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.     

A probabilistic model for cleavage fracture with a length scale - Parameter estimation and predictions of growing crack experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint. Int J Fract 2002;118:99-118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.     

Development of the Euro fracture toughness dataset

Ten European laboratories have generated the Euro fracture toughness dataset in order to provide an experimental data base sufficiently large to study specimen size and temperature effects on cleavage fracture toughness in the ductile-to-brittle fracture transition regime. The Euro fracture toughness dataset quantifies the fracture behaviour of the quenched and tempered pressure vessel steel DIN 22NiMoCr37. This material is frequently used in nuclear power plants. About 800 fracture toughness tests were performed using compact tension specimens with a size range from 1/2T to 4T.In the lower shelf temperature regime, no significant specimen size effects on cleavage fracture toughness scatter was observed. At higher temperatures, the lower tails of the toughness scatter bands are not significantly effected by the specimen size but with decreasing specimen size the toughness scatter increases due to the fact that the upper part of the scatter band is extended. The presence of a specimen size effect on fracture toughness scatter coincides with the appearance of single cleavage initiation sites at the fracture surface. At the lower shelf temperature both, cleavage initiation sites and size effects are not observed whereas at higher test temperatures both phenomena are present. The specimen size effect trends and the corresponding fracture surface morphology support a weakest-link type cleavage fracture mechanism in the ductile-to-brittle transition regime. A unique correlation between the amount of ductile tearing and cleavage fracture toughness was observed for the steel investigated. This result offers the possibility to determine cleavage fracture toughness from post-test fracture surface examinations.Due to the large number of tests and the wide range of testing conditions, the Euro fracture toughness dataset gives a comprehensive insight into specimen size effects and temperature effects on ductile-to-brittle transition fracture. The Euro fracture toughness dataset includes a large set of raw test data such as load versus load line displacement curves and raw tensile test data for deriving stress-strain curves. The Dataset can be downloaded from the internet via the address ftp://ftp.gkss.de/pub/eurodataset.     

A statistical model for cleavage fracture in notched specimens of C–Mn steel

A statistical model for cleavage fracture in notched specimens of C-Mn steel has been proposed. This model is based on a recently suggested physical model. This statistical model satisfactorily describes the distributions of the cumulative failure probability and failure probability density of 36 notched specimens fractured at various loads at test temperature of −196 °C. The minimum notch toughness has also been discussed.     

Temperature Dependence of Brittle Fracture Toughness of Reactor Pressure-Vessel Steels upon Ductile Crack Growth

The main mechanisms of brittle fracture upon ductile crack growth are studied on the basis of the probabilistic model of brittle fracture and the deterministic model of ductile fracture, which were put forward by the authors earlier. The investigations are carried out on the reactor pressure-vessel steel 15Kh2NMFAA in the initial and embrittled states. The dependences of brittle-fracture probability on the stress intensity factor and the value of ductile crack growth are calculated for various temperatures. The temperature dependence of brittle fracture toughness in the initial and embrittled states is predicted with and without regard for ductile crack growth. The authors analyze the main factors that govern the above-mentioned relationships. The calculated results are compared to test data for CT-type compact specimens.     

A probabilistic analysis on thickness effect in fracture toughness

Fracture toughness values are often influenced by specimen thickness and they indicate generally decreasing toughness with increasing thickness. In the present paper, a probabilistic analysis has been carried out by using various kinds of toughness data in order to clarify the applicability of the weakest link model to thickness effect in fracture toughness. Moreover, a new statistical method is proposed for determining fracture toughness distribution, which is necessary for the above analysis, with taking the temperature dependency of fracture toughness into account. Thickness effect in fracture toughness is brought about by its statistical nature and the weakest link model can be applied to evaluate the thickness effect for both steel plate and its welds with heterogeneity in toughness. This thickness effect is considerably affected by Weibull shape parameter and the probability of cleavage fracture for the material. The statistical method proposed newly in this paper is sufficiently applicable and superior to the conventional method. By using this new method, Weibull parameters at a temperature of interest can be determined with much the same reliability as in the conventional method, and also Weibull parameters at lower and higher temperatures can be obtained with a certain confidence depending on the number of specimens tested.     

A probabilistic model for cleavage fracture with a length scale-influence of material parameters and constraint

A probabilistic model for the cumulative probability of failure by cleavage fracture with a material related length scale is developed in this study. The model aims at describing the random nature of fracture in ferritic steels in the brittle-to-ductile transition temperature region. The model derives from use of an exponential function to describe the distribution of microstructural entities eligible to take part in the fracture initiation process, where also a dependence on effective plastic strain is incorporated. A nonlocal stress measure, calculated as the average stress in a spherical volume, drives the contribution to failure probability of an infinitesimal material volume. The radius of the spherical volume enters as the material length in this model. This length has a significant influence on failure probability predictions in geometries exposed to strong stress gradients as found ahead of cracks. The material length is associated with a fracture toughness threshold value. In a fracture application three model parameters need to be estimated based on testing; a parameter directly related to the mean fracture toughness, a parameter that primarily is related to crack-tip constraint effects and the material length parameter. The model is explored in a parametric study showing model features in concord with typical features found in toughness distributions from fracture mechanics testing in the transition region.     

A probabilistic model for the pearlite-induced cleavage of a plain carbon structural steel

The cleavage fracture of a carbon structural steel is shown to deviate from what is typical of a ferritic matrix. This occurs at temperatures ranging from −150 to 20 °C and affects the scatter of fracture toughness, and fractographic features. To explain the observed discrepancies a probabilistic model is developed by linking physical mechanisms of cleavage with continuum mechanics analysis applied to fracture. The model assumes that cleavage is nucleated and triggered in pearlite within the blunting zone of the crack tip by the mechanism of Miller and Smith. Once the model is calibrated for the steel, its predictions are shown to agree with the experimental results.     

UNIFIED CORRELATIONS IN TRANSITION TEMPERATURES OF LOW ALLOY STEELS AND WELD METALS OF VARIOUS TOUGHNESSES

Four types of toughness were measured over a range of temperatures using CVN, COD, 4PB and PCI specimens made of low alloy steels and weld metals. It was found that there were unified correlations in transition temperatures among the various toughness parameters which could be realized by the dependence of the yield strengths of the test materials on both temperature and strain rate. The intrinsic reason for the correlations could be attributed to local cleavage conditions, which control the ductile-to-brittle transition during ductile fracture processes, whether the specimens were notched or precracked, under static or dynamic loading conditions. It is suggested that the ductile fracture process itself was independent of test temperature, but the local cleavage condition remains to be more fully understood in future work.     

A model for predicting the influence of warm pre-stressing and strain ageing on the cleavage fracture toughness of ferritic steels

A micromechanistic model of warm pre-stressing is extended to predict the combined effects of warm pre-stressing and strain ageing on the cleavage fracture toughness of ferritic steels. The crack tip stress distribution after a cycle of pre-straining and strain ageing is estimated by superposition of the appropriate monotonic loading stress distributions. The Ritchie, Knott and Rice model of cleavage fracture and its associated fracture criterion are employed in conjunction with the crack tip stress distribution to predict the critical stress intensity factor after warm pre-stressing and strain ageing. Illustrative calculations are presented, based upon the published material's properties of a high nitrogen mild steel. Available experimental data for pressure vessel steels bear out the form of the predictions. At low temperatures, and after heavy pre-loads, the benefits of warm pre-stressing dominate strain ageing induced embrittlement and the toughness is apparently enhanced. At higher temperatures, or after small pre-loads, however, strain ageing dominates and the apparent toughness is reduced. Various assumptions and approximations inherent in the model are discussed. These generally tend to render the predictions conservative. Finally it is noted that the model should be equally applicable to the prediction of the combined effect of warm pre-stressing and neutron irradiation on the cleavage fracture toughness of ferritic steels.     

Probabilistic treatment of fracture using two failure models

A probabilistic methodology for brittle fracture based on two local failure models is presented. Probabilistic fracture parameters are obtained using a weakest link and a chain-of-bundles formulation. Both models define limiting distributions for the fracture stress described by a two-parameter Weibull distribution. Numerical procedures employing measured toughness data and finite element solutions are also described to calibrate the Weibull parameters. An application of the methodology then follows to predict geometry and stable crack growth effects on the distribution of macroscopic fracture toughness (J_c) for a high-strength steel. Measured fracture toughness values for a high-constraint geometry that exhibit no prior ductile tearing are effectively ‘transferred' to a different geometry having much lower constraint and in which tearing precedes cleavage. The inherent difficulty in predicting the scatter of experimental fracture toughness, as well as constraint and ductile tearing effects, within the scope of conventional procedures appears greatly reduced in the framework presented in this work.     

STATISTICAL MODELLING OF INTERGRANULAR BRITTLE FRACTURE IN A LOW ALLOY STEEL

The intergranular brittle fracture (IBF) behaviour of a low alloy steel 16MND5 (A508 Cl. 3) was investigated. A temper embrittlement heat treatment was applied to the material to simulate the effect of local brittle zones (ghost lines) which can be found in the as-received material condition. An increase in the Charpy V toughness transition temperature and a significant decrease in the fracture toughness measured on CT-type specimens were observed in the embrittled material, as compared to the reference material which was submitted to the same austenitizing and tempering heat treatment, but which was not subjected to the temper embrittlement treatment. Tensile tests on notched specimens were carried out to measure the Weibull stress and scatter in the results. A statistical model, the Beremin model, originally proposed for brittle cleavage fracture was applied to IBF. It is shown that this model is not able to fully account for the results, in particular for the existence of two slopes in a Weibull plot. Systematic fractographic observations showed that the low slope regime in this representation was associated with the existence of MnS inclusions initiating brittle fracture, while the larger slope was related to microstructural defects. Initiation of IBF from MnS inclusions can occur when the material is still elastically deformed while the second population of microstructural defects is active in the plastic regime. A modified statistical model based on the Beremin model and taking into account these specific aspects is proposed in the framework of the weakest link theory. The parameters of this model are identified from test results on notched specimens. It is shown that this model is able to predict the temperature dependence of fracture toughness and the scatter in the experimental results.     

IRRADIATION EMBRITTLEMENT OF A LOW ALLOY STEEL INTERPRETED IN TERMS OF A LOCAL APPROACH OF CLEAVAGE FRACTURE

Abstract— One heat of A 508 steel is investigated in both the unirradiated and the irradiated condition to determine the variation of the fracture toughness with temperature and specimen thickness. CT type specimens with three thicknesses B (12.5, 25 and 50 mm) are used. Two fluence levels (3·10¹⁹ and 8·¹⁹ n/cm²)( E < 1 MeV) are investigated. It is shown that the fracture toughness is a decreasing function of both specimen thickness and temperature. A model developed previously by Beremin is used to interpret the results. Axisymmetric notched specimens are tested to determine the factors used in the statistical approach of cleavage fracture. It is confirmed that the Beremin model is able to account for the large scatter in fracture toughness observed at a given temperature on the unirradiated material. The specimen thickness effect is also reasonably well interpreted by the model. The irradiation embrittlement can be explained by assuming that the cleavage fracture resistance is not modified by irradiation and by taking into account only the variations of yield strength with irradiation and test temperature.     

A CRITERION FOR INTERGRANULAR BRITTLE FRACTURE OF A LOW ALLOY STEEL

Abstract— The intergranular brittle fracture behaviour of a A533 B Cl 1 steel was investigated by applying a temper embrittlement heat treatment to simulate the presence of local brittle zones (ghost lines) in the as-received material. This heat treatment produced an embrittled material that failed by an intergranular mode at low temperature. An increase in the Charpy transition temperature and a significant decrease in fracture toughness were observed in the embrittled steel as compared to the as-received material. Tensile tests on smooth specimens and on notched bars were carried out to determine the critical stress corresponding to brittle intergranular fracture and to investigate the scatter in the results. It is shown that the mean value of the critical stress seems to be an increasing function of temperature. A statistical model, the Beremin model, initially proposed to describe brittle cleavage fracture was applied to intergranular fracture. Modifications are introduced in this model to take into account the temperature dependence of the critical stress. It is shown that this modified model is able to predict the temperature dependence of fracture toughness and the scatter in the experimental results.     

Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part I: experimental results

This study is devoted to the ductile-brittle transition behavior of a French A508 Cl3 (16MND5) steel. Due to its importance for the safety assessment of PWR vessels, a full characterization of this steel with Charpy V-notch test in this range of temperature was undertaken. The aim of this study is to provide a wide experimental database and microstructural observations to supply, calibrate and validate models used in a local approach methodology. Mechanical and fracture properties of the steel have been investigated over a wide range of temperatures and strain-rates. Effects of impact velocity on ductile-brittle transition curve, on ductile tearing and on notch temperature rise are presented and discussed. A detailed study of ductile crack initiation and growth in Charpy specimens is also carried out. From fractographic investigations of the microvoids nucleation around carbide second phase particles, a plastic strain threshold for nucleation is determined for this material. A508 Cl3 steels undergo a transition in fracture toughness properties with temperature, due to a change in fracture mode from microvoids coalescence to cleavage fracture. A systematic investigation on the nature and the position of cleavage triggering sites and on any change in the ductile to brittle transition (DBT) range has been carried out. This leads to the conclusion that manganese sulfide inclusions do not play an increasing role with increasing test temperature as recently mentioned in other studies on A508 Cl3 steel with a higher sulfur content. In a companion paper [Tanguy et al., Engng. Fract. Mech., in press], the numerical simulation of the Charpy test in the ductile-brittle transition range using fully coupled local approach to fracture is presented.     

Analysis of ductile to cleavage transition in part-through cracks using a cell model incorporating statistics

This paper describes an approach to study ductile/cleavage transition in ferritic steels using the methodology of a cell model for ductile tearing incorporating weakest link statistics. The model takes into account the constraint effects and puts no restriction on the extent of plastic deformation or amount of ductile tearing preceding cleavage failure. The parameters associated with the statistical model are calibrated using experimental cleavage fracture toughness data, and the effect of threshold stress on predicted cleavage fracture probability is investigated. The issue of two approaches to compute Weibull stress, the 'history approach' and the 'current approach', is also addressed. The numerical approach is finally applied to surface-cracked thick plates subject to different histories of bending and tension, and a new parameter, ψ, is introduced to predict the location of cleavage initiation.     

Der Mischbruch im Zugversuch

Mixed fracture in the tension test If a tensile test specimen does not break before by cleavage, voids are nucleated at second-phase particles and inclusions during plastic deformation. At the center of the necked region these voids coalesce by internal necking or shearing of the material between them forming a fibrous crack which expands radially. In a temperature range which is dependent on the material cleavage fracture is initiated by the fibrous crack, resulting in a mixed fracture. If no cleavage fracture is initiated a completely fibrous fracture is formed. Mixed fracture surfaces consist of a cleavage fracture zone surrounding the central fibrous fracture zone and the tensile specimen behaves like a fracture mechanics specimen. Fracture toughness can be calculated by equations for tensile specimens with a central penny shaped crack. A comparison of fracture toughness values obtained by the use of unnotched tensile specimens and of fracture mechanics specimens show good agreement inbetween the temperature range of valid K_lc values according to standards of linear-elastic fracture mechanics.     

An application of the J-Q model for estimating cleavage stress in the brittle-to-ductile transition

A recent model was proposed by the authors to predict cleavage failure for steels based on a weak link mechanism and a crack tip stress field modified for planar constraint by the J – Q theory. The model uses the distribution of toughness results at a single temperature to predict a toughness distribution at a different temperature and/or geometry. In this model a material cleavage stress is needed to predict when the weak link fracture is triggered. This cleavage stress is a key input for the application of the model but it is not a property that is routinely measured and it is hence not available for most steel alloys. In this paper, a method to estimate the average value of the cleavage stress is presented, based on a characteristic of the model to predict cleavage failure. Examples of cleavage stress are given for several steels and these results are used to predict the toughness distributions for structural component models.     

On the relation between the mode I fracture toughness of a composite laminate and that of a 0° ply: Analytical model and experimental validation

This paper proposes a simple model to predict the fracture toughness of multidirectional carbon–epoxy composite laminates using the fracture toughness of the 0° ply. The model is based on a combination of Linear-Elastic Fracture Mechanics and lamination theory, and uses as material properties the ply elastic properties and the fracture toughness of the 0° ply measured in compact tension test specimens. A good correlation is obtained by comparing the model predictions and experimental data obtained in center-cracked specimens manufactured using different lay-ups and materials.     

Determination of the Fracture Toughness of a Low Alloy Steel by the Instrumented Charpy Impact Test

An attempt to establish a non-empirical relationship between the Charpy V-notch energy CVN and the fracture toughness K _Ic is presented. We focus our study on the lower shelf of fracture toughness and on the onset of the ductile-to-brittle transition of a A508 Cl.3 low alloy structural steel. The methodology employed is based on the `local approach'. Brittle cleavage fracture is modelled in terms of the Beremin (1983) model, whereas the ductile crack advance preceding cleavage in the transition region is accounted for with the GTN model (Gurson, 1977; Tvergaard, 1982; Tvergaard and Needleman, 1984. Mechanical testing at different strain rates and temperatures allowed the establishment of the constitutive equations of the material in a rate dependent formulation. Numerous fracture tests on different specimen geometries provided the large data set necessary for statistical evaluation. All specimen types were modelled with finite element analysis. Special consideration was taken in order to handle the dynamic effects in the Charpy impact test in an appropriate way. The fracture toughness could be predicted from Charpy impact test results, on the lower shelf, by applying the `local approach'. In the transition region the parameters of the Beremin model were found to deviate from those established on the lower shelf. Detailed fractographic investigations showed that the nature of `weak spots' inducing cleavage fracture changes with temperature. It is concluded that the Beremin model must be refined in order to be applicable in the ductile-to-brittle transition region.