Showing papers by "John W. Hutchinson published in 2005"

Onset of Buckling in Drying Droplets of Colloidal Suspensions

Abstract: Minute concentrations of suspended particles can dramatically alter the behavior of a drying droplet. After a period of isotropic shrinkage, similar to droplets of a pure liquid, these droplets suddenly buckle like an elastic shell. While linear elasticity is able to describe the morphology of the buckled droplets, it fails to predict the onset of buckling. Instead, we find that buckling is coincident with a stress-induced fluid to solid transition in a shell of particles at a droplet's surface, occurring when attractive capillary forces overcome stabilizing electrostatic forces between particles.

An analytical model of rumpling in thermal barrier coatings

Abstract: Multilayer thermal barrier coatings (TBCs) deposited on superalloy turbine blades provide protection from combustion temperatures in excess of 1500 °C. One of the dominant failure modes comprises cracking from undulation growth, or rumpling, of the highly compressed oxide layer that grows between the ceramic top coat and the intermetallic bond coat. In this paper, a mechanistic model providing an analytical approximation of undulation growth is presented for realistic cyclic thermal histories. Thickening, lateral growth straining and high temperature yielding of the oxide layer are taken into account. Undulation growth in TBC systems is highly nonlinear and characterized by more than 20 material and geometric parameters, highlighting the importance of a robust yet computationally efficient model. At temperatures above 600 °C, the bond coat creeps. Thermal expansion mismatch occurs between the superalloy substrate and the oxide layer and, in some systems, the bond coat. In addition, some bond coats, such as PtNiAl, exhibit a martensitic phase transformation accompanied by nearly a 1% linear expansion, giving rise to a large effective mismatch. These two mismatches promote undulation growth. Nonlinear interaction between the stress in the bond coat induced by the constraining effect of the thick substrate and normal tractions applied at the surface of the bond coat by the compressed, undulating oxide layer produces an increment of undulation growth during each thermal cycle, before the stress decays by creep. A series of problems for systems without the ceramic top coat are used to elucidate the mechanics of undulation growth and to replicate trends observed in a series of experiments and in prior finite-element simulations. The model is employed to study for the first time the effect on undulation growth of a shift in the temperature range over which the transformation occurs, as well as the relative importance of the transformation compared to thermal expansion mismatch. The role of the top coat and other viable ways of reducing undulation growth are considered.

Self-assembled Shells Composed of Colloidal Particles: Fabrication and Characterization

Abstract: We construct shells with tunable morphology and mechanical response with colloidal particles that self-assemble at the interface of emulsion droplets. Particles self-assemble to minimize the total interfacial energy, spontaneously forming a particle layer that encapsulates the droplets. We stabilize these layers to form solid shells at the droplet interface by aggregating the particles, connecting the particles with adsorbed polymer, or fusing the particles. These techniques reproducibly yield shells with controllable properties such as elastic moduli and breaking forces. To enable diffusive exchange through the particle shells, we transfer them into solvents that are miscible with the encapsulant. We characterize the mechanical properties of the shells by measuring the response to deformation by calibrated microcantilevers.

The Mechanics of Indentation Induced Lateral Cracking

Abstract: The mechanics governing the lateral cracks that form when a hard object plastically penetrates a ceramic is presented. The roles of indentation load, penetration depth, and work of indentation are all highlighted, as are the influences of the mechanical properties of the material. A closed form solution for cracking induced by expansion of a two-dimensional cavity is used to bring out essential features related to parametric dependence and scaling. The three-dimensional axisymmetric problem for an annular crack driven by a rigid spherical or conical indenter is solved using numerical methods. The region of highest tensile stress is identified corresponding to the location where a crack is most likely to nucleate. This location coincides with the depth below the surface where the crack will expand parallel to the surface under mode I conditions. The solutions have been substantiated by comparison with measurements of the cracks that form upon Vickers indentation. The basic formula for the crack radius has been used to predict trends in cracking upon static penetration and impact by a projectile. In both cases, the extent of the cracking is substantially diminished by increasing the toughness of the material. The yield strength has a much smaller effect. The cracks caused by penetration and the volume removed per impact both decrease marginally at higher yield strength.

Composite Laminates in Plane Stress: Constitutive Modeling and Stress Redistribution due to Matrix Cracking

Abstract: Plane-stress constitutive relations for laminate composites undergoing matrix cracking are developed that can be fit to data from uniaxial tests. The constitutive equations are specialized to brittle-matrix composites in the form of cross-plies and quasi-isotropic laminates. The effect of nonlinear stress-strain behavior on stress redistribution around holes and notches in laminate plates is illustrated.

Coupled Plastic Wave Propagation and Column Buckling

Abstract: The plastic buckling of columns is explored in a regime where plastic wave propagation and lateral buckling are nonlinearly coupled. Underlying the work is the motivation to understand and quantify the dynamic crushing resistance of truss cores of all-metal sandwich plates where each truss member is a clamped column. Members are typically fairly stocky such that they buckle plastically and their load carrying capacity decreases gradually as they buckle, even at slow loading rates. In the range of elevated loading rates of interest here, the columns are significantly stabilized by lateral inertia, resisting lateral motion and delaying buckling and loss of load carrying capacity to relatively large overall plastic strains. The time scale associated with dynamic axial behavior, wherein deformation spreads along the column as a plastic wave, is comparable to the time scale associated with lateral buckling such that the two phenomena are coupled. Several relevant problems are analyzed using a combination of analytical and numerical procedures. Material strain-rate dependence is also taken into account. Detailed finite element analyses are performed for axially loaded columns with initial imperfections, as well as for inclined columns in a truss core of a sandwich plate, with the aim of determining the resistance of the column to deformation as dependent on the loading rate and the relevant material and geometric parameters. In the range of loading rates of interest, dynamic effects result in substantial increases in the reaction forces exerted by core members on the faces of the sandwich plate with significant elevation in energy absorption. DOI: 10.1115/1.1825437

Non-uniform Hardening Constitutive Model for Compressible Orthotropic Materials with Application to Sandwich Plate Cores

Abstract: A constitutive model for the elastic-plastic behavior of plastically compressible orthotropic materi- als is proposed based on an ellipsoidalyield surface with evolving ellipticity to accommodate non-uniform hard- ening or softening associated with stressing in different directions. Themodel incorporatesrate-dependencearis- ing from material rate-dependence and micro-inertial ef- fects. The basic inputs are the stress-strain responses under the six fundamental stress histories in the or- thotropicaxes. Special limitsofthemodel includeclassi- cal isotropichardening theory, the Hill model for incom- pressible orthotropic solids, and the Deshpande-Fleck model for highly porous isotropic foam metals. A pri- mary motivation is application to metal core structure in sandwich plates wherein the core is modeled by a con- tinuumconstitutivemodel. The constitutivemodel is im- plemented withinafinite element framework to represent the behavior of square honeycomb metal cores of sand- wich plates subject to quasi-static and dynamic loads. Input identification is illustrated for numerical formula- tionsthatemployoneelement throughthecorethickness. Representationsof the core with oneelement through the thickness are shown to be able to capture most of the im- portant influences of nonlinear core behavior on overall response of sandwich plates under both quasi-static and dynamic loadings. a general class of plastically compressible, orthotropic solids based on an ellipsoidal yield surface which incor- porates non-uniform hardening. The constitutive model has considerable flexibility. Limits of the model include many of the important phenomenologicalconstitutivere- lations for elastic-plastic solids: classical isotropic plas- ticity, Hill's theory for incompressible orthotropic plas- ticity, and the Deshpande-Fleck theory for highly com- pressible isotropic metal foams. A salient feature of the formulation is its ability to model distinct hardening or softening behaviors under different stressing conditions, with applicationto both plasticallyincompressiblesolids and highly compressible materials. For application to metal sandwich cores, the approach requires inputsspecifyingthe stress-strainbehaviorchar- acterizing single component stressing in orthotropicaxes for each of the six components of stress. These basic inputs can be obtained from theoretical models, exper- imental data or numerical simulations, or combinations of all three. Once the inputs are characterized, the con- stitutive model can be used to represent the core in con- nection with standard finite element codes. In this paper, the commercial code ABAQUS Explicithas been used in connection with a user-supplied subroutinethat has been constructed based on the constitutive model. The pa- per illustrates the process of identifying the input stress- strain data for square honeycomb cores. It also demon- strates that representing the core by elements extending all the way through the core can be accurate and highly efficient in the analysis of sandwich plates deformed un- der quasi-static and dynamic loads to large deflections. Simulations based on full three-dimensional meshing of the core demonstrate the validity of the approach. The present paper continues the effort underway for sev- eral years by a number of groups to develop contin- uum constitutiverelations to characterize a range of core structures and to validate them for structural applica- tions (Deshpande, Fleck and Ashby (2001); Hanssen, Langseth and Hopperstad (2002); Mohr and Doyoyo

Stress and Strain Evolution in Cast Refractory Blocks during Cooling

Abstract: A computational model has been developed to study the stress and strain histories experienced by zirconia-containing cast refractory blocks when they are cooled from the casting temperature. Incorporated into the model are strong temperature dependencies of the following material properties: elastic modulus, flow strength, thermal conductivity, and thermal expansion. The pressure-sensitive Drucker-Prager plasticity model has been used to account for the substantial difference between the tensile and compressive stress-strain behaviors found in these refractories. The temperature-induced phase transformation in the zirconia, as well as the overall thermal contraction, are united by introducing a coefficient of total dilatation. A nonuniform radial distribution of the transforming phase is also incorporated. The parameters that control the time-dependent stress and strain responses are identified by performing calculations that span the range of expected variables. Process strategies for manufacturing crack-free blocks are suggested.

Technical Cost Framework for High-Temperature Manufacturing of Small Components and Devices

Abstract: The high-temperature step that is required in a manufacturing process can contribute substantially to the cost. A technical cost framework (TCF) that allows trends in these costs to be determined as a function of the essential variables provides opportunities for their minimization. The basic variables are the furnace capacity, the operating temperature, and the furnace construction. The dependent variables are power, acquisition, and replacement. Information from thermal and process models as well as the furnace element life expectancy provides the functions needed to conduct the minimization through the TCF. The overall strategy is developed and illustrated with examples.