LOCA frequency evaluation using expert elicitation

The double-ended-guillotine break (DEGB) criterion of the largest primary piping system in the plant, which generally provides the limiting condition for the emergency core cooling system requirements, is widely recognized as an extremely unlikely event. As a result, US Nuclear Regulatory Commission (NRC) staff are currently considering a risk-informed revision of the design-basis break size requirements for commercial nuclear power plants. In support of this effort, loss-of-coolant accident (LOCA) frequency estimates have been developed using an expert elicitation process by consolidating service history data and insights from probabilistic fracture mechanics (PFM) studies with knowledge of plant design, operation, and material performance. Baseline LOCA frequency estimates for the 5th percentile, median, mean and 95th percentile were determined from each panelist's elicitation responses. Group estimates were determined by aggregating the individual estimates using the geometric mean of the individual estimates for each frequency parameter. Group variability was estimated by calculating 95% confidence bounds for each of the group frequency parameters (i.e., median, mean, and 5th and 95th percentiles). A number of sensitivity analyses were conducted to examine the effects on the quantitative results from varying the assumptions, structure and techniques of the baseline analysis procedure.     

Evaluation of a method to characterize material inhomogeneity in ferritic steels within the ductile-to-brittle transition regime

The ASTM “Standard Test Method for Determination of Reference Temperature, T_o, for Ferritic Steels in the Transition Range,” (ASTM E1921) has been developed to characterize the onset of cleavage cracking in the ductile-to-brittle transition regime for ferritic structural steels. This standard determines T_o, the reference temperature at which the median fracture toughness of a 25 mm thick specimen is 100 MPa . Material inhomogeneity has been shown to have a strong effect on T_o, and suggestions on how to characterize and quantify the effects of inhomogeneity have been developed within a proposed annex for E1921.This study demonstrates that for small data sets neither the current E1921 outlier procedure nor the method in the proposed annex can effectively distinguish between homogeneous and inhomogeneous materials. This study also shows that the bimodal inhomogeneity analysis in the proposed annex only accurately characterizes materials if (1) at least 30 specimens are tested, and (2) the difference between the T_o values that describe each unique homogeneous population within the inhomogeneous material is greater than 20 °C, and (3) the percentage of the smallest homogeneous material population is greater than 20%.     

A Weibull stress model to predict cleavage fracture in plates containing surface cracks

This study applies recent advances in probabilistic modelling of cleavage fracture to predict the measured fracture behaviour of surface crack plates fabricated from an A515-70 pressure vessel steel. Modifications of the conventional, two-parameter Weibull stress model introduce a non-zero, threshold parameter (σ_w-min ). The introduction of σ_w-min brings numerical predictions of scatter in toughness data into better agreement with experimental measurements, and calibration of this new parameter requires no additional experimental data. The Weibull modulus ( m ) and scaling parameter (σu ) are calibrated using a new strategy based on the toughness transferability model, which eliminates the non-uniqueness that arises in calibrations using only small-scale yielding toughness data. Here, the Weibull stress model is calibrated using toughness data from deep-notch C(T) and shallow-notch SE(B) specimens, and is then applied to predict the measured response of surface crack plates loaded in different combinations of tension and bending. The model predictions accurately capture the measured distributions of fracture toughness values.     

Determination of constraint limits for cleavage initiated toughness data

The proper constraint limits for cleavage initiated toughness data within the ductile-to-brittle transition regime have been studied extensively using both numerical analysis and analysis of experimental data. Historically, the experimentally based constraint limits have supported less conservative limits. This study conducts analysis of existing and new experimental data developed using data sets targeted to exhibit constraint loss toughness enhancement. Constraint herein is quantified in terms of the scaled specimen deformation level, more commonly known as M. It is expected that data with low M values will exhibit the greatest affect of constraint loss. Large data sets are therefore developed and extracted from the literature that include data with a large range of M levels and at least the required number of uncensored results with M > 30 for valid T₀ measurement as per ASTM E1921-02. Differences in the calculated T₀ values using censoring limits of 5-500 are then determined. The onset of T_lim differences due to constraint loss is examined by simply increasing the censoring limit, M_lim, utilized in determining the indexing temperature, T_lim, and evaluating differences between T₀ and the T_lim values obtained using higher constraint limits. Bias resulting from this censoring procedure is examined using a Monte-Carlo analysis and shown to be small.Measurement of a high constraint T₀ in bend specimens is shown to require M_lim > 200. As M_lim increases from 30 to 200 in bend specimens, the corresponding T_lim can increase by approximately 15 °C. Further increases in M_lim do not result in substantial increases in T_lim. This evolution buttresses previous numerical findings by Dodds and co-workers [Specimen size requirements for fracture toughness testing in the ductile-to-brittle transition regime, J Test Eval 1991;191:123-34; Size and deformation limits to maintain constraint in K_Ic and J_c testing of bend specimens. In: Kirk M, Ad Bakker, editors. Constraint effects in fracture theory and applications: second volume. ASTM STP 1244, 1995; Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens, Int J Fract 1995;74:131-61] and provides a strong justification for changes to ASTM E1921-02 if a conservative, geometry insensitive, and transferable reference temperature, T₀, is to be determined using this standard. Possible short-term changes to ASTM E1921-02 could include raising M_lim and requiring an upward shift of SE(B) T₀ values. A more desirable solution is to adjust individual K_Jc toughness values before evaluation of T₀ to eliminate specimen geometry bias.     

Weibull stress model for cleavage fracture under high-rate loading

This paper examines the effects of loading rate on the Weibull stress model for prediction of cleavage fracture in a low-strength, A515-70 pressure vessel steel. Interest focuses on low-to-moderate loading rates ( K˙ _I < 2500  MPa √m  s⁻¹ ). Shallow cracked SE(B) specimens were tested at four different loading rates for comparison with previous quasi-static tests on shallow notch SE(B)s and standard C(T)s. To utilize these dynamic experimental data, we assume that the Weibull modulus ( m ) previously calibrated using quasi-static data remains invariant over the loading rates of interest. The effects of dynamic loading on the Weibull stress model enter through the rate-sensitive material flow properties, the scale parameter ( σ _u ) and the threshold Weibull stress ( σ _w-min ). Rate-sensitive flow properties are modelled using a viscoplastic constitutive model with uniaxial, tension stress–plastic strain curves specified at varying plastic strain rates. The analyses examine dependencies of σ _w-min and σ _u on K˙ _I . Present results indicate that σ _w-min and σ _u are weak functions of loading rate K˙ _I for this pressure vessel steel. However, the predicted cumulative probability for cleavage exhibits a strong sensitivity to σ _u and, consequently, the dependency of σ _u on K˙ _I is sufficient to preclude use of the static σ _u value for high loading rates.     

Prediction of the T0 Shift between Specimens of Different Constraints Using the T-Stress Based T-Functions

Microcracking in piezoelectrics is found to produce two major effects on the effective piezoelectric properties: it weakens the electromechanical coupling and it changes its "directionality", i.e. the direction of mechanical (electrical) response to the applied electrical (mechanical) loads. The latter effect implies that microcracking in piezoelectric sensors and actuators reduces the accuracy of the devices. We quantify the mentioned loss of accuracy. This can also be viewed as a quantification of the "piezoelectric fatigue".