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TUTORIAL 2-Solution ENT 112 – Materials Engineering MECHANICAL PROPERTIES OF MATERIALS 1. Distinguish between elastic and plastic deformation. Solution: Elastic deformation of metal takes place when the metal is able to return to its original dimensions once the deforming force is removed. Plastic deformation takes place if the metal does not fully recover its original dimensions after the deforming force is removed. 2. Calculate the engineering stress in SI units on a bar 25 cm long and having a cross section of 9.00 mm x 4.00 mm that is subjected to a load of 3500 kg. Solution: 3. The following engineering stress-strain data were obtained at the beginning of a tensile test for a 0.2% C plain-carbon steel. i) Plot the engineering stress-strain curve for these data. ii) Determine the 0.2 percent offset yield stress for this steel. iii) Determine the tensile elastic modulus of this steel. (Note that these data only give the beginning part of the stress-strain curve.) 1 Solution: (a) See stress-strain plot below. (b) The 0.02 % offset yield stress was found graphically as approximately 450 MPa. (c) The modulus of elasticity is found from the slope of the 0.2% offset curve as: 4. A twenty-cm-long rod with a diameter of 0.250 cm is loaded with a 5000 N weight. If the diameter of the bar is 0.490 at this load, determine (a) the engineering stress and strain and (b) the true stress and strain. Solution: 2 5. A circular specimen of aluminium oxide is loaded using a three point bending mode. Compute the minimum possible radius of the specimen without fracture, given that the applied load is 430 N, the flexural strength is 115 x 106 Nm-2 @ MPa and the separation between load points is 55 mm. Solution: Flexural strength, which, when substituting the parameters stipulated in the problem statement, yields (430 N )(55 10 3 m) R 6 2 (115 10 N / m )( ) 1 3 R = 4.0 x 10-3m 6. The modulus of elasticity for silicon carbide having 2.5 vol.% porosity is 320 GPa. i) Compute the modulus of elasticity for the non-poros materials ii) Compute the modulus of elasticity for the 5 vol.% porosity materials Solution: i) 3 Eo 320 GPa 335 GPa # 1 - 1.9(0.025) 0.9(0.025) 2 ii) E = 335 GPa [1-1.9(0.05) + 0.9(0.05)2] = 304 GPa 7. (i) Define the hardness of a metal and (ii) How is the hardness of a material determined by a hardness testing machine? Solution: i) Hardness is a measure of the resistance of a metal to permanent deformation. ii) Hardness is measured by forcing an indenter into the metal surface. The hardness measurement is made either from the depth of penetration of the indenter or by the size of the indentation. 8. A 10 mm diameter Brinell Hardness indenter produced an indentation 2.50 mm in diameter in a steel alloy when a load of 1000 kg was used. Compute the HB of this materials Solution: 4 9. Following is tabulated data that were gathered from a series of Charphy impact tests on a commercial low-carbon steel alloy. Temperature (oC) 50 40 30 20 10 0 -10 -20 -30 -40 i) ii) iii) Impact Energy (J) 76 76 71 58 38 23 14 9 5 2 Plot the data as impact energy vs temperature Determine a ductile-to-brittle transition temperature as that temperature corresponding to the average of the maximum & minimum impact energies Determine a ductile-to-brittle transition temperature as that temperature at which the impact energy is 20 Joule Solution: i) The plot of impact energy versus temperature is shown below. 5 ii) The average of the maximum and minimum impact energies from the data is As indicated on the plot by the one set of dashed lines, the ductile-to-brittle transition temperature according to this criterion is about 10°C. iii) Also, as noted on the plot by the other set of dashed lines, the ductile-to-brittle transition temperature for impact energy of 20 J is about –2°C. 6