Solutions are presented for mode I and mode II crack tip fields for plane strain deformations of an elastic-plastic solid whose constitutive behavior depends on both strains and strain gradients. The constitutive law is the simplest generalization of the J 2 deformation theory of plasticity to include strain gradient effects. Only one new constitutive parameter enters, a length parameter characterizing the scale over which gradient effects become important. The formulation is cast within the framework of coupled stress theory. Crack tip solutions are obtained which display the transition from the HRR fields, governing behavior in an intermediate region with the plastic zone, to the dominant fields at the tip. The dominant fields are obtained in closed form, and finite element methods have been used to produce the solution over the entire field. Some of the difficulties encountered in arriving at an accurate numerical scheme are detailed. Implications of the solutions for fracture are discussed, as are avenues for further research.
Statistical aspects of height of rise and fall in continuous random loading relevant to fatigue failure
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An elastic analysis is presented for the tensile stretching and bending of a plate containing a surface crack penetrating part-through the thickness, Fig. 1. The treatment is approximate, in that the two-dimensional generalized plane stress and Kirchhoff-Poisson plate bending theories are employed, with the part-through cracked section represented as a continuous line spring. The spring has both stretching and bending resistance, its compliance coefficients being chosen to match those of an edge cracked strip in plane strain. The mathematical formulation reduces finally to two-coupled integral equations for the thickness averaged force and moment per unit length along the cracked section. These are solved numerically for the case of a semi-elliptical part-through crack, with results compared to a simple but approximate closed-form solution. Extensive results are given for the stress intensity factor at the midpoint of the part-through crack for both remote tensile and bending loads on the plate. These results indicate that the stress-intensity factor is substantially lower, in general, than for a similarly loaded strip in plane strain with a crack of the same depth.
ADVERTISEMENT RETURN TO ISSUEPREVNoteNEXTSynthesis of a Phosphonate Analog of Sialic Acid (Neu5Ac) Using Indium-Mediated Allylation of Unprotected Carbohydrates in Aqueous MediaJinming Gao, Valeri Martichonok, and George M. WhitesidesView Author Information Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138 Cite this: J. Org. Chem. 1996, 61, 26, 9538–9540Publication Date (Web):December 27, 1996Publication History Received1 October 1996Published online27 December 1996Published inissue 1 January 1996https://pubs.acs.org/doi/10.1021/jo961290yhttps://doi.org/10.1021/jo961290ybrief-reportACS PublicationsCopyright © 1996 American Chemical SocietyRequest reuse permissionsArticle Views451Altmetric-Citations43LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information SUBJECTS:Indium,Mixtures,Organic compounds,Organic reactions,Organophosphorus compounds Get e-Alerts
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Abstract This chapter discusses the contributions of the Nurses' Health Study (NHS) and Health Professionals' Follow-up Study (HPFS) to the nutritional epidemiology of coronary heart disease (CHD). Compelling evidence from these studies indicates that CHD is heavily influenced by dietary and lifestyle factors. Replacing saturated and trans fats with unsaturated fats, including sources of n-3 fatty acids, substituting whole grain forms of carbohydrate for refined grains and potatoes, consuming an abundance of fruits and vegetables, and controlling body weight will dramatically reduce the risk of CHD. The magnitude of benefit achievable through diet and lifestyle is large and substantially greater than that due to drug treatment of blood cholesterol or hypertension.