Project topics and materials
Get Complete Project Material File(s) Now! »
Effect of the main chemical elements.
The mechanical properties and corrosion resistance of stainless steels depend strongly on their chemical composition. Some effects of the main alloying elements of austenitic stainless steels, as C, Cr, N i, M o and N, are described below.
Carbon C
Carbon is generally considered to be one of the most important elements in steels. The C atoms located at the interstitial sites of the crystallographic cell. This improves the mechanical strength of iron. Moreover, carbon is more soluble in austenite than in ferrite, therefore stabilizes the austenitic domain of steels [8]. Low carbon content makes it possible to improve the tenacity and the ductility and thus the cold working behavior [9]. However, with the addition of chromium, carbon is likely to be incorporated in chromium carbide precipitates, particularly at grain boundaries, favoring intergranular corrosion. That leads to the attempts of decreasing the cabon content and the ‘L’ austenitic stainless steel subtype discussed in subsection 1.1.1.
Chromium Cr
Chromium is an influent element in stainless steels, since it allows the formation of a passive film, which provides high corrosion resistance. The passive film is thicker as the chromium content is higher. However, chromium has a body-centered cubic structure (BCC), such as ferrite. Therefore, it is a ferrite stabilizer.
The higher the chromium content, the larger the risk of intermetallic phase formation. During high temperature operation, the chromium-rich intermetallic phases (such as σ phase) are described in the equilibrium diagram of the pseudo-binary section of the Fe-Cr-Ni ternary system (Fig. 1.2b) [7].
Nickel Ni
As an austenite stabilizer, the addition of nickel in sufficient quantity in Fe-Cr steel makes it possible to obtain an austenitic steel (Face-centered cubic (FCC) structure). Nickel is also known to improve corrosion resistance in chloride envi-ronments [10].
Molybdenum Mo
The addition of molybdenum improves significantly the resistance to uniform and localized corrosion in austenitic stainless steels. Nevertheless, molybdenum promotes the precipitation of carbides and intermetallics, such as M23C6 and σ phase.
Nitrogen N
Nitrogen is an austenite stabilizer. Similarly to carbon, nitrogen is located at the interstitial sites of austenite cells. The increase in nitrogen content leads to an increase in twinning in austenite by decreasing the stacking fault energy, especially for steels with low nickel content [11]. This effect could explain that the nitrogen-containing steels display better mechanical properties, as 316L(N).
In addition, nitrogen is more soluble than carbon in solid solution in austenite and ferrite, which reduces the risk of nitride precipitation compared to carbide precipitation. Elements such as chromium and manganese are known to increase the solubility of nitrogen in iron, whereas nickel decreases it [12].
Grain size
Grain boundaries play an important effect in creep properties, through grain boundary sliding, grain boundary diffusion and grain boundary cavitation. There-fore, the creep resistance is strongly influenced by grain size. However, no clear conclusion arises from by experimental results [13, 14]. Creep can be decomposed into intergranular creep and intragranular creep. Intergranular creep is expected to be affected by changing the grain size.
The grain size is controlled by the heat-treatment. For the AISI 316L(N) and Incoloy 800, the grain sizes are 15-30µm and 50-150µm, respectively.
It should be noticed that two Incoloy 800 grades differ by their respective heat-treatments: ‘Grade 1’, corresponds to anneal at approximately 980◦C (grain size 10-20µm) and ‘Grade 2’, to anneal at approximately 1150◦C (grain size 50-250µm) [15]. In this study, only Grade 1 is considered.
Secondary phases
It is observed on isothermal section of ternary Fe–Cr–Ni phase diagram at 1100◦C [6] (Fig. 1.2a) and pseudo-binary section of the Fe-Cr-Ni ternary system at 70% Fe [7] (Fig. 1.2b), that 316L(N) is concentration range for which both austenite and ferrite phases co-exist. Since they are obtained by quenching from temperature range 1000 − 1200◦C, it is thus understood why austenitic steels often contain a small percentage of ferrite.
When a stainless steel is subjected to a heat-treatment at a temperature T1, the element contents are higher than the solubility thereof at temperature T2 (work condition) (T2 < T1). Then, during further ageing at high temperature or creep, atoms can diffuse and more stable second phases1 are produced. Their nature depends on temperature, the previous heat-treatment and the cooling conditions. The main precipitates and intermetallics observed in AISI 316L(N) and Incoloy 800 are presented in Table 1.2.
Hence, the second phases observed in 316L(N) stainless steels and Incoloy 800 alloy in the as-received state or formed during creep are described in the following subsection.
Carbides
The most frequently observed carbides in austenitic steels and Incoloy 800 during heat-treatments are M23C6, where M accounts mainly for mainly chromium, partially substituted by Fe, Mo or Ni [18]. The M23C6 particles are known to nucleate generally first at grain boundaries, resulting in a significant decrease in intergranular corrosion resistance [8]. However, the M23C6 particles could also be observed at the twin boundary and in the matrix [24, 28, 29]. Hong et al. [17] and Padilha and Rios [9] studied the relationship between carbide germination and grain boundary disorientation. They showed that the increase in grain disorientation leads to a change of M23C6 geometry, from a platelet geometry to triangular one [9]. The size of the intergranular M23C6 particles is generally below 0.5µm [29–31].
The M23C6 particles are generally the first type of second phases to be nucle-ated in austenitic stainless steels because they may be coherent or semi-coherent with the austenite crystal. Indeed, the mesh parameter of the face-centered cu-bic M23C6 is approximately 3 times that of austenite. And these two phases are approximately in a cube on cube orientation relationship, [16, 18]:
{110}M23C6 k{110}γ h001iM23C6 kh001iγ (1.2)
Other types of carbides such as M7C3, M6C and M C have also been observed during ageing of austenitic stainless steels. Precipitation of M7C3 occurs only in high-carbon austenitic steels, or in processes such as carburization [8]. The M6C precipitates, with a diamond FCC structure, are generally much rarer than other carbides and are favored by the addition of molybdenum and nitrogen [9, 21]. The M C carbides have a FCC structure of NaCl type. Finally, the introduction of elements such as V, Nb, Ti, Zr, Al, Hf and Ta, are known to lead to the nucleation of highly stable MC-type intragranular carbides. That is generally used to hinder M23C6 precipitation [9].
G Phase
The G phase is a silicide, formed in austenitic steels stabilized with titanium and niobium [18]. It is also observed when decomposing ferrite at temperatures below 500◦C [9]. The G phase is particularly rich in nickel and silicon and its stoichiometric composition is N i16Si7T i6 (Table 1.2).
In the case of G phase nucleated during the decomposition of ferrite, the particle size is very law, in order of the one to the ten nanometers. And they are dispersed in the metallic matrix [32].
In AISI 316 and Incoloy 800 alloys, the G phase is observed after short term ageing (1000h, 600◦C). Under such conditions, the G phase particles are located along grain boundaries and at triple points, with a size up to 500nm [2, 15].
σ Phase
The σ phase is known to be hard and brittle, rich in chromium and molybde-num, resulting in a drastic reduction of the mechanical properties and corrosion resistance [33–35].
Nilsson [33] pointed out that high chromium and molybdenum contents ac-celerate the precipitation kinetics and increase the volume fraction of σ phase, whereas nickel increases the kinetics of precipitation but decreases the volume fraction of σ phase.
It is generally believed that σ phase particles nucleate lately in AISI 316 steels. However, once the nucleation of σ phase has occurred, the size of σ phase particles may rapidly reach 1µm [2]. Nevertheless, the precipitation mechanisms are still not fully clear.
χ Phase
The lattice parameter of the intermetallic χ phase is about three times that of ferrite, allowing χ growth in a cube on cube orientation relationship with ferrite, where the {111} planes and h001i directions of the two phases are parallel. Since the strong crystallographic coherence of the two phases, the energy required for the nucleation of the χ phase in ferrite is low. Therefore, the χ phase formation kinetics is faster than the σ phase one. The χ phase is, however, less stable than the σ phase and could be absorbed by the σ phase for longer ageing times [36]. The χ phase is richer in molybdenum than the σ phase and its formation is triggered by an increase in the molybdenum content [21].
Laves phase η
Laves phase particles could be observed in the matrix and at grain boundaries. The laves phase (η) is a minor constituent of stainless steels containing Mo (such as AISI 316). Its chemical composition is F e2M o. Theoretically, laves phases do not exist in the material in its as-received state. They can appear after a in-service time over 100h [2].
γ0 (N i3(T i, Al))
This precipitate is observed in Incoloy 800 after a few hundred hours of service at temperatures between 500 and 650◦C. Contrarily to carbides formed at grain boundaries, the γ0 phase nucleates homogeneously in the matrix. The γ0 phase particles are spheroidal. Their size and density are controlled by the chemical composition, the heat-treatment conditions and creep conditions. However, the size of γ0 is generally below 100nm.
The long-term elevated-temperature strength of Incoloy 800 is affected by the strengthening effects of γ0 particles. Unfortunately, this phase may also cause decrease in long term ductility [26].
During creep, the γ0 particles could be either sheared or circumvented by dis-location gliding. Consequently, parameters, such as precipitate size, inter particle distance and volume fraction in matrix, affect the creep resistance of Incoloy 800 after long term service at high temperature. That affects the evolution of its creep ductility, with temperature and time.
Ti(C,N)
The T i(C, N) particles are generally rectangular large precipitates (1 − 5µm), embedded in the grains of Incoloy 800 alloys [15]. The affinity of titanium to carbon is higher than the Cr one, thus T i(C, N) precipitates are much more stable than M23C6 precipitates [27]. Therefore, the presence of T i(C, N) could inhibit M23C6 precipitation. However, M23C6 particles nucleate preferentially at in-service temperatures because M23C6 is more stable at high temperature [27].
δ Ferrite
The residual δ ferrite has a higher chromium concentration than the austenitic matrix, and because of its structure, the diffusion rate of these elements is faster. During annealing, this phase can be decomposed into thermodynamically stable austenite and into a wide variety of second phases, according genetic decompo-sition: δ −→ γ + precipitate (1.3)
These precipitates are mainly M23C6 carbides. Depending on temperature, the intermetallics may also be formed, but in smaller quantities because their pre-cipitation kinetics are slower.
Fig. 1.3 shows the microstructure in one sheet of as-received AISI 316L(N). Some ferrite bands are observed. Villanueva et al. [37] observed that the initial δ ferrite bands arise from the solidification. They are indeed elongated and parallel to the rolling direction. This observation agrees with the observations of Rieth et al. [38], Padilha et al. [20], Slattery et al. [23] and Odnobokova et al. [39].
Figure 1.3: Microstructure of the as-received material, 1/2 of the plate thickness, observed by optical microscopy (×100) [40].
Microstructure evolution at high temperature
At high temperature, the microstructure of austenitic steels is unstable. The microstructure changes in function of temperature, time, stress and strain.
Villanueva et al. [37] studied the precipitation of σ phase in AISI 316L. Their observations show that, during creep, the formation of σ phase occurs at grain boundaries and at triple points. And no σ phase was detected in the metallic matrix.
The microstructural evolution of 316H TB in function of time and tempera-ture is shown in Fig. 1.4a. At 550◦C, the M23C6 precipitate appears after almost 2000h. And no σ phase particle is observed even after 105h. However, this TTP diagram is established only based on the observation of the microstructure of the specimen head portions. Hence, the stress and viscoplastic strain effect is not included in this TTP diagram. Fig. 1.4b is based on the analysis of the data provided by the NIMS data sheet [2]. It illustrates that, under stress and vis-coplastic strain, the σ phase particles could be observed after 100h (at 700◦C), which is much earlier than under the unloaded condition (specimen heads, pure ageing). Therefore, it can be concluded that the stress and viscoplastic strain has a strong effect on precipitation at high temperature.
As shown in Fig. 1.5, the NIMS data sheet provides the size evolution of M23C6 and σ phase particles during creep in AISI 316H TB [2]. In the head portion, the size of M23C6 is lower than 250nm. Unfortunately, no specific in-formation about the size of M23C6 carbides in the gauge portion is given. From SEM or TEM image in literature [17, 41], we deduce that the size of M23C6 is generally lower than 0.5µm, which is much lower than the size of σ phase. More-over, once σ phases are observed, their size reaches 1 or 2µm [2]. This holds in both in the head and gauge portions.
The kinetics of precipitation during creep depends on many factors, includ-ing temperature, stress, chemical composition, crystallographic structure, grain size and heat-treatment. Therefore, these precipitation phenomena are difficult to be studied either experimentally or theoretically. Nevertheless, CALPHAD computations [42] demonstrated that the G phase is not stable at high temper-ature. The χ phase appears only at high temperature (> 700◦C) as shown in Fig. 1.4a. Furthermore, along grain boundaries, the M23C6 precipitates and the σ phase particles are generally observed compare to others. Consequently, only the M23C6 precipitates and the σ phase particles are considered in Chapters 2, 3 and 4.
Figure 1.4: Time-temperature-precipitation (TTP) diagram (a) for specimen head portions of 316H TB [2]; (b) of σ phase for both specimen head and gauge portions of 316H TB obtained by analyzing NIMS data sheet [2].
Creep background
Viscoplastic materials deform continuously when subjected to a constant load and temperature. This phenomenon is called creep.
Creep deformation is thermally activated, i.e. relatively small variations in temperature cause considerable variations in strain rate. Creep is possible at all temperatures above absolute zero. However, for metallic alloys, creep occurs generally significantly only at temperatures close to or higher than about 0.4Tm, with Tm the melting temperature. Thus, creep deformation is most often negligi-ble for alloys used in the construction of structures such as bridges or ships. This is not the case for many materials which may be used in the nuclear power plants of Generation IV, which will be subjected to temperatures above 500◦C during several decades. The short and long term creep behaviors of AISI 316L(N) and Incoloy 800 alloys, are therefore, studied in the present work.
Creep deformation
Creep is a deformation process observed when applying a constant engineering stress, σeng, to a specimen at high temperature. A few authors impose a constant true stress, σtrue. A typical creep curve for metals and alloys is shown in Fig. 1.6.
Figure 1.6: Typical creep curve in metals and alloys.
Three stages are delineated in the creep curve:
– the primary stage (first stage), the deformation rate decreases due to the increasing of dislocation and low angle boundary densities and the effect of intergranular viscoplastic strain incompatibilities and resulting internal stress;
– the steady-state creep stage (or secondary stage), during which the strain rate is approximately constant. This strain rate is generally called as the minimum strain rate, ε˙min. The constant strain rate is caused by a balance between dislocation annihilation and deformation hardening. Then, the dislocation density is almost constant during this stage. This is a dynamic equilibrium.
– the tertiary stage. The strain rate accelerates up to fracture, due to neck-ing, internal cracks or voids, and the decrease in cross-section area of the specimen in case of constant force lading.
The relationships between engineering and true strains and stresses are the fol-lowings:
εtrue = ln(1 + εeng) (1.4a)
σtrue = σeng • (1 + εeng) (1.4b)
The minimum true strain rate, ε˙truemin, could be determined by plotting the evolu-tion of true strain rate in function of the true strain or time.
A significant indicator of the involved creep fracture mechanisms is the re-duction in fracture area, Z. The area of fractured surface, Sf , is generally used to calculate the reduction in area, Z. The reduction in area is the ratio between the variation of transversal section, S0 − Sf , and the initial section area, S0:
S0 •
Z(%) = S0 − Sf 100% (1.5)
Creep deformation and fracture have been studied phenomenologically for almost hundred years.
Phenomenological viscoplasticity laws
The phenomenological creep deformation and fracture laws are presented in this subsection.
Phenomenological creep laws
Andrade’s Law
In 1910, a mathematical law ruling the viscoplastic strain during the primary stage (Fig.1.6) was proposed by Andrade [43]: ε(t, σ, T ) = C1 • tC2 • σn1 (1.6) where the coefficients C1, C2 and n1 are temperature-dependent.
The strain rate during the primary stage is calculated using Eq. 1.7, which assumes deformation hardening. ε˙ = C3 • εC4 • σn2 (1.7)
In this equation, ε˙ (% h−1 or s−1) denotes the strain rate for a given creep strain, ε(%), under stress σ (M P a or P a) and at temperature T (◦C).
The coefficients C1, C2, n1, C3, C4 and n2 are adjusted using experimental creep curves. The values of the coefficients of 316L(N) are provided by the RCC-MR design code [1], and more recently, reevaluated by Cui [44] for the materials under study. In Chapters 2 and 3, these parameters will be used for Finite Element simulations. For Incoloy 800, these parameters are not provided by the MCC-MR code [1].
Norton’s Law
In 1929, Norton [45] proposed a phenomenological law which links the minimum strain rate to the stress. ε˙mintrue = C • (σeng)n (1.8)
where C(M P a−nh−1 or P a−ns−1) and n(T ) are temperature dependent material constants, ˙truemin (h−1 or s−1) is the minimum true strain rate and σeng (M P a or P a) is the engineering stress. The values of coefficients C and n are provided in Chapter ?? (Incoloy 800) and Chapter 2 (316L(N)).
For describing the thermally-activation of creep deformation, the temperature dependence can be expressed as an Arrhenius-type expression as proposed by Sherby and Burke [46]:
ε˙min = ASB • exp(−RT ) (1.9)
where R is the gas constant (8.314Jmol−1K−1), ASB is a constant, and Q is the activation energy for creep deformation (Jmol−1).
Webster and Ainsworth [47] combined Eq. 1.8 and Eq. 1.9, proposed Eq.
Phenomenological lifetime predictions
Using conventional uniaxial creep tests to estimate long term creep lifetime of structural materials may require impractically long testing times. In fact, the laboratory creep test duration is generally less than one year, which is very short compared to the in-service condition (duration up to 60 years). Few laboratory, as NIMS [2], ORNL [48, 49], have long term test up to 25 years, which is always shorter than the in-service ones.
Therefore, over the past decades, many studies aimed to develop predictive models, based on short term test results, to estimate long term lifetime. Firstly, creep lifetimes are predicted by phenomenological laws, especially the Monkman-Grant relationship and the Larson-Miller relationship. Both laws make it pos-sible to extrapolate from the available experimental test lifetimes at different temperatures and/or lower stresses.
Monkman-Grant relationship
The Monkman-Grant relationship [50] has been shown to be valid for a wide range of metals and alloys. The strain rate is assumed to be constant during the creep test and equal to the minimum strain rate. The well-known Monkman-Grant law describes the relationship between minimum strain rate (ε˙min) and fracture lifetime (tf ) [50]. ε˙minmMG • tf = CMG (1.11)
where mMG is a constant that is originally evaluated by Monkman and Grant to be between 0.8 and 1 for metals and alloys and CMG is the Monkmann-Grant constant. Therefore, considering mMG = 1, the product of minimum strain rate and fracture time is constant and independent of test temperature (Fig. 1.7) [51].
Based on this equation, results of short term, high stress creep tests can be extrapolated to long term low stress creep conditions. The value of mMG depends on each material microstructure, and small values of mMG is associated with large grain materials [51, 52].
The Larson-Miller relationship
In Larson-Miller approach, a constant parameter called CLM is defined as a function of test temperature, fracture time and materials constant. Knowing this material constant, the fracture time can be extrapolated from short term laboratory tests result at temperature/stress higher than the in-service ones.
The Larson-Miller parameter is defined by the following relationship:
P (σ) = T (CLM + logtf ) (1.12)
From the results of tests carried out under different stresses, the Larson-Miller function of the stress, P (σ), can be deduced. P (σ) determines the time to reach a given strain with different couples of (σ, T ).
Fig. 1.8 shows experimental creep failure results for various alloys, which justifies the use of a value of CLM of almost 20 [54]. Nevertheless, the Larson-Miller relationship is only a phenomenological law used to predict long term creep fracture properties without a well defined physical basis.
Figure 1.7: Minimum strain rate in function of lifetime in copper (Eq. 1.11) [53].
Figure 1.8: Larson Miller representation of experimental creep lifetimes, t, for various alloys [54] (Psi = pound per square inch).
The extrapolations carried out based on phenomenological models may lead to a large over- or underestimations of long term creep lifetime. Therefore, the understanding of the physical deformation and damage mechanisms are necessary to predict more reliable long term creep lifetimes.
Creep deformation mechanisms
The minimum strain rate has been shown to be well predicted by the Mukherjee-Bird-Dorn equation [55], which expresses the creep rate in terms of stress, tem-perature and grain size, as:
AMBDµb b σ
ε˙min = Db(T )( )p( )n (1.13)
kbT dg µ(T)
where AMBD is a dimensionless constant, Db(T ) is the bulk self-diffusion coef-ficient, dg is the grain size, µ(T ) is the elastic shear modulus, n is the stress exponent.
More precisely, several mechanisms are known to contribute to the creep deformation of steels, such as diffusion, grain boundary sliding and climb/glide of dislocations. Each mechanism of deformation depends on stress, temperature and metallurgical structure.
A first classification of the mechanisms is proposed by Cannon and Langdon
[56] in function of the value of p. If the crystal deformation mechanism is dom-inant and the grain boundary sliding plays a negligible role, then, p = 0. If the grain boundaries contribute to the deformation process, p takes values from 1 to 3.
In the following, the main mechanisms of pure diffusion creep are described and then those involving dislocation.
Table of contents :
1 Introduction
1.1 Materials under study
1.1.1 Chemical composition
1.1.2 Effect of the main chemical elements
1.1.3 Grain size
1.1.4 Secondary phases
1.1.5 Microstructure evolution at high temperature
1.2 Creep background
1.2.1 Creep deformation
1.2.2 Phenomenological viscoplasticity laws
1.3 Creep deformation mechanisms
1.3.1 Diffusion creep
1.3.2 Grain Boundary Sliding
1.3.3 Dislocation creep
1.3.4 Deformation map
1.4 Damage mechanisms
1.4.1 Necking
1.4.2 Intergranular fracture
1.4.3 Physically-based lifetime prediction
1.5 Conclusion and summary of the manuscript
2 Modeling of creep cavity nucleation
2.1 Introduction
2.2 Experimental background and results
2.2.1 Material under study
2.2.2 Microscopic observations
2.3 Macroscopic and crystalline constitutive laws
2.3.1 Macroscopic isotropic creep flow rules
2.3.2 Crystal constitutive laws
2.4 Interfacial stress field calculations
2.4.1 Influence of the particle elasticity constants
2.4.2 Influence of the random orientations of the two neighbor grains
2.4.3 Time evolution of the normal stress fields
2.4.4 Influence of temperature and remote stress
2.4.5 Relationship between interface stresses and the orientation of each grain boundary with respect to the tensile axis
2.5 Interface fracture
2.5.1 The stress criterion
2.5.2 First prediction of cavity nucleation rate
2.6 Discussion
2.6.1 Local interfacial stress
2.6.2 The fracture criterion
2.6.3 Evaluation of the Dyson law prefactor
2.7 Conclusion
3 Effect of the particle geometry
3.1 Experimental observations
3.2 Interfacial stress field calculations
3.3 Precipitate shape factor effect
3.3.1 The Eshelby theory
3.3.2 Finite Element calculations
3.4 Precipitate sharp tip effect
3.4.1 Precipitate symmetric tip
3.4.2 Precipitate asymmetric tip
3.5 Discussion of the modeling assumptions
3.5.1 2D-3D comparison
3.5.2 Evolution of the average inclusion stresses during straining
3.5.3 Influence of the lattice rotation
3.6 Summary and conclusion
4 Lifetime prediction of 316L(N)
4.1 Introduction
4.2 Creep damage mechanisms
4.2.1 Necking
4.2.2 Intergranular damage
4.2.3 Thermally-activated nucleation of stable vacancy nuclei
4.2.4 Interface fracture
4.3 stress concentrators
4.3.1 Slip bands
4.3.2 Grain boundary sliding
4.3.3 Intergranular inclusion embedded in metallic grains
4.4 Long term lifetime prediction
4.4.1 Final evaluation of the Dyson law prefactor
4.4.2 lifetime predictions in 316 SSs
4.5 Discussion and conclusion
4.5.1 Cavity nucleation model
4.5.2 Evaluation of cavity nucleation rate
4.5.3 Lifetime predictions
4.5.4 Comparison of the long term creep resistance in Incoloy 800, 316L(N) and Grade 91 steel
5 Conclusions, work in progress and perspectives
5.1 Conclusions
5.1.1 Experimental investigation of damage mechanisms
5.1.2 Finite element calculations
5.1.3 Enhanced prediction of creep lifetimes
5.2 Work in progress
5.3 Perspectives
5.3.1 Local stress concentration
5.3.2 Intergranular Diffusion
5.3.3 Precipitation
A Uncertainty in 0
B Interface normal stress values
C Cohesive law: HINTE
