researcharticle shot peening effect on fatigue crack...

Research ArticleShot Peening Effect on Fatigue Crack Repaired Weldments

J. Efrain Rodriguez-Sanchez, Alejandro Rodriguez-Castellanos,and Faustino Perez-GuerreroInstituto Mexicano del Petroleo, Eje Central Lazaro Cardenas Norte 152, 07730 Ciudad de Mexico, Mexico

Correspondence should be addressed to J. Efrain Rodriguez-Sanchez; [email protected]

Received 1 March 2017; Accepted 10 April 2017; Published 30 April 2017

Academic Editor: Paolo Ferro

Copyright © 2017 J. Efrain Rodriguez-Sanchez et al. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Fracture mechanics calculations are required to validate the safety level defined in design codes to prevent a fatigue failure. Theperiodic inspection-assessment cycle can lead to the implementation of a fatigue crack repair by crack removal. To improve thefatigue performance of the crack repair, residual compressive stresses induced by peening can be considered.This paper is in relationto the peening effect estimation on stress intensity factors in fatigue crack repaired weldments, since the stress intensity factoris a key parameter in fracture mechanics calculations. A set of T-butt specimens were experimentally fatigue tested and crackpropagation data was gathered for the calculation of stress intensity factors.The experiments were designed to estimate the residualcompressive stress depth layer and its effect on crack propagation inhibition. Experimental estimation of the peening effect on stressintensity factors in fatigue crack repaired weldments was validated by comparison against an analytical weight function solution.Experimental stress intensity factors determined from a set of fatigue tested T-butt specimens allowed estimating preliminarilythat peening has a limited effect on fatigue crack propagation inhibition for edge repaired T-butt weldments subjected to bendingloading.

1. Introduction

Inspection of components subjected to fatigue loading canreveal fatigue cracks presence; thus, depending on the par-ticular component, the option of component replacement orrepair in situ is an issue. In the offshore industry, repair in situis the most feasible option, since offshore structures have tooperate continuously.

Alternative to joint clamping, a fatigue crack repair proce-dure based on the removal of cracked material by grindinghas been proposed for offshore structures [1–3]. The repairprofile has a predesigned geometry to reinstate a fatigue lifethat can be even larger than the as welded fatigue life.

Research on improvements to fatigue crack repair foroffshore structures incorporated metal filling of the groundnotch by dry or wet welding to improve the fatigue perfor-mance of the repaired weldment surface [4].

This paper describes the addition of compressive residualstresses by shot peening to the ground notch surface toimprove the fatigue performance of the repaired weldment. Itis expected that compressive stresses improve the fatigue

crack performance, since cracks grow due to the openingeffect induced by tensile stresses. This research is focused onthe estimation of the peening effect on stress intensity factors,since 𝐾 is a key input in fracture mechanics calculations forfatigue life predictions.

Analytical estimation of 𝐾 in weldments consideringresidual stresses is a complex task, since a distribution ofresidual stresses through the plate thickness during crackgrowth is required. For the case of a shot peened weldment,residual stresses are the result of adding residual stresses bywelding plus compressive residual stresses by shot peening.

The International Institute of Welding [5] recommendsfatigue tests for the verification of a procedure such as peen-ing in the endurance range of interest. Recommended upper-bound welding residual stress profiles for use in analyses aregiven in Structural Integrity Assessment Procedures forEuropean Industry [6–8].

Despite the uncertainty in estimating aweldment residualstress distribution, it is possible to estimate 𝐾 values for agiven crack location and geometry. Experimental measure-ments of residual stresses by neutron diffraction and X-ray

HindawiAdvances in Materials Science and EngineeringVolume 2017, Article ID 3720403, 11 pageshttps://doi.org/10.1155/2017/3720403

https://doi.org/10.1155/2017/3720403

2 Advances in Materials Science and Engineering

diffraction [9] can be done. The experimental residual stressdistribution is implemented in an analytical method and 𝐾can be determined.

The most common analytical approaches to calculate 𝐾values are the weight function method and the finite elementmethod.The weight function method has been used in manycases with welding residual stress distributions such as thoseproposed by Structural Integrity Assessment Procedures forEuropean Industry and stress intensity factors associatedwithwelding residual stresses (𝐾res) are determined [10].There aremore𝐾res calculations published [9–11] than peening residualstress intensity factors calculations [12, 13], where the conceptof cohesive zonemodel is usedwith the finite elementmethodto estimate compressive stress relaxation in shot peenedspecimens.

2. Peening

Peening is the process of impacting a metal surface causingplastic deformation in the surface. The impact objects can behard small particles, a bunch of needles, a simple hammer, ora laser beam and the process would be known as shotpeening, needle peening, hammer peening, or laser peening,respectively. The mechanisms of fatigue improvement usingpeening are cold work and residual compressive stress.

Cold work is used to improve the strength of metals byincreasing the surface hardness; however, the brittleness isalso increased and consequently there is a limit to whichcold working may be carried out without danger of fracture.Fatigue improvement by peening ismainly due to the residualcompressive stress rather than due to the coldwork hardeningprocess.

Residual compressive stress is probably the most impor-tant benefit of peening in terms of fatigue improvement.The residual stress is produced, since the surface layer ofmaterial is deformed beyond its yield point by peening;however, it cannot deform freely as the material underneathis not affected by the peening and therefore has not beenplastically deformed. So, a residual stress is kept in the surfacematerial due to the constraint imposed by the deeper layers.A graphical representation of this effect can be represented ina two-layer system [14] as shown in Figure 1.

Random high tensile loads, such as those that many com-ponents experience in service, reduce the beneficial effects ofpeening, since plastic deformation is caused at points of highstress concentration when the loading is applied.

Residual compressive stresses reduce the resultant rangeof fatigue stress and crack growth, since the applied tensilestress decreases when it is combined with the residualcompressive stress.Thus, residual compressive stress does notchange the applied stress range but increases 𝑅 ratio (mini-mum stress/maximum stress), since tensile maximum stressis reduced. However, there are still difficulties in makingquantitative predictions of the effect on fatigue life as a resultof a particular peening process. Fracture mechanics proce-dures have not been easily applied for peened components;moreover, peening has a greater effect on the crack initiationphase, where fracture mechanics cannot be applied.

Compression

Tension

Layer A

Layer B

Initial condition

Layer A lengthening by peening

Induced stresses to rejoin layersto be of the same length

Figure 1: Creation of residual stress in a two-bar system [14].

Dissipation effect of residual compressive stress in highyield stress materials is lower, since they can sustain highertensile loads before deforming plastically [4]. A peenedsurface is not smooth; thus, itmay cause crack starting points.Once a crack starts to propagate across the residually com-pressed layers, the magnitudes of the residual stresses areneeded to make predictions of crack growth, but there is nota generally reliable and practical method to obtain residualstress information.

If the shot peened component under consideration isachieving a reversed bending endurance limit close to 0.5 ofthe tensile strength in steels or 0.25 in other alloys, furtherimprovement by peening is unlikely. The maximum residualcompressive stress induced by shot peening is approximately60% of the ultimate tensile strength in compression [14].

Behaviour of cracks growing from a peened surface infatigue is that minute cracks already exist in the surface buttheir initial growth rate is considerably slower than thatof cracks which are eventually initiated in an as welded(unpeened) surface.The crack eventually starts to grow againprobably due to the residual stress relaxation by the imposedalternating stress [14].

The magnitude and depth of the residual stress field arethe major factors controlling the fatigue effect of peening andthese depend on the intensity of peening. For the case of shotpeening, the size of the pellets determines the depth of theresidual stress field [15] as can be seen in Figure 2.

Intensity will vary greatly with circumstances; one tech-nique used in a wide variety of circumstances is to peen aflat strip of metal on one side while it is clamped to thecomponent and then measure how much it curves when itis released. This is the Almen strip method. The strips haveto be of certain dimensions and have to be made frommetal with specified properties. Peening intensity is linkedto this curvature, which is easily measured, as an arc-height.Large curvatures and therefore large arc-height values gowith higher intensities. Almen strips are seen as a very goodway of monitoring consistency of a peening process but

Advances in Materials Science and Engineering 3

Surface stretched by the impact ofa high speed pellet

Unstretched core exerts acompressive force to restore thesurface to its original condition

Compression

Tension

d

d

2d

Figure 2:Depth of the residual stress field produced by shot peening[15].

not a fundamental way of comparing peening processeswith different parameters; hence, the same curvature can beobtained by a combination of different magnitudes of the fol-lowing parameters: time of exposure, blast pressure, and shotsize.

Hertzian pressure theory allows estimating the stressmagnitude and distribution due to the contact of two sur-faces; thus, this theory can be implemented to estimate stressmagnitude and distribution in a plate underneath a shotimpact. However, due to the nature of the shot peeningprocess, a shot can impingemore than once on the same placein a random manner; thus, it becomes difficult to predict theaccumulated impingement effect in terms of final residualstress magnitude and distribution underneath the deformedsurface by the Hertzian pressure theory. Therefore, exper-imental measurements by neutron diffraction and X-raydiffraction [9] methods are used to estimate compressiveresidual stresses produced by shot peening.

Most of the metal working processes (unless they arevery carefully controlled) have a detrimental effect on fatiguelife and resistance to stress corrosion cracking. Welding isthe worst of them: welding creates very high residual tensilestresses and introduces a mechanical stress concentrationarea, a very hard brittle layer, and an annealed area, all inthe heat affected zone (HAZ) adjacent to the weld metal.This combination can lower the fatigue strength to a smallpercentage of that of an integrally machined component(rather than welded). Peening can be applied to reduce thetensile stresses produced during the welding process improv-ing the performance of the component. Figure 3 shows a T-butt specimen used in the experimental work during shotpeening process and described in the following sections.

3. Fracture Mechanics Calculations

Fracture mechanics is a means to estimate whether or not adefect of given size will propagate under service loading andto calculate the degree of safety that the system owns againstfailure by fracture [21].

Fracturemechanics allows estimating the local conditionsof stress and strain around a crack in terms of global parame-ters such as load, shape and size of the crack, geometry of thecomponent, and material properties [22]. The most popular

Figure 3: T-butt welded specimen during shot peening process(blast suspended).

fracture mechanics parameter is the stress intensity factor(𝐾); it can characterise the stress field ahead of a sharp crackaccording to the linear-elastic fracture mechanics theory.

4. Determination of Stress Intensity Factors

Various methods for the determination of 𝐾 can be con-sidered ranging from the consultation of handbooks to theapplication of complicated mathematical analysis with inte-gral transforms and complex variables; numerical methodscan also be considered such as the finite element method andthe boundary element method and a final option can be theuse of experimental techniques.

This paper provides results from the extraction of Δ𝐾from experimental data; additionally, an analytical method isused to validate the experimental data. With the applicationof equipment able to provide crack growth measurementslike the ACPD, the crack growth rate per cycle 𝑑𝑎/𝑑𝑁 canbe determined experimentally and knowing the fatigue con-stants of the material𝐶 and𝑚, it is possible to apply Paris law[23] expressed in the following equation:

𝑑𝑎𝑑𝑁 = 𝐶 (Δ𝐾)

𝑚

Δ𝐾 = ( 1𝐶𝑑𝑎𝑑𝑁)1/𝑚

.(1)

Using crack growth data collected during experimentalfatigue testing of a component, the calculated stress intensityfactor would correspond to the specific conditions of loading,geometry of the component, and crack size variation duringthe test.

Life to failure can be determined rearranging the Parisequation proposed in the 1960s and still considered as themost widely accepted expression.

𝑁𝑓 = ∫𝑎𝑓

𝑎𝑖

𝑑𝑎𝐶 (Δ𝐾)𝑚 . (2)

𝑎𝑖 has an important impact on life to failure estimation from(2) and direct measurement of 𝑎𝑖 from welded specimens isimprecise as, for an edge crack, 𝑎𝑖 can vary along the specimenwidth where initiation can take place.Thus, life to failure wasdetermined directly from experiments when crack size pen-etrated through the full thickness.


Table 1: Data for experimentally tested T-butt specimens.

T-butt specimen Repair profile(mm) Shot peened

Specimenwidth(mm)

Thickness𝑇 (mm)

NotchSCF

Nominalstress(MPa)

𝐿𝑅(min/max)

Nominalstress range

(MPa)As welded No No 200 20 3.2 250 0.03 243Edge repaired 𝐷 = 4; 𝑅 = 2 No 200 30 3.4 82 0.1 74Edge repaired &shot peened 𝐷 = 4; 𝑅 = 2 Yes 200 30 3.4 112 0.1 101

The stress intensity factor rangeΔ𝐾 can also be expressedas

Δ𝐾 = 𝑌Δ𝜎√𝜋𝑎. (3)

Equation (3) is a general expression that can be applied toany crack geometry and loading mode by considering thecorresponding 𝑌 factor. The 𝑌 factor varies as a function ofvarious parameters.

For the calculation of the fatigue life of a crack repairedjoint by crack removal, the 𝑌 factor should include theparticular characteristics of the crack initiating in the repairnotch and propagating through the thickness of the structuralmember.𝑌 factors can be obtained as the product of different

effects and a recommended form is

𝑌 = 𝑌𝑠𝑌𝑤𝑌𝑒𝑌𝑔𝑌𝑘𝑌𝑚. (4)

For the calculation of 𝑌 factors, various methods have beendeveloped and can be broadly classified as empirical andanalytical methods.

5. Extraction of 𝑌 Factors fromExperimental Data

Empirical models are especially useful for the determinationof 𝑌 factors for complex structural models due to theanalytical difficulty in considering multiple factors that havean effect on crack growth and their interaction during crackgrowth evolution.

Crack growth experimental data presented here wasobtained from T-butt fatigue repaired specimens. Crackgrowth rates, stress intensity factor range, crack shape char-acteristics, and 𝑌 factors were determined. In general, crackgrowth rates and Δ𝐾 are determined for the deepest point onthe crack front for surface cracks and an average depth foredge cracks. Equations (5a), (5b), (6a), and (6b) were used toprocess the experimental data.

𝑑𝑎𝑖𝑑𝑁𝑖 = 𝐶 (Δ𝐾𝑖)

𝑚 (5a)

Δ𝐾𝑖 = [ 1𝐶 (𝑑𝑎𝑖𝑑𝑁𝑖)]

1/𝑚

. (5b)

Knowing values of Δ𝐾𝑖 and since Δ𝜎𝑖 is known as it isdefined for experimental purposes, a solution for 𝑌𝑖 factorscan be obtained rearranging (6a) into (6b):

Δ𝐾𝑖 = 𝑌𝑖Δ𝜎𝑖√𝜋𝑎𝑖 (6a)

𝑌𝑖 = Δ𝐾𝑖Δ𝜎𝑖√𝜋𝑎𝑖 . (6b)

𝑌 values are determined in this work for an as welded T-butt and fatigue crack repaired T-butt specimens to provideuseful understanding of fatigue crack growth of repairedconnections.

Parameters 𝐶 and 𝑚 in the Paris equation were set to𝐶 = 4.5 × 10−12 and 𝑚 = 3.3 for 𝑑𝑎/𝑑𝑁 in m/cycle and Δ𝐾in MNm−3/2. These values correspond to the upper boundobtained from a least squares geometric regression fromexperimental results obtained for BS 4360 50D steel in alaboratory air environment; minimum yield strength forthickness over 16mm is 355MPa [24].

6. Application of Compressive ResidualStresses for Fatigue Improvement

The application of compressive residual stresses to reducethe magnitude of tensile stresses on the repaired surfacesto improve the fatigue life of repaired connections wasinvestigated. The shot peening technique was consideredamong needle peening and hammer peening due to its wideindustrial application.

This paper aims to estimate 𝑌 factors produced by peen-ing on a crack repaired component. The repair procedure isextensively described in [1, 16] and is based on the removalof the cracked material by grinding during early crackpropagation stage.The repair profile is based on a selection of𝐷, 𝑅, and repair length to design a specified geometry toreinstate a fatigue life that can be even larger than the aswelded fatigue life.

7. Experimentally Determined 𝑌 FactorsTable 1 shows the shot peened and repair profile data for theexperimentally tested T-butt specimens under pure bendingloading. The geometry of the experimentally tested T-buttspecimens, weld toe crack initiation location, and edge regionwhere repair and peening are applied is shown in Figure 4.

Based on 𝐷 and 𝑅 dimensions selected for the crackremoval, semicircular orU-shaped notches are produced. For


Weldment

Weld toeEdge repair region

30mm

30mm

400mm

200mm

Figure 4: T-butt dimensions showing edge repair region and weldtoe.

the𝐷 ≤ 𝑅 case, a semicircular repair is produced and, for𝐷 >𝑅, a U-shaped repair is produced. A graphical description ofthe U-shaped repair profile 𝐷 = 4, 𝑅 = 2 experimentallytested, based on Table 1 data, is shown in Figure 5.

A four-point bending set-up was used for fatigue testing,since it produces a constantmoment distribution between thetwo internal loading points. The set-up consists basically of atop and bottom set of rollers which are bolted to a framework.The bottom set of rollers sits on a plate which has a hingeconnection on top of the actuator. The hinge has the purposeof adjusting the set-up with the specimens.This adjustment isespecially important in a four-point bending set-up to assurethat each roller applies equal load to the specimen. The topset of rollers is fixed to the loading machine framework. Thefatigue load is applied with a 1 Mega-Newton servohydraulicactuator controlled with a load or position controller (seeFigure 6). Tests were performed under load control, so evenwhen stiffness of the specimen changed as crack grows, themagnitude of the load cycle applied did not change.

Crack depth evolution was monitored from early stagesof growth using the ACPD technique.The technique requiresthe injection of an alternating current on the surface ofthe specimen. The current follows the contour of surfacebreaking defects like cracks and since the potential gradienton the metal surface and on the crack faces is assumed tobe linear, measurements of the potential difference across thecrack and adjacent to the crack can be used for the calculationof the crack depth.

Experimental data for the T-butt fatigue tests is shown inTable 1; data details are as follows: tested specimens are codedas follows: as welded, edge repaired, and edge repaired andshoot peened. Repair profile dimensions define repair geom-etry type: U-shaped (𝐷 > 𝑅) or semicircular (𝐷 ≤ 𝑅) (seeFigure 5); the repair geometry used for the experiments wasU-shaped𝐷 = 4 and 𝑅 = 2. Edge repaired and shoot peenedspecimen has a repair profile with compressive residualstresses induced by shot peening. Specimen width is the totalweld length along which at the weld toe edge repairs aremachined, peening is applied, and edge cracks grow. NotchSCF is at the weld toe for the as welded specimen and in thebottom of the edge repairs where the crack initiates. Nominalstress is the stress unaffected by weldment, weld toe, and

repair profile (see Figure 4).𝑅 is the ratio of min tomax loadsapplied for testing. Nominal stress range is the differencebetween the max testing stress and min testing stress in astress cycle unaffected by SCFs.

Cracks initiated along the specimen width at the weld toefor the as welded specimen and in the bottom of the repairprofiles for the edge repaired specimens. Initial crack size 𝑎𝑖was not measured for fatigue life estimation purposes sincethe total fatigue life was experimentally determined whencrack depth penetrated through the plate thickness. A fatiguelife initiation to total fatigue life ratio of 0.2 was experimen-tally determined for the as welded specimen. Figure 7 showsa slice of a T-butt edge repaired specimen after fatigue testing;edge crack depth can be seen through the thickness but cracklength along the edge repair is imperceptible for the nakedeye.This is a relevant issue regarding fatigue crack inspection,since fatigue cracks cannot be detected on a routine surfacevisual inspection but crack depth can be almost through thefull thickness.

Figure 8 shows fatigue crack growth versus number ofload cycles for fatigue tested specimens. Crack growth rateand total fatigue life are different for the three specimens sincethey were designed with different features according to theobjective of this research (see Table 1).

Figure 9 shows plots of 𝑑𝑎/𝑑𝑁 versus crack depth andFigure 10 show plots of Δ𝐾 versus crack depth for the threetested specimens; it can be seen that the effect due to thedifferences between the specimens is consistent with Figure 8.A weight function flat plate curve is shown in Figures 9 and10 which is explained further on when experimental resultsare validated.

Even though different nominal stress rangeswere used fortesting, experimental data allow estimating the compressivestress effect induced by peening on fatigue crack. Although𝑌 factors do depend on load type, they do not depend onload level; thus 𝑌 factors were extracted and compared fromexperimental data, as explained when (6b) was introduced.

The hypothesis of the experiment was to consider the “aswelded T-butt” specimen tested in an as welded conditionas a reference for 𝑌 factors comparison. Thus, the 𝑌 factorsobtained from the “edge repaired T-butt” are expected tobe lower than the 𝑌 factors determined from “as welded T-butt” specimen, since the repair notch removed surface welddefects and the notch geometrywas designed to have a similarSCF compared to the “as welded T-butt” specimen (seeTable 1). Finally, 𝑌 factors from “edge repaired + shot peenedT-butt” specimen are expected to be lower than 𝑌 factorsdetermined from “edge repaired T-butt” specimen, sinceboth specimens have the same notch repair geometry; thusSCFs are the same but induced compressive stresses by shotpeening tend to inhibit crack initiation and crack propagationuntil a certain depth.

Experimentally determined 𝑌 factors are shown in Fig-ure 11. The experimental 𝑌 values obtained from each one ofthe T-butt specimens in Table 1 provided information to val-idate the previously stated hypothesis as it is explained in thefollowing section and also allowed the estimation of thecompressive stress depth effect induced by shot peening.


Weld toe Weld toe

Repair profileD4R4

Repair profileD4R2

Weldment Weldment

T

U-shaped notch (D > R)Semicircular notch (D ≤ R)

D = 4mm

R = 2mm

D = 4mm

R = 4mm

Figure 5: Semicircular and U-shaped repair profiles and dimensions.

Actuator

Specimen

Fixed

35.0mm

340.0mm

35.0mm

Figure 6: Loading set-up for fatigue testing.

From Figure 11, 𝑌 factors for the “edge repaired + shotpeened T-butt” specimen are lower than the𝑌 factors of “edgerepaired T-butt” specimen. Since the only difference betweenthese specimens is that the first one has a compressive stresslayer induced by shot peening, it can be estimated that thereis a crack initiation inhibition effect induced by the shotpeening compressive stresses. However, once the crack ini-tiates and propagates, there is a certain depth where the

Edge cracks

WeldmentEdge repair

30mm

30mm

Figure 7: Slice of fatigue tested T-butt edge repaired specimen.

0

2

4

6

8

10

12

14

16

18

Edge repaired + shot peened T-buttEdge repaired T-buttAs welded T-butt

N (cycles)

a(m

m)

2.5E + 052.0E + 051.5E + 051.0E + 055.0E + 040.0E + 00

Figure 8: Fatigue crack growth versus number of load cycles forfatigue tested specimens.


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

da/d

N (m

m/c

ycle

)

As welded T-buttEdge repaired T-butt

Edge repaired + shoot peened T-buttWeight function flat plate

a/T

1.0E − 03

1.0E − 04

1.0E − 05

1.0E − 06

1.0E − 07

Figure 9: 𝑑𝑎/𝑑𝑁 versus crack depth for fatigue tested specimens.

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4a/T

As welded T-buttEdge repaired T-butt

Edge repaired +shot peened T-buttWeight function flat plate

ΔK

Mpa

(m)1

/2

Figure 10: Δ𝐾 versus crack depth for fatigue tested specimens.

compressive stress layer effect is null; thus the𝑌 factors for the“edge repaired + shot peened T-butt” specimen are similar tothe ones of the “edge repaired T-butt” specimen. For this par-ticular experiment, 𝑌 factors for the edge repaired specimenstend to be similar from 𝑎/𝑇 > 0.07. Since the only differencebetween these specimens is the compressive stress layerinduced by shot peening, it can be estimated that the com-pressive stress layer depth is 𝑎 = 0.07𝑇. For the “edge repaired+ shot peened T-butt” specimen, the plate thickness toconsider is 𝑇 minus 4mm since crack initiation takes placeat the bottom of the repair notch. Thus, the estimated com-pressive stress layer is 0.07(30 − 4) = 1.8mm for 𝑇 = 30mm.

Edge repaired specimens had a repair notch 𝐷 = 4mmand 𝑅 = 2mm at the weld toe along the total specimen width.These specimens were fatigue tested until failure and it wasfound that an edge crack developed at the bottom of thenotch. The crack started almost simultaneously all along the

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Y

0 0.07 0.14 0.21 0.28 0.35 0.42

a/T

As welded T-buttEdge repaired T-buttEdge repaired +shot peened T-butt

Weight function flat plateCompressive stress depth effect

Figure 11: Experimental 𝑌 factors and estimation of residualcompressive stress depth effect.

specimen width at the bottom of the notch, confirming thelocation of crack initiation and the area where shot peeninghas to be applied. This finding also confirms that it is notrequired to shot peen the walls of the repair notch, sincecracking does not initiate there. This situation neglects therelevance of the impossibility that the striking material doesnot hit the walls of the notch at 90 degrees due to interferenceproduced by the opposite wall when directing the nozzle tothe target wall (see Figures 4 and 5).

8. Compressive Residual Stress Depth

Considering that the only difference between the “edgerepaired + shot peened T-butt” and “edge repaired T-butt”specimens is the compressive stress layer induced by shotpeening, the compressive stress layer depth has been esti-mated from Figure 12 as the depth from which 𝑌 factors aresimilar. From the experimental results, the compressive stresslayer has been estimated in the order of 1.8mm for BS 436050D used for the T-butt.

From a literature review, compressive residual stressdistribution is reported byHoffmeister et al. [16] for a residualstress relaxation study in shot peened samples made of Ni-based superalloy IN718 and by Tosha [17] for a study on theeffect of shot peening on surface integrity and residual stressdistributions induced by shot peening for a medium carbonsteel (S45C) and a carburized steel (SCM415). Residualstresses were measured by X-ray diffraction stress analyses.Although the objective of the first study is to determine therelaxation effect varying the temperature and time for stressrelieve, Figure 12 provides the residual stress distribution atroom temperature (RT) before residual stress is relieved; themaximum shot peening residual stress is at depth 𝑋max =70 𝜇m and the depth where residual stress is nil is at 𝑋0 =220𝜇m. For the second study, Figure 13 shows shot peeningresidual stress distributions varying shot diameter (𝐷) and


0

−200

−400

−600

−800

−1000

−1200

Resid

ual s

tress

𝜎RS

(MPa

)

0 50 100 150 200 250

Distance from the surface (𝜇m)

RT, t = 0hT1, t = 100hT3, t = 100hT5, t = 1hT5, t = 100h

Xmax X0

Figure 12: Shot peening residual stress depth distributions forvarious heat relaxation treatments (RT: room temperature; 𝑋max =70 𝜇m and𝑋0 = 220 𝜇m) [16].

Residual stress (Mpa)

Dep

th b

elow

surfa

ce (m

m)

−1200 −800 −400 00

0.1

0.2

0.3

0.4

0.5

0.6

SCM415

P: 3 atmD: 0.92mm

SCM415

P: 3 atmD: 0.39mm

S45C

P: 5 atmD: 0.16mm

Figure 13: Residual stress distributions induced by shot peening fora medium carbon steel (S45C) and a carburized steel (SCM415) [17].

blast pressure (𝑃); it can be seen that for the mediumcarbon steel (S45C) the residual stress is nil at approximately0.2mm depth. For the carburized steel (SCM415) the stressdistribution plot does not show the depth where the residualstress is nil; it can be deduced that it is definitively deeper than0.6mm.

Direct comparison of experimentally determined shotpeening compressive stress layer of 1.8mmwith shot peeningcompressive stress layers reported by Hoffmeister et al. [16]and by Tosha [17] is not feasible, since shot peening data

1.2

1.0

0.8

0.6

0.4

0.2

Y

0.0 0.4 0.8 1.2 1.6 2.0

a

Notchbending

R/T0.25

0.125

1

0.0625R/T

0.25

0.125

0.0625

SCF2.96

2.80

2.87

M

R

a M

T

Figure 14: Weight function 𝑌 factors for an edge crack at a sem-icircular notch in an infinite plate subjected to in plane bending [18].

like time of exposure, shot size, and blast pressure whichdetermine the residual stress depth distribution cannot becorrelated.

Thus, validation of experimental results would be done bycomparison against weight function 𝑌 factors.

9. Weight Function versusExperimental 𝑌 Factors

In order to validate the experimental results, analytical𝑌 factors were determined by using the weight functiondeveloped byWu and Carlsson [18] presented in Figure 14 fora similar edge repair profile used in the experimentally testedspecimens under bending load. From Figure 14, it is possibleto identify that 𝑌 factors do not depend on load level but dodepend on load type which is bending for the case studied.

The weight function corresponds to an edge crack at asemicircular notch in an infinite plate. FromFigure 14, weightfunction 𝑌 factors consider 𝑅 centre on the surface of theplate; thus, given 𝐷 = 4mm, the 𝑅 value has to be 4mm (seeFigure 5). On the other hand, the repair profile used for theexperiments is𝐷 = 4mm and𝑅 = 2mm, which is a U-shapedrepair notchwith𝑅 centre 2mmbelow the surface of the plate(see Figure 5). Thus, 𝑌 factors by the weight function weredetermined for𝐷 = 4mm and𝑅 = 4mmnotch geometry andcompared with the experimentally determined 𝑌 factors for𝐷 = 4mm and 𝑅 = 2mm repair notch as shown in Figure 11.

There are two main differences between the weightfunction model shown in Figure 14 and the experimentallytested T-butt specimens: (1) weldment effect: available weightfunction 𝑌 factors data is for edge repaired flat plates andexperimental 𝑌 factors data correspond to repaired T-butts;(2) notch geometry: weight function 𝑌 factors data is for a


0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14

SCF

As welded SCFs

0.010.020.040.066

weld angle = 45∘T = thickness = 30

r = weld toe radius

r/T bending

D = 4mmD = 6mmD = 8mm

(R) Repair radius (mm)

SCFs bending loading modeT-butt with semicircular or U-shaped edge repairs

4.363.502.922.38

Figure 15: Stress concentration factors for a T-butt with semicircular and U-shaped edge repairs under bending loading [19].

semicircular notch and experimental data correspond to a U-shaped notch edge repair.

It is expected that the weight function𝑌 factors values arelower than the experimental T-butt𝑌 factors values shown inFigure 11, since theweight function𝑌 factors correspond to aninfinite flat plate; thus, they do not have the stress concentra-tion effect produced by the T-butt weldment.

Despite the two main differences mentioned, the weightfunction 𝑌 factors data allow validating the experimentalresults, since both data sets follow a similar distribution asshown in Figure 11 and an explanation of magnitude differ-ences has been identified and described as follows:

(1) Weldment effect: edge repaired flat plates versus T-butts 𝑌 factors. The experimental 𝑌 factors weredetermined from crack data recorded in the bottomof U-shaped edge repairs. The U-shaped edge repairsremoved the weld toe; thus, the weld toe effect iserased and the only weld effect that remains is due tothe weldment geometry (see Figure 5).Analytical findings on notch repair geometryreported by Rodriguez et al. [19] confirmed that theweld toe effect is erased in a weld notch repair andthe weldment geometry effect is reduced as the repairradius increases.From Figure 15, the fatigued specimens with repairgeometry𝐷 = 4mm and 𝑅 = 2mm have an SCF = 3.4which is higher than SCF= 2.9 that corresponds to theaverage SCF value of a flat plate weight function solu-tion 𝐷 = 4mm and 𝑅 = 4mm (see Figure 14). Thus,experimental 𝑌 factors are expected to be moderatelyhigher than estimated by the weight function untilthe weldment effect is nil as crack depth propagatesthrough the thickness, as can be seen in Figure 11 for𝑎/𝑇 > 0.20.

(2) Notch geometry: semicircularweight function versusU-shaped experimental 𝑌 factors. The concept of equiv-alent notch configurations establishes that, for anygiven notch geometry, there is always an equivalent Unotchwith the samemaximumstress at the notch root[20] (see Figure 16). Thus, SCF values from U-shapedand semicircular notches are equivalent, given that𝐷and 𝑅 values are the same for both cases.

The repair geometry difference between the experimentalwork and the weight function is due to increasing 𝑅 from 2to 4mm, respectively (see Figure 5). From Figure 15, it can beobserved that, for 𝐷 = 4mm as used in the experiments andin the weight function, a change in 𝑅 from 2mm to 4mmprovides a SCF reduction from 3.4 to 2.9 which is a 15% stressdifference. Therefore, it is expected that the weight function𝑌 factors are moderately lower than obtained experimentallywithin the range where weldment and notch geometry havean influence 0 < 𝑎/𝑇 < 0.20 (see Figure 11). As crack propa-gates through the thickness, the weldment and notch geom-etry effect on 𝑌 factors fade out and beyond 𝑎/𝑇 > 0.17weldment and notch geometry have no influence on crackpropagation; thus experimental andweight function𝑌 factorsare the same.

10. Discussion

A T-butt welded edge repaired weight function solution isnot available in the published literature; the most similaravailable solution corresponds to an edge repaired flat plate.The absence of weldment geometry leads to an approximateSCF reduction of 18% at the notch compared to the T-buttcase (flat plate from Figure 14, D4R4, 𝑇 = 30, SCF = 2.8; andT-butt from Figure 15, D4R2, 𝑇 = 30, SCF = 3.4); thus, flatplate𝑌 factors are lower in early stages of crack growth. Once


𝛼

(a) (b) (c)

(d) (e)

𝛼 𝛼

Figure 16: Equivalent notch configurations [20].

the crack propagates, the weldment SCF influence decreasesand 𝑌 factors for the flat plate weight function and T-buttexperimental data tend to merge for 𝑎/𝑇 > 0.20 as shownin Figure 11.

Although weight function data versus T-butt experi-mentally determined 𝑌 factors have two main differences,weldment effect and notch geometry, the experimental resultsshowed that the weldment and notch geometry effectsbecome nil as crack propagates through the thickness 𝑎/𝑇 >0.20 (see Figure 11), thus validating the experimentally deter-mined 𝑌 factors.

Based on validated 𝑌 factors experimental data, dif-ference between “edge repaired + shot peened T-butt” and“edge repaired T-butt” specimens is the compressive stressdistribution layer induced by shot peening and included in𝑌 factors as 𝑌𝑔. However, it is not possible to estimate 𝑌𝑔isolated effect. From Figure 11, it is possible to estimate alayer of 1.8mm depth where the residual compression stressinduced by peening has a retardant influence on crack growthin fatigue crack repaired weldments. This finding cannot beextrapolated due to the reduced sample of repaired T-buttspecimens tested. For a future research, it is recommended toextend the scope of the experimental work to investigate theeffect of parameters such as time of exposure, blast pressure,and shot size in the residual compressive stress induced byshot peening.

A relevant observation regarding life extension of fatiguecracked welds by notch repair can be derived from theanalysis of experimental SCF data reported in this work. Therepair geometry𝐷 = 4mm and𝑅 = 2mmhas an approximateSCF = 3.4 (see Figure 15), and this value is close to an averagevalue of an as welded T-butt SCF = 3.2 (see right-hand sidebox in Figure 15).Thismeans that, by appropriately designinga repair geometry, the repaired profile SCF can be similarto the as welded condition. A comparison of the as weldedand repaired profiles SCFs in Figure 15 shows the possibilityto identify repair notch dimensions with even lower SCFvalues than in as welded condition. For example, the repairgeometry 𝐷 = 4mm and 𝑅 = 2mm has a SCF = 3.4 which

is lower than a SCF = 4.36 that corresponds to 𝑟/𝑇 = 0.01 aswelded T-butt.

11. Conclusions

Stress intensity factors for a set of as welded, edge repairedpeened, and edge repaired unpeened T-butt specimens wereexperimentally determined. The as welded T-butt specimenprovided the base line of stress intensity factors to comparewith. Stress intensity factors from peened and unpeenededge repaired T-butt specimens allowed depth estimationof compressive residual stresses induced by peening in afatigue crack repair notch. A residual compressive stresslayer of 0.07 of the plate thickness was estimated for thefatigue tested specimens. This finding cannot be extrapo-lated, since the residual stress compressive layer induced bypeening depends on time of exposure, blast pressure, andshot size; thus, these three parameters can vary for eachpeening application. Experimental estimation of the peeningeffect on stress intensity factors in fatigue crack repairedweldmentswas validated by comparison against the analyticalweight function solution for an edge repaired flat plate.From experimental comparison of stress intensity factors, apreliminary estimate is that peening has a limited effect oncrack propagation inhibition for fatigue crack repaired T-buttspecimens subjected to bending loading.

Nomenclature

𝑎: Crack depth𝑎𝑖: Initial crack length𝑎𝑓: Final crack lengthACPD: Alternating Current Power Drop𝐶: Material constant𝑑: Pellet diameter𝐷: Repair depth𝑑𝑎/𝑑𝑁: Crack growth rateHAZ: Heat affected zone𝑚: Material constant


𝑁𝑓: Cycles to failure𝑌: Modification factor (𝑌 factor)𝑌𝑖: 𝑌 factor “𝑖”𝑌𝑠: Correction for a free front surface𝑌𝑤: Correction for finite plate width𝑌𝑒: Correction for crack geometry𝑌𝑔: Correction for nonuniform stress field𝑌𝑘: Correction for the presence of geometrical

discontinuity𝑌𝑚: Correction for changes in structural restraint𝐾: Stress intensity factor𝐾res: Residual stress intensity factor due to welding

processΔ𝐾: Stress intensity range𝐾max–𝐾minΔ𝐾𝑖: Stress intensity range “𝑖”𝑁𝑖: Number of cycles at Δ𝐾𝑖 and 𝑎𝑖𝑟: Weld toe radius𝑅: Repair radius𝐿𝑅: Minimum load/maximum loadSCF: Stress concentration factor𝑇: Plate thickness𝑊: Plate widthΔ𝜎: Surface stress range of uncracked welded joint

at the crack siteΔ𝜎𝑖: Surface stress range “𝑖” of uncracked welded

joint at the crack site𝛼: Repair orientation.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

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