VTechWorks Repository :: Browsing by Author "Curtin, William A. Jr."

Browsing by Author "Curtin, William A. Jr."

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Analytic Results for Hopping Models with Excluded Volume Constraint
Toroczkai, Zoltan (Virginia Tech, 1997-09-04)
Part I: The Theory of Brownian Vacancy Driven Walk We analyze the lattice walk performed by a tagged member of an infinite 'sea' of particles filling a d-dimensional lattice, in the presence of a single vacancy. The vacancy is allowed to be occupied with probability 1/2d by any of its 2d nearest neighbors, so that it executes a Brownian walk. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. Thus, the tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a random walk "driven" by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after n-steps of the vacancy, are derived. Neither is a Gaussian! We also show that the only nontrivial dimension where the walk is recurrent is d=2. As an application, we compute the expected energy shift caused by a Brownian vacancy in a model for an extreme anisotropic binary alloy. In the last chapter we present a Monte-Carlo study and a mean-field analysis for interface erosion caused by mobile vacancies. Part II: One-Dimensional Periodic Hopping Models with Broken Translational Invariance.Case of a Mobile Directional Impurity We study a random walk on a one-dimensional periodic lattice with arbitrary hopping rates. Further, the lattice contains a single mobile, directional impurity (defect bond), across which the rate is fixed at another arbitrary value. Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. Analytic solution for the distributions in the steady state limit is obtained. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. As an application, we extend the Duke-Rubinstein reputation model of gel electrophoresis to include polymers with impurities and give the exact distribution of the steady state.
Characterization of Ferroelectric Films by Spectroscopic Ellipsometry
Dickerson, Bryan Douglas Jr. (Virginia Tech, 2003-07-18)
Process dependent microstructural effects in ferroelectric SrBi2Ta2O9 (SBT) thin films were characterized and distinguished from material dependent optical properties using a systematic multi-layer modeling technique. Variable angle spectroscopic ellipsometry (VASE) models were developed by sequentially testing Bruggeman effective-media approximation (EMA) layers designed to simulate microstructural effects such as surface roughness, porosity, secondary phases, and substrate interaction. Cross-sectional analysis by atomic force microscopy (AFM), transmission and scanning electron microscopy (TEM) and (SEM) guided and confirmed the structure of multi-layer models for films produced by pulsed laser deposition (PLD), metal-organic chemical vapor decomposition (MOCVD), and metal-organic deposition (MOD). VASE was used to estimated the volume percentage of second phase Bi2O3 in SBT thin films made by MOD. Since Bi₂O₃ was 10 orders of magnitude more conductive than SBT, second phase Bi₂O₃ produced elevated leakage currents. Equivalent circuits and percolation theory were applied to predict leakage current based on Bi₂O₃ content and connectivity. The complex role of excess Bi2O3 in the crystallization of SBT was reviewed from a processing perspective. VASE helped clarify the nature of the interaction between SBT films and Si substrates. When SBT was deposited by MOD and annealed on Si substrates, the measured capacitance was reduced from that of SBT on Pt due mainly to the formation of amorphous SiO₂ near the SBT/Si interface. VASE showed that the thickness and roughness of the SiO₂ reaction layer increased with annealing temperature, in agreement with TEM measurements. Unlike PZT, SBT crystallization was not controlled by substrate interaction.
Characterizing the Mechanical Properties of Composite Materials Using Tubular Samples
Carter, Robert Hansbrough (Virginia Tech, 2001-07-16)
Application of composite materials to structures has presented the need for engineering analysis and modeling to understand the failure mechanisms. Unfortunately, composite materials, especially in a tubular geometry, present a situation where it is difficult to generate simple stress states that allow for the characterization of the ply-level properties. The present work focuses on calculating the mechanical characteristics, both on a global and local level, for composite laminate tubes. Global responses to axisymmetric test conditions (axial tension, torsion, and internal pressure) are measured on sections of the material. New analysis techniques are developed to use the global responses to calculate the ply level properties for tubular composite structures. Error analyses are performed to illustrate the sensitivity of the nonlinear regression methods to error in the experimental data. Ideal test matrices are proposed to provide the best data sets for improved accuracy of the property estimates. With these values, the stress and strain states can be calculated through the thickness of the material, enabling the application of failure criteria, and the calculation of failure envelopes.
Computational Alchemy: The Rational Design of New Superhard Materials
Teter, David Michael (Virginia Tech, 1998-06-29)
First--principles electronic structure calculations have been performed to help identify and direct the synthesis of new superhard compounds. An improved figure of merit for hardness is identified and used to show that carbon nitrides are not likely to be harder than diamond.
Durability of Ceramic Matrix Composites at Elevated Temperatures: Experimental Studies and Predictive Modeling
Halverson, Howard Gerhard (Virginia Tech, 2000-05-08)
In this work, the deformation and strength of an oxide/oxide ceramic matrix composite system under stress-rupture conditions were studied both experimentally and analytically. A rupture model for unidirectional composites which incorporates fiber strength statistics, fiber degradation, and matrix damage was derived. The model is based on a micromechanical analysis of the stress state in a fiber near a matrix crack and includes the effects of fiber pullout and global load sharing from broken to unbroken fibers. The parameters required to produce the deformation and lifetime predictions can all be obtained independently of stress-rupture testing through quasi-static tension tests and tests on the individual composite constituents. Thus the model is truly predictive in nature. The predictions from the model were compared to the results of an extensive experimental program. The model captures the trends in steady-state creep and tertiary creep but the lifetime predictions are extremely conservative. The model was further extended to the behavior of cross-ply or woven materials through the use of numeric representations of the fiber stresses as the fibers bridge matrix cracks. Comparison to experiments on woven materials demonstrated the relationship between the behavior of the unidirectional and cross-ply geometries. Finally, an empirical method for predicting the durability of materials which exhibit multiple damage modes is examined and compared to results of accurate Monte Carlo simulations. Such an empirical method is necessary for the durability analysis of large structural members with varying stress and temperature fields over individual components. These analyses typically require the use of finite element methods, but the extensive computations required in micromechanical models render them impractical. The simple method examined in this work, however, is shown to have applicability only over a narrow range of material properties.
Ferroelectric Thin Films for High Density Non-volatile Memories
Song, Yoon-Jong (Virginia Tech, 1998-08-13)
Ferroelectric random access memories (FRAM) are considered as future memories due to high speed, low cost, low power, excellent radiation hardness, nonvolatility, and good compatibility with the existing integrated circuit (IC) technology. The non-volatile FRAM devices are divided into two categories, based on reading technique: destructive readout (DRO) FRAM and non-destructive readout (NDRO) FRAM. Lead zirconate titanate (PZT) is recently considered as one of the most promising materials for DRO FRAM devices due to its excellent ferroelectric properties. There are remarkable advances in the applications of PZT thin films, but the direct integration into high density CMOS devices is restricted by high processing temperatures. Hence, it is desirable to lower processing temperature and develop novel high temperature electrode-barrier layers for achieving high density DRO FRAM devices. The NDRO FRAM devices have been developed mainly using metal-ferroelectric-semiconductor (MFS) and metal-ferroelectric-metal-insulator-semiconductor (MFMIS) structure. This devices use the remanent polarization of ferroelectric films to control the surface conductivity of a silicon substrate. The problem of the NDRO FRAM is that the actual electric field applied to ferroelectric films is very small compared to the external electric field, because of the large depolarization field in the MFS structure and the high capacitance ratio of ferroelectric capacitor and SiO2 capacitor in series in the MFMIS structure. Since the typical ferroelectric films show very high dielectric constant over 400, it is desired to develop ferroelectric films with low dielectric constant and low coercive electric field. This research is primarily focused on developing low temperature processing and high temperature electrode-barrier layers for DRO FRAM application, and exploiting novel ferroelectric materials for NDRO FRAM application. The low temperature processing was achieved by a novel sol-gel processing, which takes advantage of in-situ electrode template layer, rapid heating-treatment without pyrolysis step, and molecularly modified precursors. The PZT films with various composition were also investigated as a function of Ti content. In order to study the integration issues for these PZT films, a substrate was constructed as Pt/TiN/TiSi₂/poly-Si, which represents a scheme of capacitor in high density DRO FRAM devices. The ferroelectric films were incorporated into the substrate, and their ferroelectric properties were investigated as a function of annealing temperature. Excellent ferroelectric properties were observed for the thin films processed at a low temperature of 500 °C as contacting between top Pt and bottom polysilicon. The other approach we have taken to overcome the integration problems in high density DRO FRAM devices is to develop high temperature electrode barrier layers. In this research, Pt/IrO2/Ir hybrid layers were prepared on poly-Si substrate as high temperature electrode-barriers. The PZT films fabricated on the Pt/IrO₂/Ir/poly-Si substrates exhibited good ferroelectric properties and outstanding fatigue properties after high temperature processing. It was observed from Auger electron spectroscopy (AES) profiles that the hybrid oxide electrode minimized fatigue problem by reducing the oxygen vacancies entrapment at the electrode/ferroelectric interfaces. This results indicated that Pt/IrO₂/Ir high temperature electrode-barrier layers promise to solve major problems of PZT integration into high density DRO memory devices. For the NDRO FRAM devices, Sr₂Nb₂O₇ and La₂Ti₂O₇ thin films were prepared on Pt-coated silicon, Si(100), and Pt/IrO₂/SiO₂/Si substrates by metalorganic deposition (MOD) technique. The Sr₂Nb₂O₇ and La₂Ti₂O₇ thin films showed the dielectric constant values of 48 and 46, respectively. However, no ferroelectricity was observed at room temperature, which might be attributed to extremely small grains. Extensive studies on preparation and properties of Sr₂(Ta_1-xNb_x)O₇ (STN) both in bulk and thin film form were carried out as a function of composition. The STN films exhibited small dielectric constant of around 46, irrespective of the composition.
Improving fatigue life predictions: theory and experiment on unidirectional and crossply polymer matrix composites
Halverson, Howard Gerhard (Virginia Tech, 1996-05-15)
A method is presented by which fatigue life predictions of polymer matrix composites may be improved. First a "critical element", whose failure defines global failure of the material. is identified. The global stiffness changes of the specimen during a fatigue test are monitored and taken to be inversely proportional to the increase in applied stress on the critical element. Using a cumulative damage model, the complicated stress history of the critical element is reduced to a "critical element SN curve", which defines the fatigue response of the critical element. The residual strength of the critical element may then be continuously evaluated to predict failure. The statistical nature of material strength is accounted for by forcing the critical element SN Curve to yield a specimen initial strength distribution in fatigue which is equivalent to the quasi-static tensile distribution. In contrast to most methods, the predictions are based on the stiffness history of the specimen in question, rather than on generalized phenomenological models. The critical element SN curve is then applied to (90°/0°) crossply materials to evaluate their fatigue response. Simulations and the variation of experimental parameters are examined for their effect on the predictions. The unidirectional fatigue predictions were vastly improved over the traditional SN Curve. While the crossply predictions were not as good, they still demonstrated the applicability of the critical element SN curve to a material with a different geometry. Additionally. such a method may have application in real-time durability evaluation of composite components.
Interfacial Mechanics in Fiber-Reinforced Composites: Mechanics of Single and Multiple Cracks in CMCs
Ahn, Byung Ki (Virginia Tech, 1997-12-12)
Several critical issues in the mechanics of the interface between the fibers and matrix in ceramic matrix composites (CMCs) are studied. The first issue is the competition between crack deflection and penetration at the fiber/matrix interface. When a matrix crack, the first fracture mode in a CMC, reaches the interface, two different crack modes are possible; crack deflection along the interface and crack penetration into the fibers. A criterion based on strain energy release rates is developed to determine the crack propagation at the interface. The Axisymmetric Damage Model (ADM), a newly-developed numerical technique, is used to obtain the strain energy in the cracked composite. The results are compared with a commonly-used analytic solution provided by He and Hutchinson (HH), and also with experimental data on a limited basis. The second issue is the stress distribution near the debond/sliding interface. If the interface is weak enough for the main matrix crack to deflect and form a debond/sliding zone, then the stress distribution around the sliding interface is of interest because it provides insight into further cracking modes, i.e. multiple matrix cracking or possibly fiber failure. The stress distributions are obtained by the ADM and compared to a simple shear-lag model in which a constant sliding resistance is assumed. The results show that the matrix axial stress, which is responsible for further matrix cracking, is accurately predicted by the shear-lag model. Finally, the third issue is multiple matrix cracking. We present a theory to predict the stress/strain relations and unload/reload hysteresis behavior during the evolution of multiple matrix cracking. The random spacings between the matrix cracks as well as the crack interactions are taken into account in the model. The procedure to obtain the interfacial sliding resistance, thermal residual stress, and matrix flaw distribution from the experimental stress/strain data is discussed. The results are compared to a commonly-used approach in which uniform crack spacings are assumed. Overall, we have considered various crack modes in the fiber-reinforced CMCs; from a single matrix crack to multiple matrix cracking, and have suggested models to predict the microscopic crack behavior and to evaluate the macroscopic stress/strain relations. The damage tolerance or toughening due to the inelastic strains caused by matrix cracking phenomenon is the key issue of this study, and the interfacial mechanics in conjunction with the crack behavior is the main issue discussed here. The models can be used to interpret experimental data such as micrographs of crack surface or extent of crack damage, and stress/strain curves, and in general the models can be used as guidelines to design tougher composites.
Life prediction of fiber-reinforced composites: macro- and micro-mechanical modeling
Iyengar, Nirmal (Virginia Tech, 1996-07-14)
In homogenous materials the life of a component is controlled by damage associated with a single crack while that of non-homogenous materials is the result of a distributed damage state. The life prediction of composite materials is thus carried out using damage mechanics two common approaches of which are, macro- and micro-mechanical modeling. The former assumes homogeneity at the lamina level while the latter evaluates failure processes at the fiber-matrix level. In the first part of this study the remaining strength life prediction methodology MRLife, modified for ceramic composites (CCLife), is integrated into the finite element package CSTEM. to create an integrated design tool for ceramic matrix composites. Using this tool, a case study is carried out to predict the life of a notched Nicalon™/Silicon Carbide 2-D woven laminated composite coupon with a temperature distribution subject to fatigue loading. Global failure of the notched plate is predicted based on a Whitney-Nuismer type average strength criterion. In the second part of this study, simulation of events occurring at the fiber-matrix level are used to develop micro-mechanical models for the time-dependent behavior of fiber-reinforced composites due to shear creep of the fiber-matrix interface and slow crack growth in the fibers. At first, simulations of the time-dependent failure of the composite are performed using a modified Monte-Carlo fast-fracture model the results of which are then used to validate the analytical models developed for the two mechanisms. Finally, an analytical model for the time-dependent failure of a composite due to the combined effects of the two mechanism, shear creep and slow crack growth is presented. The potential for including the time-dependent failure model into CCLife is evaluated by comparing these results with those form CCLife results under the same conditions.
Materials for High Temperature Thin Film Thermocouple Applications
Vedula, Ramakrishna (Virginia Tech, 1998-04-07)
The thermocouple systems used for the measurement of surface temperature in high temperature applications such as advanced aerospace propulsion systems and diesel engine systems are expected to perform in rapidly fluctuating and extremely high heat fluxes corresponding to high temperatures (in excess of 1400 K) and high speed flows. Traditionally, Pt/Pt-Rh based thin film thermocouples have been used for surface temperature measurements. However, recent studies indicated several problems associated with these thermocouples at temperatures exceeding 1000 K, some of which include poor adhesion to the substrate, rhodium oxidation and reaction with the substrate at high temperatures. Therefore, there is an impending demand for thermoelectric materials that can withstand severe environments in terms of temperature and heat fluxes. In this study, thin films of titanium carbide and tantalum carbide as well as two families of conducting perovskite oxides viz., cobaltites and manganates (La(1-x)SrxCoO3, M(1-x)Cax MnO3 where, M=La,Y) were investigated for high temperature thin film thermocouple applications as alternate candidate materials. Thin films of the carbides were deposited by r.f. sputtering while the oxide thin films were deposited using pulsed laser ablation. Sapphire (1102) was used as substrate for all the thin film depositions. All the thin films were characterized for high temperature stability in terms of phase, microstructure and chemical composition using x-ray diffraction, atomic force microscopy and electron spectroscopy for chemical analysis respectively. Electrical conductivity and seebeck coefficients were measured in-situ using a custom made device. It was observed that TiC/TaC thin film thermocouples were stable up to 1373 K in vacuum and yield high and fairly stable thermocouple output. The conducting oxides were tested in air and were found to be stable up to at least 1273 K. The manganates were stable up to 1373 K. It was observed that all the oxides studied crystallize in a single phase perovskite structure. This phase is stable up to annealing temperatures of 1373 K. The predominant electrical conduction mechanism was found to be small polaron hopping. Stable and fairly high electrical conductivities as well as seebeck coefficients accompanied with phase, structure, composition and microstructure stability indicate that these materials hold excellent promise for high temperature thin film thermocouple applications.
Mechanisms of Deformation and Fracture in TiAl: An Atomistic Simulation Study
Panova, Julia B. (Virginia Tech, 1997-05-15)
The intermetallic compound TiAl possesses a unique complex of properties that include sufficiently low material density, high values of the strength-to-ductility ratio, high elastic moduli, high oxidation resistance, low creep rate, and improved fatigue characteristics. These properties make TiAl alloys very attractive, particularly for structural applications for aerospace and aeronautic industries, where, at certain temperatures, they might be capable of replacing heavy nickel-based superalloys. However, so far applications of TiAl alloys have been limited by their poor ductility. Many of the recent studies have focused on the source of this limited ductility and on methods to improve this property. It has been found out experimentally that the strength and ductility of $gamma$-TiAl alloys can be affected by many different parameters, including alloy stoichiometry, heat treatment, deformation temperature, impurity content, grain size, and ternary element additions. In this thesis we present the results of our computer simulations of deformation and fracture in TiAl. In contrast to many previous studies our simulations include the interaction of the crack with point defects in the lattice. We use the molecular statics technique with atomic interactions described in terms of the embedded atom method. We simulate the crack propagation along (100), (001), (110) and (111) planes in TiAl. The cleavage along (100) and (001) planes shows purely brittle behavior, whereas the cleavage along (110) and (111) planes is accompanied by extensive dislocation emission. Our studies of the crack interaction with point defects reveal that vacancies and antisites near the crack tip can influence the amount of plastic deformation. Another important observation is that the antisite formation energy near the crack tip is generally lower than in the perfect lattice. This observation suggests the formation of relatively disordered zones near the crack tip at high temperatures, and leads us to a formulation of a new mechanism of a brittle-to-ductile transition in TiAl.
Micromechanics-based approach to predict strength and stiffness of composite materials
Caliskan, Ari Garo (Virginia Tech, 1996-08-16)
One of the key issues concerning the durability of composites is the strength and stiffness degradation during service. Traditionally, these materials have been analyzed by methods which do not take into account variations in the material at the fiber/matrix level. In addition, manufacturing techniques have advanced enough so that composites can be designed from the fiber/matrix level up. As a result, it is important to predict the effect microlevel variations in the material have on macroscopic behavior. Therefore, it is vital to use a micromechanics model to calculate stress and displacement variations. In this study, the strength and stiffness of polymer matrix composites will be determined. To accomplish this, a variational model which calculates microstresses and strains due to damage is used in conjunction with a statistical strength model to predict strength. The results are compared to experimental results of uniaxial strength of carbon fiber composites. In addition, the stiffness of a continuous fiber composite was predicted and compared to a rule of mixtures equation of stiffness. A comparison showed very good agreement. To study the effect of damage, the stiffness of a continuous fiber composite with fiber fragmentation is predicted as a function of fragmentation length and fiber volume fraction. Finally the stiffness of a short-fiber composite is predicted and compared to analytical and experimental results.
Processing of Aluminum Alloys Containing Displacement Reaction Products
Stawovy, Michael Thomas (Virginia Tech, 1998-07-15)
Aluminum and metal-oxide powders were mixed using mechanical alloying. Exothermic displacement reactions could be initiated in the powders either by mechanical alloying alone or by heat treating the mechanically alloyed powders. Exponential relationships developed between the initiation time of the reaction and the mechanical alloying charge ratio. The exponential relationships were the result of changes in the intensity and quantity of collisions occurring during mechanical alloying. Differential thermal analysis of the mechanically alloyed powders indicated that increased milling time inhibited the initiation of the displacement reactions. It is believed that the reactions were inhibited because of heat dissipation from reacting oxide particles in the surrounding metal. Determining the effects of mechanical alloying on displacement reactions will lead to a more thorough understanding of the kinetics of mechanical alloying. Reacted powders were densified by uniaxial compaction and extrusion. Metallographic analysis of the reacted specimens confirmed the findings of the thermal analysis. Increased mechanical alloying inhibited the chemical reactions. Densified specimens from longer-milled mechanically alloyed specimens showed finer, more uniformly dispersed reaction products. These samples also showed increased mechanical properties as a result of their finer microstructure. Current particle strengthening models were used to accurately predict room temperature properties. Because of the fine microstructures produced, it may be possible to use similar techniques to yield new high-temperature aluminum alloys.
Scaling Effects on Damage Development, Strength, and Stress-Rupture Life on Laminated Composites in Tension
Lavoie, J. André (Virginia Tech, 1997-04-04)
The damage development and strength of ply-level scaled carbon/epoxy composite laminates having stacking sequence of [+Tn/-Tn/902n]s where constraint ply angle, T, was 0, 15, 30, 45, 60, and 75 degrees, and size was scaled as n=1,2,3, and 4, is reported in Part I. X-radiography was used to monitor damage developments. First-ply failure stress, and tensile strength were recorded. First-ply failure of the midplane 90 deg. plies depended on the stiffness of constraint plies, and size. All 24 cases were predicted using Zhang's shear-lag model and data generated from cross-ply tests. Laminate strength was controlled by the initiation of a triangular-shaped local delamination of the surface angle plies. This delamination was predicted using O'Brien's strain energy release rate model for delamination of surface angle plies. For each ply angle, the smallest laminate was used to predict delamination (and strength) of the other sizes. The in-situ tensile strength of the 0 deg. plies within different cross-ply, and quasi-isotropic laminates of varying size and stacking sequence is reported in Part II. No size effect was observed in the strength of 0 deg. plies for those lay-ups having failure confined to the gauge section. Laminates exhibiting a size-strength relationship, had grip region failures for the larger sizes. A statistically significant set of 3-point bend tests of unidirectional beams were used to provide parameters for a Weibull model, to re-examine relationship between ultimate strength of 0 deg. plies and specimen volume. The maximum stress in the 0 deg. plies in bending, and the tensile strength of the 0 deg. plies (from valid tests only) was the same. Weibull theory predicted loss of strength which was not observed in the experiments. An effort to model the durability and life of quasi-isotropic E-glass/913 epoxy composite laminates under steady load and in an acidic environment is reported in Part III. Stress-rupture tests of unidirectional coupons immersed in a weak hydrochloric acid solution was conducted to determine their stress-life response. Creep tests were conducted on unidirectional coupons parallel and transverse to the fibers, and on ±45°. layups to characterize the lamina stress- and time-dependent compliances. These data were used in a composite stress-rupture life model, based on the critical element modeling philosophy of Reifsnider, to predict the life of two ply-level thickness-scaled quasi-isotropic laminates.
Tensile and Flexure Strength of Unidirectional Fiber-Reinforced Composites: Direct Numerical Simulations and Analytic Models
Foster, Glenn C. (Virginia Tech, 1998-02-20)
A Local Load Sharing (LLS) model recently developed by Curtin and co-workers for the numerical simulation of tensile stress-strain behavior in fiber-reinforced composites is used to predict the tensile strength of metal matrix composites consisting of a Titanium matrix and unidirectionally aligned SiC fibers. This model is extended to include the effects of free boundary conditions and non-constant load gradients and then used to predict the strength of a Ti-6Al-4V matrix reinforced with Sigma SiC fibers under 4-point flexure testing. The predicted tensile and flexure strengths agree very well with the values measured by Gundel and Wawner and Ramamurty et al. The composite strength of disordered spatial fiber distributions is investigated and is shown to have a distribution similar to the corresponding ordered composite, but with a mean strength that decreases (as compared to the ordered composite) with increasing Weibull modulus. A modified Batdorf-type analytic model is developed and similarly extended to the case of non-uniform loading to predict the strength of composites under tension and flexure. The flexure model is found to be inappropriate for application to the experimental materials, but the tensile model yields predictions similar to the Local Load Sharing models for the experimental materials. The ideas and predictions of the Batdorf-type model, which is essentially an approximation to the simulation model, are then compared in more detail to a simulation-based model developed by Ibnabdeljalil and Curtin to more generally assess the accuracy of the Batdorf model in predicting tensile strength and notch strength versus composite size and fiber Weibull modulus. The study shows the Batdorf model to be accurate for tensile strength at high Weibull moduli and to capture general trends well, but it is not quantitatively accurate over the full range of material parameters encountered in various fiber composite systems.
Tensile behavior of unidirectional and cross-ply ceramic matrix composites
Herrmann, Rebecca K. (Virginia Tech, 1996-02-15)
The tensile behavior of two ceramic matrix composites (CMC's) was observed. The materials of interest in this study were a glass-ceramic matrix composite (GCMC) reinforced with Nicalon fibers and a Blackglas™ composite also reinforced with Nicalon fibers. Both had a symmetric cross-ply layup. Initial observations of the composites showed significant porosity and some cracking in the Blackglas™ samples. The GCMC samples showed considerably less damage. From the observed tensile behavior of the cross-ply composites, a 'back-out' factor for determining the 0° ply data of the composite was calculated using Classical Lamination Theory (CLT). The predicted behavior of the 0° ply was then compared to actual data supplied by McDonnell Douglas Corporation. While the Blackglas™ material showed good correlation, the GCMC did not. Analysis indicates that the applicability of this technique is strongly influenced by the initial microstructure of the composite, i.e., porosity, cracking. Fracture mirror measurements were also observed to determine the in-situ strength of the Nicalon fibers. Resulting characteristic strength and Weibull modulus values combined with measured fiber pullout lengths were then used to determine material parameters such as the ultimate tensile strength, strain to failure, work of pullout, sliding distance at the characteristic strength, and interfacial shear stress. Comparisons of measured and calculated ultimate tensile strengths and strains to failure showed good agreement. This research was sponsored by the Naval Surface Warfare Center (NSWC) in Dahlgren VA.
Time-dependent damage evolution and failure in materials. I. Theory
Curtin, William A. Jr.; Scher, H. (American Physical Society, 1997-05-01)
Damage evolution and time-to-failure are investigated for a model material in which damage formation is a stochastic event. Specifically, the probability of failure at any site at time t is proportional to sigma(i)(t)(eta), where sigma(i)(t) is the local stress at site i at time t and differs from the applied stress because of the stress redistribution from prior damage. An analytic model of the damage process predicts two regimes of failure: percolationlike failure for eta less than or equal to 2 and ''avalanche'' failure for eta > 2. In the percolationlike regime, failure occurs by gradual global accumulation of damage culminating in a connected cluster which spans the system. In the avalanche regime, failure occurs by rapid growth of a single crack after a transient period during which the critical crack developed. The scalings of the transient period, the subsequent crack dynamics, and the time-dependent probability distribution for failure are determined analytically as functions of the system size and the exponent eta. Specific predictions are that failure is more abrupt with increasing eta, failure times scale inversely with a power of the logarithm of system size, and the distribution of failure times is a double exponential and broadens with increasing eta, so that the failure becomes less predictable as it is becoming more abrupt. The conditions for the transition to the rapid growth regime are identified, offering the possibility of early detection of impending failure. In a companion paper, numerical simulations of this failure process in two-dimensional lattices are compared in detail to the analytical predictions.
Time-dependent damage evolution and failure in materials. II. Simulations
Curtin, William A. Jr.; Pamel, M.; Scher, H. (American Physical Society, 1997-05-01)
A two-dimensional triangular spring network model is used to investigate the time-dependent damage evolution and failure of model materials in which the damage formation is a nucleated event. The probability of damage formation r(i)(t) at site i at time t is taken to be proportional to the local stress at site i raised to a power: r(i)(t) = A sigma(i)(t)(eta). As damage evolves in the material, the stress state becomes heterogeneous and drives preferential damage evolution in regions of high stress. As predicted by an analytical model and observed in previous electrical fuse network simulations, there is a transition in the failure behavior at eta = 2: for eta less than or equal to 2, the failure time and damage density are independent of the system size; for eta > 2, the failure time and damage decrease with increasing time and failure occurs by the formation of a finite Critical damage region which rapidly propagates across the remainder of the material. The stress distribution prior to failure exhibits no abrupt changes or scalings that indicate imminent failure. The scalings of the failure time and the failure time distribution are investigated, and compared with analytic predictions. The failure time scales as a power law in In N-T, where N-T is the system size, but the exponent is not the predicted value of 1 - eta/2; this is attributed to a difference in the stress concentration factors (scf) between the discrete lattice and a continuum model. Using the scf values for the lattice lead to predicted scalings consistent with the simulations. Predicted absolute failure times versus size are generally in good agreement with simulation results at larger eta values. The coefficient of variation of the failure time distribution is observed to be nearly constant, in slight contrast to the predicted scaling of (InNT)(-1). Overall, the simulation results quantitatively and qualitatively validate many of the critical predictions of the analytic model.
Toughening in disordered brittle materials
Curtin, William A. Jr. (American Physical Society, 1997-05-01)
The growth of a planar crack through a heterogeneous brittle material is investigated using a discrete cubic lattice of springs with distributed spring toughnesses and lattice Green's functions to determine crack propagation. The toughness, or stress required to grow an initial crack, is found to be a stochastic quantity and depends on the width of the distribution. For narrow distributions, the toughness is less than the thermodynamic value and is controlled by the nucleation of kinks at low toughness regions (weakest links), which then grow laterally in an unstable manner. For brood distributions, the average toughness approaches the thermodynamic value, with some specific configuration having greater values, and is controlled by high toughness regions pinning a rough crack front. The rough crack front exhibits nontrivial scaling with crack width and a ''strongest-link'' behavior that differs from the usual weak-link behavior found in weakly disordered materials. Materials with broad distributions are also less sensitive to small preexisting defects. The difference in toughness between narrow and broad distributions is only about 10%; that is much smaller than suggested by similar studies on 2d materials and demonstrates the very important role played by geometry-dimensionality in this problem. One implication of these results is that toughness in complex or heterogeneous materials does not stem from simple disorder in toughnesses; more complex and microstructure-specific mechanisms such as microcracking and grain bridging must occur.

Browsing by Author "Curtin, William A. Jr."

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