International Journal of Fatigue Volume 25 Issue 1 2003 S. Curtis; E.R. de Los Rios; C.a....

8/10/2019 International Journal of Fatigue Volume 25 Issue 1 2003 S. Curtis; E.R. de Los Rios; C.a. Rodopoulos; A. Levers --

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International Journal of Fatigue 25 (2003) 5966

www.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, UKb 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 and

loading 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:NavarroRios model; Notches; Controlled shot peening; Residual stresses; Surface roughness; Crack arrest; Fatigue life; Aluminium

alloys

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 [24]. In terms of fatigue damage, surface

Corresponding author. Tel.: +44-114-227-710; fax: +44-114-

227-890.

E-mail address: [email protected] (C.A.

Rodopoulos).

0142-1123/02/$ - see front matter. 2002 Elsevier Science Ltd. All rights reserved.

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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 ofthe strain hardening and the corresponding amount ofsurface roughening, it is realistic to assume that CSP will


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60 S. Curtis et al. / International Journal of Fatigue 25 (2003) 5966

Nomenclature

a Crack length

ci Fatigue damage (crack and plastic zone)D Grain diameter

Kt Elastic stress concentrationmi Grain orientation factor of the ith grain

s1 Crack closure stresss2 Resistance to plastic deformations3 Stress at the micro-structural barrierspiarrest Plain crack arrest stress of the ith half grain(spiarrest)closure Crack arrest stress of the ith half grain for a peened component considering the effect of crack

closure

(spiarrest)notchclosure Crack arrest stress of the ith half grain for a peened component considering the effect of crack

closure and surface roughness

sFL Fatigue limitsSPFL Fatigue limit after shot peeninga Notch depth

b Notch half widthr Notch radiusZi Notch factor of the ith half grain

mainly 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 different

theories especially in the case of single crystals [6,7]. In

polycrystalline materials, where most commercial alloys

are classified, crack initiation is assumed to occur almostimmediately the component is loaded at stresses above

the fatigue limit [8]. Hence, the crack initiation stage can

be seen as the early propagation of a crack from the

materials micro-defects [9].

Based on the above observations, it is clear that thesteady propagation of a short crack will define 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 two

decades, has been approached by a variety of method-

ologies [1012].Thus, to better understand the effects of CSP surface

modifications 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. CSPcrack arrest

It is well known that materials do not fail by fatigue

when tested at stresses below the fatigue limit. In theearly days, the fatigue limit was wrongly considered as

the stress level below which fatigue cracks do not

nucleate. During the last two decades, the understanding

of the fatigue limit has changed. Today, the fatigue limit

is considered as the maximum stress level below which

an existing crack or crack-like defect will not propagate

in to failure within a predetermined life span (10100M cycles). With the realisation that grain boundaries and

other micro-structural features act as barriers to crack

propagation [1315], the KitagawaTakahashi threshold

stress [9] has been redefined as the applied stress that isunable to overcome micro-structural barriers ahead of acrack of a given length [15]. According to Navarro and

de los Rios [1517], the crack arrests when two con-ditions are satisfied: (a) the crack tip plastic zone is con-strained by the barriers, and (b) the local stress at the

barriers ahead of the crack is unable to extend crack tip

plasticity 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 at

micro-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 notch

geometry on fatigue is classified into three categories,namely, short notches, crack-like notches, and blunt

notches [20]. However, most of the notch/fatigue mod-

els, a selection of which are presented in Ref. [5], fail

to provide a relationship between the geometry of the

notch and the micro-structure of the material. Such

relationship was successfully provided by Vallellano et

al. [21,22]. According to their work, the stress applied


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61S. Curtis et al. / International Journal of Fatigue 25 (2003) 5966

Fig. 1. Experimental crack arrest data for 2024-T351 at a stress ratio

of 0.3. The average grain size is 52 m.

to the notched member, which is required for the crack

to overcome theith barrier in the notch zone, is given by

sNiarrest Zispiarest

(1)

wheresNiarrest is the threshold stress for a notched compo-nent,sPiarrest, the analogous stress for a plain surface andZ represents the effect of the notch geometry given by

Zi i

a bb

li

a

1 l2i1/2,

li 1

a2b2[a(a iD2/ 2)2a2 b2 (2)

b(a iD/ 2)]

The parametersa (2a/D) andb (2b/D) represent,in a dimensionless form, the notch depth aand the notchhalf width b. The parameter D represents the distancebetween two successive barriers. In the case of grain

boundaries,D is regarded as the grain diameter. The pos-

ition of the ith barrier is defined by i 2a/D with abeing the crack length. In Ref. [17] it was proposed that

a model crack is constituted by three zones (see Fig. 2),

and when the system of internal and external forces are

in equilibrium, the stress at the active barrier is given by

s3 1

cos1n2(s2s1)sin1n1s2sin1n2 2s (3)

where s1 is the closure stress acting on the crack wake,s2, the resistance to plastic deformation and s3, thestress at barrier. More details regarding this micro-struc-

tural fracture mechanics crack model can be found in

Ref. [15]. Based on Eq. (3), the conditions of crack arrest

are satisfied when n1 n2 1. Hence, Eq. (3) can bewritten as

2

si3cos

1ni2 si

1 spiarrest

(4)

Fig. 2. Schematic representation of the three zones (crack, plastic

zone, grain boundary), which comprise the fatigue damage according

to the Navarrode los Rios model [17]. The parameter i represents half

grain intervals (i 1,3,5). The parameter iD/2 represents the extend

of the fatigue damage (ci), D is the grain size and r0 is the width of

the grain boundary.

The parameterspiarrestis the stress required by the crackto overcome the ith barrier in a plain specimen. In Ref.

[16], it was shown that Eq. (4) can be written as

4

misc(r0/iD)

1/2 si1 s

piarrest

(5)

where the parameters r0 and D are given in Fig. 2 andmi is the grain orientation factor. The plain fatigue limit

is found by calculating spiarrest for i 1 (first grain)4

m1sc(r0/D)

1/2 si=11 sFL (6)

From Eqs. (5) and (6) the crack arrest can beexpressed as

mi

m1

sFLsi=11

i si1 s

piarrest

(7)

The grain orientation factor, (mi/m1), for aluminium

alloys has been experimentally estimated to follow the

progression [23]

mi

m1 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, the

curve will shift either up or down depending on whetherthe CSP process is beneficial or detrimental in terms ofthe fatigue resistance. The two CSP effects that are sig-

nificant for the crack arrest capability of a surface engi-neered material are the compressive residual stresses and

surface roughness, the former being beneficial and thelatter detrimental.


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Fig. 3. Schematic representation of the KitagawaTakahashi diagram

showing the possible effect of CSP on the crack arrest capability of a

surface engineered material. The arrows indicating loss or gain are

used to show either the beneficial or detrimental effect of CSP. The

mechanical parameters used are: sFL

220MPa and D

52m.

In practical terms, it is important to derive the CSP

conditions that produce benefits to the fatigue resistanceof the material, i.e. when the positive aspect

(compressive residual stress) of CSP compensates the

negative aspect (surface roughness). In this respect, it is

imperative to identify the limit conditions by which

crack closure derived from the compressive residual

stress will counteract the stress concentration due toroughness. Such analysis is discussed subsequently.

In Eq. (7) si1 is the closure stress of a crack spanningover the ith barrier. It should be noted that for i 1,

spiarrest in Eq. (7) converts into the plain (un-notched)fatigue limit. If we temporarily neglect the effect of the

surface roughness and consider only the effect of the

closure stress introduced by the CSP, Eq. (7) should read

(spiarrest)closure mi

m1

sCSPFL si=11

i si1 (9)

where sCSPFL sFL si 11 . The parameters

CSPFL makes

clear that the fatigue limit will increase due to the clos-

ure stress exerted within the first half grain. Hence, Eq.(9) becomes

(spiarrest)closure mi

m1

sFL

i si1 (10)

Using Eqs. (1) and (9), the effect of both crack closure

and surface roughness on the ability of the peened

component to arrest cracks is given by

(spiarrest)notchclosure Zi(s

piarrest

)closure (11)

From Eq. (11) it is clear that in crack arrest of CSP

components, the two competing effects are the crackclosure stress and the surface roughening. It is, therefore,

necessary to determine a lower limit above which there

would be an improvement of the crack arrest capacity

of the material by CSP. Such boundary condition is

obtained by determining the closure stress that will fully

neutralise the effect of the notch. Such rationale is

expressed as

mi

m1

sFL

i Zi

mi

m1

sFL

i si1

(12)

From Eq. (12) the parameter si1 can be calculated as

si1 mi

m1

sFL

i1

Zi1 (13)

Li et al. [24], proposed that the elastic stress concen-

tration Kt introduced by multiple micro-notches in CSP,is somehow lower than the one determined in the case

of a single notch of similar depth and width. The abovefinding reflects the uniformity of the micro-notches onthe surface. According to Li et al., the resulting Kt from

CSP is given by

Kt 1 2.1RtS (14)

where the parameters Rt and S are, respectively, the

means of peak-to-valley heights and spacing of adjacent

peaks in the surface roughness profile. 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

Kt

1

2.1a

2b (15)At the beginning of this section it was pointed out that

the bluntness of the notch can significantly affect thestrain generated at the root of the notch and consequentlythe propagation rate of the crack. In light of that, Smith

and Miller [18] proposed that Kt should be determined

by

Kt 1 2ar (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 (a2/g) and thus Eq. (16) can be rewrit-ten as

Kt 1 2ga (17)wheregis the notch half width that considers the blunt-ness of the notch. By equating Eq. (17) with Eq. (15),

the parameter gcan be expressed in terms of the para-meters aandb. Substitution ofg into Eq. (17) can pro-vide the dual effects of multiple micro-notches and notch

bluntness in terms of a single notch


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Fig. 4. The distribution of the required crack closure stress to fully

neutralise the effect of surface roughness for crack arrest in 2024-

T351. The parameters used in the calculation are: S 2branging from170 to 250 m, Rt a 50m and sFL 220MPa. The negative

sign (compression) in the closure stress values represent compression.

Kt 1 1.05a

b (18)

In Fig. 4, the limit closure stress given by Eq. (13) is

plotted in terms of crack length. The data correspond to

a notch depth ofa 50m, D 52m and differentKt values. The curves in Fig. 4 represent the boundarycondition established by Eq. (13). Closure stress values

either below or above the curve will, respectively,decrease or increase the crack arrest capacity of the

material.

A closer examination of Eq. (13) reveals the ability

of the boundary condition to provide an insight into the

complex relationship between CSP surface modifi-cations, the material and the loading conditions. The

effect of the stress ratio and the mechanical properties

of the material in Eq. (13) is shown in Figs. 5 and 6.

Fig. 5. The effect of the stress ratio on the magnitude of the crack

closure stress to neutralised surface roughening for Kt 1.4.

Fig. 6. The limit value of the closure stress to enhance the crack

arrest capacity of two different aluminium alloys for Kt 1.4 at

R 0.1. The values used are; 2024-T351: sFL 220,D 52m and7150-T651:sFL 270MPa,D 58m.

From Fig. 5, it is clear that the use of CSP components

at high stress ratios will require a significantly highermagnitude of closure stresses to neutralise the effect of

the surface roughness. In addition, Fig. 6 reveals that

CSP could have a more profound effect (in a sense that

it will be more feasible to achieve improvement) on thecrack arrest capacity of the materials that are character-

ised by low values of fatigue limit and smaller grain size.

The above-mentioned observation comes as a conse-

quence to the fact that fine grained materials are moresensitive to stress raisers.

2.2. CSP and fatigue life

In Ref. [25], de los Rios et al. proposed that the

fatigue life of polycrystalline materials can be determ-

ined by

N1

A2ic

i 1

ni

c

ni

s

(iD/ 2)1m2dni1

CTODm2(19)

where A2, m2 are the parameters from the Paris law of

crack propagation, CTOD, the crack tip opening dis-

placement and nis, and ni

c are the limit values of n1. InEq. (19) the parameters nisand n

i

crepresent, respectively,

the position of the crack tip at the beginning and end of

each interval i of crack growth. These two parameters

are calculated by

nic cos2

sspiarrests2

nis n

i2c

i2

i ,i 1 (20)

ni=1s 0.2


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wheres2 is theflow resistance of the material. The con-ditionni 1s 0.2 is justified in Ref. [17]. From Eq. (20)it is clear that the number of cycles required by the crack

to propagate throughout the ith grain, depends solely on

the parameter nic for the same CTOD.For CSP components, the parameter nic has to be

modified in a way that it would take into account theroughening of the surface and the crack closure stresses

nic cos2

s/Zi(spiarrest

)notchclosure

s2si

1 (21)

where the parameter Zi is identical to that used in Eq.

(2) and (spiarrest)notchclosure is given by Eq. (11). The applied

stresssis divided by Zi in order to increase the appliedstress due to the surface roughness. Determination of the

closure stresses needed to fully neutralise the surface

roughening effect can be achieved by equating Eq. (20)

with Eq. (21) and solving for si1

si1 s2i(1Zi)s

Zi((mi/m1)sFL i(s2s))(22)

In Eq. (22), the negative sign is to convert the residual

stress into compressive. To express Eq. (22) in terms

of crack length, knowledge of the crack tip plasticity is

required. In the case ofs s2, such condition is ful-filled by making use of the Dugdale plastic strip model[26]. According to Dugdale, the extent of fatigue dam-

age, ci, can be approximated by

c

i

i

D

2

a[sec(s/ 2s2)] (23)

hence,

i 2a[sec(s/ 2s2)]

D (24)

It should be noted that the strain hardening effect of

CSP has been intentionally neglected. Such disregard

can be justified by observing that: (a) the strain harden-ing due to CSP is usually less than the intrinsic harden-

ing of cyclically hardening materials; (b) strain harden-ing is usually limited to a depth close to the free surface

(for 2024-T351 that ranges to a depth of 200 m [25]);

and (c) solution of Eq. (22) would give conservative

results. Figs. 79, show the effect of different stress lev-els, different materials and different stress ratios on Eq.

(22). Fig. 7 shows that the amount of closure stressincreases with the applied stress. The analysis justifiesthe fact that CSP has little or no effect on the low cycle

fatigue region. Fig. 8 reveals the effect of different

mechanical and micro-structural properties on Eq. (22).

In general, CSP on materials with high values of cyclicyield stress is expected to have a more profound effect.

Such notion should not be generalised since different

materials could have different responses to CSP. Finally,

Fig. 7. Magnitude of the crack closure stress necessary to fully neu-

tralise the effect of surface roughness at different applied stress levels

for 2024-T351. The results were obtained considering Kt 1.4 and

R 0.1.

Fig. 8. Closure stress distribution for two different materials at

s 300MPa and Kt 1.4. Values of cyclic yield stress of 450 and495 MPa were, respectively, used for the 2024-T351 and the 7150-

T651 aluminium alloys.

Fig. 9 gives an indication towards the effect of stress

ratio on CSP components. According to Eq. (22), low

values ofsFL (low or negative R) would require highermagnitude of closure stresses and therefore would

reduce the beneficial effect of CSP.

3. Determination of the residual stress profile

The residual stress profile of CSP has been, in mostcases, successfully represented by the Robertson for-

mula [27]

Y Aexp2(xxd)2W2

B (25)where Y is the residual stress, x, the depth below the


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Fig. 9. The effect of stress ratio on the required closure stress for

2024-T351. The applied stress was 300 MPa and a Kt 1.4 was used.

surface,A B, the maximum residual stress, W, a meas-ure of the width of the curve and xd, is the depth to the

maximum residual stress. In Ref. [25], it was proposed

that integration of Eq. (25) can provide the correspond-

ing crack closure stress

s1 1

xx

0

Aexp2(xxd)2W2

B (26)where x is now the crack length. A typical profile ofresidual and crack closure stresses is shown in Fig. 10.

Due to the mathematical nature of the Robertsons for-

mula and the crack closure profile produced from theapplication of Eq. (22), a direct relationship between

Eqs. (26) and (22) is impossible to be defined accurately.To overcome such difficulty the following assumptionsare implemented: (a) B 0, rationalised by the fact thatthe residual stresses will realistically tend to zero with

Fig. 10. Residual and corresponding closure stress profiles according

to Robertson considering arbitrary values of A B 231.5MPa,

W 0.228mm and xd 0.190mm.

Fig. 11. Comparison between the requested closure stress profile pro-

vided by Eq. (22) and the exponential fitting in terms of Eq. (26). The

conditions are; 2024-T351: s 300MPa,R 0.1 and Kt 1.4. Thefitting parameters are: A 117MPa, W 0.1mm and xd

0.013mm.

depth, and (b) the parametersxdand A should be determ-

ined directly from Eq. (22). By implementing the above

assumptions, the application of a technique to providethe parameters A, W and xd is possible. The technique

is based on the iterativefitting of an exponential formulato Eq. (26). Completion of the iteration is achieved with

the interception of the two curves. The above condition

allows the minimisation of the fitting error. A typicaloutcome in terms of closure stress and residual stressprofile is depicted in Figs. 11 and 12, respectively.

4. Discussion and conclusions

In this work, surface roughness and residual stress dis-

tribution are considered to be the dictating parameters

that determine the performance of CSP in terms of

Fig. 12. The residual stress profile according to the fitting parameters

determined in Fig. 9.


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fatigue resistance. Operating under the assumptions that:

(a) the residual stresses will not relax; (b) strain harden-

ing is not significant in the case of cyclic hardenedmaterials; and (c) the stress gradient will not promote

sub-surface cracking, it is sound to argue that the com-pressive residual stresses are beneficial to fatigue resist-

ance, while surface roughening is expected to decreasethe fatigue life of the engineering components by

allowing the earlier initiation and faster propagation of

short fatigue cracks.In order to understand the competition between the

detrimental and beneficial effects of CSP, a boundarycondition was sought that would allow the total neutral-

isation of the surface roughening by the crack closure

stress profile. Such boundary was established using amicro-mechanical notch sensitivity model and the Nav-arrode los Rios model for crack propagation. Theapproach allows the determination of a closure stress

profile from which a corresponding residual stress profilecan be obtained. Making use of the advantages provided

by the micro-mechanical notch sensitivity model, the

effects of material and mechanical properties on the

boundary condition were analysed. From these analyses,

the following conclusions can be drawn regarding the

performance of CSP:

High values of stress ratio will promote fatigue life

improvement by CSP.

Low values of stress ratio will promote crack arrest

improvement by CSP.

The benefits from CSP are expected to be more sig-

nificant for conditions of high cycle fatigue (lowapplied stress levels).

In general, CSP is expected to increase the fatigue

life of high fatigue limit and yield stress materials.

Acknowledgements

The authors are indebted to the Royal Academy of

Engineering, The Engineering and Physical Science

Research Council, Airbus UK, and the technical staff of

SIRIUS for their support.

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