A finite elastostatic analysis of bimaterial interface cracks

A numerical method is developed to study the bimaterial interface problem in Neo-Hookean materials under plane stress conditions. Comparison is made with the analytical predictions for the asymptotic field of the problem. The range of dominance of the asymptotic solution at different load levels is established and the amplitudes of the crack-tip asymptotic field are related to the far field loading. The numerical model is extended to analyze the experiments conducted on specimens with an edge crack at the interface between two dissimilar Solithane plates that are characterized by Mooney-Rivlin material behavior.

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Résumé On met au point une méthode numérique pour l'étude d'un problème d'interfaces entre deux matériaux néo-Hookiens sollicités en état plan de tension. On compare les résultats avec les prédictions analytiques étabiies pour un champ asymptotique. On établit la gamme dans laquelle la solution asymptotique est dominante, à différents niveaux de charge, et on met en relation l'ampleur du champ asymptotique à l'extrémité de la fissure avec celle du champ de contraintes à une certaine distance. Le modèle numérique est étendu à l'analyse d'essais sur éprouvettes comportant une fissure de bord à l'interface de deux tôles de Solithane caractérisée par un comportement de matériau de Mooney-Rivlin.

     

Reducing energy-related CO2 emissions using accelerated weathering of limestone

The use and impacts of accelerated weathering of limestone (AWL; reaction: CO₂+H₂O+CaCO₃→Ca²⁺+2(HCO₃⁻) is explored as a CO₂ capture and sequestration method. It is shown that significant limestone resources are relatively close to a majority of CO₂-emitting power plants along the coastal US, a favored siting location for AWL. Waste fines, representing more than 20% of current US crushed limestone production (>10⁹ tonnes/yr), could provide an inexpensive or free source of AWL carbonate. With limestone transportation then as the dominant cost variable, CO₂ mitigation costs of $3-$4/tonne appear to be possible in certain locations. Perhaps 10–20% of US point–source CO₂ emissions could be mitigated in this fashion. It is experimentally shown that CO₂ sequestration rates of 10⁻⁶ to 10⁻⁵ moles/sec per m² of limestone surface area are achievable, with reaction densities on the order of 10⁻² tonnes CO₂ m⁻³day⁻¹, highly dependent on limestone particle size, solution turbulence and flow, and CO₂ concentration. Modeling shows that AWL would allow carbon storage in the ocean with significantly reduced impacts to seawater pH relative to direct CO₂ disposal into the atmosphere or sea. The addition of AWL-derived alkalinity to the ocean may itself be beneficial for marine biota.     

An approximate analysis of the effect of micro fractures on the caustic of a dynamically moving crack tip

The optical recording of the conditions at the tips of dynamically moving cracks is often associated with a wave pattern which arises from what we call here radial waves. This observation is prevalent for tough solids, especially when the observation tools involve surface deformations such as the caustic method. These waves can modify the caustic shape and size and thus influence the interpretation of measurements. The quantification of the sources of these waves poses a very difficult problem so that a precise evaluation of that phenomenon is not yet possible. However, in an attempt to better understand the limitation imposed on the method of caustics by this set of waves this paper analyzes primarily the change of shape in the caustic associated with the passage of radial waves over the region of the initial curve of the caustic. The analysis is approximate in that the radial waves are assumed to be insensitive to the presence of the crack surfaces, but otherwise accounts for the three dimensional character of wave propagation in a plate of finite thickness.

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Résumé On associe souvent l'enregistrement optique des conditions présentes à l'extrémité de fissures en cours de propagation spectaculaire, à une disposition ondulée, due à ce que l'on dénomme ici des ondes radiales. L'observation vaut surtout pour les corps à haute ténacité, et en particulier lorsque les méthodes d'observation tiennent compte des déformations de surface, comme la méthode des caustiques. Les ondes radiales peuvent altérer la forme et la dimension d'une caustique, et, de ce fait, influencer l'interprétation des mesures. Une évaluation précise de ce phénomène n'est pas encore possible, car la quantification des sources de ces ondes pose un problème trés délicat. Néanmoins, en vue de mieux comprendre les limites qu'impose à la méthode des caustiques la formation de ces ondes, on a analysé essentiellement le changement de forme de la caustique lorsque se développent des ondes radiales sur la région couverte par la courbe originale de la caustique. On procède à une approximation dans la mesure où on suppose que les ondes radiales sont insensibles à la présence des surfaces de la fissure, mais prennent par ailleurs en considération le caractère tridimensionnel de la propagation d'une fissure dans une plaque d'épaisseur finie.

     

A review of fracture in viscoelastic materials

This review is written in honor of Max L. Williams who not only started this International Journal of Fracture (the author’s Ph.D. advisor. Originally the Journal was called International Journal of Fracture Mechanics) but who had a seminally fundamental influence on the course of fracture mechanics in general, and specifically as applied to the time dependent failure of elastomers/polymers. In view of that background this article reviews developments over more than 50 years, as colored by my own experiences in regard to this topic. It seems appropriate to include a historical perspective that starts during pre-journal times and addresses the need for understanding time dependent processes governing fracture in rate sensitive materials. To the largest extent, the rate dependence is important where polymers are involved, though under more limited conditions metals and igneous solids as well as ligneous ones exhibit time dependent fracture characteristics. Such facts notwithstanding, the major discussion in this contribution is devoted here to the time dependent fracture of polymeric materials, and elastomeric ones in particular. The emphasis will be thus on time dependent issues governed primarily by the fracture processes in elastomeric solids, which have evolved largely in parallel to problems devoted to the more rigid polymers. Because consideration of fracture of the rigid polymers has often, if not usually, minimized the time dependence, only cursory attention is paid to these, in spite of the fact that they constitute a very important class of materials in the modern engineering community. From an engineering perspective this review is motivated also by an exposition of a persistent lack of knowledge concerning time dependent fracture issues. Most of the work attached to the notion of viscoelastic fracture is—intentionally or by omission—associated with the phenomenon of crack growth under steady state conditions with the expectation that this understanding leads implicitly to resolution of problems governed by transient loadings. Besides reviewing the historical evolution of the knowledge in this field over the past half century, it is a main purpose of this paper to offer information that has either been ignored or has not been explored (this includes the work of the author), but which contradicts this “popular” perception. It is thus an intentionally large part of this presentation which documents compelling motivation for addressing fracture aspects, that are generally important from an engineering design and analysis point-of-view: specifically, it is intended to illustrate the remarkable degree by which the steady state solution to crack propagation deviates from experimental information when transient conditions prevail, and the large range of time scales over which this failure behavior is observed.     

Improved relaxation time coverage in ramp-strain histories

Standard methods for deriving relaxation data from measurements invariably involve some form of ramp-type deformation history, the initial portion of which is typically not employed for modulus evaluation. In fact, the “ten-times-rule” or a variant thereof is widely used at the expense of short term data acquisition. This paper suggests a simple if (not) obvious method to extend the range of relaxation data that can be acquired from a single test at a single temperature. The method draws on new computational developments for inverting ill-conditioned systems of equations which allows the determination of relaxation parameters nearly routinely and trouble-free. We demonstrate this process for extraction of relaxation characterization from ramp strain histories through (a) numerical evaluation with a virtual test sequence, as well as through (b) data measured in the laboratory. Limitations regarding the time range over which the relaxation modulus can be extracted from laboratory measurements in terms of equipment resolution and stability are discussed. With these constraints in mind it appears feasible to extend the time range by three to four decades towards shorter times when compared with the application of the “ten-times-rule”. Similar treatments apply to the acquisition of creep compliance data.     

The sensitivity of the time-temperature shift process to thermal variations—A note

Because of the highly nonlinear relation between time-shift and temperature it is generally not admissible to assume that the appropriate temperature for the shifting process equals the average temperature during the measurement interval. It is shown here that temperature variations around a mean can produce shifts that can be significantly larger than the mean temperature would indicate. Alternatively this paper can aid in providing numerical estimates that indicate for what range of thermal variations acceptable engineering data may be acquired. As a guide one finds that a one degree centigrade variation (±0.5°C) around a mean value limits the shift factor error to less than 4%, which translates into a misrepresentation of two weeks out of a year.     

The role of damage-softened material behavior in the fracture of composites and adhesives

Failure mechanisms of materials under very high strain experienced at and ahead of the crack tip such as the formation, growth and interaction of microvoids in ductile materials, microcracks in brittle solids or crazes in polymers and adhesives are represented by one-dimensional, nonlinear stress-strain relations possessing different post-yield softening (strain-softening) behavior. These reflect different ways by which the material loses capacity to carry load up to fracture or total separation. A DCB type specimen is considered in this study. ^* The nonlinear material is confined to a thin strip between the two elastic beams loaded by a wedge. The problem is first modelled as a beam on a nonlinear foundation. The pertinent equation is solved numerically as a two-point boundary value problem for both the stationary and the quasi-statically propagating crack. A finite element model is then used to model the problem in more detail to assess the adequacy of the beam model for the use of experimental data to determine in-situ properties of the thin interlayer.It is found that the energy release rate derived by assuming built-in conditions at the crack tip can be used to calculate the fracture (surface) energy more accurately and conveniently than Berry's scheme [2] even in cases where the built-in assumption is apparently invalid. The analyses suggest that it is possible to infer from detailed macroscopic measurements of the deformations of the beam prior to and during crack growth the approximate characteristics of the complete (uniaxial) material stress-strain behavior of the cohesive interlayer including loading and strain-softening.

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Résumé On représente les mécanismes de rupture de matériaux sous de trés fortes déformations appliquées à l'extrémité ou en amont de fissures tels que la formation, la croissance et l'interaction de micro-lacunes dans les matériaux ductiles, les micro-fissures dans les matériaux fragiles ou les craquelures dans les polymères et les adhésifs, par des relations contraintes-déformations non linéaires, unidimensionnelles et présentant des comportements différents d'adoucissement à l'écrouissage. Ces mécanismes reflètent diverses voies selon lesquelles un matériau perd sa capacité de supporter une charge avant rupture ou séparation totale. Dans cette étude, on considère une éprouvette de type double Cantilever, un matériau non élastique étant ramené à une bande mince comprise entre deux poutres élastique étant ramené à une bande mince comprise entre deux poutres élastique étant ramené à une bande mince comprise entre deux poutres élastiques sollicitées par un coin. On commence par représenter le problème comme une poutre reposant sur un support non linéaire. Par voie numérique, on résoud l'équation correspondante dans les cas d'une fissure stationnaire et d'une fissure en propagation quasi-statique. On utilise ensuite un modèle par éléments finis pour représenter avec plus de détails le problème en vue de vérifier l'adéquation du type d'éprouvette pour l'utilisation des données expérimentales à la détermination des propriétés in situ de l'intercouche mince.On trouver que la vitesse de relaxation de l'énergie obtenue en supposant des conditions de consolidation à l'extrémité de la fissure peut être utilisée pour la calcul de l'énergie de rupture (en surface) de mainère plus précise et plus commode que l'approche de Berry, même dans les cas où une hypothèse de consolidation n'est apparemment pas valable. L'analyse suggère qu'il est possible de déduire les caractéristiques approchées du comportement complet du matériau du point de vue contraintes-dilatations (uniaxiales) relatives à l'intercouche de liaison, tant pour la mise en charge que pour l'adoucissement, à partir de mesures macroscopiques détaillées des déformations de la poutre avant et durant l'expansion de la fissure.

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This paper is a shortened version of part of [1].

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An experimental program is being conducted in our laboratories to study the strain-strain characteristics of a number of polymeric solids using the DCB model discussed in this paper.

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An experimental program is being conducted in our laboratories to study the strain-strain characteristics of a number of polymeric solids using the DCB model discussed in this paper.     

Sonography and quantitative measurements

A preliminary study of coronary artery wall topography and mechanical properties is presented. The aim of this study was to give a brief demonstration of scanning acoustic microscopy (SAM) as a sonographic technique, and to apply the time-resolved SAM (TR-SAM) technique for quantification of coronary artery wall mechanical properties under passive conditions ex-vivo, and compare the data for the tunica externa and tunica media of the wall. The authors chose the diagonal branches of the left anterior descending coronary artery (LADCA) of young healthy pigs for measurements. It is concluded that SAM is well suited for sonography at the micrometer level, and TR-SAM provides a refined tool for biorheological quantification ex-vivo, provided that a number of physical factors influencing measurements and tissue properties are considered and dealt with. With time and effort, SAM may also become a valuable tool for recognizing important relations of composition and structure to function. For future SAM studies of arteries, more detailed analyses of layer interfaces and better models of biorheology should be applied to describe the anisotropy and nonlinear viscoelasticity of the wall