Marcus P. Corrosion mechanisms in theory and practice

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typical characteristics of the corrosion fatigue behavior are given in Figure 13 as

a function of the stress intensity factor ΔK. Interactions with SCC are emphasized.

The models then propose that the rate of crack growth corresponds either to

the sum of pure mechanical fatigue and the rate of stress corrosion cracking or to the

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Figure 11. (Continued).

Figure 12 Influence of environment on the crack propagation velocity for a 4130 steel [4].

fastest available mechanisms among those described in the following. Figure 14

summarizes the influence of corrosion on the fatigue crack growth characteristics

[13–15]. To the purely mechanistic mode I crack propagation behavior under

vacuum (curve 1) must be added (a) the effect of closure [4,6] and mode II on the

near-threshold (curve 2), (b) the hydrogen-assisted crack propagation behavior

(curve 3), and (c) the influence of absorption and diffusion of hydrogen at low

loading R ratio (curve 4) and at higher R ratio (curve 5). One must also take into

account dissolution and film effects.

However, it has been shown that short cracks propagate at stress intensity

factors well below the long crack threshold, as shown in Figure 15 for carbon steel

in seawater.

The application of microstructural fracture mechanisms (MFMs) has been

successfully used to predict the growth of short cracks during fatigue in air [16].

These models have been adapted to characterize and predict the uniaxial and

multiaxial corrosion fatigue loading [17].

The two following equations provide the basis of the Brown-Hobson model

[18], in which the fatigue crack growth rate is expressed as a function of an

equivalent strain term γ

for stage I and stage II cracks, respectively.

Corrosion Fatigue Mechanisms 463

Figure 13 Schematic of fatigue and corrosion fatigue crack growth rate as a function of

crack tip stress intensity.

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Figure 14 Schematization of the different CF crack growth mechanisms [13].

Figure 15 Comparison of long and short CF crack growth rates for carbon steels (σ

= 500

MPa) in artificial water, 0.2 Hz, R = 0.1 [15].

where a is the crack length; d a microstructural parameter such as grain size; i the

number of grains through which the crack has traversed; B

, B

and β

, β

are

constant depending upon the material-environment system; and D is the long

crack threshold.

The determination of the crack tip environment is not easy because of the

numerous electrochemical reactions and the associated mass transport and

thermodynamic criteria that govern this environment. The nature of the solution

(composition, pH, species, corrosion products that can induce roughness, etc.) can

be very different at the crack tip and in the bulk solution. Figure 16 shows the

possible electrochemical reactions at the crack tip. Both anodic dissolution effects

and a coupled hydrogen reaction must often be taken into account. The mathematical

modeling of the localized crack tip chemistry is therefore possible [19].

One can find in Ref. 20 a very significant effect of the transport properties

of the crack solution on the CF crack growth rates of steel in seawater.

Anodic Dissolution Effects

Anodic dissolution has been shown to occur preferentially in slip bands [11] very

near the crack tip, which leads to many effects on the CF behavior as shown in

Figure 17. A restricted slip reversibility model for stage I fatigue crack propagation

has been proposed. The average crack growth increment per cycle, Δ

χ,

is determined

by factors controlling slip reversibility on the forward slip planes (i.e., S1 and S4).

For fcc materials, it involves alternating slip on (111) planes near the crack tip.

The slip reversibility is controlled by the degree of work hardening and recovery

on a slip plane and the presence of corrosion products (oxides) on the slip steps.

The rate of hydrated oxide nucleation plays a critical role in this model and therefore

is expected to control stage I fatigue crack growth of an austenitic stainless steel

in Cl

–

solutions.

This localized dissolution process is not easy to take into account in numerical

modeling of crack propagation. The slip dissolution model for CF is based on the

fact that for many alloys in different solutions the crack propagation rate is

proportional to the oxidation kinetics. Thus, by invoking Faraday’s law, the average

environmentally controlled crack propagation rate V

–

for passive alloys is related

to oxidation charge density passed between film rupture events, Q

Corrosion Fatigue Mechanisms 465

Figure 16 Possible electrochemical reactions at a corrosion fatigue crack tip.

where t

is the film rupture period. Thus:

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Figure 17 Schematic diagram of stage I corrosion fatigue crack propagation

mechanism [21].

where ε

is the strain rate and ε

the strain for film rupture (about 10

–3

If we take a classical law for current transients at the crack tip,

Then, for t

> t

, β > 0,

Even if mechanical analyses give good approximations for ε

at the crack tip, some

problems still remain with the previous equation. In particular, the value of

β evolves all along cycling. But the main effect is related to the localized corrosion-

deformation described previously. It has been shown that vacancy generation at

the crack tip due to localized dissolution can induce cyclic softening effects and

that hydrogen absorption, which can also be coupled to localized dissolution, can

also enhance the local cyclic plasticity. This is why improvement of CF predictive

laws is needed even if V

can be adjusted in the equation, which is still very useful.

New models based on the description of Figure 17 but taking into account the

localized corrosion deformation processes are under study.

Moreover, films related to solid-state oxidation (M + H

O→MO + 2H

–

) can also play a role in the crack advance. This needs further studies to be

quantitatively more relevant [22].

Hydrogen Effects

Hydrogen-assisted cracking is often invoked, particularly for body-centered

cubic (bcc) materials but also together with anodic dissolution for fcc alloys.

Figure 18 shows schematically a hydrogen-assisted cracking event. Interactions

between a discretized dislocation array and the crack tip under an applied stress

produce a maximum stress field from behind the tip. When the hydrogen con-

centration reaches a critical value, a microcrack is nucleated because either the

local cohesive strength is reduced or dislocation motion is blocked in the

hydrogen-enriched zone, or both. The microcrack arrests about 1 μm ahead of

the original location of the tip and these processes then repeat, leading to

discontinuous microcracking.

Other mechanisms have been proposed, particularly the hydrogen-induced

plasticity model for precipitates containing materials such as Al-Zn-Mg alloys.

This model is shown in Figure 19 [5].

Absorbed hydrogen atoms weaken interactomic bonds at the crack tip and

thereby facilitate the injection of dislocations (alternate slip) from the crack tip. Crack

growth occurs by alternate slip at crack tips, which promotes the coalescence of

cracks with small voids nucleated just ahead of the cracks. In comparison with the

behavior in neutral environments, the CF crack growth resistance decreases as the

Corrosion Fatigue Mechanisms 467

Figure 18 Schematic illustration of hydrogen-assisted cracking mechanism [22].

proportion of dislocation injection to dislocation egress increases. More closely

spaced void nuclei and lower void nucleation strains should also decrease the

resistance to crack growth in CF. This mechanism is proposed for Al-Zn-Mg alloys

and is highly supported by observations that environmentally assisted cracking can

occur at high crack velocities in materials with low hydrogen diffusivities and that

the characteristics of cracking at high and low velocities are similar.

Other hydrogen-dislocation interactions at the corrosion fatigue crack tip

must be taken into account. One can show, for instance, that hydrogen promotes

planar slip in fcc materials. Cross-slip ability can be discussed for the peculiar

situation of the dissociation of a perfect screw dislocation into two mixed partials

separated by a stacking fault ribbon (Fig. 20). The cross-slip probability depends

on the work necessary for recombination.

Each partial is subjected to two forces: the repulsion due to the other partial

and the attraction due to the stacking fault (Γ ~

–

100 mJ/m

in nickel, for instance).

In the absence of an external stress, the partials are in equilibrium at a distance

where the two forces annihilate.

Hydrogen interacts only with the edge parts of the partials (hydrostatic

stresses). It migrates to the tensile zone of the edge parts, as shown in Figure 20

from an initial concentration C

(for calculations, see Ref. 23).

The dilatation strains due to the antisymmetric hydrogen distribution induce a

net shear component along the dislocation line, whose sign is opposed to that of the

edge dislocation. Because the Burger’s vectors of the two edge parts of the partials

have opposite sign, hydrogen segregation will induce a supplementary effect, which

is to reduce their normal attraction. From the viewpoint of the mixed partials, the

repulsion between the screw parts is the leading term, and hydrogen induces a

supplementary repulsion by “screening” the attraction between the edge components.

This screening of the pair interactions between coplanar edge dislocations was

shown to be independent to the first order on the distance between dislocations [23],

provided that diffusion time and temperature allowed the hydrogen distribution to

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Figure 19 Schematization of the hydrogen-induced plasticity model for CF cleavage like

cracking [5].

reach a configuration “in equilibrium with the local stress.” Under these conditions,

the relative screening of the pair interactions (i.e., the “hydrogen component” of

the resolved shear stress normalized by that of the dislocation itself) was shown

by numerical simulations to be given with excellent accuracy by the following

simple expression [23]:

Corrosion Fatigue Mechanisms 469

Figure 20 Equilibrium hydrogen distribution around a dissociated screw dislocation in

nickel (C

is the initial concentration of hydrogen).

where C

is the remote hydrogen concentration (in atom fraction); T is the absolute

temperature; R is the gas constant; E, v, and V

are Young’s modulus, Poisson’s

ratio, and the molar volume of the host metal; and V

is the hydrogen partial molar

volume. The coefficient β contains all the material parameters that influence the

hydrogen screening effect as a function of temperature and concentration. In nickel,

β = 2.34 × 10

–4

–1

. Using this expression for the dissociated configuration of

Figure 20, Figure 21 shows the forces on one partial versus the width of the stacking

fault ribbon in nickel for an initial amount of hydrogen n

= 0.05 at room

temperature. The d

and d

are respectively, the equilibrium distances in the

absence and in the presence of hydrogen, neglecting a possible decrease of Γ.

The recombination work is represented by the hatched areas between the curves.

In the presence of hydrogen at concentration C = 0.05, calculations show that the

recombination work is increased by 50%. The elastic effect of hydrogen is to increase

the recombination work and then to decrease the cross-slip ability. This confirms

experimental studies that show that hydrogen promotes planar glide [24].

Finally, it must be said that very often anodic dissolution and hydrogen

effects must both be taken into account.

MONTE CARLO-TYPE SIMULATIONS OF CORROSION FATIGUE

LIFETIMES FROM THE EVOLUTION OF SHORT SURFACE CRACKS

Introduction

The modeling of fatigue and corrosion fatigue damage is still not completely

solved. Its definition is controversial, and it depends on the scale of interest in the

study. The high-cycle fatigue regime was first investigated, and it has been summed

up as due to the propagation from scratch of a single crack leading eventually to

fracture [25,26]. Hence, an equivalence between the level of damage and the

fatigue crack depth was considered [27]. In this case, fatigue damage accumulation

corresponds to the bulk growth rate of one crack. Those speculations have proved

to be both successful and satisfactory.

The next step aimed at extending the latter definitions from high- to low-cycle

fatigue. However, as multiple cracks nucleate and propagate simultaneously in low-

cycle fatigue, the previous definitions of both fatigue damage and fatigue damage

accumulation are ambiguous. The majority of cracks are comparable to each other

from a surface length viewpoint. Moreover, all crack lengths are comparable to

grain size throughout all the fatigue lives.

On the one hand, the mechanical approach describes the behavior of long

through-cracks in a macroscopically elastic field [7,25]. It has given interesting

empirical laws but is unable to take into account the physical processes of fatigue

damage. On the other hand, the microscopic approach was developed with the

analysis of the dislocation behavior, the corresponding strain hardening or softening

effects, and the formation of persistent and intense slip bands [28,29]. Nevertheless,

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Figure 21 Effect of hydrogen on the work of recombination of partials in nickel at 300 K.

this approach is generally limited to the formation of the first microcracks: the

corresponding physical and numerical models concern only the first 10% of the

fatigue lifetime for polycrystalline materials. Moreover, when applied to crack

propagation, the microscopic approach does not take into account the influences

of other formed cracks. Thus, the classical mechanical and microscopic approaches

cannot be used to model the evolution of a population of surface cracks and the

corresponding low-cycle fatigue damage.

In this section an investigation of the fatigue damage process at an intermediate

scale (i.e., a mesoscopic scale corresponding to the grain size) is addressed. The

importance of the latter scale to modeling low-cycle fatigue lifetimes is pointed out

through the physical analysis of fatigue damage and of fatigue damage accumulation.

Particular attention is paid to the evolution of populations of surface short cracks.

Experimental results mainly correspond to push-pull low-cycle fatigue tests of 316L

stainless steel in air and in 3% NaCl solutions. From these results and from

assumptions concerning surface short crack behavior, a numerical model is developed.

Monte Carlo principles are used to deal with random crack nucleation and crack

interactions. It is finally shown that such an analysis is very relevant to prediction

of corrosion fatigue lifetimes of austenitic stainless steels in chloride solutions.

Physical Description of the Fatigue Damage

The experimental results on the low-cycle fatigue damage of 316L stainless steel

have been fully discussed elsewhere [30,31]. Transgranular cracking is generally

observed in the 316L polycrystalline stainless steel for fully reversed push-pull

tests at intermediate plastic deformation amplitudes (Δε

/2 in the range [5 × 10

–5

5 × 10

–3

], the plastic deformation rate being 10

–3

–1

Multiple short cracks are observed at the specimen surface. Different surface

short crack types are introduced according to both cracking behavior and surface

lengths. Surface short cracks, the lengths of which are less than one grain size (i.e.,

less than 50 μm, which is the average grain size in the case of classical 316 alloy),

are the more numerous ones. Every crack propagates first crystallographically, i.e.,

within the intense slip bands. The first main obstacles to their propagation are the

grain boundaries. The closer to the grain boundary, the lower the crack growth rate

[30,32]. Once the grain boundary is crossed, the propagation speeds up to the next

grain boundary. It has been observed experimentally that two to three grain

boundaries need to be crossed for the change of cracking behavior to take place.

Surface crack propagation evolves from crystallographic to “mechanical”

growth. The surface cracks are then observed to grow perpendicular to the specimen

axis (likely to be related to the onset of the so-called stage II cracking). The preceding

cracking process leads to distinction of three main categories of surface short cracks.

Type I cracks have a surface length less than one grain size. Type II cracks are

longer than one grain size at the surface but smaller than three (two to three grain

boundaries have been overcome by the surface short crack). Type III crack surface

length goes from 3 up to 10 grain sizes. A fourth type concerns cracks longer than 10

grain sizes at the surface. The latter cracks are numbered in the range 1 to 3 per

specimen and form during the last 10% of the fatigue lifetime, following completion

of N

cycles. N

corresponds to the number of cycles to form the type IV short crack.

It is about 90% of the fatigue lifetime [30,31].

Corrosion Fatigue Mechanisms 471