Showing papers by "John W. Hutchinson published in 2000"

Metal Foams: A Design Guide

Abstract: Introduction Making Metal Foams Characterization Methods Properties of Metal Foams Design Analysis for Material Selection Design Formulae for Simple Structures A Constitutive Model for Metal Foams Design for Creep with Metal Foams Sandwich Structures Energy Management: Packaging and Blast Protection Sound Absorption and Vibration Suppression Thermal Management and Heat Transfer Electrical Properties of Metal Foams Cutting, Finishing and Joining Cost Estimation and Viability Case Studies Suppliers of Metal Foams Web Sites Index .

An extended model for void growth and coalescence

Abstract: A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

Mechanism-based strain gradient plasticity—II. Analysis

Abstract: A mechanism-based theory of strain gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on strain gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based strain gradient plasticity, and kinematic relations among strains, strain gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic strain gradients. In bending of thin beams and torsion of thin wires, mechanism-based strain gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to strain gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that strain gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.

Ordering of Spontaneously Formed Buckles on Planar Surfaces

Abstract: This paper describes the spontaneous formation of patterns of aligned buckles in a thin film of gold deposited on the surface of an elastomer [poly(dimethylsiloxane), PDMS]. The surface of the elastomer is patterned photochemically into areas differing in stiffness and coefficient of thermal expansion. The gold is deposited while the surface of the patterned elastomer is warm (T ∼ 100 °C). On cooling, shrinkage in the elastomer places the gold film under compressive stress. The buckles relieve this compressive stress. The distribution of stresses and buckle patterns is described during the pre- and postbuckling regimes using solutions from calculations describing a model comprising a thin stiff plate resting on a thick elastic foundation.

Crack patterns in thin films

Abstract: A two-dimensional model of a film bonded to an elastic substrate is proposed for simulating crack propagation paths in thin elastic films. Specific examples are presented for films subject to equi-biaxial residual tensile stress. Single and multiple crack geometries are considered with a view to elucidating some of the crack patterns which are observed to develop. Tendencies for propagating cracks to remain straight or curve are explored as a consequence of crack interaction. The existence of spiral paths is demonstrated.

The influence of imperfections on the nucleation and propagation of buckling driven delaminations

Abstract: The influence of prototypical imperfections on the nucleation and propagation stages of delamination of compressed thin films has been analyzed Energy release rates for separations that develop from imperfections have been calculated These demonstrate two characteristic quantities: a peak that governs nucleation and a minimum that controls propagation and failure These quantities lead to two separate criteria that both need to be satisfied to cause failure They involve a critical film thickness for nucleation and a critical imperfection wavelength for buckling Implications for the avoidance of failure are discussed

Asymmetric Four-Point Crack Specimen

Abstract: Accurate results for the stress intensity factors for the asymmetric four-point bend specimen with an edge crack are presented. A basic solution for an infinitely long specimen loaded by a constant shear force and a linear moment distribution provides the reference on which the finite geometry solution is based.

Chapter 2 - Making metal foams

Abstract: This chapter describes the nine processes used for producing metal foams, five of which are established commercially They fall into four broad classes: first, where the foam is formed from the vapor phase; second, where the foam is electrodeposited from an aqueous solution; third, where it depends on liquid-state processing; and fourth, where the foam is created in the solid state The properties of metal foam and other cellular metal structures depend on the properties of the metal, the relative density, and the cell topology The nine processes include bubbling gas through molten Al-SiC or Al-A1 2 O 3 alloys; stirring a foaming agent (typically TiH 2 ) into a molten alloy (typically an aluminum alloy) and controling the pressure while cooling; consolidation of a metal powder with a particulate foaming agent followed by heating into the mushy state when the foaming agent releases hydrogen, expanding the material; manufacturing a ceramic mold from a wax or polymer-foam precursor followed by burning-out of the precursor and pressure infiltration with a molten metal or metal powder slurry which is then sintered; vapor phase deposition or electro deposition of metal onto a polymer foam precursor; trapping of high-pressure inert gas in pores by powder hot isostatic pressing; sintering of hollow spheres; co-pressing of a metal powder with a leachable powder; and dissolution of gas in a liquid metal under pressure

Chapter 4 - Properties of metal foams

Abstract: The characteristics of foam are best summarized by describing the material from which it is made, its relative density, and stating whether it has open or closed cells. The foam properties are influenced by structure, anisotropy, and defects such as wiggly, buckled or broken cell walls, and cells of exceptional size or shape.. Open-cells foams have a long, well-defined plateau stress , where the cell edges yield while bending. Closed-cell foams show more complicated behavior that can cause the stress to rise with increasing strain as the cell faces carry membrane (tensile) stresses. The plateau continues up to the densification strain , beyond which the structure compacts and the stress rises steeply. The tensile stress-strain behavior of metal foams differs from that in compression. The slope of the stress-strain curve before general yield is less than E , implying considerable micro-plasticity even at very small strains. The damping capacity of metal foam is typically five to ten times greater than that of the metal from which it is made, and they also have some capacity as acoustic absorbers. The melting point, specific heat, and expansion coefficient of metal foams are the same as those of the metal from which they are made.

Heat generation during the fatigue of a cellular Al alloy

Abstract: The heat generation from a notch during the compression-compression fatigue of a cellular Al alloy has been measured and compared with a model. The measurements indicate that heat is generated because of hysteresis occurring in narrow cyclic plastic zones outside the notch. This process continues until the notch closes. At closure, a brief period of heat generation arises because of friction along the notch faces. A plasticity model based on the Dugdale zone is shown to provide a reasonably accurate characterization of the heat generated, with the proviso that an “ineffective” zone be transposed onto the notch tip. It is found that the temperatures generated are too small to cause fatigue by thermal softening. A fatigue mechanism based on either geometric softening of the cells or crack growth in the cell walls is implied.

Chapter 11 - Energy management: Packaging and blast protection

Abstract: This chapter reviews energy absorption in metal foams, comparing them with other competing systems. The function of packaging is to protect the packaged object from damaging acceleration or deceleration, which may be accidental. The damage tolerance of an object is measured by the greatest acceleration or deceleration it can tolerate without harm. Ideal energy absorbers have a long, flat stress-strain curve. Energy absorbers for packaging and protection are chosen so that the plateau stress is just below that which will cause damage to the packaged object. The best choice is the one which has the longest plateau, and therefore absorbs the most energy. Solid sections do not perform well in this role. Hollow tubes, shells, metal honeycombs, and foams have the right sort of stress-strain curves. The thickness of foam is chosen in a way that all the kinetic energy of the object is absorbed at the instant, when the foam crushes to the end of the plateau. Thin-walled metal tubes are efficient energy absorbers when crushed axially. It is important to separate the effect of strain rate and the impact velocity on the dynamic response of metallic foam. When metal foam is impacted at a sufficiently high velocity, a plastic shock wave passes through it and the plateau stress rises. Explosives create a pressure wave of approximately a triangular profile, known as a “blast.” Blast protection is achieved by attaching a heavy buffer plate, mounted on an energy absorber, to the face of the object to be protected.

Chapter 3 - Characterization methods

Abstract: The cellular structure of metallic foams requires special precautions in characterization and testing. This chapter summarizes reliable methods for characterizing metallic foams in uniaxial compression, uniaxial tension, and shear and multiaxial stress states, under conditions of creep and fatigue, and during indentation. A metal foam is characterized structurally by its cell topology, relative density, cell size, cell shape, and anisotropy. Optical microscopy is helpful in characterizing metal foams provided that the foam is fully impregnated with opaque epoxy (or equivalent) before polishing. Scanning electron microscopy (SEM) is straightforward, where the only necessary precaution is related to surface preparation. X-ray Computed Tomography (CT) gives low magnification images of planes within the foam, which can be assembled into a three-dimensional image. The ratio of the specimen size to the cell size can affect the measured mechanical properties of foams. Uniaxial compressive tests are best performed on prismatic or cylindrical specimens of foam with a height-to-thickness ratio exceeding 1.5. Uniaxial tension tests can be performed on either waisted cylinder or dog-bone specimens. The shear modulus of metallic foams is most easily measured by torsion tests on waisted cylindrical specimens. An alternative test for the measurement of shear strength is ASTM C-273. The most useful form of fatigue test is the stress-life S-N test, performed in load control. Care is needed to define the fatigue life of a foam specimen. There are three types of fatigue: tension–tension fatigue, shear fatigue, and compression–compression fatigue.

Chapter 17 - Case studies

Abstract: This chapter provides eight case studies on the potential applications of metal foams. Karmann designs and produces vehicles for original equipment makers (OEMs). The first case study is on Aluminum Foam System, developed by Karmann, which introduced a revolutionary technology in body panels. It claims that these aluminum foams offer cost-effective performance as structural automotive parts that are up to ten times stiffer and 50% lighter than the equivalent parts made of steel. In a typical compact family sedan, this would lead to a mass saving of 60 kg, translating into a reduction in fuel consumption of 2.6 miles per gallon. The second case study focuses on integrally molded foam parts such as MEPURA ALULIGHT, which can be molded to give complex shapes having dense skins with foamed cores. A small amount of metal reduces the thermal conductivity significantly, but the electrical conductivity remains high. The structure also has good damage tolerance and an energy-absorbing capability. The third study is on ALPORAS, developed by Shinko Wire Company Ltd, for use as soundproofing material that can be installed along the sides of a road or a highway, to reduce traffic noise. The company manufacturer claims that the material is fire resistant, does not generate harmful gases in the presence of a flame, has excellent durability, has resistance to weathering, does not absorb water, and can be washed down to keep it clean.

Chapter 6 - Design formulae for simple structures

Abstract: This chapter illustrates design formulae for simple structures, which are used for approximate analyses of the response of structures to load. Each involves one or more material properties. The properties of metal foams differ greatly from those of solid metals. Constitutive equations for mechanical response, elastic deflection of beams and panels, failure of beams and panels, buckling of columns, panels and shells, torsion of shafts, contact stresses, vibrating beams, tubes and disks, and creep are reviewed. Constitutive equations are the basic equations that determine mechanical response. When a beam is loaded by a force, F, or moments, M, the initially straight axis is deformed into a curve. Used as beams, foams have approximately the same index value as the material of which they are made; as panels, they have a higher one. There are three criteria for failures of beams: when stress reaches the yield strength, σ y , of the material of the beam, small zones of plasticity appear at the surface; when maximum fiber stress reaches the brittle fracture strength, σ f , of the material of the beam, a crack nucleates at the surface and propagates inward; and when the plastic zones penetrate through the section of the beam, linking to form a plastic hinge.

Chapter 8 - Design for fatigue with metal foams

Abstract: In structural applications for metallic foams, such as in sandwich panels, it is necessary to take into account the degradation of strength with cyclic loading. A major cause of this degradation is the nucleation and growth of cracks within the foams. This chapter demonstrates that the characteristic feature of metallic foams is their high damage tolerance, where the degradation in strength due to the presence of a hole or a crack in the foam is usually minor, and there is no need to adopt a fracture mechanics approach. In tension–tension loading, a single macroscopic fatigue crack develops at the weakest section and progresses across the section with negligible additional plastic deformation. In compression–compression fatigue, the behavior is strikingly different. After an induction period, large plastic strains, of magnitude up to 0.6, gradually develop and the material behaves in a quasi-ductile manner .The underlying mechanism is thought to be a combination of distributed cracking of cell walls and edges, and cyclic ratcheting under non-zero mean stress. Both the mechanisms lead to the progressive crushing of the cells. Type I behavior, Type II behavior, and Type II behavior are the three types of deformation patterns developed.

Chapter 5 - Design analysis for material selection

Abstract: A material is selected for a given component when its property profile matches the demands of an application. The desired property profile characterizes the application. This chapter describes how property profiles of metal foams are established. A property profile is a statement of the characteristics required of a material if it is to perform well in a given application. It is identified by examining the function of the component, the objectives that are foremost in the designer's mind, and the constraints that the component must meet if it is to perform adequately. It identifies simple property limits that are dictated by constraints imposed by the design and identifies material indices that capture design objectives.. Materials indices help identify applications in which a material might excel. Material-selection charts allow the values of indices for metal foams to be established and compared with those of other engineering materials.

Chapter 10 - Sandwich structures

Abstract: Sandwich panels offer high stiffness at low weight. Their cores have the drawbacks that they cannot be used much above room temperature, and that their properties are moisture-dependent. The deficiencies can be overcome by using metal foams as cores. This chapter discusses the potential of the metal-foam-cored sandwich structures. Met foam-cored sandwiches are isotropic, can be shaped to doubly curved surfaces, and can be less expensive than attachment-stiffened structures. Syntactic foams—foams with an integrally shaped skin—offer additional advantages, allowing cheap, light structures to be molded in a single operation. The syntactic polymer foams command a large market. Technologies are emerging for creating syntactic met foam structures. Strength and stiffness, both are important while designing a sandwich beam. To exploit sandwich structures to the full, they must be optimized , usually by seeking to minimize mass for a given bending stiffness and strength. The benchmarks for comparison between optimized sandwich structures and rib-stiffened structures are stringer or waffle-stiffened panels or shells and honeycomb cored sandwich panels. Weight-efficient designs of panels, shells, and tubes subject to bending or compression are determined by structural indices based on load, weight, and stiffness. Weight is minimized subject to allowable stresses, stiffnesses, and displacements, depending on the application.

Chapter 12 - Sound absorption and vibration suppression

Abstract: The ability to damp vibration coupled with mechanical stiffness and strength at low weight makes an attractive combination. Metal foams have higher mechanical damping than the solid of which they are made, but this is not the same as sound absorption. Sound absorption can occur in many ways: by direct mechanical damping in the material itself, by thermo-elastic damping, by viscous losses as the pressure wave pumps air in and out of the cavities in the absorber, and by vortex-shedding from sharp edges. Metal forms are good absorbers but not as good as the materials like felt or fiberglass. More significant is that the high flexural stiffness, low mass of foam, and the foam-cored panels result in high natural vibration frequencies, and this makes them hard to excite. So, while metal foams and met foam-cored panels offer some potential for vibration and acoustic management, their greater attraction lies in the combination of this attribute with others such as of stiffness at light weight, mechanical isolation, fire protection, and chemical stability. All the materials dissipate some energy during cyclic deformation, through intrinsic material damping and hysteresis. Damping becomes important when a component is subject to input excitation at or near its resonant frequencies.

Chapter 13 - Thermal management and heat transfer

Abstract: The cellular metal is envisaged as a system that transfers heat from a hot surface into a fluid. The thermal conductivities of metal foams are at least an order of magnitude greater than their non-metallic counterparts, so they are generally not suited for simple thermal insulation though they can provide some fire protection. The thermal conductivities of closed-cell foams are; however, lower than those of the fully dense parent metal by a factor of between 8 and 30, offering a degree of fire protection. Open-cell metal foams can be used to enhance heat transfer in applications such as heat exchangers for airborne equipment, compact heat sinks for power electronics, heat shields, air-cooled condenser towers, and regenerators. This chapter summarizes the heat-transfer characteristics of open-cell metal foams. Open-cell foams having different morphology are expected to have different coefficients. As the heat transfer coefficient increases, the pressure drops across the medium. The latter can sometimes be a limiting factor in application because of the limitations on the available pumping power.

Chapter 9 - Design for creep with metal foams

Abstract: Creep of metals and of foams made from them becomes important at temperatures above about one-third of the melting point. The creep of metallic foam depends on its relative density and on the creep properties of the solid from which it is made. The dominant mechanism of creep depends on stress and temperature. The time to rupture for a solid metal can be found by assuming that the failure is associated with a constant critical strain in the material so that the product of the time to rupture and the secondary strain rate is constant. The primary creep regimen is short. The tertiary creep, terminated by a rupture, follows the extended period of the secondary creep. In compression, the behavior is somewhat different. The chapter provides models for the steady–state creep of foams. The secondary creep rate under multi axial stresses is found using a constitutive equation for the metallic foams. Both normal and shear stresses are significant for the metal foam core sandwich beams.

Chapter 7 - A constitutive model for metal foams

Abstract: The plastic response of metal foams differs fundamentally from that of the fully dense metals because foams compact when compressed, and the yield criterion is dependent on pressure. A constitutive relation characterizing this plastic response is an essential input for design with foams. Fully dense metals deform plastically at constant volume. The yield criterion, which characterizes the plastic behavior of dense metals, is independent of mean stress. The theory presented in the chapter can be modified in a straightforward manner to account for the effect of porosity on the yield criterion and strain-hardening law for metallic foam. Some metallic foams harden in compression but soften after yielding in tension. This behavior, not captured by the present constitutive law, is caused by the onset of a cell-wall fracture mechanism that progressively weakens the structure as the strain increases.

Chapter 16 - Cost estimation and viability

Abstract: Viability means that the balance between performance and cost is favorable It has three ingredients: a technical model of the performance of the material in a given application, a cost model giving an estimate of material and process costs, and a value model which balances performance against cost Constructing a value function that includes measures of both performance and cost assesses viability It allows ranking of materials by both economic and technical criteria Balancing cost against performance is an example of multi objective optimization This chapter discusses the role of cost and performance metrics in determining viability Performance metric measures the performance offered by the material in a particular application The manufacture of foam consumes resources The final cost is the sum of these resources This resource-based approach to cost analysis is helpful in selecting materials and processes At present, all metal foams are produced in small quantities using time and labor-intensive methods The role of a cost model is to assess, identify cost drivers, examine the ultimate limits to cost reduction, and guide process development

Chapter 14 - Electrical properties of metal foams

Abstract: The electrical conductivity of metal foam is less than that of the metal. Though reduced, the conductivity of metal foams is more than adequate to provide good electrical grounding and shielding of electromagnetic radiation. The large, accessible surface area of open-cell metal foams makes them attractive as electrodes for batteries. Nickel foams are extensively used in this application. The electrical resistivity of a thick metal foam sheet can be measured using a four-point probe technique. There is a very little data for the electrical resistivity of metal foams. Electrical conductivity depends on relative density. A four-point probe method is used for measuring the electrical conductivity of metal foams. The conductivity varies in a non-linear way with relative density.