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IDMEC
ADMIRE Athens meeting, June 20-21, 2002 1
THE INFLUENCE OF COLD-WORKON THE STRESS INTENSITY FACTOR
OF CRACKED HOLESAND PIN LOADED JOINTS
Silvestre T Pinho, Helder B M Martins,Pedro P Camanho, Paulo M S T de Castro
IDMEC - Porto, Portugal
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ADMIRE Athens meeting, June 20-21, 2002 3
to develop a simplified procedure to relate holeexpansion (internal pressure / mandrel interference) of
an infinite isotropic plate, with the residual stress fieldand plastic zone
to assess the reduction of Kresulting from the cold-work process, in both open and riveted holes.
objectives
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ADMIRE Athens meeting, June 20-21, 2002 4
-110
-90
-70
-50
-30
-10
10
10 12 14 16 18 20 22 24 26 28 30
r [mm]
MPa]
Semi-analytical Solution
Numerical Solution
rr
semi-analytical and numerical
residual stress fields (von Mises)
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ADMIRE Athens meeting, June 20-21, 2002 5
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7
r/ri
y
von Mises
Tresca
rr
residual stresses
obtained using von Misesand Tresca yield criteria
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plate with open hole
a
ri
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ADMIRE Athens meeting, June 20-21, 2002 7
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
r/ri
y
Residual c ircumferencial stress
Stress due to uniform remote tensile load
Resulting stress
stress field due to cold-workand remote loading
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ADMIRE Athens meeting, June 20-21, 2002 8
2.5
3
3.5
4
4.5
5
5.5
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
Elastic-perfectly plastic material
Alclad alloy
p
3 3/ 10 10ir
relationship between appliedpressure and radial interpenetration
central hole in infinite plate
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ADMIRE Athens meeting, June 20-21, 2002 9
1
1.05
1.1
1.15
1.2
1.25
1.3
0.55 0.6 0.65 0.7 0.75 0.8 0.85
Elastic-perfectly plastic material
Alclad alloy
mesh size
(semi-analytical)
(finite element)
p
cr
plastic/elastic interface coordinateas a function of the pressure applied;
von Mises yield criterion;central hole in infinite plate
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ADMIRE Athens meeting, June 20-21, 2002 10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 1.1 1.2 1.3 1.4 1.5
dimension of the plastically deformed region / hole radius
y
a/ri=1.00
a/ri=1.05
a/ri=1.10
a/ri=1.15
a
ri
remote stress requiredto open two symmetrically located
cracks in a cold-worked hole
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ADMIRE Athens meeting, June 20-21, 2002 11
2024 Alclad
uniaxial stress-strain relations
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ADMIRE Athens meeting, June 20-21, 2002 12
14
15
16
17
18
19
20
21
22
23
24
12 12.5 13 13.5 14 14.5 15 15.5 16 16.5
a (mm)
Alcalad Al 2924-T3
Elastic-perfectly plastic material
No cold-work
Case 1
Case 2
Case 3
MPa mK
285MPay
100MPat
a
ri10mm
ir
Kas a function of crack lengthand cold-working
Alclad Al 2024-T3
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ADMIRE Athens meeting, June 20-21, 2002 14
a
ri
riveted joint
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ADMIRE Athens meeting, June 20-21, 2002 15
comparison between Ksolutionsfor a plate with a riveted hole
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85
2.9
1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65a/r
K/K0
rigid pin
Ref. [24]
a
ri
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ADMIRE Athens meeting, June 20-21, 2002 16
cosine and calculated distributionsof radial contact stress
0
2
4
6
8
10
12
14
0 15 30 45 60 75 90
a ( )
s rr/ s o
rigid pin
Ref. [24]
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7.045E-4
1.409E-3
2.113E-3
2.818E-3
equivalent plastic straindue to cold-work
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ADMIRE Athens meeting, June 20-21, 2002 18
yystress gradientcracked cold-worked pin-load joint
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ADMIRE Athens meeting, June 20-21, 2002 19
yystress gradient
cracked cold-worked pin-load jointdetail
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ADMIRE Athens meeting, June 20-21, 2002 20
Kas a function of crack lengthand cold-work
111
112
113
114
115
116
117
118
119
12 12.5 13 13.5 14 14.5 15 15.5
Elastic-perfectly plastic m aterial
Alclad Al 2924-T3
a (mm)
Case 3
Case 2
Case 1
No cold-work
MPa mK
a
ri
1mmu Al 2024-T3
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ADMIRE Athens meeting, June 20-21, 2002 21
analytical and semi-analytical solutions are derivedfor the characterization of the residual stress fieldand plastic zone sizes of cold-worked holes forelastic-perfectly plastic materials
the cold-working process is shown to reduce Kfordifferent dimensions of plastically deformed regions,and for different crack lengths, for both a remotely
loaded plate containing an open hole, and for ariveted joint.
conclusions I
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the reduction of stress intensity factor value for thecracked open hole problem was found to be greater
than the Kvalue reduction for the pin-loaded joint.This implies that claims of fatigue enhancementsolely based upon the performance of open holespecimens may be optimistic in actual connections
conclusions II