【正文】 queezing group （壓應(yīng)力狀態(tài)類） Upsetting Close die fing Fing （鍛造） Extrusion （擠壓） Forward Backward Punch (沖頭 ) Workpiece (工件 ) Rolling （軋制） Tensile stress state Drawing group （拉應(yīng)力狀態(tài)類） s1 s2 s3 ?Drawing of sheet, tube, bar and wire. F s1 s2 s3 ?Deep drawing. s1 s2 s3 Dending group （彎曲類） Tensile stress state on one side. Compression stress state on the another side. Stress gradient flanging Stretch concave （拉伸彎曲） Shrink concave (壓縮彎曲 ) Straight (矯直 ) Cutting group （切削類） Machining, Drill, Turn, Mill Forming Limts (成形極限 ) The condition of plastic deformation Shear stresses The extent of plastic deformation that can be achieved is highly dependent on the nature of the stress state induced. The limit of plastic deformation: a) necking （頸縮） b) Buckling（屈曲） c) fracture （斷裂） A limit to forming is imposed when uniform plastic flow ceases and forming limit is determined by whichever defect occurs first. The forming limits depend on the state of stress induced in the workpiece. 材料成形力學(xué) （雙語教學(xué)） 2 Stress Analysis Specification of stress at a point Internal forces (in. f.) （內(nèi)力） 一點(diǎn)的應(yīng)力狀態(tài) No external forces Internal forces exist External forces act. Mutual position of molecular change Distances between them change Additional internal forces The additional forces are what we are interested in and are called internal forces External forces (En. f.) （外力） External forces Act on every particles Act on contact surface Gravitational Magic Normal pressure Friction forces In the direction opposite to the moving direction of the body Convert : In. f. Ex. f. Section method Body forces Contact forces Stress at a point in a continuous body (連續(xù)體內(nèi)一點(diǎn)的應(yīng)力 ) System of ex. f. A body In equilibrium （外力系） （處于平衡狀態(tài)） Body intersectioned by a section plane through pass point P Use section method: F?Part A. Part B. (remove) FF? :Resultant exerted by B on A, A in equilibrium F :Resultant exerted by A on B (remain) in equilibrium Around point P on section plane isolate Elemental area A?Resultant exerted by A on is A? F?Average stress on is A? FA?? （ 上的平均應(yīng)力為 ） A? FA??A B P F1 F2 F3 F4 F5 F6 F7 F8 A?P B F5 F6 F7 F8 F?when 0A? ?0rAF d FA d Alim?? s?? ??(contract around point P) (Force/(lngth)2) Intensity of internal force at the point P on the section plane, in. f. / per unit area. rs: Stress at the point P on the section plane For another section plane passing through the point P ,we have another stress at the same point. In general, 0rs0rrss?The stress state at a point can be considered defined if the stress on any section plane passing through the point have been determined. （如果過一點(diǎn)任意截面上的應(yīng)力已知，則可以認(rèn)為過該點(diǎn)的應(yīng)力狀態(tài)便確定了。） Stress ponents (應(yīng)力分量 ) F?rs, and also, needs not be normal to the section plane. F?resolve （分解） sF?NF?: Normal to the reference plane : tangential to the reference plane NF?sF?F?A?PNormal stress (正應(yīng)力 ) NNA0F d FA d Alim??s????(Normal to the section plane) Positive: elongation Negative: pression Shear stress (剪應(yīng)力 ) ssA0F d FA d Alim???????(tangential to the section plane) Change in shape （改變物體的形狀） Nine ponents and stress tensor (九個分量和應(yīng)力張量 ) Coordinate system: Oxyz Take an infinite small element from the body around point P. Six section planes parallel to the coordinate planes Parallelpiped (平行六面體 ) Three orthogonal planes: xoy, yoz and zox On the face parallel to the plane xoy ( normal direction is oz ) Normal stress: z zzss? (In the oz direction) Shear stress: z?resolve zx?zy?Along ox direction Along oy direction Double subscript notation First subscript: The direction of the normal to the plane on which the stress acts. second subscript: The sense of the stress . z y x O zszx?zy?xs xy?xz? ysyx?yz?yoz zox xoy ox oy oz yysxxszzsxy?yx?xz?yz?zy?zx?plane normal direction Sense of stress ox oy oz Another specified coordinate system oxyz? ? ?Another ponent system yys??xxs??zzs??xy???yx???xz???yz???zy???zx???They can be transformed Coordinate system infinite ponent system infinite Stress tensor Determine the stress state at the point Expression of stress tensor ( matrix of tensor) －－應(yīng)力張量的表示方法（張量的矩陣形式） x x x y x zy x y y y zz x z y z zs s ss s ss s s????????x x y x zy x y y zzx zy zs ? ?? s ?? ? s????????x x x y x zy x y y y zz x z y z zs ? ?? s ?? ? s????????( , , , )ij i j x y zs ?Row Act on the same plane, but in the different direction Columm Act on the different plane, but in the same direction 1. The nine stress ponents constitute a unity which is not 2. The stress ponents depend on the choice of the coordinate 3. The stress ponents can be transformed when referring to different coordinate 相互轉(zhuǎn)換 4. The stress ponents can constitute stress invariants independent of the choice of the coordinate 可以構(gòu)成應(yīng)力不變量，該應(yīng)力不變量與坐標(biāo)系的選擇無關(guān) 5. It is a symmetric Properties of stress tensor －－應(yīng)力張量的性質(zhì) Differential equation of equilibrium in the neighbourhood of a point x z y x?z?y?A B C D E F G O Force equilibrium (力平衡 ) xsxy?xz?ysyx?yz?zszx?zy?Take an element using section method. Analyses the stresses on the face of the element. Stress ponents are the continuous function of the Cartesian coordinate. ? ?0 ,ij ij x y zss?（力平衡微分方程） ? ?,Aij ij x x y y z zs s ? ? ?? ? ? ?AijsExpand into Taylor’s series: ? ? ? ?, , , , i j i j i ji j i jx x y y z z x y z x y zx y zs s ss