Marcus P. Corrosion mechanisms in theory and practice

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transitions between intergranular and transgranular cracking in stainless steels in

high-temperature water [1].

Hydrogen Embrittlement Mechanisms

The general concepts and concerns behind the various hydrogen models have been

reviewed by Thompson and Bernstein [52], Hirth [53], Nelson [54], and Birnbaum

[55]. In brief, the subcritical crack propagation rate due to hydrogen embrittlement

in aqueous environments depends on a sequence of events (Fig. 7) [56].

• Diffusion of a reducible hydrogen-containing species (e.g., H

) to the crack

tip region

• Reduction of the hydrogen-containing ions to give adsorbed hydrogen

atoms

• Absorption of the hydrogen adatoms followed by interstitial diffusion of

these hydrogen atoms to a “process” zone at a distance, X, in front of the

crack tip

• Once the hydrogen concentration in a “process” zone has reached a critical

level, C

crit

, over a critical volume, d

crit

, localized crack initiation within this

zone is followed by rapid propagation back to the main crack tip [57]

Setting aside the specifics of these localized fracture mechanisms in the

process zone for the present, it is apparent that hydrogen embrittlement models

predict discontinuous crack propagation at an average rate of

614 Ford and Andresen

Figure 7 Schematic of various reactions at crack tip associated with hydrogen

embrittlement mechanisms in aqueous environments. (From Ref. 45.)

where X is the distance from the main crack tip to the process zone (which, in turn,

is defined by the values of C

crit

and d

crit

) and t

is the time for the concentration of

absorbed hydrogen, C

x,t

, to reach a critical value, C

crit

, over the volume d

crit

. To

evaluate the validity of Eq. (7), quantitative data for X and T

are needed.

Unfortunately, these are difficult to predict from first principles [58] and rely

mechanistically on the validity of the various atom-atom rupture hypotheses (e.g.,

decohesion [59,60], gas rupture [61,62], enhanced plasticity [63,64], hydride

formation [65], and martensite formation [66]) that have been made.

Although traditionally such hydrogen embrittlement mechanisms have been

applied qualitatively to high-strength alloys, Hanninen, Torronen, and co-workers

[67,68] have suggested that a hydrogen embrittlement mechanism is operating in the

relatively ductile pressure vessel steels in 288°C water. The prime experimental

evidence for this hypothesis is the observation of the “brittle” cracks associated

with elongated MnS stringers ahead of the main crack tip. The degree of

environmental enhancement in fatigue crack growth rates is therefore directly

correlated with the extent of these “brittle” fracture areas on the fracture surface. The

following steps are hypothesized [68] to occur in these systems:

• Enhanced oxidation (dissolution and oxide reformation) at the strained

crack tip.

• Hydrolysis of the cations with corresponding acidification of the crack

environment.

• Dissolution of exposed MnS particles in this acidic environment, leading to

the creation of H

S and incorporation of sulfur into the reforming oxide.

• Creation of adsorbed hydrogen atoms due to the local hydrogen ion reduction

reaction, followed by absorption. The kinetics of these reactions are believed

to be accelerated both by the necessity to balance the enhanced oxidation

reactions and by the presence of the sulfur species in the crack tip environment.

• Recombination of hydrogen atoms at MnS inclusions in front of the crack

tip, leading to the formation of brittle cracks at the inclusion-matrix interface,

which propagate under the action of hydrogen gas pressure and triaxial tensile

stress.

• Linkage of these microcracks to give a discontinuous crack propagation over

and above that due to “mechanical” fatigue failure.

PREDICTION METHODOLOGY FOR DUCTILE STRUCTURAL ALLOYS

IN LWR SYSTEMS

Thermodynamic and kinetic criteria have been applied to determine which of the

above candidate crack propagation mechanisms are valid for various alloy-

environment systems [12,45]. However, it is comparatively rare that a candidate

cracking mechanism can be categorically dismissed using this reasoning. Thus,

qualitative predictions of cracking have centered around the observation that the

rate-determining step in all of the cracking mechanisms is not necessarily the

atom-atom rupture process itself but is one or a combination of (a) mass transport

of species to and from the crack tip; (b) the oxidation or reduction reactions; and (c)

the dynamic strain processes at the crack tip [11,12]. Thus, changes in cracking

Corrosion in Nuclear Systems 615

susceptibility for most ductile alloy–aqueous environment systems with, e.g., changes

in temperature, electrode potential, stressing mode (dynamic or static stress, plane

strain or plane stress, dislocation morphology, etc.), or environment composition

can be explained [11,12] by movement over a reaction rate surface (Fig. 8) regardless

of the specific atom-atom rupture mechanism at the crack tip.

Recognition of the fundamental importance of controlling mass transport,

oxidation and reduction rates, and crack tip strain rates has proved invaluable in

identifying the system changes that are likely to solve a particular environmentally

controlled cracking problem. For instance, increasing the cracking resistance by

increasing the passivation rate at the crack tip by controlling the corrosion potential,

anionic activity, and material composition or by reducing the crack tip strain rate

(for a given imposed stress history) by attention to dislocation morphology, etc.,

can be understood within this skeleton of fundamental logic [11,12]. Moreover,

this knowledge can be used to predict limiting system conditions below which

cracking will be minimal. An example is the evaluation of threshold stresses for

cracking via their influence on a minimal crack tip strain rate and, thereby, crack

propagation rate [69]. In recent years, as economic and technical pressures dictate

longer design and operating lives, the emphasis has been on studying cracking in

dilute environments where the relevant crack propagation rates are < 10

–7

mm/s,

and on developing the quantitative prediction capability outlined in Figure 1.

Thus, in the following section, the advances in quantifying the crack tip atom-atom

rupture mechanisms and their rate-determining reactions are described.

To limit discussion, attention is focussed on the quantitative prediction of

cracking in austenitic type 304/316 stainless steels in 288°C high-purity water (e.g.,

616 Ford and Andresen

Figure 8 Reaction rate surface illustrating the variation in crack propagation rate with

the rate controlling parameters in the slip dissolution, film-induced cleavage, and hydrogen

embrittlement mechanisms for environmentally assisted cracking in ductile alloy—aqueous

environment systems [11,12].

BWR environments) in which it is assumed [1] that the slip dissolution model is a

reasonable working hypothesis for the crack propagation mechanism. This baseline

prediction methodology is then extended to treat the effects of irradiation on the

cracking of stainless steel. Further extension to other alloys (e.g., nickel-base,

low-alloy steels) and environments (PWR) is also outlined.

The starting point in this process is the theory and quantitative elements in

Eq. (5). To develop this concept to a state of practical usefulness, it is necessary to

redefine this fundamental equation in terms of measurable engineering or operational

parameters. This involves (a) defining the crack tip alloy-environment composition

in terms of, e.g., bulk alloy composition, anionic concentration or solution

conductivity, dissolved oxygen content or corrosion potential, etc.; (b) measuring the

reaction rates for the crack tip alloy-environment system that corresponds to the

“engineering” system; and (c) defining the crack tip strain rate in terms of continuum

parameters such as stress, stress intensity and loading frequency. Extensive work has

been conducted in these areas, and the progress will be reviewed only briefly in this

chapter before illustrating how these advances have been incorporated into verified,

quantitative life prediction methodologies.

Definition of Crack Tip Alloy-Environment System

On the basis of direct measurements on stainless steel, alloy 600, and low-alloy

steel-water systems at 288°C, it is known that the electrode potential and pH

conditions at the tip of a crevice or crack can differ markedly from those at the

exposed crevice or crack mouth [1,70–74]. These variations are understood and have

been extensively reviewed [45,75–77] in terms of the thermodynamics of various

metal oxidation and metal cation hydrolysis reactions and how they are influenced by

the reduction processes of e.g., dissolved oxygen at the crack mouth. From a

practical viewpoint, the corrosion potential which exists at the deaerated crack tip is

controlled primarily by pH, but it can be defined [1] in terms of the measurable

dissolved oxygen content in the external water environment (Fig. 9) (or preferably

by the measurable corrosion potential of the external system) and the purity of the

external water.

The transient and steady-state concentrations of anions in the crack have also

been experimentally measured and analytically modeled [1,70,78]. The anion level

present at the crack tip is directly dependent on the external anionic activity, the

dissolvable metallurgical impurities (e.g., MnS) level, the corrosion potential

difference between the crack mouth and tip, and convective influences. For example,

the steady-state sulfur anion concentration at the crack tip in low-alloy steels can be

defined by the MnS content, aspect ratio, and orientation; the solution flow rate; and

the oxygen concentration in the water [1,79,80]. Under specific conditions the

dissolved sulfur concentration can be of the order of 3 ppm versus <10 ppb in the bulk

solution. For stainless steel exposed under normal BWR conditions, the potential

drop down the crack length leads to a concentration of anions at the crack tip such

that typical crack tip anion concentrations between 0.1 and 1.0 ppm are expected;

under deaerated operating conditions, where no potential drop exists along the crack

length, the (non-OH

–

) anion content at the crack tip will approximate that in the

bulk environment (e.g., ≈15ppb). To maintain electroneutrality in the crack

enclave, it is necessary that there be a corresponding concentration of cations at the

Corrosion in Nuclear Systems 617

crack tip. Because of the low solubilities of most transition metal cations, hydrolysis

occurs and the pH decreases at the crack tip under most conditions. However,

under water purity conditions relevant to BWRs, the concentration of (non-OH

–

)

anions is only sufficient to produce acidification of 1–2 pH units [70]. In the

absence of non-OH

–

anions, acidification cannot occur and generally a slight

increase in pH is observed both in aerated [70] and deaerated [88] water.

Apart from the influence of MnS inclusions, the alloy composition at the tip

of transgranular cracks is generally assumed to be that of the bulk alloy. However,

the alloy composition at the tip of an integranular crack may be considerably

different from the bulk composition if metal solute segregation or denudation at

the grain boundary exists; such compositional heterogeneity will be controlled by,

e.g., thermal diffusion and/or irradiation assisted damage. Discussion of these

metallurgical aspects is outside the scope of this chapter, but adequate knowledge

exists, including extensive analytical electron microscope studies, to permit

definition of the grain boundary composition in terms of the bulk alloy composition

and the thermal history during fabrication or irradiation history during reactor

operation [81–86]. Thus, the crack tip alloy-environment system can be defined in

terms of measurable or definable bulk system parameters.

Evaluation of Reaction Rates at Crack Tip

Various techniques have been used to create a macroscopic analogy to the crack tip

bare surfaces on which the oxidation and reduction rates can be measured. These

include mechanical methods to rupture the surface oxide that involve slowly [87–91]

or rapidly [92,93] straining the alloy, complete fracturing of the specimen to create a

bare fracture surface [94,95]; cyclic straining [88,96], scratching the alloy surface

[97–102], and grinding [103]. Electrochemical methods have also been used to

cathodically reduce the oxide [1,104–106] and then pulse to the potential of interest.

618 Ford and Andresen

Figure 9 Crack tip potential variations as a function of dissolved oxygen content in water

external to the crack. The observed data for crack tip conditions at 288°C are for carbon steel,

A533B, and stainless steel [1,45,88].

Most of these techniques have been applied in the study of environmentally

assisted cracking. The experimental difficulties with these techniques have been

reviewed [45,107,108], along with the interpretations of the atomistics of the

reaction rate [45] as a strained crack tip. These topics will not be covered further

in this chapter.

The main conclusions with regard to dissolution and repassivation kinetics in

structural materials in 288°C crack tip environments are that both the oxidation and

reduction reaction rates are increased when the protective oxide is removed. The bare

surface oxidation rate, i

, is a function of the electrode potential and the dissolved

anion content, as shown in Figure 10 for the effect of sulfur on the bare surface disso-

lution rate of low-alloy steels [1,88,109]. Explanations for this behavior range those by

Ford, Andresen, and their colleagues [1,70], who argue that the rate-controlling

process for bare surface dissolution is the diffusion of solvating water molecules to the

oxidizing surface (and the influence of anionic activity and pH and on the solubility of

impeding oxide precipitates), to those of Combrade [88], who argues that adsorbed

sulfur on the surface impedes the incipient solid-state passivating oxide nucleation.

Oxide formation leads to a decrease in the overall oxidation rate, according

to Eq. (3). The value of n in this equation [which is the same as in the crack

propagation rate Eq. (5)] varies with the alloy chemistry [e.g., chromium content for

a denuded grain boundary of type 304 stainless steel, or sulfur content for low-alloy

steels (Fig. 11)], electrode potential, and anionic activity, and this can be related to

e.g., solid-state oxide growth, dissolution-precipitation reactions, and oxide

breakdown [1,11]. Thus, all of the parameters in Eq. (5), apart from

⋅

, can be

quantified for the crack tip system, which can, in turn, be related to definable or

measurable bulk system conditions.

Definition of Crack Tip Strain Rate

It has been recognized for many years that the oxide rupture prerequisite for crack

advance leads to a relationship between cracking susceptibility and slip morphology,

since coarse slip at the crack tip will more readily rupture a brittle film of given

Corrosion in Nuclear Systems 619

Figure 10 Relationship between the bare surface dissolution rate, i

, on low-alloy steel

at –620 mV

she

and the dissolved sulfur activity [1,88,109].

thickness [110] than fine slip. This relationship has been observed [52] for various

alloys in both aqueous and gaseous environments, where the different dislocation

morphologies are related to changes in stacking fault energy, short-range order,

precipitate-matrix coherence, and precipitate distribution.

Despite these known effects of microscopic hetergeneity of plastic flow at a

crack tip on the cracking susceptibility, the main emphasis in formulating

expressions for the periodicity of film rupture has been on continuum parameters

such as strain rate and oxide fracture strain. Reviews of the formulations for crack

tip strain rate have been conducted by Parkins et al. [111], Lidbury [112], and Ford

[45,113], among others. These reviews address the need for the crack tip strain

rate formulations to account for various observed factors, including:

1. Can the strain rate formulations account for the limiting stress conditions for

cracking, defined by σ

, ΔK

, or K

Iscc

? This aspect has been covered by e.g.,

Parkins and co-workers [69] in assessing the criteria for maintaining a critical

creep rate and how this might be achieved by various stressing conditions.

2. How will the crack tip strain rate vary with time-dependent stressing conditions

and the degree of plastic constraint? A subsidiary aspect is the examination of

the belief that σ

and K

Iscc

are system constants.

3. How does the fact that the crack is propagating affect the crack tip strain rate

when dislocation movement is governed by an exhaustion theory of creep?

Associated with this is the definition of the criteria that determine the onset of

crack arrest.

Numerous formulation approaches have been suggested and reviewed

[45,111–113] but currently these questions have not been completely answered.

However, an earlier section reviewed the urgent practical importance of evolving

usable life prediction algorithms, and preliminary crack tip strain rate algorithms

have been developed for LWR systems in the following form:

620 Ford and Andresen

Figure 11 Relationship between the value n in Eq. (3) for the same system as in Figure 10.

(From Ref. 1).

In all of these equations, it is recognized that the crack tip strain rate is a

function, not only of the applied stress, stress intensity, or strain rate, but also of the

crack propagation rate, V

–

. In other words, the movement of the crack tip stress field

into the underlying metal matrix by an amount, x

, activates new dislocation

sources in a given time period, thereby increasing the strain rate above that in a

stationary crack.

Despite the simple yet sound logic inherent in the above formulations, they

have proved to be remarkably difficult to quantify in terms of crack tip plasticity and

to verify independently. For instance, uniaxial creep deformation laws at low

homologous temperatures are not necessarily applicable to the multiaxial stress

conditions in the surface region adjacent to the crack tip, and the use of linear elastic

fracture mechanics has limitations in the region of high plastic deformation near the

crack tip. These difficulties have been discussed in some detail [45,111–113] and will

not be covered further. Despite these fundamental difficulties, empirical formulations

between the crack tip strain rate and “engineering” parameters have evolved which

have proved useful for a wide range of stressing conditions for structural alloys in

288°C water (Table 1) [1,45].

VERIFICATION AND USE OF CRACKING PREDICTIONS

FOR LWR SYSTEMS

The methodology outlined above provides a specific framework for quantitatively

predicting environmentally assisted cracking in structural alloy–water systems at

288°C. This is illustrated below for stainless steels under both unirradiated and

irradiated conditions, where intergranular stress corrosion has been observed, e.g., in

weldsensitized and thermally sensitized piping, and irradiated core components.

The methodology is also illustrated for transgranular stress corrosion cracking

of A533B and A508 low-alloy steels used for pressure vessel plates and forgings

and forintergranular cracking of nickel-base alloys used for safe ends, weldments,

etc. Remarks are then made about the extension of these capabilities to other,

e.g., PWR, systems.

Corrosion in Nuclear Systems 621

Table 1 Crack Tip Strain Rate (s

–1

) Formulations for Unirradiated Steels in 288°C Water

K(ΔK) = stress intensity (amplitude in MPa √

—

⋅

app

= applied strain rate in s

–1

;

⋅

= frequency

of (symmetrical) load cycle in s

–1

; A

= constant in “dry” Paris Law = 2.44 × 10

–11

(for R ≤ 0.42)

= –2.79 × 10

–11

+ 1.115× 10

–10

R + 5.5 × 10

–11

(for R > 0.42); R = minimum load/

maximum load.

Sensitized or Irradiated Type 304 Stainless Steel/BWR System

Extensive investigations of the relevant fundamental reactions pertinent to crack

tip systems have led to a quantification of the basic parameters in Eq. (5). For

stainless steels, this equation may be simplified [1] to

622 Ford and Andresen

As discussed previously, n is fundamentally related to the crack tip environment

(pH, potential, anionic activity) and material (chromium denudation at grain

boundaries) conditions. For practical use, n has been reformulated [1] in terms of

measurable system parameters such as anionic activity (or solution conductivity, κ),

corrosion potential (φ

, which, in turn, is a function of the dissolved oxygen,

hydrogen peroxide, and dissolved hydrogen concentrations), and the electrochemical

potentiokinetic repassivation (EPR) parameter (which is related to the chromium

denudation in the grain boundary). The formulation is of the form (Fig. 12)

The crack tip strain rate,

⋅

, in Eq. (11) is related to the engineering stress (or

stress intensity) parameters via the formulations in the Table 1.

The validity of the prediction methodology with respect to the strain rate

sensitivity is indicated in Figure 13, which covers data obtained on sensitized type

304 stainless steel in 288°C water containing 8 ppm oxygen and stressed over a wide

range of constant load, monotonically increasing load, and cyclic load conditions [1].

The solid line is the theoretical relationship and illustrates the applicability of the

methodology to the whole stress corrosion–corrosion fatigue spectrum. The specific

effects of changes in corrosion potential and solution conductivity on the propagation

rate under constant load are shown in Figures 14 and 15. An example the effect of

compositional changes is illustrated later in reference to irradiation-induced

chromium denudation at the grain boundaries.

The comparison between the theoretical and observed crack growth

rate-stress intensity relationships are shown for a sensitized stainless steel in a some-

what impure BWR environment (Fig. 16a) and a more modern “hydrogen water

chemistry” BWR environment (Fig. 16b). The agreement between observation

and theory is apparent, as is the inapplicability of a single life prediction law such as

the “NRC disposition line” to a system which can exhibit a wide range of conditions

within a nominal specification.

The broad agreement between observation and theory for propagation of envi-

ronmentally assisted cracking in the stainless steel–water system at 288°C is shown

in Figure 17. In this diagram, the data refer to a wide range of material, environment,

and stressing conditions for the generic “stainless steel–water system at 288°C.

Again, the agreement between observation and theory is apparent. Indeed, given the

sensitivity of the crack propagation rate to relatively small changes in the system

conditions (e.g., Figs. 14–16), it has been proposed [1] that the scatter in Figure 17 is

due primarily to relatively small unmeasured changes in the system conditions. For

instance, unmonitored changes in corrosion potential of ≈l00 mV in 200 ppb oxygen

water–a range which is perfectly possible because of flow rate effects, etc.–would give

Corrosion in Nuclear Systems 623

Figure 12 Relationships between n in Eqs. (2) and (5) and the corrosion potential and

bulk solution conductivity for a sensitized (EPR = 15 C/cm

) type 304 stainless steel in

water at 288°C. (From Ref. 1).

Figure 13 Observed and theoretical crack propagation rate–crack tip strain rate

relationships for sensitized type 304 stainless steel in oxygenated water at 288°C.

(From Ref. 1).