关於固体的现实应力空间(续)

前文[1]综合四理论[2],[3],[4],[5]构成固体现实应力空间之一初步理论,大体反映固态静力学性质,对金属较对非金属固体反映得当,后者受范形变曲面有异于弥氏圆柱。总起来看,前文仅涉及原则概念,未触及具体问题。为使此理论对金属压力加工及材料试验研究有所帮助,本文进一步研究几个问题:1)由应力空间图形比较不同金属的静力学性质;2)受范形变效率及其计算;3)形变过程之轨迹;并得到一定数量或质量上的结论。同时,附带对前文[1]中一个实验记录图的错误作修正,包括在附录内。     

关於固体的现實应力空间

固体不能在一切应力状态下无限受力这意味着只是某一部份应力空间对固体有现实意义。本文所谓“固体的现实应力空间”即指此一部份应力空间而言。在恒温状态下,固体的现实压力空间成何形状?其组成及性质如何?这个问题到现在为止甚至没有一个具体的概念。本文主要引用两方面的理论,结合起来分析这一个重要问题:一为作者前文中所得理论分析结论;一为弥氏(von-Mise)塑性方程。本文分析说明:在恒温状态下,固体之现实应力空间为钟形,对称于流体静应力轴,钟顶在纯张力象限,为最低位能状态、弹性柱、塑性区域断、裂钟面及一未知曲面所构成。此钟形应力空间之构造及性质,明确地反映了一固体在一切应力状态之可塑性与不可塑性,符合于现存实验事实及工业经验所提供的概念。钟形应力空间的构造与性质,提供合符事实而且理论概念明确的条件以作各种变形过程之分类。对固体现实应力空间问题提出一个具体明确的概念,本文是第一次。     

摩擦綫与(辊轧)压力分布间之相互关系

Frequently, it was thought that frictional slip would occur in the direction of least resistance, which was unfortunately taken as the direction of the shortest normal to the free boundary. In this paper, the condition of least resistance is accepted, but the direction of resistance is properly determined without assumption. The result is "the rule of gredient", that is, at a given point on the contact surface, the direction of least resistance is the direction of the gredient of unit friction τ, which is related to the unit pressure P and the coefficient of friction, f, by τ=fP, the gredient lines of τ and P coincide with each other. Consequently, the family of least resistance lines of friction is exactly the family of curves orthogonal to the pressure contours, and can be determined from the experimental surface distribution of pressure. One case of such friction-lines in rolling is presented, the curves bear remarkable resemblance to the under-evalu-ted "probable" lines of friction derived by siebel from deformation meassurements. The way to consider change in direction of τ in one-dimensional theory of rolling is to take an average friction line whose direction cosine, cos φ, vanishes at the neutral section according to the gredient rule. By doing so, f cos φ corresponds to the "coefficient of friction" which vanishes at the neutral section according to Brown's theory. The Karman's equation is written in the mean value form by taking τ_x=fP cos φ instead of τ_x=fP. The modified equation yields solutions smoothly continuous at the neutral section, and two such continuous solution to Karman's equation for the case of solid friction are presented, detailed investigation is left to another paper. By simple arguement, it is thought that the boundary of no-slip region should be a crossed curve given by a pressure contour which is a roop according to experimental results.The rule of gradient has already led to three concequences, and is expected to be a very useful relation for plasticity under compression, because up to this paper the differential equation for slip direction remains unknown.     

塑压接触平面上之长程滑动与短程滑动(等倾陡线规律)

塑压接触面之质点滑动线称“摩擦线”。滑动现象有两种基本类型,一为“长程滑动”,摩擦线为质点之长程连续轨迹,如抽拔,挤压,冲压等塑性过程中之滑动;一为“短程滑动”,质点仅在摩擦线上滑动一微小距离,如锻,轧,压力实验等过程中之滑动(小压缩时)。过去对这两种滑动现象之规律未曾分别处理。本文将摩擦力接纯力学关系视为一切应力,即压应力p与摩擦应力τ,以边界平衡关系,相系于一应力函数F: τ=Fp, F=((l₁²p₁²+l₂²p₂²+l₃²p₃²)/(l₁²p₁+l₂²p₂+l₃²p₃)²)^1/2-1, p₁,p₂,p₃为内部主应力; l₁,l₂, l₃为p对p₁,p₂,p₃之夹角余弦。除视τ为p之函数τ=τ(p)外,对摩摩力之物理性质不作规定。在此基础上,以住意质点滑动之最小摩阻功为基本条件分析滑向规律,一如任意质点滑动之最小摩阻力条件之于“陡线规律”。如此,则问题类于古典变分问题,变分方程引出两结论:在短程滑动中,滑向规律为已知之陡线规律;在长程滑动中为以下将提出之“等倾陡线规律”。并得到几个有关重要推论。     

《物理化学力学进展》问世 一个新创的热力学第二定律告成

《物理化学力学进展》刊登各种物质系统的物理、化学、力学、物理化学、物理力学、化学力学、物理化学力学等基础科学和技术科学两方面的创造性科学论文。每年一卷由湖南科技出版社出版。编委中有刘叔仪,蒋丽金,方励之,王仁,秦元勋,许顺生,赵敏光,龙期     

最小摩阻场

前文简略地提到塑压陡线规律。本文视最小摩阻条件所定义之塑压接触面为一曲面“流”场,旨在于提出此“最小摩阻场”之场线规律与场函数(摩擦应力τ,压应力p)规律。主要结果为:推广前文之陡线规律于广泛情况,指出“摩擦场”与“滑质场”之基本区别在于前者为发散场,向外减阻;后者为收敛场,向内减阻。二者之复合场有“分水岭”,内场收敛,外场发散。金属表面之粘性粘着区须为一收敛场。陡线规律之库仑标量方程引出两重要推论:(1)摩擦力正比于压力之陡率(并给出比例函数之实例);(2)一切塑性压力分布皆为摩擦线弧长之函数,常含一指数项。这概括进现存不少特解。由严格不滑动条件定出具体之粘着区域。试图研究(τ,p)在应力圆中定义之“摩擦点”变化规律。以重叠应力圆法定出平面应变时此点之变域,说明在平压中摩擦系数不大时,压力约近于第一主应力。本文仅涉及原则问题。场函数解法之一见作者另文。     

塑压摩擦线理论与平面压力分布问题之总解答

作者新近分析了塑压摩擦线之陡线规律,即按最小滑动阻力条件,塑压接触面上之质点滑动方向为摩擦力之陡度方向: τ=fp;其中τ为单位摩擦力,f为摩擦系数,P为单位压力。因而摩擦线族之微分方程为:或 dy/(P/y)=dx/(P/x) dy/(P/y)=dx/(P/y)对于曲面,以弧长代替x,y。按此,摩擦线族为等压线之正交族,可由实验压力曲面作出,例如图1为辊轧摩擦线族之平面投影,有齐别尔实验线族之基本性质。 命曲线坐标系(u,v)为此正交系,摩擦线为:等压线为 v(x,y)= 常数, u(x,y)=常数。陡线规律又谓 P=P(u),在一条摩擦线上 P=P(s)。 物理学报其中s为摩擦线弧长,由不滑动点或线量起。 为方便起见,定义穿过边界内一切等压线之摩擦线为“全摩擦线”。当全摩擦线上之压力分布为已知时,按陡线规律,整个压力分布曲面确定,因为全部等压线之压力值已给出,因此,有可能将表面压力分布的问题,化为u或s之常微分方程,全摩擦线端点上之一点初值确定一特解曲面。 本文限于平面问题,目的有二:第一是由力学关系作出(2)式,并于特殊情况下解之;第二是按上述理论,将整个平面压力分布问题总起来解,求出为未定函数之定型函数在任意平面几何条件下之压力解。 用下列两简化条件: 1)当f≠0时,最大切应力方向仍距滑移线不远,按此,忽略小角度,算作P约为第