A model for the compressive buckling of extended chain polymers

A model for the compressive buckling of an extended polymer chain is presented. The application of classical elastic instability analysis to an idealized polymer chain reveals that the bending rigidity and critical buckling loads for a chain are proportional to the force constants for valence bond angle bending and torsion. Highly oriented polymer fibres are treated as a collection of elastic chains that interact laterally. The critical stresses to buckle this collection of chains are calculated following a procedure developed to predict the compressive strengths of fibre-reinforced composites. This buckling stress is predicted to be equal to the shear modulus of the fibres and is the limiting value of compressive strength. Comparison of experimental and predicted values shows that the theory overestimates the compressive strength, but that there is a correlation of shear modulus with axial compressive strength. Consideration of flaws in both the theory and the material indicate that the compressive strength should be proportional to either the shear modulus or shear strength of the fibres.Nomenclature P axial compressive load (force) - P _cr critical buckling load (force) - M,M _i bending moments - l length of a link - p number of links - k elastic hinge constant - , _i angular rotation of hinges - L overall chain or column length - v,v _i lateral deflection of buckled chain or column - x, y, z Cartesian coordinate axes - E Young's modulus of isotropic column - I moment of inertia - a _ij matrix coefficients - A _p coefficient for exact buckling loads of chains - T energy change due to work of external load on buckled column or chain - U ₁ bending strain energy change of buckled column or chain - U ₂, U ₂ ^e , U ₂ ^s strain energy changes in elastic foundation, where e refers to extension mode buckling and s refers to shear mode buckling - E _t transverse modulus - G longitudinal shear modulus - b dimension associated with chain packing - A cross-sectional area per chain (=b ²) - f(x) curve fitted to shape of buckled chain - m,n,r integers - a _n coefficients of trigonometric series - _y normal strain iny-direction - _y normal stress iny-direction - xy shear strain inxy plane - xy shear stress inxy plane - u _x displacement inx-direction - u _y displacement iny-direction - V volume     

The behavior of small fatigue cracks at notches in corrosive environments

The behavior of small cracks growing out of the roots of blunt notches in compact type specimens of an austenitic steel was characterized under fatigue loading in wet H ₂ plus air environment. The growth rates of cracks in the size range of 0.125 mm to 0.75 mm were up to two orders of magnitude higher than the rates expected for conventional cracks at equal stress intensity range, K. It was also observed that the small cracks grew at these fast rates only in corrosive environments when the loading frequency was 0.02 Hz or less. At a frequency of 10 Hz, the behavior was in agreement with the trend predicted for conventional size cracks.The above observations are rationalized in terms of the breakdown of the concept of a single parameter representation of the crack tip stress and strain field by K or in terms of differences in crack tip environments between small and long cracks for the same bulk environment. A simple engineering model is proposed which adequately represents the observed small crack growth behavior.

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Résumé On a procédé à la caractérisation, sous charges de fatigue en atmosphère humide de H ₂ et d'air, de petites fissures se développant à partir des racines d'entailles arrondies dans des éprouvettes compactes.Les vitesses de croissance des fissures d'une taille allant de 0,125 à 0,750 mm se sont révélé être de deux ordres de grandeur plus grandes que les vitesses prévues dans le cas de fissures conventionnelle, soumises aux mêmes variations de l'intensité de contrainte K. On a également observé que de petites fissures croissaient à ces grandes vitesses seulement dans des atmosphères corrosives, lorsque la fréquence de sollicitation était de 0,02 Hz ou moins. A la fréquence de 10 Hz, le comportement observé s'est trouvé en accord avec les tendances prévues pour des fissures de taille conventionnelle.Les observations ci-dessus sont rationnalisées en un élargissement du concept de représentation monoparamétrique par le facteur K du champ de contraintes et de dilatation à l'extrémité de la fissure, ou en termes des différences rencontrées dans l'environnement local de l'extrémité d'une fissure, selon que celle-ci est longue ou courte, et ce dans un même environnement global.On propose un modèle simple utilisable en pratique, pour représenter de manière adéquate le comportement à la croissance observé pour des petites fissures.

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Metallurgy Department     

Recognition of moving objects using feature signatures

An important application of machine vision systems is the recognition of known three-dimensional objects. A major difficulty arises when two or more objects project the same or similar two-dimensional image, often resulting in misclassification and degradation of system performance. The changes in images which result from the motion of objects provide a source of three-dimensional information which can greatly aid the classification process, but this three-dimensional analysis is computationally complex and subject to many sources of error. This work develops a methodology which utilizes the information derived from the apparent changes in object features over time to facilitate the recognition task, without the need to actually recover the three-dimensional structure of the objects under view. The basic approach is to generate a ``feature signature' by combining the feature measurements of the individual regions in a long sequence of images. The static information in the individual frames is analyzed along with the temporal information from the entire sequence. These techniques are particularly applicable in situations where static image processing methods cannot discriminate between ambiguous objects. Two example implementations are presented to illustrate the application of the techniques of object recognition using motion information.     

Carbonitriding at 700°C with subsequent hardening of the surface layer

Conclusion Carbonitriding at 700°C in a mixture of 70–30% of ammonia and 30–70% of endogas (or natural gas) is recommended for the production of a diffusion layer with a good set of operational properties (for example, with high wear resistance).Moreover, the use of a gaseous atmosphere based on commercial nitrogen (50–90%) with ammonia, natural-gas, oxygen, or carbon dioxide additives is promising for carbonitriding at 700°C. Here, this medium should not contain more 0.5–1.0% of O₂ and 3% of CO₂. The nitrogen-based gaseous atmospheres ensure the attainment of quality diffusion layers with decreased risk of explosion and saving of energy resources.Moscow Automobile Traffic and Highway Construction Institute. Nongovernmental Production Union "All-Union Scientific-Research and Experimental Design Institute for Trade Machine Construction. Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 5, pp. 32–36, May, 1987.     

Feature detection in 3-d medical images using shape information

Three methods for identifying the left ventricular apex in 3-D medical images of the heart called gated blood pool tomograms were investigated. The first method assumed a known orientation and positioning of the entire blood pool. The second and third methods used shapes described by quadratic surfaces, which are invariant to position and orientation. The first method performed best when the blood pool was accurately oriented, but as expected, could not handle blood pools in the wrong orientations. The quadratic surface methods performed well whether or not the blood pool was accurately oriented. The best quadratic surface method predicted the x, y, z value of the apex with correlations of 0.97, 0.98, 0.99.     

Limited Angle Reconstruction in Tomography via Squashing

We give a new algorithm for reconstructing a density f in the plane from its projections along those lines making an angle greater than a fixed delta > 0 with the x axis. Of course, the performance of the algorithm depends on delta and on the smoothness of f, but it appears to give a practical and simple solution to the problem whenever one exists. The basic idea, which seems to be new, is to make an affine (squashing) scale change of f to g for which the projections are then known at n equally spaced angles, so that we know how to find g, and then we obtain f from g by inverting the scale change.