Tutorials Pt 1 - Materials Science

March 25, 2018 | Author: Vassish Dassagne | Category: Crystal Structure, Fracture, Fatigue (Material), Ultimate Tensile Strength, Strength Of Materials


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Mechanical and Production Engineering DepartmentUNIVERSITY OF MAURITIUS FACULTY OF ENGINEERING Mechanical and Production Engineering Department MECH 2006Y/MECH 2001Y TUTORIAL 1 – Atoms & Basics Chemistry Qu.1 Explain what is meant by the following terms: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) (xiv) (xv) (xvi) Atom Molecule Element, Compound Mixture Symbol Formula Relative Atomic Mass Atomic number Mass number Avogadro’s Constant Isotopes Atomic Structure Ionisation Energy Bohr Atomic Model Wave Mechanical Atomic Model. 2. State the Dalton Atomic theory 3. State the Heisenberg Uncertainty principle. 4. State the Pauli’s Exclusion principle. 5. Give the four Quantum numbers that are used to specify the electronic configuration of atoms. 6. What is the significance of the periodic table in engineering materials? 7. Explain what is an alloy? 8. What is a phase? 9. Explain the difference between crystalline structure and amorphous structure. 10. Explain what is a eutectic mixture? 11. Why are gases such as neon, argon, helium and krypton inert? 12. What is the largest principal quantum number of iron? S. Venkannah Ext 7845 [email protected] Does the decrease in melting point with increasing atomic number which is displayed by the elements in Group IV appear in all the groups? 4. 4. [0. Cu. Faculty of Engineering B. Using the ionic radii given in the table below.04] 5. ½.8 eV of energy. Comment on the discrepancy in the two values (if any). and show that it may be written in the from E= e2 [1 – 1/(n-1)] 2 (40r ) 2.mu .) Mechanical Engg. 6. What is the energy expenditure in transferring an electron from an isolated sodium atom to an isolated chlorine atom? Using the expression given in problem 1 above. 5.7  at equilibrium. S.732.Bonding & Crystal Structure 1. Venkannah Ext 7845 [email protected] in the unit cell. SiC. where the exponent n is about 10 and C is a constant./Manufacturing Engg. calculate the length of the body diagonal. calculate the length of the face diagonal in the unit cell and hence show that the structure is stable only when r 1 > 0. while adding an electron from infinity to a Cl atom to form the Cl. and hence derive the value of the radius ratio at which the structure just becomes unstable./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y TUTORIAL 2 .Mechanical and Production Engineering Department University of Mauritius. Obtain an expression for the equilibrium distance r0 between the ions in terms of C and n. Compare your result with the theoretical value of the heat of vaporization of NaCl of 153 kcal/mole. To remove an electron to infinity from a Na atom.Eng (Hons. RbBr. calculate the energy change when the two isolated atoms are brought together to from an NaCl molecule. GaAs. given that the ionic separation is 2. SnTe. NH3. [Ans:1. The attractive force between ions with unlike charges is e2/(40r2) while the repulsive force may be written as Ce2/rn. and that the exponent n in the expression for the energy is equal to 10. Hence deduce an expression fro the energy E required to separate the ions to an infinite distance apart. Ni? Place the materials in the expected order of increasing melting points.33eV.ion liberates 3. What crystal structure do you expect to find in the following solids: BaO. let the ionic radii be r1 and r2 (r2>r1).414r2. 1. BN. Compare with the melting points given in a standard reference book. Assuming that the anions just touch the cations. find the size of the largest impurity ion which can be accommodated interstitially in the CsCl lattice with its center at the point ½. If the radii of the ions in the NaCl structure are r1 and r2 (r2>r1).ac. In the CsCl structure.13eV of energy must be used.8eV] 3. 96 2. 9. 4. 13 Explain why covalently bonded materials are generally less dense than ionically or metallically bonded ones. 2806’] 3 10. D and  are constants whose values depend on the specific material.78 0. Calculate the density of graphite if the interplanar distance is 3. and Ag are respectively 4. The density of solid copper is 8900 kg/m .34 0. In an X ray diffraction experiment the unit cell of copper is found to be face centred cubic. 12 The net potential energy EN between 2 adjacent ions is sometimes represented by the expression EN = (-C/r)+ D exp (-r/) ---------1 in which r is the interionic separation and C. Determine the expression for E0 by substitution for C in Eq. What factors might give rise to a discrepancy between them. Differentiate EN with respect to r and set the resulting expression equal to zero.05 1. while Cu and Ag have FCC structures.81 1.  and r0 3. Calculate the number of atoms per cubic metre.0. (a) Derive an expression for the bonding energy E 0 in terms of the equilibrium interionic separation r0 and the constants D and  using the following procedure. [2250 kg/m3] 8.50*1028m-3] Ion Li+ Na+ K+ Rb+ Cu+ Be2+ Mg2+ Ba2+ Radius () 0.ac.e. Both Na and K have BCC structures.24. Calculate the angles for first order diffraction (i. K. n=1) from the (100) and (110) planes of a simple cubic lattice of side 3 when the wavelength is 1.4 and the interatomic distance within the plane is 1. Cu.20 1.33 1.98 1.Mechanical and Production Engineering Department 7. and 4.74 11 On the basis of the values permissible for the four quantum numbers. derive the number of quantum states corresponding to the fourth principal shell (n = 4).96 0.61. 3. Venkannah Ext 7845 [email protected] . [8. S. Deduce another figure for the number of atoms per cubic metre and compare the two results.49 0. 8.35 Ion U4+ ClBrIO2S2- Radius () 1. 2.61.50*1028m-3.78 1.08. If the lattice were BCC. would you expect to find diffracted beams at the same angles? [9036’.32 1.4. Solve for C in terms of D. C and  using procedure analogous to the one outlined in part (a).62. and the lattice parameter is 3. and hence deduce the atomic radius of each metal. 1. Calculate in each case the distance between the centers of neighbouring atoms. 1 (b) Derive another expression for E0 in terms of r0. The lattice constants of the metals Na. 3a/4] 20. and (iii) a monoatomic SC crystal.81. melting point and boiling point of the following inert gas crystals: He. FCC and DC Crystals. 16 The potential energy W of a system of two atoms varies as a function of their distance of separation r as follows: W= . Give the Miller indices of the family of close packed directions in SC. and (iii) the bond energy W0 = A * (m-n) r0n m 17. <110>. BCC. 3a/2. 24 X ray analysis of a Mn-Si alloy with 75 atomic percent of Mn and 25 atomic percent of Si showed that the unit cell is cubic and the lattice parameter a= 2. 21 Find the size of the largest sphere that will fit an interstitial void in a BCC crystal as a function of the atomic radius r.4 versus -850C). 18. bond length. Make a plot of the melting points and the boiling points of materials of different bonding characteristics as a function of their bond energy.mu . ¼) and other equivalent positions. The void is located at (0. <111>.ac.66] S. a. Ne. [<100>. indicating the closest distance of approach between neighbouring atoms. Ar.Find the diameter of the largest atom that would fit an interstitial void in FCC nickel without distortion.A/rn + B/rm Show that at equilibrium (i) r = r0 = (mB/nA) 1/m-n (ii) the energy of attraction is m/n times the energy of repulsion. ½. (II) Cite 2 important refinements that resulted from the wave-mechanical atomic model. a Mg = 3. even though HF has a lower molecular weight. [0. None. 25 Calculate the density of the CsCl crystal from the radii of the ions: Cs+ = 1. Explain why the bond lengths increase with increasing atomic number although there is an increase in the bond energy.86 .Mechanical and Production Engineering Department 14 Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride (HCl) (19. 15 (I) Cite 2 important quantum-mechanical concepts associated with the Bohr model of the atom. Venkannah Ext 7845 [email protected] Why does the polymer melt at a much lower temperature? 27 Find the radius of the largest sphere that will fit an interstitial void in magnesium (HCP). 19.65  and Cl.= 1. The density of the alloy is 6850 kg/m3. Find the number of atoms in the unit cell. 26 The bonds in diamond are predominantly covalent in character and so are the bonds along the chains of a long chain polymer. 22.21. Xe. a/2. Compare the bond energies. (ii) a monoatomic BCC crystal. Kr. Take the c/a ratio of Mg to be the ideal value. 23 State the differences and common points between (i) CsCl. Distinguish between atom sites and lattice points in a monoatomic FCC crystal and a NaCl crystal. 35 Draw a (11-1) plane in the unit cell of a cubic crystal. Determine their distances from a parallel plane through the origin.61. Venkannah Ext 7845 [email protected] Materials Science and Engineering – A first Course by Vv.ac. Can you pack atoms more closely than in (111) plane? 32 Calculate the number of atoms per unit area of (111). (110) and (100) planes of a BCC crystal. 33 Express the edge. (110) and (100) planes of copper (FCC) with the lattice parameter of 3. Higgins 4. face diagonal and body diagonal of the unit cell in terms of the atomic radius r for SC. 30 A BCC crystal is used to measure the wavelength of some X rays.54 are used to calculate the spacing of (200) planes in aluminium. 31 Calculate the atomic density (number of atoms per unit area) in (111). BCC and FCC crystals.40. [a/3. What is the size of the unit cell of the aluminium crystal? Determine the structure of the crystal. a/(23)] REFERENCES: 1. 34 Sketch a (110) plane in the unit cell of a cubic crystal. Show all the <111> directions that lie on this plane. Raghavan 3. What is the wavelength? The lattice parameter of the crystal is 3. The answer may be derived as a function of the lattice parameter a. giving the Miller indices of each atom of them. Materials Science and Engineering by W. Determine the lattice parameter and the atomic diameter.20.mu .15. 1 by Hearns. The Bragg angle for this reflection is 22. Engineering Metallurgy by R. The Bragg angle for reflection from (110) planes is 20. Materials for Engineering by Bolton 5. 36 Draw a (111) plane and a (222) plane in the unit cell of a cubic lattice with lattice parameter a.V S. D. Mechanics of Materials – vol. 29 The distance between (111) planes in a FCC crystal is 2. Callister 2.Mechanical and Production Engineering Department 28 X rays with a wavelength of 1. giving the Miller indices of each one of them. A. Show all the <110> directions that lie on this plane. the co-ordination number iv. the no.02 E23 atoms/mol. Faculty of Engineering B./Manufacturing Engg. Hexagonally Closed Pack (HCP) (b) For each of the crystal lattices given in (a) above determine the following.023  1023 atoms/mol 4. the different types of faults and dislocations that exist in the lattice structure of pure metals. what you understand by edge dislocation? 2 Describe. Venkannah Ext 7845 [email protected] explain what you understand by the following crystal lattice i. Determine the lattice parameters (a & c) in the terms of the radius R of the atom for a hexagonally closed packed crystal structure.Eng (Hons.mu . the lattice parameter in terms of the radius R ii.) Mechanical Engg.982 g/mol Determine the following for aluminium: (Show all your calculations and diagrams) (i) the lattice parameter (j) the number of atoms associated with each unit cell (ii) the co-ordination number (iii) the density Avogadro’s number = 6. the Atomic packing factor (APF) c. Edge dislocation is one type of line imperfection that may occur in crystal structures.587. The Atomic mass of the metal is 47.1475nm and c/a = 1. Show your calculations. 3 (a)Using suitable diagrams.143 nm and its atomic mass is 26. Face centred cubic (FCC) iv. Body centred cubic (BCC) iii. S. Aluminium has a face centred cubic (FCC) structure at room temperature./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y TUTORIAL 3 .Mechanical and Production Engineering Department University of Mauritius.9 g/mol and Avogadro’s number = 6. Simple cubic (SC) ii. The atomic radius of Aluminium is 0. Calculate the density of HCP titanium at room temperature for the atomic radius of 0. with the help of diagrams. of atoms associated with each unit cell iii.Bonding & Crystal Structure 1 (a) Discuss how the properties of materials are affected by the types of bonding present in the structure? (b) The crystal structures are not always perfect. Explain. with the help of proper diagram/s. i. c= 4. HCP .286nm).956 Å.85.87 g/cm3. [8. titanium goes through a phase change analogous to iron except that in this case the crystal structure changes from BCC to HCP. [2. What is the volume change? 17. of atoms per unit area) in (111). Calculate the planar density of atoms in BCC iron in the (100). The density of NaCl is 2. Determine the Miller indices of the direction common to both planes. 8 Calculate the density of BCC iron at room temperature from the atomic radius of 1. (c) Draw a (110) and a (111) plane inside the cubic unit cell.85 Å ] 13 How many atoms per square millimetre are there on the (100) plane of lead (FCC)? Assume the atomic radius as 1.32Å . Calculate the distance between two adjacent atoms.18 g/cm3. Calculate the density of copper.61 Å . Calculate the linear density of atoms in the [100].5. a = 2.847 g/mol & Avogadro’s no = 6. and [111] directions in BCC iron (a 0 = 0. 9 Copper has FCC structure and the atomic radius is 1. and (111) planes (a0 = 0. (b) Sketch the (110) plane in a FCC lattice structure and calculate its planar density. (a) Sketch the [111] direction in a BCC lattice structure and calculate it’s linear density. [2. (110). 14 Calculate the atomic density (no.746 Å . 6 .74. 2.ac.278 Å .92 g/cm3] 10 NaCl crystals have FCC structure. Sketch the following directions and planes in a BCC unit cell. BCC : a = 3.683 Å.Mechanical and Production Engineering Department 5. 1.9 Å and density 7.02 E23 atoms/mol).746 Å . ( 110) and (100) planes of copper (FCC) atoms with lattice parameter 3. 7. Derive answers in terms of lattice parameter a. (Atomic mass 55. Given the atomic weight of copper 63. Venkannah Ext 7845 [email protected] 15 Calculate the number of atoms per unit area of (111). [110].81 Å ] 11 Calculate the number of atoms per unit cell of a metal having the lattice parameter 2. (110) and (100) planes of a BCC crystal.24 Å .mu . Find the spacing of (I) (200) planes and (ii) (220) planes and (iii) (111) planes.286nm).465. 16 On cooling through 8800C. [100] [110] [111] (100) (110) (111) S. Atomic weight of the metal is 55. [2] 12 :Lead is a FCC with an atomic radius of r = 1. It is observed that  for 111 planes decreases by 0.110 as the silver is heated from room temperature to 8000C. (1/2 . 22 Determine the Miller indices of plane ABC in the BCC unit cell shown in Fig Qu. which has an FCC structure and one atom per lattice point is 8902kg/m3. 1. The wavelength is 0. 0) respectively.7 43. that of the lattice containing the interstitial spheres (Assume the spheres of the cubic lattice to be of unit diameter) S.16 Å is obtained with a monochromatic X-ray beam of wavelength 1.ac. (b) Calculate the diameter of the largest sphere that can be accommodated in the interstitial spaces of such a lattice.mu .3 29. the packing factor of the simple cubic lattice and ii.6 Determine the interplanar spacing and the miller indices of the reflecting plane. if at 9100C a = 0. 23 Derive Bragg’s law. and find the values of i.05nm: What is the interplanar spacing? 24 a) Sketch a simple cubic lattice. The BCC form is stable at temperature below 9100C. r0 = 0.144 nm) is placed in an x-ray camera and irradiated with molybdenum-characteristic radiation (0. 19 The diffraction pattern of a cubic material of lattice parameter a = 3. 1. The coordinates of the A.363 nm for FCC and a = 0. 0. 1. Given that the crystal structure remains the same upon heating. while the FCC form is stable above 9100C. 0) and (0.293 nm for BCC. (b) Pure iron undergoes an allotropic transformation at 9100C. B. A second order diffraction maximum occurs at an angle of 150 to the original direction of a beam of X rays incident on a crystal. The first four lines on the pattern were observed to have the following values LINE 1 2 3 4  ( degrees) 20.54 Å. find the change in a due to the heating. and C are (0. The atomic weight of nickel is 58. relating the interplanar spacing in a crystal lattice to the wavelength and diffraction pattern of X rays falling on it. (b) Calculate the atomic density of the (111) plane of Rhodium (FCC) with lattice parameter 0. 20 (a) The density of nickel. Calculate the volume change for the transformation BCC FCC. and indicate on it (I) the 112 plane and (ii) the 221 direction. Calculate (I) the lattice parameter (ii) the atomic radius of nickel 21 (a) A specimen of silver (FCC.Mechanical and Production Engineering Department 18 Draw a (110) and a (111) plane inside the cubic unit cell. Explain clearly the steps involved. Determine the Miller indices of the direction common to both planes.2 36. Venkannah Ext 7845 [email protected] nm.0709 nm).71 g/mol. 3/4). For which set of crystallographic planes will a first order diffraction peak occur at a diffraction angle of 44.530 for FCC nickel when monochromatic radiation having a wavelength of 0.1542 nm is used. (Atomic radius of nickel – 0.mu .Mechanical and Production Engineering Department 25 Derive Bragg’s law. Venkannah Ext 7845 [email protected] relating the interplanar spacing in a crystal lattice to the wavelength and diffraction pattern of X-rays falling on it.125 nm) S.ac. 8931 nm and a density of 7. Determine a.Eng (Hons./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y TUTORIAL 4 .) Mechanical Engg. -Mn has a cubic structure. Determine the crystal structure for the following: a. Beryllium has a hexagonal crystal structure.47 Mgm-3.4949 nm. and one atom per lattice point b.848 Mgm-3.613 5.6326 nm and a density of 7. and the atomic weight is 9. Calculate the atomic radius in cm for the following: a. The number of atoms in each unit cell b. The atomic radius is 0. with a0 = 0.808 Mgm-3 and the atomic weight is 208.175 nm. Bismuth has a hexagonal structure.3294 nm and one atom per lattice point. Lattice parameter and b.4086 nm and one atom per lattice point. r = 0. b.ac. Faculty of Engineering B.22858 nm and c0 = 0.Mechanical and Production Engineering Department University of Mauritius.60849 0. the atomic radius Metal Density Atomic weight (kgm-3) (gmol-1) potassium 855 39.4546 nm and c0 = 1./Manufacturing Engg.1858 nm.186 nm. with a0 = 0.42906 nm.Bonding & Crystal Structure 1. BCC metal with a0 = 0. The atomic weight S. and one atom per lattice point 3. Calculate the following for each of the metal given in the table below: a.09 Thorium 11720 232 Iron 7800 55. r = 0. with a0 = 0.35842 nm. How many atoms are in each unit cell 6.01 gmol-1. 2.mu . with a0 = 0.85 4.62 132.91 weight Lattice parameter (nm) 0. Determine the crystal structure of the following metals given that they have cubic structures: Metal A B Density (kgm-3) 2600 1892 Atomic (gmol-1) 87. The density is 9. density is 1.1143 nm.98 gmol-1. -Mn has a different cubic structure. Venkannah Ext 7845 [email protected] FCC metal with a0 = 0. Determine the a. A metal with a0 = 0. The volume of the unit cell b.26 Mgm-3. A metal with a0= 0. The packing factor in the unit cell 7. 035 Radius (nm) Atomic 58. NiO b. A diffracted X ray beam is observed from the (311) planes of iron at a 2 of 78.mu . Higgins 9.Mechanical and Production Engineering Department of manganese is 54. Callister 7. Determine the planar density and the planar packing fraction for the (111) and the (222) planes of MgO.167 0.10 when X rays of 0. Would you expect the following compounds to have the CsCl. A diffracted X ray beam is observed from the (220) planes of iron at a 2 of 99.132 0.938 gmol-1 and the atomic radius is 0. has a lattice parameter of 0. Venkannah Ext 7845 [email protected] Determine the percent volume change that would occur if -Mn transforms to -Mn. The lattice parameter b.069 0.71+16) g mol-1 The molecular weight of UO2 would be 1 U4+ + 2 O2. 1 by Hearns. Materials Science and Engineering by W. Mechanics of Materials – vol.0 9. MgO which has the NaCl structure. Calculate the lattice parameter of the iron. What ions are present on each plane? REFERENCES: 6.097 0.71 16. 11.112 nm. A. Calculate the lattice parameter of the iron.012 Weight (gmol-1) (Note: The molecular weight of NiO would be 1 Ni2+ + 1 O2-= (58.9 79.V S.30 when X rays of 0. D.= (238 + 2*(16)) g mol-1 9. 10. Raghavan 8. The density c.00 132.91 238. Engineering Metallurgy by R.15418 nm wavelength are used.15418 nm wavelength are used.ac. Materials Science and Engineering – A first Course by Vv. UO2 c. NaCl. BeO d. Materials for Engineering by Bolton 10.196 0. ZnS or Fluorite structure: a. (NOTE: Many lattice structures may have more than one atom per lattice site) 8. CsBr Determine the following for the above mentioned compounds: a. The packing factor (volume) Ions Ni2+ O2Cs+ BrU4+ Be2+ Ionic 0.396 nm. 8 4.5 14.6 16. / mm 2.5 35.0 32. The test piece had a diameter of 10 mm and a gauge length of 50 mm.5 25. Stress/ Mpa Strain/ x10-4 0 0 90 5 170 10 S.2 23.5 38.5 30.28 mm and a gauge length of 56 mm.1 31.097 32.5 1. The following results were obtained from a tensile test of an aluminium alloy./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y Tutorial 5 ./Manufacturing Engg.0 6.59 0. Plot the stress-strain graph and determine (a) the tensile strength (b) the 0.33 2.081 30 0.0 22.5 10.5 35.049 20 0.ac.0 40. The following data was obtained from a tensile test on a stainless steel test piece.033 15 0.8 0. a thickness of 3mm and a gauge length of 80 mm.17 0.065 25 0. Load/kN 0 Ext.) Mechanical Engg.0 21.4 10.0 27.5 5.5 39. The test piece had a diameter of 11.0 61.2% proof stress.1% proof stress © the modulus of resilience.2 8.0 25.0 7.106 35.Mechanical and Production Engineering Department University of Mauritius.Eng (Hons. The following results were obtained from a tensile test of a polymer.0 86 2.0 39. Determine (a) the limit of proportionality stress (b) the tensile modulus © the 0. Faculty of Engineering B. /mm 0 0. 3.Mechanical Properties 1.0 37.00 2. Loa 0 d/k N Ext/ 0 mm Loa d/k N Ext. Plot the stress-strain graph and determine (a) the tensile modulus (b) the 0./mm 0 5 0.2% strain Load 0 100 200 300 400 500 600 650 630 /kN Ext.5 15.250 1. Plot the stress-strain graph and determine (a) the tensile strength (b) the secant modulus at 0. Venkannah 255 15 345 20 495 30 605 40 700 50 Ext 7845 760 60 805 70 845 80 880 90 895 100 [email protected] 28.mu .08 0.016 10 0.88 1. The test piece had a width of 20 mm.35 0.0 12.3 19.5 20.0 17. The following results were obtained from a tensile test of a steel specimen.0 12.40 .1% proof stress © the yield stress and (d) the tensile modulus.5 0. fracture surfaces…) Describe two commonly used impact testing techniques.64 12850 1. 7. Describe tests to predict the lifetime of components subjected to fatigue creep.25 9870 0. 8. fatigue strength. 12.20 8140 0.5 mm and the final cross sectional area was 58.91 14100 3.strain curve and hence determine.mu .Mechanical and Production Engineering Department Describe the process through which a material undergoes (I) Ductile fracture Brittle fracture (crack formation and propagation.1mm rectangular test specimen of magnesium.2 x 19.08 5630 0. (a) the Young’s modulus of elasticity (b) the modulus of resilience (c) the tensile strength (d) the 0. List measures to increase the resistance to fatigue of a metal alloy. (ii) 6.99 (fracture) The initial length of the specimen was 63.42 mm2. What do you understand by the Ductile to Brittle transition of a material? Fatigue and Creep are two common forms of failure. 11. 5. (paying attention to terms such as fatigue limit. fatigue life.13 7430 0. Venkannah Ext 7845 [email protected] 9.72 12500 6. Explain the terms (I) fatigue (ii) creep. steady state creep rate…. Give metallurgical/processing techniques that can be employed to enhance creep resistance of metal alloys.ac. List the factors that affect the fatigue life. LOAD (N) EXTENSION (mm) 0 0 1380 0.) 10.2% proof stress (e) the percentage elongation (f) the percentage reduction in area (g) the true stress at fracture 14 Differentiate between : (i) toughness and hardness (ii) engineering stress and true stress (iii) yield strength and tensile strength (iv) creep and fatigue S. Plot the stress .03 2780 0. 13 The following data were collected from a 3.45 13830 5.18 14340 4. 6 1.0 ( Maximum Load) 7. 17 What mechanical properties of a material are determined by tensile testing? What valuable information can be determined from the results of a tensile tests? 18 What is the difference between a ductile material and a malleable material? S.mu . The following results were obtained from a tensile test on a 20-mm diameter S.0370 0.35 mm. 16.ac. Plot the data and calculate (a) (b) (c) (d) (e) (f) (g) (h) the 0. Venkannah Ext 7845 [email protected] 0. the gauge length is 47. cast iron specimen having a gauge length of 40 mm.52 (fracture) After fracture.0185 0.2% proof strength the tensile strength the modulus of elasticity the % elongation the % reduction of area the engineering stress at fracture the true stress at fracture.42 mm and the diameter is 18. (iv) toughness (v) Ultimate tensile stress.G. and the modulus of resilience.0555 0. Load (kN) 25 50 75 90 105 120 131 125 Extension (mm) 0.56 4.Mechanical and Production Engineering Department 15 Explain what you understand by the following terms (I) fatigue (ii) creep (iii) hardness. Discuss how the properties of the oxide films of metals affect the immunity of metals to corrosion? Steel can be protected against corrosion by metallic coatings using elements such as Zinc. Draw the Iron-Iron Carbide phase equilibrium diagram labelling all the important points on the diagram. What are the effects of different cooling rates on the structure and properties of steel of different percentage carbon content? 6. ductility. elongation.ac. 3../Manufacturing Engg. What are the effects of increasing the percentage carbon content of steel on its properties such as tensile strength. Explain why? 4.Eng (Hons.) Mechanical Engg.12% carbon is slowly cooled to room temperature? Calculate the relative proportions by mass of ferrite and cementite in the steel at 7230C. Calculate the relative proportions by mass of ferrite and cementite in pearlite. 14. 12./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y Tutorial 6 . Faculty of Engineering B. 10. explain what happens when a steel melt of 0. etc. What do you understand by the “solidus” and “liquidus” curve? With reference to the diagram drawn in 9 above. It is sometimes more useful to use a modified TTT diagram also known as a Continuous-Cooling Transformation diagram.? 5. What are these phases and explain how they are formed? 2. What are the compositions of the phases present? S. What do you understand by plain carbon steel? What are the different elements that might be present and their effects on the properties and structure of the steel? 7. weldability.. Venkannah Ext 7845 [email protected] hardness. 13. Draw the aluminium-magnesium phase equilibrium diagram. What do you understand by a Time-Temperature-Transformation diagram? Explain how you would use such a diagram to determine the phases present in a particular quenched specimen. 11. (available from any metallurgy book) (i) What is the maximum solubility of magnesium in aluminium? (ii) Over what temperature range will an alloy containing 7% magnesium exist as a single solid phase? (iii) At what temperature does an alloy containing 5% magnesium begin to melt on heating? (iv) An alloy containing 16% magnesium is at 5200C. There are some other phases that can be present in steel cooled under certain conditions. 9.Mechanical and Production Engineering Department University of Mauritius.mu . hardenability. Tin. Aluminium and Lead? Discuss why and how these elements protect the steel? Explain what you understand by the following reactions:  Peritectic  Eutectoid Draw the phase equilibrium diagram of the following binary systems:      Zinc-Lead Bismuth-Cadmium Copper-Nickel Tin-Lead Platinum Silver 15.Phases 1. What is/are the difference/s between plain carbon steel and alloy steel? What are the different alloying elements used in alloy steels? What are the benefits of using each of the alloying element? 8. An alloy containing 70% gold starts to solidify at 14000C by separating crystals of 37% gold.0% at 00C.0% solidifies and cools slowly to 00C. 15% ferrite + 85% pearlite b. An Alloy containing 80% bismuth starts to solidify by separating crystals containing 75% antimony. (iv) A eutectic is formed at 7000C containing 40. 17.mu . Draw the cooling curve 20. Draw the equilibrium diagram to scale labeling all important features and regions ii. a. Check the crystal structure factor and calculate the relative size factor for these metals b. (a) Draw the equilibrium diagram to scale and label all important features and regions (b) For an alloy containing 70% gold I. i.50C. Give the temperature of initial solidification ii.0% Y. (viii) Which will be stronger in (vii) – (a) or (b)? 16. 70% pearlite + 30 %cementite c. Bismuth melts at 271. An alloy containing 50% bismuth starts to solidify at 5050C by separating crystals of 90% antimony. For an alloy containing 40% antimony i.0% at 7000C and 2. Give the chemical composition and relative amounts of the phases present at 4300C iv. The melting point of platinum is 17690C and that of gold is 10630C. (iii) Y is soluble in X in the solid state to the extent of 20. An alloy containing 40% gold starts to solidify at 16000C by separating crystals of 15% gold.ac. 30%ferrite + 70% cementite 18. Draw a thermal equilibrium diagram representing the system between two metals X and Y. Venkannah Ext 7845 [email protected] and Production Engineering Department (v) In what proportions will the phases in (iv) be present? (vi) What is the % increase in solubility of magnesium in aluminium in an alloy containing 12% magnesium as the temperature rises slowly from 60 0C to 3500C? (vii) Sketch the structure of an alloy containing 10% magnesium (a) slowly cooled from 4500C. Give the temperature of final solidification III. Draw the cooling curve 19. (b) after it has been heated for some time at 7000C and then water quenched.0% X and 60.30C and antimony melts at 630. Bismuth and Antimony are completely soluble in both the liquid and the solid states. Describe what happens when an alloy containing 70. Determine the percentage Carbon content in carbon steel containing the following: a. (b) water quenched from 4500C. given the following: (i) X melts at 10000C and Y at 8000C (ii) X is soluble in Y in the solid state to the extent of 10. Give the temperature of final solidification iii. Give the chemical composition and relative amounts of the phases present at 13400C IV. Give the temperature of the initial solidification II. Sketch the microstructures of an alloy containing 15% Y (a) after it has cooled slowly to 00C. Platinum and gold are completely soluble in both the liquid and solid states.0% at 7000C and 8% at 00C. Using the phase equilibrium diagram you have drawn determine the following: S. Draw the Tin-Lead equilibrium phase equilibrium diagram. The first solid to solidify is of composition 20% lead iii. When solidification is complete the microstructure of the alloy consists of primary  crystals in an ( + ) eutectic mixture matrix. what fraction exists as the  phase at 2200C? What fraction of this alloy is liquid just above the eutectic temperature? Determine the fractions of  and  phases just below the eutectic temperature in 90% Sn alloy and the eutectic alloy. When solidification is complete the microstructure of the alloy consists of primary  crystals in an ( + ) eutectic mixture matrix. BCC d. The cooling curve shows 3 discontinuities 21. Higgins Materials for Engineering by Bolton Mechanics of Materials – vol. f. Callister Materials Science and Engineering – A first Course by Vv. BCT e.ac.Mechanical and Production Engineering Department a. Does not involve diffusion 22. c. When solidification is complete the microstructure of the alloy consists of an ( + ) eutectic mixture vii. A. A martensitic transformation a. 1 by Hearns. D. e. Which of the following statements apply to an alloy containing 80% Tin? i. Hard b. What fraction of the total weight of the 90% Sn alloy will have eutectic structure. The cooling curve shows 2 discontinuities xi. Can only lead to a change in the crystal structure of the phases d. just below the eutectic temperature? g. The first solid to solidify is of composition 20% Tin ii. An equilibrium phase REFERENCES:      Materials Science and Engineering by W. 90% Sn. viii. Ductile c. The first solid to solidify is of composition 80%tin vi. b. What is the eutectic composition? What are the compositions of the solid phases in equilibrium at the eutectic temperature? For an alloy containing. Venkannah Ext 7845 [email protected] Is extremely rapid c. The first solid to solidify is of composition 2% lead v. Can lead to a change in composition of the phases e. The cooling curve shows one discontinuity x. Martensite in steel is a. The first solid to solidify is of composition 2% Tin iv. Involves the precipitation of an equilibrium precipitate b. d. S.mu . ix. Raghavan Engineering Metallurgy by R. Fe/Ti.Mechanical and Production Engineering Department University of Mauritius.92 g/cm3. (a) Which metal corrodes? (b) Write equations to describe the reactions which occur at each electrode. (b) Give two examples of natural passivity of metals./Mechatronics Materials Science – MECH 2006Y/MECH 2001Y Tutorial 7 . Cu20 = 6. At high temperatures. Fe/Zn.) Mechanical Engg. Question 7. assuming each metal has a valency of 2. (a) Explain what is meant by the term 'passivity' in the context of corrosion. The following couples with equal areas are immersed in fresh water: Fe/Cd. Question 6. (a) Give two useful functions of E/pH (Pourbaix) diagrams. with the help of suitable diagrams. (b) Give two limitations to their use. Would this oxide be protective according to the Pilling-Bedworth criterion? Densities are: Cu = 8.Corrosion Question 1. Iron is connected to copper and then immersed in a solution containing both Fe2+ and Cu2+ ions. Fe/Cu. Question 4. Question 2. most metals and alloys are affected by one of the different types of corrosion processes depending on the environmental conditions.ac. Faculty of Engineering B. (ii) Which alloy is prone to dezincification? (iii) Which elements may be added to the alloy to minimize dezincification? S.Eng (Hons. (i) Explain what is meant by dezincification./Manufacturing Engg. In service. Question 3. copper reacts with air to form the oxide Cu20.0 g/cm3. Briefly define each one of the following: (a) Corrosion (b) Standard electrochemical potential (c) Exchange current (d) Polarisation (e) Double layer. Explain. the following terms as used in corrosion. (a) In which one of the four will the iron corrode the fastest? (b) Which combination offers the best protection to the iron? Question 5. (c) Calculate the maximum possible potential of the resulting corrosion cell. Venkannah Ext 7845 [email protected] . (i) Passivation (ii) Selective leaching (iii) Sacrificial anode (iv) Cathodic protection Question 8. What is the effect of the rate of flow of a corrosive solution upon the rate of corrosion? Question 13. What are the advantages of electro galvanizing over hot dip galvanizing? Question 17.0.Mechanical and Production Engineering Department Question 9.00500 M respectively.5% C steel rust more quickly in the normalized condition than in water quenched state? Question 16. Question 18. Show how this nail is likely to rust when immersed in rain water. Venkannah Ext 7845 [email protected]] Question 11.ac. Question 10. Why does a 0. What is Aluminising? Give the steps in Aluminising mild steel. What is the cause of caustic embrittlement? Question 14. S.00100 M and 0. [ANS 1.mu . What is hydrogen overvoltage and what is its effect upon the rate of corrosion? Question 12. The solid electrodes are both in the elemental form of the element. A mild steel nail has a cold forged head. Discuss the various considerations at the design stage to mitigate the effect of corrosion on a structure. What is Sherardising? Question 19. Using the Nernst equation determine the value of the overall cell potential consisting of Zn +2 +2 and Cu when the cell concentrations of Zn and Cu are at 0. the activity for each (and hence the concentration term) is reduced to 1. What is anodizing? By what process does it tend to reduce corrosion? Question 15.
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