Materials Week '97: Wednesday AM Session

Focusing on physical metallurgy and materials, Materials Week '97, which incorporates the TMS Fall Meeting, features a wide array of technical symposia sponsored by The Minerals, Metals & Materials Society (TMS) and ASM International. The meeting will be held September 14-18 in Indianapolis, Indiana. The following session will be held Wednesday morning, September 17.

NON-LINEAR EFFECTS IN MATERIALS SCIENCE: Session III: Mechanical Behavior

Session Chairperson: A.J. Markworth, Dept. of Materials Science, The Ohio State University, Columbus, OH 43210-1179

A NEW MECHANISM OF DISLOCATION GENERATION AT FINITE TEMPERATURES: RELATION TO THE BRITTLE-TO-DUCTILE TRANSITION: V. Vitek, M. Khantha, D.P. Pope, Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104

Unlike dislocation generation by Frank-Read sources, the mechanism described in this contribution is a thermally-driven, stress-assisted cooperative instability of many dislocation loops. The dislocation loops are formed by thermal fluctuations and the small plastic strain associated with them invokes an effective decrease of the moduli of the medium. The self-energy of such loops is proportional to these effective moduli and, as the temperature increases, the density of the loops increases and this in turn leads to the decrease of the effective moduli. This feedback ultimately triggers off a collective unstable expansion of many loops above a critical temperature, Tc. Without mechanical loading this mechanism corresponds to the Kosterlitz-Thouless model of defect-mediated melting transition but under large applied loads the instability occurs well below the melting temperature. Such loads can be attained near the crack tips and/or in dislocation free materials, such as whiskers. In both cases Tc represents the temperature at which the material becomes suddenly ductile and corresponds thus to the brittle-to-ductile transition temperature. This research was supported by the US Air Force Office of Scientific Research grant no. 95-1-0143.

9:00 am INVITED

BIFURCATIONS AND SINGULARITIES IN ICE BREAKING: Dale G. Karr, Department of Naval Architecture and Marine Engineering, The University of Michigan, 2600 Draper Road, Ann Arbor, MI 48109-2145

Several nonlinear effects prevalent in descriptions of the mechanical behavior of ice are discussed in this paper. Polycrystalline ice is a rate dependent material often subject to the nucleation and growth of microcracks which is a source of nonlinearity in the stress-strain relations. The types of bifurcations include localization, which is associated with a bifurcation of the homogeneous deformation, and general bifurcation, associated with lose of uniqueness of the stress-strain relations. Another nonlinear effect arises when structures dynamically interact with ice such as during the operation of ice breaking vessels or the impingement of ice fields against offshore platforms. The forces exerted on the structures are nonlinear and intermittent due to the breakage and clearing of the ice medium. These nonlinear effects lead to very complex nonlinear dynamic behavior exhibiting bifurcation of periodic response, multiple periodicity, and chaotic oscillation of structures. Singular conditions such as grazing and breaking thresholds play dominant roles in the development of response bifurcations and in bounding the nonlinear dynamic motions of the structure.

9:30 am INVITED

STATISTICAL MODEL FOR MECHANICAL FAILURE: Miron Kaufman, Physics Department, Cleveland State University, Cleveland, OH 44115; John Ferrante, NASA Lewis Research Center, Cleveland, OH 44135

In this paper we analyze an equilibrium statistical mechanics model of a solid. This model solid is made of "springs". We go beyond the Hooke law for harmonic "springs" by using the nonlinear energy versus atomic distance developed by Ferrante and his collaborators. If the energy of such a spring is larger than a threshold energy the "spring" is assumed to fail. Assuming that the relaxation times are short compared to the measurement time, we use equilibrium statistical mechanics to compute the various thermodynamic quantities. We find two transitions: (i) the softening transition corresponding to a thermodynamic instability when the isothermal derivative of the stress with respect to strain is zero; (ii) when the network of failed springs percolates the solid becomes brittle. In the temperature-stress phase diagram, the two transition lines intersect at a novel multicritical point. The model is extended to account for correlations between failed springs by using a mapping to the Potts model.

10:00 am INVITED

MECHANICAL BEHAVIOR OF SILICA ELEMENTS IN PHOTONIC STRUCTURES WITH CONSIDERATION OF THE NON-LINEAR ELASTICITY OF THE MATERIAL: E. Suhir, Bell Laboratories, Lucent Technologies, 600 Mountain Ave., Room 1D-443, Murray Hill, NJ 07974

Mechanical behavior of silica elements in various photonic (fiber-optic) structures is predicted, taking into account the non-linear elastic stress-strain relationship for the silica material. The following problems are considered: low temperature microbending of dual-coated (infinitely long) optical fibers; elastic stability of short bare and metallized fibers subjected to thermally induced compression; thermally induced stresses and strains in fused biconical taper (FBT) lightwave coupler experiencing thermal contraction mismatch with its base; free vibrations of glass fibers subjected to large deformations during "two-point bending". The analyses are carried out under an assumption that the non-linear stress-strain relationship obtained experimentally for the case of uniaxial tension (Krause, Testardi, and Thurston, (1979) holds also for other deformations. It is concluded that the deviation of the stress-strain relationship from Hooke's law can have a significant effect on the mechanical behavior of silica elements in photonic structures and should be accounted for.

10:30 am BREAK

10:40 am INVITED

CONSTITUTIVE BIFURCATION AND SHEAR BAND INITIATION OF RATE INDEPENDENT BRITTLE DAMAGE MATERIALS: Xin Sun, Research Scientist, Battelle Memorial Institute, 505 King Ave., Columbus, OH 43201

Continuum damage mechanics (CDM) has been widely used to model the mechanical behavior of brittle damage materials. In this paper, the stability issues of the CDM models are studied. The stress-strain relations derived from CDM theory are shown to possess bifurcation points associated with the loss of uniqueness of the constitutive configurations. It is shown that this nonlinear degradation of the material, despite restriction to infinitesimal strain, leads to the presence of multiple constitutive paths. The stability of the constitutive paths is analyzed by considering augmented dynamical systems. The effects of material degradation on failure modes of a brittle material are also investigated. Bifurcations from the homogeneous deformation mode in the form of shear bands are captured for loading conditions of plane strain compression and uniaxial compression. In contrast with previous research on shear band initiation, that all rely on plasticity and flow theory formulation, the present study finds it sufficient for the shear band to emerge in the regime of infinitesimal strain for brittle damage materials.

11:10 am

CHAOTIC EFFECTS IN ELECTRON DRAG PROCESSES: J.M. Galligan, Dept. of Metallurgy and Materials Engineering, University of Connecticut, Storrs, CT 06269-3136; L.N. Gumen, Departamento de Matematicas, Universidad Popular Autonoma del Estado de Puebla, Puebla, 72160 Mexico; I.V. Krivoshey, Kharkov State University, Kharkov, Ukraine; A.A. Krokhin and G.A. Luna-Acosta, Instituto de Fisica de la UAP, Puebla, 72570 Mexico

The non-linear trajectory type effect is applied to electron-dislocation interactions. It is shown, using chaotic criteria based on topological properties of the potential energy surface, that, in classically strong magnetic fields, chaotic states are formed near an edge dislocation. For this case the electron motion is treated in the diffusion approximation, resulting in a non-linear dependence of the electron drag upon the magnetic field. This theory is in good agreement with experimental data, obtained for a zinc crystal sample. Numerical simulations confirm the chaotic character of electron motion near dislocations.

11:30 am

YIELDING, MOBILE DISLOCATIONS AND CHAOS: J.M Galligan, T.J. McKrell, Dept. of Metallurgy and Materials Engineering and the Institute of Materials Science, University of Connecticut, Storrs, CT 06269-3136

A method of measuring the instantaneous mobile dislocation density has been used to examine what happens when lead alloy crystals deform. This measurement, which relates magnetic flux flow to the instantaneous mobile dislocation, shows that yielding occurs in bursts. During these bursts there is a large amount of correlation among the mobile dislocations. These bursts are followed by dislocation activity in which there is little or any correlation among the dislocations, interspersed with deformation regions with large, positive correlations. Such measurements show that mobile dislocation behavior has a random component superimposed on correlated motion of dislocations.

11:50 am

ELEVATED TEMPERATURE MECHANICAL PROPERTIES OF AN ACTIVE METAL VERSION OF THE 92Au-8Pd BRAZE ALLOY: J.J. Stephens, Materials Joining Department, Sandia National Laboratories, Albuquerque, NM 87185-0367

Calculations of residual stresses in brazed metal/ceramic assemblies are often limited by a lack of mechanical properties data for braze alloy(s) of interest. In recent years, a significant data base has been developed on the elevated temperature properties of both conventional and active metal alloys used in specific projects at Sandia. This talk will focus on a recently developed active metal version of the conventional 92Au-8Pd alloy, which was developed as a high temperature alloy for brazing to silicon nitride ceramics. The active element addition (2 wt.% V) serves to significantly increase the creep strength relative to the conventional braze alloy. For both alloys, a high temperature power law creep equation applies, followed by a transition to a Garofalo sinh equation at mid and lower temperatures. Microstructures and fracture behavior of both alloys will also be discussed. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy Contract number DE-AC0494AL85000.