Temperature-dependent microtensile testing of thin film materials for application to microelectromechanical system

A specially designed microtensile apparatus capable of carrying out a series of tests on microscale thin films for microelectromechanical system (MEMS) applications at room temperature and at temperature up to 400°C has been developed and tested, and is described here. Several MEMS-applicable thin films were measured with it, including thermally grown silicon dioxide, gold, and gold–vanadium. The silicon dioxide was tested at room temperature. Gold and gold–vanadium films were tested at room temperature and at 200 and 400°C. Examples of these results are presented.

     

A finite element method for the probabilistic creep of solids

We outline here a finite element technique for the creep of solids whose constitutive equation contains one or more random parameters. In contrast to other finite element techniques for the prediction of random structural response, the present method is based upon exact relations from the theory of probability. It yields, at a given value of time, the probability density function for the field variable of interest, e.g. stress or displacement components. The method is illustrated by a simple creeping beam problem, using a power-law creep constitutive equation. The calculated distributions are found to be highly skewed, and in excellent agreement with the results of Monte Carlo simulation.     

Some selected topics in creep cavitation

The nucleation and growth of intergranular cavitation is one of the major contributors to high-temperature failure. We focus here on three developments in this area. The first is the effect of combined creep deformation and diffusive mass transport upon void growth. Second, we discuss environmental influences upon cavity growth, principally in the form of gas-producing internal reactions. Finally, we outline some of the experimental observations concerning randomness in creep cavitation and modeling efforts intended to capture some of these random effects. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Temperature-dependent microtensile testing of thin film materials for application to microelectromechanical system

A specially designed microtensile apparatus capable of carrying out a series of tests on microscale thin films for microelectromechanical system (MEMS) applications at room temperature and at temperature up to 400°C has been developed and tested, and is described here. Several MEMS-applicable thin films were measured with it, including thermally grown silicon dioxide, gold, and gold–vanadium. The silicon dioxide was tested at room temperature. Gold and gold–vanadium films were tested at room temperature and at 200 and 400°C. Examples of these results are presented.     

The steadily propagating viscoplastic crack with elastic unloading

We analyze the crack-tip near field for a crack propagating under steady-state, quasi-static, antiplane strain conditions in a viscoplastic material. The constitutive model employed is a state variable model due to Robinson, which displays kinematic hardening characteristics, and which allows for the possibility of elastic unloading. Given a continuity assumption on the state variable components across the loading/unloading boundary, we find that the crack-tip near field is completely uninfluenced by conditions in the remote field. This conclusion is in agreement with earlier analyses in which the possibility of an elastic unloading zone was not admitted.     

On the scatter in creep rupture times

We report here the results of three series of replicated creep rupture experiments carried out on copper bicrystals. The intent of this study is to investigate the scatter in creep rupture times in order to determine whether creep rupture may be viewed as an essentially deterministic phenomenon or if it contains intrinsic probabilistic features. The use of bicrystals is advantageous in such an investigation, because they are much less sensitive to the effects of loading eccentricity than poly crystalline specimens. The results indicate that where failure is due to a mixed cavitation/ductile rupture mode, the scatter in the failure times may be accounted for entirely by the effects of random variations in the experimental conditions. However when the failure mode is essentially intergranular creep cavitation, the scatter in the failure times is substantially greater than can be explained by the effects of experimental variability. This leads to the conclusion that under these conditions, the creep rupture phenomenon contains intrinsic probabilistic features. Formerly with Lehigh University, Bethlehem, PA Formerly with Lehigh University     

An analysis of the Hui-Riedel equation

We consider several of the features exhibited by the equation derived by Hui and Riedel for the angular variation of the stress function near the tip of a crack propagating under steady-state, quasi-static, antiplane strain conditions in an elastic/power-law creeping material. We show that the regularity condition imposed in front of the crack tip by Hui and Riedel as an extra boundary condition is in fact implicit in the physically derived boundary conditions, and does not therefore constitute an independent boundary condition. On the other hand, these physical boundary conditions do not imply that the solution is regular on the crack flank. Despite an apparent shortage of boundary conditions, uniqueness of positive solutions can be explained as behavior typical of certain kinds of nonlinear eigenvalue problems. We further examine the asymptotic behavior of the solution for large values of the power-law exponent. Here it is shown that the solution is not the elastic-perfectly plastic solution, as might be supposed, but rather a solution which is in good agreement with the numerical results of Hui and Riedel.

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Résumé On considère diverses caractéristiques que présente l'équation dérivée par Hui et Reidel pour la variation angulaire de la fonction de contrainte au voisinage de l'extrémité d'une fissure, qui se propage sous des conditions de déformation stable quasi-statique et anti-planaire dans un matériau soumis à fluages élastique et non-élastique. On montre que la condition de régularité imposée au front de l'extrémité de la fissure par Hui et Reidel est, comme condition aux limites supplémentaires, en fait implicite dans les conditions aux limites dérivées de la physique et qu'elles ne constituent dès lors pas une condition aux limites indépendantes. D'autre part, ces conditions aux limites physiques n'impliquent pas une solution régulière sur le flanc de la fissure. En dépit d'une apparente limitation des conditions limites, l'unicité des solutions positives peut être expliquée par le comportement typique de certaines sortes de problèmes non linéaires d'eigenvalue. On examine en outre le comportement asymptotique de la solution dans le cas de valeurs élevées de l'exposant de la loi de déformation. On montre que la solution n'est pas une solution élastique-parfaitement plastique comme on pourrait le supposer, mais plutôt une solution qui est en bon accord avec les résultats numériques de Hui et Reidel.

     

ISovector fields and self-similar solutions for power law creep

Isovector methods are a recently developed technique for systematically investigating properties of the solutions of systems of differential equations. These methods are applied to the nonlinear equations of power law creep with elastic strains under conditions of plane and antiplane strain. Among the results are a family of self-similar solutions which are shown to be the only ones extant for the cases investigated. Some light is also shed upon the existence of conservation laws for these equations, and upon the existence of mappings which transform the governing equations into a set of equivalent linear equations.     

Creep, relaxation and cyclic behavior of a beam using a state-variable constitutive model

Numerical solutions are presented for the time-dependent inelastic behavior of a Bernoulli-Euler beam under a variety of time-dependent moment loadings. The inelastic constitutive representation employed is the recently developed state-variable constitutive law of Robinson. Robinson's equations have several novel features, and these are examined within the context of the behavior of a beam. Despite the fact that the beam may contain relatively complex inhomogeneous stress fields, the overall behavior is shown to be analogous to that observed in simple uniaxial tests.     

Creep cavitation in the neighborhood of stress concentrations

The results of several experiments into the formation and distribution of creep cavitation in the neighborhood of stress concentrations in Mo and 304 stainless steel are reported. Of particular interest is the use of an image analyzing computer to construct quantitative maps of cavity sizes and distributions. Comparisons are drawn in one case with the results of a finite element simulation, and some degree of overall agreement is noted.