1、 Tensile stress,s:Shear stress,t:s FtAooriginal area before loadingStress has units:N/m2 or lb/in2ENGINEERING STRESS Elastic modulus,E E curvature at roL F Ao=E Lo Elastic modulus r larger Elastic Modulus smaller Elastic Modulus Energy ro unstretched length E is larger if Eo is larger.PROPERTIES FRO
2、M BONDING:E Elastic Shear modulus,G:t1Gt=G Elastic Bulk modulus,K:Special relations for isotropic materials:PPPMM G E2(1)K E3(1 2)simpletorsiontestpressuretest:Init.vol=Vo.Vol chg.=VOTHER ELASTIC PROPERTIES Tensile strain:Lateral strain:Shear strain:q/2/2L/2L/2Lowo=tan qStrain is alwaysdimensionless
3、.(L)(-LL)ENGINEERING STRAIN(c)2003 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark used herein under license.Figure 6.3 (a)Tensile,compressive,shear and bending stresses.(b)Illustration showing how Youngs modulus is defined for elastic material.(c)For nonlinear materia
4、ls,we use the slope of a tangent as a variable quantity that replaces the Youngs modulus constantThe Tensile Test:Use of the Stress-Strain DiagramoLoad-The force applied to a material during testing.oStrain gage or Extensometer-A device used for measuring change in length and hence strain.oGlass tem
5、perature(Tg)-A temperature below which an otherwise ductile material behaves as if it is brittle.oEngineering stress-The applied load,or force,divided by the original cross-sectional area of the material.oEngineering strain-The amount that a material deforms per unit length in a tensile test.(c)2003
6、 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark used herein under license.Figure 6.7 A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead.The cross-head movement can be performed using screws or a hydraulic mechanism(c
7、)2003 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark used herein under license.Figure 6.9 Tensile stress-strain curves for different materials.Note that these are qualitative Ductilefracture isdesirablefor structural applications!Classification:Ductile:warning before
8、fracture,i.e.changes geometry before failureBrittle:No warningAdapted from Fig.8.1,Callister 6e.DUCTILE VS BRITTLE FAILURE(c)2003 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark used herein under license.Figure 6.10 The stress-strain curve for an aluminum alloyFbonds s
9、tretchreturn to initial1.Initial2.Small load3.UnloadElastic means reversible!ELASTIC DEFORMATION31.Initial2.Small load3.UnloadPlastic means permanent!Flinear elasticlinear elasticplasticPLASTIC DEFORMATION(METALS)(c)2003 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark
10、used herein under license.Figure 6.11 (a)Determining the 0.2%offset yield strength in gray cast ion,and(b)upper and lower yield point behavior in a low-carbon steelTrue Stress and True StrainoTrue stress The load divided by the actual cross-sectional area of the specimen at that load.oTrue strain Th
11、e strain calculated using actual and not original dimensions,given by t ln(l/l0).Figure 6.17 The relation between the true stress-true strain diagram and engineering stress-engineering strain diagram.The curves are identical to the yield pointThe Bend Test for Brittle MaterialsoBend test-Application
12、 of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load.oFlexural strength or modulus of rupture-The stress required to fracture a specimen in a bend test.oFlexural modulus-The modulus of elasticity calculated fr
13、om the results of a bend test,giving the slope of the stress-deflection curve.Figure 6.18 The stress-strain behavior of brittle materials compared with that of more ductile materialsFigure 6.19 (a)The bend test often used for measuring the strength of brittle materials,and(b)the deflection obtained
14、by bendingFigure 6.21 (a)Three point and(b)four-point bend test setup2323wtPLbs242)(3wtlLPbsHardness of MaterialsoHardness test-Measures the resistance of a material to penetration by a sharp object.oMacrohardness-Overall bulk hardness of materials measured using loads 2 N.oMicrohardness Hardness of
15、 materials typically measured using loads less than 2 N using such test as Knoop(HK).oNano-hardness-Hardness of materials measured at 110 nm length scale using extremely small(100 N)forces.Figure 6.23 Indentors for the Brinell and Rockwell hardness tests)(:)(:/8544.1/)2/136sin(222mmdiagonalakgloadWa
16、WaWSWHvVickers Hardness,HvFRACTURE TOUGHNESS Fracture toughness:Kc=Ysc(pa)0.5=Y(2Es)0.5 Kc is a material property Y 1,depends on geometrysaa K s pa K 1.1s pa unitsof K:MPamor ksi inincreasingBased on data in Table B5,Callister 6e.Composite reinforcement geometry is:f=fibers;sf=short fibers;w=whisker
17、s;p=particles.Addition data as noted(vol.fraction of reinforcement):1.(55vol%)ASM Handbook,Vol.21,ASM Int.,Materials Park,OH(2001)p.606.2.(55 vol%)Courtesy J.Cornie,MMC,Inc.,Waltham,MA.3.(30 vol%)P.F.Becher et al.,Fracture Mechanics of Ceramics,Vol.7,Plenum Press(1986).pp.61-73.4.Courtesy CoorsTek,G
18、olden,CO.5.(30 vol%)S.T.Buljan et al.,Development of Ceramic Matrix Composites for Application in Technology for Advanced Engines Program,ORNL/Sub/85-22011/2,ORNL,1992.6.(20vol%)F.D.Gace et al.,Ceram.Eng.Sci.Proc.,Vol.7(1986)pp.978-82.FRACTURE TOUGHNESS Crack growth condition:Ys pa Largest,most stre
19、ssed cracks grow first!-Result 1:Max flaw size dictates design stress.-Result 2:Design stress dictates max.flaw size.sdesignKcYpamax amax1pKcYsdesign2K KcDESIGN AGAINST CRACK GROWTHaYKWBSPfICfss2232/32)/(1)/(21)/(7.2)/(93.315.2)/1()/(99.1 WaWaWaWaWaWaY)/()/()/()/()/()2/(8544.15.14.035.15.025.112CPHEAKCPHEAKCPAKaPHVCVCCV
