Toughness Scaling Model Research Articles

Investigation on Beremin parameters based on the toughness scaling model

The toughness scaling model (TSM for short) is one of the methods to correct the constraint loss of small specimens. The principle of this method is the fracture toughness conversion at equal Weibull stress. However, related research shows that this fracture toughness scaling model can only accurately estimate the characteristic toughness J0. The scaled toughness distribution of small specimens always deviates from that of the standard specimens. In response to this widespread deviation, this paper studies the factors that significantly affect Weibull stress, such as the crack tip radius and parameter calibration methods. This research aims to determine the requirements for accurate fracture toughness conversion and minimize the deviation under the existing conditions. After studying the data of three different specimens, it is found that the TSM based on equal σw/σu and Minami's calibration method can accurately convert the toughness distribution of small specimens. However, the calibrated Weibull modulus of the two specimens must be close enough. Since it is difficult to guarantee that the calibrated parameters of the Beremin model are constant, the requirements for this accurate toughness conversion are relatively harsh. However, appropriately relaxing the Weibull modulus requirements can make the toughness scaling model more comfortable to build. Although the deviation cannot be avoided, it is still significantly reduced compared to the original toughness scaling model. On the other hand, this paper found that as long as the scale J0 of small specimens is equal to the J0 of standard specimens, an accurate reference temperature estimation can be easily obtained.

Prediction of brittle fracture from defects at groove face of complete joint penetration welded joints

This paper concerns the applicability of the Weibull stress approach, instead of toughness scaling model approach, for prediction of brittle fracture initiated at defects existing at the weld terminations. Beam-to-diaphragm joint models, which were designed to represent a connection of an I-section beam to RHS column member with through diaphragms, were tested under cyclic loads. Complete joint penetration groove welds were used for the connection between the beam flange and the diaphragm. Specimens had those discontinuities at the roots of welds to the beam bottom flanges, which were created by inserting copper plates into the grooves before welding or by using wire electrical discharge machining. The prediction of brittle fracture with a variety of defect sizes by using the FE analysis was conducted. The fracture moment predicted by using the critical Weibull stress accorded with the test results of specimen with defects such as the blowhole.

Defect Tolerance for Cast Steel Connections in Braced Frames

During the last decade, various steel casting products for steel building structures have been developed, such as connectors between brace members and gusset plates in braced frames. Some casting products are welded to steel sections such as tubular members and I-section members in building structures, where these members are expected to develop their capacity during a large-scale earthquake. In this situation, brittle fracture can be another concern of the casting products if there are defects in the connections. A study of defect tolerance for cast steel connections is therefore very important to prevent brittle fracture from weld defects or casting defects. This paper describes defect tolerances for cast steel connections in braced frames and explores the possibility of brittle fracture from assumed defects in typical cast steel connectors. A parametric study, which investigates the sensitivity of brittle fracture to defect size, defect location, and material mismatch effects, is described through cast steel connector models. A toughness scaling model is used for evaluating the occurrence of brittle fracture from assumed defects in the models.

BRITTLE FRACTURE INITIATING AT ENDS OF CJP GROOVE WELDED JOINTS WITH DEFECTS

A series of tests, which reproduced brittle fracture starting from the region around the terminations of CJP (complete joint penetration) groove welded joints, was conducted. The joint models under study were portion of welded beam flange-to-through diaphragm joints in beam-to-column connections. Various artificial defects were installed in the welded joints prior to testing. This paper describes the effects of plastic constraint on brittle fracture from the welded joints with the defects at the ends of CJP groove welds. A toughness scaling model, which considers the effects of plastic constraint, was used for evaluating the occurrence of brittle fracture and was found to predict well the test results, compared with a conventional prediction method using fracture toughness Jc.

An engineering assessment methodology for non-sharp defects in steel structures – Part I: Procedure development

This Part I paper describes a new engineering assessment methodology for ferritic steel structures containing non-sharp defects within the context of a Failure Assessment Diagram (FAD) approach. Although the modification of the FAD for non-sharp defects can be applied whether the initiating failure mechanism is cleavage or ductile tearing, this paper focuses on cleavage fracture. The parameters describing the sensitivity of the material toughness to the notch effect can either be measured by testing notched specimens of the same thickness as the structure, or for cleavage fracture they can be obtained using look-up tables generated using the Weibull stress toughness scaling model. The other parameters in the procedure can either be conservatively estimated using simple equations or they can be determined more accurately using finite element analysis. Validation of the new method is presented in the companion Part II paper: this shows that assessments of U-notched SE(B) specimens have significantly reduced conservatism when using the new assessment methodology compared to the standard FAD approach for sharp cracks.

Effect of Plastic Constraint on Brittle Fracture in Steel: Evaluation Using a Toughness Scaling Model

Over the past two decades, plastic constraint effects have been an issue of concern in both fracture mechanics and structural integrity research, and several methods have been proposed for considering loss of plastic constraint. This paper shows the ability of a simplified model to predict brittle fracture under low plastic constraint conditions. Fracture toughness tests are performed on single-edge notched bend (SENB) steel specimens with deep and shallow notches, as well as on double-edge notched tension and center-notched tension (CNT) specimens. When compared with SENB specimens with a deep notch, the CNT specimens show high fracture toughness as a result of the loss of plastic constraint at the crack tip. Here, the Weibull stress approach and a toughness scaling model (TSM) are used to consider the effects of the loss of plastic constraint on the fracture toughness of the specimens. The corrected fracture toughness values evaluated by the TSM are found to be close to the toughness values observed in the tests and to the values predicted by the Weibull stress approach. This paper also briefly discusses the effect of ductile crack growth on brittle fracture.

Prediction of cleavage fracture from non-sharp defects using the Weibull stress based toughness scaling model

The structural integrity assessment of engineering plant is based on the principles of fracture mechanics that assume defects to be sharp cracks. Whilst conservative, this assumption may be overly conservative in some situations, e.g. for defects that are non-sharp. This paper describes the prediction of cleavage fracture initiation from blunt notches of varying root radii using the Weibull stress based toughness scaling model. Failure predictions are compared with the results of experiments performed on single edge notch bend SE(B) specimens containing both cracks and notches of varying notch root radii. Cleavage initiation sites were located close to the peak tensile stress ahead of the notch, implying that a tensile stress criterion is the main controlling factor for cleavage fracture. The cleavage fracture predictions from the toughness scaling model correlate well with the experimental data; but care needs to be taken to ensure that calibration of the Weibull parameters references fracture toughness data from constraint levels that span that of the defect of interest. This ensures the model interpolates between the constraint states used for calibration, rather than extrapolating outside the range of applicability.

06/01198 The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint: Kozdk, V. and VIcek, L. Nuclear Engineering and Design, 2005, 235, (17–19), 1889–1896

06/01198 The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint: Kozdk, V. and VIcek, L. Nuclear Engineering and Design, 2005, 235, (17–19), 1889–1896

The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint

An extensive investigation has been carried out on the sensitivity parameters determination describing the fracture behaviour of the body with a crack with respect to the character change of the true stress–strain curve with the dominant region of Lueders deformation. This paper presents the consideration on the change judgement of the J-integral and the constraint as the base parameters of two-parameter fracture mechanics. The Weibull stress model for cleavage fracture originally proposed by Beremin group requires calibration of two micromechanics parameters ( m, σ u). The Weibull stress σ w seems to be a parameter for the prediction of cleavage failure of cracked bodies and the study is focused on the assessment of the effects of constraint loss on the cleavage fracture toughness ( J c). To quantify the effects of the constraint variation on the cleavage fracture toughness the form of the toughness scaling model based on the Weibull stress σ w is investigated. Local material parameters have been calculated from Beremin approach and the calibration is performed on various approaches. Methods are based on the weakest link assumption and the incremental fracture probability, which depends not only on the maximum principal stress, but also on the equivalent plastic strain. The fracture resistance has been assessed using data from static tests of three point bend specimens.

On the transition toughness of two RA martensitic steels in the irradiation hardening regime: a mechanism-based evaluation

An analysis of the transition fracture toughness and constitutive behavior of F82H and Eurofer97 reduced activation martensitic steels are presented in both unirradiated and irradiated conditions. The unirradiated toughness data for F82H show very steep temperature dependence and the Eurofer97 toughness data measured with 5 mm versus 10 mm thick specimens are systematically higher. Both of these observations indicate a loss of constraint. Constraint loss adjustments are applied using a three-dimensional finite element analysis based toughness scaling model. The adjusted F82H results can be represented by a master curve (MC) and the corresponding 5 and 10 mm adjusted data fall in the same scatter band. The 10 mm irradiated specimens, with generally lower toughness levels, suffer minimal constraint loss. The irradiation induced MC T 0 shifts (Δ T 0) are analyzed in terms of changes in constitutive properties. The Δ T 0 are generally consistent with the observed irradiation hardening. However, the effects of irradiation on post-yield strain hardening behavior must be considered to obtain self-consistent hardening-shift relations.

Transferability of elastic–plastic fracture toughness using the Weibull stress approach: significance of parameter calibration

This study focuses on the Weibull stress approach to assess the effects of constraint loss on cleavage fracture toughness ( J c). The investigation addresses the significance of the Weibull modulus m (which bears direct connection with parameter calibration schemes) on the correlation of macroscopic fracture toughness for varying crack configurations. In particular, we question the ability of current calibration procedures to provide reliable values for the Weibull parameters ( m, σ u) and present arguments that a non-uniqueness arises in the calibrated values, i.e., many pairs of ( m, σ u) provide equally good correlation of critical Weibull stress values with the distribution of measured fracture toughness values. Our analyses also show a strong sensitivity of corrected J c-values (LSY→SSY constraint correction) on parameter m for several specimen geometries and different material flow properties; such results provide compelling support to introduce an alternative, improved calibration procedure based on a toughness scaling model. Results of a parameter study suggest typical values of m for a wide range of material flow properties and toughness values. An example illustrates application of the toughness scaling model to construct Weibull stress based, constraint corrections for measured J c-values to provide the Weibull modulus, m, for a structural C–Mn steel (BS 4360 Gr 50D).

A Proposal for Specimen Size Requirements in Toughness Qualification with the Weibull Stress Criterion

Abstract The specimen size requirements in toughness qualification are discussed on the basis of a statistical local fracture criterion approach. The Weibull stress criterion for cleavage fracture is applied to the constraint loss field at the crack tip described with the toughness scaling model (TSM). The proposed new model demonstrates that the TSM is a particular case for a material with a particular combination of the Weibull shape parameter, m, and the strain hardening exponent, n. Based on this model, alternative size requirements for ASTM standards are proposed.

Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: a Weibull stress model

This study examines crack front length and constraint loss effects on cleavage fracture toughness in ferritic steels at temperatures in the ductile-to-brittle transition region. A local approach for fracture at the micro-scale of the material based on the Weibull stress is coupled with very detailed three-dimensional models of deep-notch bend specimens. A new non-dimensional function g(M) derived from the Weibull stress density describes the overall constraint level in a specimen. This function remains identical for all geometrically similar specimens regardless of their absolute sizes, and thus provides a computationally simple approach to construct (three-dimensional) fracture driving force curves σw vs. J, for each absolute size of interest. Proposed modifications of the conventional, two-parameter Weibull stress expression for cumulative failure probability introduce a new threshold parameter σw−min. This parameter has a simple calibration procedure requiring no additional experimental data. The use of a toughness scaling model including σw−min>0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1T SE(B) specimen, which improves the agreement of computational predictions and experimental estimations. Finally the effects of specimen size and constraint loss on the cleavage fracture reference temperature T 0 as determined using the new standard ASTM E1921 are investigated using Monte Carlo simulation together with the new toughness scaling model.

Measurement of fracture toughness transition behaviour of Cr–Ni–Mo–V pressure vessel steel using pre-cracked Charpy specimens

The potential application of small pre-cracked Charpy specimens for the prediction of the fracture toughness of the 1T-thickness specimens and the reference temperature T 0 has been examined. Transition fracture behaviour of plane sided, side-grooved and 1T SENB specimens, respectively, was investigated over a wide temperature range. The fracture toughness regions with various fracture initiation mechanisms were defined and ductile to brittle transition temperatures denoted. The fracture toughness transition region of small pre-cracked specimens was shifted to lower temperatures as compared with that of 1T SENB specimens. The fracture toughness data of small pre-cracked specimens have been size corrected (weakest link) to 1T thickness and used to establish the reference temperature T 0 and K J c(mean) fracture toughness vs. temperature curve. The calculated temperature T 0 has been in consistence with that of the 1T SENB specimen. However, some corrected fracture toughness data lay outside the scatter band of 1T thickness specimens and the shape of the K J c(mean) curve has been quite different from the K J c(med)(1T) curve. It was found out that the original measured fracture toughness results of corrected data points lying outside the scatter band violated the validity condition b 0 R p0.2/ J c≥30. Bearing in mind the work of Koppenhoefer and Dodds Jr. (Engng Fract Mechanics (1997);58:249–270), and the most recent analysis of Ruggieri et al. (Engng Fract Mechanics (1998);60:19–36), the fracture data of small pre-cracked specimens having the validity parameter lower than 50 have been first constraint adjusted using the cleavage fracture toughness scaling model of Dodds and coworkers (J Testing Evaluation (1991);19:123–134; Int J Fracture (1995); 74:131–161; Engng Fract Mechanics (1997);58:249–270), and only then size corrected. The K J c(mean) curve of such treated data was identical with K J c(med)(1T) .

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.

Specimen Size Requirements for Cleavage Fracture Toughness based on the Weibull Stress Criterion

The specimen size requirements in toughness qualification are discussed on the basis of statistical local fracture criterion approach. The Weibull stress criterion for cleavage fracture is applied to the constraint loss field at the crack tip described with the toughness scaling model (TSM). Proposed new model (WSSM) demonstrates that the TSM is a particular case fora material with a particular combination of the Weibull shape parameter, m and the strain hardening exponent, n. The correlation between TSM and WSSM were also confirmed with 2 dimensional and 3 dimensional finite element analysis. The 3 dimensional analysis with Jp-δ for the stress intensity suggested the less constraint loss effect rather than 2 dimensional analysis in spite of the strong dependency of the constraint loss effect on Weibull shape parameter, m. The 3 dimensional analysis also suggested that the thickness effect on toughness mainly resulted from the statistical volume effect.The values of the hardening exponent, n and Weibull shape parameter, m, that are the dominant factors for the specimen size requirement suggested from WSSM, were investigated from the experimental results for the practical constructive steels. These results demonstrated that the specimen size requirements prescribed in ASTM could be too conservative.

Constraint effects on reference temperature, T0, for ferritic steels in the transition region

This study presents the methodology and key results derived from stochastic simulations to examine the effect of constraint loss on the reference temperature, T 0, at which the median fracture toughness of 1 T size specimens equals 100 MPa m for ferritic steels in the transition region. Using the Weibull stress as a local fracture parameter for transgranular cleavage, nonlinear three dimensional finite element analyses provide a quantitative description of constraint loss along crack fronts in deeply-notched SE(B) specimens in terms of a toughness scaling model. The simulations employ a Monte Carlo procedure to generate trial sets of small-scale yielding fracture toughness data which follow the three parameter Weibull distribution prescribed in the ASTM draft standard to determine T 0. Reverse corrections of the SSY values using the toughness scaling model predict large-scale yielding values (that would be measured in a fracture test). The differences in reference temperatures for the SSY and LSY toughness values represent the shift due to constraint loss. Results of extensive experimental testing programs, complemented by these simulations, provide key information needed by testing standard committees to specify appropriate censoring (deformation) limits on measured fracture toughness data relative to specimen size and material flow properties.

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised ‘in-plane’ constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide ‘effective’ thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised η-plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.

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/ σ 0, 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.

J-Q and toughness scaling model solutions for M(T), DE(T), SE(B), SE(T) and C(T) specimens

This report provides J-Q trajectories and TSM curves derived from plane strain analyses of M(T), DE(T), SE(T) and C(T) specimens for a range of a/W ratios, E/σ ratios and hardening exponent (n)