Figure 2.9 Positioning of compliance gauges used for closure measurements.

Transcription

1 96 BACK FACE STRAIN (BPS) ^ G/UGE CRACK MOUTH OPENING DISPLACEMENT (CMOO) GAUGE a a 'tt O O 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.

2 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]).

3 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-

4 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.

5 100 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]).

6 101 Figure 2.18 Growth rate data which is rations!.^rn<i sir.g. >o closure parameter AKe f, (after ref. [79]), >. M fr * ( m m / c y c k ) L"0 OO O jo li't - L ) Id* r?? OF AK Figure 2.19 Growth rate data which is rot totally retiiv.aliseu by AKeff, (after ref. [70]).

7 102 Figure 2.20 Strongly bovred fatigie crack front for 25 mm thick CT specimen following growth under compressive loading (after ref [100]).

8 103 Notch plastic arising from compression zone Notch esidua] tensile stresses (tensile plastic zone) after compressivu load has been renoved Reverse plastic zone that moves - along with the crack tip (decreasing in size) Figure 2.21 a) The development of tensile stresses under compressive loading, b) Movement of the tensile stresses (reverse plastic zone) during compressive loading.

9 104 FATIGUE CRACK LENG TH, olmml z -8 o < o _j -12 Mumericol Resul'r., Plane Strain Experimer'ol Results -16 I A P I (o) (b) (c) (kn) 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]).

10 105 S u r a c e 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 be vsed to determine the crack length at which the da/dn vs AK curves converge for small and large cracks for several alloy systems (after ref. [118]).

11 106 i.oj" 3. * -... s u : t n n--- r C r t.* 0.5 o.«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]).

12 &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]).

13 Figure 2.30 Variation of K0p level with crack length as of AK (after rel. [53]). function *1--- Z 6 i s 3 7 \ : / i----- J-----I L ] _. I,1 I., l. 0.1 a (m m ) ' 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]).

14 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.

15 110 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 m m 75 m m 30mm Figvire 3.4 Short crcck specimen geometry, similar to that used by Larson (131].

16 Ill Figure 3.5 Typical fractograph of a short crack used to determine a/c ratios. BACK FACE ^ STRAIN (BFS) GAUGE f 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.

17 112 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.

18 113 CT Specimens tensile tensile Figure 3.9 Residual stress distribution around fatigue crack notch afte'- compressive loading.

19 Figure 4.1 Representation of R ratio variation relative to Kop. CT Specimen Screw Clamp..Wedge, which is positioned while the.specimen is being 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.

20 PWNMh: V V* 115 op r p max Natural trace Offset Displacement S' 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.

21 116 s 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.

22 117 da/dn (mm/cyclr) Figure 5.3 Growth rate vs AKe, illustrating the inability of closure concepts to reduce growth rates onto a single line.

23 J. * i 118 Figure 5. 4 Growth rate data for 5 mm thick heat treated CT specimens at R CLOSURE DATA 5 mm Heat Treated 8- :c 1 P * O _ 0 o 0.6 o _ O e O a ito K (MPa s/ni) Flf.-re 5 5a Closure data corresponding to growth rate data In Fig 5.4.

24 g /-s 1*5 7 > O Q_ r 3E 6 w Kop vs AK < B P 0 5 mm Hisat Treated R a io i.: 14 is D e lt a K (MPa >/m) Figure 5.5b Closure data presented as K0p vs AK illustrating the consistency of the Kop magnitude, 1C-4 - n m ;---- r" " " I1 1 1 p * * R win H o o t T r s a t» d - - -r J o :. - - r _ : I O. g O o S 8 <*> 0 r* : 0 : - 0 r j s J M i l 1 1» 1 «1 2 I 4 S SO Onlto K'eff <MPo /m) Figure 5.5c Growth rate presented as da/dn vs AKef for 5 mm heat treated CT specimens.

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

26 121 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 IMII 1 1 T T T Growth Rot«v«A K «ff HT - _ o r m : R o : o R R 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,* 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.

27 122 Del to K (MPo»/m) Closure Kop/Kmox Golta K (MPa 7m) Figure 5.9 a) A comparison between the AR and HT growth rate data and the b) closure data.

28 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.

29 124 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.

30 125 Delta K (MPa /m) Figure 5.14 Closure dat.i for all R ratios tested in the heat treated condition. o xu \ E E 3 u o *D cn o C r o c k G r o w t h u n d a r C o m p r «*» l v «L o a d i n g P a o k C o m p r » I v «Loc'4 " 13 K M Crack Growth (mm) Figure 5.15 Fatigue crack growth under compressive loading.

31 126 Figure 5.It Fatigue strlations produced by growth under a) tensile loading and b) compressive loading.

32 127 < 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.

33 128 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.

34 Crock increment (mm) Figure 6.5 Closure development at AK - 5 MPaVm. Figure 6.6 Closure development at AK - 6 HV&Jm.

35 130 Closure: Kop/Ki Growth Rots (mm/cycic) Crack Increment (mm) Figure 6.7 Closure development at AK - 9 MPa^/m.

36 r 121 Closure development rollowing x o E be s Q- O X I o.g E growth under ccmp-essive locdlnc 1ncreos1ng ^ K e>0.;»«, A r r a a t I 0 L ln In d le e t a p o in t * a t w h ic h lo a d 1 n c r * a» * d l.s Crack Increment (mm) Figure 6.8a Closure development for increasing AK, starting with AK MPa^m. 0 T a n i 1 1 g r o w t h f o l l o w i n g c o m p r a a a t v a looding. C o m p r a a a sva g - o w t h 1.24 mm C i o a u r a f i r s t O a t a c t a d f o r o mm. ^-Long 3 r o w t h r o t a doto c S ci I V 6 5 S 8 o - C. 31» lo V D a l t o K (H P o vts) Figure 6.8b Fatigue crack growth rates obtained from an increasing AK method, after a crack had been produced ur>hr compressive cyclic loading.

37 132 Figure 6.9 Fatigue crack growth at R 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'") I E. z m < d X K socc z x> o * o < c o UJ => o Figure 6.10 Fatigue crack growth rates in a 2124 T351 alloy at R for short and long crack growth. AK had to be increas d continually to allow short crack growth to continue.

38 133 Figure 6.11 Offset displacement vs load traces obtained from BFS gauges showing uncharacteristic curvature.

39 t- i Sho-t CrocH HT R C. 2 «* o b e 234 MPc D<0 A c ' 1S? MPa I r 5 - l0* r»»» o 2c * 700 u* j 1 4 S SO C SC 0 ZZ (urn) b ) Dal to K <MPo./m) Figure 7.1 Short crack growth data for the HT material at R plotted as a) da/dn vs 2c and b) da/dn vs AK.

40 135 a) Zc (yin) Figure 7.2 Shorr crack growth data for the AP. material at R - 0.1

41 136 a C^och OoptK a (/j«0 Figure Short crack growth rates at R for the HT material. s. ' O a lta K <MPa /m ) Figure 7.3 b) Comparison between short and long crack data in the HT material.

42 137 D al t o K (MPa v^s) Figure 7.4 Comparison between shore crack data at R and R for the HT material showing a difference in growth rates for AK ranges greater than 2.2 MPaVm'.

43 137 Dal to K impa s/m) Figure 7.4 Comparison between shore crack data at R and R for the HT material showing a difference in growth rates for AK ranges greater than 2.2 MPaVm'.

44 Author Garz Reiner Ernst Name of thesis Fatigue Crack Closure And Closure Development In A High Strength Aluminium Alloy PUBLISHER: University of the Witwatersrand, Johannesburg 2013 LEGAL NOTICES: Copyright Notice: All materials on the University of the Witwatersrand, Johannesburg Library website are protected by South African copyright law and may not be distributed, transmitted, displayed, or otherwise published in any format, without the prior written permission of the copyright owner. Disclaimer and Terms of Use: Provided that you maintain all copyright and other notices contained therein, you may download material (one machine readable copy and one print copy per page) for your personal and/or educational non-commercial use only. The University of the Witwatersrand, Johannesburg, is not responsible for any errors or omissions and excludes any and all liability for any errors in or omissions from the information on the Library website.