Master Curve Approach Research Articles

A prediction model of brittle crack arrest toughness in TMCP heavy plates

Micro-alloyed low carbon MnCrNiCuMo steels were proposed to produce heavy plates with a maximum thickness of 100 mm. An integrated industrial route including a thermo-mechanical control process (TMCP) based on a study on continuous cooling transformation was applied in industrial production. Comprehensive mechanical properties tests including the measurement on resistance against crack initiation using crack tip opening displacement (CTOD) approach were conducted. Large scale wide-plate temperature gradient double tension (DT) technique was employed to evaluate the crack arrest toughness Kca in the heavy plates under different conditions. Nil-ductility transition temperature (NDTT) was also tested across the entire thickness section of the plates. The results showed that heavy steel plates were qualified being brittle crack arrest (BCA) products at EH47 grade with yield strength high than 460 MPa. High crack initiation toughness was exhibited by both Charpy-V notch impact property and CTOD values. Crack arrest toughness at −10 °C greater than 253 MPa √m was achieved in a plate even with thickness of 100 mm. The mean value of crack arrest toughness at different temperature measured by the DT approach can be indexed by the highest NDTT in the interior section of the heavy plates leading to an empirical prediction model. Further, fracture mechanics based master curve approach was used to statistically predict crack arrest toughness distribution over a wide range of temperatures showing improved predictability over the empirical model and an existing model in the literature.

On comparison of fracture toughness of irradiated and thermally aged decommissioned nuclear weld metals with miniature specimen test technique

This paper investigates the fracture toughness of thermally aged and irradiated weld metals extracted from head and beltline regions of a decommissioned nuclear reactor pressure vessel. Miniature compact tension specimens are fabricated from the thermally aged reactor pressure vessel head weld as well from the circumferential and axial beltline welds having fluences of 2.90 × 1016n/cm2 and 7.94 × 1017n/cm2, respectively. Master curve approach in accordance with the ASTM E1921 is applied to determine the reference temperature T0 and it is found to be − 113.5 °C, −104.4 °C, and − 89.3 °C for the reactor pressure vessel head, axial beltline, and circumferential beltline welds, respectively. In addition, the multimodal reference temperature Tm to assess the homogeneity of welds as well as key curve analysis for the quality assurance of testing are also provided. Fractographic analysis identified variations in crack initiation sites and microstructural inhomogeneities, particularly in the irradiated beltline welds. Overall, fracture mechanical testing of the materials demonstrated that miniature compact tension specimens are effective for characterizing the fracture toughness of limited surveillance weld materials, revealing differences due to irradiation and weld location.

Steady-state crack propagation during DCB test with viscoelastic-viscoplastic interface – Correlation between rheological behavior and effect of crack propagation rate

Adhesively bonded joints are known to suffer from creep and relaxation phenomena due to the viscous nature of the adhesive. These effects are detrimental to the durability of structural joints as they can lead to progressive and slow crack propagation rate phenomena and possible delayed failure. Master curve approaches are often used to assess the durability of structural assemblies, but the physical justification for such approaches requires additional investigation to more accurately assess the coupling between structural effects and the possible complex long-term rheological behaviour of the adhesive layer. Following similar approaches developed to study the steady-state crack propagation regime in bulk materials, an Eulerian description of crack propagation along a viscous adhesive layer during a double cantilever beam test is implemented. Taking into account viscoelastic-viscoplastic and various hardening rules, some master curves can be obtained describing the evolution of the crack propagation rate as a function of the stationary loading conditions. With such a model, the role of adhesive layer behaviour and joint geometry on crack propagation conditions can be discussed, as well as the applicability of such a master curve approach.

A Simplified Protocol for Permanent Deformation Characterization of Asphalt Concrete

Abstract Permanent deformation (PD; or rutting) is one of the major distresses in flexible pavements. To predict PD in asphalt concrete, repeated and recovery load tests are usually conducted in the laboratory. The full-blown repeated load permanent deformation (RLPD) is time-consuming, limiting its use in research programs and developing correlations. Therefore, a quicker yet reliable procedure is needed for use in performance prediction programs. This paper presents a simplified and quicker procedure to obtain PD model parameters. It is illustrated using laboratory tests on field specimens. The procedure uses one specimen, compared with three specimens in the full-blown RLPD test, to be tested at two temperatures, the highest and lowest in the RLPD test, under the same conditions as in the RLPD test. The results of any intermediate temperature are obtained from the calibrated model. Two approaches are presented for analyzing the test results: the power equation in the AASHTOWare program, and the construction of a master curve. In the full-blown testing program with three specimens and three temperatures, the master curve approach fitted the results better than the power law. In the simplified procedure, the fitting of the two approaches is almost identical. Results obtained from tests conducted on six mixes show (1) testing one specimen at the highest temperature only and extrapolating the results overpredicts the material behavior at intermediate and low temperatures, and (2) the master curve from the simplified procedure compares very well with the one from the full-blown RLPD program.

The Main Results of Structural Materials Research for Safe Long-Term Operation of LWR NPPs from the Viewpoint of Dissemination Activities

One of the main points of any project implementation is the dissemination of the obtained results among the nuclear community, young researchers, public, stakeholders, etc. Communication and dissemination activities are considered as high-priority elements in European collaborative research projects. The article briefly presents EUROATOM project “STRUctructural MATerials Research for Safe Long-Term Operation of LWR NPPs” (STRUMAT‑LTO), that was started in September 2020, describes its goals, main steps, expected outputs, approaches used for dissemination and communication activities and brief status update on interim results after 2 years’ implementation. In general, the deployment of the STRUMAT-LTO project was dedicated to studying synergetic effects of Ni-Mn-Si on RPV embrittlement at high fluences by exploiting unique RPV model steels irradiated in LYRA-10 irradiation experiment and assessing the Embrittlement Trend Curves for LTO and Master curve approach for LTO. All these activities are aimed at finding a solution to justify safe LTO until 80 years of operation.

On the use of mini-CT specimens to define the Master Curve of unirradiated reactor pressure vessel steels with relatively high reference temperatures

The safe operation of nuclear plants requires an accurate characterization of the fracture toughness of reactor pressure vessel materials, which can be reduced over time due to irradiation or thermal aging processes. This necessity is a challenge itself since the availability of specimens inside the surveillance capsules of the vessels is generally scarce. Therefore, innovative techniques have to be applied, in order to increase the reliability of fracture toughness measurements and at the same time to reduce the volume of material needed for the tests. In this paper, the Master Curve (MC) approach has been employed, combined with the use of mini-CT specimens made from two different reactor pressure vessel (RPV) steels (ANP-5 and A533B LUS). The MC methodology allows the fracture toughness of the material to be evaluated by using a single parameter: the reference temperature, T0. This parameter has been previously estimated using mini-CT specimens in a number of unirradiated steels, most of them with relatively low T0 values (-120 °C to −60 °C), providing satisfactory results. This paper adds further validation of the use of mini-CT specimens to define the T0 of unirradiated RPV steels with relatively high values of this parameter. Additionally, the analysis of the fracture surfaces confirms the existence of cleavage fracture following the weakest link theory (i.e., one single initiation point), as required by the Master Curve approach.

Estimation of Fracture Toughness of API 2W Gr.50 Steel in Ductile to Brittle Transition Behavior Using Master Curve Approach

Welding is used as the main joining method in various industries, including the shipbuilding industry. In the case of welded structures, structural integrity assessment is essential to ensure the safety of the structure because many defects inevitably exist during the manufacturing process. The value of reliable fracture toughness is required for structural integrity assessment. It is obtained by the fracture toughness test, but the fracture toughness test requires a lot of time and effort. Therefore, many studies have been conducted on efficient methods to evaluate fracture toughness. Among the various studies that estimate fracture toughness, some have been conducted using the Charpy impact test, which is relatively simple compared to the fracture toughness test. This study conducted a series of experimental investigations on API 2W Gr.50 steel applied with different welding conditions. Based on the Charpy impact test results, the fracture behavior was well estimated in the ductile to brittle transition region according to the temperature. However, there was a difference in the accuracy of predicting fracture behavior depending on the welding process. Therefore, additional consideration reflecting the various welding conditions is required to ensure the safety of welded structures.

Influence of Material Toughness on Fracture Reliability in Steel Bridges

The fracture limit state of the AASHTO LRFD Bridge Design Specifications is addressed by requiring minimum impact toughness values for base material and mitigating potential fracture initiators through proper structural detailing. This fracture control approach has been successful in minimizing the number of fractures in steel bridges designed since its inception; however, it is not a calibrated limit state and the structural reliability against sudden brittle fracture has not been previously established. Accordingly, the objective of this study was to quantify the relationship between material toughness and fracture reliability in steel bridge members, considering the probabilistic distribution of fracture toughness and applied stress for a variety of structural steels and assumed crack sizes. The master curve approach is used to account for the probabilistic distribution of fracture toughness, and reliabilities are determined using Monte Carlo simulation and the Hasofer-Lind approach. The results indicate that the fracture reliability for modern bridge steels is consistent with the reliability of AASHTO strength limit states, and that certain steels currently available on the market can provide enough reliability against fracture to essentially eliminate brittle fracture as a limit state of concern. This finding holds the potential for a new way of approaching the design of fracture-critical members.

A master curve approach to model short- and long-term time-dependent nonlinear behavior of polyethylene

This paper presents a new approach for modeling the constitutive behavior of time-dependent materials by applying two phenomenological constitutive models to creep curves. Data obtained from short-term test are used for predicting the long-term behavior. The nonlinear viscoelastic response is modeled by using the multi-Kelvin model and the viscoplastic behavior is described by a power law. The methodology proposed herein for obtaining the constitutive formulation is based on developing master curves. Results obtained for polyethylene are discussed and compared using creep tests at different stress levels and has proved to be reliable based on the results analyzed in this work.

Quantitative Assessment and Analysis of Non-Masing Behavior of Materials under Fatigue

Quantitative assessment of non-Masing behavior is studied, and a new method is proposed for the estimation of cyclic plastic strain energy density and fatigue life. Low cycle fatigue tests were performed on 304L stainless steel employing strain amplitudes ranging from ±0.25% to ±1.0% at a strain rate of 3 × 10-3 s-1. The material exhibited Masing behavior at lower strain amplitudes and non-Masing behavior at higher strain amplitudes. Secondary hardening was observed at relatively higher strain amplitudes. Both the secondary hardening and non-Masing response were found to be associated with the deformation induced martensitic transformation. The master curve approach, which is generally used for the analysis of non-Masing response, could not be used as experimental data could not be represented in the form of a master curve. The proposed method of quantification of non-Masing response could estimate the cyclic plastic strain energy density of 304L stainless steel well within a scatter band of 1.2. The fatigue life of 304L stainless steel could also be predicted within a scatter band of 2. The proposed approach could also estimate the cyclic plastic strain energy density and fatigue life of materials of different grades within scatter factors of 1.2 and 2, respectively.

Structural Integrity Assessment of a Nuclear Vessel through ASME and Master Curve Approaches Using Irradiation Embrittlement Predictions

Abstract The assessment of the structural integrity of nuclear vessels is based on a series of procedures developed in the 1970s and 1980s. On one hand, curves that, according to the American Society of Mechanical Engineers code, describe the relationship between steel toughness and temperature in the ductile-to-brittle transition region, based on the reference temperature concept RTNDT, were adopted in 1972. On the other hand, the material embrittlement derived from the exposure of steel to neutron irradiation is determined through the model included in “Regulatory Guide 1.99 Rev. 2,” published in 1988. Since then, there have been enormous advances in this field. For example, the Master Curve, based on the reference temperature T0, describes the relationship between toughness and temperature in the transition zone more realistically and with much more robust microstructural and mechanical foundations and uses the elastic-plastic fracture toughness KJc. Moreover, improved models have been developed to estimate the embrittlement of steel subjected to neutron irradiation, such as ASTM E900, Standard Guide for Predicting Radiation-Induced Transition Temperature Shift in Reactor Vessel Materials. This study is aimed at comparing the results obtained using traditional procedures to the improved alternatives developed later. For this purpose, the behavior of the steel of a nuclear vessel that is currently under construction has been experimentally characterized through RTNDT and T0 parameters. In addition, the material embrittlement has been quantified using “Regulatory Guide 1.99 Rev. 2” and ASTM E900. These experimental results have been transferred to the assessment of the structural integrity of the vessel to determine the pressure-temperature limit curves and size of the maximum admissible defect as a function of the operation time of the plant. The results have allowed the implicit overconservatism present in the traditional procedures to be quantified.

A combined CFD and FEM analysis of pressurized thermal shock applied to the probabilistics of cleavage fracture

In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by the injection of cold water in the still pressurized reactor pressure vessel (RPV). The combination of pressure and thermal stresses provides a complex stress state in the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. The critical stress intensity for brittle cleavage fracture depends on the ductile to brittle transition temperature. This complex combination of stresses, absolute temperatures and temperature gradients in combination with radiation damage requires an integral approach for the evaluation of the probability for the occurrence of cleavage fracture. This problem is simulated with a combined CFD and FEM approach. A quarter of the reactor pressure wall including the cooling nozzle is simulated during the 1000 seconds of the cooling transient. This method can accurately predict the thermal profile and the corresponding stress field. This approach is applied to a reactor pressure vessel containing pre-existing semi-elliptical cracks. The stress intensities for every time step, the temperature, the effects of radiation damage, and the material properties of two types of RPV steel; (SA-508gr.3 and SA-508gr.4N) contribute to the probability for a brittle cleavage crack to form. An estimation of the probability for cleavage fracture is made through the Master Curve approach. These probabilities are calculated for different crack locations, sizes, aspect ratios and for two different grades of RPV steel. The influence of these geometric factors and material properties under the influence of radiation have been analysed. The material just below the nozzle is cooled down further and the thermal gradient is more severe. This is reflected in a higher probability for cleavage fracture. The new generation of RPV steel; SA-508gr.4N is very promising for its resistance to radiation induced embrittlement and for its higher strength, both factors leading to a lower probability of cleavage fracture in the reactor pressure vessel. Increasing the safety of the RPV.

Validation of the Master Curve Approach Based on Charpy Impact Test with Groove Shapes

Validation of the Master Curve Approach Based on Charpy Impact Test with Groove Shapes

A method to determine minimum design metal temperature of pressure vessels made from ferritic steel by Master Curve approach

The four impact exemption curves in ASME are convenient to estimate the minimum design metal temperature (MDMT) of ferritic steel. However they can’t distinguish low temperature fracture toughness of ferritic steel well. Materials with similar fracture toughness, divided into different impact exemption curves will have different MDMT and conservative degree. And the MDMT of ferritic steel are estimated by the steel grade. There are differences in toughness for steel with same steel grade from different factories and different heats and batches of the same factory. In this paper, the seven MDMT curves, identified with labels I, II, III, IV, V, VI and VII are proposed based on assumed yield strength and seven reference temperatures, (T0MC = 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C) which can cover the temperature range for commonly used pressure vessels made from ferritic steel. The MDMT for a ferritic steel can be determined once the reference temperature and yield strength are measured. SA508-3 and Q345R, as a representative of ferritic steel are used to illustrate the applicability of the MDMT curves.

Plasticizer loss in a complex system (polyamide 12): Kinetics, prediction and its effects on mechanical properties

Plasticizer migration is a major concern for plasticized polymers because it leads to unwanted changes in mechanical properties and, in many cases, contamination of the environment. In cases of slow migration, it is of practical importance to be able to perform accelerated testing and estimate migration rates from high temperature experiments. Despite the importance, a critical evaluation of different ways of extrapolating mass loss data has hitherto not been reported. Therefore, in this article, three different methods (involving for the first time a master-curve approach to mass loss data) to estimate low temperature migration from high temperature data are presented and critically evaluated. The system chosen was a plasticized polyamide 12 pipe, an important component in vehicle fuel-line systems. This system was challenging since the lower part of the temperature range in which the material is used overlaps with the glass transition region. All three methods (using data at 80–145 °C) over-estimated, although to different extents, the low-temperature mass loss rate (60 °C). The main reason for the over-estimation was the partial overlap with the glass transition region. Hence, there is a built-in safety factor when predicting plasticizer loss over glass transition regions, and the predictions are conservative. It was observed that plasticizer loss and annealing effects were the main reasons for changes in mechanical properties (increase in flexural stiffness/strength) during ageing.

Evaluation of Fracture Toughness of a SA580 Gr. 3 Reactor Pressure Vessel Using a Bimodal Master Curve Approach

Abstract The standard master curve (MC) approach has a major limitation in that it is only applicable to homogeneous datasets. In nature, steels are macroscopically inhomogeneous. Reactor pressure vessel (RPV) steel has different fracture toughness with varying distance from the inner surface of the wall due to the higher cooling rate at the surface (deterministic material inhomogeneity). On the other hand, the T0 value itself behaves like a random parameter when the datasets have large scatter because the datasets are for several different materials (random inhomogeneity). In this paper, four regions, the surface, 1/8 T, 1/4 T, and 1/2 T, were considered for fracture toughness specimens of Korean Standard Nuclear Plant (KSNP) SA508 Gr. 3 steel to provide information on deterministic material inhomogeneity and random inhomogeneity effects. Fracture toughness tests were carried out for the four regions at three test temperatures in the transition region and the microstructure of each region was analyzed. The amount of upper bainite increased toward the center, which has a lower cooling rate; therefore, the center has lower fracture toughness than the surface so reference temperature (T0) is higher. The fracture toughness was evaluated using the bimodal master curve (BMC) approach. The results of the BMC analyses were compared with those obtained via a conventional master curve analyses. The results indicate that the bimodal master approach considering inhomogeneous materials provides a better description of scatter in the fracture toughness data than a conventional master curve analysis does.

Spreadsheet-based method for predicting temperature dependence of fracture toughness in ductile-to-brittle temperature region

A spreadsheet-based simplified and direct toughness scaling method to predict the temperature dependence of fracture toughness Jc in the ductile-to-brittle transition temperature region is proposed. This method uses fracture toughness test data and the Ramberg–Osgood exponent and yield stress at the reference temperature, and yield stress at the temperature in interest to predict Jc. The physical basis of the simplified and direct toughness scaling method is the strong correlation between Jc and yield stress. The simplified and direct toughness scaling method was validated for Cr–Mo steel Japan Industrial Standard SCM440 and 0.55% carbon steel Japan Industrial Standard S55C by comparing the simplified and direct toughness scaling prediction results with the median results of an experiment performed at four temperatures ranging from −55°C to 100°C and at three temperatures ranging from −85°C to 20°C, respectively. The simplified and direct toughness scaling method can predict Jc from both low to high temperatures, and vice versa. Thus, 12 and 6 predictions were made for each material. The prediction discrepancy for these 18 cases ranged from −50.4% to +25.8% and the average absolute discrepancy was 22.1%. These results were acceptable considering the large scatter generally observed with Jc. In particular, in case of predicting Jc at temperatures higher than the lowest temperature of −55°C for SCM440, the simplified and direct toughness scaling method predicted Jc more realistically than the American Society for Testing and Materials E1921 master curve approach. Although the simplified and direct toughness scaling method requires additional tensile test data compared with the master curve approach, the acceptable prediction accuracy at high temperatures seems beneficial because the mass and time required for tensile tests are admissible.

Application of a master curve and the modified superposition principle for modeling creep and loading rate effects at small strains in high-density polyethylene

Studying the nonlinear viscoelastic behavior of high-density polyethylene (HDPE) at small strains and stresses is still a matter of interest in engineering applications such as laying submerged pipelines. Although sound modeling of such behavior requires complex phenomenological or micromechanical constitutive laws, many works have focused on the development of simplified procedures for approximating this type of nonlinear response. Usually, when these simplified methods are employed to reproduce creep behavior, they are not capable to simultaneously provide good estimates for traction tests even at constant stress or strain rates. This work describes a methodology, which has shown a good compromise to reproduce both types of responses within a given stress range. The procedure can be understood as an interpolative approach based on a master curve and the modified superposition principle to account for nonlinear effects. With this strategy, it is possible to predict the nonlinear creep behavior for an HDPE sample subjected at any constant stress level within a given experimental range. Once this predictive capability is achieved, we use an incremental algorithm based on the modified superposition principle to simulate traction tests at constant strain rates. We show that the combined application of the proposed master curve approach and the modified superposition principle results in good approximations for creep tests and simultaneously leads to remarkable agreement with experimental traction tests reported in the literature.

Application of new constraint based Master Curve in fracture assessment of pressure vessels

This paper represents the ability of the recently developed methodology for evaluating fracture probability of the ferritic steel components based on the Master Curve methodology. Due to crack-tip constraint, a cracked component may experience a significant change in its effective fracture toughness under a given load and temperature, whereas the Standard Master Curve (SMC) method cannot take into account this change. In this study the conservatisms associated with SMC method for low constraint geometries is investigated for a pressurized cylindrical vessel containing an internal semi-elliptical axial crack. A modification of SMC is developed based on the Q parameter as the crack-tip constraint. The usability of the Modified Master Curve (MMC) approach for structure integrity assessment of the pressure vessel is demonstrated. Three different assessment methodologies including, classical fracture mechanics, SMC, and MMC are compared for failure assessment of a cracked pressure vessel in ductile-to-brittle transition (DBT) region. It is shown that the developed MMC approach has appropriate capability to reduce the overly conservatism in failure assessment results obtained from the other two methods.

Application of the small punch test in combination with the master curve approach for the characterisation of the ductile to brittle transition region

The Master Curve approach allows the full characterisation of the ductile to brittle transition region (DBTR) of ferritic steels to be performed with a reduced number of tests. In this paper, the approach has been combined with the application of the small punch (SP) test. Modified SP specimens have been successfully employed to estimate the fracture toughness values of a pressure vessel steel and three structural steels. In addition, a methodology has been proposed, including a validity criterion for the performed tests. The estimated reference temperatures have been compared to the values obtained by means of full-scale conventional techniques. A unique simple relationship between both methodologies has been established for all the analysed materials. Therefore, this paper confirms the suitability of the small punch testing technique for the characterisation of the DBTR of several ferritic steels. It is a promising, simple and cost-effective test, which can be performed with simple equipment.