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 1 Mechanical Propen Tensile Strength Yield Strength Stiffness, modulus of elasticity Toughness Ductility/Brittleness Fracture Strength Hardness Mechanical Properties Stress and Strain Definition of Stress Tensile Stress "Language" of Mechanical Properties: Stress and Strain Shear Stress 9l__ F Stress a = [MPa] F = load [N], An = cross sectional area [m2] tensile load Stress tensile compressive shear torsional bending j----------------------- shear Mechanical Properties compressive load j----------------------------- torsion OH) Strain Strain (stretch) Al Al < l0 No Stress s = [m/m] "o Al = elongation F Stress 10 = original length Mechanical Properties 4 Stress-Strain Diagram a [MPa] TS ay y^ e/p * f / H / Stress - Strain Diagram / a = E.8 0 8 Mechanical Properties 5 Stress-Strain Diagram Stress - Strain Behavior O-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 cr-s curve F Fracture, Break Point Mechanical Properties 6 Mechanical Properties Hooke's Law Elastic deformation ^ Hooke's Law ct = 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 Shear Shear Strength = 40% Tensile Strength Mechanical Properties 9 Ductility Ductility is given by: %Elongation (fractured specimen) %Reduction in Cross Sectional Area Metals 30-50% Polymers >100% Ceramics 0% Mechanical Properties 10 Poisson's Ratio Poisson's Ratio The stress-strain curve does not show an Important feature of plastic deformation; a contraction perpindiculer to the extension caused by a tensile stress. The effect is characterized by Pais$onTs Ratio: elongation . -?X V h v = Q.29 for ductile iron v = 0.35 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 Brittle b Strain Mechanical Properties 13 Toughness Toughness ■^ energy absorbed by the material up to the point of fracture ->area under the cr-e 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 Strain,& True stress otrm = K Asri Uňl ] High strength + Low ductility = Low toughness High strength -i- High ductility ^High toughness Low strength + High ductility = Low toughness Strain, e High toughness depends on the proper combination of strength and 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) aTS = 3.38.HB [MPa] (HB > 175) Hardness scale Mohs scale Rockwell HR Brinell HB Vickers HV Knoop HK Berko vichHV Shore HS (Durometer) 1 -10, minerals cone or sphere 10 mm sphere diamond pyramid diamond pyramid diamond pyramid 20° needle - i I» njBDSO I DO HNU ?Ü JO 40 1900 - £ »o T—r i '(Hm m irtňH..í*> h*t IM — mů jjt» — i« 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 Hrincll Vicfcws /k Berkovi ch 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 1 Diameter Dj 1 f D > F load [kg] 1 -1000 g ^. 130 / 1 long diagonal of a rhombohedral <^^^ Mechanical Properties 24 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 25 Shore (Durometer) nQm l títtfdfiňi 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 1 16-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 1 ů-in. ball 100 cast iron, aluminum, and magnesium alloys Rockwell F HRF 1 16-in. ball 60 annealed copper alloys, thin soft metals Superficial Rockwell T 30 T 1 16-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 27 28 , Rockwell C Stale BriraU Hardness Vitkerj Hardness Tensile Strength (appro*.) RockweB Brinell C State 1 Hardness Vikerj Hardness T*ftsile Strength tipp««.) ink Perietratcr lOnwn Tunesien Carbide Bill Pyramidic Diamond Brilc Penetrator lOmm Tungsr.cn Carbide Pyramidic Diamond ISOkjf l.OOOkgf lOkr ksi fcjp'mm' ISfcjí i.OOOkflf lOkjrf lest kjjf'rnm' 67 - 900 - - 43 400 423 201 141 i,t - 665 _ - 42 J90 112 196 138 65 739 tin - - 41 181 402 191 134 64 721 BOO - - 40 171 392 186 131 63 705 772 - - 39 162 382 1 BI 127 62 688 746 - - 38 153 372 176 124 61 670 '20 - - 37 144 161 Ti 121 60 «4 697 - - 36 136 354 167 118 S9 634 674 J29 232 35 127 34S 161 IM 58 615 653 319 224 34 119 336 159 1 12 57 595 633 307 216 33 111 327 154 109 a 577 613 :■..-■ 209 32 -•'. í 18 149 lOfr ss 560 595 :e« 202 31 294 J 13 146 ICi 54 54 J 577 279 196 30 286 302 142 99 S3 525 560 269 189 29 279 294 138 97 S2 512 544 262 184 28 271 286 134 94 Si 496 S2B 253 176 27 264 279 130 92 ■ SO 4ft 1 513 245 !72 26 ;>e 272 127 BS 49 469 493 238 i 67 25 253 266 125 88 48 455 484 231 162 24 247 260 :: B5 47 44) 471 221 IS8 23 243 254 ■::.i B4 46 432 45fi 2l8 IS! 22 237 248 1 16 82 M 421 446 212 149 21 231 24 J Ml BO 44 409 434 206 145 20 226 238 III 78 . For the source or Rockwell. Brinell and Viekers Hardnesi dau see endnote 4. Aproximace Comparison of Hardness Scales ■ 10,000 Diamond ■5000 - 2000 000 -100 so ""- 80 - -40-: 20 - 0 -1 Rockwell C Rockvell B SD SA Nitride« steels Cutting tools 1 File band Easily "whinrrt steels R""" ■ Cast Iron =Alurninum Brass -Copper -Bakelite and aluminum----------Gray PVC alloys Most Plastics Brinell Hardness Shore Hardness Mark Doggett IT 283 Mechanical Properties Ceramics Transverse bend test ctfs = Flexural strength, Fracture strength, Modulus of ru A L A ^ h-^ ^ O aFS d dps FL 7cr- 3FL 2bd2 Mechanical Properties Ceramics $ only elastic deformation at room temperature AC\ HU 1 1 1 1 1 1 1 1 1 1 — 250 30 / — 200 O ■—i X B £ vi /AJuminLimoxrde 150 | 1 in LOO 10 - J / ^**^£\ass. 50 ň [j^f\\...... 1 0 U 3 0.0004 O.O008 0.0012 Strain 31 Mechanical Properties Ceramics ^ voids dominate behavior E = E0(l - 1.9P + 0.9P2) E0 elasticity modulus of the nonporous material P volume fraction porosity aFS = a0 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 ct = -------- A, n materials constants v-n 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 Ra ____ AFM Atomic force microscopy, stylus 100 angstrom 0 um 0 75mn _______________________________________|: "■' .- I range 1B.39niri Ra : 0.71 Rq : 0.90 Rsk: 0.4S Rku: 3.67 Rz : 4.63 t i^t, 075 Lin Mechanical Properties :65ir*fl 019i*fl inn LSflum 35