Shear and Torsion Typical Mechanical Properties of Metals Shear stres:t= F/A F is applied parallel to upper and lower faces each having ar Shear strain: y=tane (x 100%6 Load- applied torque T Strainrelated to the angle of twist, o Elastic moduli are relatively insensitive to these effects Yield and tensile strengths and ature. d modulus of elasticity decrease with increasing temp Ductility increases with temperature. Brittleness Zirconia, ZrOz materials: nd nitrides or carbides 2370C cubic CaF,(enofZ.r=计+0 ubstance m.p.(C) M-o() baddeleyite, stable form (e n. ofzr=7) 6.10gcm3 1923 Zro, is not appropriate as a high T ceramie: it crack d B 2350 heating when the tran rupture has begun. The result ttleness is one of the most severe drawbacks of ceramic materials The brittleness may be modified by doping with impurities. a Use volume effect to reduce the brittleness Tough ness Elastic Recovery During Plastic Deformation MMaterial deformed plastically with a er than the original yield Toughness ability to absorb energy up to fracture that it will take before Units: the energy per unit volume, e.g. J/'m called elastic strain recovery3 Shear and Torsion Shear stress: t = F / Ao F is applied parallel to upper and lower faces each having area A0 . Shear strain: g = tanq (´ 100 %) q is strain angle Torsion: is like shear. Load: applied torque T Strain:related to the angle of twist, f. Shear Torsion Typical Mechanical Properties of Metals The yield strength and tensile strength vary with thermal and mechanical treatment, impurity levels, etc. Variability is related to the behavior of dislocations. Elastic moduli are relatively insensitive to these effects. Yield and tensile strengths and modulus of elasticity decrease with increasing temperature. Ductility increases with temperature. Metal Alloy Yield Strength MPa Tensile Strength MPa Ductility (%EL) [in 50mm] Aluminum 35 90 40 Copper 69 200 45 Brass(70Cu-30Zn) 75 300 68 Iron 130 262 45 Nickel 138 480 40 Steel (1020) 180 380 25 Titanium 450 520 25 Molybdenum 565 655 35 Brittleness The brittleness may be modified by doping with impurities. Ceramic materials: oxides, silicates, and nitrides or carbides. They have strong chemical bonds and show high m.p. Substance m.p. (oC) M-O (Å) MgO 2800 2.12 CaO 2580 2.40 SrO 2430 2.56 BaO 1923 2.76 SiO2 1700 SiC 2700 B4C 2350 BN 3000 Because of the short range of action of the chemical bonds, the material suffers a substantial loss of strength once a rupture has begun. The resulting brittleness is one of the most severe drawbacks of ceramic materials. Zirconia, ZrO2 > 2370oC cubic CaF2 (c.n. of Zr = 8) 1170 –2370oC tetragonal (c.n. of Zr = 4+4) < 1170oC baddeleyite, stable form (c.n. of Zr = 7) monoclinic tetragonal 5.56 6.10 gcm-3 On heating, 9% contraction in volume accompanies the transition Pure ZrO2 is not appropriate as a high T ceramic: it cracks during heating when the transition temperature of 1170°C is reached. By doping with 10 to 20 percent of CaO, MgO or Y2O3 (these oxides form solid solutions with the high T, cubic polymorph of ZrO2 and these cubic solid solutions are stabilized to much lower T) the tetragonal form can be stabilized down to room temperature. Use volume effect to reduce the brittleness 1170oC Toughness Toughness: ability to absorb energy up to fracture Area under the strain-stress curve up to fracture Units: the energy per unit volume, e.g. J/m3 Material deformed plastically and stress is released, the material ends up with a permanent strain. If stress is reapplied, the material again responds elastically at the beginning up to a new yield point that is higher than the original yield point. The amount of elastic strain that it will take before reaching the yield point is called elastic strain recovery. Elastic Recovery During Plastic Deformation