The Loading Curve of Spherical Indentions Is Not a Parabola and Flat Punch Is Linear

• 作者: Gerd Kaupp
• 来源期刊: 材料物理与化学进展(英文)
• 学科: 数学
• 关键词: Closed Formula for SPHERICAL INDENTATION Challenge of ISO14577 Mathematical Proofs Volume Instead of Area Correct FLAT Indentations Physical INDENTATION HARDNESS HARDNESS Dependence on Indenter Shape Data Treatment Detection
• 年，卷（期）: 2019,（8）
• 页码范围: 141-157
• 页数: 17页
• 分类号: O1

摘要

The purpose of this paper is the physical deduction of the loading curves for spherical and flat punch indentations, in particular as the parabola assumption for not self-similar spherical impressions appears impossible. These deductions avoid the still common first energy law violations of ISO 14577 by consideration of the work done by elastic and plastic pressure work. The hitherto generally accepted “parabolas’” exponents on the depth h (“2 for cone, 3/2 for spheres, and 1 for flat punches”) are still the unchanged basis of ISO 14577 standards that also enforce the up to 3 + 8 free iteration parameters for ISO hardness and ISO elastic indentation modulus. Almost all of these common practices are now challenged by physical mathematical proof of exponent 3/2 for cones by removing the misconceptions with indentation against a projected surface (contact) area with violation of the first energy law, because the elastic and inelastic pressure work cannot be obtained from nothing. Physically correct is the impression of a volume that is coupled with pressure formation that creates elastic deformation and numerous types of plastic deformations. It follows the exponent 3/2 only for the cones/pyramids/wedges loading parabola. It appears impossible that the geometrically not self-similar sphere loading curve is an h3/2 parabola. Hertz did only deduce the touching of the sphere and Sneddon did not get a parabola for the sphere. The radius over depth ratio is not constant with the sphere. The apparently good correlation of such parabola plots at large R/h ratios and low h-values does not withstand against the deduced physical equation for the spherical indentation loading curve. Such plots are unphysical for the sphere and so tried regression results indicate data-treatments. The closed physical deduction result consists of the exponential factor h and a dimensionless correction factor that is depth dependent. The non-parabola against force plot using published data is concavely bent even for large radius/depth-r