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First Name
Last Name
Student Number
University of Toronto
Faculty of Applied Science and Engineering
Department of Chemical Engineering and Applied Chemistry
Mech. Prop. of Biocomposites and Biornaterials
Examiner: Prof. Ning Yan
-
CHE 475S
FINAL EXAM
April, 2019
Duration: 2 hrs and 30 minutes
Please answer all 5 questions.
Exam is type a.
Non programmable calculator.
Use available space in your answer book.
Please do not separate pages from your answer book.
Qi
Q2
Q3
Q4
QS
'Total
/30
/10
/30
/10
/20
/100
CHE475S
Final Exam
2019
150 minutes
Answer all questions:
1. Provide short answers to the following questions: (30 pts)
What are the major components of wood? Which of these components provide
strength and why? Explain why wood is both light-weight and mechanically strong.
(5 pts.)
Define resilience', explain the functional significance of the fact that resilience
for resilin (insect wing hinge) is 97% and for spider silk is 35%. (5 pts.)
Please discuss what are some major structural features in bone that make the
material both strong and tough? Please briefly discuss the bone remodeling
process? What is your understanding of "bone quality"? (10 pts.)
Describe what are polymer storage and loss modulus. Suggest a method to measure
these values? (5 pts.)
Explain what is "Time-Temperature correspondence"? (5 pts.)
Page 2/7
2. At a temperature of 70°C. a biopolymer with a glass transition temperature of 30°C has
a 15 minutes relaxation modulus of 0.02GPa. How long does it take to reach the same value
of the relaxation modulus at a temperature of 90°C? The time-temperature shift constants
are given below: (10 pts.)
To (K)
Tg
Tg+60
Page 3/7
C1
-17.44
-8.86
C2
51.6
101.6
3. The viscoelastic behaviour of a composite material can he modeled as a three elements
model, shown in Figure 1. Derive stress-strain (E-o relationship for the three elements
model depicted. If immediately after applying the stress, the strain is 0.003; after 2000s,
the strain is 0.008; after a very long time, the strain approaches 0.009; what is the relaxation
time of the dashpot? (30 pts.)
E1
Al
Figure 1. Three elements model
Page 4/7
4. The stress history of a biopolymer (cross-section: 0.21nch by 0.3inch) is given in the
following table:
Load (lbs)
10
20
5
60
5
Duration (hrs)
200
100
100
100
50
Calculate the strain at 100 hours and 500 hours given the following creep
compliance data (10 pts.)
Time (hrs)
0
100
200
300
400
500
psi1bs/(inch x inch).
Page 5/7
J(t) (psi-' x 10-4)
0.3
0.35
0.37
0.40
0.45
0.47
5. The stress relaxation modulus of a certain biopolymer can be described as G(t)=Goexp
(-t/'r) and is equal to 4 GPa and 1 GPa at t0 and 103 s, respectively. Derive the biopolymer
creep compliance and evaluate the strain at 10000 s after rapid application of a stress of 50
MPa. (20 pts.)
Page 6/7
Equations:
F
=
2G(1 + v)
F
FE
F
=
E 1 V1 + F,,, V,,
F
=
V1 Em + V F 1
2
It E
17
16
/
d
\2
L
V1
1
G G 1 G,
F
E=E e T
3(1 — 2v)
0.5
2E
n= Ef(1+v,fl)Ln(1/Vf)
=
ii
sinh(nx / r) sec h(ns)
a 1 =E 1s(1—
tanh(ns)
fls
na0 cot h(iL/r)
cosh z =
e +e
2
2
C1 (T—T9)
log(a)
sec hz=
=
F,,,
J=1 (1_ e t)
1
C2 +T—T9
2
e +e
Ix
F,
+ Ec V
cothz=
dy
dx
Page 7/7
e- +e
e —e
V
V
F,,
E
+ (1— x)(--+ —f-)
For y'+f(x)y=G(x); y = e -JJ
For
)
=a; y=ax+C
()cL
[S
F = E0 (1 —1.9V + 0.9V)
f(x)dx
g(x)e
dx + Cl