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.     

Structural integrity assessment of aging nuclear reactor pressure vessels

Irradiation embrittlement reduces both the cleavage fracture toughness and the ductile tearing toughness of reactor pressure vessel (RPV) steels. Extensive research programs have investigated the fracture behavior of heavy-section vessels containing flaws. Information obtained from that research has been used to develop regulatory guidance for evaluating the structural integrity of irradiated RPVs. Additional research programs have developed fracture analysis methods, and generated the data required for their implementation. Regulatory guidance employs fracture analysis technology to assure that adequate fracture-prevention margins for RPVs are maintained throughout the licensed operating period of nuclear power plants.     

Results and conclusions from the first pressurized-thermal-shock experiment

The first pressurized-thermal-shock test of a 148 mm thick steel pressure vessel with a 1 m long flaw was performed to investigate fracture behavior of a vessel under conditions relevant to a flawed nuclear reactor pressure vessel during an overcooling accident. The objectives were to observe crack arrest and stability on the ductile upper shelf and the effects of warm prestressing on crack initiation. Three coordinated pressure and thermal transients were imposed on the vessel, which was preheated to 290°C. Two episodes of crack propagation and arrest occurred. The thermal transients were induced by coolant at −29 to 15°C. Pressure transients were as high as 94.4 MPa. The experimental objectives were attained. The inhibiting effects of warm prestressing were definitely demonstrated. Crack propagation was nearly pure cleavage, and arrest at 30 K above the onset of the Charpy upper-shelf was experienced in a positive K₁ gradient and with K₁ = 300 MPa√m. Fracture-mechanics analysis of brittle fracture based on small-specimen toughness measurements was reasonably accurate. Flaw evaluation by procedures of the ASME Boiler and Pressure Vessel Code conservatively predicted vessel failure, which did not occur. No ductile tearing occurred after each crack arrest, although some stable tearing had been predicted on the basis of tearing resistance data.     

First spinning cylinder test analysis using a local approach to fracture

In recent years, several experimental programmes on large-scale specimens have been organized to evaluate the capabilities of the fracture mechanics concepts employed in structural integrity assessment of pressurized water reactor pressure vessels. During the first spinning cylinder test, a geometry effect was revealed experimentally showing the difficulties of transferring toughness data from small-scale to large-scale specimens. An original analysis of this test, by means of a local approach to fracture, is presented in this paper. Both compact tension specimen and spinning cylinder fracture behaviour were computed using a continuum damage mechanics model developed at EDF. We confirmed by numerical analysis that the cylinder's resistance to ductile tearing was considerably larger than in small-scale fracture mechanics specimen tests, about 50%. The final crack growth predicted by the model was close to the experimental value. Discrepancies in J R curves seemed to be due to an effect of stress triaxiality and plastic zone evolution. The geometry effect inducing differences in resistance to ductile tearing of the material involved in the specimens can be investigated and explained using a local approach to fracture methodology.     

On the required toughness for the application of the net section yield criterion on nuclear power plant components

The principles of plastic limit load are recaptured. A method is developed to calculate lower bound estimates of critical crack sizes for nuclear plant components. More than 250 fracture mechanics experiments on specimen and component geometries have been evaluated focussing on the material toughness in terms of Charpy-V energy. The thus determined Charpy threshold value for the application of the aforementioned method is 45 J regardless whether the material has already reached the upper shelf toughness or is still within the transition region. The method is not able to cope with the phenomenon of “ductile tearing”. However when predicting critical crack sizes the method yields conservative results even when ductile tearing must be expected.     

Micromechanisms and toughness for cleavage fracture of steel

A complete understanding of the fracture mechanisms of steel in the ductile/brittle transition region requires analysis not only of crack initiation, but also of crack propagation. This paper reviews micrographic and fractographic experiments that give insight into both phenomena, and suggests a frame-work through which both may be related.Unstable cleavage crack initiation can occur after some blunting of the original fatigue precrack or after some stable crack growth. In either event, instability appears to be triggered by the fracture of a brittle micro-constituent ahead of the precrack. The large scatter in reported K_Ic values within the transition region reflects the size distribution and relative scarcity of these “trigger” particles.While a large number of models have attempted to correlate toughness in the ductile/brittle transition regime to events occurring ahead of the crack tip, surprisingly little attention has been paid to events occurring behind the crack front. Fractographic evidence as well as metallographic sectioning of arrested cracks show that the mechanism of rapid crack propagation by cleavage is affected strongly by partial crack-plane deflection which leaves unbroken ligaments in its wake. The tearing of these ligaments by dimple-rupture is the dominant energy-absorbing mechanism. Etch-pit experiments using an Fe-Si alloy show that the crack-tip stress intensity based on plastic zone size is extremely low. It is suggested that the mechanism of crack arrest should be modeled using a sharp crack which is restrained by a distribution of discrete pinching forces along its faces. The same model is applied to crack initiation.     

Ductile fracture behavior of circumferentially cracked type 304 stainless steel piping under bending load

A ductile pipe fracture test program has been conducted in Japan Atomic Energy Research Institute (JAERI) to investigate the ductile fracture behavior of circumferentially cracked pipes and to demonstrate the validity of the leak before break concept in LWR pipings.In the paper are described the scope of the pipe test program and current test results for 6-inch diameter type 304 stainless steel pipes. Test pipes with a through-wall or a part-through crack in the circumferential direction were bent under low or high compliance condition, and stable or unstable pipe fracture behavior was investigated. J based tearing instability criterion and the net section collapse criterion are compared with the pipe test results, and the validity of these fracture criteria is discussed. Furthermore, geometries of acceptable flaws in pipes are evaluated considering the leak before break condition.     

Performance of low-upper-shelf material under pressurized-thermal-shock loading

The second pressurized-thermal-shock experiment (PTSE-2) of the Heavy-Section Steel Technology Program was conceived to investigate fracture behavior of steel with low ductile-tearing resistance. The experiment was performed in the pressurized-thermal-shock test facility at the Oak Ridge National Laboratory. PTSE-2 was designed primarily to reveal the interaction of ductile and brittle modes of fracture and secondarily to investigates the effects of warm prestressing, A test vessel was prepared by inserting a cracklike flaw of well-defined geometry on the outside surface of the vessel. The flaw was 1 m long by ≈ 15 mm deep. The instrumented vessel was placed in the test facility in which it was initially heated to a uniform temperature and was then concurrently cooled on the outside and pressurized on the inside. These actions produced an evolution of temperature, toughness, and stress gradients relative to the prepared flaw that was appropriate to the planned objectives. The experiment was conducted in twoseparate transients, each one starting with the vessel nearly isothermal. The first transient induced a warm-prestressed state, during which K_I, first exceeded K_Ic. This was followed by repressurization until a cleavage fracture propagated and arrested. The final transient was designed to produce and investigate a cleavage crack propagation followed by unstable tearing. During this transient, the fracture events occurred as had been planned.     

Pipe fracture safety analysis using limit load and J-integral techniques

J-integral fracture toughness tests were performed on full scale pipe specimens to assess the fracture safety performance of two reactor piping alloys. The two alloys investigated were ASTM A106 Grade B carbon steel and circumferentially welded Type 304 stainless steel.The full scale pipe fracture tests were performed on 1.2 m long, circumferentially cracked pipes loaded in four-point bending on a variably compliant test bed. Results of the experiments were analyzed using the limit load approach currently being considered for inclusion in Section XI of the ASME Code. The results were also evaluated using two tearing instability approaches. One approach assumed elastic-perfectly plastic material behavior and the other accounted for material hardening by requiring actual load and displacement data.The limit load analysis provided a good prediction of the maximum load carrying capacity of the pipe specimens in most cases. The results were especially good for the ASTM A106 steel pipes when the materials property data was used to calculate the flow stress. The J-integral tearing instability analysis was shown to accurately describe the ductile tearing instability behavior of the ASTM A106 steel pipe providing material hardening was taken into account.     

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.     

Some fractographic aspects of hydrogen-induced delayed cracking in Zr–2.5 wt% Nb alloys

The fractographic features after hydrogen-induced delayed cracking (HIDC) in Zr-2.5 wt% Nb pressure tube material have been studied as a function of stress intensity factor (K), temperature and hydride dispersion. The important observations were of regularly spaced ductile striations parallel to the main crack front, and brittle cleavage markings between the striations. The striations were cusped due to dimple formation, and individual cleavage regions were separated by ductile ridges or shear cliffs. The size and morphology of the cleavage regions was consistent with the size and preferred orientation of hydrides near the crack tip. The inter-striation spacing increased exponentially with temperature, but within the range of study, was essentially independent of K. Neither hydride content nor dispersion had a significant effect on the fracture morphology. The results are consistent with a discontinuous mechanism of crack propagation involving the accumulation of hydride at the crack tip, followed by fracture through this embrittled region and subsequent crack arrest. The observations support recent theoretical models for HIDC which interpret the inter-striation spacing as a critical hydride length for crack advance.     

Effect of prior crack growth on cleavage fracture of low toughness precracked Charpy specimens

Cleavage fracture of reactor pressure vessel steels in the upper ductile to brittle transition region generally occurs with prior significant ductile crack growth. For low upper shelf materials and using PreCracked Charpy v-notch (PCCv) specimens that can be obtained from conventional surveillance programs, the effect of prior crack growth could be particularly important. In practice, the shape of the Master Curve and the failure distribution could be affected by ductile crack growth. To quantify the effect in practical applications, the effect of prior ductile on cleavage is evaluated on PCCv specimen.The methodology use finite element calculations to grow a ductile crack and infer the brittle failure probability using the local approach to fracture. It is found that for very low upper shelf toughness materials, ductile crack growth enhances the failure probability, induces a steeper failure distribution and affects the shape of the Master Curve. However, for low toughness materials, the enhanced failure probability due to crack growth is compensated by loss of constraint.     

In situ studies and modeling the fracture of Zircaloy-4

In situ fracture studies were performed on non-irradiated Zircaloy-4 using tensile specimens and pre-cracked Compact Tension (CT) specimens to clarify the mechanism for fracture initiation in the constrained and non-constrained state. Similar approaches have been taken in the literature to understand the role of hydrides on the fracture of Zircaloy-4, but hydride-free Zircaloy-4 has received little study. Both annealed and beta-treated Zircaloy-4 were tested in the longitudinal, transverse, and short-transverse orientations to study the role of microstructure and orientation. Unstable crack extension is shown to occur under plastic constraint by a process of void nucleation, growth, and coalescence initiating from the Laves phase particles in the microstructure. A micromechanical model is developed for ductile tearing by void growth and coalescence. Excellent agreement between the model and experiments are observed. Aspects of the fracture mechanism and model are discussed.     

2D crack growth simulation with an energetic approach

It is well known that the tearing resistance curve J–Δa is not a material property. A recent approach, based on an energetic critical parameter to model ductile tearing propagation, is used to model 3D effects. The approach considered in this work aims to estimate the dissipated energy in the fracture process during ductile tearing represented by an intrinsic parameter G_fr. A fracture criterion, which accounts for the crack extension length, is defined and lies on a critical energy release rate, noted G_c, which is compared to G_fr. Previously, this parameter was obtained from a numerical local energy release rate, which handicaps the application field of the approach: a fine mesh for the whole propagation area was needed and the criterion allowed only to model 1D propagation. A new manner to estimate G_c is then proposed in this article, based on the J plastic part variation, which allows to model 2D propagation by defining a local criterion. This new calculation method is validated on a CT specimen made in Tu52b ferritic steel, by comparing the results obtained from the two methods of G_c calculation. Then, the 2D crack growth case is studied, by modelling the propagation in a ring, loaded in compression. It is shown that a 3D effect, such as tunnel effect, could be successfully represented with this approach.     

Elastodynamic fracture analysis of large crack-arrest experiments

Recent elastodynamic fracture analysis results are summarized from Heavy-Section Steel Technology (HSST) studies in two major areas that related to assessing nuclear reactor pressure vessel integrity under pressurized-thermal-shock (PTS) conditions. These areas are crack run-arrest behavior in wide plates under nonisothermal conditions and fracture behavior of a thick-wall vessel under combined thermal and pressure loadings.The WP-1 series of HSST wide-plate crack-arrest tests are being performed at the National Bureau of Standards (NBS), Gaithersburg, MD, using specimens from HSST Plate 13A of A533 grade B class 1 steel. The six tests in the WP-1 series are aimed at providing crack-arrest data at temperatures up to and above that corresponding to the onset of the Charpy upper-shelf, as well as providing information on dynamic fracture (run and arrest) processes for use in evaluating improved fracture analysis methods. Elastodynamic analyses have been completed for the actual test conditions of the four tests, WP-1.1 through WP-1.4, conducted thus far in the WP-1 series. In this paper, the computed results are compared with data for crackline strain-time response, crack-propagation speed, arrest location and post-arrest tearing. The paper includes a summary of the arrest toughness calculations compiled in the four tests at temperatures that range from transition to upper-shelf values for the wide-plate material.These same elastodynamic fracture analysis techniques have been applied to the analysis of the first pressurized-thermal-shock experiment (PTSE-1) performed at ORNL. The experiment addressed warm-prestressing phenomena, crack propagation from brittle to ductile regions, and crack stabilization in ductile regions. Test and analysis results are summarized in the paper.     

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.     

Ductile crack growth in pre-cracked CVN specimens: numerical studies

This study describes plane strain, finite element analyses to model ductile crack extension in pre-cracked Charpy specimens subjected to static and impact loading. The Gurson–Tvergaard (GT) dilatant plasticity model for voided materials describes the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer along the crack plane provide an explicit length scale for the continuum damage process. Outside of this layer, the material remains undamaged by void growth, consistent with metallurgical observations. The finite strain constitutive models include the effects of high strain rates on the material flow properties. Parametric studies focusing on numerically generated R-curves quantify the relative influence of impact velocity, material strain rate sensitivity, and properties of the computational cells (thickness and the initial cell porosity). In all cases, impact loading elevates significantly the R-curve by increasing the amount of background plasticity. The strong effects of impact loading on the driving force for cleavage fracture are illustrated through evolution of the Weibull stress. The analyses suggest a negligible, additional effect of tearing on the Weibull stress under impact loading. Validation of the computational cell approach to predict loading rate effects on R-curves is accomplished by comparison to static and impact experimental sets of R-curves for three different steels.     

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.     

Influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress

The aim of this work is to determine the influence of temperature, strain rate and specimen geometry on the microscopic cleavage fracture stress σ_f*. Besides, the dependence of the initiation temperature for shear fracture T_i and the temperature for general yield T_gy on strain rate is investigated. Finally, the local values of stress triaxiality and equivalent plastic strain at the occurrence of cleavage fracture for several steels and specimen types are compared with the failure curve for ductile fracture to check the validity of the theory of stress controlled cleavage fracture and the strain/triaxiality controlled shear fracture in the transition region. Based on experimental tests, the results are obtained by finite element analyses. The investigation shows, that σ_f* is dependent on temperature and strain rate and increases with decreasing test temperature and increasing strain rate. The transition temperatures T_i and T_gy increase with increasing strain rate. The theories of stress controlled cleavage fracture and of shear fracture controlled by equivalent plastic strain and stress triaxiality seem to be valid. That fracture mechanism occurs for which the critical condition is reached first.     

On the behavior of crack surface ligaments

Small ligaments connecting the fracture surfaces just behind a moving crack front are assumed to exist under certain conditions. The ligaments are rapidly torn as the crack advances. Inelastic straining of such ligaments influences the energy balance in the fracture process. The rapid tearing of a single ligament is studied both numerically and experimentally. An elastic visco-plastic material model is adopted for finite-element calculations. The results show that relatively large amounts of energy are dissipated during the tearing process. Further, the energy needed to tear a ligament increases rapidly with increasing tearing rate. The computed behavior is partly verified in a few preliminary experiments. The implications for slow stable crack tip speeds during dynamic fracture are discussed.