96

BACK FACE_____STRAIN (BPS) ^ G/UGE

CRACK MOUTH OPENING DISPLACEMENT (CMOO) GAUGE

0 8 3O

a a 'tt 3 2 1O

CRACK TIP CLIP GAUGES

CRACK TIP STRAIN GAUGES

NEAR TIP STRAIN GAUGES

Figure 2.9 Positioning of compliance gauges used for closure measurements.

LOAD

Figure 2.10 Sketch showing how the point P0p is determined using the onset of linearity and using the intersection of tangents.

97

Figure 2.11 An example showing how the method used Co determine closure alters the closure trend as R ratio varies. If closure is measured using the intersection of tangents (dotted linos) Kop increases with R, whereas if Kop is measured using the onset of linearity (indicate by markers) Kop remains remains fairly constant as R increases (data from ref. [55]).

Figure 2.12 Comparison of the offset elastic displacement technique t- > measure closure compared with the conventional compliance determination of the crack opening point (after ref. [19]).

98

Figure 2.Ill Characteristic regions of the offset displacement curve (after ref. [56]).

Figure 2.14 Illustration of typical differences between pop and pcl-

99

Half Crock Linglh 0 tern)

Figure 2.15 An Estimation of the resolution of the closure measuring technique by using the crack increment between the minimum growth rate value and the maximum closure value, from data according to [62].

Figure 2.16 Fatigue load cycle showing the magnitude, of the parameter CTOD relative to AK and AKeff.

100

Figure 2.17 Fatigue fracture surfaces illustrating the type of surface roughness which produced closure a) comparud to that which did not produce closure b), (after ref. [25]).

( mm/cyck)

101

Figure 2.18 Growth rate data which is rations!. rn<i sir.g . >o closure parameter AKe£f, (after ref. [79]),

Id*

>.■ M fr *

■L"0OO

’O jO li'T -L )

r ? ?OF

AK

Figure 2.19 Growth rate data which is rot totally retiiv.aliseu by AKeff, (after ref. [70]).

102

Figure 2.20 Strongly bovred fatigie crack front for 25 mm thick CT specimen following growth under compressive loading (after ref [100]).

103

Notch

Reverse plastic zone that moves - along with the crack tip (decreasing in size)

esidua] tensile stresses (tensile plastic zone) after compressivu load has been renoved

Notch plastic •arising from compression

zone

Figure 2.21 a) The development of tensile stresses under compressive loading, b) Movement of the tensile stresses (reverse plastic zone) during compressive loading.

104

FATIGUE CRACK LENGTH, olmml

0.1 0.2 0.3 0.4 0.5

-4

z£ -8 o < o _j

-12

-16

Mumericol Resul'r., Plane Strain Experimer'ol Results

I A P I (kN) (o) 13.50 (b) 24.30(c) 31.95

Figure 2.22 A comparison between numerically and experimentally determined crack tip opening loads obtained under compressive loading (aiter ref. [28]) .

Figure 2.23 Schematic representation of da/dN vs AK for short and long cracks (after ref. [30]).

105

Sur£ace crack length 2c (mm)

igurp 2.24 Variation of aspect ratio with surface crack length ,.fr»r ref. [71].

Figure 2 25 Grain size (GS) vs plastic zone size (rpc) which can bevsed to determine the crack length at which the da/dn vs AK curvesconverge for small and large cracks for several alloy systems (after ref. [118]).

106

i.o j"3 . * -

...C. 7 •

0. 6 r

n---rs u : t n

t.* 0 .5

o.«0.)0.2

0.1

0

O o o

Figure 2.26 Short crack closure data obtained by a) Morris [123] and b) Larson [131].

Crack Unglh a [[Inn)

Figure 2.27 Development of crac!; closure (^op^^max^ with increasing crack length, from FFM cc -ations (after ref. [79]).

&J,mMNrrT* 107

Figure 2.28 Growti. race data correlating short (a S 0.18 nun) and 1l (a fc 25 mm) crack growth in A533B ste<jl, .'sing the ilastic plastic fracture mechanics parameter AJ (after Dowling [135]).

Figure 2.29 Graphs showing the increase in crack lenfth and closure ratio with number of cycles following d reduction ix.closure caused by the application of compressivc overloads (a*ter ref.128]).

Figure 2.30 Variation of K0p level with crack length as of AK (after rel. [53]).

*1---

Z 6

i s

3

7

\

: /

■i-----J-----I---------L___] _. I ,1 I . , „ l .0.1 a (mm) '

function

Figure 2.31 Variation of Kop with crack length a) for a 2024 T351 Al alloy (ref. [140]) and b) for a nodular cast Iron (ref. [141]).

Figure 3.1 Composite 3-D microstructure of treated material conditions.

the as-received and heat

Figure 3.2 Dimensions of compact tension (CT) specimen.

110

Figure. 3.3 Orientation of CT and short crack specimens relative to the rolling direction of the aluminium plate.

7 5mm L__J

2 PLACES

175 mm

|75 mm

30mm

Figvire 3.4 Short crcck specimen geometry, similar to that used by Larson (131].

Ill

Figure 3.5 Typical fractograph of a short crack used to determine a/c ratios.

BACK FACE_____ ^STRAIN (BFS) f GAUGE

CRACK MOUTH OPENING DISPLACEMENT (CMOO) GAUGE

NEAR TIP STRAIN GAUGES

Figure 3.6 Positioning of the various gauges used ';o measure closure on CT specimens.

112

Figure 3.7 Layout of cra^k closure system. (K represents stress intensity, 6 represents strain or displacement and f represents offset displacement.)

Of f set Displacement

Load

Figure 3.8 Load vs offset displacement trace indicating the points at which P0p and were ch^'en.

113

CT Specimens

tensile

tensile

Figure 3.9 Residual stress distribution around fatigue crack notch afte'- compressive loading.

Figure 4.1 Representation of R ratio variation relative to Kop.

CT Specimen •Screw Clamp

..Wedge, which is positioned while the .specimen isbeing loaded

Hatched regions indicate areas of contact ie Clamp does not hold both top and bottom part of specimen

Figure 4.2 Sketch of triangular shaped wedge clamped into the mouth of a CT specimen, used to compare physical wedgeing with closure.

PWNMh: V’V*115

OffsetDisplacement

S'

Natural trace

op rpmax

Load

Figure 4.3 Offset displacement vs load traces illustrating the effect of wedge contact on the curvature of the trace.

= 0.05 nun

CTOD at K=7MPa/m~ is approximately 0.1um thus a particle of lum should have an effect if it is within say 0.05 mm from the cr^ck tip.

= 0.1 nun

Figure 4.4 Illustration of wcdgeing effect caused by a particle a) close to the crack tip, b) far from the crack tip.

§■s

116

Delta K (MPo >/H>

figure 5.1 Growth rates in the AR condition for 5 mm, 15 mm and 25 mm thick CT specimens.

D e lta K (MPa 7 i )

Figure 5.2 Closure data in the AR inattiial for 5 mm, 15 mm and 21 mm thick CT specimens corresponding to growth rate da.a in Fig. 5.1.

da/dN

(mm/

cycl

r)

117

Figure 5.3 Growth rate vs AKe £•£■, illustrating the inability of closure concepts to reduce growth rates onto a single line.

118

Figure 5. at R — 0.

8-:c

Flf.-re 5

4 Growth rate data for 5 mm thick heat treated CT specimens 1.

1.2

CLOSURE DATA 5 mm Heat Treated

1 P - 0. 1

* O

0.8 . 0

© ©

_0

o0.6

o ©_

© O©

©

0.4

• -

J. *■

i

0 14 6 e 10 12 14 16

O a ito K (MPa s/ni)

5a Closure data corresponding to growth rate data In Fig 5.4.

10

9

g

/-s1*5 7 >O

Q_ r 3E 6w

8- 5 4

3

24 6 a io i.: 14 is

D e lta K (MPa >/m)

Figure 5.5b Closure data presented as K0p vs AK illustrating the consistency of the Kop magnitude,

119

Kop vs AK 5 mm Hisat Treated

R - 0. 1

©

< B P 0

1C-4

S

■8

- n --- 1— m -------------- ;---- r"" " I1 1 1 — p

• *

* R ■ 0 . 1 5 win H o o t T r s a t » d -

- -r

J o :

• .

- © -

r _

: © I• O. g

O o

<*> 0r* 0 0

—’ 0 :

■ 0 :■

0-

r —j s- -

- 0 .

- -

5 - J --- 1-- 1-1 M i l __________ 1 1 » 1 « 12 I 4 S 10 20 10 40 SO

Onlto K'eff <MPo /m)

Figure 5.5c Growth rate presented as da/dN vs AKef£ for 5 mm heat treated CT specimens.

Figure 5.6 High R growth rate data for the heat treated material.

121

Delta K (MPa /in)

Figure 5.7 Closure presented as K0p vs AK for growth rate data presented in Fig 5.6.

• i i i I M I I 1 1 T T T ■Growth Rot« v« AK«ff HT -

_ o r - 0. 1 m

: ► R - 0. 75 |o :

■ o R - 0. 85 •■ 0 R - 0. 0 -

r O 1; O j. 0 .■ O 0

* 0•

- —• 6 z

; I. ■bt> .-

0 ► ►p

>

“. •

■ 0> >

.► ■

m -L J___1__JL-L-J-J I ’ - - « - « i i i u-ii

,* .1 .4 .1 .7 t 1 I * S 10

Dalto K «ff (MPo Stn)

Figure 5.8 Growth rate vs AKeff for 5 mm thick heat treated CT specimens.

Closure

Kop/Kmox

122

Del to K (MPo »/m)

Golta K (MPa 7m)

Figure 5.9 a) A comparison between the AR and HT growth rate data and the b) closure data .

Figure 5.10 Straining gauge used to strain CT specimens in the SEM.

pm

Figure 5.11 Roughness trace of the fracture surface for a 25 mm thick CT specimen in the AR condition.

124

Figure 5.12 Fractographs of fracture surfaces representative of growth rates a) b. ''•» 10' * mm/cycle and b) above 10"^ ram/cycle.

Figure 5.13 Schematic representation of the possible strain intensi­fication due ti limited asperity contact.

125

Delta K (MPa /m)

Figure 5.14 Closure dat.i for all R ratios tested in the heat treated condition.

oxu\EE

3■uo*Dcno

C rock G rowth undar C o m p r « * » l v « Loading

Paok Compr« » » I v « Loc'4 " 13 K M

2 2.5 3Crack Growth (mm)

Figure 5.15 Fatigue crack growth under compressive loading.

126

Figure 5.It Fatigue strlations produced by growth under a) tensile loading and b) compressive loading.

127

<

Figure 6.1 Fractured 25 nun chick CT specimens showing extensive curvature along the crack front.

Crack Increment (mm)

'

Figure 6.2 Closure developmenc for the AR material after closure had been eliminated by wake removal and a compressive overload.

128

Figure 6.3 Closure development in the HT material at AK - 3 MPa/m followed by closure development at AK - 6 MPa 'm.

Crack Increment (mm)

Figure 6.4 Closure development at AK - 4 MPaVm.

Crock increment (mm)

Figure 6.5 Closure development at AK - 5 MPaVm.

Figure 6.6 Closure development at AK - 6 HV&Jm.

Closure:

Kop/Ki

130

Crack Increment (mm)

Figure 6.7 Closure development at AK - 9 MPa /m.

Growth

Rots

(mm/

cyci

c)

r121

xoEbesQ-OX

Io. g

0.8 0.7 0. E

0.5 0. 4 0. 3 0.2 0. 1 . 0

C l o s u r e d e v e l o p m e n t rollowing

g r o w t h u n d e r c c m p - e s s i v e locdlnc

1n c r e o s 1ng ^ K

A r r a a tI0

L ln « » In d le e t a p o in t * a t w h ich

load 1 n c r* a » *d

e>0. ;• »«,0.2 0.4 0.6 0.8 1 1. 2 1. 4 l.S

Crack Increment (mm)

Figure 6.8a Closure development for increasing AK, starting with AK - 1.56 MPa^m.

5S■8

0 T a n i 1 1• g rowth following compraaatva

looding.

Compraaa s va g-owth ■ 1.24 mm

C i oaura first Oatactad

f o r o • 0 . 31 mm.c

•^-Long 3r o w t h rota doto

S ci¥I |V 6

o - C. 31 ♦» ♦

lO’V

D a l t o K (H Po vTS)

Figure 6.8b Fatigue crack growth rates obtained from an increasing AK method, after a crack had been produced ur>H«»r compressive cyclic loading.

132

Figure 6.9 Fatigue crack growth at R - 0.75. Comparing growth rates obtained during load increasing schemes after a crack had been developed under compressive loading (circles) with growth rates obtained during load shedding (band indicated by the solid lines), (after Suresh et al [23]).

flK (kil-ln'")

IE.zm■©<dXKsocco*o<coUJ=>o

zx>

Figure 6.10 Fatigue crack growth rates in a 2124 T351 alloy at R - 0.1 for short and long crack growth. AK had to be increas’d continually to allow short crack growth to continue.

133

Figure 6.11 Offset displacement vs load traces obtained from BFS gauges showing uncharacteristic curvature.

134

10- t-i

Sho-t CrocH HT R • C. 2

«* o b e • 234 MPc

D<0 Ac ' 1S? MPa

I r5- l0*‘r »»»

▼ o

® 2c * 700 u*

j

1 4 S 10 20 SO 100 20C 500 1000 SC 0

ZZ (urn)

b ) Dal to K <MPo ./m)

Figure 7.1 Short crack growth data for the HT material at R - 0.1 plotted as a) da/dN vs 2c and b) da/dN vs AK.

135

Zc (yin)a)

Figure 7.2 Shorr crack growth data for the AP. material at R - 0.1

•a

Figure 7.31.

s.

'

Figure 7.3 material.

136

C^och OoptK a (/j«0

Short crack growth rates at R - 0.55 for the HT material.

O a lta K <MPa /m )

b) Comparison between short and long crack data in the HT

137

D al t o K (MPa v^S)

Figure 7.4 Comparison between shore crack data at R - 0.1 and R - 0.55 for the HT material showing a difference in growth rates for AK ranges greater than 2.2 MPaVm'.

137

Dal to K iMPa s/m)

Figure 7.4 Comparison between shore crack data at R - 0.1 and R - 0.55 for the HT material showing a difference in growth rates for AK ranges greater than 2.2 MPaVm'.

Author Garz Reiner Ernst Name of thesis Fatigue Crack Closure And Closure Development In A High Strength Aluminium Alloy. 1988

PUBLISHER: University of the Witwatersrand, Johannesburg

©2013

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