QUESTION/ANSWER BOOKLET CHEMMAT 121 Page 1 of 22 THE UNIVERSITY OF AUCKLAND SUMMER SCHOOL 2020 Campus: City CHEMICAL AND MATERIALS ENGINEERING Materials Science (Time Allowed: TWO hours) NOTE: Attempt ALL questions. Please see the Appendix for useful formulae. The mark value of each question is indicated at each question. Total marks = 100. All working and answers are to be entered on this EXAM SCRIPT. Calculated answers will not be marked unless your workings are shown. Write your name and ID number on this EXAM SCRIPT. Restricted calculator is allowed. Surname: …………………………….…………….. Forenames: ………………………… University of Auckland ID number: ………………………… QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 2 of 22 This page is left blank intentionally. QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 3 of 22 1. The above graph shows the result of a 120mm long aluminium rod 8mm in diameter being pulled in tension until failure. [5 marks] a) What is the yield stress of the aluminium rod? Yield Stress = ________________ b) At the ultimate tensile strength, if the load was removed, what would be the new length of the rod? Length = _________________ c) What is the Young’s Modulus of the aluminium? Young’s Modulus = _______________ d) After failure, the diameter of the rod at the fracture site is 6.34mm. What is the ductility of the aluminium? Ductility = ________________ QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 4 of 22 2. A piece of 10mm thick aluminium sheet is to be rolled to a final thickness of 1.2mm so that it can be used to manufacture drink cans. This is done via a series of cold rolling followed by annealing. [11 marks] a) If the thickness before the final cold rolling step was 2.8mm, calculate the cold work done to the aluminium. % Cold Work = _______________ b) By cold rolling the aluminium, the yield stress will increase. Identify and describe the process by which this occurs. c) The following graph describes the relationship between the final grain size present in the final annealed aluminium sheet, d (in mm), and its yield strength. If the drink can is required to have a yield strength greater than 80 MPa, what must the grain size be? Grain size = _____________ (mm -1/2 ) QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 5 of 22 d) Complete the following table to name and describe the 3 stages of annealing: Driving Force: Description: Stage 1: N/A Stage 2: Stage 3: e) The final annealing step is conducted at 180 ˚C and takes 220 minutes. The manufacturer wishes to speed up this final step to improve efficiency. Using the information provided, what temperature should the aluminium be annealed at to finish in only 60 minutes? Q = 148 kJ/mol R = 8.314 J/mol.K Temperature = _______________ QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 6 of 22 3. On the set of axes provided, construct a phase diagram from the following information: a) Pure metals A and B for a binary eutectic phase diagram. b) Pure metal A melts at 750 ˚C, pure metal B melts at 500 ˚C. c) For an overall composition of 65 wt% B, 100% liquid exists down to 400 ˚C at which point it transforms into two solid phases. d) The maximum solubility of metal B in metal A is 10 wt% e) The maximum solubility of metal A in metal B is 25 wt% f) Both metals have complete insolubility in each other at room temperature. [5 marks] QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 7 of 22 4. The following phase diagram shows the interstitial solid solution of carbon in iron to create steel. Use this diagram to answer questions 4. a) – e). [6 marks] a) Consider a steel consisting of 1.5 wt% carbon. How much austenite is present at the following temperatures: i. 1000 ˚C: __________________ ii. 800 ˚C: ___________________ iii. 600 ˚C: ___________________ b) For the steel described in part a), draw the microstructure of the steel as it is slow cooled at the following temperatures: 1000 ˚C 800 ˚C 600 ˚C QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 8 of 22 c) Consider a steel consisting of 0.5 wt% carbon. What is the composition of the austenite phase at 728 ˚C? Wt% Fe = _______________ Wt% C = _______________ d) For a steel of eutectoid composition at room temperature, what is the ratio of ferrite to cementite in the pearlite present? QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 9 of 22 5. Alloy systems can utilise a number of different strengthening mechanisms to increase yield strength. [13 marks] a) Explain the general rule of thumb behind how strengthening mechanisms work. b) Explain, using a diagram, how solid solution strengthening can increase yield strength. c) Explain, using a diagram, how multiphase strengthening can increase yield strength. QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 10 of 22 d) Explain, by filling in the following table, how age-hardening heat treatment is performed. Description: Microstructure: Stage 1: Solution Heat-Treat Stage 2: Quench into 2-phase region Stage 3: Ageing e) Describe two of the potential problems that can occur during the quenching process, and explain how these can be overcome. f) When an age-hardening alloy is quenched into the two phase region, a metastable solid phase is formed. Explain what is meant by the term “metastable”, and use a diagram to demonstrate how this metastable phase is formed in the iron-carbon alloy system (also known as martensite). QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 11 of 22 6. Ceramics are a class of engineering materials that consist of a combination of metallic and non-metallic elements. [7 marks] a) Using an appropriate diagram, explain why ceramics are typically very brittle. b) Would you expect ceramic fibres to be stronger or weaker than bulk ceramic? Briefly explain your answer using an appropriate diagram. QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 12 of 22 c) Clay is an example of a traditional ceramic with a silicate structure that can be formed into a vase using a technique called “hydroplastic forming”. Using an appropriate diagram, briefly explain why the addition of a small amount of water makes clay very plastic AND why the drying and firing process is necessary to harden the clay. QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 13 of 22 7. When molten silica is cooled slowly, it forms a crystalline ceramic. However, if it is cooled rapidly, it would form an amorphous glass instead. [4 marks] a) In the following diagram, sketch what would be observed if molten silica is cooled rapidly. Label the glass transition temperature Tg in the horizontal axis. Note: the existing curve shows what happened when molten silica was cooled slowly to form a crystalline ceramic solid. b) Briefly explain why glass is usually optically transparent. Tmelt Crystalline solid V o lu m e V o lu m e Temperature Liquid SiO2 Slow-cooling QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 14 of 22 8. Polymers are a collection of many long chains of molecules (usually hydrocarbons) packed together to form a solid. [9 marks] a) The mechanical properties of polymers are greatly influenced by the degree of polymerisation (DP), as shown in the following diagram. Using this diagram, briefly explain why: i. Polymers with very small DP show virtually zero yield strength. ii. Polymers with relatively small DP show lower yield strength than polymers with high DP. iii. There is a maximum amount of yield strength that can be achieved by increasing the DP of the polymer. Y ie ld S tr en g th Degree of Polymerisation (DP) QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 15 of 22 b) Elastomers are a class of polymers that can exhibit large elastic strain. Briefly state THREE requirements for a polymer to show large-strain elastomeric behaviour. c) Viscoelastic models that involve springs and dashpots can model the mechanical behaviour of polymers. Complete the missing information in the table below regarding these viscoelastic models. Model Response over time under CONSTANT STRESS Description Fully _________________ instantaneous deformation. Most likely caused by polymer chains stretching and contracting. Also known as the Kelvin- Voigt model. Consists of a spring and a dashpot in ____________ configuration. Also known as the Maxwell model. Describes the stress- relaxation behaviour of polymers when CONSTANT STRAIN is applied. S tr ai n Time Unloading QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 16 of 22 9. BCC metals (such as the ferrite phase in steel) are typically ductile, but can exhibit brittle failure at low temperatures. [12 marks] a) In the set of axes provided below, sketch the response that you would expect to see for a BCC metal sample undergoing the Charpy impact test at different temperatures. Clearly label the ductile-brittle transition temperature TT, and label the regions where you think the metal is brittle and where it is ductile. b) Briefly state and explain FOUR different ways you can decrease the ductile-brittle transition temperature of steel. Way to decrease Explanation Im p ac t E n er g y ( J) Temperature (°C) QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 17 of 22 10. During a routine inspection, an engineer located a 6.1 cm deep edge crack on one of the steel cables sustaining a particular harbour bridge as shown in the diagram to the right. There are 256 identical cables sustaining the bridge. Assume that any force on the bridge is evenly distributed to every single steel cable. Unfortunately, that particular steel cable fractured uncontrollably during a traffic jam where 4,000 identical cars, each with two passengers, were on the bridge at the same time. Assume: Each car (with two passengers) has the same mass of 1,500 kg. The harbour bridge has a mass of 52,800,000 kg. Each steel cable has the same perfectly circular diameter of 100 mm. Gravitational acceleration, = 9.81 /2. The geometric factor = 1.0 for the steel cable. The failure only occurred because at that point 1 > 1 for that particular steel cable and no other factor is involved. [8 marks] a) Determine the stress that each steel cable was subjected to, assuming that the only forces acting on the cable were due to the mass of the bridge and the 4,000 cars. b) Determine the fracture toughness of the particular steel cable. Bridge Steel cable with crack QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 18 of 22 11. Briefly state and explain TWO different ways you can improve the creep resistance of metallic alloys. [4 marks] I. __________________________________________________________________________ Explanation: II. __________________________________________________________________________ Explanation: QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 19 of 22 12. Corrosion is a big problem in the engineering world wherever metals are used, as it leads to major economic loss and hazards. The following table shows the galvanic series that can be used to predict the corrosion behaviour of engineering materials. [5 marks] a) Based on the galvanic series, state what would happen if a cobalt metal coated with silver was scratched and the base metal was exposed to moist aerated conditions. QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 20 of 22 b) Based on the galvanic series, state what would happen if plates in the hull of a boat made out of aluminium were joined together with copper bolts. Will this situation lead to a slow or a rapid corrosion? QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 21 of 22 13. A stainless steel tank containing orange juice is undergoing corrosion where it uniformly loses 0.0025 mm of thickness over a surface area of 12.5 m 2 in one year. Determine the corrosion current that is responsible for this process. Assume: Density of stainless steel is 8,000 kg/m3. Faraday’s constant is 96,500 A.s / mol. The anodic reaction is → 2+ + 2−. There are 365 days in a year. Molecular weight of iron is 56 g/mol. [5 marks] QUESTION/ANSWER BOOKLET CHEMMAT 121 ID: ………………………… Page 22 of 22 14. The following diagrams shows the stress-strain curves of a certain ceramic fibre, a certain polymer matrix, and a composite made out of those fibres and polymer. [6 marks] a) Label the curve that you think shows the ceramic fibre response as F, the curve that you think shows the polymer matrix response as M, and the curve that you think shows the composite response as CM. b) Using the diagram above, briefly explain what you think happens to the composite material when it is subjected to a tensile stress bigger than 50 MPa. Do you think it will lead to a catastrophic failure? S tr es s Strain 50 MPa APPENDIX CHEMMAT 121 Page 1 of 2 THE UNIVERSITY OF AUCKLAND SUMMER SCHOOL 2020 Campus: City CHEMICAL AND MATERIALS ENGINEERING Materials Science APPENDICES BOOKLET APPENDIX CHEMMAT 121 Page 2 of 2 Data sheet τσσ /)( t ot e −= nF ItMgmass =)( RTQCe /1 −= τ )( aYK fIC πσ= Ac NV nA =ρ rTtotal TooT T ρρρ αρρρ += ∆+= nP ofs e −=σσ Q RTrate Ae − = 2/1−+= kdoy σσ − = RT Q n s Ae Gdt d .1ρ 2r FL π σ = EC = VAEA + VB EB ρc = VAρA + VBρB += ⊥ B B A A C E V E V E 1 = 2 4Ra = 3 4Ra = E ητ = x z ε υ ε − = = −() ∆ ∆ = − ()� NA = 6.023 x 1023 mol-1 k = 8.62 x 10-5 eV/atom.K R = 8.314 J mol-1 K-1 F = 96,500 C mol-1 Electronic charge = 1.602x10-19 C
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