EG5906/11
UNIVERSITY OF ABERDEEN
SESSION 2010-2011
Degree Examia!i" i EG5096 FATIGUE AND FRA#TURE $E#%ANI#S && 'a(ar) 2011
Note: (i) (ii) (ii)
Time
Candidates Candidates ARE permitted permitted to use an approved approved calculator calculator Data Data shee sheets ts are are att attac ached hed to the paper paper
Candidates should attempt ALL questions.
*+EASE NOTE T%E FO++O,ING
(i)
You m(! "! have in your possession any material other than that expressly permitted in the rules approp appropria riate te to this this exami examinat nation ion.. Where Where this this is permi permitted tted,, such material material m(! "! be amended, annotated or modified in any way.
(ii)
m(! "! "! have in your possession any material that could be determined as giving you an You m(! advantage in the examination.
(iii)
m(! "! "! attempt to communicate with any candidate during the exam, either orally or by You m(! passing written material, or by showing material to another candidate, nor must you attempt to view another candidate’s work.
Fai.(re !" "m.) i! !e a3"4e i.. 3e regare a ea!ig a ma) .ea !" ii.iar) a!i" a iia!e i !e Aaemi Aaemi (a.i!) %a3""7 8 a3a( a3a(7/regi!r)/:(a.i!)/a 7/regi!r)/:(a.i!)/aeix;x1< eix;x1< = Se!i" >1> a 5
EG5906/11
. (a) #iscuss how the Soderberg relationship may be used in the fatigue design of components and sketch the relationship in its normal form for tensile loading. $% marks& (b) 'he drive shaft to a pump is subected to a steady bending moment of %%*m and, simultaneously, to an alternating bending moment of %%%*m in the same section. +f the yield stress of the shaft material is %-a and the fatigue limit in reversed bending is /%-a, what shaft diameter will be re0uired for infinite life1 You may assume that a factor of safety of . applies. $ marks&
. (a) #iscuss the concept of 2rack Tip Opening Displacement as a fracture characterising parameter indicating when it would be used. $% marks& (b) 3 pressure vessel is to be protected from excessive pressure by a bursting disc comprising a flat, circular plate clamped at its edges with a sharp notch of depth a, machined across the diameter in the unpressurised side. 'he plate is 4% mm in diameter and " mm thick and is made from high strength steel with the following properties5 Yield stress, σ y = %% -*!m6 Young’s modulus, E = %% 7*!m6 oisson’s ratio, ν = %.886 critical 2'9#, δ c = "µm. :or the disc it can be assumed that K c
= ( E σ y δ c )
! ,
.
'he maximum stress acting perpendicular to the notch can be determined from5 σ θ
=
σ
r
=
8 p
c
r ,
, 4h
( + ν )
where pc is the applied pressure, h, is the disc thickness and r , the disc radius and around the ! , notch, K = .,σ θ ( π a ) . What depth of notch is re0uired for a bursting pressure of % -*!m 1 $% marks& #ue to the potentially corrosive nature of the pressurised fluid, there has been a suggestion that a high toughness stainless steel should be used for the bursting disc. What comments would you have on this suggestion1 $ marks&
Please turn over
EG5906/11
8. (a) +n the assessment of fatigue cracking, discuss why the data obtained from ;<* curves is of limited value and why knowledge of the aris =aw is important in determining fatigue life. $% marks& (b) 3 cylindrical pressure vessel of wall thickness, B, has a longitudinal crack of length, L, and depth, a , along its internal surface. 3 net internal pressure, p, cycling between values po /2 and po may affect crack growth. 'he evaluation assumes that L>> a , such that the relatively stationary crack ends do not retard crack growth, significantly, at the centre of the crack. 'he initial crack depth (i)
a = ao
> mm, B = mm and the vessel internal radius R = %%mm.
#etermine the maximum value of po for which the crack remains stationary if the threshold stress intensity range for the vessel steel is ∆ K = " -*!m8!. $ marks& o
(ii)
?nder a substantially higher load range the crack is assumed to propagate according to5 da d!
= ∆ K m
#etermine the maximum number of pressure cycles before the crack penetrates the vessel wall if, for the vessel steel5 m > 8, > %< -*<8m!c< and K " > "%-*!m8! 'he operating value of po is %-*!m and, for the crack, you can assume ! , K " = ."σ ( π a ) . $% marks&
". (a) #iscuss the principle of #ltrasonic inspection, highlighting the types of defect techni0ue can locate.
that the $% marks&
(b) What limitations are inherent in using the ultrasonic inspection techni0ue1 $@ marks& (c) 3n $sset Deterioration Ris% &atri' can be used to identify the likely impact of deterioration of components in a production system. Axplain the role of non
END OF E&A$INATION *A*ER
EG5906/11
EG5096 - %ANDOUT Ue<(. E:(a!i"
( π a )
K = ( σ
σ a
σ = σ D − m σ y
da d! *
! ,
=
= ( ∆ K ) m − K t −
K )
Ue<(. !re aa.)i <"rm(.ae
:or a beam of uniform circular cross section5 " =
π d
"
@"
:or a thin
=
pr t
