《材料成型双语chapter_6stressevaluationapproach》由会员分享，可在线阅读，更多相关《材料成型双语chapter_6stressevaluationapproach（54页珍藏版）》请在金锄头文库上搜索。
1、6 Stress evaluation approach (slab method) (应力分析方法工程法),Assumption 1,Plane section remain plane.,Element cut from a plastic deformed material with sections parallel to the plane section.,Equilibrium equations,(1),Assumption 2,Take some special directions as the principal direction.,For example:,For p
2、lane strain:,Horizontal ( width ). ox,vertical ( thickness ). oy,y. c.,For axisymmetrical problem:,Axis of a work-piece oz,Radial direction . or,s1 s3 = 2k =Y,(2),(1) + (2),Stress boundary condition: for determining integration constants.,Assumption 3: Friction condition,1) Sliding friction, coulomb
3、 friction law: t =mp ( m = 0 , frictionless),2) Sticking friction (常摩擦应力区) (粘着摩擦),滑动摩擦, 遵守库仑摩擦定律(常摩擦系数区),t =k ( in hot working, rough tooling surface),3) Constant friction law （摩擦应力递减区）,t = mk (0md, t = mp k,When xd, t = k= K/2,When x=d, mp= K/2,Determine C,At x = w,When x=d, mp= k=K/2,When xd, t =
4、k= K/2,When x=d, mp= K/2,6.3 Quasi- static plane strain drawing of sheet material through a wedge shaped die,1) Description of the process,Small semi-angle: a,t = m p (lubricate well),s longitudinal tensile stress from back tension,Problem : Drawing force t=?,2) Take element and analyze the stress,A
5、ssumption: vertical section remain plane.,Slab cut with vertical section,Normal stress: Uniform,Shear stress: no.,x , x + dx,Stress analysis,x , sx,x + dx sx+dsx,Top and bottom die-workpiece interface:,p , t = mp,Uniform on a section and there is no shear stress,Equilibrium equations. S x = 0 ( in h
6、orizontal direction),Neglect the second order of the term,The stresses in the vertical direction,Because m1 and a is very small.,Therefore,(A),3) The assumption of the principal direction,Principal direction,sx (- p) = K,(B),4) Drawing force at the exit,Let,Integrate (C),(D),Determine the integrate
7、constant A by means of boundary condition .,At entrance,y = H,sx = s,(D),5) Maximum fractional reduction in a single pass （单道次最大压下率）,If t attains the yield stress in uniaxial tension (leaving the die), then the sheet yields. The limit condition is,When back tension is employed,If back tension is not
8、 employed,For example.,cota = 5.6713.,B = mcota = 0.2836.,(1+B ) / B = 4.53.,Therefore .,Hence .,Thus .,6) Normal pressure on the die face （模具表面的正压力）,At exit,7) Compression with inclined platens,a,h,H,t1,o,t2,w2,w1,Neutral plane,On the left side of the neutral plane,Yield criterion,sx (- p) = K,sx =
9、 K- p,dsx = - dp,s.b.c. x = -w2,sx = t2,p = K t2,a,h,H,t1,o,t2,w2,w1,Neutral plane,On the right side of the neutral plane,Yield criterion,sx (- p) = K,sx = K- p,dsx = - dp,s.b.c. x = w1,sx = t1,p = K t1,Flow stress depends on strain rate ( strain rate sensitive) High friction coefficient.,6.4 Quasi-
10、 static plane strain cold rolling of plate and strip metal,1) Description of the process,hot rolling,stiction,cold rolling,Flow stress is independent of strain rate Low friction coefficient.,Coulomb law,section material,plate, strip,elongation - rolling direction,spread - transverse direction,compression- vertical direction,3- Dimensional flow,elongation,spread 10,The velocity of strip (vs) in passing through the roll gap,at the entry,vs = v vr cos f.,vr : the linear velocity of rolls (circumference),
