2005/08/27 by Alexander M. Korsunsky, Korsunsky, Alexander M.
Engineering · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Hydrogen embrittlement and corrosion behaviors in metals #Material Properties and Failure Mechanisms #Materials Science (cond-mat.mtrl-sci) #Microstructure and Mechanical Properties of Steels #cond-mat.mtrl-sci
paper · pdf · doi:10.48550/arxiv.cond-mat/0508653
14 pages, 14 figures
arxiv created 2005/08/27 · openalex publication_date 2005/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables of interest is the object dimension, or time. The prevalence of a simple power law over the entire range of dimensions or times can be helpfully interpreted as size or time independence of the corresponding compound physical parameter of the system. However, it is also often found that a simple power law only persists for some extreme values, e.g. for very large and/or small sizes, or very short or long times. Transitions between regimes of different power law asymptotic behaviour are encountered frequently in the description of a wide variety of physical systems. While asymptotic power law behaviour may often be readily predicted, e.g. on dimensional grounds, the evaluation of the relationship between system parameters in the transition range usually requires laborious detailed solution. To obviate this difficulty we introduce, on rather general basis, something we refer to as the merging, or 'knee' function. The function possesses sufficient flexibility to describe transitions of various sharpness. To demonstrate its usefuness, the merging function is applied to a variety of well-known scaling laws in the mechanics and strength of materials and structures.