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Effect of the strain rate on stress corrosioncrack velocities in face-centred cubic alloys.

A mechanistic interpretation

S.A. Serebrinsky, J.R. Galvele*

Comisioon Nacional de Energa Atoomica, Departamento Materiales, Instituto de Tecnologia, Avda.

Libertador 8250, 1429 Buenos Aires, Argentina

Received 28 August 2002; accepted 2 July 2003

Abstract

Constant extension rate tests on smooth samples, with strain rate (SR) values from 106 s1

up to 20 s

1

, were used to study stress corrosion cracking (SCC) systems in face-centred cubicalloys. It was found that by increasing the SR a monotonic increase of the log CPR (crack

propagation rate) takes place. It was also observed that the slope a in log CPR vs. log SR plots

had different values for different SCC morphologies. Intergranular SCC is more steeply ac-

celerated by SR, aIG 0:50.7, than transgranular SCC, aTG 0:20.3. The differences foundbetween intergranular SCC and transgranular SCC were analysed under the light of the

available SCC mechanisms.

2003 Elsevier Ltd. All rights reserved.

Keywords: A. Stainless steel; Silver; Brass; C. Stress corrosion; Effects of strain

1. Introduction

Numerous variables have a strong effect on the stress corrosion cracking (SCC)

process in metals and alloys, the strain rate (SR) being one of them [1,2]. In a recent

publication Serebrinsky et al. [3] studied the effect of SR on the crack propagation

rate (CPR) for a variety of alloyenvironment systems. In their study the authors

covered a wide range of SR values, going from 106 s1 up to 20 s1. They found

that, while an increase in the SR produced an increase in the CPR, the effect was

*Corresponding author. Tel.: +54-11-6772-7390; fax: +54-11-6772-7404.

E-mail address: [email protected] (J.R. Galvele).

0010-938X/$ - see front matter 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/S0010-938X(03)00172-0

www.elsevier.com/locate/corsci

Corrosion Science 46 (2004) 591612
http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/

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more significant for intergranular SCC than for transgranular SCC. The results

showed that the slope a in log CPR vs. log SR plots was aIG 0:50.7 for inter-granular cracking, while it only reached values of aTG 0:20.3 for transgranular

cracking. This difference in behaviour between transgranular cracking and inter-granular cracking, was confirmed by Alvarez et al. [4]. Alvarez et al. compared single

crystals of Ag10Au alloy with polycrystalline samples of the same alloy. These

authors strained the samples in both a 1 M HClO4 solution and a 1 M KCl solution,

and found slopes similar to those reported by Serebrinsky et al. [3].

In the present work a systematic study was made of all the cases studied by Ser-

ebrinsky et al. [3] in their preliminary work. Only homogeneous face-centred cubic

(fcc) alloys were considered in this study, assuming that similar plastic behaviour

would be found when straining the different fcc alloys. The previously reported

slopes for both intergranular and transgranular SCC were confirmed. An analysis

was made of the experimental results, under the scope of the available SCC mech-

anisms [5,6], and it was concluded that the surface mobility SCC mechanism ac-

counted for the experimental observations.

2. Experimental method

2.1. Materials

Only homogeneous alloys, with an fcc structure, were used in the present work.The samples were 0.8 mm diameter wires. All the samples were degreased in acetone

and subjected to a thermal treatment, as described below. Before each test, the

samples were again degreased with acetone. The alloys used were identified by their

commercial name, except for the silver alloys, which were identified by their nominal

atomic % composition. The analytical composition of the alloys used, in wt.%, were:

type AISI 304 stainless steel (Cr 16.9, Ni 8.0, Si 0.7, Mo 0.4, C 0.08, S 0.03, Fe

balance), Ag15Pd (Pd 15.5, Pb < 0.01, Cd < 0.01, Cu 0.030.1, Al 0.003, Si 0.001, Fe

0.01, Mg 0.01, Pt < 0.005, Au < 0.005, Rh < 0.15, Ir < 0.015, Ag balance), and yellow

brass (Al 0.002, Si < 0.02, Fe 0.05, Ti 0.02, Mg 0.0002, Mn 0.0005, Sn 0.02, Pb 0.02,

Cr 0.0050.02, Ni 0.050.2, Zn 34.8 0.1, Cu balance). The composition of the alloysAgxAu, where x 2, 5 and 15 at.% is given in Table 1. In the present work thesealloys are referred to as AISI 304, AgPd, AgAu and brass, respectively.

Table 1

Chemical composition of the AgAu alloys used

Alloy

(at.%)

Element (wt.%)

Au Al Cu Pt Si Fe Mg Ag

Ag2Au 3.99

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All the thermal treatments were carried out in argon atmospheres. The AISI 304

was annealed for 30 min at 1100 C, and water quenched. The AgPd and AgAu

alloys were annealed at 800 C for 1 h, and air-cooled. Brass was annealed for 24 h at454 C and water-quenched. No traces of b phase were detectable in the annealed

brass samples.

The mechanical properties of all the alloys were measured at strain rates ranging

from 105 s1 up to 1 s1. The properties measured were: the conventional flow stress

for 0.2% plastic strain (r0:2), the ultimate tensile strength (UTS) and the true strain to

rupture (er). For all the alloys the three parameters either increased slightly with SR,

or remained constant. In general the variation of UTS with SR was slightly higher

than that of r0:2. No measurements of mechanical properties were made in the range

120 s1. Since the change of the mechanical properties with SR, in the measured

range was small and smooth, it was assumed that the same should be expected for

the SR values not covered during the mechanical properties measurements. Table 2

shows the mechanical property values found at 105 s1.

2.2. Environments

All the solutions used were prepared with analytical grade reagents and triply

distilled water with a minimum resistivity of 18.2 MX cm. AISI 304 was tested in an

11.8 M LiCl solution at 130 C. In this case the temperature was kept constant within

1

C. All the other systems were tested at room temperature. The AgPd alloy wastested in aqueous 1 M KCl and 1 M KI solutions. The AgAu alloys were tested in

aqueous 1 M HClO4 solution. Brass was tested in 1 M NaNO2 solution and in a

solution with the following composition: 0.05 M CuSO4 + 1 M (NH4)2SO4, the pH of

the solution was adjusted to 6.5 with NH4OH. In the text this last solution is referred

to as Mattsons solution.

2.3. Polarization curves

Anodic polarization curves were measured in a conventional three-electrode glass

cell, with a potential scanning rate of 0.5 mV s1. The solutions were deaerated withprepurified nitrogen [7], in a scrubber connected to the cell. After a 60 min deaer-

ation, the solution was transferred to the cell. The samples were allowed to reach a

Table 2

Mechanical properties of the alloys used, at 105 s1

Alloy r0:2 (MPa) UTS (MPa) er (%)

AISI 304 206 885 34.5Ag15Pd 113 321 26.6

Ag2Au 55 182 18.8

Ag5Au 55 178 15.9

Ag15Au 53 180 16.4

Brass 95 495 40.0

No significant differences were observed when varying the strain rate.

S.A. Serebrinsky, J.R. Galvele / Corrosion Science 46 (2004) 591612 593

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steady potential, and then the potential was scanned, beginning at a potential 100

mV below the corrosion potential. The reference electrodes used were: for AISI 304

in the LiCl solution a calomel saturated reference electrode, for brass in aqueous

NaNO2 solution, as well as for AgPd alloy in KI solution and for AgAu alloys inHClO4 solution a mercurous sulphate reference electrode, for AgPd in KCl, a silver

chloride reference electrode, prepared according to [8]. In the case of brass in

Mattsons solution a pure copper wire was used as a reference electrode. All the

potentials are reported in the standard hydrogen electrode (SHE) scale, with the only

exception of brass in Mattsons solution, where the potential applied in the straining

experiments was the equilibrium potential of copper in the solution.

2.4. Stress corrosion tests

The SCC tests were carried out at constant strain rate. For convenience, the ex-

periments were divided in three strain rate ranges: slow strain rate tests (SSRT) for

SR values in the range of 106104 s1, intermediate strain rate tests (ISRT) for SR

values in the range of 1041 s1, and ultrafast strain rate tests (UFSRT) for SR

values higher than 1 s1. For SSRT and ISRT the machines used were conventional

constant crosshead speed straining machines, and the cell used was described in [9].

The total length of the sample, between grips, was 120 mm, and the part of the

samples exposed to the corrosive solutions had an initial area of 0.8 mm 2. The

UFSRT were performed in a drop weight apparatus described in [10], and the cell

was similar to that for SSRT, but arranged for vertical straining. In the UFSRT thefailure time tr was calculated by detecting the starting point and the end of the test

with two switches wired to a Tektronix TDS-210 digital oscilloscope. With the fixed

image in the oscilloscope tr ttotDLr=DLtot was calculated, ttot and DLtot being thetotal time and length of the mobile grip displacement, and DLr the elongation to

rupture.

The electrode potentials were measured through a Luggin capillary and were kept

constant with a LYP M7 potentiostatgalvanostat. The procedure for loading the

solution into the cell as well as the reference electrodes used were those described for

the polarization curves. After the samples reached a steady potential, the chosen

potential was applied. The samples were kept at constant potential for a short time,and then the straining of the samples was started. The exposure at constant potential

pointed to obtaining a reproducible initial surface, but without allowing for excessive

surface corrosion. Typical exposure time values, at constant potential, were the

following: for AISI 304 and AgPd, 10 min, for AgAu, between 15 s and 10 min,

depending on the current density and for brass in Mattsons solution, 3 min. The

potentials applied for each experiment, are described in the next section.

The samples were strained to fracture. Afterwards the fracture surface and lateral

surfaces of the samples were observed with a Phillips 500 scanning electron mi-

croscope (SEM). Then the samples were mounted for metallographic sectioning and

observation. The crack propagation rate was calculated by dividing the crack lengthLf by the failure time tf. The former was found either by measuring the maximum

radial length of the brittle part on the fracture surface observed by SEM, or by

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measuring the maximum crack length on the mounted section. In those cases where

both measurements were taken into consideration, the former observations were

identified as SEM values, and the latter ones as MET values.

3. Experimental results

3.1. Polarization curves

3.1.1. AISI 304 in LiCl

The polarization curve of AISI 304 in 11.8 M LiCl solution at 130 C shows a

passive range was observed between the corrosion potential, Ecorr 0:5 VSHE, and

)0.1 VSHE. The passive current density was of the order of 10

5

A/cm2

. At potentialsabove Ep 0:1 VSHE, pitting corrosion started, and the current density rose untilohmic drop limitations appeared. The results obtained were similar to those reported

by Wilde [11], and by Duffoo et al. [12].

3.1.2. AgPd in halides

Fig. 1 shows the polarization curves for pure silver and for Ag15Pd in a 1 M KCl

solution. The arrows indicate the potential values used in the present work for the

stress corrosion tests. The curves found were similar to those reported by Duffoo and

Galvele [13]. A detailed analysis of the polarization curves was reported by these

authors. According to Duffoo and Galvele, for Ag15Pd, in 1 M KCl solution, be-tween 0.2 and 0.4 VSHE selective dissolution of silver was taking place. No traces of

Pd were detected by them in the solution after exposing the alloy for 22 h at 0.4 VSHE.

On the other hand, above 0.45 VSHE the increase in the current density was

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

-3

10-2

10-1

100

101

102

103

1M KClAg 99.99%Ag - 15Pd

I(A/m2

)

E(V/SHE)

Fig. 1. Polarization curves of Ag15Pd and Ag 99.99% in 1 M KCl solution. The arrows show the po-

tentials applied in stress corrosion tests.


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accompanied by simultaneous dissolution of Ag and Pd. At 0.6 VSHE the amount of

Pd found by them in the solution indicated a quasi-stoichiometric dissolution of the

alloy.

3.1.3. AgAu in HClO4The polarization curves for pure silver and for AgxAu (x 2; 5; and 15 at.%)

alloys in a 1 M HClO4 solution were similar to those reported by Maier et al. [14].

These authors measured the dissolution rate of the alloys in 1 M HClO4 solution, at

constant potential, and calculated the rate of formation of dealloyed films on the

metal surface.

3.1.4. Brass in Mattsons solution

No measurements were made for the polarization curve in this system. The SCC

tests in this system were made at the equilibrium potential of pure copper in the

corrosive solution. This choice was based on the observations published by Montoto

et al. [15].

3.1.5. Brass in NaNO2For the SCC tests in this system the polarization curves published by Alvarez

et al. [16] were used.

3.2. Stress corrosion tests


Under the experimental conditions chosen, the fracture surface of AISI 304 was

always transgranular (TG). The experimental conditions were selected to disfavour

intergranular (IG) cracking. In this way the complications in the interpretation of the

results due to mixed cracking morphology were avoided. As shown by Galvele et al.

for hot MgCl2 [17] and LiCl [12] solutions, when increasing the potential the TG

fraction in the cracks increased. The fracture surfaces of the samples strained in the

present work showed typical features of TG cracking, such as river patterns and fan-

shaped marks starting from the initiation points. The longest cracks were usually

observed to initiate at large pits. For the lowest SR (2.4 106

s1

), usually there wasonly one, passing-through, crack. Sometimes, tiny cracks appeared in the region

close to the main crack. When SR increased, up to about 5 103 s1, a higher

number of cracks, with a length similar to the longest one, was found. For higher SR

the number of cracks decreased again, but this fact should be associated to a limi-

tation in the detection of cracks rather than to their absence. For example, for the

highest SR value in the ISRT (0.044 s1) pitting was still effective in inducing

cracking, but no cracks were detectable in the UFSRT, at 18 s1.

Scanning electron microscopy (SEM) and metallographic mounting (MET) usu-

ally gave comparable values of CPR. Fig. 2 shows crack propagation rates versus

strain rate. In the same figure the lower detection limit of the constant strain ratetechnique is shown. This limit is defined as the length of the smallest detectable crack

Lfis;min (here taken conservatively as 4 lm) divided by the largest cracking time tr;max.


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As mentioned in a previous publication [3] and confirmed in the present work,

there is a significant difference in the slope, a, of the loglog plot when intergranular

SCC is compared with transgranular SCC. The slope a of the loglog plot is defined

as

a o logCPR

o logSR; 1

and in the case of AISI 304 in LiCl it was 0.31. An extrapolation of this linear re-

lationship to a SR of 18 s1 showed that the expected crack propagation rate was

below the detection limit, even when the expected CPR was as high as 2 105 m s1.

If cleavage cracks, longer than 4 lm were produced, they should have been detect-

able. Nevertheless, in the present work no such cracks were found for transgranular

SCC of AISI 304 in LiCl solution.


This system has been previously studied with SSRT [13]. It was found that the

CPR generally increased with the potential, from the potential of formation of the

silver halide up to an overpotential of %300 mV. For higher potentials the CPRreached a plateau [13].

As reported by Duffoo and Galvele [13], fracture morphology was always IG in

both KI and KCl solutions, with no traces of TG cracking. The fracture surfaces

were covered with AgI and AgCl, respectively, as identified by EDAX. For low

potentials in KCl, the coverage was incipient, and only a small number of crystals

were observed. On the other hand, for high potentials a dense coverage with manysilver halide crystals was found. Similarly as in AISI 304, for low SR there was only

one, passing-through, crack. Small number of cracks were also observed for high

10

-6

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

110

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

CPR

(m/s)

Strain Rate (s-1)

Lower Det. Lim.

NF

2 tests

AISI 304 in 11.8M LiCl

SEM

MET

Fig. 2. Effect of strain rate on crack propagation rates of AISI 304 strained in a 11.8 M LiCl solution at

)0.1 VSHE and 130 C. The lower detection limit expected for the experimental technique used is shown.

NF indicates that no cracks were detected at the end of the experiment.


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potentials. When SR increased, or the potential decreased, a larger number of cracks

with similar length appeared. A characteristic feature, quite common in intergran-

ular stress corrosion fracture surfaces, was the presence of shallow pits or vacancy

clusters, as previously reported by Maier et al. [14].

Unlike to what was observed with AISI 304 in LiCl, AgPd alloy in halide so-

lutions gave measurable cracks for UFSRT. The cracks in a sample strained in 1 MKI at 5 s1 were about 100 lm in size. The samples strained in KCl showed shorter

cracks, but still above the detection limit of the experimental technique. The slopes a

in the logarithmic plot of Fig. 3 were clearly steeper than those found for AISI 304 in

LiCl solution. The values measured for a were between 0.5 and 0.65, and were listed

in Table 3. One important observation was that, as shown in Fig. 4, in the UFSRT,

the cracks measured at 5 s1 were always longer than those measured at 18 s1. This

observation was important because if the cracks produced at 5 s1 were due to a

single pseudo-cleavage type event, the same crack length should have been expected

for the experiments at 18 s1.

Fig. 5 shows the effect of electrode potential on the crack propagation rate atvarious strain rate values, for Ag15Pd in 1 M KCl solution. It was observed that an

increase in the potential (E) produced an increase in CPR, up to an overpotential of

about 300 mV, where a plateau was reached. The shape of the curves of CPR in

function of E was similar for all strain rates tested, but the curves were shifted to

higher CPR values as the SR increased. The present results could lead to introduce in

Eq. (1) the effect of the potential:

log CPRSR;E fE a log SR 2

suggesting that the effects of the electrochemical variable (E) and the mechanical

variable (SR) could be independent. The slope a remained fairly independent of E.According to the measurements of Yu and Parkins, Eq. (2) is also valid for brass in

nitrites [18]. The inverse slopes p of the ascending part of the CPRE curves were

10-6

10-5

10-4

10-3

10-2

10-1

100

101

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Lower Det. Lim.

1M KCl 0.322VSHE 0.522VSHE0.372V

SHE0.572V

SHE

0.422VSHE

0.622VSHE

0.472VSHE

1M KI-0.15V

SHE

Ag-15Pd

CPR(m/s)

Strain Rate (s-1)

Fig. 3. Effect of strain rate on crack propagation rates of Ag15Pd in 1 M KI and KCl solutions.


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approximately 75 mV/decade, close to the value of 100 mV/decade reported by Galvele

et al. for low-gold AgAu alloys in 1 M potassium halide solutions at SSRT [19].

3.2.3. AgAu in HClO4

This system has been previously studied by Maier et al. [14] at SSRT, and byDuffoo and Galvele [20] and by Kelly et al. [21] at UFSRT. The experimental results

from the present work are shown in Figs. 6 and 7.

Table 3

Compilation of the slopes in log CPRlog SR plots from the present work

Alloy Environment Potential (VSHE) Morph. a a0

AISI 304 11.8 M LiCl,130 C

)0.10 TG 0.31 0.31

Ag15Pd 1 M KI 0.15 IG 0.65 0.52

Ag15Pd 1 M KCl 0.32 IG 0.59

Ag15Pd 1 M KCl 0.37 IG 0.63 0.58

Ag15Pd 1 M KCl 0.42 IG 0.53

Ag15Pd 1 M KCl 0.47 IG 0.53 0.51

Ag15Pd 1 M KCl 0.52 IG 0.55 0.47

Ag15Au 1 M HClO4 0.90 IG 0.59 0.50

Ag15Au 1 M HClO4 1.00 IG 0.57

Ag15Au 1 M HClO4 1.15 IG 0.62 0.48

Ag5Au 1 M HClO4 0.90 IG 0.45

Ag2Au 1 M HClO4 0.90 IG 0.40

a-brass Mattsons sol.a (0.0 VCu0=Cu ) IG 0.54 0.44

a-brass 1 M NaNO2 0.20 TG 0.19 0.19

The a0 values were calculated excluding the measurements for SR higher than 1 s1.a 0.05 M CuSO4 +1 M (NH4)2SO4 + NH4OH adjusted to pH 6.5.

100 1010

10

20

30

40

50

60

Lower Det. Lim.

Strain Rate (s-1)

Lfis

(m)

0.372VSHE0.472VSHE0.522V

SHE0.572VSHE0.622VSHE

Ag-15Pd in 1M KCl

Fig. 4. Crack lengths measured at 5 s1 and at 18 s1 for Ag15Pd in 1 M KCl solutions. By increasing the

SR, in the UFSRT region, the crack lengths were found to decrease.


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The fracture surfaces found were always intergranular, though small isolated

transgranular patches were also detected. Vacancy clusters or shallow pits, as de-

scribed by Maier et al. [14], were also present in this system. The effect of the po-

tential and strain rate on the number and length of the cracks was the same as for

Ag15Pd in KCl, i.e. few and long cracks, with one much longer than the others, was

the situation favoured by high potentials and low SR.In this system a comparison was made on the effect of SR on CPR as a

function of alloy composition, Fig. 6, and also for one alloy at different potentials,

300 350 400 450 500 550 600 65010

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Strain Rate:

Ag-15Pd in 1M KCl

2.3 E-61/s8.8 E-61/s

7.3 E-51/s1.8 E-31/s4.4 E-21/s5.01/s18 1/s

CPR(m/s)

E(mV/SHE)

Fig. 5. Effect of potential on the crack propagation rate at various strain rate values, for Ag15Pd in 1 M

KCl solution.

10-6

10-5

10-4

10-3

10-2

10-1

100

101

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Lower Det. Lim.

Ag-2AuAg-5AuAg-15Au

Ag-xAu in 1M HClO4, 0.9VSHE

CPR(m/s

)

Strain Rate (s-1)

Fig. 6. Effect of strain rate on crack propagation rates of AgAu alloys in 1 M HClO4, at one potential

0.9 VSHE.


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Fig. 7. The effect of SR was the same as found with AgPd alloy, the slopes a

were higher than those found with AISI 304. The a values found were between 0.4

and 0.65.

Fig. 7 shows the effect of the electrode potential on the SR versus CPR for Ag

15Au in 1 M HClO4. When the potential was increased it was found that the CPRalso increased. The inverse slopes pwere about 230 mV/decade, for SSRT, ISRT and

UFSRT. These results were very close to the value of ca. 200 mV/decade for Ag

2Au, Ag5Au, Ag10Au and Ag15Au at SSRT reported by Galvele et al. [19]. In

the present system no plateau velocity was reached, possibly due to the very high

dissolution rate at high potentials. The effect of increasing SR was again to shift the

CPRE curves upwards, while keeping the shape of the curves. Here again Eq. (2)

was applicable.

3.2.4. Brass in Mattsons solutionThis system showed intergranular stress corrosion cracks on the fracture surfaces,

with occasional transgranular patches. The variation of the number and distribution

of the length of cracks with strain rate was similar to that described in the previous

systems, including the decrease in the number of cracks at UFSRT observed in AISI

304. Fig. 8 shows the logarithmic plot of CPRSR, where a slope a of 0.54 was

found.

3.2.5. Brass in 1 M NaNO2 solution

The fracture surfaces in this system were transgranular, as described by Alvarezet al. [16] and by Rebak et al. [22]. The results of the straining experiments are shown

in Fig. 9, and the slope for a was 0.19 [3].

10-6 10-5 10-4 10-3 10-2 10-1 100 10110

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

0.9VSHE

1VSHE1.1V

SHE

1.15VSHE

Ag-15Au in 1M HClO4

CPR(m/s)

Strain Rate (s-1)

Lower Det. Lim.

Fig. 7. Effect of the electrode potential on the SR versus CPR for Ag15Au in 1 M HClO4.


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4. Discussion

4.1. Difference between IG and TG cracking

The analysis of the experimental results described above indicates that there is aclear and consistent difference in the values of the logarithmic slope a, Eq. (1), when

intergranular SCC systems are compared with transgranular SCC systems. It was

10

-6

10

-5

10

-4

10

-3

10

-2

10

-1

10

0

10

110

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Lower Det. Lim.

CPR(m/s)

Strain Rate (s-1)

Brass in Mattson's solution

Fig. 8. Effect of strain rate on crack propagation rates of brass in Mattsons solution (0.05 M CuSO4 + 1

M (NH4)2SO4 + pH 6.5 adjusted with NH4OH) at 0 VCu.

10-6

10-5

10-4

10-3

10-2

10-1

100

101

10-9

10-8

10-7

10-6

10-5

10-4

10

-3

10-2

10-1

CPR - UTS

CPR - 0.2

Lower Det. Lim.

CPR(m/s)

Strain Rate (s-1)

Brass in 1M NaNO2solution

Fig. 9. Effect of strain rate on crack propagation rates of brass in 1 M NaNO2 solution at 25 C and 0.2

VSHE. The meaning of the CPR lines will be considered in Section 4.


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always found that the slope for intergranular SCC was higher than that for trans-

granular SCC:

aIG > aTG: 3

Table 3 shows the values for a found in the present work. Since the values of CPR

could not be measured in some systems for UFSRT, Table 3 also includes the values

for a0, defined by the same Eq. (1) but taking into account the measurement for SR

up to 1 s1 (i.e. neglecting UFSR tests).

The data in Table 3 shows that Eq. (3), either for a or a0, is satisfied in all the

systems studied. One objection that could be raised is that different systems were

compared. In support of the conclusion reached in Eq. (3) the following facts should

be taken into account. (a) Only fcc alloys were considered. Thus systems with similar

deformation mechanisms were compared. (b) One same alloy, from the same batch

(brass), was subjected in the present work to IGSCC (Mattsons solution) and

TGSCC (1 M NaNO2 solution) and the results were compared. The values found,

for the same alloy in two different environments, were aIG 0:54 and aTG 0:19,which confirms Eq. (3). (c) Alvarez et al. [4] studied one single alloy system (AgAu

alloy) in the same environment, and produced IGSCC and TGSCC. For this purpose

these authors compared AgAu single crystals with AgAu poly-crystals. The studies

were made in 1 M HClO4 solution and in 1 M KCl solution. As shown in Table 4,

and discussed below, Alvarez et al. were able to confirm the validity of Eq. (3).

To further confirm the validity of Eq. (3), values of a published in previous

publications were collected in Table 4. As mentioned above, a major point in the

analysis of the present results is provided by the work of Alvarez et al. [4]. Theseauthors strained single crystals of Ag10Au in 1 M HClO4 and 1 M KCl solutions.

As for the gold contents x, Maier et al. [14] showed that for x between 2.2 and 15

at.% Au there was no noticeable effect of the alloy composition on CPR, in experi-

ments made at a slow strain rate. In the present work it was found that this

observation is correct also when measurements are made with the ISRT. As a

consequence, the measurements made by Alvarez et al. [4] can be compared with

those reported in the present work. Alvarez et al. found for TGSCC aTG 0:22,while for IGSCC they found aIG 0:48. In the present work the lowest value for

Table 4Compilation of the slopes a in logCPRlog SR plots from previous publications

Alloy Environ-

ment

Reference Potential

(VSHE)

Morph. a a0

Ag20Au 1 M HClO4 [20] 1.20 IG 0.60

Ag20Au 1 M KCl [20] 0.70 IG 0.63 0.69

Ag15Au 1 M KCl [4] 0.50 IG 0.68

Ag15Au 1 M HClO4 [4] 0.90 IG 0.48

Ag10Au

single crystal

1 M KCl [4] 0.50 TG 0.30

Ag10Au

single crystal

1 M HClO4 [4] 0.90 TG 0.22

IG: Intergranular SCC; TG: Transgranular SCC. The a0 values exclude measurements for SR higher than

1 s1.


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IGSCC (a0 for Ag2Au) was aIG 0:4, all the other a values being higher. When themeasurements were made in KCl solution, the difference between IGSCC and

TGSCC was maintained. Alvarez et al. measured for TGSCC aTG 0:30 and for

IGSCC aIG 0:68. Duffoo and Galvele [20] reported for IGSCC of Ag20Au in 1 MKCl aIG 0:63 and in 1 M HClO4 aIG 0:60.

Finally, it is important to point out that in the present work, in the case of

TGSCC of stainless steels in hot concentrated chloride solutions, as well as brass in

nitrite solutions, no cracks were detected after UFSRT. On the other hand, no

reference was found in the literature of detection of any incipient transgranular

cracks after an UFSRT. If there were any cracks, they were smaller than the de-

tection limit of the technique used in the present work.

4.2. Mechanistic interpretation

The above results will be analysed within the scope of the surface mobility SCC

mechanism. When appropriate, references to the film induced cleavage SCC mech-

anism [5], and the anodic dissolution SCC mechanism [5] will be made. Since the

above analysis involves the use of the equations developed for the surface mobility

SCC mechanism, a brief review of those equations will be made.

The surface mobility mechanism [5,23,24] is based on the assumption that the

environment acts by increasing the surface mobility of the alloy, and that the cracks

propagate by capture of vacancies at the tip of the stressed crack. This mechanism

was used to quantitatively explain numerous cases of SCC [5,6,10,24,25]. The fol-lowing equation was developed for the crack propagation rate [23,24]:

CPR DS

Lexp

rTa3

kT

1

; 4

DS being the surface self-diffusion coefficient at the crack walls, L the diffusion dis-

tance of the vacancies, rT the elastic stress at the tip of the crack, a the atomic size,

k the Boltzmann constant, and T the temperature in K.

Since measured DS values, for the conditions of interest for SCC, are very scarce

two different approaches can be used to calculate the value ofDS. When a solid film,with a known melting point, contaminates the crack surface, an empirical equation,

based on the work of Gjostein [26] and Rhead [27,28] can be used to calculate DS[23]:

DS m2 s1 740 104 exp126Tm=RT 0:014 10

4 exp54Tm=RT;

5

R being the molar gas constant (R 8:314 J mol1 K1), T the absolute temperaturein K, and Tm the melting point of the surface film in K.

On the other hand, when no surface films are formed, but the SCC process isspecifically affected by the concentration of cations of the noble metal of the alloy, as

in the case of AgCd alloy in AgNO3 solution, Galvele and Duffoo [29] developed an


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equation for the calculation ofDS, based on the alloy composition and the exchange

current density of the noble metal.

4.3. Transgranular stress corrosion cracking


The crack propagation rate values measured with SSRT for AISI 304 in LiCl

solution at 130 C, Fig. 2, are very close to those found by Speidel [30] using fracture

mechanics techniques. This coincidence in the measured CPR values proved that the

SSRT is a valid technique for measuring crack propagation rates in the present

system.

As mentioned by Duffoo et al. [12] for this SCC system, assuming that the surface

mobility SCC mechanism was operative, the analysis of the temperature dependenceof CPR showed that DS at 130 C was approximately 3 10

15 m2 s1. For SSRT the

predicted CPR values, with the stress rT equal to r0:2 (206 MPa, Table 2), agreed

very well with the present experimental results. When increasing the strain rate, the

samples fractured with noticeable plastic deformation. Then it is reasonable to as-

sume that the value of rT will increase, eventually reaching the UTS value (885 MPa,

Table 2). As shown in Fig. 10, using these two rT values (Table 2) the extreme CPR

values predicted by the surface mobility mechanism contain the experimentally

measured values.

There is no information about the exact values rT will have at different strain

rates. Nevertheless, in SSRT the samples fracture with very small plastic deforma-tion; consequently it is reasonable to assume that the stress at the tip of the crack will

be close to r0:2. On the other hand, under high strain rates, where cracks propagate

while the samples are undergoing strong plastic deformation, the first assumption

would be that the maximum value reached by the stress at the tip of the crack would

be that given by the UTS. The results in Fig. 10 suggest that the surface mobility

SCC mechanism could give a good account for the correlation found between CPR

and SR for transgranular SCC. No equations were found in the literature for a

similar analysis from the point of view of the film induced cleavage SCC mechanism,

or the anodic dissolution SCC mechanism. Consequently, from Fig. 10 no conclu-

sions can be drawn either supporting or disqualifying these two mechanisms.

4.3.2. Brass in NaNO2The reactions taking place at the tip of the crack, during SCC of brass in NaNO 2

solutions are only ambiguously known. Newman and Burstein [31] suggested that

decomposition of nitrite ions could lead to the formation of ammonia, with subse-

quent stability of copper ions by complex formation. On the other hand Rebak et al.

[22] concluded that passivity breakdown was the step previous to SCC of brass in

NaNO2 solution. For any of these alternatives, the environment at the crack tip

would be a solution with a high concentration of copper ions, providing a highexchange current density i0 of Cu$Cu

. In this case, surface diffusion would be

associated with the exchange current density, as in the model of Galvele and Duffoo


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[29]. Giordano et al. [32] and Montoto et al. [15] confirmed the validity of this hy-

pothesis.

When the value of DS is not known, but experimental CPR values are available

for a given experimental condition, Eqs. (4) and (5) can be used to predict the CPR

value at a different condition. This was done, for example, to predict CPR values foralloy 600 at different temperatures [25]. In the present case it will be assumed that in

a SSRT the value of rT is equal to r0:2 and with the CPR value measured at SSRT,

plus Eqs. (4) and (5), a DS value fitting these results can be calculated. Assuming that

this value does not change with the SR, and also assuming, as done above, that the

maximum stress value at the tip of the crack will be the UTS, the maximum CPR

expected can be calculated. Fig. 9 shows that, as it was the case with AISI 304 in LiCl

solution, the CPR values measured at different SR for SCC of brass in NaNO 2solutions fall between the extreme values predicted by the surface mobility SCC

mechanism.

4.4. Intergranular stress corrosion cracking

4.4.1. Brass in Mattsons solution

Speidel [33], using fracture mechanics techniques, for brass, of a composition

equal to that used in the present work and exposed to a NH 4OH solution, reported

CPR values very close to those found in the present work, with SSRT (Fig. 8). As

mentioned above for AISI 304, this observation gives support to the validity of the

CPR values measured with SSRT.

The same procedure used for brass in NaNO2 solutions, was applied to the CPRresults measured for brass in Mattsons solution. As before, the value of DS fitting

the SSRT results was calculated. Then with the DS value found, the CPR for rT equal

10-6 10-5 10-4 10-3 10-2 10-1 100 10110

-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Lower Det. Lim.

NF2 tests

AISI 304 in 11.8M LiCl

SEM CPR - 0.2MET CPR -

UTS

CPR(m/s)

Strain Rate (s-1)

Fig. 10. Crack propagation rates of AISI 304 in 11.8 M LiCl at 130 C. Comparison of measured values

with the predicted range of the surface mobility SCC mechanism.


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to the UTS was calculated. As shown in Fig. 11, contrary to what was found for

transgranular SCC, Figs. 9 and 10, the extreme values of CPR predicted by the

surface mobility SCC mechanism were not the limits for the experimentally found

CPR for intergranular SCC. As shown in Fig. 11, when the strain rate increased, the

measured crack propagation rates exceeded the values predicted by surface mobility,if as done before, the maximum stress rT acting at the tip of the crack was considered

to be the UTS. A calculation of the maximum stress rT required by Eq. (4) to fit the

CPR measured in UFSRT gave a value of 2.7 GPa, which was about five times larger

than the UTS. The stress values required by Eq. (4) to fit the experimental CPR

values are shown in Fig. 12.

One possible reason for the different effect on SR, between intergranular and

transgranular SCC, could be the fact that grain boundaries act as barriers for the free

movement of dislocations, leading to dislocation pileups [34]. At an atomic level, at

the tip of the crack, this process will lead to an increase in the value of rT well above

the externally applied stress. As discussed below, the dislocation pileups could ac-count for the required stress values mentioned in Fig. 12. A very crude calculation of

the formation rate of dislocations, at different strain rates, can be attempted by using

the equations developed by Van Bueren [35]. Fig. 13 shows the results of such cal-

culations for copper. It is interesting to point out the similarity between Fig. 13 and

Figs. 7 and 8. If the role of dislocations was to produce a surface slip step, where

corrosion would be localised, as it is assumed in the slip-step anodic dissolution SCC

mechanism [5], an increase in the strain rate should produce an increase in the crack

propagation rate, as found in the present work. Nevertheless, the anodic dissolution

SCC mechanism does not predict a difference in behaviour between IGSCC and

TGSCC. On the other hand, any mechanism based on the elastic stresses at the tip ofthe crack will be able to explain the difference between IGSCC and TGSCC, because

of the higher stress values induced by the dislocation pileups at the grain boundaries.

10-6

10-5

10-4

10-3

10-2

10-1

100

101

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

CPR - UTS

CPR - 0.2

CPR(m/s)

Brass in Mattsons solution

Strain Rate (s-1)

Fig. 11. Comparison of crack propagation rates of brass in Mattsons solution (0.05 M CuSO4 + 1 M

(NH4)2SO4 + pH 6.5 adjusted with NH4OH) at 0 VCu, measured and predicted by surface mobility.


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The same procedure used above was applied to the CPR results measured for Ag

Pd in halide solutions. As before, the values ofDS fitting the SSRT were calculated.

Then, with the DS values found, the CPR for values rT equal to the UTS were

calculated.

For potassium iodide environment, with the calculated value ofDS, results similar

to those in Fig. 11 were found. The relation of rT=UTS required to fit the measuredCPR had a maximum value of 4.5, very close to the value %5 indicated in Fig. 12.This observation supports the same assumptions made above for IGSCC.

10-6 10-5 10-4 10-3 10-2 10-1 100 1010

500

1000

1500

2000

2500

3000

Stress(MPa)

0.2

UTS

required

Strain Rate (s-1)

Brass in Mattson's solution

Fig. 12. Stresses rT of Eq. (4) required to fit the measured crack propagation rates of brass in Mattson s

solution (0.05 M CuSO4 + 1 M (NH4)2SO4 + pH 6.5 adjusted with NH4OH) at 0 VCu.

10-6

10-5

10-4

10-3

10-2

10-1

100

101

104

105

106

107

108

109

1010

1011

1012

Disloc.

Density(cm

s

)

-2

-1

Strain Rate (s-1)

Fig. 13. Rough estimate of the rate of production of dislocations, in copper, at various strain rates, based

on Van Buerens equations [35].


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For potassium chloride environment a range of potentials was applied, and more

data is available. The polarization curve, Fig. 1, shows a noticeable discontinuity at

about 0.45 VSHE, related to the change in the mode of dissolution of the alloy.

Nevertheless, as reported by Duffoo and Galvele for SSRT [13], and confirmed in thepresent work with different SR values, no discontinuities were observed in CPR at

any SR, Figs. 3 and 5. These observations suggest that, at least for IGSCC of Ag

15Pd in 1 M KCl solution, the dissolution mode of the alloy had no effect on the

SCC process.

As regards Eq. (2), and following the predictions of the surface mobility SCC

mechanism, the present results suggest the following: apparently, if Eq. (4) is taken

into account, the effect of SR is concentrated mainly on the mechanical variable rT,

while the potential Eacts mainly by changing the value ofDS (and possibly to some

extent L).

4.4.3. AgAu in HClO4Due to the high solubility of AgClO4 in water, 26.9 moles per litre of water [36], it

is probable that during dissolution, an acid concentrated AgClO4 solution will be

present next to the alloy interface, but no surface compounds will be expected. No

measurements are available at present of the DS value expected in this system. Vela

et al. [37] reported that the rate of step movement on pure Ag surfaces, in 1 M

HClO4 solution, was an order of magnitude higher than in vacuum. On the other

hand, Duffoo and Galvele [20] reported that SCC of Ag20Au alloy was faster in 1 M

AgClO4 solution than in 1 M HClO4 solution. While the operating mechanism is stillnot clear, it is safe to assume that the DS value in this system is high.

Using the same approach applied in the above discussed SCC systems, it was

found again that with the calculated value ofDS, results similar to those in Fig. 11

were found. The relation rT=UTS required to fit the measured CPR was very close tothat shown in Fig. 12.

These are two facts that should be pointed out. The first one is that the effect of

potential and SR on the CPR can be described by Eq. (2), as it was the case with Ag

Pd in halides. The second one is that Alvarez et al. [4] found that the inverse slope p

from a log CPREplot is the same for both IGSCC and TGSCC. These observations

indicate that there is an association between SR and rT, as well as for a with the SCCmorphology and also an association between E and DS, if the surface mobility

mechanism is considered, Eq. (4). As a further contribution to this point, Alvarez

et al. [38] have recently found that the activation energy for IGSCC of AgAu alloy

was equal to that for TGSCC for the same alloy, and that there was a coincidence

between the activation energy predicted by the surface mobility SCC mechanism and

the experimental results.

As for the film induced cleavage (FIC) mechanism, Maier et al. [14] showed that

there was no relation between the rate of dealloyed film formation and the CPR, as

should be expected if the FIC mechanism was operative. The supporters of the FIC

[39] attributed particular importance to the critical potential for selective dissolution(Ec) in alloys like AgAu. Maier et al. [14] found that changes in the nature of the

selective dissolution process had no effect on the CPR. This observation was


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particularly evident for Ag15Au, Ag25Au and Ag40Au alloys 1 M HClO4 so-

lution [14]. No breaks were found in the CPR vs. Ecurve when the potential crossed

the critical potential value. These results showed that SCC of AgAu alloys in

HClO4 solution was independent of the Ec value, and that there was no experimentalevidence correlating the SCC with that critical potential value. A similar observation

regarding Ec was reported by Lichter et al. [40] for CuAu alloys.

4.5. Mechanistic considerations

The above observations indicate that the slope in Eq. (1) is higher for IGSCC than

for TGSCC, Eq. (3). Besides the numerous considerations made above, the in-

volvement of SCC mechanisms, other than the surface mobility mechanism, will be

further considered.In the case of the film rupture, or slip step anodic dissolution mechanism, it

should be expected that, as found in the present work, an increase in the strain rate

will lead to an increase in the SCC rate. Nevertheless, as mentioned above, the effect

should be the same for IGSCC and for TGSCC. In the literature of slip step anodic

dissolution mechanism no explanation was found for the observation indicated by

Eq. (3).

As for the FIC SCC mechanism, as mentioned above, numerous contradictions

were found by various authors between the predictions of this mechanism and the

experimental results. On the other hand, the literature published on this mechanism

does not give, so far, any clue for the observation indicated by Eq. (3). Besides, in thepresent work, Fig. 4, longer cracks were found for 5 s1 than for 18 s1. From the

descriptions given for the FIC mechanism, a single event of crack propagation

should be expected at both strain rates, and no difference in the crack length should

be observed. Unfortunately no further quantitative comparisons can be made for

this mechanism at the present state of development of the FIC model.

5. Conclusions

The following conclusions can be drawn from the present work:

An increase of the strain rate generally accelerates the crack propagation process

according to the relation (1), or equivalently

log CPR / alog SR: 6

The slope a is different for transgranular and intergranular cracking. The values are

aTG 0:20.3 and aIG 0:40.7.The effect of potential can be incorporated as an additional term fE in Eq. (6),

not having a noticeable effect on the SR-dependent term.

No information was found in the anodic slip step dissolution mechanism, thatcould explain the present experimental results. The FIC mechanism requires further

development to account for the differences found between IGSCC and TGSCC.


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The surface mobility SCC mechanism can account for the dependence of crack

propagation rate on strain rate. With an increasing strain rate, the stress at the crack

tip zone will increase due to the formation of dislocation pileups, which is equivalent

to say that the driving force for the movement of surface vacancies increases.The surface mobility SCC mechanism can account for the separate effect of strain

rate and potential on crack propagation rates, according to Eq. (2). The strain rate

affects the stress at the tip of the crack, as indicated above, and the potential affects

the surface diffusion coefficient.

The absence of transgranular cracks, when very high strain rates are used, favours

a continuous crack propagation model and sheds doubts on any mechanism based

on very fast and discontinuous crack propagation events.

Acknowledgements

The present research has been supported by the Consejo Nacional de Investi-

gaciones Cientficas y Teecnicas, Argentina, and by the FONCYT, Secretara de

Ciencia y Tecnologa, Argentina.

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