JP2000258336A - Method for creating corrosion environment scc crack progress prediction system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To create an SCC crack progress prediction expression under wide environmental conditions by obtaining a crack tip distortion speed and an active solution characteristic constant (n value) in the theoretical model expression of SCC crack progress, rearranging the n value with the independent variable of environmental/ material factors, and determining a parameter constant in an n-value analysis expression by the multivariate analysis. SOLUTION: The database of SCC(stress corrosion crack) crack progress is rearranged by environment/stress/material factors. The database and the theoretical model expression of SCC crack progress in high-temperature and high-pressure water are used to calculate a crack tip distortion speed and an n value in the theoretical model expression of the crack progress. Further, the calculated n value is used to determine a parameter constant in the analysis expression of the n value is determined by the multivariate analysis, and an SCC crack progress prediction expression in corrosion environment is created. The expression is a theoretical prediction expression based on a physical model consisting of an atomic theory mechanism due to stress at the crack tip part and an electrochemical mechanism due to environment and can be applied under wide conditions by appropriately selecting parameters and constants.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for preparing an SCC crack growth prediction formula for predicting the stress corrosion cracking (SCC) crack growth of a material exposed to a corrosive environment. The present invention relates to a method for preparing a suitable corrosion environment SCC crack growth prediction formula for predicting crack growth of a generated material.

[0002]

2. Description of the Related Art As various types of plants, such as nuclear power plants, become larger and more complicated, the use environment of structural materials becomes more severe, and accordingly, material damage which is considered to be caused by a corrosive environment has become apparent. Alloy materials such as stainless steel, which are widely used as structural materials, may cause SCC in a high-temperature water environment. SCC occurs and S
When a CC crack grows, the material strength is reduced by the SCC crack, and if the strength is lower than the design strength, the structural material is broken. Therefore, it is desired to create a crack growth prediction formula that can accurately predict the SCC crack growth in a corrosive environment. It is rare.

[0003] SCC is considered to occur under a condition in which three factors of stress, environment, and material are superimposed. In the SCC crack growth process, slip at a crack tip generated under stress is an essential role. It is considered to make. In particular, it is necessary to create an SCC crack growth prediction equation that takes into account the interaction between the generation of a slip step at the crack tip and the corrosion due to the environment of the crack tip. In the case of stainless steel SCC, it is called an active path corrosion type SCC based on the anodic reaction, and when a slip step is generated at the crack tip, the film breaks down and the new slip surface is exposed, and the new slip surface is exposed by the corrosive environment. Anodic dissolution occurs, while repassivation (repair of the film) at the crack tip proceeds.

As a conventional technique, for example, “Corrosion
−Assisted Cracking of Stainlessand Low−Alloy Ste
els in LWR Environments ”, EPRI NP-5064M (1987), the SCC crack growth prediction formula does not consider the generation of a slip step at the crack tip due to stress, but simply calculates the film fracture strain at the crack tip. It was created as an equation for predicting the SCC crack growth of stainless steel under high temperature and high pressure.

[0005]

SUMMARY OF THE INVENTION The object of the present invention is to provide an SC
Since the slip deformation at the crack tip in the C crack propagation causes the two slip systems to work simultaneously by the action of stress to form a continuous slip step, the strain rate at the crack tip is the motion speed of the dislocation on the slip surface at the crack tip. Mechanism and the electrochemical mechanism of repassivation at the crack tip, which proceeds with active dissolution on the new slip surface. The object of the present invention is to construct a theoretical model formula for SCC crack propagation based on a mechanochemical mechanism of sliding step / active dissolution composed of an atomistic mechanism and an electrochemical mechanism.

Further, parameter constants in an analysis method of an active dissolution characteristic constant governing an electrochemical mechanism are determined by using a database of SCC crack growth rates arranged by environment, stress, and material factors, so that a wide range of environment can be determined. SC that is applicable under conditions and has high accuracy and reliability
An object of the present invention is to provide a method for creating a C crack growth prediction equation.

[0007]

SUMMARY OF THE INVENTION The present invention uses a theoretical model formula for SCC crack growth in high-temperature and high-pressure water and a database of SCC crack growth rates organized by environment, stress and material factors. Crack tip strain rate (dε _ct / dt) and active dissolution characteristic constant (n value) in the theoretical model formula
The corrosion environment SCC crack growth prediction equation shown in the procedure (FIG. 1) in which the parameter constant in the analytical equation of the active dissolution characteristic constant is determined by multivariate analysis using the calculated active dissolution characteristic constant On how to create

[0008] The present invention relates to (a) SCC crack growth basic formula in a theoretical model formula by a mechanochemical mechanism,
(B) Crack tip strain rate equation, (c) Active dissolution characteristic constant (n value) analytical equation and SCC crack growth prediction equation will be described separately.

(1) Theoretical model formula (a) Basic formula of SCC crack growth As shown in FIG. 2, SCC crack growth occurs in a plane perpendicular to the tensile stress axis. Work simultaneously to generate successive slip steps, the crack will propagate toward the tip of the crack surface. The crack tip strain rate dε _ct / dt at that time is:

[0010]

Dε _ct / dt = 2ρ _d · b · cos θ · (dX / dt) (1) where, ρ _d : dislocation density, b: Burgers vector of dislocation θ: between slip direction and stress axis The angle dX / dt is given by the average velocity of the dislocation.

When a slip step is generated at the crack tip to cause film destruction and the new slip surface is exposed, dissolution of the new slip surface by an anodic reaction in a corrosive environment starts.
At that time, the anode current decreases exponentially with time, and re-passivation occurs due to restoration of the film.

Anode current density after time: t: i
Is generally given by the following equation, as shown in FIG.

[0013]

(Equation 2)

Here, i ₀ : surface melting current density, t ₀ :
Any time constant n: active dissolution characteristic constant slip surface at an average anode current density when occurring dissolution and repassivation repetition of: i _a is newborn sliding surface moves at an average speed of movement dislocations along the sliding surface When but a slip formation time and t _slip that appears,

[0015]

(Equation 3)

## EQU1 ##

[0017] The slip forming time: t _slip, the number of slip bands that worked: and N _s, the number of dislocations that contributed to the formation of one of slip bands: and n _d, is established the following relationship.

[0018]

T _slip · (dX / dt) = N _s · n _d · b (4) where N _{s is} the number of active slip bands _nd : the number of dislocations that contributed to the formation of one slip band Therefore, the average anode current density is

[0019]

(Equation 5)

## EQU1 ##

Since the dissolution at the crack tip is governed by the current density due to the anodic reaction, the amount of crack propagation is given by the following equation according to Faraday's law regarding electrolysis, which is proportional to the amount of dissolved substance and the amount of electricity.

[0022]

(Equation 6)

[0023] Here, da / dt: crack growth rate, M: metal atomic weight z: number of electrons involved in dissolution, [rho _m: density of the metal, F: Faraday constant average anode current density: the on i _a (5) Substituting the expression gives

[0024]

(Equation 7)

Further, the average movement speed of the dislocation is expressed by (1)
By substituting the relational expressions of the equations, the theoretical crack growth basic equation can be expressed by the following equation.

[0026]

(Equation 8)

This theoretical crack growth basic formula can be simplified and represented by a crack growth rate coefficient: A ₀ , a material factor constant: C _m and a crack tip strain rate: dε _ct / dt as follows.

[0028]

(Equation 9)

[0029] _{Here, A 0 = M / z ·} F · ρ m · i 0 · t 0 n / (1-n) C m = 2 · ρ d · cosθ · N s · n d · b 2 (b ) Crack tip strain rate equation According to the kink pair formation theory, the average motion velocity of a dislocation when a dislocation moves along a slip surface is expressed by the following equation.

[0030]

(Equation 10)

Here, d: period of Peierls potential, b: Burgers vector of dislocation, l _c : critical distance of kink pair, l: movement distance of kink pair, ν _D : Debye frequency, and E _dk ^f : kink pair. Formation energy k _B : Boltzmann's constant, T: temperature Kink pair formation energy: E _dk ^f is as follows, assuming that the energy of a kink when a dislocation passes over a potential peak in a stress-free state is E _k ^0. Is represented by

[0032]

E _dk ^f = 2E _k ⁰ −b · l ₀ · d ₀ · σ _eff = 2E _k ⁰ −b · l ₀ · d ₀ · (σ _a −σ _L ) (11) where l ₀ : distance between dislocation obstacles, d ₀ : resistance width of dislocation obstacle σ _eff : effective stress, σ _a : external stress, σ _L : resistance stress Accordingly, the average movement speed of dislocation is expressed by the following equation.

[0033]

(Equation 12)

In the case where slip occurs due to the movement of dislocations at the crack tip due to the application of external stress, the stress intensity factor at the tip of the slip step is expressed by the following equation: stress at the crack tip: σ.

[0035]

(Equation 13)

Here, σ ₀ : flow stress, K: stress intensity factor, r: distance from crack tip α: dimensionless constant, n ′: Ramberg-Osgood type strain hardening index, and effective stress intensity factor: K Let _eff be K _eff ≡K _I -K _ISCC
Then, effective stress: σ _eff and effective stress intensity factor: K
_The following relational expression is established with _eff .

[0037]

[Equation 14]

Here, K _ISCC : SCC lower limit stress intensity factor, β: constant.

[0039]

(Equation 15)

Is given by

Therefore, the crack tip strain rate equation is expressed as follows from equation (1).

[0042]

(Equation 16)

(C) Analytical expression of active dissolution characteristic constant When a new slip surface appears at the crack tip, the anode current density due to dissolution of the new slip surface: i decreases exponentially with time and follows the -n power law. Therefore, it is given by the above equation (2) using n which is the active dissolution characteristic constant.

[0044]

[Equation 17]

Accordingly, the active dissolution characteristic constant n is expressed as follows.

[0046]

(Equation 18)

On the other hand, the anode dissolution current density at the crack tip:
i, the partial anodic current density: i _a and the partial cathode current density becomes the difference of i _c, is given by the relation known as the formula for a Butler-Volmer.

[0048]

[Equation 19]

Where, i ₍₀₎ : exchange current density, α: transfer coefficient, η _t : transition overvoltage, Z: valence, F: Faraday constant, R: gas constant. The effects of sensitization, conductivity, and corrosion potential, which are independent variables of the factors, are modeled, but the environmental factors are considered to be independent and do not affect each other.

(I) Influence of the degree of sensitization Since a Cr-deficient region is formed at the grain boundary that has been sensitized, the area ratio between the parent phase and the Cr-depleted phase at the grain boundary is defined as f _mat and f _sen , respectively. Then, with f _mat + f _sen = 1, the anode current density: i is as follows.

[0051]

I _A = f _mat · i _mat + f _sen · i _sen (20) where i _mat : mother phase current density, _isen : Cr-deficient phase current density Cr-deficient phase current density: _isen Assuming that the matrix current density is λ times larger than i _mat , given by the following equation,

[0052]

I _sen = λ · i _mat (21) The area ratio of the Cr-deficient phase: f _sen is given by the following equation obtained by multiplying the area ratio of the mother phase: f _mat by a proportional constant ζ.

[0053]

F _sen = ζ · f _mat (22) Anode current density: i is expressed as follows.

[0054]

(Equation 23)

The coefficient term in the above equation is converted to a sensitivity-influencing factor: F _EPR
And sensitization degree: EPR is represented by a linear approximation as follows.

[0056]

(Equation 24)

Here, C ₁ : parameter constant Accordingly, the anode current density: i is given by the following equation using EPR as an independent variable.

[0058]

(25) i = (1 + C ₁ · EPR) · i _mat (25) (ii) Influence of conductivity When the conductivity in the environment changes, the cation concentration of the dissolved metal changes, so that it passes through the Helmholtz double layer. Exchange current density: i
_It is considered that ₍₀₎ changes.

When the dissolved metal ion concentration changes from C _s to C ′ _s , the concentration overpotential: η _c is given by the following equation.

[0060]

(Equation 26)

On the other hand, a Tafel linear relationship holds between the overvoltage: η and the current density: log (i),

[0062]

[Equation 27]

Therefore, the following relational expression is established.

[0064]

[Equation 28]

The right side of the above equation is defined as a conductivity affecting factor: F _κ, and the conductivity: κ is represented by a linear approximation as follows.

[0066]

(Equation 29)

Here, C ₂ : parameter constant, C ₃ : parameter constant Accordingly, the exchange current density: i ₍₀₎ is given by the following equation using the conductivity: κ as an independent variable.

[0068]

I ′ ₍₀₎ = (C ₂ · κ + C ₃ ) · i ₍₀₎ (30) (3) Influence of Corrosion Potential Anode current density of sensitized material in an environment where conductivity changes: i , Butler-Volmer equation and sensitization influencing factors:
Using F _EPR and conductivity influencing factors: F _κ ,

[0069]

(Equation 31)

The transition overvoltage: η _t is the anode reaction potential:
Δφ and equilibrium potential: difference between Δφ ₀

[0071]

Η _t = Δφ−Δφ ₀ (32) Therefore, by using the corrosion potential of the bulk: φ _c ,

[0072]

[Equation 33]

Is represented by a linear approximation

[0074] Thus, the anode current density: i is the corrosion potential: given by the following equation with respect to phi _c.

[0075]

I = F _EPR · F _κ · i ₍₀₎ · (C ₄ · φ _c + C ₅ ) · exp {α · (C ₄ · φ _c + C ₅ )} (34) Anode dissolution characteristic constant: analytical expression of n substitutes the above equation to the equation (18), sensitization degree influence factor: F _EPR Te conductivity influencing factors: applying F _kappa, and finally be expressed as follows .

[0076]

(Equation 35)

Here, EPR: degree of sensitization, κ: electric conductivity, φ _c : corrosion potential C _{1 to} C ₇ : parameter constant (d) Creation of SCC crack growth prediction formula From the above, based on the mechanochemical mechanism, The theoretical model formula of SCC crack growth in hot, high-pressure water can be expressed in the following general form.

[0078]

[Equation 36]

[0079]

(37)

[0080]

Equation 38] Materials factors _{Constants: C m = 2 · ρ d} · cosθ · N s · n d · b 2 ... (38)

[0081]

[Equation 39]

[0082]

(Equation 40)

Where K: stress intensity factor, κ: conductivity, E
CP: Corrosion potential, EPR: Sensitization For the SCC crack growth of stainless steel in high-temperature and high-pressure water, the crack growth rate coefficient, material factor constant, and crack tip strain rate are obtained by substituting the material constants and the like into the above equations. And is shown as follows.

[0084]

[Formula 41] Crack growth rate coefficient: A ₀ = 1.1 × 10 ⁻⁷ (41)

[0085]

(42) Material factor constant: C _m = 4.4 × 10 ⁻⁴ (42)

[0086]

[Equation 43]

However, since the active dissolution characteristic constant (n value) is difficult to measure experimentally for each independent variable, it is arranged by environment, stress and material factors, that is, EPR, conductivity. It is necessary to calculate using a database of the SCC crack growth rate under each test condition such as ECP, ECP and stress intensity factor. The procedure is described below.

First, the stress intensity factor: K, which is a test condition of each data, is substituted into the above-described strain rate equation of crack tip of stainless steel: Equation (43), and the strain rate of crack tip of each data: dε _ct / Find dt. The calculated crack tip strain rate: dε _ct / dt is calculated by the above equation (36), equation (41),
Crack growth rate of stainless steel by the mechanochemical mechanism given by equation (42): Substituted into the term on the right side of equation (44), and the data value of each crack growth rate in the database on the left side of equation (44): (da / Dt) By substituting _data ,
The active dissolution characteristic constant: n under each test condition (EPR, conductivity, ECP) can be calculated by the following equation (45).

[0089]

[Equation 44]

[0090]

[Equation 45]

Active dissolution characteristic constant in high-temperature high-pressure water: n
Is given as independent variables of EPR, conductivity, and ECP. Therefore, the analytical formula of the active dissolution characteristic constant: n: (4
When the parameter constants in the equation (0): C _{1 to} C ₇ are determined by multivariate analysis, the active dissolution characteristic constants of stainless steel in high-temperature, high-pressure water: n are EPR, conductivity, ECP
Is represented by the following expression, where is an independent variable.

[0092]

[Equation 46]

FIG. 1 shows a procedure for creating an SCC crack growth prediction equation.

The equation for predicting the SCC crack growth of stainless steel in high-temperature, high-pressure water prepared as described above is expressed as follows.

[0095]

[Equation 47]

[0096]

Here, the crack growth rate coefficient: A ₀ = 1.1 × 10 ⁻⁷ (48)

[0097]

(49) Material factor constant: C _m = 4.4 × 10 ⁻⁴ (49)

[0098]

[Equation 50]

[0099]

(Equation 51)

[0100]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described based on embodiments.

FIG. 4 shows an active dissolution characteristic constant obtained by the method of the present invention by using the expression of n:
3 shows a surface dependent on EPR, conductivity, and corrosion potential of n.

Active dissolution characteristic constant according to the method of the present invention: n
Is 1 as the corrosion potential increases and goes in the noble direction.
As the conductivity becomes higher, the active dissolution characteristic constant: n tends to become smaller. Also, when the degree of sensitization: EPR increases, the active dissolution characteristic constant: n also decreases, indicating that the anode dissolution at the crack tip progresses with time and the SCC crack progresses. The dependence of such an active dissolution characteristic constant, n, on EPR, conductivity, and corrosion potential is consistent with the crack growth behavior of stainless steel.

Next, using the SCC crack growth prediction formula for stainless steel prepared according to the present invention, high-temperature and high-pressure water (28
The results of analyzing the crack growth behavior of stainless steel at 8 ° C.) will be described.

FIG. 5 plots the relationship between the crack growth rate: da / dt and the stress intensity factor: K in stainless steel at a temperature of 288 ° C. according to the crack growth prediction formula of this embodiment and the conventional formula.

In the case of this embodiment, the crack growth rate
From the lower limit stress intensity factor K _ISCC = 9 MPa√m, a sharp rise is shown, and thereafter, the crack growth rate becomes slower as the stress intensity factor increases, and the stress intensity factor becomes about 12 MPa√.
m or more, the crack tip strain rate is proportional to the stress intensity factor: K to the power of 2.7. Therefore, the SCC lower limit stress intensity factor which is the threshold value of the stress intensity factor at which SCC crack growth starts:
It can be seen that the existence of K _ISCC is reproduced.

On the other hand, in the conventional formula, the crack growth rate is given in a form simply proportional to the fourth power of the stress intensity factor: K. Therefore, even when the stress intensity factor: K is very small, crack growth occurs. Also, when the stress intensity factor: K is large, the crack growth rate is increased, which results in overestimating the crack growth of stainless steel. Therefore, the SCC crack growth prediction formula created according to the present embodiment can realistically predict the growth of the SCC crack, and can make a more reliable prediction than the conventional one.

[0107]

As described above, the corrosion environment SCC crack growth prediction formula by the preparation method according to the present invention is a physical model composed of an atomistic mechanism by stress at the crack tip and an electrochemical mechanism by environment. Since it is a theoretical prediction formula based on SCC, it is possible to provide a prediction of SCC crack growth applicable under a wide range of environmental conditions by appropriately using parameter variables and constants. Further, as for the prediction of SCC crack growth, a more realistic prediction than before can be made, and a more reliable prediction can be made.

[Brief description of the drawings]

FIG. 1 is a flowchart for explaining creation of a corrosion environment SCC crack growth prediction formula according to the present invention.

FIG. 2 is an explanatory view schematically showing an atomistic mechanism of crack propagation at a crack tip.

FIG. 3 is an explanatory view schematically showing an electrochemical mechanism of crack propagation at a crack tip.

FIG. 4 is a characteristic diagram showing a relationship between an active dissolution characteristic constant and an independent variable in Examples.

FIG. 5 is a graph showing prediction results of a relationship between an SCC crack growth rate and a stress intensity factor in Examples.

[Explanation of symbols]

 n: active dissolution characteristic constant; EPR: degree of sensitization.

Claims (3)

[Claims] 1. Using a theoretical model formula of SCC crack growth in high-temperature and high-pressure water and a database of SCC crack growth rates organized by environment, stress and material factors, a crack tip in the theoretical model formula of SCC crack growth Strain rate (dε _ct / d
t) and the active dissolution characteristic constant (n value) are calculated. Further, the active dissolution characteristic constant is arranged by independent variables of environment and material factors, and the parameter constant in the analytical expression of the active dissolution characteristic constant is determined by multivariate analysis. A method for creating a SCC crack growth prediction equation for a corrosive environment, comprising creating an SCC crack growth prediction equation applicable to a wide range of environmental conditions based on a database of SCC crack growth rates. 2. A sliding step consisting of an atomistic mechanism by stress at a crack tip and an electrochemical mechanism by environment in a model model of SCC crack growth in high-temperature and high-pressure water in consideration of superposition of stress and environment. A method for preparing a corrosion environment SCC crack growth prediction formula, characterized by using a theoretical model formula based on a mechanochemical mechanism of active dissolution. 3. A theoretical model formula for SCC crack growth in high-temperature and high-pressure water, wherein a crack growth rate coefficient takes a constant value independent of environmental conditions, and a crack tip strain rate equation is a SCC lower limit stress intensity factor. (K _ISCC ) A method for preparing a corrosion environment SCC crack growth prediction equation, characterized in that the active dissolution characteristic constant is given by a function of independent variables: sensitization, corrosion potential, and conductivity.