Marcus P. Corrosion mechanisms in theory and practice

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Microbially Influenced Corrosion 603

Corrosion in Nuclear Systems:

Environmentally Assisted Cracking in

Light Water Reactors

F. P. Ford and Peter L. Andresen

General Electric Company, Schenectady, New York

INTRODUCTION

The phenomena of initiation and subcritical propagation of cracks in structural

materials due to the conjoint actions of stress, material microstructure, and

environment have been recognized for many years, and the mechanisms have

been extensively investigated. This is especially the case for stressed alloys in

environments containing high anionic concentrations of e.g., chlorides, phosphates,

and hydroxides, either in the bulk environment (e.g., in the paper, chemical,

petrochemical, and marine industries) or in localized environments where boiling or

gradients in electrochemical potential, temperature etc. can concentrate species.

However, it has been recognized that environmentally assisted cracking under static

or cyclic loading (i.e., stress corrosion or corrosion fatigue) can occur in

ultrahigh-purity water even when the concentration of non-OH

–

anions is < l0 ppb.

Although the cracking susceptibility is generally lower than in the concentrated

environments, it is sufficient to cause concern when extended lives or high

levels of plant availability are required, as in the power generation industry and

especially for light water reactors (LWRs). The objective of this chapter is to

discuss the development and use of mechanistically based models of

environmentally assisted cracking of structural materials in highpurity water, with

special emphasis on boiling water reactors (BWR) and occasional reference to

pressurized water reactors (PWR).

THE PRACTICAL PROBLEM AND THE PROPOSED SOLUTION

There have been well-documented instances of environmentally assisted cracking in

high-temperature water of austenitic stainless steels, nickel-base alloys, low-alloy and

carbon steels, and their weld metals in various subcomponents of pressure vessels,

pressurizers, steam generators, piping, deaerators, etc. Consequently, there is a

strong driving force to derive design and life prediction codes which can account for

605

the multitude of material, stress, and environmental combinations relevant to these

systems. This requirement has posed a difficulty for the experimentalist, since it

is not easy to control adequately the system conditions (e.g., water purity, loading)

and to measure crack propagation rates with a sensitivity that is relevant to a

typical 40-year design life. As a result, the current life prediction codes for

environmentally assisted cracking of structural materials in high-temperature

water usually represent upper bounds of the available data base and do not account

for the wide range of material and environment conditions that are possible for the

“nominal” system. This conservative “upper-bound” scenario can put unreasonable

constraints on the continued operation of specific plants which are operating under

far different system conditions than those represented by the design or life evaluation

code. In other cases, life prediction codes do not exist either because of wide scatter

in the data (e.g., stress corrosion of low-alloy pressure vessel steels) or because of

lack of relevant data (e.g., irradiation-assisted cracking of stainless steel).

This unsatisfactory situation is offset, however, by the increase in mechanistic

understanding of environmentally assisted cracking, which has accelerated in the

last decade because of the availability of experimental and analytical procedures

that allow quantification and validation of various cracking hypotheses. The

ultimate validation of any such mechanistically based model is its ability to

predict the extent of crack penetration as a function of the wide combination of

the material, stress, and environment factors relevant to LWR operation (Fig. 1).

Since the precise shape of the crack depth–operational time curve in Figure 1

must be a function of the specific material, environment, and stressing conditions, it

follows that if there is a range in the actual system conditions, there will be a

predictable range in the observed data, with the distribution of the range in cracking

mirroring the distribution of system conditions which affect the propagation process.

This provides a bridge between deterministic and statistical or probabilistic life

prediction methodologies [1,2].

606 Ford and Andresen

Figure 1 Schematic crack depth–time relationships for a range of relevant material,

environment, and stress conditions.

CANDIDATE CRACKING MECHANISMS

Historically, environmentally assisted cracking has been divided into the “initiation”

and “propagation” periods. To a large extent this division is arbitrary, for in most

investigations initiation is defined as the time at which a crack is detected, or when

the load has relaxed a specific amount (in a strain-controlled test); in these cases such

a definition of initiation corresponds to a crack depth of significant metallurgical

dimensions (e.g., ≥2 mm). Thus, for the purpose of lifetime modeling it is assumed

(Fig. 2) that, phenomenologically, initiation is associated with microscopic crack

formation at localized corrosion or mechanical defect sites generally associated with

pitting, intergranular attack, scratches, weld defects, or design notches. If it is further

assumed that the probability of such initiation sites existing or developing relatively

early in the life of the component is high, then the problem of life prediction devolves

to understanding the growth of small cracks from these geometrically separated

initiation sites and the coalescence of these small cracks to form a major crack, which

may then accelerate or arrest depending on the specific material, environment, and

stress conditions.

There has been relatively little fundamental work on the growth of such

microscopically short cracks. For brevity, this will not be reviewed in detail, apart from

mentioning that most work has been done under fatigue loading [3–7], with emphasis

on the microstructural interactions required for microscopic crack arrest or

propagation and modifications to linear elastic fracture mechanics analyses to account

for the observed behavior in this crack size range. In the area of environmentally

assisted cracking, the coalescence of microscopically small cracks has been

investigated for carbon steels in carbonate-bicarbonate solutions [8,9] and stainless

steels and nickel-base alloys [10] in high-temperature water. In these cases it is observed

that the crack growth rate increases as the small cracks coalesce and approaches a

Corrosion in Nuclear Systems 607

Figure 2 Proposed sequence of crack initiation, coalescence, and growth for steels

undergoing subcritical cracking in aqueous environments.

steady-state value when the mean crack depth is about 20 to 50 μm (Fig. 3);

thereafter the crack propagation rate may be analyzed in terms of linear elastic

fracture mechanics normally applicable to “deep” cracks. Thus, attention can be

focused on current mechanistic knowledge of crack propagation rates for deep

cracks (e.g., ≈1 grain diameter and greater), recognizing that the resultant life

prediction may be conservative because the microscopic crack initiation and crack

coalescence periods are not accounted for.

The basic premise for all of the proposed crack propagation mechanisms for

ductile alloys in aqueous solutions is that the crack tip must propagate faster than

the corrosion rate on the unstrained crack sides so that the crack does not degrade

into a blunt notch [11,12]. Based on this criterion, the material-environment

conditions for cracking can be defined based on the thermodynamic criteria for the

existence of a protective oxide, salt, or compound film on the crack sides. For

instance, cracking susceptibility of mild steel in hydroxide, carbonate-bicarbonate,

nitrate, phosphate, and molybdate solutions can be predicted to occur in the specific

potential-pH ranges where the protective film is thermodynamically stable [13].

Very similar thermodynamic arguments may be made for other systems, (e.g.,

brassammoniacal solutions [14]), and may be extended to kinetic arguments [15–17]

which require that the electrochemical reaction rates (e.g., dissolution or oxidation)

at the strained crack tip be significantly higher than those on the crack sides for an

“electrochemical knife” [15] to propagate. Indeed, the suppression of stress corrosion

and corrosion fatigue in many systems may be explained in terms of chemical

blunting of cracks during the early propagation stage. The cracking of mild and

low-alloy steels in aqueous environments offers ideal examples of this criterion.

For instance, low-alloy steels will not exhibit stress corrosion in acidic or concentrated

chloride solutions unless the general corrosion-blunting effect is counteracted with

608 Ford and Andresen

Figure 3 Crack depth–time relationship for intergranular cracks initiating, coalescing,

and growing in a notched 1T CT specimen of sensitized stainless steel in 288°C water.

(From Ref. 10.)

chromium or nickel alloying additions [13,18]. Similarly, in high-purity water

systems, carbon steel will not undergo stress corrosion cracking in low-temperature,

oxygenated environments, since the embryo crack will be blunted by pitting;

however, at temperatures >150°C, cracking is possible because of the protective

nature of magnetite, Fe

[19], which constitutes the inner film of the duplex

surface oxide.

For systems in which chemical blunting is not an issue, numerous crack

propagation mechanisms were proposed in the period 1965–1979 [20–31], ranging

from preexisting active path mechanisms, to strain-assisted active path mechanisms,

to mechanisms that depend on various adsorption-adsorption phenomena (e.g.,

hydrogen embrittlement mechanisms). There was considerable debate concerning

the dominant mechanism in a given system, promulgated in part by the fact

that up to 15 years ago there were few analytical techniques to test the various

hypotheses quantitatively. Parkins [32] pointed out early on, however, that it was

likely that there was a “stress corrosion spectrum” which logically graded the

cracking systems between those that were mechanically dominated (e.g., hydrogen

embrittlement of high-strength steels) to those that were environmentally dominated

(e.g., preexisting active path attack in the carbon steel–nitrate system). Indeed, it

was suggested that two mechanisms may operate in one alloy-environment system

with a dominant mode being determined by relatively small changes in the material,

environment, or stressing condition. This was followed by the suggestion (e.g.,

[1,11,32–34] that a similar spectrum of behavior occurs between constant load

(stress corrosion), dynamic load (strain induced cracking), and cyclic load (corrosion

fatigue) conditions.

With the advent in the last 15 years of more sensitive experimental and

analytical capabilities, many of the earlier cracking hypotheses have been shown

to be untenable, and the candidate mechanisms for environmentally assisted crack

propagation (stress corrosion and corrosion fatigue) have largely been narrowed

down to slip dissolution, film-induced cleavage, and hydrogen embrittlement.

These mechanisms are briefly described below, followed by a discussion of the

development of the slip dissolution model for life prediction for austenitic

stainless steels in BWR coolant. Modifications to the basic model to explain

changes in cracking susceptibility due to (a) irradiation for reactor core components,

(b) material (e.g., nickel-base or low-alloy alloys), and (c) environment (e.g., BWR

vs PWR) are then outlined.

Slip Dissolution Mechanism

Various crack advance theories have been proposed to relate crack propagation to

oxidation rates and the stress-strain conditions at the crack tip, and these theories

have been supported by a correlation between the average oxidation current

density on a straining surface and the crack propagation rate for a number of

systems [12,35]. There have been various hypotheses about the precise atom-atom

rupture process at the crack tip—for example, the effect that the environment has

on the ductile fracture process (e.g., the tensile ligament theory [36], the increase

in the number of active sites for dissolution because of the strain concentration

[37], the preferential dissolution of mobile dislocations because of the inherent

chemical activity of the solute segregation in the dislocation core [38]).

Corrosion in Nuclear Systems 609

Experimentally validated elements of these earlier proposals have been

incorporated in the current slip dissolution model, which relates the crack

propagation to the oxidation that occurs when the protective film at the crack tip is

ruptured [39–44]. Different types of protective films have been proposed, including

oxides, mixed oxides, salts, or noble metals left on the surface after selective

dissolution of a more active component in the alloy. As discussed below, quantitative

predictions of the crack propagation rate via the slip dissolution mechanism are

based on the faradaic relationship between the oxidation charge density on a surface

and the amount of metal transformed from the metallic state to the oxidized state

(e.g., MO or M

The change in oxidation charge density with time following the rupture of a

protective film at the crack tip is shown schematically in Figure 4. Initially, the

oxidation rate and, hence, crack advance rate will be rapid, typically controlled by

activation or diffusion kinetics as the exposed metal dissolves, although availability

of the balancing cathodic reduction current is also clearly necessary. However, in

most LWR cracking systems, a protective oxide re-forms at the bared surface and

the rate of total oxidation (and crack tip advance) decreases with time. Thus, crack

advance can be maintained only if the film rupture process is repetitive. Therefore,

for a given crack tip environment, corrosion potential, and material condition, the

crack propagation rate will be controlled by the change in oxidation charge density

with time and the frequency of film rupture at the strained crack tip. This latter

parameter will be determined by the fracture strain of the film, ε

, and the strain rate

at the crack tip,

⋅

. By invoking Faraday’s law, the average environmentally

610 Ford and Andresen

Figure 4 Schematic oxidation charge density–time relationship for a strained crack tip

and unstrained crack sides. (From Ref. 11.)

controlled crack propagation rate,

–

, can be related to the oxidation charge density

passed between film rupture events, Q

, and the strain rate at the crack tip,

⋅

Corrosion in Nuclear Systems 611

where M, ρ = atomic weight and density of the crack tip metal

F = Faraday’s constant

z = number of electrons involved in the overall oxidation of an atom of

metal

Because the oxidation charge density on a bare surface varies with time at a

rate that is dependent on the material and environment compositions that control

the passivation rate at the crack tip, Eq. (1) can be adequately represented (and

reformulated) in terms of a power law relationship:

where A and n are constants that depend on the material and environment

compositions at the crack tip. These constants are related to the oxidation reaction

rates, or current densities, in the specific crack tip material-environment system

[45]. The current transients generally have an initially high bare surface dissolution

current density, i

for a short time, t

; thereafter, oxide formation or precipitation

leads to a decay in the oxidation current density which often follows a general

power law relationship:

If a bare surface condition is maintained at the crack tip (i.e., ε

⋅

< t

), then

integration of Eq. (3) leads to a predicted maximum crack propagation rate:

This relationship is the quantitative basis for the early empirical observations

discussed at the beginning of this section relating the oxidation current density on

a straining surface and the crack propagation rate. However, these early correlations

were obtained primarily for alloys in concentrated environments (boiling MgCl

9 M NaOH solutions, etc.) under dynamic straining conditions. By comparison, in

relatively dilute environments characteristic of LWRs it is expected that (a) the

passivation rate will be high, and thus “n” [in Eq. (3)] will be high and t

will be

short, and (b) under constant load or displacement conditions, the periodicity of

oxide rupture, ε

⋅

, will be much greater than t

. Under these circumstances a

bare surface will not be maintained at the crack tip, and the crack propagation rate

will be given by the integration of Eq. (3).

This is an expanded version of Eq. (2) and relates the parameters A and n to the specific

oxidation rates [e.g., Eq. (3)] and the fracture strain of the oxide at the crack tip.

Under constant load or displacement conditions, the crack tip strain rate can

be related, as discussed later, to the creep processes at a moving crack tip [1,45].

Under monotonically or cyclically changing bulk strain conditions,

⋅

can be

related to an applied strain rate

⋅

app

. Thus, the slip dissolution mechanism may be

applied to not only stress corrosion but also strain-induced cracking [46] and

corrosion fatigue. Under cyclic loading conditions, however, the crack is also

moving forward be irreversible cyclic plastic deformation, e.g., fatigue striation

formation. Since this mechanical crack advance is occurring independently of the

crack advance by oxidation processes, these two crack advance mechanisms

(striation formation and oxidation) are considered additive, as shown by the

dashed lines in Figure 5.

Film-Induced Cleavage Mechanism

In some incidences of transgranular cracking it has been observed [47] that the

faradaic equivalent of the oxidation change density at a strained crack tip is

insufficient to account for the observed crack advance. Moreover, the cleavage-like

crystallographic features on the fracture surfaces are hard to rationalize convincingly

in terms of a dissolution-oxidation model. Consequently, several authors [47–51]

have proposed that transgranular environmentally controlled crack propagation may

occur by a combination of oxidation and brittle fracture mechanisms. Specifically,

the crack front is envisioned to move forward by an oxidation process that is

controlled by the same rate-determining steps as those in the slip dissolution model

but, when the film rupture event occurs, the crack in the film may rapidly penetrate a

small amount, a

, into the underlying ductile metal matrix (Fig. 6). Thus, Eq. (1) is

modified as follows:

612 Ford and Andresen

Figure 5 Illustration of the strain rate dependence of the crack propagation rate due to the

slip dissolution model, and the additive properties of the mechanical and environmental

components of crack advance during corrosion fatigue.

The extent of the additional film-induced cleavage component of crack

advance, a

, is governed [47] by the state of coherence between the surface film and

matrix, the fracture toughness of the substrate, the film thickness, and the initial

velocity of the cleavage crack emerging from the surface film. Although the surface

film has been traditionally considered to be an oxide, more recent investigations

[50,51] have shown that dealloyed surface films (e.g., copper-rich films in Cu-Zn or

nickel-rich films in Fe-Cr-Ni alloys) can also form, exhibit “passive” behavior, and

be very brittle. The extent of the cleavage propagation into the matrix is estimated

to be of the order of 1 μm and to depend on the plasticity and microstructural factors

mentioned above. Although there is evidence for this mechanism in copper-base

alloys and austenitic nickel-base alloys and stainless steels in some low-temperature

environments (i.e., <115°C), it has not been extensively tested for other alloy systems,

including those relevant to LWRs. Its attractiveness is, however, that it provides a

rational basis for explaining the interrelationships between the electrochemical

parameters and the transgranular fractographic features in e.g., the carbon and

low-alloy steel–high-temperature water systems peculiar to nuclear reactor

pressure vessels and steam generator shells and quantitatively predicting the

Corrosion in Nuclear Systems 613

Figure 6 Schematic illustration of the elements of the film induced cleavage mechanism

of crack propagation [1]. Note similarity to the slip dissolution model (Fig. 5) during initial

stages of propagation cycle.