44/04 AMME 2302/5302- Materials 1. Semester 2, 2009

Ss The University of Sydney

Examination Paper

Faculty of Engineering & Information TechnologiesSchool of Aerospace, Mechanical and Mechatronic Engineering

November 2009 Time Allowed: Two Hours

Answer all 5 questions. Marks for each question and parts of a question aregiven in the brackets.

Question 1 (20 Marks)

(a) What is the critical transfer length of a fibre? Describe its role in fibre reinforcement ofcomposites. (3 marks)

(b) Explain why in brittle materials, such as ceramics and glasses, (i) there are significantscatters in fracture strength, and (ii) why the fracture strength decreases with increasingspecimen size. (3 marks)

(c) Compare and contrast thermoplastic and thermosetting polymers in terms of (i)mechanical properties upon heating, and (ii) molecular structures. (4 marks)

(d) The following figure shows the influence of cold work on the stress-strain behaviour of alow carbon steel. Curves are shown for 0%, 4%, and 24% cold work. Please explain whycold work (i) increases the strength, and (ii) reduces the ductility of the low-carbon steel.(5 marks)

600

500

rn400a..:::iE~300

lJl~

U5 200

100

0.2 0.25

(e) The AI-rich side of the AI-Cu phase diagram is shown on the left-hand side below.(i) Please specify the range of compositions over which AI-Cu alloys may beprecipitation hardened. (2 marks)(ii) A heat treatment procedure for the composition Co includes three stages - solutiontreatment, cold work and precipitation, as shown schematically on the right-hand sidebelow. Please explain the purpose of each stage and choose a temperature for the solutiontreatment. (3 marks)

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- 44/04 AMME 2302/5302 - Materials 1. Semester 2, 2009 Examination Paper

Time

Precipitation

Cold work

Temperature

Solution treatment

504030

a+ tJ

Compositton (wt ~!l') Cu}

2010

Question 2 (20 Marks)

(a) Define ductile to brittle transition temperature (DBTT). Hence explain why, on 15 April1912, the Titanic sank when it hit an iceberg. (5 marks)

(b) The following true stresses produce the corresponding.true.plastic strains for a brass alloy:

True stress (MPa) True· strain410 0.15480 0.25

What true stress is necessary to produce a true plastic strain of 0.21 ? Assume the brass alloyobeys the true stress-true strain relationship given by: aT = k (ET) n,where k and n areconstants. (10 marks)

(c) What is the "homologous temperature"? Explain why at room temperature lead pipescreep but steel pipes do not. (5 marks)

Question 3 (20 Marks)

(a) A thick high strength steel plate contains a crack of total length (2a) equal to 10 mm,which runs perpendicular to the applied stress. For this steel, the plain strain fracturetoughness (Klc) is 105 MPa-Vm, and the yield stress (ay) is 700 MPa. If the applied stressis increased steadily, will the plate fail by brittle fracture or by general yielding? [Hint:The fracture toughness equation is: K1c = a cY(xa)1/2, where a c is fracture stress and Y=1.0](7 marks)

(b) An aluminium unidirectional composite is reinforced with 40% by volume of steel wireswith 2.00 mm diameter. The two materials have elastic moduli of70 GPa and 210 GPa,and yield strengths of75 MPa and 300 MPa, respectively.(i) If this composite is loaded in tension, which material (aluminium or steel) will

yield first? (3 marks)

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44/04 AMME 2302/5302 - Materials 1. Semester 2, 2009 Examination Paper 44/04 AMME 2302/5302 - Materials 1. Semester 2, 2009 Examination Paper

(d) The following figure shows the isothermal transformation diagram for an iron-carbonalloy of eutectoid composition: A = austenite; B = bainite; M = martensite; and P = pearlite.What are the final microstructures (in terms of the microconstituents and approximatepercentages of each) for each of the following five cooling conditions? Assuming thespecimen begins with the equilibrium structure at 760°C (1400°F). (5 marks)

z

(ii) How much stress can the composite carry in tension without plastic yielding?(5 marks)

(iii) What is the elastic modulus of the composite? (2 marks)(iv) What is the thermal expansion coefficient of the composite given these coefficient

values for aluminium and steel are 23xl0-6 1°C and 12xl0-6/°C, respectively.(3 marks)

Question 4 ( 15 Marks)

(a) A unit cell is shown schematically below. Determine the index of vector DB and the indexofplane ABcO. Note that point D is located at the a/2 position of the X-axis. (5 marks)

1200

400

1400

200

600

- 1000

B

p

102 103 104 105

Time(s)

10

~\I'~5..9.~!.....~~l~OJot

A

A .,,-- Eutectoid temperature.......--. ...,-..__....__.... -.............Af_.... . .... ......--... _

700

800 --....-------...----...-----.-----.

600

200

100 ---

300.-

500e<I>:51 400 -."E(l)I-

(i) Cool rapidly to 350°C, hold for 103

s, then quench to room temperature.(ii) Rapidly cool to 600°C, hold for 4 s,rapidly cool to 500°C, hold for lOs,then quench to room.temperature.(iii) Rapidly cool to 600°C, hold for 4 s,rapidly cool to 450°C, hold for lOs,then quench to room temperature.(iv) Rapidly cool to room temperature,and then reheat the specimen to 400°Cfor 1 h.(v) Rapidly cool to 300°C, hold for 10 s,then quench to room temperature.

(b) A hexagonal close-packed (HCP) crystal structure with cia = 1.633 is shown below.Calculate the atomic packing factor of the structure (Hint: use the hard sphere model and thevolume of a sphere is {1lr 3

, where r is the sphere radius) (5 marks)

Tc

1Bsites

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44/04 AMME 2302/5302 - Materials 1. Semester 2, 2009 Examination Paper 44/04 AMME 2302/5302 - Materials 1. Semester 2, 2009 Examination Paper

5020

TB ... """ .......... _."" ..... _""."'<"' ..... ~;.@:i:~~::..:~i_...-.-...-;

..laI

I. Csolid)i4~S~~: Ii: I

1200

and

1300

(b) Part of the Cu-Ni equilibrium phase diagram is shown below. Prove that the weightfractions of the liquid phase and the solid a phase at temperature TB can be expressed by:

Please do not directly apply the lever rule tothis question. (5 marks)

Q

spacingbetween

_____- ........~~-.....-._..~- planes

extradistancetravelled.s-.. ... s ~AI_'.I""'" "2~'

~ . Monochromatic+'r. °0/1 ........ coherent~ .~.~d' ~~ ~.,

~ 7·~

(c) X-ray diffraction is used to determine crystal structures based on Bragg's law:

2dsin8 = nA (see the schematic diagram below), in which d is inter-planar distance, 8 is the

incident angle of X-rays relative to the plane normal, A is the wavelength of the X-rays and n

= 1, 2, 3, ... Please explain why the X-ray wavelength A must be smaller than the inter-planar

distances of a crystal in order to determine the structure of the crystal using X-ray diffraction.

(5 marks)

Question 5 (25 Marks)

(a) A portion of the Cu-AI equilibrium phase diagram is shown below. Please write down theequations of the phase transition at points 1, 2, 3, 4 and 5 when the system is cooled downfrom high temperature. (5 marks)

(c) A hypothetical eutectic phase diagram is shown below. The eutectic composition is 36wt% A-64 wt% B. The composition of the a phase at the eutectic temperature is 88 wt% A-12wt% B. Determine

BComposition (wt% B)

(8)

Cl .l.........----"'--.......-1-....-....-..-._-'---~--.....;i._'"'-----'-----'----J

A

(7)

•(3) (4)

( 6)( 5)

(i) the composition of an alloy that willyield primary pand total pmass fractions of0.367 and 0.768, respectively, and thecomposition of the pphase at the eutectictemperature (8 marks)(ii) the equilibrium structure of the alloyat the temperature immediately below theeutectic temperature by selecting the correctnumber in the parentheses under the 8schematic structures below. (2 marks)

161284o(Cu)

400 .10-"".."." ; ;.. · ·.. · ·.. ·······.···,·.····.·.·;;··.·.······Ir······; .

900

,.-.....

U0 800..........,

<D'-:J...ca 700'-Q)a. 12E

600CDI-

5=00

Composition (wt% AI)

1000 :t--:........••..............................: " 1: ··1···························,··· .. ·•·· ··········.:·······;I·:I·;"'·j~;;·;I'······'~>··· :.~;;; ;; ;.

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