1、Simulations of plastic processing: elasto-plastic deformationPart 3: plastic deformationTeacher: 法法 QQ号：2306847727， office 523 A区Content Tensile test (拉伸测试) Compression test Engineering and true stress/strain Theory of plastic deformation (塑性变形理论)Lashen ceshiSuxing bianxing lilunTensile testHypothes
2、is: During the tensile test, the tensile direction and the force are aligned The surfaces normal to the tensile direction (=section) stay normal to the tensile direction= no shear of the sample During plastic deformation, the volume is constantTensile test Tensile specimens - round and flatTensile t
3、est l0 = initial length l = current length at time t Strain = Deformation = xx = ln(l/l0) (l-l0)/l0 is call the engineering strain ln(l/l0) is the true strain If a sample is deformed 2 times, from l0 to l1 and from l1 to l2, the total strain is: = ln(l1/l0) + ln(l2/l1) = ln(l1/l0*l2/l1) = ln(l2/l0)
4、Tensile test The stress is defined by: = zz = F/S Engineering stress: = F/S0 True stress: = F/SThe volume is constant: 1/S=l/(S0l0) = Fl/(S0l0)S0l0SlFTensile testNecking 颈缩-jingsuo strictionRupture 断裂- duanlie ruptureUltimate tensile strength UTS 抗拉强度- kangla qiangdu Limite de rsistance mcanique RmS
5、tress 应力 - contrainte Elongation A(%)- 延伸率- yanshenlv allongement rupturePlastic deformation 塑性变形 - dformation plastiqueElastic strain 弹性应变 - dformation lastiqueYield strength Ys 屈服强度- qufu qiangdu Limite dlasticiteStrain -应变 - dformationTensile testTensile testCompression testHypothesis: During the
6、 compression test, the compression direction and the force are aligned The surfaces normal to the compression direction (=section) stay normal to the compression direction, but shear can happen in the compression plane During plastic deformation, the volume is constantCompression test h0 = initial h
7、igh h = current high at time t The strain is in theory negative, but by convenience we adopt positives values Strain = Deformation = xx = -ln(h/h0)=ln(h0/h) (h0-h)/h0 is call the engineering strain ln(h0/h) is the true strain True strains are additivesCompression test The stress is defined by: = zz
8、= F/S Engineering stress: = F/S0 True stress: = F/SThe volume is constant: 1/S=h/(S0h0) = Fh/(S0h0)S0FSh0hCompression testEngineering and true stress/strain Total strain=elastic strain + plastic strain When the sample (or material) is unloaded (stress=0), the elastic strain is null. Elastic strain c
9、hanges the volume of the sample (except if =0.5) When we draw the stress-strain curves, samples are loaded, but we make the approximation that the volume is constant.Engineering and true stress/strain Exercises: change engineering stress into true stress and vice-versa change engineering strain into
10、 true strain and vice-versa By convention, negative stress are compressive and reduction induce negative strain; but in uniaxial loading by convenience the values are positives.Engineering and true stress/strain Exercise1: compression True strain = ln(h0/h) Enginering strain E=(h0-h)/h0=1-h/h0 = =-l
11、n(1-E) = E=1-exp(-)Engineering and true stress/strainExample:True strain is: =500+500(1-exp(-7)Figures show Engineering stress-strain in tension and compressionEngineering and true stress/strain True stress-strain are modeled by power laws (voce law): =n =0+n =0+k(1-exp(-n)Engineering and true stres
12、s/strainTheory of plastic deformation Dislocations slip(位错的滑移) Grain boundary sliding (晶界的滑移)(at HT) Twinning（孪生）ParentTwinsWeicuo de huayiJingjie de hualiTheory of plastic deformation Dislocations slip in the slip plane Dislocations produce a shear of the lattice (位错产生晶格的剪切)Weicuo chansheng jingge
13、de jianqieTheory of plastic deformation Slip systems in face centered cubic (Al, Cu) Planes 111 Directions 12 slip systems (with 2 direction each) (plane)direction=0 (they are perpendicular )Theory of plastic deformation Body Centered Cubic (BCC) crystals Planes 110 (or 112 or 123) Directions Theory
14、 of plastic deformation Hexagonal close packed (HCP) crystals Basal slip: (0001) Prismatic slip: 10-10 Pyramidal slip: 10-11 Pyramidal slip: 11-22 10-11Theory of plastic deformationThe deformation of single crystals (单晶体):Active slip planerotation( Without constraints due to the apparatus )Rotation
15、of the planeTensile axisTheory of plastic deformation In single crystals, the applied stress depend on the orientation of the activated slip systemStress vs basal plane orientation of Mg Singlecrystal E.C. Burke and W.R. Hibbard, Plastic Deformation of Magnesium Single Crystals”, Transaction AIME, J
16、ournal of metals-295 (1952)Theory of plastic deformation Slip generates a shear of the crystal and a rotation of the latticexynb/2xyxy/2/2 around z=+Burgers vectorSlip planeTheory of plastic deformation n= is the plane normal b= is the normalized burger vector Schmid Factor: M= cos()cos() = bz*nzZXY
17、nbnx ny nzbx by bzTheory of plastic deformationSchmid Factor computed for different values of and : if b, n and the loading direction are in the same plane, so = 90 - M= cos()cos() If b (or n) is normal to the loading direction, SF=0Theory of plastic deformation Schmid Factor: For single crystal in
18、uniaxial deformation, the activated slip system is the system with the highest Schmid Factor.ZXYnbTheory of plastic deformation The Schmid Factor depend on the orientation of the slip system (plane and burger vector) The Schmid Factor is used to compute the shear stress s s is the shear in the slip
19、plane, along the burger vector, whereas is the stress along the loading direction in the sample coordinate s=MTheory of plastic deformation The slip system is activated (dislocations move and crystal deforms) when the shear stress s is equal to the critical resolved shear stress (CRSS) cs: s=cs=M The CRSS is a property of the material, temperature and strain rate
