Applied Science 278 Final Exam 7 December 2011

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THE UNIVERSITY OF BRITISH COLUMBIA

Department of Materials Engineering APPLIED SCIENCE 278 Engineering Materials

FINAL EXAMINATION

December 7th, 2011 This is a Closed Book Examination. The use of calculators having stored information of relevance to this course is forbidden. Time: 2.5 hours Answer all questions (total marks=100). The complete exam is 7 pages in length. Some useful formulae, material data and a phase diagram are given on the last 2 pages of the exam. The use of sketches or schematic diagrams are encouraged wherever these will aid in solving or discussing a problem. Show all work !! Good Luck !

Marks 10 Q1 Sketch a typical stress-strain curve for a low carbon steel when tested at +20C.

6 (a) On the curve identify the following regions: elastic deformation, work hardening, yield stress, ultimate stress, necking.

2 (b) With the aid of your sketch, discuss the significance of: (i) toughness (ii) modulus of resilience

2 (c) How would the stress strain curve differ if the test were done at 77K in liquid nitrogen?

15 Q2. You are a performer in a country fair, and want to challenge the locals to a strength contest. You take a bar of annealed 70% Cu 30% Zn brass and bend it. You then challenge any local to bend it back to the original shape.

5 (a) If you strain the bar by an average of 20%, how much stronger does the local have to be to straighten out the bar? (Ignore geometrical effects)

5 (b) can you recommend some other strain that you should bend the bar to, which would make you look even stronger? (Hint: think about the shape of the curve)

2 (c) Briefly discuss why the strength increases with increased cold working. 3 (d) You wish to reuse the bar for future shows. What can you do?

Applied Science 278 Final Exam 7 December 2011

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Figure 1 Mechanical properties as a function of cold work

15 Q3. A lead-tin alloy of composition 50 wt%Sn-50 wt%Pb is slowly cooled from a temperature of 300C. See Figure 2.

3 (a) At what temperature does the first solid phase form? 3 (b) What is the composition of this solid phase? 3 (c) At what temperature does complete solidication of the alloy occur? 3 (d) What is the composition of the last liquid remaining prior to complete solidification? 3 (e) The resulting microstructure is shown in Figure 3. Describe the features of this

image.

Applied Science 278 Final Exam 7 December 2011

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Figure 2 Pb-Sn Binary Phase diagram

Figure 3 50% Pb 50% Sn microstructure

10 Q4 3 (a) Sketch the cellular structure of wood. Define the alignment of this structure

relative to the tree axis. 3 (b) Describe the detailed microstructure of the cell wall of wood with the aid of sketches. 4 (c) Given that the density of balsa is 0.15 g/cm3, and that of oak is 0.8 g/cm3, how

much stiffer is oak than balsa in the different directions?

Applied Science 278 Final Exam 7 December 2011

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15 Q5

3 .(a) A cubic unit cell contains Au atoms (filled circles) at the corners and on one face of the cell and Cu atoms (open circles) on the other faces of the cell. What is the unit cell structure and what is the coordination number for this structure?

Figure 4 cubic unit cell

4 (b) The edges of this unit cell are all 0.3852 nm. What is the density of the solid in g/cm3?

4 (c) A first order diffraction peak is observed at =20.26 using Cu X-radiation ( = 0.154 nm). What is the d-spacing between the planes of atoms giving this diffraction peak?

4 (d) In a few words and/or a picture, describe the planes of atoms that are separated by the distance in (c) (HINT: divide your answer in (c) by the edge of the unit cell. Note that sqrt(1/ 3) = 0.5773 and sqrt(1/ 2) = 0.7071).

15 Q6. A continuous fibre unidirectional composite laminate has 50% by volume of glass fibres in an epoxy resin matrix. Assume that the values of E and the UTS are 70 and 1.4 GPa for the glass fibres and 4.0 and 0.10 GPa for the epoxy.

3 (a) Calculate the modulus (E) of the laminate parallel to the fibres 3 (b) Calculate the modulus (E) of the laminate perpendicular to the fibres. 3 (c) Calculate the fraction of the load carried by the fibres when both the fibres and

matrix are being loaded elastically parallel to the fibres. 4 (d) Assuming neither the matrix or fibres deform plastically, which breaks first on

continuous loading when loaded parallel to the fibres? 2 (e) Sketch the deformation you will get if this unidirectional laminate is loaded at 45

Applied Science 278 Final Exam 7 December 2011

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10 Q7. A type 1 cement typically has the following composition: C3S 55%

C2S 20% C3A 12% C4AF 9%

3 (a) Discuss the strengthening role of each constituent during the setting and hardening processes.

2 (b) Discuss the role of air entrainment agents. 2 (c) What is the purpose of a slump test? 3 (d) Compare and contrast the failure mechanisms of concrete and reinforced concrete

when loaded in bending.

10 Q8 3 (a) Polyethylene (PE) is semicrystalline. Discuss with the aid of a sketch the nature of

its crystalline and amorphous molecular structure. 2 (b) Why does PE become transparent when deformed? 2 (c) Discuss why PE fibres such as Spectra have such high strength and modulus

values. 3 (d) What happens to the internal bonding of an amorphous polymeric structure at the

glass transition temperature? Sketch the modulus vs temperature curve for such a material, and identify the Tg.

Applied Science 278 Final Exam 7 December 2011

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Useful Formulae

z

y

z

x

E G 2 1

22

1 2

EU yyr

2

toughness fuy

1T 1lnT

T TnK

c

A

VNnA / =

n d 2 sin

da

h k lhkl 2 2 2 12

rate Ae Q RT

RTQrecrx eAt

21 dkyo

n

s K 1 NA=6.023 x 1023 atoms/mol R = 8.314 Jmol-1K-1

exp s nK QRT

2

N N QRTv

v exp

theoretical E 10

coscosR

21

21t

oma

m o ta 2

12

csE

a

21

2

212

aE ps

c

yy frK2

aYK B KIc

y

2 5

2

.

max

min

R

iin MxM

iiw MwM

mMnDP nnn

mMnDP www

sin( )2

L Nd

ndr or nr i.e. d

t ot exp

E t tro

( )

E Ew ss

ll

E Ew ss

2

mmffc VEVEE

mffm

fmc VEVE

EEE FF

= E VE V

f

m

f f

m m

FF

= E / EE / E V / V

f

c

f m

f m m f

c

fc

dl

2

*

Ec=KEfVf + EmVm

Figure A.1 Iron Carbon Phase diagram

Table A1 Characteristics of selected elements Element Symbol Atomic Number Atomic Weight(gmol-1) Density (gcm-3)

Aluminum Al 13 26.98 2.71 Bromine Br 35 79.90 - Carbon C 6 12.011 2.25 Chlorine Cl 17 35.45 - Copper Cu 29 63.55 8.94 Fluorine F 9 19.00 - Gold Au 79 196.97 19.32 Hydrogen H 1 1.008 - Nickel Ni 28 58.69 8.90 Nitrogen N 7 14.007 - Oxygen O 8 16.00 - Titanium Ti 22 47.88 4.51 Tungsten W 74 183.85 19.3 Zinc Zn 30 65.39 7.13