Inferring the temperature dependence of Beremin cleavage model parameters from the Master Curve

The temperature dependence of Beremin model parameters in the ductile-to-brittle transition region was addressed by employing the Master Curve. Monte Carlo simulation was performed to produce a large number of 1T fracture toughness data randomly drawn from the scatter band at a temperature of interest and thus to determine Beremin model parameters. In terms of the experimental data of a C-Mn steel (the 16MnR steel in China), results revealed that the Weibull modulus, m, decreases with temperature over the lower transition range and remains a constant in the lower-to-mid transition region. The Weibull scale parameter, σ_u, increases with temperature over the temperature range of investigated. A small sample may lead to a considerable uncertainty in estimates of the Weibull stress parameters. However, no significant difference was observed for the average of Weibull stress parameters from different sample sizes.     

Three-dimensional interpretation of cleavage fracture tests of cladded specimens with local approach to cleavage fracture

Electricité de France has conducted during these last years an experimental and numerical research programme in order to evaluate fracture mechanics analyses used in nuclear reactor pressure vessels integrity assessment, regarding the risk of brittle fracture. Two cladded specimens made of ferritic steel A508 Cl3 with stainless steel cladding, and containing shallow subclad flaws, have been tested in four point bending at very low temperature to obtain cleavage failure. The crack instability was obtained in base metal by cleavage fracture, without crack arrest. The tests have been interpreted by local approach to cleavage fracture (Beremin model) using three-dimensional finite element computations. After the elastic–plastic computation of stress intensity factor K_J along the crack front, the probability of cleavage failure of each specimen is evaluated using m, σ_u Beremin model parameters identified on the same material. The failure of two specimens is conservatively predicted by both analyses. The elastic–plastic stress intensity factor K_J in base metal is always greater than base metal fracture toughness K_1c. The calculated probabilities of cleavage failure are in agreement with experimental results. The sensitivity of Beremin model to numerical aspects is finally exposed.     

Experimental and numerical investigations of the warm-prestressing (WPS) effect considering different load paths

The effect of warm prestressing has been investigated representative for the core weld metal of the RPV Stade. Model experiments on CT specimens show a significant rise of effective fracture toughness K_eff after warm prestressing and the conservative WPS hypothesis, ‘no failure, if ∂K_I/∂t≤0’, is verified. Partial unloading and reheating show no influence on the effective fracture toughness K_eff. The magnitude of the WPS effect as a function of warm prestress level and temperature, path of unloading and cooling can be predicted using a modified Beremin model with temperature dependent parameters. It is shown that the Weibull stress is an appropriate crack tip loading parameter for decreasing load paths.     

Influence of hydrogen content on fracture toughness of CWSR Zr–2.5Nb pressure tube alloy

In this work, influence of hydrogen and temperature on the fracture toughness parameters of unirradiated, cold worked and stress relieved (CWSR) Zr–2.5Nb pressure tube alloys used in Indian Pressurized Heavy Water Reactor is reported. The fracture toughness tests were carried out using 17 mm width curved compact tension specimens machined from gaseously hydrogen charged tube-sections. Metallography of the samples revealed that hydrides were predominantly oriented along axial–circumferential plane of the tube. Fracture toughness tests were carried out in the temperature range of 30–300 °C as per ASTM standard E-1820-06, with the crack length measured using direct current potential drop (DCPD) technique. The fracture toughness parameters (J_Q, J_Max and dJ/da), were determined. The critical crack length (CCL) for catastrophic failure was determined using a numerical method. It was observed that for a given test temperature, the fracture toughness parameters representing crack initiation (J_Q) and crack propagation (J_Max, and dJ/da) is practically unaffected by hydrogen content. Also, for given hydrogen content, all the aforementioned fracture toughness parameters increased with temperature to a saturation value.     

Constraint effects on fracture toughness of impact-loaded, precracked Charpy specimens

Impact-loaded, precracked Charpy specimens often play a crucial role in irradiation surveillance programs for nuclear power plants. However, the small specimen size B = W = 10 mm limits the maximum value of cleavage fracture toughness J_c that can be measured under elastic—plastic conditions without loss of crack tip constraint. In this investigation, plane strain impact analyses provide detailed resolution of crack tip fields for impact-loaded specimens. Crack tip stress fields are characterized in terms of J—Q trajectories and the toughness-scaling model which is applicable for a cleavage fracture mechanism. Results of the analyses suggest deformation limits at fracture in the form of b > MJ_c/σ₀, where M approaches 25–30 for a strongly rate-sensitive material at impact velocities of 3–6 m s⁻¹. Based on direct comparison of the static and dynamic J values computed using a domain integral formulation, a new proposal emerges for the transition time, the time after impact at which interial effects diminish sufficiently for simple evaluation of J using the plastic η factor approach.     

Fracture assessment of shallow-flaw cruciform beams tested under uniaxial and biaxial loading conditions

A technology to determine shallow-flaw fracture toughness of reactor pressure vessel (RPV) steels is being developed for application to the safety assessment of RPVs containing postulated shallow surface flaws. Matrices of cruciform beam tests were developed to investigate and quantify the effects of temperature, biaxial loading, and specimen size on fracture initiation toughness of two-dimensional (constant depth), shallow, surface flaws. The cruciform beam specimens were developed at Oak Ridge National Laboratory (ORNL) to introduce a far-field, out-of-plane biaxial stress component in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock or pressure–temperature loading of an RPV. Tests were conducted under biaxial load ratios ranging from uniaxial to equibiaxial. These tests demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for an RPV material. The cruciform fracture toughness data were used to evaluate fracture methodologies for predicting the observed effects of biaxial loading on shallow-flaw fracture toughness. Initial emphasis was placed on assessment of stress-based methodologies, namely, the J–Q formulation, the Dodds–Anderson toughness scaling model, and the Weibull approach. Applications of these methodologies based on the hydrostatic stress fracture criterion indicated an effect of loading-biaxiality on fracture toughness; the conventional maximum principal stress criterion indicated no effect. A three-parameter Weibull model based on the hydrostatic stress criterion is shown to correlate with the experimentally observed biaxial effect on cleavage fracture toughness by providing a scaling mechanism between uniaxial and biaxial loading states.     

Assessment of toughness in long term service CrMo low alloy steel by fracture toughness and small punch test

Small punch test (SPT) is a miniature sample test technique which can evaluate in-service material properties with an almost non-destructive method. In this paper, the 2.25Cr1Mo steel samples serviced for 10 years in hydrogenation reactor (with temper embrittlement), 1.25Cr0.5Mo supper-pressure vapor pipe serviced for 14 years at 520 °C and several other low alloy steels have been studied by J_IC fracture toughness and SPT. The linear relationship between the small punch (SP) equivalent fracture strain and the fracture toughness of J_IC was created. The correlations applied to the experimental data indicated advantages of using SPT for the determining fracture toughness of in-serviced low alloy steels. Additionally, size affects the fracture pattern. Small punch samples of small size show dimple fractures whereas large fracture toughness samples show quasi-cleavage fractures.     

Prevision of the cleavage fracture properties using a local approach: Application to the welded joint of a structural C-Mn steel

The local approach of cleavage fracture developed by Beremin is applied to the weld metal of welded joints prepared with a fine-grained structural C-Mn steel. The two parameters of the model (cleavage stress and inhomogeneity exponent) are determined by tensile testing of axisymmetry notched specimens.The analytical application of this approach predicts successfully the fracture toughness values found on precracked specimens. The transition and the scatter of the fracture toughness measurements as a function of temperature are correctly estimated for very different specimen geometries (type and in-plane dimensions).It is thus shown that a realistic estimation of the statistical distribution of fracture toughness can be obtained by testing single tensile specimens.     

The application of constraint based fracture mechanics to engineering structures

Elastic-plastic crack tip fields can be characterised by two parameters, J and T/Q which describes crack tip constraint. This forms the foundation of a constraint based fracture mechanics in which toughness is expressed as a function of constraint in the form of a J–(T/Q) locus. The enhanced toughness associated with shallow cracks and defects can be used in a systematic manner by constraint matching, and implemented through a simple modification to a failure assessment diagram. This methodology enables the conservatism associated with the use of deeply cracked fracture toughness measurements to be relaxed. In this work these methods have been applied to a tubular welded joint.     

Fracture toughness of the hydrogen charged EUROFER 97 RAFM steel at room temperature and 120 °C

The static fracture toughness of EUROFER 97 reduced activation ferritic-martensitic steel was investigated in presence of higher content of hydrogen. The hydrogen effect is shown during fracture toughness testing both of base and weld metals at room temperature and at 120 °C. At the room temperature testing the J_0.2 integral values will decrease depending on hydrogen content in the range of 2-4 wppm. The same hydrogen content of 2 wppm manifests itself by an uneven level of hydrogen embrittlement for base metal and weld metal. This corresponds to a different J_0.2 integral value and a different mechanism of fracture mode. At the hydrogen content of 4 wppm more evident decrease of J_0.2 was observed for both metals. At 120 °C hydrogen decreases J_0.2 integral in base metal at a limited scale only in comparison to weld metal. At room temperature and hydrogen content of about 4 wppm the base metal specimen exhibits inter-granular fracture and trans-granular cleavage on practically the whole crack surface. The weld metal fracture has shown inter-granular and trans-granular mechanism with ductile and dimple rupture.     

Pressure vessel steel fracture toughness in the regime from room temperature to 400°C

The fracture toughness of steels that are susceptible to dynamic strain aging shows a minimum at temperatures higher than the upper shelf starting temperature. This phenomenon is caused simultaneously by strain aging and plastic deformation. The first aim of the present work is to analyze the effect of dynamic strain aging on the fracture toughness values of three pressure vessel steels in the temperature range between room temperature and 400°C. Fracture mechanics tests were carried out on A533 GB, A516 G70 and 304L steels to obtain the following parameters: J_IC, CTOD_m and the J-R curves. These values were compared against those available in the present references, and good agreement was found. Charpy V notch tests were also carried out on A516 G70 steel at the same test temperatures as for the fracture mechanics tests to analyze the effect of the strain rate. The critical wide stretch zones of the 304L steel specimens were also measured to verify another author's hypothesis about a toughness drop at the upper shelf temperature.     

Elastic-plastic fracture toughness behavior of heavy section steels for nuclear pressure vessels

Fracture toughness tests were performed in the transition region for ASTM A508 Class 3 steel using about 160 specimens. The K_J-values which are converted from J_c of the smaller specimens indicated a wide scatter ranging from below the K_Ic-value to much higher toughness. The fast brittle fracture behavior in the transition regime can be divided into two regions: (1) the region where fracture occurs on a blunting line (Region I) and (2) the region where fracture occurs on an R-curve (Region II). The scatter of the K_J-values in each region is caused by the amount of crack extension contained in the specimens. The methods to obtain the fracture toughness equivalent to the K_Ic from the K_J values were also presented.In the upper shelf region, the ductile fracture behavior of A508 Class 3 base metal and weldments was investigated. The 25% side grooved specimen was recommended for measuring the resistance against ductile crack growth. The weld heat affected zone (HAZ) has comparatively higher tearing modulus, whereas the weld metal shows the lowest one.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

Proposed modifications of ASTM E813-81 standard test method for JIc

This paper contains a critical examination of the present ASTM E813-81 J_Ic test standard and proposed modifications of this standard. It is suggested that a value J corresponding to a ductile tearing, $\text{Δa}{}^1$, of 0.2 mm be regarded as an engineering approximation of initiation fracture toughness. This amount of ductile tearing is obtained by intersecting the initial part of the J-Δa curve with an intercept line parallel to the blunting line. An improved blunting line has been derived by accounting for the material's strain hardening properties. Finally, the application of the modified J_Ic procedure will be demonstrated using several materials.     

Global equations for Weibull Parameters in a ductile-to-brittle transition regime

Approaches to fracture prediction based on local stress and toughness use the Weibull distribution model based on weakest link theory. Accuracy of predictions as part of the integrity assessment of structural steels containing defects and often subjected to a thermal and mechanical loading history relies on the precision of distribution parameters. Extensive research work has recently been conducted to characterize the ductile-to-brittle transition (DBT) behavior of ferritic steels. This paper investigates geometry and temperature dependence of distribution parameters and uses the ‘Euro fracture dataset’ to estimate the Weibull parameters in a ductile-to-brittle transition regime. ‘Global’ equations for determination of distribution parameters are then proposed based on calibration to available data.     

A modified Beremin model to simulate the warm pre-stress effect

Starting from the pioneering work of Beremin (Met. Trans. A 14A (1983) 2277), a modified Beremin model is proposed. As a result of temperature effect on mechanical fields heterogeneity at the micromechanical scale, an apparent temperature dependence of the macroscopic cleavage stress is first introduced to fit correctly the brittle to ductile transition. Then, the classical Beremin–Weibull fracture probability expression is extended to take account of non monotonic thermomechanical loadings. The modified Beremin model is applied to warm pre-stress (WPS) tests performed on low alloy ferritic steel compact tension specimens (see IAEA Specialists’ meeting, Rockville (2000)). Apart from ‘load–unload–cool–fracture’ (LUCF) cycles, for which additional investigations are needed, these simulations are in good agreement with experiments provided that an additional microcrack propagation condition is introduced, namely, necessary slip activity. This additional condition is consistent with the classical Beremin model restricted to monotonic loading paths.     

Irradiation embrittlement characterization of the EUROFER 97 material

The paper summarizes original results of irradiation embrittlement study of EUROFER 97 material that has been proposed as one candidate of structural materials for future fusion energy systems and GEN IV.Test specimens were manufactured from base metal as well as from weld metal and tested in initial unirradiated condition and also after neutron irradiation.Irradiation embrittlement was characterized by testing of toughness properties at transition temperature region - static fracture toughness and dynamic fracture toughness properties, all in sub-size three-point bend specimens (27 × 4 × 3 mm³). Testing and evaluation was performed in accordance with ASTM and ESIS standards, fracture toughness K_JC and K_Jd data were also evaluated with the “Master curve” approach. Moreover, J-R dependencies were determined and analyzed.The paper compares unirradiated and irradiated properties as well as changes in transition temperature shifts of these material parameters. Discussion about the correlation between static and dynamic properties is also given.Results from irradiation of EUROFER 97 show that this steel - base metal as well as weld metal - is suitable as a structural material for reactor pressure vessels of innovative nuclear systems - fusion energy systems and GEN IV. Transition temperature shifts after neutron irradiation by 2.5 dpa dose show a good agreement in the case of EUROFER 97 base material for both static and dynamic fracture toughness tests. From the results it can be concluded that there is a low sensitivity of weld metal to neutron irradiation embrittlement in comparison with EUROFER 97 base metal.     

New approaches to improve the RPV materials data base

The models for the local approach to cleavage fracture and to ductile tearing include the effects of specimen geometry and loading situation on the damage development. Thus, these concepts can be used to predict fracture toughness and tearing resistance curves for different sizes of specimens or structures, based on an analysis of tests with small, simple specimens. This advantage is especially valuable if only small pieces of material are available for testing which do not allow for standard fracture specimens. The paper outlines the basic ideas of the Beremin concept for the fracture process in brittle-to-ductile transition regime and of the modified Gurson model for ductile fracture in the upper shelf. A systematic study for the brittle-to-ductile transition regime showed that the Beremin model has to be modified to take into account the effect plastic strain has on the fracture process. For ductile fracture, it was demonstrated that by testing and modeling a smooth bar and a fracture mechanics specimen, one set of material parameters may be found which can be subsequently applied to other structures and, hence, used to extend the material data base.     

Influence of microstructural inhomogeneities on the fracture toughness of modified 9Cr–1Mo steel at 298–823 K

Quasistatic fracture behaviour of two heats of modified 9Cr–1Mo steel for steam generator applications have been assessed at 298, 653 and 823 K. J–R curves were established and the elastic–plastic fracture toughness values at 0.2 mm crack extension (J_0.2) were determined. The fracture mechanisms were entirely different for the two steels at 298 K, with brittle fracture controlled by cleavage crack initiation in one and ductile fracture in the other by void nucleation and growth. At 653 and 823 K, fracture in both materials was by ductile crack growth. The difference in behaviour between the two steels at 298 K was attributed to the differences in microstructure, distribution and density of inclusions as well as phosphorous contents.