Marcus P. Corrosion mechanisms in theory and practice

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(PSB)–grain boundary interactions are often observed to be preferential crack

initiation sites during CF, as well as localized pits around metallurgical heterogeneities.

The main need in fatigue crack initiation modeling is related to the quantitative

approach to local synergistic effects between environment and cyclic plasticity. In this sec-

tion, quantitative approaches to corrosion fatigue crack initiation from different electro-

chemical conditions are presented. Then improvement of such models is given through

corrosion-deformation interaction effects. Finally, an interesting example is given of the

coupling effects between cyclic plasticity and corrosion that must be taken into account to

improve the crack initiation resistance of duplex stainless steels in chloride solutions.

Classical Approaches to Corrosion Fatigue Damage

Electrochemical corrosion can be schematized as an “electronic pump or an

electronic circuit” related to oxidation and reduction reaction:

M → M

+ ne

–

anodic dissolution

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together with a cation hydrolysis reaction: M

+ nH

O → M(OH)

+ nH

Here M

is a solvated ion, e

–

is an electrorn, and n represents the ion state of

charge. The electrons, liberated by the oxidation, must flow through the material M

to be consumed in an appropriate cathodic reaction. Beyond a solubility limit,

precipitates of hydroxide or hydrated oxide are formed, and this surface film can

provide a barrier to further dissolution. In fact, there are two film formation

mechanisms: the dissolution-precipitation mechanism addressed before and also the

solid-state oxidation process M + H

O → MO + 2H

+ 2e

–

. Some films are termed

“passive,” for stainless steels or aluminum alloys, for instance. These films can play

an important role in environment-sensitive crack initiation and fracture. Under

thermodynamic equilibrium conditions, the film stability may be inferred from

E = f(pH) diagrams, where E is the electrical potential related to the chemical free

energy G by G = –nEF, and F is Faraday’s number. At equilibrium, one can define

the electrode potential (related to ΔG) and the current density I (I ~ e

–ΔG*/RT

where

ΔG

is the activation energy of dissolution).

Thus, the relation E =f(I) gives different corrosion rates for a given metal in a

given solution. Figure 1 shows such a relation (polarization curve) in the case of an

austenitic stainless steel in an acidic Cl

–

solution. Five domains can be considered for

corrosion and corrosion fatigue damage:

(1) In zone 1, E > E

, pitting occurs by destabilization of the passive film. Pits

act as stress concentrators during fatigue. During CF under pitting conditions, pits

grow into the material. If such a pit reaches a critical depth d

, a fatigue crack can

develop. The critical depth is then a function of the applied stress range [8].

Let us suppose the following conditions:

Constant corrosion conditions (pH, concentration of bulk solution)

Constant alternating load, dΔP/dt =0

Constant loading frequency dv/dt = 0

It is well established that growth kinetics of corrosion pits are determined by a

simple power law such as

Corrosion Fatigue Mechanisms 453

Figure 1 General polarization curve for an austenitic stainless steel in acidic Cl

–

solutions.

where t

is the incubation time for pit nucleation. If the pit depth reaches the critical

value:

corrosion fatigue crack initiation occurs. The critical pit depth d

depends on the

applied stress range Δσ

, the cyclic yield strength σ

(which can be different from

the tensile yield strength), the fatigue crack growth threshold ΔK

, and the geometry

of the specimen, expressed in terms of a geometric factor G. It can be calculated by

elastic-plastic fracture mechanisms based on the Dugdale model [7]. Then d

is,

given by the following equation:

The number of cycles to initiate a corrosion fatigue crack under pitting conditions

is, by combining the previous equations with N = tv,

The dependence of N

on the applied stress range Δσ

, calculated according to the

previous equation, is schematically represented in Figure 2a. Also, under pitting

conditions no corrosion fatigue limit exists. For N

≤ vt

, the influence of corrosion

on the fatigue crack initiation life disappears (only if pitting is the necessary effect).

Then, the lifetime is determined by the air fatigue behavior. Figure 2b shows an

example for which the proposed calculation of N

seems quite appropriate.

Nevertheless, the main problem is related to the fact that the coefficients C and β of

the pit kinetics are often not constant during cycling; it is a clear example of a

cooperative effect between plasticity and electrochemistry that needs finer analyses.

Figure 3 illustrates the fatigue crack initiation from a pit in a face-centered

cubic (fcc) Fe-Mn-Cr alloy cyclically deformed at low strain rate in a Cl

–

solution.

In many multiphase engineering materials, the presence of constituent particles

favors pitting and crack initiation.

(2) In zone 2, E

< E < E

, pits are repassivated. If the plastic strain amplitude

is too small for localized depassivation (by slip band emergence), pits will

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Figure 2 Corrosion fatigue crack initiation by pitting corrosion: (a) Schematic

representation of a σ-N curve. (b) Comparison of experimentally and theoretically derived

fatigue lives for the 20Cr-Ni-Mo alloy in 30 g/L NaCl solutions [8].

Figure 3 Crack initiation from a pit for a Fe-17Mn-13Cr alloy during CF in a 110°C Cl

–

solution at a plastic strain amplitude Δε

/2 = 4 × 10

–3

and a strain rate ε

= 10

–5

–1

not grow and the CF behavior is then close to that in air. On the other hand, pits

can grow if mechanical depassivation occurs and the CF behavior is then close to

that of zone 1.

(3) In the passive region 3, a competition between the kinetics of depassivation

by slip and that of repassivation takes place. Thus the influence of the plastic strain

amplitude and strain rate is quite obvious. In the same mechanical conditions as in

(1), the quantity of matter dissolved per cycle (related to a distance) in the

depassivated slip bands can be expressed, using Faraday’s law:

Corrosion Fatigue Mechanisms 455

where i (repassivation) is generally of the form i

max

exp(–γt) with γ taken as a

constant. Then N

= N (for dN = d

). If d

is taken as the grain size φ, for instance, then

A schematic representation of the equation is given in Figure 4a and corresponding

experimental results are shown in Figure 4b.

Neverthless, one of the main problems is that the repassivation law evolves

during cycling as shown in Figure 5. This result also emphasizes the synergy in

CF that leads to a complex predictive approach.

(4) In zone 4, generalized dissolution occurs, which is generally quite

dangerous for materials even without stress! In some cases, general corrosion can,

however, blunt the cracks, which improves the fatigue life.

Figure 4 (a) Schematic representation of a σ-N curve for CF crack initiation under passive

conditions. (b) Comparison of experimentally and theoretically derived fatigue lives for the

X1 Cr MoNb 182 alloy in 30 g/L NaCl at 80°C [8].

(5) In zone 5, cathodic reactions are favored. If reduction of hydrogen occurs,

we can have

+ 2e

–

→ H

→ 2H

adsorbed

→ H

ads

→ H

absorded

which can induce hydrogen diffusion and/or transport by dislocations, often leading

to macroscopic brittle fracture under stress.

The electrochemical approach presented here has many limitations. First of

all, the kinetics of the electrochemical reactions are closely dependent on the

cyclic plasticity and the number of cycles [9,10]. Thus, predictive laws are very

complex. Moreover, these laws use the local current densities, which are very

difficult to model. Finally, this approach does not really take into account the local

corrosion-deformation interactions (CDIs) and the effects of the corrosive solution

on the deformation mode. Indeed, such synergetic effects between corrosion and

deformation can be of prime importance; the following examples emphasize the

role of CDI in crack initiation processes.

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Figure 5 Simultaneous evolution of the cyclic stress σ, the average potential, and the

shape of the cyclic potential transients for a 316L alloy in 30 g/L Na Cl (Δε

/2 = 10

–3

= 10

–2

–1

Influence of Cyclic Plasticity on Electrochemical Reactions

The evolution of dissolution current density transients during cycling of ferritic and

austenitic stainless steels in NaCl solutions is shown in Figure 6, where curves

= f(N) are plotted. Here J

is the peak current density related to the depassivation

process due to cyclic plasticity, and N is the number of cycles. During the first cycles

the amount of dissolution increases, particularly at a high strain rate. One of the

ferritic steels exhibits twinning, which induces a more marked depassivation during

cycling, compared with the behavior of the second ferritic steel, which deforms by

pencil glide [11].

Figure 6 clearly illustrates the influence of the deformation mode on the

electrochemical reactions and the evolution of such electrochemical transients as

a function of N (i.e., the localization of the plastic deformation with a decrease of

after the first cycles and then the formation of microcracks with a new increase

of J

until fracture due to a more difficult repassivation process).

PSBs and intense slip bands are very prone to specific dissolution, not only

for passivated alloys but also in conditions of generalized dissolution as shown in

Figure 7 for copper single crystals in NaClO

solution [9].

As soon as the PSBs form, the anodic current increases even though the applied

plastic strain remains constant. This effect is related not only to the localization of the

cyclic plasticity but also to the influence of the dislocation microstructure of PSBs on

the free energy of dissolution (–ΔG) and the energy of activation (ΔG

) [10].

Moreover, cyclic plasticity has also been shown to promote localized pitting

well below the pitting potential without stress [10]. Thus, for the ferritic Fe-26Cr-

1 Mo stainless steel in 3.5% NaCl solution, a high strain rate ε

promotes strain

localization at grain boundaries, which induces intergranular pitting for an applied

potential of about 400 mV below the pitting potential without stress effect.

Corrosion Fatigue Mechanisms 457

Figure 6 J

= f(N) curves for stainless steels during CF in a 3.5% NaCl solution.

The applied strain rate (or frequency) is a very sensitive parameter for CF

damage. Figure 8 gives an interesting example for an Al-Li 8090 alloy in NaCl

solutions. N

is defined as the number of cycles to obtain a rapid 3% decrease of the

saturation stress [10]. At high strain rate (ε

> 5 × 10

–3

–1

), the anodic dissolution

occurs at slip band emergence and induces an enhancement of the transgranular

mechanical microcracking. At medium strain rate (5 × 10

–5

–1

< ε

< 5 × 10

–3

–1

pitting is favored and responsible for crack initiation. So when the plastic strain

decreases, pitting is more profuse (because of time) and the reduction in the fatigue

life to crack initiation is more pronounced in comparison with air.

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Figure 7 Influence of the PSB formation on the dissolution current for Cu single cyrstals in

NaClO

[9].

Figure 8 Influence of strain rate on 8090 Al-Li alloy fatigue life to crack initiation in a

3.5% NaCl solution for Δε

/2 = 4 × 10

–3

at free potential.

At low strain rate (5 × 10

–6

–1

< ε

< 5 × 10

–5

–1

), the fatigue time to initiation

increased by blunting of the mechanically formed microcracks because of

generalized pitting that acts as general corrosion. At very low strain rate (ε

< 5 ×

–6

–1

), CF crack initiation occurs by intergranular stress corrosion due to

localized dissolution at grain boundaries. The rapid occurrence of stress corrosion

cracking (SCC) induces a marked decrease of N

Softening Effect due to Anodic Dissolution

CF tests on smooth specimens were performed at room temperature on a 316 L

austenitic stainless steel in a 0.5 N H

solution at different electrochemical

potentials and for a prescribed plastic strain amplitude of 4 × 10

–3

(ε

= 10

–2

–1

The depassivation-repassivation process occurs in a very regular way, well

before any microcracks can form [11]. It is of particular interest to follow the

evolution of the maximum flow stress in the corrosive solution at free potential

and at imposed cathodic potential and to compare this evolution with that

observed in air (Figure 9). It clearly appears that (a) a cyclic softening effect

occurs at the free potential in comparison with the behavior in air; (b) this soft-

ening effect disappears when the cathodic potential is applied (and the anodic

dissolution is markedly reduced), after about 150 cycles; (c) the softening effect

then occurs in the same way when the free potential is reestablished; and (d) a

delay in the evolution of the flow stress with regard to the number of cycles for

which a potential change is imposed can be observed for the free potential to the

cathodic potential change (and vice versa).

This effect has also been observed during creep in corrosive solutions for

copper [1]. It corresponds to the time during which vacancies due to dissolution are

still acting on the dislocation mobility.

The macroscopic cycling softening effect observed in H

solution at room

temperature (which is not due to microcracking) is very relevant to take into account

Corrosion Fatigue Mechanisms 459

Figure 9 Evolution of the peak stress Δσ/2 during cycling in a 0.5 N H

solution at

free potential for Δε

/2 = 4 × 10

–3

and

= 10

–2

–1

compared with the air behavior.

quantitatively the local dissolution-deformation interactions that will lead to the

fatigue crack initiation process.

Influence of Corrosion on PSB Configurations

Electrochemical control of corrosion has been shown to affect significantly the

morphology of surface deformation. A modification of the number of persistent

slip bands (PSBs) and of the slip offset height in PSB has been observed for Ni

single crystals [4] in 0.5 N H

and in copper single crystals [4,9] according to

the applied potential, in comparison with air. It is easy to understand that such

influences on PSB distribution will affect the crack initiation conditions. Figure 10

shows histograms of the PSB distribution produced on monocrystalline nickel in

0.5 N H

at a constant strain amplitude.

Experiments conducted at the corrosion potential and at +160 mV/SCE

result in a reduction of the inter-PSB distance and a reduction of slip offset height.

An Example of Mechanical and Electrochemical Coupling Effects:

The CF Crack Initiation Mechanisms of a Two-Phase Stainless Steel

in NaCl Solutions

Mechanical and electrochemical coupling effects are generally the key for

understanding the crack initiation mechanisms in multiphase alloys. This is

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Figure 10 Histograms of distance between PSB clusters, from the replicate Ni single-

crystal specimens fatigued for 1000 cycles under total strain control Δε

. Shear strain = 0.12%,

(a) air and (b) +160 mV/SCE in 0.5 N H

[4].

clearly illustrated for a duplex α/γ stainless steel (without nitrogen) in a 3.5% NaCl

solution at pH 2 and free potential [11]. At low plastic strain amplitude, the softer

γ phase is depassivated but this phase is cathodically protected by the non–

plastically deformed α phase [11]. This coupling effect reduces the dissolution of

the γ phase and delays CF damage, which is not the case at higher strain amplitude

when the α phase is also depassivated by slip band emergence.

Observations of the crack initiation sites by scanning electron microscopy

showed that at low plastic strain amplitudes (Δε

/2 < 10

–3

) for which the fatigue

resistance of the α-γ alloy is close to that of the γ alloy, cracks nucleate only in the

austenitic phase (Fig. 11a), but at higher strain amplitudes (Δε

/2 < 10

–3

), the first

cracks nucleate principally in the ferritic phase (Fig. 11b). The excellent CF

resistance of duplex stainless steels (for Δε

/2 < 10

–3

) can then be understood through

the electrochemical and mechanical coupling effects on crack initiation processes.

CORROSION FATIGUE PROPAGATION MECHANISMS

Phenomenology

One can find an enormous amount of mechanistic work about corrosion fatigue

crack growth in the literature (see, for instance, Refs. 4,6,7,12). The aim of this

section is not to review such studies but to analyze the possible mechanisms at the

crack tip leading to crack advance. The question is, “What is the crack tip driving

force that controls the corrosion fatigue crack growth?” among the different

mechanical (stress, strain, strain rate) and chemical (dissolution, film formation,

hydrogen production) effects.

Figure 12 shows the influence of different environments on the crack growth

rate of a classical industrial steel [4]. Moist air is shown to have a marked influence

on the crack growth rate in comparison with vacuum. Crack tip velocity is very

sensitive to sodium chloride solution.

In fact, one must distinguish between long crack growth and short crack

growth. For long crack growth, using linear elastic fracture mechanics (LEFM),

Corrosion Fatigue Mechanisms 461

Figure 11 Crack initiation in a duplex stainless steel at ε

=2× 10

–3

–1

. (a) In the γ phase

at Δε

/2 = 3 × 10

–4

. (b) In the α phase at Δε

/2 = 4 × 10

–3