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International Journal of Fatigue Volume 25 Issue 1 2003 S. Curtis; E.R. de Los Rios; C.a. Rodopoulos; A. Levers -- Analysis of the Effects of Controlled Shot Peening on Fatigue Da

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  International Journal of Fatigue 25 (2003) 59–66www.elsevier.com/locate/ijfatigue Analysis of the effects of controlled shot peening on fatiguedamage of high strength aluminium alloys S. Curtis  a , E.R. de los Rios  a , C.A. Rodopoulos  a, ∗ , A. Levers  b a  Division of Aeronautical Applications, Department of Mechanical Engineering, Structural Integrity Research Institute of the University of Sheffield (SIRIUS), The University of Sheffield, P.O. Box 600 Mappin Street, Sheffield S1 4DU, UK  b  Airbus UK, Chester Road, Broughton, Chester CH4 0DR, UK  Received 13 December 2001; received in revised form 16 April 2002; accepted 22 April 2002 Abstract The use of two micro-mechanical models for notch sensitivity and fatigue life allowed the development of boundary conditionsthat would evaluate potential life improvement after controlled shot peening (CSP) in high strength aluminium alloys. The boundaryconditions describe the state of equal weight between surface roughening and residual stresses and the implication of material andloading parameters. From the boundary conditions, the performance of CSP on crack arrest and fatigue life can be investigated. ©  2002 Elsevier Science Ltd. All rights reserved. Keywords:  Navarro–Rios model; Notches; Controlled shot peening; Residual stresses; Surface roughness; Crack arrest; Fatigue life; Aluminiumalloys 1. Introduction For many years, shot peening was considered as a sur-face treatment of questionable benefits regarding cyclicloading [1]. These contradictory results were partly dueto ignorance of the shot peening process and partly dueto the lack of a sufficient background that would allowthe characterisation of the role of surface modificationsproduced by shot peening in fatigue damage. Today, theparameters that control the performance of shot peening,i.e. media, intensity and coverage, are better understoodand the new designation, that of controlled shot peening(CSP), has emerged.CSP is a cold working treatment in which mediaimpinge the surface under controlled kinetic/impact con-ditions. The surface modifications produced by the treat-ment are: (a) roughening of the surface; (b) an increased,near-surface, dislocation density (strain hardening); and(c) the development of a characteristic profile of residualstresses [2–4]. In terms of fatigue damage, surface ∗ Corresponding author. Tel.:  + 44-114-227-710; fax:  + 44-114-227-890.  E-mail address:  c.rodopoulos@sheffield.ac.uk (C.A.Rodopoulos). 0142-1123/02/$ - see front matter.  ©  2002 Elsevier Science Ltd. All rights reserved.PII: S0142-1123(02)00049-X roughening will accelerate the nucleation and earlypropagation of cracks, strain hardening will retard thepropagation of cracks by increasing the resistance toplastic deformation and the residual stress profile willprovide a corresponding crack closure stress that willreduce the driving force for crack propagation [4].Considering that there is no relaxation of the residualstress profile, caused by either the applied stress level,the crack tip or the operating temperature, and that sur-face and not sub-surface fatigue cracks are responsiblefor fatigue damage, it is plausible to assume that theperformance of CSP will depend on the balance betweenits beneficial and detrimental effects. Hence, in order toachieve a favourable fatigue performance, the role of theabove effects has to be analysed and understood. To ach-ieve such undertaking, it is essential to simultaneouslyacknowledge their interaction with other parameters,such as the nature of the target material and the load-ing conditions. 2. CSP and fatigue damage In light of the residual stress profile, the magnitude of the strain hardening and the corresponding amount of surface roughening, it is realistic to assume that CSP will  60  S. Curtis et al. / International Journal of Fatigue 25 (2003) 59  –  66  Nomenclature a  Crack length c i  Fatigue damage (crack and plastic zone)  D  Grain diameter K  t  Elastic stress concentration m i  Grain orientation factor of the  i th grain s  1  Crack closure stress s  2  Resistance to plastic deformation s  3  Stress at the micro-structural barrier s  p i arrest  Plain crack arrest stress of the  i th half grain( s  p i arrest ) closure  Crack arrest stress of the  i th half grain for a peened component considering the effect of crack closure( s  p i arrest ) notchclosure  Crack arrest stress of the  i th half grain for a peened component considering the effect of crack closure and surface roughness s  FL Fatigue limit s  SPFL  Fatigue limit after shot peening a   Notch depth  b  Notch half width  r  Notch radius  Z  i  Notch factor of the  i th half grainmainly affect the stages of fatigue damage that corre-spond to the initiation and propagation of short cracks.It is well documented that the above stages are respon-sible for more than 70% of the fatigue life of a compo-nent [5].Crack initiation is a controversial subject, which formany years provided the ground for numerous differenttheories especially in the case of single crystals [6,7]. Inpolycrystalline materials, where most commercial alloysare classi fi ed, crack initiation is assumed to occur almostimmediately the component is loaded at stresses abovethe fatigue limit [8]. Hence, the crack initiation stage canbe seen as the early propagation of a crack from thematerials micro-defects [9].Based on the above observations, it is clear that thesteady propagation of a short crack will de fi ne the lifeexpectancy of the component. Similar to crack initiation,the propagation of short fatigue cracks is another contro-versial subject of research, which throughout the last twodecades, has been approached by a variety of method-ologies [10 – 12].Thus, to better understand the effects of CSP surfacemodi fi cations on fatigue damage, it is necessary to separ-ate their role into: (a) the arrest of fatigue cracks, and(b) the crack propagation stage, i.e. fatigue life. 2.1. CSP  —  crack arrest  It is well known that materials do not fail by fatiguewhen tested at stresses below the fatigue limit. In theearly days, the fatigue limit was wrongly considered asthe stress level below which fatigue cracks do notnucleate. During the last two decades, the understandingof the fatigue limit has changed. Today, the fatigue limitis considered as the maximum stress level below whichan existing crack or crack-like defect will not propagatein to failure within a predetermined life span (10 – 100M cycles). With the realisation that grain boundaries andother micro-structural features act as barriers to crack propagation [13 – 15], the Kitagawa – Takahashi thresholdstress [9] has been rede fi ned as the applied stress that isunable to overcome micro-structural barriers ahead of acrack of a given length [15]. According to Navarro andde los Rios [15 – 17], the crack arrests when two con-ditions are satis fi ed: (a) the crack tip plastic zone is con-strained by the barriers, and (b) the local stress at thebarriers ahead of the crack is unable to extend crack tipplasticity beyond those barriers. The possibility of crack arrest, as depicted in Fig. 1, will uphold for any cracks,short or long, provided that the above conditions are met.On shot peened surfaces, cracks are likely to form atmicro-notches (dents). Early studies by Smith and Miller[18] and Tanaka [19] indicate that the propagation of cracks from notches depends on the bluntness of thenotch, given by    a   /   r . From these early works, ourunderstanding of the effects of notches has been con-siderably broadened. Today, the effect of the notchgeometry on fatigue is classi fi ed into three categories,namely, short notches, crack-like notches, and bluntnotches [20]. However, most of the notch/fatigue mod-els, a selection of which are presented in Ref. [5], failto provide a relationship between the geometry of thenotch and the micro-structure of the material. Suchrelationship was successfully provided by Vallellano etal. [21,22]. According to their work, the stress applied  61 S. Curtis et al. / International Journal of Fatigue 25 (2003) 59  –  66  Fig. 1. Experimental crack arrest data for 2024-T351 at a stress ratioof 0.3. The average grain size is 52  µ m. to the notched member, which is required for the crack to overcome the  i th barrier in the notch zone, is given by s  N i arrest   Z  i s  p i arest  (1)where  s  N i arrest  is the threshold stress for a notched compo-nent,  s  P i arrest , the analogous stress for a plain surface and  Z   represents the effect of the notch geometry given by  Z  i    i a    b   b l i  a    1   l 2 i  1/2 ,  l i  1 a  2   b 2 [ a    ( a   iD 2  /2) 2  a  2   b 2 (2)   b ( a   iD  /2)]The parameters  a  ¯    (2 a   /   D ) and  b ¯   (2  b  /   D ) represent,in a dimensionless form, the notch depth  a   and the notchhalf width  b . The parameter  D  represents the distancebetween two successive barriers. In the case of grainboundaries,  D  is regarded as the grain diameter. The pos-ition of the  i th barrier is de fi ned by  i  2 a  /   D  with  a being the crack length. In Ref. [17] it was proposed thata model crack is constituted by three zones (see Fig. 2),and when the system of internal and external forces arein equilibrium, the stress at the active barrier is given by s  3  1cos  1 n 2  ( s  2  s  1 )sin  1 n 1  s  2 sin  1 n 2  π 2 s    (3)where  s  1  is the closure stress acting on the crack wake, s  2 , the resistance to plastic deformation and  s  3 , thestress at barrier. More details regarding this micro-struc-tural fracture mechanics crack model can be found inRef. [15]. Based on Eq. (3), the conditions of crack arrestare satis fi ed when  n 1  n 2  1. Hence, Eq. (3) can bewritten as2 π s  i 3 cos  1 n i 2  s  i 1  s  p i arrest  (4) Fig. 2. Schematic representation of the three zones (crack, plasticzone, grain boundary), which comprise the fatigue damage accordingto the Navarro – de los Rios model [17]. The parameter  i  represents half grain intervals ( i  1,3,5 … ). The parameter  iD  /2 represents the extendof the fatigue damage ( c i ),  D  is the grain size and  r  0  is the width of the grain boundary. The parameter  s  p i arrest  is the stress required by the crack to overcome the  i th barrier in a plain specimen. In Ref.[16], it was shown that Eq. (4) can be written as4 π m i s  c ( r  0  /  iD ) 1/2  s  i 1  s  p i arrest  (5)where the parameters  r  0  and  D  are given in Fig. 2 and m i  is the grain orientation factor. The plain fatigue limitis found by calculating  s  p i arrest  for  i  1 ( fi rst grain)4 π m 1 s  c ( r  0  /   D ) 1/2  s  i = 11   s  FL  (6)From Eqs. (5) and (6) the crack arrest can beexpressed as m i m 1 s  FL  s  i = 11   i  s  i 1  s  p i arrest  (7)The grain orientation factor, ( m i  /  m 1 ), for aluminiumalloys has been experimentally estimated to follow theprogression [23] m i m 1  1  0.35ln( i ) (8)Eq. (7) is plotted in Fig. 3. Any combination of applied stress and crack length below the curve willresult in crack arrest. In the case of CSP material, thecurve will shift either up or down depending on whetherthe CSP process is bene fi cial or detrimental in terms of the fatigue resistance. The two CSP effects that are sig-ni fi cant for the crack arrest capability of a surface engi-neered material are the compressive residual stresses andsurface roughness, the former being bene fi cial and thelatter detrimental.  62  S. Curtis et al. / International Journal of Fatigue 25 (2003) 59  –  66  Fig. 3. Schematic representation of the Kitagawa – Takahashi diagramshowing the possible effect of CSP on the crack arrest capability of asurface engineered material. The arrows indicating loss or gain areused to show either the bene fi cial or detrimental effect of CSP. Themechanical parameters used are:  s  FL  220MPa and  D  52 µ m. In practical terms, it is important to derive the CSPconditions that produce bene fi ts to the fatigue resistanceof the material, i.e. when the positive aspect(compressive residual stress) of CSP compensates thenegative aspect (surface roughness). In this respect, it isimperative to identify the limit conditions by whichcrack closure derived from the compressive residualstress will counteract the stress concentration due toroughness. Such analysis is discussed subsequently.In Eq. (7)  s  i 1  is the closure stress of a crack spanningover the  i th barrier. It should be noted that for  i  1, s  p i arrest  in Eq. (7) converts into the plain (un-notched)fatigue limit. If we temporarily neglect the effect of thesurface roughness and consider only the effect of theclosure stress introduced by the CSP, Eq. (7) should read( s  p i arrest ) closure  m i m 1 s  CSPFL   s  i = 11   i  s  i 1  (9)where  s  CSPFL   s  FL  s  i  11  . The parameter  s  CSPFL  makesclear that the fatigue limit will increase due to the clos-ure stress exerted within the  fi rst half grain. Hence, Eq.(9) becomes( s  p i arrest ) closure  m i m 1 s  FL   i  s  i 1  (10)Using Eqs. (1) and (9), the effect of both crack closureand surface roughness on the ability of the peenedcomponent to arrest cracks is given by( s  p i arrest ) notchclosure   Z  i ( s  p i arrest ) closure  (11)From Eq. (11) it is clear that in crack arrest of CSPcomponents, the two competing effects are the crack closure stress and the surface roughening. It is, therefore,necessary to determine a lower limit above which therewould be an improvement of the crack arrest capacityof the material by CSP. Such boundary condition isobtained by determining the closure stress that will fullyneutralise the effect of the notch. Such rationale isexpressed as m i m 1 s  FL   i   Z  i  m i m 1 s  FL   i  s  i 1   (12)From Eq. (12) the parameter  s  i 1  can be calculated as s  i 1  m i m 1 s  FL   i   1  Z  i  1   (13)Li et al. [24], proposed that the elastic stress concen-tration  K  t  introduced by multiple micro-notches in CSP,is somehow lower than the one determined in the caseof a single notch of similar depth and width. The above fi nding re fl ects the uniformity of the micro-notches onthe surface. According to Li et al., the resulting  K  t  fromCSP is given by K  t  1  2.1   R t S    (14)where the parameters  R t  and  S   are, respectively, themeans of peak-to-valley heights and spacing of adjacentpeaks in the surface roughness pro fi le. In the case of asemi-elliptical notch and a high degree of uniformity(CSP coverage percentage of more than 100%), Eq. (14)can be written as K  t  1  2.1  a  2  b   (15)At the beginning of this section it was pointed out thatthe bluntness of the notch can signi fi cantly affect thestrain generated at the root of the notch and consequentlythe propagation rate of the crack. In light of that, Smithand Miller [18] proposed that  K  t  should be determinedby K  t  1  2   a  r  (16)where  r  is the notch root radius. In the case of a semi-elliptical notch, the notch root radius can be approxi-mated by  r  ( a  2  /  g  ) and thus Eq. (16) can be rewrit-ten as K  t  1  2   g a   (17)where  g   is the notch half width that considers the blunt-ness of the notch. By equating Eq. (17) with Eq. (15),the parameter  g   can be expressed in terms of the para-meters  a   and  b . Substitution of   g   into Eq. (17) can pro-vide the dual effects of multiple micro-notches and notchbluntness in terms of a single notch
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