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1、 Tensile stress,s:,Shear stress,t:,Stress has units:N/m2 or lb/in2,ENGINEERING STRESS,Elastic modulus,E,E curvature at ro,E is larger if Eo is larger.,PROPERTIES FROM BONDING:E,Elastic Shear modulus,G:,t=G g,Elastic Bulk modulus,K:,Special relations for isotropic materials:,simpletorsiontest,pressur
2、etest:Init.vol=Vo.Vol chg.=DV,OTHER ELASTIC PROPERTIES,Tensile strain:,Lateral strain:,Shear strain:,q,Strain is alwaysdimensionless.,(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,co
3、mpressive,shear and bending stresses.(b)Illustration showing how Youngs modulus is defined for elastic material.(c)For nonlinear materials,we use the slope of a tangent as a variable quantity that replaces the Youngs modulus constant,The Tensile Test:Use of the Stress-Strain Diagram,Load-The force a
4、pplied to a material during testing.Strain gage or Extensometer-A device used for measuring change in length and hence strain.Glass temperature(Tg)-A temperature below which an otherwise ductile material behaves as if it is brittle.Engineering stress-The applied load,or force,divided by the original
5、 cross-sectional area of the material.Engineering strain-The amount that a material deforms per unit length in a tensile test.,(c)2003 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
6、in the tensile test by means of the moveable crosshead.The cross-head movement can be performed using screws or a hydraulic mechanism,(c)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 differen
7、t materials.Note that these are qualitative,Ductilefracture isdesirablefor structural applications!,Classification:,Ductile:warning before fracture,i.e.changes geometry before failure,Brittle:No warning,Adapted from Fig.8.1,Callister 6e.,DUCTILE VS BRITTLE FAILURE,(c)2003 Brooks/Cole,a division of T
8、homson Learning,Inc.Thomson Learning is a trademark used herein under license.,Figure 6.10 The stress-strain curve for an aluminum alloy,1.Initial,2.Small load,3.Unload,Elastic means reversible!,ELASTIC DEFORMATION,3,1.Initial,2.Small load,3.Unload,Plastic means permanent!,PLASTIC DEFORMATION(METALS
9、),(c)2003 Brooks/Cole,a division of Thomson Learning,Inc.Thomson Learning is a trademark 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 steel,True Stress and True Strain,True stress The lo
10、ad divided by the actual cross-sectional area of the specimen at that load.True strain The 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
11、 are identical to the yield point,The Bend Test for Brittle Materials,Bend test-Application 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.Flexural strength or modulus of rupture-The stress required to fr
12、acture a specimen in a bend test.Flexural modulus-The modulus of elasticity calculated from 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 materials,Figure 6.19(a)The bend test
13、 often used for measuring the strength of brittle materials,and(b)the deflection obtained by bending,Figure 6.21(a)Three point and(b)four-point bend test setup,Hardness of Materials,Hardness test-Measures the resistance of a material to penetration by a sharp object.Macrohardness-Overall bulk hardne
14、ss of materials measured using loads 2 N.Microhardness Hardness of materials typically measured using loads less than 2 N using such test as Knoop(HK).Nano-hardness-Hardness of materials measured at 110 nm length scale using extremely small(100 N)forces.,Figure 6.23 Indentors for the Brinell and Roc
15、kwell hardness tests,Vickers Hardness,Hv,FRACTURE TOUGHNESS,Fracture toughness:Kc=Ysc(pa)0.5=Y(2Egs)0.5 Kc is a material propertyY 1,depends on geometry,increasing,Based on data in Table B5,Callister 6e.Composite reinforcement geometry is:f=fibers;sf=short fibers;w=whiskers;p=particles.Addition data
16、 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,Golden,CO.5.(30 vol%)S.T.Bul
17、jan 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:,Largest,most stressed cracks grow first!,-Result 1:Max flaw size dictates design stress.,-Result 2:Design stress dictates max.flaw size.,K Kc,DESIGN AGAINST CRACK GROWTH,
