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 PlastlC (permanent) deformation - governed by the motion of dislocations Mechanical Properties 1 Mechanical Properties Tensile Strength Yield Strength Stiffness, modulus of elasticity Toughness Ductility/Brittleness Fracture Strength Hardness Mechanical Properties 2 Stress and Strain Definition of Stress "Language" of Mechanical Properties: Stress and Strain Tensile Stress Stress a = [MPa] F = load [N], A0 = cross sectional area [m2] Shear Stress 1— F 23ľ Stress tensile compressive shear torsional bending tensile load s / ,.-"' S compressive load Mechanical Properties torsion CTQ) Strain Strain (stretch) = relative elongation Al s = --------- [m/m] L 'o F Al = elongation 10 = original length Mechanical Properties < 10 No Stress Stress 4 Stress-Strain Diagram a [MPa] VrF Stress - Strain Diagram Mechanical Properties 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 a-s curve F Fracture, Break Point Mechanical Properties 6 Stress - Strain Behavior Mechanical Properties 7 Stress-Strain Curve for Ductile Material s Elastic Limit lastic Region Vicld Point Plastic Region o*n«uon | m j Strain Mechanical Properties Hooke's Law Elastic deformation ^ Hooke's Law (j = E. s E = Stiffness or Young's modulus or modulus of elasticity [GPa] Slope of the linear elastic portion of the a-s curve E ~ D (bond energy) Energy Mechanical Properties Ductility Ductility is given by: %Elongation (fractured specimen) %Reduction in Cross Sectional Area Metals 30-50% Polymers >100% Ceramics 0% Mechanical Properties Poisson's Ratio Poisson's Ratio Trie stress-strain curve does not show an Important feature of plastic deformation: a contraction perpindicularto the extension caused by a tensile stress. The effect is characterized by Poisson's Ratio: elongation ._fx V = v = 0.29 for ductile iron v = 0,36 for magnesium contraction Mechanical Properties 11 Bulk Modulus Bulk Modulus, B Compressibility, k B = 1/k B = (Nc/4)(1971 - 220 I) r3 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 Madelung constant n Born coefficient q charge r0 bond distance Mechanical Properties 12 Aq2(n-1) B= ------------------- 72 ti s0 r04 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 Strain Mechanical Properties 13 Toughness Toughness ■^ energy absorbed by the material up to the point of fracture ->area under the a-s 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 14 Toughness Strength and Toughness Strains True stress olrw = _ P Asa Uňl ) High strength + Low ductility = Low toughness High strength -i- High duct N it y ^JHigh toughness Low strength + High ductility = Low toughness Strain, e High toughness depends on the proper combination of strength arid ductility. Mechanical Properties 15 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 16 Hardness Hardness ■^ resistance to local plastic deformation aTS = 3.55.HB [MPa] (HB < 175) ctts = 3.38.HB [MPa] (HB > 175) Hardness scale Mohs scale Rockwell HR Brinell HB Vickers HV Knoop HK BerkovichHV Shore HS (Durometer) 1 -10, minerals cone or sphere 10 mm sphere diamond pyramid diamond pyramid diamond pyramid 20° needle _| BO TOBQ BQ IDO HPrH řO JO JO m Mt 'i ľ i '1 ŕJÍ> tfoo MŮ 1 | iüü° I*» Ť * m ■_ IDO WO »»1*^^ 'GUT i«ŕ irrnl.,1*:. DD *' 1 1 ň í 1» ÍW ":■ *Oť SUU IhÉufl Tiwfn^B *IH^.rr Mechanical Properties 17 Mohs scale Friedrich Mohs Hardness of minerals, surface scratching nonlinear not suitable for fine-grained, friable, or pulverulent materials 1 Talc 2 Gypsum CaS04.2H20 3 Calcite CaC03 4 Fluorite CaF2 5 Apatite Ca5(P04)3(OH) 6 Orthoclase KAlSi308 7 Quartz Si02 8 Topaz Al2(Si04)(F/OH)2 9 Corundum A1203 10 Diamond C Mechanical Properties Rockwell Penetration depth of an indenter under a specified load Rockwell Indenter Load, kg Application B 1.6 mm ball 100 kg Soft steel, nonferrous metals T 1.6 mm ball 15,30, 45 Thin soft metals N 120° diamond (brale) 15,30, 45 Hard thin sheet metals A 120° diamond (brale) 50 Cemented carbides R 1.6 mm ball 10 Polymers C 120° diamond (brale) 150 Hardened metals Mechanical Properties 19 Indenters Brincll Vickers d Knoop Berkovich Mechanical Properties 20 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) Indenter Diameter D BHN = I Applied Force F Indentation Diameter D; '. £dr]L".i:r Carbide fcili Pyranidic Diamond Strength Upprox.j Brak Peneirator 10mm Tungsten Carbide Bil Pyramid ie Diamond Svengch (approx) ISOkgŕ l.OOOkgf iOktf It» fcjp'mm' 150^ i.OOOktf lOkgf ks» kjjŕmm' 67 - 900 - - 43 400 423 201 14! 66 - 665 - - 42 390 412 IM 138 65 739 «Z - - 41 381 402 191 134 64 721 BOO - - 40 371 392 Üb 131 63 ■XI T72 - - J9 361 ■a i 181 127 62 «n 746 - - 38 3S3 372 176 124 61 670 720 - - 37 344 363 172 121 60 «54 697 - - 36 336 354 167 HS S9 «34 674 329 232 35 327 345 163 IM sä «IS 653 319 224 3 1 3ŕ9 336 159 1 12 57 595 635 307 216 33 311 327 154 109 S6 S77 613 297 m 32 301 318 149 1 05» ss S 60 S9S :es 202 31 294 310 146 102 54 543 577 279 19« 30 286 302 142 99 S3 S15 56 J 269 189 29 279 294 138 17 SI 512 544 262 184 28 271 286 134 94 SI 4« 528 253 178 27 264 279 130 92 so 481 SI3 245 !72 26 258 272 127 89 49 469 496 23S 167 25 253 266 125 68 48 4S5 484 231 162 24 247 260 .22 85 47 443 471 lit se 23 243 :54 ■::< B4 46 4« 45« 218 153 22 237 248 1 16 82 45 421 446 212 14$ 21 231 243 113 30 +4 409 ijl Xb 145 20 226 ;jb III 78 For the source of Rockwell, Brinell and Vtcker* Hardnesi data see endnote 4. Aproximace Comparison of Hardness Scales ■10,000 Diamond "1000 200 -100 "20 "-5 Brinell Hardness 110 _UUL= SO ' 60- 20 0 -■ Rockvell C -100- SD SA Shore Hardness Nitrided steels I Cutting tools i File band Easily machined steels Rra"as ■ Cast Iron -Aluminum Brass -Copper -Bakelite and ujuiiiinuii---------Gray PVC alloys Mast Plastias Mark Doggett IT 283 Mechanical Properties Ceramics Transverse bend test (jFS = Flexural strength, Fracture strength, Modulus of ru A L A O r d aFS FL 7ir- 3FL 2bd2 Mechanical Properties Ceramics & only elastic deformation at room temperature 40 I I I I I I ......In 250 200 J? 150 £ vi 100 — 50 0.0004 O.O008 0.0012 Strain Mechanical Properties 31 Ceramics # voids dominate behavior E = E0(l - 1.9P + 0.9P2) E0 elasticity modulus of the nonporous material P volume fraction porosity crFS = cr0 exp(- nP) n, a0 experimental constants & tension not the same as compression tensile strength is one-tenth of compressive strength !!!! Mechanical Properties 32 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 = -------- A, n materials constants V"" V volume of material Mechanical Properties 33 Superplasticity in Ceramics Zr02, 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 SiAlON 470% elongation Mechanical Properties 34 Surface Roughness Ra = aritmetic average of the peak-to-valley height of surface asperities [um] Profilometer, stylus of finite radius (2, 5,10 um) cannot reach the bottom of valleys True roughness = 4x R AFM Atomic force microscopy, stylus 100 angstrom r~ äjK Oum 0.75 un ISO wo Ra : 0,71 Rq : 0,90 Rsk: 0,45 Rku: 3,67 Rz : 4.63 IBJMnm »■19nm Iran V^A^^^a^a^^ Zrarge. 16.39nifi dum O.ííiiTi 1.50 um Mechanical Properties 35