Mechanical Properties 1 Mechanical Properties Mechanical properties = response of a material to an applied load or force (deformation) Two important regimes of mechanical behavior: Elastic (non-permanent) deformation - governed by the stretching of atomic bonds Plastic (permanent) deformation - governed by the motion of dislocations Mechanical Properties 2 Mechanical Properties Tensile Strength Yield Strength Stiffness, modulus of elasticity Toughness Ductility/Brittleness Fracture Strength Hardness Mechanical Properties 3 Stress and Strain F A0 Stress = [MPa] F = load [N], A0 = cross sectional area [m2] Stress tensile compressive shear torsional bending "Language" of Mechanical Properties: Stress and Strain Mechanical Properties 4 Strain F l l0 No Stress Stress l l0 Strain (stretch) = [m/m] l = elongation l0 = original length Mechanical Properties 5 Stress-Strain Diagram [MPa] F TS Y H E/P TS Y 0 = E. Stress - Strain Diagram Mechanical Properties 6 Stress-Strain Diagram Stress ­ Strain Behavior 0 ­ E/P Elastic Deformation, recoverable E/P ­ F Plastic Deformation, irrecoverable 0 ­ H Linear Region, Small Strain, Hooke's Law H Proportional Limit Y Yield Point, Engineering Yield Strength (at 0.2% strain) TS Tensile Strength = a maximum of the - curve F Fracture, Break Point Mechanical Properties 7 Stress ­ Strain Behavior Mechanical Properties 8 Hooke's Law Elastic deformation Hooke's Law = E . E = Stiffness or Young's modulus or modulus of elasticity [GPa] Slope of the linear elastic portion of the - curve E ~ D (bond energy) r 0 Energy Mechanical Properties 9 Shear Shear Strength = 40% Tensile Strength Mechanical Properties 10 Ductility Ductility is given by: %Elongation (fractured specimen) %Reduction in Cross Sectional Area Metals 30-50% Polymers >100% Ceramics 0% Mechanical Properties 11 Poisson's Ratio Mechanical Properties 12 Bulk Modulus Bulk Modulus, B Compressibility, B = 1/ B = (Nc/4)(1971 ­ 220 I) r-3.5 Nc average coordination number r bond distance I ionicity 0 for Group 14 (diamond, Si) 1 for Group 13/15 (BN) 2 for Group 12/16 (ZnS) A q2 (n ­ 1) 72 0 r0 4 A Madelung constant n Born coefficient q charge r0 bond distance B = Mechanical Properties 13 Ductility and Brittleness Ductility ­ plastic deformation before fracture Metals ­ slip, dislocations move easily Brittleness ­ no plastic deformation Ceramics ­ ionic, difficult to slip ­ covalent ­ strong bonds Mechanical Properties 14 Toughness Toughness energy absorbed by the material up to the point of fracture area under the - curve up to the point of fracture combination of high strength and medium ductility the ability of a material to resist fracture, plus the ability to resist failure after the damage has begun a tough metal can withstand considerable stress, slowly or suddenly applied, will deform before failure the ability of a material to resist the start of permanent distortion plus the ability to resist shock or absorb energy Mechanical Properties 15 Toughness Mechanical Properties 16 Hardness Hardness Resistance to plastic deformation, usually by indentation Stiffness or temper, or resistance to scratching, abrasion, or cutting It is the property of a material, which gives it the ability to resist being permanently, deformed (bent, broken, or have its shape changed), when a load is applied. The greater the hardness of the metal, the greater resistance it has to deformation. Macro Micro Nano Mechanical Properties 17 Hardness Hardness resistance to local plastic deformation TS = 3.55.HB [MPa] (HB < 175) TS = 3.38.HB [MPa] (HB > 175) Hardness scale Mohs scale 1 ­ 10, minerals Rockwell HR cone or sphere Brinell HB 10 mm sphere Vickers HV diamond pyramid Knoop HK diamond pyramid BerkovichHV diamond pyramid Shore HS 20° needle (Durometer) Mechanical Properties 18 Mohs scale Friedrich Mohs Hardness of minerals, surface scratching nonlinear not suitable for fine-grained, friable, or pulverulent materials 1 Talc 2 Gypsum CaSO4.2H2O 3 Calcite CaCO3 4 Fluorite CaF2 5 Apatite Ca5(PO4)3(OH) 6 Orthoclase KAlSi3O8 7 Quartz SiO2 8 Topaz Al2(SiO4)(F/OH)2 9 Corundum Al2O3 10 Diamond C Mechanical Properties 19 Rockwell Hardened metals150120° diamond (brale) C Polymers101.6 mm ball R Cemented carbides50120° diamond (brale) A Hard thin sheet metals15, 30, 45120° diamond (brale) N Thin soft metals15, 30, 451.6 mm ball T Soft steel, nonferrous metals 100 kg1.6 mm ball B ApplicationLoad, kgIndenterRockwell Penetration depth of an indenter under a specified load Mechanical Properties 20 Indenters Mechanical Properties 21 Brinell (Germany) Diameter of indentation made by a 10 mm ball (hardened steel or WC) under a specified load (500, 1500, 3000 kg) for a specified time (10, 15, 30 s) HB = the Brinell hardness number F = the imposed load in kg D = the diameter of the spherical indenter in mm Di = diameter of the resulting indenter impression in mm Mechanical Properties 22 Vickers (UK) Diamond pyramid indenter HV = 1.8544(F/d2) F load [kg] 1-120 kg d diagonal of a square indentation [mm] Mechanical Properties 23 A comparison of the deformation around an indentation as a function of the force applied. For (A), a 100-g load was applied, resulting in a 41- m-diameter indent, while for (B), a 10-kg load was applied, resulting in a 410- m- diameter indent. Mechanical Properties 24 Knoop (US) Diamond pyramid indenter HK = 14.2294(F/l2) F load [kg] 1 - 1000 g l long diagonal of a rhombohedral impression [mm] Mechanical Properties 25 Berkovich Triangular diamond pyramid indenter 115° HK = 1.5677(F/d2) F load [kg] 1 - 1000 g d long diagonal of a triangular impression [mm] Mechanical Properties 26 Shore (Durometer) Mechanical Properties 27 Common Applications and Nomenclature for Hardness Tests Test Abbreviation Indenter Test load (kg) Application Brinell HBW 10-mm ball: tungsten carbide 3000 cast iron and steel Brinell HBS 10-mm ball: steel 500 copper, aluminum Rockwell A HRA brale 60 very hard materials, cemented carbides Rockwell B HRB -in. ball 100 low-strength steel, copper alloys, aluminum alloys, malleable iron Rockwell C HRC brale 150 high-strength steel, titanium, pearlitic malleable iron Rockwell D HRD brale 100 high-strength steel, thin steel Rockwell E HRE -in. ball 100 cast iron, aluminum, and magnesium alloys Rockwell F HRF -in. ball 60 annealed copper alloys, thin soft metals Superficial Rockwell T 30 T -in. ball 30 materials similar to Rockwell B, F, and G, but of thinner gauge Superficial Rockwell N 30 N brale 30 materials similar to Rockwell A, C, and D, but of thinner gauge Vickers HV diamond 10 hard materials, ceramics, cemented carbides Vickers HV diamond 0.5 all materials Knoop HK diamond 0.5 all materials, case-depth determination Mechanical Properties 28 Hardness Scales Mechanical Properties 29 Mechanical Properties 30 Ceramics Transverse bend test F L b d r FS = FS = FL r3 3FL 2bd2 FS = Flexural strength, Fracture strength, Modulus of rupture Mechanical Properties 31 Ceramics only elastic deformation at room temperature Mechanical Properties 32 Ceramics voids dominate behavior E = E0(1 ­ 1.9P + 0.9P2) E0 elasticity modulus of the nonporous material P volume fraction porosity FS = 0 exp(­ nP) n, 0 experimental constants tension not the same as compression tensile strength is one-tenth of compressive strength !!!! Mechanical Properties 33 Ceramics strength determined by the largest flaws, sample size dependent L. DaVinci: The longer the wire, the smaller the load to fail it. Weibull statistical theory of strength A V-n A, n materials constants V volume of material x = Mechanical Properties 34 Superplasticity in Ceramics SiAlON 470% elongation ZrO2, SiC, Si3N4, SiYAlON Grain boundary sliding at elevated temperatures, grains wetted with glass phase, viscous fluid acts as a lubricant, equiaxed fine grains solution-precipitation, diffusion Mechanical Properties 35 Surface Roughness Ra = aritmetic average of the peak-to-valley height of surface asperities [m] Profilometer, stylus of finite radius (2, 5, 10 m) cannot reach the bottom of valleys True roughness = 4x Ra AFM Atomic force microscopy, stylus 100 angstrom