Prediction of creep crack initiation time based on constraint parameters in specimens with different geometries
Introduction
Creep crack initiation (CCI) and growth (CCG) are the primary mechanisms of failure on high-temperature components [1]. The CCI time is generally defined as the time required to reach a small measureable crack extension (it is typically 0.2 mm or 0.5 mm) from a defect [[2], [3], [4]]. The operational and plant assessment experience indicate that in the majority of cases where the CCI and CCG in high temperature components are likely to originate from welded joints (welds, heat-affected zones (HAZs) or parent metals) [[5], [6], [7]]. Many investigations have shown that the difference of creep deformation properties between weldment constituents [[8], [9], [10]], load level and initial crack position [11] have important effects on creep failure behavior of welded joints. Thus, for operational power plant, the key inspections usually focus on the integrity of high temperature welded joints. Because CCI time can occupy a large fraction (80%) of a component service lifetime, it is fundamental and essential to assess the CCI life of high temperature component [1].
A lot of experimental and numerical investigations have shown that the CCI time is significantly affected by the specimen geometry sizes (such as specimen width W and thickness B) and crack depths (a/W) [[12], [13], [14], [15], [16], [17], [18]]. This size effect is usually caused by the crack-tip constraint, and called constraint effect. The constraints are divided into in-plane and out-of-plane constraints. The in-plane constraint is related to crack depth a/W and specimen width W, and the out-of-plane constraint is related to thickness B. In addition, the loading modes of specimens can also affect the crack-tip constraint. The constraint level of specimens with bending loading (such as C(T) specimen) is higher than that of specimens with tension loading (such as M(T) specimen). The CCI time decreases with the increase of creep crack-tip constraint [[16], [17], [18]]. For a given C* value, the CCI time in high constraint C(T) specimens are significantly shorter than those obtained in low constraint M(T) specimens for 316H stainless steel [18] and Cr–Mo–V steel [16,17]. It has also been shown that long term CCI time is shorter than the CCI time of prediction line from short term test for a given C* value [13]. Different approaches for CCI time assessments have been developed, such as time-dependent failure assessment diagram (TDFAD) [19,20], two-criteria diagram (2CD) [[21], [22], [23]] and Nikbin-Smith-Webster model (NSW model) [23]. In these approaches, the creep constraint effects have not been incorporated. As a result, the conservative CCI prediction results may be produced. To reduce the excessive conservatism and establish the CCI and CCG life assessment approaches incorporating creep constraint effects, some creep crack-tip constraint parameters have been proposed, such as Q [[24], [25], [26]], Tz [27], R [28], R* [29,30] and Ac [[31], [32], [33], [34]] etc. The parameters Q, R and R* based on creep crack-tip stress field can mainly characterize the in-plane constraint and the out-of-plane constraint was characterized by parameter Tz. In recent work of Ma et al. [[31], [32], [33], [34]], an in-plane and out-of-plane unified creep constraint parameter Ac based on crack-tip equivalent creep strain has been proposed. Based on the parameter Ac, the material constraint caused by material mismatch in welded joints and geometry constraint induced by specimen geometries and crack size can be unified characterized. And the correlations of geometry and material constraint with creep crack growth rate of parent Cr–Mo–V steel and P92 welded joints have been established [32,34,35]. In recent work of authors [36,37], the creep constraint parameter R* solutions for pressurized pipes with circumferential and axial semi-elliptical surface cracks have been studied and given. Based on the two-parameter C*-R* approach, the CCG life has been assessed considering constraint effect for pressurized cracked pipes [38].
In recent papers of authors, the three-dimensional (3-D) creep constraint has been characterized by using the creep constraint parameters R* and Ac [39] and the influence of constraint on CCI time [17] have been investigated for the recommended specimen geometries and size ranges in ASTM E1457 standard [2]. However, the quantitative correlations of CCI time with constraint over a wide range of C* region have not been established, and the prediction of CCI time based on constraint parameters in specimens with different geometries has not been investigated.
In this work, the quantitative correlation equations of CCI time with two constraint parameters R* and Ac for Cr–Mo–V steel at 566 °C were established. By using the correlation equations and finite element calculations of the two constraint parameters, the CCI time in specimens with different geometries and dimensions has been predicted. The predicted results have been compared with experimental data available and results of finite element simulations based on creep ductility exhaustion model. The capability of the two constraint parameters R* and Ac for predicting CCI time or life incorporating constraint effects for high-temperature components (such as high-temperature pressure pipes and vessels) also has been discussed.
Section snippets
Material and specimen geometry
The material used in this paper is a Cr–Mo–V steel (Chinese 25Cr2NiMo1V steel) for making steam turbine rotor. The material is original forging piece, and its microstructure is tempered bainite. The chemical composition and properties of this steel at 566 °C are shown in Table 1, Table 2, respectively. The two-region Norton (2RN) creep model for this steel has been developed and expressed as Eq. (1) by using the creep strain rate connected with stress [40]. The different Norton model parameters
Calculations of constraint parameters R* and Ac
In order to quantify the correlation of CCI time with constraint and predict CCI time incorporating constraint effect, the creep constraint parameters need to be calculated for specimens with different geometries. Recently, the creep constraint parameter R* based on crack-tip stress field and the unified creep constraint parameter Ac based on crack-tip equivalent creep strain have been proposed and developed. The load independent creep constraint parameter R* at steady-state creep has been
Constraint-dependent CCI time over a wide range of C* region
By analogy to the method for establishing the correlation of CCG rate with creep constraint parameters R* and Ac which has been given in detail in the recent work of authors [32,39], the quantitative correlation formulas of CCI time (t0.2 and t0.5) with creep constraint parameters R* and Ac may be established over a wide range of C* region. The t0.2 and t0.5 are the CCI time for a small crack growth length of 0.2 mm and 0.5 mm, respectively. Because the average constraint R*avg and Ac-avg can
Validation of constraint dependent CCI time equations
The CCI time of specimens or components may be assessed by using the CCI time equations in Table 3 based on two-parameter (C*-R* or C*-Ac) approach to consider crack-tip constraint effect. For actual high-temperature components with a certain geometry and loading condition, the creep fracture mechanics parameter C* can be obtained by reference stress method or FE calculations. And the corresponding constraint parameter Ac-avg or R*avg can be calculated using FE analysis. Therefore, the
Prediction of CCI time for a wide range of specimen geometry constraint and C* levels
In order to investigate the constraint-dependent CCI time equations whether or not can be used to predict the CCI time for a wide range of specimen geometry constraint and C* levels, the constraint and CCI time of C(T), SEN(T) and M(T) specimens with a wide range of thickness were analyzed, and the dimensions of these specimens are shown in Table 5. The load-independent average constraint parameters R*avg and Ac-avg along crack fronts were calculated by FEM and listed in Table 5. Then based on
Conclusions
- (1)
Based on recent FE calculations of CCI time and creep constraint parameters R* and Ac, the constraint-dependent CCI time equations of a Cr–Mo–V steel at 566 °C have been established over a wide range of C* region. It was found that the equations are independent on the choice of the reference specimen. This may bring convenience for their application.
- (2)
The predicted CCI time from the constraint-dependent CCI time equations for specimens with different geometries and sizes agrees well with the
Author statement
J.Z. He: Formal analysis, Investigation, Data curation, Writing – original draft. G.Z. Wang: Conceptualization, Methodology, Writing – review & editing. F.Z. Xuan: Project administration, Writing – review & editing. S.T. Tu: Supervision, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was financially supported by the Projects of the National Natural Science Foundation of China (51975212, 51835003).
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