S. Nemat-Nasser

Brittle Failure in Compression: Splitting, Faulting and Brittle-Ductile Transition

The micromechanics of brittle failure in compression and the transition from brittle to ductile failure, observed under increasing confining pressures, are examined in the light of existing experimental results and model studies. First, the micromechanics of axial splitting and faulting is briefly reviewed, certain mathematical models recently developed for analysing these failure modes are outlined, and some new, simple closed-form analytic solutions of crack growth in compression and some new quantitative model experimental results are presented. Then, a simple two-dimensional mathematical model is proposed for the analysis of the brittle—ductile transition process, the corresponding elasticity boundary-value problem is formulated in terms of singular integral equations, the solution method is given, and numerical results are obtained and their physical implications are discussed. In addition, a simple closed-form analytic solution is presented and, by comparing its results with those of the exact formulation, it is shown that the analytic estimates are reasonably accurate in the range of the brittle response of the material. Finally, the results of some laboratory model experiments are reported in an effort to support the mathematical models.

Electromechanical response of ionic polymer-metal composites

An ionic polymer-metal composite (IPMC) consisting of a thin Nafion sheet, platinum plated on both faces, undergoes large bending motion when an electric field is applied across its thickness. Conversely, a voltage is produced across its faces when it is suddenly bent. A micromechanical model is developed which accounts for the coupled ion transport, electric field, and elastic deformation to predict the response of the IPMC, qualitatively and quantitatively. First, the basic three-dimensional coupled field equations are presented, and then the results are applied to predict the response of a thin sheet of an IPMC. Central to the theory is the recognition that the interaction between an imbalanced charge density and the backbone polymer can be presented by an eigenstress field (Nemat-Nasser and Hori, Micromechanics, Overall Properties of Heterogeneous Materials, 2nd Ed., Elsevier, Amsterdam, 1999). The constitutive parameter connecting the eigenstress to the charge density is calculated directly using a s...

Micromechanics of Actuation of Ionic Polymer-metal Composites

Ionic polymer-metal composites (IPMCs) consist of a polyelectrolyte membrane (usually, Nafion or Flemion) plated on both faces by a noble metal, and is neutralized with certain counter ions that balance the electrical charge of the anions covalently fixed to the backbone membrane. In the hydrated state (or in the presence of other suitable solvents), the composite is a soft actuator and sensor. Its coupled electrical-chemical-mechanical response depends on: (1) the chemical composition and structure of the backbone ionic polymer; (2) the morphology of the metal electrodes; (3) the nature of the cations; and (4) the level of hydration (solvent saturation). A systematic experimental evaluation of the mechanical response of both metal-plated and bare Nafion and Flemion in various cation forms and various water saturation levels has been performed in the author’s laboratories at the University of California, San Diego. By examining the measured stiffness of the Nafion-based composites and the corresponding bare Nafion, under a variety of conditions, I have sought to develop relations between internal forces and the resulting stiffness and deformation of this class of IPMCs. Based on these and through a comparative study of the effects of various cations on the material’s stiffness and response, I have attempted to identify potential micromechanisms responsible for the observed electromechanical behavior of these materials, model them, and compare the model results with experimental data. A summary of these developments is given in the present work. First, a micromechanical model for the calculation of the Young modulus of the bare Nafion or Flemion in various ion forms and water saturation levels is given. Second, the bare-polymer model is modified to include the effect of the metal plating, and the results are applied to calculate the stiffness of the corresponding IPMCs, as a function of the solvent uptake. Finally, guided by the stiffness modeling and data, the actuation of the Nafion-based IPMCs is micromechanically modeled. Examples of the model results are presented and compared with the measured data.

Hopkinson techniques for dynamic recovery experiments

Novel techniques are introduced to render the classical split Hopkinson bar apparatus suitable for dynamic recovery experiments, where samples can be subjected to a single pulse of pre-assigned shape and duration, and then recovered without any additional loading, for post-test characterization; i. e., techniques for fully controlled unloading in Hopkinson bar experiments. For compression dynamic recovery tests, the new design generates a compressive pulse trailed by a tensile pulse (stress reversal), travelling toward the sample. Furthermore, all subsequent pulses which reflect off the free ends of the two bars (incident and transmission) are rendered tensile, so that the sample is subjected to a single compressive pulse whose shape and duration can also be controlled. For tension recovery experiments, the new design provides for trapping the compression pulse reflected off the sample, and the tensile pulse transmitted through the sample. In addition, a sample can be subjected to compression followed by tension, and then recovered, allowing the study of, e. g. the dynamic Bauschinger effect in materials.

Determination of temperature rise during high strain rate deformation

Abstract The energy converted to heat during high strain rate plastic deformation is measured directly using an infra-red method for Ta−2.5% W alloy and, indirectly, using UCSDs recovery Hopkinson bar technique for the same alloy, as well as for commercially pure Ti, 1018 steel, 6061 Al and OFHC Cu. The infra-red measurement yields a 70% conversion of work to heat for Ta−2.5% W and generally underestimates this factor for all tested materials. The final temperature at a given strain can be determined indirectly, based on the calculated plastic work. For this, three separate measurements are made: First, a sample is deformed at a high strain rate to a total strain of, say, 60%; this is essentially an adiabatic test. Then a second sample is deformed at the same strain rate to about 30% strain; this should reproduce the first half of the previous adiabatic stress-strain curve and in our test it does. This sample is then allowed to cool down to the initial room temperature. This sample may then be heated to the temperature as was measured by the infra-red detectors and then deformed at the same strain rate to check if the adiabatic curve is traced. It is observed that only when the sample temperature is increased based on 100% conversion of the plastic work to heat, that the original adiabatic stress-strain curve is traced. It is thus concluded that the infra-red detection system records a lower (surface) temperature than the actual temperature of the sample.

Mechanical properties and deformation mechanisms of a commercially pure titanium

The mechanical behavior of a commercially pure titanium (CP-Ti) is systematically investigated in quasi-static (Instron, servohydraulic) and dynamic (UCSDs recovery Hopkinson) compression. Strains over 40% are achieved in these tests over a temperature range of 77-1000 K and strain rates of 10 ˇ3 -8000/s. At the macroscopic level, the flow stress of CP-Ti, within the plastic deformation regime, is strongly dependent on the temperature and strain rate, and displays complex variations with strain, strain rate, and temperature. In particular, there is a three-stage deformation pattern at a temperature range from 296 to 800 K, the specific range depending on the strain rate. In an eAort to understand the under- lying mechanisms, a number of interrupted tests involving temperature jumps are performed, and the resulting microstructures are characterized using an optical microscope. Based on the experimental results and simple estimates, it is concluded that the three-stage pattern of deformation at temperatures from 296 to 800 K, is a result of dynamic strain aging, through the directional diAusion of dislocation-core point defects with the moving dislocation at high strain rates, although the usual dynamic strain aging by point defects segregating outside the dislocation core through volume diAusion is also observed at low strain rates and high temperatures. The microscopic analysis shows that there is substantial deformation twinning which cannot be neglected in modeling the plastic flow of CP-Ti. The density of twins increases markedly with increasing strain rate, strain, and decreasing temperature. Twin intersections occur, and become more pronounced at low temperatures or high strain rates. In sum, the true stress-true strain curves of CP-Ti show two stages of deformation pattern at low temperatures, three stages at temperatures above 296 K, and only one stage at temperatures exceeding 800 K, although all three stages may exist even at 1000 K for very high strain rates, e.g. 8000/s. While the dislocation motion is still the main deformation mechanism for plastic flow, the experimental results suggest that dynamic strain aging should be taken into account, as well as the eAect of deformation twinning. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

Comparative experimental study of ionic polymer–metal composites with different backbone ionomers and in various cation forms

An ionic polymer–metal composite (IPMC) consisting of a thin perfluorinated ionomer (usually, Nafion or Flemion) strip, platinum, and/or gold plated on both faces and neutralized by a certain amount of appropriate cations undergoes large bending motion when, in a hydrated state, a small electric field is applied across its thickness. When the same membrane is suddenly bent, a small voltage of the order of millivolts is produced across its surfaces. Hence IPMCs can serve as soft bending actuators and sensors. This coupled electrical–chemical–mechanical response of IPMCs depends on the structure of the backbone ionic polymer, the morphology and conductivity of the metal electrodes, the nature of the cations, and the level of hydration (or other solvent uptake). We have carried out extensive experimental studies on both Nafion- and Flemion-based IPMCs in various cation forms, seeking to understand the fundamental properties of these composites, to explore the mechanism of their actuation, and finally, to optimize their performance for various potential applications. The results of some of these tests on both Nafion- and Flemion-based IPMCs with alkali-metal or alkyl-ammonium cations are reported here. Compared with Nafion-based IPMCs, Flemion-based IPMCs with fine dendritic goldelectrodes have higher ion-exchange capacity, better surface conductivity, higher hydration capacity, and higher longitudinal stiffness. They also display greater bending actuation under the same applied voltage. In addition, they do not display a reverse relaxation under a sustained dc voltage, which is typical of Nafion-based IPMCs in alkali-metal form. Flemion IPMCs thus are promising composites for application as bending actuators.

Elastic fields of interacting inhomogeneities

Abstract A rather general technique—called the “method of pseudotractions”—is presented for the calculation of the stress and strain fields in a linearly elastic homogeneous solid which contains any number of defects of arbitrary shape. The method is introduced and illustrated in terms of the problems of elastic solids containing two or several circular holes and solids containing two or several cracks, including the cases of rows of holes or cracks. It is shown that the solution of these and similar problems can be obtained to any desired degree of accuracy. Furthermore, if only estimates are needed, then the method is capable of yielding closed-form analytic expressions for many interesting cases, e.g. the stress intensity factors at the crack tips.

Double-inclusion model and overall moduli of multi-phase composites

Abstract The double-inclusion model consists of an ellipsoidal inclusion which contains an ellipsoidal heterogeneity and is embedded in an infinitely extended homogeneous domain. The elasticity of the inclusion, its heterogeneity, and that of the infinite domain may be distinct and arbitrary. The ellipsoidal heterogeneity may include other inclusions, or it may have variable elasticity. Average field quantities for the double inclusion are estimated analytically with the aid of a theorem which generalizes the Tanaka-Mori observation (1972; J. Elast. 2, 199–200). It is shown that the averaging scheme based on the double-inclusion model produces the overall moduli of two-phase composites with greater flexibility and hence effectiveness than the self-consistent and the Mori-Tanaka (1973; Acta Metall. 21, 571–574) methods, and, indeed, includes as special cases these methods, providing alternative interpretations for them. The double-inclusion model is then generalized to multi-inclusion models where, again, all the average field quantities are estimated analytically. As examples of the application of the multi-inclusion model, a composite containing inclusions with multilayer coatings and a composite consisting of several distinct materials are considered, and their overall moduli are analytically estimated. In addition, for a set of nested ellipsoidal regions of arbitrary aspect ratios and relative locations, which is embedded in an infinitely extended homogeneous elastic solid of arbitrary elasticity, and which undergoes transformations with uniform but distinct transformation strains within each annulus, it is shown that the resulting strain field averaged over each annulus can be computed exactly and in closed form; the transformation strains in the innermost region need not be uniform. Explicit results are presented for an embedded double inclusion, as well as a nested set of n inclusions.

On composites with periodic structure

Abstract The overall moduli of a composite with an isotropic elastic matrix containing periodically distributed (anisotropic) inclusions or voids, can be expressed in terms of several infinite series which only depend on the geometry of the inclusions or voids, and hence can be computed once and for all for given geometries. For solids with periodic structures these infinite series play exactly the same role as does Eshelbys tensor for a single inclusion or void in an unbounded elastic medium. For spherical and circular-cylindrical geometries, the required infinite series are calculated and the results are tabulated. These are then used to estimate the overall elastic moduli when either the overall strains or the overall stresses are prescribed, obtaining the same results. These results are compared with other estimates and with experimental data. It is found that the model of composites with periodic structure yields estimates in excellent agreement with the experimental observations.