Academic Malpractice can result from a deliberate act of cheating and may be committed
unintentionally. Academic malpractice can take many different forms. Plagiarism is only one
example. The University defines plagiarism as, presenting the ideas, work or words of other people
without proper, clear and unambiguous acknowledgement. There are University guidelines on
avoiding plagiarism and other forms of academic malpractice such as; collusion or the fabrication
or falsification of data that are explained in, The University of Manchester Guidance To Students
on Plagiarism and Other Forms of Academic Malpractice, from the Teaching and Learning Support
Office;
http://www.tlso.manchester.ac.uk/map/teachinglearningassessment/assessment/sectiondtheprocessofassessment/academicmalpracticeincludingplagiarism/
Academic malpractice is taken seriously by the University and further information on plagiarism can
be found in the ‘School of MACE, Undergraduate/Postgraduate Course Handbook’ which you
received during Welcome Week.
To help you avoid plagiarism, the University Library has a number of resources on the Library
Website: http://subjects.library.manchester.ac.uk/referencing
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 2 of 5
Question 1 [20 Marks]
A circular tube, 6.60 m in diameter, with a wall thickness of 18.5 mm, is fractured in a brittle
manner during hydrostatic testing at a pressure of 3.7 MPa. On examining the fracture surfaces,
the origin of the fracture appeared to be a flaw of 2.8 mm extending from the inside surface of
the wall and along the longitudinal direction of the cylinder.
(i) Calculate the nominal stress at unstable crack growth?
[10 Marks]
(ii) Estimate the critical stress intensity factor for the steel at the origin of fracture?
[10 Marks]
Question 2 [30 Marks]
Applying the principle of superposition on mode-I stress intensity factors, estimate
approximately (i.e. using equivalent point loads for the given pressure distribution and then
apply the solution given for the wedge loads) the stress intensity factor without using definite
integrals for a large plate with a centre-crack subjected to a linearly varying (between 0.5σ and
σ) internal pressure acting on the crack faces as shown in Figure Q2 (a).
Figure Q2: A large centre-crack plate subjected to:
(a) Internal pressure (varying between 0.5σ and σ), and (b) a pair of wedge loads
Note: Use the following expressions are given for the stress intensity factors for a large plate with
a centre-crack subjected to a pair of wedge forces as shown in Figure Q2 (b). KIA is the stress intensity
factor at the crack tip A; KIB is the stress intensity factor at the crack tip B; x is the distance between
the centre of the crack and the position of the wedge loads; and P is the force per unit plate
thickness.
??? =
?
√?? √
(? + ?)
(? − ?)
??? =
?
√??
√
(? − ?)
(? + ?)
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 3 of 5
Question 3 [50 Marks]
A fuselage is manufactured by bolting Al 2024 T3 aluminium sheets together along longitudinal and
circumferential directions. Assume that the fatigue failure of the bolted fuselage connections can be
estimated by considering the in-service cyclic loading conditions (potentially causing collinear cracks with
identical lengths at each bolt hole perpendicular to the in-plane loading as shown in Figure Q3) and
neglecting the curvature of the skins. The in-service load (see Figure Q3, p is per unit length and is in
kN/mm) is simplified and assumed to fluctuate with constant amplitude, between 0 and 0.5 kN/mm, during
normal service conditions; but a peak accidental load of 0.8 kN/mm is also expected at any time.
Figure Q3: Al 2024 T3 plates connected with bolts and subject to in-plane fluctuating load, and
fatigue cracks at each hole. Thickness t = 20 mm; d = 20 mm; and W = 150 mm.
Figure Q3* (a): A large centre-crack plate with through-thickness collinear cracks subject to a
remotely applied uniform load.
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 4 of 5
Figure Q3* (b): A large centre-crack plate subjected to a pair of wedge loads.
The following expressions are given for the stress intensity factors for a large plate with collinear throughthickness cracks subject to a remotely applied uniform load and also a centre-crack subjected to a pair of
wedge forces as shown in Figures Q2* (a) and (b), respectively.
For the case in Figure Q2(a), the stress intensity factor is, ?? = [ ???(??/?) (??/?) ] 1/2 ?√?? For the case in Figure Q2 (b), KIA is the stress intensity factor at the crack tip A; KIB is the stress intensity
factor at the crack tip B; x is the distance between the centre of the crack and the position of the wedge
loads; P is the force per unit plate thickness.
??? =
?
√?? √
(? + ?)
(? − ?)
??? =
?
√?? √
(? − ?)
(? + ?)
By applying LEFM (and use MATLAB as required), answer the following:
(a) What is the critical crack size for catastrophic failure?
(i) When failure occurs without the accidental peak load?
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 5 of 5
[10 Marks]
(ii) When failure occurs with the accidental peak load?
[10 Marks]
(b) What is the size of crack tip plasticity just before catastrophic failure?
(i) Using the Irwin’s approach is considered for plane stress and plane strain conditions.
[10 Marks]
(c) Explain of the material properties (i.e. fracture toughness, tensile strength), service conditions (i.e.
temperature and corrosion) and geometry (i.e. bolt hole) of the structure in Figure Q3 influence fatigue
life?
[20 Marks]