Please wait a minute...
Acta Metall Sin  1957, Vol. 2 Issue (4): 349-365    DOI:
Current Issue | Archive | Adv Search |
THEORETICAL AND EXPERIMENTAL INVESTIGATION ON FRICTION-LINES OF ELLIPTIC PLATES IN PLASTIC COMPRESSION
LIU SHU-I;WANG MING-TZONG Institute of Metallurgy and Ceramics; Academia Sinica
Cite this article: 

LIU SHU-I;WANG MING-TZONG Institute of Metallurgy and Ceramics; Academia Sinica. THEORETICAL AND EXPERIMENTAL INVESTIGATION ON FRICTION-LINES OF ELLIPTIC PLATES IN PLASTIC COMPRESSION. Acta Metall Sin, 1957, 2(4): 349-365.

Download:  PDF(6424KB) 
Export:  BibTeX | EndNote (RIS)      
Abstract  This paper is one of the developments of our previous investigations (forexample,). In a recent paper a set of general plane differential equations forfriction-lines and for pressure contours were obtained as:θ=angle (x, second principal stress);τ=unit frictional force. As shown in the chinese text, these two equations and the general curvilineardifferential equation (C) for pressure distribution all hold for any case of plasticfriction: P=unit pressure; h=thickness of the plate; f_2(ε)=strain function (see[2]); K=uniaxial yielding point; s=arc length of the complete friction-line.For the case of elliptical plates a set of solutions were obtained as shown in Fig1 of the chinese text, by taking θ as defined by the tangents of concentric ellipses.In this paper, we show that a second set of solutions can be deduced by taking θas defined by regular elliptic coordinates. As shown in Fig. 2 and Fig. 3, the new solutions for friction-lines and pressure contours are radii and circles, the pressuredistribution has a finite peak at the center. To check the validity of these theoretical results, experimental determinationof friction-lines was made for lubricated plates of lead and plastic mass by photo-graphic and isoclinic methods. The methods are obvious in the Fig. 4 to 17, andneed not be elabourated here. As Liu Shu-i has pointed out in a paper to be published soon, the surfacestream-lines and the instantaneous friction-lines are two different families of curvesobeying different laws-the rule of gradient for instantaneous friction-lines andLiu's rule of isoclinic gradient for stream-lines called long-rang friction-lines. Fig. 9 to 11 are surface stream-lines from which the instantaneous friction-lines were deduced by isoclinic method as shown in Fig. 12 to 17. Each figure forfriction-lines consists of two families: the isoclinics and the friction-lines (witharrows). Fig. 18 provides an indication of a no-slip point at the center of the plate. It appears that the theoretical solution of the last paper yields friction-lineswith curvatures greater than the experimental curves and the solution given in thispaper is close to the experimental curves only for ellipses with axial ratio not too farfrom unity. However, the solution of last paper mathematically holds, if the axialratio is replaced by an arbitrary constant. This will allow us to interpret moreexperimental facts on the basis of that solution. The case of bipolar plate is under investigation, we have obtained the dif-ferential equation for friction-lines as equation (D), its solution will be published inanother paper.tanφ={(y/x)([(a~2+y~2-x~2)~2-4x~2y~2](a~2+y~2+x~2)-4x~2(a~2+y~2-x~2)(a~2-y~2-x~2))/(4y~2(a~2+y~2-x~2)(a~2+y~2+x~2)+[(a~2+y~2-x~2)-4x~2y~2](a~2-y~2-x~2)); (y/x)(a~2+y~2+x~2)/(a~2-y~2-x~2); when(a~2+y~2-x~2)>0. when(a~2+y~2-x~2)=0. (y/x)([(a~2+y~2-x~2)-4x~2y~2](a~2+y~2+x~2)+4x~2(a~2+y~2-x~2)(a~2-y~2-x~2))/(-4y~2(a~2+y~2-x~2)(a~2+y~2+x~2)+[(a~2+y~2-x~2)~2-4x~2y~2](a~2-y~2-x~2));}(D) when(a~2+y~2-x~2)<0.α=constant in the equation of bipolar coordinates.
Received:  18 April 1957     
Service
E-mail this article
Add to citation manager
E-mail Alert
RSS
Articles by authors

URL: 

https://www.ams.org.cn/EN/     OR     https://www.ams.org.cn/EN/Y1957/V2/I4/349

[1] 刘叔仪:物理学报,12,1(1956) ,p.41--49.
[2] 刘叔仪:物理学报,12,6(1956) ,p.491--510.
[3] 刘叔仪:平塑压接触面上之长程滑线与短程滑线,第一届全国力学学术报告会,1957,2.
[4] 刘叔仪:“双极板塑压摩擦线研究”,中国科学院冶金陶瓷研究所,研究结果.v
No related articles found!
No Suggested Reading articles found!