Page 184 - Plastics Engineering

Mechanical Behaviour of Plastics 167

25l A plastic shaft of circular cross-section is subjected to a steady bending moment of 1 Nm
and simultaneously to an alternating bending moment of 0.75 Nm. Calculate the necessary shaft
diameter so as to avoid fatigue failure (the factor of safety is to be 2.5). ‘ihe fatigue limit for the
material in reversed bending is 25 MN/m2 and the creep rupture strength at the equivalent time
may be taken as 35 MN/m2. Calculate also the shaft diameter if the fatigue strength reduction
factor is to be taken as 2.
2.55 A 10 mm diameter uPVC shaft is subjected to a steady tensile load of 500 N. If the
fatigue strength reduction factor is 1.8 and the factor of safety is to be 2 calculate the largest
alternating bending moment which could be applied at a frequency of 5 Hz if fatigue failure is not
to occur inside lo7 cycles. The creep rupture characteristic for the material is given in question 3.1
and the reversed bending fatigue behaviour is described by the equation u = (43.4 - 3.8 log N)
(where N is the number of cycles to failure and u is the stress in MN/m2). It may be assumed
that at 5 Hz, thermal softening will not occur.
2.56 A uPVC rod of diameter 12 mm is subjected to an eccentric axial force at a distance of
3 mm from the centre of the cross-section. If the force varies sinusoidally from -F to F at a
frequency of 10 Hz, calculate the value of F so that fatigue failure will not occur in 10 cycles.
Assume a safety factor of 2.5 and use the creep rupture and fatigue characteristics described in
the previous question. Thermal softening effects may be ignored at the stress levels involved.
2.57 For the purposes of performing an impact test on a material it is proposed to use an elastic
stress concentration factor of 3.5. If the notch tip radius is to be 0.25 mm estimate a suitable
notch depth.
2.58 On an impact testing machine for plastics the weight of the pendulum is 4.5 kgf. When the
pendulum is raised to a height of 0.3 m and allowed to swing (a) with no specimen in position and
(b) with a plain sample (4 x 12 mm cross-section) in position, the pendulum swings to heights of
0.29 and 0.2 m respectively. Estimate (i) the friction and windage losses in the machine (ii) the
impact energy of the specimen (iii) the height the pendulum will swing to if it is released from
a height of 0.25 m and breaks a sample of exactly the same impact strength as in (ii). (Assume
that the losses remain the same and that the impact strength is independent of srrike velocity).
2.59 A sheet of polystyrene 100 mm wide, 5 mm thick and 200 mm long contains a sharp
single edge crack 10 mm long, 100 mm from one end. If the critical stress intensity factor is
1.75 MN m-3/2, what is the maximum axial force which could be applied without causing brittle
fracture.
2.60 A certain grade of PMMA has a K value of 1.6 MN m-3/2 and it is known that under
cyclic stresses, cracks grow at a rate given by (2 x 10-6AK3.32). If the intrinsic defects in the
material are 50 mm long, how many hours will the material last if it is subjected to a stress cycle
of 0 to 10 MN/m2 at a frequency of 1 Hz.
2.61 A series of fatigue crack growth tests on a moulding grade of polymethyl methacrylate
gave the following results
da/dN (dcycle) 2.25 x 4.0 x 6.2 x lo-’ 11 x 17 x 29 x
AK(MN m-3/2) 0.42 0.53 0.63 0.79 0.94 1.17
If the material has a critical stress intensity factor of 1.8 MN m-3/2 and it is known that
the moulding process produces defects 40 m long, estimate the maximum repeated tensile stress
which could be applied to this material for at least 106 cycles without causing fatigue failure.
2.62 A series of uniaxial fatigue tests on unnotched plastic sheets show that the fatigue limit
for the material is 10 MN/m*. If a pressure vessel with a diameter of 120 mm and a wall thickness
of 4 nun is to be made from this material, estimate the maximum value of fluctuating internal
pressure which would be recommended. The stress intensity factor for the pressure vessel is given
by K = %&a)’/* where is the hoop stress and ‘a’ is the half length of an internal defect.