind the P-wave front in the Homalite plate and it propagates at a supershear speed with respect to the shear wave speed of Homalite. A disturbance, traveling at constant speeds between the shear wave speed and the longitudinal wave speed of Homalite, appears behind the sliding tip. Wrinkle-like opening pulses, propagating along the bimaterial interface at a constant speed between the Rayleigh wave and the shear wave speed of Homalite, are also observed. When the impact loading is applied to the steel plate, sliding at a given point initiates with the arrival of the P-wave front there, so that the rupture is sonic with respect to steel and supersonic with respect to Homalite.
In all the experiments performed on the bimaterial structure (Homalite-steel), sliding always occurred in a crack-like mode. In the case of a homogeneous system of Homalite plates however, direct physical evidence of different modes of sliding is recorded. Crack-like sliding, pulse-like sliding and mixed mode sliding in the form of pulses followed by a crack are discovered. Supersonic trailing pulses are also recorded. Behind the sliding tip, wrinkle-like opening pulses are developed for a wide range of impact speeds and confining stresses.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/WQQX-6Q19, author = {Xia, Kaiwen}, title = {Laboratory Investigations of Earthquake Dynamics}, school = {California Institute of Technology}, year = {2005}, doi = {10.7907/WQQX-6Q19}, url = {https://resolver.caltech.edu/CaltechETD:etd-02262005-161824}, abstract = {
Earthquake represents one of most destructive geological hazards. In this thesis I will attempt to understand it through controlled laboratory experiments. The earthquake dynamic rupturing process itself is a complicated phenomenon, involving dynamic friction, wave propagation, and heat production. Because controlled experiments can produce results without assumptions needed in theoretical and numerical analysis, the experimental method is thus advantageous over theoretical and numerical methods.
Our laboratory fault is composed of carefully cut photoelastic polymer plates (Homalite-100, Polycarbonate) held together by uniaxial compression. As a unique unit of the experimental design, a controlled exploding wire technique provides the triggering mechanism of laboratory earthquakes. Three important components of real earthquakes (i.e., pre-existing fault, tectonic loading, and triggering mechanism) correspond to and are simulated by frictional contact, uniaxial compression, and the exploding wire technique. Dynamic rupturing processes are visualized using the photoelastic method and are recorded via a high-speed camera. Our experimental methodology, which is full-field, in situ, and non-intrusive, has better control and diagnostic capacity compared to other existing experimental methods.
Using this experimental approach, we have investigated several problems: dynamics of earthquake faulting occurring along homogeneous faults separating identical materials, earthquake faulting along inhomogeneous faults separating materials with different wave speeds, and earthquake faulting along faults with a finite low wave speed fault core. We have observed supershear ruptures, rupture speed transition, directionality of rupture in faults with a material contrast, self-healing slip pulses in faults with a finite core, crack-like to pulse-like rupture transition in faults with a finite core.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J. and Kanamori, Hiroo}, } @phdthesis{10.7907/wver-8342, author = {Xu, Luoyu Roy}, title = {Dynamic Failure Characteristics in Layered Materials and Structures}, school = {California Institute of Technology}, year = {2002}, doi = {10.7907/wver-8342}, url = {https://resolver.caltech.edu/CaltechTHESIS:04252011-111825843}, abstract = {Systematic investigations were carried out to understand the general nature of dynamic failure mechanisms in layered materials and structures such as composite and sandwich structures, thin films, layered armors and layered rock. A series of impact experiments on model-layered specimens were conducted using high-speed photography and dynamic photoelasticity. For the first time, the sequence and interaction of two major dynamic failure modes in layered materials-inter-layer cracking and intra-layer cracking were revealed in real time. For heterogeneous three-layer systems, shear-dominated inter-layer cracking was always the first failure event for specimens subjected to low-speed impact. Interlayer cracking generally nucleated from interfacial locations where the inter-layer shear stress acquired a local maximum. Depending on impact speed and bond strength characteristics, inter-layer cracks were very transient and often became intersonic even under moderate impact speeds. Intra-layer cracking always initiated after the development of inter-layer cracks as a result of inter-layer crack kinking into the adjacent layer. The resulting intra-layer mode I cracks often accelerated and branched as they attained high speeds, causing core layer fragmentation. For homogenous-layered systems composed of bonded layers of Homalite, intra-layer cracks appeared in the form of cracks radiating from the impact site. As soon as these cracks approached an interface, interlayer cracks were often induced depending on the angle between the crack path and the interface. Direct experimental evidence of the dynamic equivalent of “Cook-Gordon mechanism” was recorded, i.e., two intersonic interfacial cracks nucleated and propagated along the interface before a fan of mode I incident cracks was ever able to reach the interface. Also, significant dependence of the failure characteristics on impact speeds and interfacial strengths was found. For the heterogeneous three-layer system subjected to a high impact speed, two clear shear shock waves associated with the intersonic inter-layer cracks were observed at the specimen center. Shock waves were also observed along the interface in heterogeneous three-layer systems featuring weak and ductile bonds. The impact momentum and loading duration were identified as two important parameters in damage spreading for a given impact energy. Motivated by the experimental observations of crack deflection/penetration at an interface, a novel wedge-loaded impact specimen was designed to explore the basic mechanics nature of this phenomenon. The deflection/penetration behavior of an incoming dynamic crack at an interface was found to depend on the interfacial angle and the interfacial fracture toughness. A dynamic fracture model, together with an energy criterion, were proposed and were found to agree reasonably well with the experimental observations.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/NHZS-D271, author = {Anderson, David Deloyd}, title = {Experimental Investigation of Quasistatic and Dynamic Fracture Properties of Titanium Alloys}, school = {California Institute of Technology}, year = {2002}, doi = {10.7907/NHZS-D271}, url = {https://resolver.caltech.edu/CaltechETD:etd-02112002-153745}, abstract = {The goal of this work is to investigate the quasistatic and dynamic fracture properties of three titanium alloys: 6Al-4V titanium, 6Al-4V titanium ELI, and Timetal 5111. While standard tests exist for measuring quasistatic fracture toughness, the dynamic investigation requires that several measurement techniques are employed including Coherent Gradient Sensing (CGS), Crack Opening Displacement (COD), and the use of strain gages. The use of these methods with difficult engineering materials in the dynamic loading regime requires methodologies to be advanced beyond that previously required with model materials having properties ideal for experimental measurements techniques.
After a description of each measurement technique is given, stress intensity factor measurements made on 12.7 mm thick pre-cracked 6Al-4V titanium specimens are compared. These specimens were dynamically impacted in three point bend in a drop weight tower. Specimens with and without side-grooves were tested as each measurement technique allows. Side-grooves are useful to increase the degree of plane strain experienced in proximity of the crack tip, allowing plane strain (geometry independent) fracture toughnesses to be obtained from specimens that may be otherwise too thin in cross section. Resulting stress intensity factor-time histories from the different techniques are compared to verify that their results mutually agree.
Advancements in employing CGS, a shearing interferometric technique, are described in more detail. First, the analysis of CGS interferograms is extended to allow experimental fringe data to be fit to very general analytical asymptotic crack tip solution to determine mixed mode stress intensity factors. As formulated in this work, the CGS technique can be used to measure stress intensity factors for non-uniformly propagating dynamic mixed mode cracks moving along arbitrary paths in homogeneous linear elastic isotropic materials. Other advancements are also detailed which improve analysis accuracy, objectivity, and efficiency.
Finally, with the equivalence of the three measurement technique results established, tests were performed on 8–17 mm thick pre-cracked three point bend specimens of the three materials to measure critical stress intensity values for crack initiation. Side-grooves are necessary for the more ductile 6Al-4V titanium ELI and Timetal 5111 materials to obtain plane strain fracture toughness values. It is found that both the 6Al-4V titanium ELI and Timetal 5111 alloys are 50-70% tougher than the 6Al-4V titanium, and for all three materials their initiation toughness does not vary significantly with loading rate over the domain tested.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/3w5m-qb27, author = {Guduru, Pradeep Reddy}, title = {An investigation of dynamic failure events in steels using full field high-speed infrared thermography and high-speed photography}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/3w5m-qb27}, url = {https://resolver.caltech.edu/CaltechETD:etd-11052003-085740}, abstract = {An infrared (IR) imaging system has been developed recently at Caltech for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8x8 HgCdTe focal plane array, with 64 parallel preamplifiers. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. Crack tip temperature rise during dynamic deformation is known to alter the fracture mechanisms and consequently the fracture toughness of a material. However, no direct experimental measurements have ever been made to determine the same because of limited diagnostic tools. Further, the temperature rise in the vicinity of the crack tip could potentially be used as a direct measure of loading and could serve as a diagnostic tool in order to extract appropriate fracture parameters. By transcending the existing experimental limitations, this investigation presents detailed, real time evolution of the transient crack tip temperature fields in two different steels (C300 and HY100 steels), using the 2-D high speed IR camera. The crack tip temperature rise at initiation in C300 steel was found to be about 55K. In case of HY100, the crack tip temperature rise was above 90K and was seen to be a strong function of loading rate. HRR elastic-plastic singular field has been used to extract J integral evolution from the measured temperature field. Critical value of J integral at initiation was seen to increase with loading rate. An experimental investigation has been conducted to study the initiation and propagation characteristics of dynamic shear bands in C300 maraging steel. Pre-fatigued single edge notched specimens were impacted on the edge under the notch to produce shear dominated mixed mode stress fields. The optical technique of coherent gradient sensing (CGS) was employed to study the evolution of the mixed mode stress intensity factors. Simultaneously, the newly developed 2-D high speed infrared (IR) camera was employed to obtain the temperature field evolution during the initiation and propagation of the shear bands. A criterion for shear band initiation is proposed in terms of a critical mode II stress intensity factor. The IR images, for the first time, revealed the transition of crack tip plastic zone into a shear band and also captured the structure of the tip of a propagating shear band. These thermographs support the notion of a diffuse shear band tip and reveal “hot spots” distributed along the length of a well developed shear band.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/745f-mb29, author = {Chow, Benjamin Bin}, title = {Application of dynamic fracture mechanics to the investigation of catastrophic failure in aircraft structures}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/745f-mb29}, url = {https://resolver.caltech.edu/CaltechETD:etd-08112005-103246}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. A dynamic fracture mechanics approach to the estimation of the residual strength of aircraft structures is presented. The dependence of the dynamic crack initiation toughness of aluminum 2024-T3 on loading rate is first studied experimentally. A drop of up to 40% in the value of dynamic initiation toughness, […], is discovered for loading rates in the range of […]. This range of loading rate corresponds to the typical rates found in an aircraft fuselage experiencing explosive loading conditions. A dramatic increase in the value of dynamic crack initiation toughness is also found for loading rates above […]. Based on these results and on established dynamic fracture mechanic concepts, a fracture mechanics based failure model is established and is used to estimate the residual strength of aircraft structures. A methodology to determine residual strength of dynamically loaded structures based on global structural analysis coupled with local finite element analysis is introduced. Local finite element calculations were performed for different loading rates, […], ranging from […] to […], to simulate the conditions encountered in an explosively loaded aircraft fuselage. Simulations were conducted at a number of loading rates for the following cases of relevance to aircraft fuselage: (i) center cracked panels, (ii) rivet holes with wing cracks, (iii) biaxially loaded panels and (iv) panels prestressed to simulate pressurization. The results from the analyses were then used in conjunction with the experimental results for the dynamic fracture toughness of a 2024-T3 aluminum alloy as a function of loading rate, […], to determine the time to failure, […], for a given loading rate. A failure envelope, […], based on the failure model and finite element analysis, is presented for the different cases and the implications for the residual strength of aircraft structures is discussed. Mixed mode dynamic crack initiation in aluminum 2024-T3 alloy is investigated by combining experiments with numerical simulations. Pre-fatigued single edge notched specimens and three point bend specimens are subjected to dynamic symmetric and asymmetric loading to generate a range of mode mixity at the cracktip. The optical technique of coherent gradient sensing (CGS) and a strain gage method are employed to study the evolution of the mixed mode stress intensity factors. The dynamic mixed mode failure envelope is obtained using the crack initiation data from the experiments at a nominal loading rate of […] and is compared with the static counterpart for 2024-T3 aluminum alloy. The fracture surfaces near the crack initiation site are investigated using a scanning electron microscope and reveal ductile void growth and coalescence. Numerical simulations of the experiments are conducted to both help in designing the experiments and to validate the results of the experiments. The numerical simulations show good correlation with the experimental results.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J. and Ravichandran, Guruswami}, } @phdthesis{10.7907/yrm2-4b88, author = {Coker, Demirkan}, title = {Dynamic Initiation and Propagation of Cracks in Unidirectional Composite Plates}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/yrm2-4b88}, url = {https://resolver.caltech.edu/CaltechTHESIS:10112010-152127073}, abstract = {Dynamic crack growth along weak planes is a significant mode of failure in composites and other layered/sandwiched structures and is also the principal mechanism of shallow crustal earthquakes. In order to shed light on this phenomenon dynamic crack initiation and propagation characteristics of a model fiber-reinforced unidirectional graphite/epoxy composite plate was investigated experimentally. Dynamic fracture experiments were conducted by subjecting the composite plates to in-plane, symmetric and asymmetric, impact loading. The lateral shearing interferometric technique of coherent gradient sensing (CGS) in conjunction with high-speed photography was used to visualize the failure process in real time. It was found that mode-I cracks propagated subsonically with crack speeds increasing to the neighborhood of the Rayleigh wave speed of the composite. Also in mode-I, the dependence of the dynamic initiation fracture toughness on the loading rate was determined and was found to be constant for low loading rates and to increase rapidly above K̇dI > 10⁵. The dynamic crack propagation toughness, KID, was observed to decrease with crack tip speed up to the Rayleigh wave speed of the composite.
For asymmetric, mode-II, types of loading the results revealed highly unstable and intersonic shear-dominated crack growth along the fibers. These cracks propagated with unprecedented speeds reaching 7400 m/s which is the dilatational wave speed of the composite along the fibers. For intersonic crack growth, the interferograms featured a shock wave structure typical of disturbances traveling with speeds higher than one of the characteristic wave speeds in the solid. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating non-uniform crack face frictional contact. In addition, shear dominated dynamic crack growth is investigated along composite/Homalite interfaces subjected to impact loading. The crack growth phenomenon was observed usivvvvng dynamic photoelasticity in conjunction with high-speed photography. Three quantized intersonic and supersonic crack tip speed regimes were identified. First conclusive evidence of crack growth at supersonic speeds with respect to lower speed material and sonic speeds with respect to the unidirectional composite was obtained. Furthermore, this investigation documents the first experimental observation of a mother/daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/51b0-1c87, author = {Samudrala, Omprakash}, title = {Subsonic and intersonic crack growth along weak planes and bimaterial interfaces}, school = {California Institute of Technology}, year = {2001}, doi = {10.7907/51b0-1c87}, url = {https://resolver.caltech.edu/CaltechTHESIS:10122010-134248309}, abstract = {A combined experimental and analytical study has been conducted to investigate the phenomena of intersonic crack propagation along weak planes in homogeneous solids and dissimilar material interfaces. A single edge notch/crack oriented along a weak plane in a brittle polymer or along a polymer/metal interface was loaded in shear by impacting the specimen with a high velocity projectile fired from a gas gun. Homalite-100 or PMMA was chosen for the polymer and 6061 Aluminum or 4340 steel was chosen for the metal. The stress field information around the propagating crack tip was recorded in real time by two different optical techniques which provide complimentary information - photoelasticity and coherent gradient sensing (CGS), in conjunction with high speed photography. Along weak planes in Homalite-100, dynamic shear cracks were observed to initiate and propagate at speeds exceeding the shear wave speed (c_s) of the polymer. The isochromatic fringe patterns reveal two distinct lines of strong stress field discontinuity (Mach waves) emanating from the crack tip. Intersonic cracks were observed to initially accelerate up to the longitudinal wave speed (c_l) of Homalite and thereafter slow down to propagate at a near constant velocity slightly above √2c_s . A series of short secondary opening cracks parallel to each other and at a steep angle to the weak plane (≈ 80°) were also observed to initiate behind the main intersonic crack tip. Motivated by the experimental observations, an asymptotic analysis was performed to obtain the near tip fields for an intersonically propagating steady state mode II crack with a finite sized shear cohesive zone in front of it. The cohesive shear stress was chosen to be either a constant or to depend linearly on the magnitude of the local slip rate. Decohesion was chosen to occur when the relative slip between the two cohesive surfaces reaches a material/interface specific critical value. Unlike the case of a point sized dissipative region, it is shown that with a finite cohesive zone, the dynamic energy release rate is finite through out the intersonic regime. The influence of crack plane shear strength and of the rate parameter on the crack propagation behavior is investigated. Isochromatic fringe patterns were constructed using the cohesive crack tip fields, which compare favorably with the experimentally observed fringe patterns, and an attempt is made to extract the relevant analytical parameters. Unlike for a mode-I crack, a cohesive stress distribution that decreases with the local slip rate is found to match the experimental observations. The rate parameter was extracted by fitting the secondary crack angle observed in the experiments to that predicted by the analytical solution based on a maximum principal stress fracture criterion. Edge notches/cracks on polymer/metal interfaces were loaded under different impact configurations and the conditions governing the attainment of intersonic crack growth along a bimaterial interface were investigated. High resolution isochromatic fringe patterns were obtained to study the nature of the crack tip fields during subsonic/intersonic transition. Careful observations of the transition of an interface crack into the intersonic regime showed the formation of crack face contact at speeds beyond c_R of the polymer. Subsequently, the contact zone is observed to expand in size, detach from the intersonic crack tip and finally vanish. The recorded isochromatic fringe patterns showed multiple Mach wave formation associated with such a scenario. Along PMMA/ Al and PMMA/steel bimaterial interfaces, dynamic cracks initiating from edge notches were observed to accelerate to speeds higher than c_l of PMMA (supersonic), almost reaching c_R of aluminum. The resulting crack growth was observed to be highly transient and the gradients of in-plane normal stress components were recorded using CGS interferometry. Motivated by the aforementioned experimental observations, an asymptotic analysis was performed to obtain the stress and deformation fields around a steadily propagating intersonic crack on an elastic-rigid interface with a finite zone of crack face frictional sliding contact located a finite distance behind the tip. A linear frictional contact model is adopted, wherein the shear stress is proportional to the normal stress through a constant, the coefficient of dynamic friction. Isochromatic fringe patterns predicted by the near-tip fields exhibit the essential features observed during the experiments. Frictional sliding contact is shown to be possible only for velocities between c_s and √2c_s of the polymer. The relevant analytical parameters were predicted by comparing the model to the experimental isochromatic fringe patterns and comments are made on the merits of the model presented.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Knauss, Wolfgang Gustav and Rosakis, Ares J.}, } @phdthesis{10.7907/xvhx-px15, author = {Conner, Robert Dale}, title = {Mechanical properties of bulk metallic glass matrix composites}, school = {California Institute of Technology}, year = {1998}, doi = {10.7907/xvhx-px15}, url = {https://resolver.caltech.edu/CaltechETD:etd-02282006-161438}, abstract = {
NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.
This report discusses two aspects of research on bulk metallic glasses. The first is an effort to increase their toughness by combining them with reinforcement to form a composite. The second is the first direct measurement of plane strain fracture toughness of bulk metallic glass.
Particulate and continuous fiber reinforced composite materials were fabricated using bulk metallic glass as the matrix. The particulate composites combined W, WC, SiC and Ta reinforcements in a matrix with the composition Zr57Nb5Al10Cu15.4Ni12.6. Continuous fiber composites were fabricated using W and 1080 carbon steel (music) wire reinforcement in a Zr41.25Ti13.75Cu12.5Ni10Be22.5 matrix. In both cases the metallic glass remained amorphous during processing.
Compressive strain to failure was greatly enhanced in both particulate and continuous fiber composites by the formation of multiple shear bands. Tungsten reinforcement provided the greatest improvement. The tungsten is wet well by the metallic glass, and forms a strong interface.
Both particulate and fiber reinforced composite showed improved tensile properties. Energy (per unit volume) to break increased 52% for 5% Vf, 150 […] W reinforced Zr57Nb5Al10Cu15.4Ni12.6 and 18% for 60% Vf music wire reinforced Zr41.25Ti13.75Cu12.5Ni10Be22.5. Tightly bonded ductile particles and weakly bonded continuous fibers proved best for enhancing the tensile properties of bulk metallic glass.
Fracture toughness of the unreinforced Zr41.25Ti13.75Cu12.5Ni10Be22.5 bulk metallic glass was determined using 3-point bend measurements and coherent gradient sensing (CGS). The measured fracture toughness is nominally 55 […]. Once initiated, cracks in the unreinforced metallic glass propagated in an unstable manner. Continuous fiber reinforcement was demonstrated to arrest crack propagation in 3-point bend fracture tests of bulk metallic glass matrix composites.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J. and Johnson, William Lewis}, } @phdthesis{10.7907/FENH-ZK36, author = {Hodowany, Jon}, title = {On the conversion of plastic work into heat}, school = {California Institute of Technology}, year = {1997}, doi = {10.7907/FENH-ZK36}, url = {https://resolver.caltech.edu/CaltechETD:etd-01102008-074409}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. The present study investigated heat evolution in metal plasticity. Specifically, experiments were designed to measure the partition of plastic work into heat and stored energy during dynamic deformations. The fraction of plastic work converted into heat has implications in a wide range of thermomechanical phenomena, including shear bands, dynamic fracture, ballistic penetration and high speed machining. Kolsky bars, in compression and torsion, were used to determine mechanical properties at strain rates between […] and […]. For dynamic loading, in-situ temperature changes were measured using a high-speed HgCdTe photoconductive detector. Specially designed infrared optics, configured in tandem with the HgCdTe detector and the Kolsky bar constituted a novel experimental configuration for determining the fraction of plastic work converted into heat, and thus, the amount of energy stored in metals. The temperature detection system was ideally suited for small temperature excursions from ambient conditions, and was sensitive to temperature changes as little as 0.5 °C. The emissivity of metals was found to increase above certain high levels of plastic strain due to changes in surface roughness, which can affect the validity of temperature calibration. A technique of sample recovery, rough surface layer removal, and reloading was employed to obtain large plastic strains in the Kolsky bar. A Materials Testing System (MTS) servo-hydraulic load frame was used to measure mechanical properties at lower strain rates, […] to […] When temperature measurement was needed within this range of strain rates, a fast E-type thin wire thermocouple, with a time response of 1 ms, was employed. The fraction of plastic work converted into heat, [beta], was treated as a constitutive function of strain and strain rate in the heat conduction equation. 2024 aluminum alloy and commercially pure [alpha]-titanium were the metal systems used in the current study to determine the functional dependence of [beta] on strain and strain rate. The T351, T4 and T6 tempers of 2024 aluminum did not exhibit strain rate dependence in flow stress over the entire range of strain rates tested. At low levels of plastic strain, all tempers of 2024 aluminum stored more than 50% of the input plastic work. At some level of plastic strain, depending on temper, 2024 aluminum could no longer store plastic work. After this point, [beta] increased to a value near 1.0 and remained nearly constant during subsequent plastic deformation. When averaged over all strains, [beta] was 0.85-0.95 depending on the particular heat treatment. The fraction of plastic work dissipated as heat was not found to be sensitive to strain rate over a wide range of strain rates. In contrast, the flow stress of [alpha]-titanium was strongly dependent on strain rate. The initial flow stress increased by more than 15% between strain rates of […] and […]. In addition, the strain hardening was also observed to be rate dependent. For fixed plastic strain, the tangent modulus increased as strain rate increased. Titanium dissipated a greater proportion of energy as heat at low strains than all tempers of 2024 aluminum. The ability to store energy in titanium decreased with increasing plastic strain. For plastic strains above 0.3, titanium dissipated nearly all input plastic work as heat. The proportion of energy dissipated as heat at fixed strain increased as strain rate increased.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Ravichandran, Guruswami and Rosakis, Ares J.}, } @phdthesis{10.7907/ehea-x787, author = {Fey, Kate Elizabeth}, title = {Experimental and theoretical aspects of dynamic crack growth along bimaterial interfaces}, school = {California Institute of Technology}, year = {1996}, doi = {10.7907/ehea-x787}, url = {https://resolver.caltech.edu/CaltechETD:etd-12132007-082556}, abstract = {This work presents findings of an experimental and theoretical study of dynamic bimaterial crack growth. Bimaterial systems composed of constituents with large material mismatch were investigated under dynamic loading conditions. The materials used in this study consisted of Poly-Methylmethacrylate (PMMA) and AISI 4340 Steel, bonded together using a Methylmethacrylate monomer. One point bend loading was achieved using a drop weight tower. Dynamic crack growth, with velocities up to eighty percent of the Rayleigh wave speed of PMMA, was observed using the lateral shearing interferometric technique of Coherent Gradient Sensing (CGS) in conjunction with high speed photography. The results of these experiments are first discussed within the realm of the validity of the linear, elastodynamic asymptotic stress fields. The complex interdependency of stress intensity and mode mixity with crack tip speed is also discussed. The interpretation of |K[superscript d]| and [phi superscript d] in a dynamic bimaterial crack is clarified through the experimental observation of crack growth. Complications in analysis arising from this interdependency between the dynamic K[superscript d]-field and velocity are examined for experimentally obtained CGS fringe patterns. Improvements of existing analyzing procedures are made, resulting in increased confidence in data obtained utilizing the method of CGS in dynamic bimaterial fracture. Special attention is given to the interaction of loading and velocity in the behavior of these crack tip fields. Previous methods of investigation have used an elastodynamic, asymptotic K[superscript d]-field to describe the deformations near a bimaterial crack tip. Attempts to develop a fracture criterion based on these results have suffered from the lack of natural length scale as the major criticism. Motivated by experimental observations, a cohesive zone model is presented in this thesis that allows an investigation of dynamic crack growth. The length of the cohesive zone is given by a combination of stress intensity and mixity, bimaterial behavior, and velocity, and emerges as a natural, time evolving length scale with which to examine the bimaterial crack problem. A fracture criterion based on critical cohesive displacements at the trailing edge of the cohesive zone is presented. This cohesive zone model is subsequently used to examine data obtained from experiment. The model enhances our ability to extrapolate our experimental measurements to the near tip region, and to thus study the neighborhood close to the propagating crack tip. Within experimental error, predictions of the proposed fracture criterion are shown to correspond to the experimentally observed dependence of |K[superscript d]| and [phi superscript d] on the instantaneous crack tip velocity. The fracture criterion based on the cohesive model presented in this paper provides the natural next step in understanding dynamic bimaterial crack growth. It provides a criterion based on physically motivated parameters, introduces a natural length scale into the problem, and increases our understanding of dynamic bimaterial fracture mechanics.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/jd42-3s83, author = {Bruck, Hugh Alan}, title = {Quasi-static and dynamic constitutive characterization of beryllium bearing bulk metallic glasses}, school = {California Institute of Technology}, year = {1995}, doi = {10.7907/jd42-3s83}, url = {https://resolver.caltech.edu/CaltechETD:etd-09112007-130646}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.
Metallic glasses were first discovered by Pol Duwez in 1960 using the fabrication technique of splat quenching. The mechanical behavior of metallic glasses were first characterized in 1969 from tensile tests conducted on thin ribbons. From these tests it was apparent that metallic glasses possessed tensile fracture strengths of approximately […], which approach theoretical limits. Compressive mechanical data became available in 1974 with the fabrication of small cylindrical rods of […]. This data indicated that the quasi-static yield behavior of metallic glasses may obey a pressure insensitive von Mises yield criterion. In 1983, Mechanical tests were conducted on […] in multi-axial stress states which further confirmed the von Mises yield behavior. However, in 1988, mechanical tests performed on […] indicated that metallic glasses may instead obey a pressure sensitive Mohr-Coulomb criterion.
There is some ambiguity in interpreting the results of mechanical tests performed on metallic glasses. The data from these tests were obtained by testing specimens whose sizes do not guarantee a well-defined stress state. Furthermore, the mechanical behavior of metallic glasses may depend on composition. In order to properly determine the yield behavior of metallic glasses in multi-axial stress states, it was necessary to fabricate specimens with geometries suitable for generating well-defined stress states.
In 1993, a new beryllium bearing bulk metallic glass with the nominal composition of […] was discovered at Caltech. This metallic glass can be cast as cylindrical rods as large as 16 mm in diameter. Specimens could then be fabricated with geometries that conformed to ASTM testing standards. These specimens were then tested in quasi-static compressive, tensile, and torsional stress states at strain rates of […] to […] in order to properly characterize the yield behavior of the metallic glass. From these tests it was determined that the beryllium bearing bulk metallic glass obeys a von Mises yield criterion. In addition it was discovered that the ductility of this metallic glass could be altered by adding Boron and varying the quench rate.
For the first time, the dynamic compressive yield behavior of a metallic glass could be characterized at strain rates of […] to […] by using the split Hopkinson pressure bar. High-speed infrared thermal detectors were also used to determine if adiabatic heating occurred during dynamic deformation of the metallic glass. From these tests it appears that the yield stress of the metallic glass is insensitive to strain rate and no adiabatic heating occurs before yielding.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J. and Johnson, William Lewis}, } @phdthesis{10.7907/36hw-c185, author = {Lambros, John}, title = {Dynamic decohesion of bimaterial interfaces}, school = {California Institute of Technology}, year = {1994}, doi = {10.7907/36hw-c185}, url = {https://resolver.caltech.edu/CaltechETD:etd-12042007-075432}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.
In the present work, findings of an experimental study of dynamic decohesion of bimaterial systems composed of constituents with a large material property mismatch are presented. PMMA/steel or PMMA/aluminum bimaterial fracture specimens are used. Dynamic one point bend loading is accomplished with a drop weight tower device (for low and intermediate loading rates) or a high speed gas gun (for high loading rates). High speed interferometric measurements are made using the lateral shearing interferometer of Coherent Gradient Sensing in conjunction with high speed photography. Very high crack propagation speeds (terminal crack tip speeds up to […], where […] is the shear wave speed of PMMA) and high accelerations ([…], where g is the acceleration of gravity) are observed and reported. Issues regarding data analysis of the high speed interferograms are discussed. The effects of near tip three dimensionality are also analyzed. In crack propagation regions governed by large crack tip accelerations it is found that for accurate analysis of the optical data use of a transient elastodynamic crack tip field is necessary. Otherwise use of a Kd-dominant analysis is sufficient. Using the dynamic complex stress factor histories obtained by fitting the experimental data, a dynamic crack growth criterion is proposed. In the subsonic regime of crack growth it is seen that the opening and shearing displacements behind the propagating crack tip remain constant, i.e., the crack retains a self-similar profile during crack growth at any speed. This forms the basis of the proposed dynamic interfacial fracture criterion. It is also found that the process of dynamic interfacial fracture is highly unstable. This is corroborated by both the very large measured values of crack tip speed and acceleration and by the observation that the energy release rate at the propagating crack tip decreases with increasing crack tip speed. A mechanism of energy transfer from the metal to the PMMA side of the specimen is believed to be responsible for the high transient and transonic effects. An analysis and discussion of this phenomenon is also presented in this work.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/k32y-0450, author = {Liu, Cheng}, title = {Dynamic fracture problems involving highly transient crack growth histories : an investigation of dynamic failure in homgeneous and bimaterial systems}, school = {California Institute of Technology}, year = {1994}, doi = {10.7907/k32y-0450}, url = {https://resolver.caltech.edu/CaltechETD:etd-12122007-141145}, abstract = {NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.
Highly transient elastodynamic fracture processes in both homogeneous and bimaterial systems have been investigated. It is found that due to the wave character of the mechanical fields during transient and dynamic crack growth, the customarily assumptions of steady state and K[superscript d]-dominance may be violated. This may be particularly true during crack growth in laboratory size specimens where crack growth seldom reaches steady state conditions due to the persistence of the initiation transients and the influence of reflected stress waves from the specimen boundaries. By relaxing both restrictions of steady state and of K[superscript d]-dominance, and by permitting the crack-tip speed and the dynamic stress intensity factor to be arbitrary functions of time, the transient asymptotic elastodynamic field near the moving crack-tip was established in the form of higher order expansion for both homogeneous solids and bimaterial systems. In homogeneous solids, we considered cracks that propagated along arbitrary smooth paths, while in bimaterial systems, we only considered crack growth along a straight interface. The higher order coefficients of the asymptotic expansion were found to depend on the time derivative of crack-tip speed, the time derivative of the dynamic stress intensity factors, and for crack propagating along curved paths, on the instantaneous value of the local curvature of the crack path.
The issue of K[superscript d]-dominance during dynamic crack initiation and transient crack growth was further investigated by solving a particular transient initial/boundary value problem. This corresponds to a planar dilatational wave impinging on a semi-infinite crack in an unbounded elastic solid. The crack initiates under the influence of the wave, and then propagates dynamically. Through comparison of this full field solution and the equivalent K[superscript d]-dominant field or the field represented by the higher order transient terms, it is found that even for points which are relatively far away from the crack-tip, or for times very close to the crack initiation, the higher order transient representation provides a very good description of the actual stress field. The K[superscript d]-dominant field, however, is incapable of approximating the complete stress field with any accuracy (lack of K[superscript d]-dominance).
The implications of the above observations (possible lack of K[superscript d]-dominance) on the interpretability of dynamic fracture experiments are also explored. The interpretation of experimental data in past laboratory investigations of dynamic fracture events is based on the assumption of K[superscript d]-dominance. However, as we have seen theoretically this assumption may often fail in laboratory situations. As a result, experimental measurements must be analyzed by techniques that allow for the possibility of the existence of transient higher order term effects. Several types of experiments are considered as examples. Plate impact experiments involving very high rates of loading are first analyzed by both a K[…]-dominant and a high order transient approach. The results clearly show the strong effects of transients on the interpretation of the data. As a second example, the optical method of caustics is reanalyzed. A new way of extracting the instantaneous value of the dynamic stress intensity factor K…, which takes transients into account, is proposed and verified theoretically. For the bimaterial system, the issues are equivalent but much more complicated analytically. Here transient effects are found to be magnified by the material property mismatch between the constituent solids. It is shown however, that the higher order transient analysis can predict accurately the fringe patterns from actual experiment performed by means of the CGS (Coherent Gradient Sensing) technique and high speed photography.
The observations of this thesis suggest that a variety of conclusions made in the literature based on interpretations of experimental data on the basis of steady state or K[superscript d]-dominance may be suspect.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/FAB4-5056, author = {Mason, James Joseph}, title = {Mechanisms and effects of heat generation at the tips of dynamic cracks and notches in metals}, school = {California Institute of Technology}, year = {1993}, doi = {10.7907/FAB4-5056}, url = {https://resolver.caltech.edu/CaltechETD:etd-08312007-094213}, abstract = {A high-speed InSb infrared detector array and the method of Coherent Gradient Sensing (CGS) are used in several experimental configurations to explore the mechanisms and effects of heat generation in dynamic fracture and deformation. First, the dependence of the measured dynamic crack tip temperature upon crack tip speed is investigated for cracks propagating dynamically in AISI 4340 carbon steel. Then, the dynamic crack tip temperature in a titanium alloy (Ti-l0V-2Fe-3Al) is measured in order to examine the role of material parameters in determining the crack tip temperature at different crack growth speeds. It is seen that the crack tip temperature increases when crack tip velocities are increased from 600 m/s to 900 m/s in 4340 steel. The extent of the active plastic zone at the surface of the specimen, however, decreases with increasing crack velocity. When the results for temperature measurements in steel are compared with those for titanium, it is seen that the material parameters that are most important are the dynamic yield strength, which determines the amount of plasticity, and the heat capacity of the material. Conductivity has little effect. Next, the nature of hyperbolic heat conduction at the tip of a dynamic crack is investigated. A mathematical model is developed to predict the temperature field around a dynamically propagating crack tip for a material that follows a hyperbolic heat conduction law. A Green’s function for the governing partial differential equation is derived. The model is solved for a variety of experimental conditions by numerical integration of the Green’s function. Various possible effects of hyperbolic heat conduction around a crack tip are explored. The model is then used to simulate the experimental conditions typically observed in dynamic fracture. Because conduction is minimal around the dynamically propagating crack tip, no effects of hyperbolic heat conduction are observed. It is also observed that the temperature field around the dynamic crack tip is adiabatic. Since adiabatic conditions are observed around a propagating crack tip, an important parameter which governs the distribution and intensity of crack tip heating is the fraction of plastic work rate converted to heat, [beta]. For this investigation [beta] is not treated as a mere parameter, the possibility of the existence of a constitutive relationship between this parameter and strain at high strain-rates is investigated using the Kolsky bar as a loading apparatus. It is found that the conversion of plastic work to heat at high strain-rates is similar to that at low strain rates for aluminum and for steel and that [beta] remains a constant independent of strain at high strains for both these materials. For rate sensitive titanium, [beta] is observed to be a function of strain possibly due to twinning deformation. It is known that heat generation can lead to the formation of shear bands especially in dynamic fracture experiments. The formation of a shear band at the tip of a notch or crack in C-300 steel is examined using the method of CGS. First, the CGS method is used to verify a model of the notch tip stress intensity factor, K[subscript II], as a function of time. Good agreement is found between the experimental measurement of K[subscript II] and the predicted value for PMMA impacted at 5 m/s. Then the method is used to investigate the formation of shear bands at the tip of a notch under the same conditions. A Dugdale crack model is used to interpret the results, and it is seen that the shear stress decreases from 1.6 GPa to 1.3 GPa as the shear band propagates. This result is in good agreement with measurements made using the Kolsky bar.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/tkxp-f839, author = {Lu, Lingyun}, title = {On the development and application of a modified boundary element method for the analysis of three-dimensional elastostatic problems in thick plates}, school = {California Institute of Technology}, year = {1992}, doi = {10.7907/tkxp-f839}, url = {https://resolver.caltech.edu/CaltechETD:etd-08072007-131209}, abstract = {A modified three-dimensional Boundary Element Method (BEM) is developed. This method is specially tailored towards applications in three-dimensional elasticity, involving regions containing two parallel planar surfaces. Typical structures are the three-dimensional plate structures. The formulation makes use of the three-dimensional fundamental solution of a concentrated load applied in an infinite three-dimensional plate of uniform finite thickness (obtained by Benitez and Rosakis in 1985). The most attractive feature of this modified BEM is that, for the class of problems involving structures described above subjected to traction-free boundary conditions on the planar surfaces, discretization is only required on the lateral surfaces of the plate and the surfaces of the cavities, holes, and cracks in the plate. No discretization is needed on the planar surfaces of the plate. In this initial study, three problems involving a pressurized hole in an infinite three-dimensional plate are analyzed. The shapes of the holes include a circular hole and two elliptical holes with the aspect ratios of 4 and 10, respectively. In all the cases, the accuracy of the modified BEM is established by direct comparison of its results with those of finite element calculations. The results of the modified BEM are also compared with the plane-stress and plane-strain approximations of the problems under consideration. This comparison make it possible to access the important three-dimensional effects near the surface of the elliptical hole.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/wv0e-g535, author = {Washabaugh, Peter D.}, title = {An experimental investigation of mode-I crack tip deformation}, school = {California Institute of Technology}, year = {1990}, doi = {10.7907/wv0e-g535}, url = {https://resolver.caltech.edu/CaltechETD:etd-11092007-101356}, abstract = {The out-of-plane displacement of amorphous polymethylmethacrylate plates rupturing at slow (0.1 mm/s), and fast (0.5 to 0.9 mm/µs) rates are measured using a Twymann-Green interferometer. The measured surface shapes within one plate thickness of the crack-tip do not compare well with the two-dimensional planar asymptotic approximation, but compare favorably with the published slopes for three-dimensional finite element solutions when normalized with the static material properties. Discrepancies, on the order of ten percent, between the magnitude of the three-dimensional finite element solutions suggest that the stress intensity factor does not fully characterize the near tip deformations.
A dynamically propagating crack is found to move in a non-steady, periodic, submicrosecond fashion. This result is supported both by the surface measurements and the fracture morphology. The material toughening, as measured by the surface roughness, correlates well with the stress intensity factor and not with the crack velocity. The details of the sub-microsecond propagation and toughening was not resolvable with the microsecond temporal resolution of the experiment.
Inhibiting the material toughening at the crack tip by artificially introducing a weak material plane augments the crack motion to velocities close to the material’s shear wave speed. The crack propagates more steadily along the weak plane than through a virgin solid, while maintaining the character of the out-of-plane displacement of a crack propagating in an unsullied material.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Knauss, Wolfgang Gustav and Rosakis, Ares J.}, } @phdthesis{10.7907/WHJV-C644, author = {Deng, Xiaomin}, title = {Dynamic Crack Propagation in Elastic-Plastic Solids}, school = {California Institute of Technology}, year = {1990}, doi = {10.7907/WHJV-C644}, url = {https://resolver.caltech.edu/CaltechETD:etd-11062003-112730}, abstract = {The present finite element study addresses several issues of interest pertaining to the phenomenon of dynamic crack propagation in elastic-plastic solids. Three classes of materials, namely elastic-perfectly plastic materials, linear hardening materials and power-law hardening materials, are considered. The materials are assumed to obey the von Mises yield criterion and the associated flow rule.
Under conditions of Mode I, plane stress, steady state and small scale yielding, we investigated the structures of the near-tip stress and deformation fields. A preliminary asymptotic analysis for crack-tip stress and velocity fields in elastic-perfectly plastic solids was provided to reveal and explain some special features of the crack tip fields observable only in the case of rapid crack propagation. We studied the theoretical basis of a fracture criterion based on the dynamic stress intensity factor for crack growth in materials which fail in a locally ductile manner. We explored the behavior of crack tip fields under non-K-dominance conditions and its effects on the dynamic fracture toughness vs. crack propagation speed relationship.
An Eulerian finite element scheme is employed. Finite element meshes with extremely small elements near the crack tip are carefully designed. The ratio of the crack tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 x 10⁴. In order to overcome numerical difficulties associated with crack-tip strain singularities and the use of small near-tip elements, an efficient stress integration algorithm is devised. The existing stress state determination procedure is modified to prevent the occurrence of negative plastic flow and to avoid mistakenly treating elastic unloading as plastic flow. The above measures are proven to be essential for the convergence of the numerical solution.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/cfz9-nk80, author = {Krishnaswamy, Sridhar}, title = {On the Domain of Dominance of the Asymptotic Elastodynamic Crack-Tip Fields}, school = {California Institute of Technology}, year = {1989}, doi = {10.7907/cfz9-nk80}, url = {https://resolver.caltech.edu/CaltechETD:etd-10292003-134326}, abstract = {A substantial part of the experimental data in dynamic fracture mechanics has been obtained under the assumption that the two-dimensional asymptotic elastodynamic stress-intensity factor field (the KdI-field) is dominant over at least the region around the crack-tip over which the experimental measurements are made. The validity of this assumption is investigated in this thesis both experimentally and through finite-element simulations of the experiments.
The experiments reported in this work were on 4340 steel, three-point bend specimens loaded dynamically using a drop-weight tower. The two cases of dynamically loaded stationary cracks and dynamically propagating cracks were considered. An optical configuration is proposed that leads to a bifocal high-speed camera capable of focusing on two different planes simultaneously. This was used in conjunction with the method of caustics to measure the apparent stress-intensity factor simultaneously from two different regions (initial-curves) around the crack-tip. If the initial-curves lie within the domain of dominance of the asymptotic field, the measured values of the dynamic stress-intensity factor must agree to within experimental error. By suitably adjusting the optical set-up, a range of initial-curves was scanned in an attempt to map the domain of dominance of the KdI-field.
The impact hammer and supports of the drop-weight loading device were instrumented in order to monitor the time dependent loads acting on the specimen. These loads were subsequently used as boundary tractions in dynamic two- and three-dimensional finite-element simulations of the experiments. The simulations were carried only up to the point of crack initiation. Comparison of the numerical simulations with the experimental results help in identifying the role of three-dimensionality and transient conditions on the measured stress-intensity factor values.
On the basis of both the experimental results as well as the numerical simulations, no sizeable annulus of dominance for the asymptotic elastodynamic field was found for the laboratory situation studied. It appears that the assumption of an underlying KdI-dominant (or two-dimensional) field might not hold to a level of accuracy that would warrant many of the conclusions made in the literature regarding the crack-initiation toughness values as well as the uniqueness of the dynamic fracture toughness - crack velocity relation or its specimen and acceleration dependence.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/f3zy-j846, author = {Zehnder, Alan T.}, title = {Dynamic Fracture Initiation and Propagation in Metals: Experimental Results and Techniques}, school = {California Institute of Technology}, year = {1987}, doi = {10.7907/f3zy-j846}, url = {https://resolver.caltech.edu/CaltechETD:etd-03052008-085910}, abstract = {Dynamic fracture initiation and propagation in ductile and brittle materials was studied experimentally using the optical method of caustics in conjunction with high speed photography. The drop weight impact test, previously used only for studies of fracture initiation, was adapted to study both dynamic fracture initiation and dynamic fracture propagation.
The results show that for a relatively brittle, quenched and tempered, high strength 4340 steel the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property. In addition, the effect of stress waves on the dynamic response of different specimen geometries is discussed and the micromechanisms of failure for this heat treatment of 4340 steel are investigated.
Extension of the optical method of caustics to applications in elastic-plastic fracture was studied with the goal of learning how to measure dynamic fracture initiation toughness in tough, ductile materials. Static experiments were performed on different specimen geometries of a ductile 4340 steel and 1018 cold rolled steel, and were compared to small scale yielding, plane stress, finite element results. Issues studied that are related to the applicability of caustics are the extent of the dominance of the plane stress HRR field, the effect of plasticity on the accuracy of caustics from the elastic region outside the plastic zone, and the extent of the crack tip region of three dimensionality.
The above approach to caustics in ductile materials was based on the assumption of validity of the HRR field. A novel approach to the use of caustics with ductile materials was taken that eliminates the concerns over the region of dominance of the HRR field, etc. In this approach a calibration experiment was performed relating the caustic diameter to the J integral for a particular specimen geometry under conditions of large scale yielding. This approach was successfully applied to optically measure for the first time the J integral under dynamic loading. Measurement of the J integral by means of strain gages was developed and applied to obtain J simultaneously with the caustics measurement.
At the same time (and on the same specimens) additional measurements were made including, load, load-point displacement, strains near the crack tip and out of plane displacements (measured with interferometry). These results are compared with excellent agreement to a three dimensional finite element simulation of the specimen.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, } @phdthesis{10.7907/RG0C-WF30, author = {Ramarathnam, Narasimhan}, title = {Mode I, Plane Stress Crack Initiation and Growth in Elastic-Plastic Solids: A Finite Element Analysis}, school = {California Institute of Technology}, year = {1987}, doi = {10.7907/RG0C-WF30}, url = {https://resolver.caltech.edu/CaltechETD:etd-11062003-094350}, abstract = {A detailed finite element analysis of crack initiation and stable crack extension is performed under Mode I plane stress, small-scale yielding conditions. A small strain, J2 incremental plasticity theory is employed and both elastic-perfectly plastic materials and power law hardening materials are considered.
Some issues pertaining to the stationary plane stress crack problem, such as the range of dominance of the asymptotic stress and deformation fields and the amount of non-proportional loading near the crack tip are addressed. Special attention is devoted to the perfectly plastic idealization, by performing a separate singular finite element analysis, to clarify some details about the asymptotic fields near the stationary crack tip. The full-field numerical solution is used to simulate synthetic (optical) caustic patterns at different distances from the crack tip, which are compared with experimental observations and with asymptotic analytical results.
A nodal release procedure is used to simulate quasi-static crack extension. It is found that the asymptotic angular extent of the active plastic zone, surrounding the propagating crack tip, is from θ = 0 to about θ = 45° for the perfectly plastic case. The near-tip angular stress distribution within the active plastic zone is in good agreement with the variation in a centered fan, as predicted by a preliminary asymptotic analysis by Rice, for the perfectly plastic case. It is also observed that the σrr stress component has a strong radial variation within the active plastic zone. The angular extent of active yielding around the moving tip increases with hardening, while its maximum radial extent ahead of the tip decreases. Clear evidence of an elastic unloading region following the active plastic zone is found, but no secondary (plastic) reloading along the crack flank has been numerically observed for any level of hardening.
The crack tip opening profile during growth is obtained for various levels of hardening. A ductile crack growth criterion is employed to investigate the nature of the J resistance curves under plane stress. Finally, the influence of hardening on the potential for stable crack growth is examined.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Rosakis, Ares J.}, }