ENT145/3 Materials Engineering
Tutorial 2 (Answer)
1.
A steel bar 100 mm long and having a square cross section 20 mm on an edge is
pulled in tension with a load of 89,000 N, and experiences an elongation of 0.10
mm. Assuming that the deformation is entirely elastic, calculate the elastic
modulus of the steel.
2.
A cylindrical specimen of aluminum having a diameter of 20 mm and length of
210 mm is deformed elastically in tension with a force of 48,800 N. Using the
data contained in Table 6.1, determine the following:
a)
The amount by which this specimen will elongate in the direction of the
applied stress.
b)
The change in diameter of the specimen. Will the diameter increase or
decrease?
3.
A cylindrical specimen of a hypothetical metal alloy is stressed in compression.
If its original and final diameters are 20.000 and 20.025 mm, respectively, and
its final length is 74.96 mm, compute its original length if the deformation is
totally elastic. The elastic and shear moduli for this alloy are 105 GPa and 39.7
GPa, respectively.
4.
A cylindrical rod 100 mm long and having a diameter of 10.0 mm is to be
deformed using a tensile load of 27,500 N. It must not experience either plastic
deformation or a diameter reduction of more than 7.5 × 10−3 mm. Of the
materials listed as follows, which are possible candidates? Justify your
choice(s).
5.
A cylindrical specimen of aluminum having a diameter of 12.8 mm and a gauge
length of 50.800 mm is pulled in tension. Use the load–elongation
characteristics shown in the following table to complete parts (a) through (f).
a)
b)
c)
d)
e)
f)
Plot the data as engineering stress versus engineering strain.
Compute the modulus of elasticity.
Determine the yield strength at a strain offset of 0.002.
Determine the tensile strength of this alloy.
What is the approximate ductility, in percent elongation?
Compute the modulus of resilience.
6.
An aircraft component is fabricated from an aluminium alloy that has plane
strain fracture toughness of 35 MPa√m. Fracture occurred at a stress of 250
MPa when the maximum internal crack length is 2.0 mm.
a)
b)
7.
Determine the value of dimensionless correction factor, Y.
If a stress level is increased to 325 MPa and the maximum internal crack
length is reduced to 1.1 mm, predict whether any fracture will occur.
Compare your answer with existing data. Justify your answer.
An Figure 2 shows the circumferential stress σ, (also called hoop stress) in a
pressurized cylindrical vessel and is calculated by the equation of 𝜎 = 𝑃𝑟/𝑡,
where P is the internal pressure, r is the radius of the vessel and t is thickness.
The vessel has 914.4 mm diameter, 6.35 mm thickness and an internal pressure
of 34.5 MPa. Assume the crack occurred at the center of the vessel and Y = 1.0.
For the fracture toughness, KIC and yield strength, σY values of each vessel
material, refer to Table A1 in Appendix.
a)
Compute the critical crack length (2a) if the vessel is made of Al 7178T651.
b)
If the material of stainless steel (17-7pH) is to be used, compare the
difference of the critical crack length (2a) with your answer in (i). Justify
your answer.
σ
t
2a
r
P
crack
σ
Figure 2
[Gambarajah 2]
Table A1 Typical Fracture Toughness Values for Selected Engineering Alloys