Does notch sensibility exist in environmentally assisted cracking (EAC)?

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j m a t e r r e s t e c h n o l . 2 0 1 3;2(3):288–295

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Review article

Does notch sensibility exist in environmentally assistedcracking (EAC)?

Jaime T. Castro, Julio Cesar Costa Leite ∗

Mechanical Engineering Department, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

a r t i c l e i n f o

Article history:

Received 21 November 2012

Accepted 7 February 2013

Available online 27 July 2013

Keywords:

Short cracks

Non-propagating cracks

Environmentally assisted cracking

a b s t r a c t

Empirical notch sensitivity factors q have been used for a long time to account for notch

effects in fatigue design. This old concept has been recently modeled using sound mechan-

ical principles to properly quantify the influence of the stress gradient around the notch

tip on the fatigue behavior of mechanically short cracks. This model can be used to cal-

culate q values from the basic fatigue resistances of the material, its fatigue limit and its

crack propagation threshold, considering all the characteristics of the notch geometry and

of the loading. This model predictions have been validated by proper tests, and based on

this experimental evidence a criterion to accept tolerable short cracks has been proposed.

In this work the mechanical principles that support this criterion are extended to account

for notch effects in environmentally assisted cracking problems.

© 2013 Brazilian Metallurgical, Materials and Mining Association. Published by Elsevier

Editora Ltda. All rights reserved.

1. Introduction

Semi-empirical notch sensitivity factors 0 ≤ q ≤ 1 are widelyused in mechanical design calculations to correlate material-independent linear elastic (LE) stress concentration fac-tors (SCF) Kt = ��/��n, to the actual notch effect on thefatigue strength of structural components, which partic-ularly for sharp notches can be much smaller than Kt

[1]. This is done by using the corresponding fatigue SCFKf = 1 + q · (Kt − 1) = �SL(R)/�SLntc(R), where �� = �max − �min isthe stress range acting at the notch tip; �max and �min are themaximum and minimum LE stresses caused by ��n at the
notch tip; ��n is the nominal stress range that would act atthat point if the notch did not affect the stress field around itstip; and �SL(R) and �SLntc(R) are the fatigue limits measured,
∗ Corresponding author.E-mail addresses: [email protected], [email protected].

2238-7854/$ – see front matter © 2013 Brazilian Metallurgical, Materials and Mhttp://dx.doi.org/10.1016/j.jmrt.2013.02.010

respectively, on standard (i.e. smooth and polished) and onnotched fatigue test specimens (TS) at a given R = �min/�max

ratio.It has been known for a long time that q is associated with

the relatively fast generation of tiny non-propagating fatiguecracks at notch tips if �SL(R)/Kt < ��n < �SL(R)/Kf, see Fig. 1 [2].Therefore, it can be expected that the notch sensitivity q can bepredicted from the fatigue behavior of short cracks emanatingfrom notch tips.

This indeed has been recently achieved by a model basedon relatively simple but sound mechanical principles, whichdo not require heuristic arguments, or any arbitrary data-fitting parameters [3–5]. The main feature of this model is

br (J.C.C. Leite).

to clearly identify that not only the SCF of the notches, butalso the gradients of the stress fields induced by them aroundtheir tips, can significantly affect the fatigue crack propagation

ining Association. Published by Elsevier Editora Ltda. All rights reserved.

dx.doi.org/10.1016/j.jmrt.2013.02.010

http://www.jmrt.com.br

mailto:[email protected]

mailto:[email protected]

dx.doi.org/10.1016/j.jmrt.2013.02.010

j m a t e r r e s t e c h n o l . 2 0 1 3;2(3):288–295 289

160

140

120

100

80

60

40

20

1 2 3 4 5 76 8 9 10 11 12 13 14 150

1020 steel,σm=σres=0,V55º/5mm notchspecimen fracturenon-propag.short cracksplate 36×7.6mm with 2V-notchescilinder d=43mm with 1 circunf.notch

plate tension/comp.cil.rotating bending

plate tension/comp.cil.rotating bending

specimen fracture

σna(MPa)

SLKt

non-propagating cracks

no cracks

Kt

Fig. 1 – Classical data showing that non-propagatingfatigue cracks are generated at the notch roots ifS

(toptsqqsttb

fdsItnp�

tr

sHsaKmc

�

SgS

1000800

600500400

300

200

100

0.05 0.1 0.2 0.5 1.0 2.0 5.0 1080

Δσ(MPa)

Δσ=ΔΚ0

HT80 steel,ΔK0=11.2MPa√m

ΔS0=575 (fatigue limit)

√

√

π(a+a0)

Δσ=ΔΚ0

ΔK0/ΔS0)2/π=0.12

πa

(ETS model)

(long crackthreshold)

a(mm)

non-propagating cracks

a0=(

Fig. 2 – Kitagawa–Takahashi plot describing the fatigue

a


L/Kt < �n < SL/Kf at R = 0 [1,2].

FCP) behavior of short cracks emanating from such tips. Inhis way, for any given material, the q value depends not onlyn the notch tip radius �, but also on its other geometricalarameters, in particular on its depth b. This means that con-rary to what is predicted by traditional empirical q-curves,hallow and elongated notches of same tip radius � may haveuite different notch sensitivities q. Note, however, that theualifier “short” is used here to mean “mechanical” not “microtructural” small cracks, since material isotropy is assumed inheir modeling. This simplified hypothesis is corroborated byhe tests, when the “characteristic short crack size” definedelow is not small compared to grain size of the material.

To understand why it is important to care about shortatigue cracks, it is necessary to realize that they must behaveifferently from long cracks, since their FCP threshold must bemaller than the traditional long crack threshold �Kth(R) [6].ndeed, otherwise the stress range �� required to propagatehem would be higher than the material fatigue limit �SL(R), aon-sense. In fact, assuming as usual that the FCP process isrimarily controlled by the stress intensity factor (SIF) rangeK ∝ ��

√(�a), if short cracks with a → 0 had the same �Kth(R)

hreshold of long cracks, their propagation by fatigue wouldequire �� → ∞, a physical impossibility.

The FCP threshold of short fatigue cracks under pul-ating loads �Kth(a, R = 0) can be modeled using Eladdad–Topper–Smith (ETS) characteristic (short crack)

ize a0 [7], which is estimated from �S0 = �SL(R = 0)nd �K0 = �Kth(R = 0). This clever trick reproduces theitagawa–Takahashi plot trend [8] (see Fig. 2), using aodified SIF range �K′ to describe the fatigue propagation

onditions of any crack, short or long, defined by:

K′ = ��√

�(a + a0), where a0 =(

1�

)(�K0

�S0

)2(1)

As ETS �K′ has been deduced using the Griffith’s plate
IF, �K = ��
√(�a), it is necessary to use the non-dimensional

eometry factor g(a/w) which complements the generalIF expression [9], �K = ��

√(�a) · g(a/w), to deal with other

propagation of short and long cracks under pulsating loadsin a HT80 steel with �K0 = 11.2 MPa

√m and �S0 = 575 MPa.

geometries, re-defining:

�K′ = g

(a

w

)· ��

√�(a + a0), where

a0 =(

1�

)[�K0

g(a/w) · �S0

]2(2)

But the tolerable stress range �� under pulsating loads onlytends to the fatigue limit �S0 when a → 0 if �� is the notchroot (instead of the nominal) stress range. However, the g(a/w)expressions found in most SIF tables usually include the notchSCF, thus they use �� instead of ��n as the nominal stress.A clearer way to define the short crack characteristic size a0

when it departs from a notch tip is to explicitly recognize thistraditional practice, separating the geometry factor g(a/w) intotwo parts: g(a/w) = � · ϕ(a), where ϕ(a) describes the stress gra-dient ahead of the notch tip, which tends to the SCF as thecrack length a → 0, whereas � encompasses all the remainingterms, such as the free surface correction. Therefore,

�K′ = � · ϕ(a) · ��√

�(a + a0), where a0 =(

1�

)[�K0

� · �S0

]2(3)

However, both from conceptual and operational point ofviews, the short crack problem can be better and easily treatedby letting the SIF range �K retain its original equation, whilethe FCP threshold expression (under pulsating loads) is modi-fied to become a function of the crack length a, namely �K0(a),resulting in

�K0(a) = �K0 ·√

a

a + a0(4)

The ETS equation can be seen as one of many possibleasymptotic matches between the short and long crack behav-iors. Following Bazant’s idea [10], a more general equation canbe used introducing an adjustable parameter � to fit experi-mental data, see Fig. 3:

�K0(a) = �K0 ·[

1 +(

a0)�/2

]−1/�

(5)

Eqs. (1)–(4) result from Eq. (5) if � = 2. The bi-linear limit,��(a ≤ a0) = �S0 for short cracks, and �K0(a ≥ a0) = �K0 for the

290 j m a t e r r e s t e c h n o l

1.0

0.5

0.2

0.10.01 0.1 10 1001

a/a0

ΔK0(a)

ΔK0

ΔK0(a)

ΔK0

=[1+(a0/a)γ/2]−1/γ

γ =8

γ =2

γ =1.5

Fig. 3 – Ratio between short and long crack propagation


thresholds as a function of a/a0.

long ones, is obtained when g(a/w) = � · ϕ(a) = 1 and � → ∞. Mostshort crack FCP data are fitted by �K0(a) curves with 1.5 ≤ � ≤ 8,but � = 6 better reproduces classical q-plots based on data mea-sured by testing semi-circular notched fatigue TS [3–5]. UsingEq. (5) as the FCP threshold, then any crack departing from anotch under pulsating loads should propagate if:

�K = � · ϕ

(a

�

)· ��

√�a > �K0(a) = �K0 ·

[1 +

(a0

a

)�/2]−1/�

(6)

where � = 1.12 is the free surface correction. As fatigue dependson two driving forces, �� and �max, Eq. (6) can be extended toconsider �max (indirectly modeled by the R-ratio) influence inshort crack behavior. First, the short crack characteristic sizeshould be redefined using the fatigue limit �SR and the FCPthreshold for long cracks �KR = �Kth(a aR, R), both measuredor properly estimated at the desired R-ratio:

aR =(

1�

)[�KR

1.12 · �SR

]2(7)

Likewise, the corresponding short crack FCP thresholdshould be re-written as:

�KR(a) = �KR ·[

1 +(

aR

a

)�/2]−1/�

(8)

Following the basic ideas exposed above, the aim of thiswork is to extend this stress analysis to environmentallyassisted cracking (EAC) problems, where the notch effects canbe as important as they are in fatigue. Although the approachused here is primarily mechanical, the corrosion influence insuch problems is by no means neglected on this model, sincethey are taken into account by their deleterious effect on theEAC resistance of the material.

2. Behavior of short cracks departing fromslender notches

Before jumping into more elaborated mechanics, it is worthto justify using relatively simple arguments why small cracksthat depart from notch roots can propagate for a while before

. 2 0 1 3;2(3):288–295

stopping and becoming non-propagating under fixed loadingconditions. This fact may appear at first sight to be a para-dox, since cracks are sharper than notches, and thus havehigher SCF. In fact, it is not unreasonable to think that if a givenfatigue load can start a crack from a notch, then it should beable to continue to propagate it. But the short cracks behavioris much more interesting than that. Indeed, start by estimatingthe SIF of a small crack with size a that departs from the notchtip of an Inglis plate loaded in mode I. Let the elliptical notchhave axes 2b and 2c, both much larger than a, with the 2b axiscentered at the x co-ordinate origin, and tip radius � = c2/b. If�n is the nominal stress perpendicular to a and b, then the SIFcan be estimated by KI(a) ∼= �n · √(�a) · f1(a, b, c) · f2(free surface),where f1(a, b, c) ∼= �y(x)/�n; �y(x) is the �y stress distribution at(x = b + a, y = 0) ahead of the notch tip when there is no crack;and f2 = 1.12. The function f1(x = b + a, y = 0) is given, e.g. by Schi-jve [11]:

f1 = �y(x, y = 0)�n

= 1 + (b2 − 2bc)(x −√

x2 − b2 + c2)(x2 − b2 + c2) + bc2(b − c)x

(b − c)2(x2 − b2 + c2)√

x2 − b2 + c2

(9)

The slender the elliptical notch is (i.e. the smaller theirsemi-axes c/b and tip radius to depth �/b ratios are), thehigher is its SCF. But high Kt imply in steeper stress gra-dients ahead of the notch tip, ∂�y(x, y = 0)/∂x, since the LEstress concentration induced by any elliptical hole drops fromKt = 1 + 2b/c = 1 + 2

√(b/�) ⇒ �y(1)/�n ≥ 3 at its tip border to an

almost fixed value 1.82 < K1.2 = �y(1.2)/�n < 2.11 (assuming b ≥ c)at a point just b/5 ahead of it. Hence, the notch influence zoneis associated with their depth b, not with their tip radius �

[1]. This is the cause for the peculiar growth of short crackswhich depart from elongated notch roots. Their SIF, whichshould tend to increase with their length a = x − b, may insteaddecrease after they grow for a short while because the SCFeffect in KI ∼= 1.12 · �n

√(�a) · f1 may fade quickly due the very

high stress drop close to the notch tip, overcompensating thecrack growth effect. This simple KI(a) estimate can be usedto roughly evaluate the size of the non-propagating fatiguecracks tolerable at notch roots, using the short crack FCPbehavior.

For example, it can be used to verify if it is possible tochange a circular central hole with diameter d = 20 mm byan elliptical one with 2b = 20 mm and 2c = 2 mm in a largesteel plate with ultimate strength SU = 600 MPa, SL = 200 MPaand �K0 = 9 MPa

√m that works under a nominal load

��n = 100 MPa at R = −1, without inducing the notched plateto fail by fatigue. Assume the axis 2b is perpendicular to �n.Neglecting the buckling problem (which can be important inthin plates), the relatively large circular hole is certainly toler-able, since it has a safety factor against fatigue crack initiationF = SL/Kf · �n = 200/150 ∼= 1.33, as its Kf

∼= Kt = 3.
But the sharper elliptical hole would not be admissi-
ble by traditional SN routines, since it has a tip radius� = c2/b = 0.1 mm, thus a very high Kt = 1 + 2b/c = 21. Its notchsensitivity estimated from the usual Peterson q plot [12] would

j m a t e r r e s t e c h n o l . 2 0 1 3;2(3):288–295 291

10

9

8

7

6

5

4

3

2

1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.11.0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

2

20

ΔKI(a)ellipticalnotch

ΔKI(a)circularnotch

ΔK(MPa√m)

ΔK0(a)

a(mm)

ΔS0=400MPaΔK0=9MPa√m

a0≅0.13mmΔσn=100MPa,R=–1

Fig. 4 – By Eq. (9), fatigue cracks should not initiate at the circular hole border, which tolerates cracks a < 1.54 mm, while thec d sto

bK

tisufnSuro

ftftbltits

s�

fhsdptwr

pt


rack that initiates by fatigue at the elliptical notch tip shoul

e q ∼= 0.32 ⇒ Kf = 1 + q · (Kt − 1) = 7.33, thus it would induce

f · �n = 376 MPa > SL.However, as this Kf value is considerably higher than

he typical values reported in the literature [1,11–13],t is worth to re-study this problem considering thehort crack FCP behavior. Supposing �Kth(R < 0) ∼= �K0 assual, �K0(a) = �K0/[1 + (a0/a)]−0.5 (by ETS), S′

L = 0.5SU (theatigue limit of the material, as FCP modeling doesot need the modifying factors required to estimate

L), estimating by Goodman �S0 = SU/1.5 = 2S′L/1.5, and

sing a0 = (1/�)(1.5�K0/1.12 · SU)2 ∼= 0.13 mm, the estimated SIFanges �KI(a) for the two holes are compared to the FCP thresh-ld �K0(a) in Fig. 4.

Note in Fig. 4 how the SIF estimated for cracks departingrom the circular notch remains below the short crack FCPhreshold curve �K0(a) up to a ∼= 1.54 mm. Thus, if a small sur-ace scratch locally augments the stress range and initiates ainy crack at the circular hole border, it would not propagatey fatigue alone under these fixed ��n = 100 MPa and R = −1oading conditions, confirming its “safe” prediction made byraditional SN procedures. Only if a crack with a > 1.54 mm isntroduced at this hole border by any other means, it wouldhen be able to propagate by fatigue under those otherwiseafe loading conditions.

On the other hand, the estimated �KI(a) curve for theharper elliptical hole starts above the FCP threshold curveK0(a) under these same loading conditions. Therefore, a

atigue crack should initiate at its border, as expected from itsigh SCF Kt. But as this tiny crack propagates through the hightress gradient ahead of the notch tip, it is driven by its rapidlyiminishing stresses during its early growth, which overcom-ensate the increasing crack size effect on �KI(a). In this way,his crack SIF becomes smaller than �K0(a) at a ∼= 0.33 mm,hen it stops and becomes non-propagating (if ��n and R

emain fixed), see Fig. 4.
As fatigue failures include not only the crack initiation
hase, but also its gradual propagation up to an eventual frac-ure, both notches could be considered safe for this assumed

p after reaching a ∼= 0.33 mm.

fixed service loading conditions (��n = 100 MPa and R = −1). Butthe non-propagating crack at the elliptical notch tip, a clearevidence of fatigue damage, renders it much less robust thanthe circular one, as discussed in Castro and Meggiolaro [1].

For more precise mechanical analysis purposes, the SIFrange of a single crack with length a emanating from a semi-elliptical notch with semi-axes b and c (where b is in the samedirection as a) at the edge of a very large plate loaded in modeI can be written as:

�KI = � · F

(a

b,

c

b

)· ��

√�a (10)

where � = 1.12, and the term F(a/b, c/b) can be expressed as afunction of the notch SCF and of the dimensionless parameters = a/(b + a) by:

Kt =[

1 + 2(

b

c

)]·{

1 +[(

0.12

(1 + c/b)2.5

)]}(11)

To obtain expressions for F, extensive finite element cal-culations were performed for cracks departing from severalsemi-elliptical notches. The numerical results, which agreedwell with standard solutions [14], were fitted within 3% by:

Kt =[

1 + 2(

b

c

)]·{

1 +[

0.12

(1 + c/b)2.5

]}, c ≤ b and s = a

b + a

(12)

F′(

a

b,

c

b

)≡ f ′(Kt, s)

= Kt[1 − exp(−K2t )]

−s/2

√1 − exp(−sK2

t )

sK2t

, c≥b (13)

Note that these SIF expressions include the semi-ellipticalnotch effect through F or F′. Indeed, as s → 0 when a → 0, themaximum stress at their tips �max → F(0, c/b) · �n = Kt · �n. Thus,

n o l


292 j m a t e r r e s t e c h

the �-factor, but not the F(a/b,c/b) part of KI, should be con-sidered in the short surface crack characteristic size a0. Noteas well that these expressions for the semi-elliptical SCF Kt

include a term [1 + 0.12/(1 + c/b)2.5], which could be interpretedas the notch free surface correction (FSC), because as theratio c/b → 0 and the semi-elliptical notch tends to a crack,its Kt → 1.12 · 2

√(b/�). However, this 1.12 factor is in fact the

notch FSC, not the usual crack FSC expressed by �. Actually,it disappears from the F expression when c/b → 0. Indeed,F(a/b, 0) = 1/

√s ⇒ �KI = � · F · �� · [� · a]0.5 = � · �� · [� · (a + b)]0.5, as

expected, since the resulting crack for c → 0 would have alength a + b. Such mechanical details may seem superfluous,but on the contrary they help to understand the physics of theodd short crack FCG behavior.

Traditional q estimates, based on the fitting of questionablesemi-empirical equations to few experimental data points,assume that its value depends only on the notch root � and onthe material ultimate strength SU. Thus, similar materials withthe same SU but different �K0 should have identical notch sen-sitivities. The same should occur with shallow and elongatednotches of identical tip radii. However, whereas well estab-lished empirical relations relate the fatigue limit �S0 to thetensile strength SU of many materials, there are no such rela-tions between their FCP threshold �K0 and SU. Moreover, it isalso important to point out that the q estimation for elongatednotches by the traditional procedures can generate unreal-istic Kf values, as exemplified above. Thus such traditionalestimates should not be taken for granted.

The proposed model, on the other hand, is based on theFCP mechanics of short cracks which depart from ellipticalnotch tips, recognizing that their q values are associated withtheir tolerance to non-propagating short cracks. It shows thattheir notch sensitivities, besides depending on �, �S0, �K0

and �, are also strongly dependent on their shape, given bytheir c/b ratio [3]. Therefore, the proposed predictions indicatethat these traditional notch sensitivity estimates should not beused for elongated notches, a forecast experimentally verified,as discussed in the following section.

3. An acceptance criterion for short cracks

Based on the encouraging life estimations for fatigue crackre-initiation data [4,5], the reverse path can be followed,assuming that the methodology presented here can be usedto generate an unambiguous acceptance criterion for smallcracks, a potentially much useful tool for practical appli-cations. Most structural components are designed againstfatigue crack initiation using εN or SN procedures, whichdo not consider crack effects. Therefore, their “infinite life”predictions may become unreliable when such cracks areintroduced by any means, say by manufacturing or assemblingproblems, and not quickly detected and properly removed.Large cracks may be easily detected and dealt with, but smallcracks may pass unnoticed even in careful inspections. In fact,if they are smaller than the guaranteed detection threshold
of the inspection method used to identify them, they simplycannot be detected.
Thus, structural components designed for very long fatiguelives should be designed to be tolerant to such short cracks.

. 2 0 1 3;2(3):288–295

However, this self-evident requirement is still not usuallyincluded in fatigue design routines, as most long-life designsjust intend to maintain the stress range at critical points belowtheir fatigue limits, guaranteeing that �� < SR/F, where F isa suitable safety factor. Nevertheless, most long-life designswork well, which means that they are somehow tolerant toundetectable or to functionally admissible short cracks. Butthe question “how much tolerant” cannot be answered bySN or εN procedures alone. Such problem can be avoided byadding Eqs. (6) and (7) to the “infinite” life design criterionwhich, to tolerate a crack of size a in its simplest version,should be written as

�� <�KR

√�a · g(a/w) · [1 + (aR/a)�/2]

1/�,

where aR =(

1�

)[�KR

��SR

]2(14)

This criterion is applied elsewhere to evaluate a rare butquite interesting manufacturing problem: a batch of an impor-tant component was marketed with small surface cracks,causing some unexpected annoying field failures [5]. Thatexample demonstrates well this model usefulness.

Note, however, that this model only describes the behav-ior of macroscopically short cracks, as it uses macroscopicmaterial properties. Thus it can only be applied to shortcracks which are large in relation to the characteristic size ofthe intrinsic material anisotropy (e.g. its grain size). Smallercracks grow inside an anisotropic and usually inhomogeneousscale; thus their FCP is also affected by microstructural barri-ers, such as second phase particles or grain boundaries [15].Nevertheless, as grains cannot be mapped in most practicalapplications, such problems, in spite of their academic inter-est, are not really a major barrier from the fatigue design pointof view.

4. A short crack acceptance criterion forEAC applications

The resistance to EAC in aggressive environments is an impor-tant problem for many industries, because the costs andparticularly the delivery times for special EAC-resistant alloyskeep increasing. For example, they are important in the oilindustry, where oil and gas fields can contain considerablyamounts of H2S, and in the aeronautical industry, where verylight structures usually made of high-strength Al alloys mustoperate in saline environments known to affect many of them.

Nevertheless, traditional design routines used to deal withsuch problems are based on simplistic structural integrityassessment (SIA) procedures based on an overly conservativepolicy of totally avoiding material–environment pairs suscep-tible to EAC conditions. Indeed, when such conditions areunavoidable during the service life of the structural com-ponent in question, the standard solution is just to choose
a nobler material to build it, one that is resistant or evenimmune to crack initiation and/or propagation by EAC mech-anisms in the operational environment. Alternatively, thedesign solution may be to recover the structural component

o l . 2 0 1 3;2(3):288–295 293

stn

cemetntdaofticpaet

hcasiudidaac

cfctcttudb

a

atiawtap

σ(MPa) σ=Sscc

KIsccσ=√πa g(a/w)

√πa g(a/w)

832

γ=1.5

Sscc(a)=KIscc[1+(a0/a)γ/2]-1/γ

ao=1π

KIscc

η.Sscc

2

a(mm)

Fig. 5 – A Kitagawa–Takahashi-like plot proposed todescribe the environmentally assisted cracking behavior of


j m a t e r r e s t e c h n

urface with a suitable properly adherent and scratch resis-ant EAC-resistant coating. However, in many cases there areo such coatings available in the market.

Such over-conservative and inflexible design criteria areertainly safe, but they can also be too expensive if an oth-rwise attractive material is summarily disqualified when itay suffer EAC in the service environment, without consid-

ring any stress analysis issues. Indeed, decisions based onhis approach may cause severe cost penalties. Moreover, toeglect the stress effect on EAC issues is equivalent to neglecthe crack growth physics, since no crack can grow unlessriven by a tensile stress, caused by the superposition ofpplied loads, residual stresses induced by previous loads orverloads, and maintenance or manufacturing procedures. Inact, even though practical EAC conditions may be difficulto define, due to the number of metallurgical, chemical, andn particular mechanical variables that affect them, SIA pro-edures in the design stage should always be associated toroper stress analysis techniques to define a maximum toler-ble flaw size. In other words, EAC cracks cannot be properlyvaluated neglecting the stress and strain fields that drivehem.

However, the main advantage of the methodology proposedere is to allow the proper evaluation of existing structuralomponents not originally designed for EAC service, when byny reason they pass to operate under such conditions due toome unavoidable operational change. For example, an exist-ng oil pipeline must pass to operate transporting originallynforeseen amounts of H2S due to changes in the well con-itions while a new one specifically designed for such service

s not built and commissioned. Such problems are not aca-emic exercises. In fact the economical pressure to take suchstructural risk may be unavoidable, since loss of profit issuesssociated with the time required for substituting a pipelinean be quite long, especially in off shore applications.

Such uneconomical or risky decisions can at least in prin-iple be potentially avoided by the methodology proposedollowing, which extends the analysis developed to mechani-ally explain the behavior of deep and shallow fatigue crackso the EAC problem. Indeed, if cracks behave well under EAConditions, i.e. if Fracture Mechanics concepts can be usedo describe them, then a Kitagawa-like diagram can be usedo quantify the stresses any cracked component can toleratender EAC conditions, using the material EAC resistances toefine a “short crack characteristic size under EAC conditions”y:

0 =(

1�

)·(

KIEAC

� · SEAC

)2(15)

In this way, all corrosion effects on EAC problems aressumed to be properly described and quantified by the resis-ance to crack propagation KIEAC and by the resistance to cracknitiation SEAC under fixed stress conditions, assuming thenalyzed material–environment pair remains fixed. In other
ords, this model supposes that the mechanical parameters
hat govern the EAC problem behave analogously to the equiv-lent parameters �Kth(R) and �SL(R) that control the fatigueroblem, see Fig. 5.

short and deep flaws for structural design purposes.

Consequently, if cracks loaded under EAC conditionsbehave as they should, i.e. if their driving force is indeed theSIF applied on them; and if the chemical effects that influ-ence their behavior are completely described by the materialresistance to crack initiation from smooth surfaces quantifiedby SEAC, and by its resistance to crack propagation measuredby KIEAC; then it can be expected that EAC cracks may departfrom sharp notches and then stop, due to the stress gradientahead of the notch tips, eventually becoming non-propagatingcracks, as in the fatigue case. In such cases, the size of non-propagating short cracks can be calculated using the sameprocedures useful for fatigue, and the tolerance to such defectscan be properly quantified using an EAC notch sensitivity fac-tor in SIA. Hence, a criterion for the maximum tolerable cracksize under EAC conditions can be proposed as:

amax ≤(

1�

)·[

KIEAC(1 + a0/a)�/2

√�a · g(a/w)

]−1/�

(16)

5. Educated guesses for tolerable cracksunder EAC conditions

It is now possible to estimate characteristic (a0) and tol-erable (amax) sizes for cracks that initiate from notches,e.g. with depth b = 10 mm and various tip radii �, usingSEAC and KIEAC data gathered on the literature for threematerial–environment pairs [16–19]. Fig. 6 defines the notchparameters and Table 1 lists the material and geometric prop-erties used in this analysis.

The reason for using just the three material–environmentpairs in Table 1 is simple: it is a little bit hard to find the param-eters KIEAC and SEAC measured under identical conditions onthe literature. Maybe this could be explained by the lack ofmodels that try to unify these parameters as joint crack drivingforces under EAC conditions.

Fig. 7 shows a graphical interpretation for the short cracktolerance predicted by the proposed model equations. Themaximum allowed crack size is obtained when the applied SIFKI(a) becomes higher than the short crack propagation thresh-old KIEAC(a). Once again, it is worth to emphasize that this
predicted behavior is totally similar to the one observed underfatigue conditions. This similitude indicates that a notch sen-sitivity factor could indeed be proposed to properly treat stress

294 j m a t e r r e s t e c h n o l . 2 0 1 3;2(3):288–295

Table 1 – Estimated results for tolerable crack sizes at some notch geometries.

Material/environment Aluminum 2024/gallium

Aluminum 2024/NACE solution

API 5L X-80 steel/NACE solution

SEAC (MPa) 70 140 440KIEAC (MPa *

√m) 1.2 8 30

a0 (mm) 0.075 0.829 1.18b (mm) 10 10 10� (mm) 0.335 3.136 4.9Kt 12.881 4.754 3.982� = SEAC/Kt (MPa) 5.434 29.448 110.5amax (mm) 1.9 6.65 5.41

σn

2ρ

σn

b

KI(a)– KIth(a) MPa m0.1

0.05

–0.05

–0.1

A

Ba (mm)

1 2 3

C

Fig. 8 – Criteria plot of propagating cracks for Al 2024 undergallium exposure.


Fig. 6 – Notch parameters for non-propagating cracks.

analysis issues in EAC problems, eliminating the need to con-tinue using overly conservative pass–fail criteria to deal withsuch problems.

Graphical solutions can provide other important visualinformation as illustrated in Fig. 8, which shows that a flaw on
the size region “A” could propagate until reaching the region“B” when it would become non-propagating because it reachesthe condition KI(a) < KIEAC(a). Nevertheless, all flaws sizes on
1.0

1.0 1.5 2.0

0.5

0.50

0

KI(a)=η⋅σ√πa g(a/w)

KIEAC(a)=KIEAC[1+(ao/a)γ/2]-1/γ

KIEAC(a)KI(MPa√m)

KI(a)

a(mm)

amax

Fig. 7 – EAC criteria plot for Al 2024 under galliumexposure.

the region “C” are considered non-acceptable cracks, since thedifference KI(a) < KIEAC(a) becomes again positive after leavingthe safe region B. This occurs because the contribution of theincreasing crack size for the loading SIF KI(a) definitely over-comes the resistance to crack growth under EAC conditionsKIEAC(a) for cracks with sizes a > amax.

6. Conclusions

A generalized El Haddad–Topper–Smith’s parameter was usedto model the threshold stress intensity range for short cracksdependence on the crack size under fatigue conditions. Thisdependence was used to estimate the notch sensitivity factorq of elongated notches, based on the propagation behavior ofshort non-propagating cracks that may initiate from their tips.It was found that the notch sensitivity of elongated slits has avery strong dependence on the notch aspect ratio, defined bythe ratio c/b of the semi-elliptical notch that approximates theslit shape having the same tip radius. These predictions werecalculated by relatively simple numerical routines, all basedon sound mechanical principles. Based on this performance,a new criterion to evaluate the behavior of small or large sur-face flaws under environmentally assisted cracking conditionswas proposed. Such estimates can certainly be very useful for
practical structural design and analysis applications, as theycan be associated with potentially huge economic savings.

o l . 2

To

C

T

A

CfRl

r

http://iopscience.iop.org/1742-6596/240/1/012033[19] Kolman DG, Chavarria R. Liquid metal embrittlement of 7075


j m a t e r r e s t e c h n

herefore, they deserve to be properly studied through a seri-us experimental program.

onflicts of interest

he authors declare no conflicts of interest.

cknowledgements

NPq and Petrobras have provided research scholarshipsor the authors. Dr. A. Vasudevan from the Office of Navalesearch of the US Navy has contributed with many stimu-

ating discussions.

e f e r e n c e s

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[8] Kitagawa H, Takahashi S. Applicability of fracture mechanicsto very small crack or cracks in the early stage. In: Int confmech behavior materials. 2nd ed. ASM; 1976.

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[11] Schijve J. Fatigue of structures and materials. Kluwer; 2001.[12] Peterson RE. Stress concentration factors. Wiley; 1974.[13] Dowling NE. Mechanical behavior of materials. 3rd ed.

Prentice Hall; 2007.[14] Tada H, Paris PC, Irwin GR. The stress analysis of cracks

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[16] Holtam C. Structural integrity assessment of C–Mn pipelineexposed to sour environments. Loughborough University;2010 [Doctor of Engineering Thesis].

[17] Dietzel W. Fracture mechanics approach to stress corrosioncracking. Ann Fracture Mech 2001;18:3.

[18] Itoh A, Izumi J, Ina K, Koizumi H. Brittle-to-ductile transitionin polycrystalline aluminum containing gallium in the grainboundaries. In: 15th int conf strength of materials(ICSMA-15). 2010. Available from:

aluminum and 4340 steel compact tension specimens bygallium. J Test Eval 2002;30(5):452–6.

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Does notch sensibility exist in environmentally assisted cracking (EAC)?