'Mathematical' Cracks Versus Artificial Slits: Implications in the Determination of Fracture Toughness

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• 作者：Ch. F. Markides ; S. K. Kourkoulis
• 关键词：Circular disc ; Rectangular slit ; Stress concentration ; Fracture toughness ; Stress intensity factors (SIFs) ; Crack ; Linear elasticity ; Complex potentials
• 刊名：Rock Mechanics and Rock Engineering
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：49
• 期：3
• 页码：707-729
• 全文大小：1,257 KB
• 参考文献：ASTM (2014) E399-12e3 Standard test method for linear-elastic plane-strain fracture toughness K Ic of metallic materials. ASTM volume 03.01: Metals-Mechanical Testing; Elevated and Low-Temperature Tests; Metallography
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• 作者单位：Ch. F. Markides (1)
  S. K. Kourkoulis (1)
  
  1. Department of Mechanics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 5 Heroes of Polytechnion Avenue, Theocaris Bld., Zografou Campus, 157 73, Athens, Greece
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geophysics and Geodesy
  Civil Engineering
  
• 出版者：Springer Wien
• ISSN：1434-453X

文摘

An analytic solution is introduced for the stress field developed in a circular finite disc weakened by a central slit of arbitrary ratio of its edges and slightly rounded corners. The disc is loaded by radial pressure applied along two finite arcs of its periphery, anti-symmetric with respect to the disc’s center. The motive of the study is to consider the stress field in a disc with a mechanically machined slit (finite distance between the two lips) in juxtaposition to the respective field in the same disc with a ‘mathematical’ crack (zero distance between lips), which is the configuration adopted in case the fracture toughness of brittle materials is determined according to the standardized cracked Brazilian-disc test. The solution is obtained using Muskhelishvili’s complex potentials’ technique adopting a suitable conformal mapping function found, also, in Savin’s milestone book. For the task to be accomplished, an auxiliary problem is first solved, namely, the infinite plate with a rectangular slit (in case the resultant force on the slit is zero and also the stresses and rotations at infinity are zero), by mapping conformally the area outside the slit onto the mathematical plane with a unit hole. The formulae obtained for the complex potentials permit the analytic exploration of the stress field along some loci of crucial practical importance. The influence of the slit’s width on the local stress amplification and also on the stress concentration around the crown of the slit is quantitatively described. In addition, the role of the load-application mode (compression along the slit’s longitudinal symmetry axis and tension normal to it) is explored. Results indicate that the two configurations are not equivalent in terms of the stress concentration factor. In addition, depending on the combination of the slit’s width and the load-application mode, the point where the normal stress along the slit’s boundary is maximized ‘oscillates’ between the central point of the slit’s short edge (intersection of the slit’s longitudinal axis with its perimeter) and the slit’s corners.