Calibration of the Weibull stress scale parameter, σu, using the Master Curve

This work proposes that the Weibull stress scale parameter, σ_u, increases with temperature to reflect the increasing microscale toughness of ferritic steels caused by local events that include plastic shielding of microcracks, microcrack blunting, and microcrack arrest. The Weibull modulus, m, then characterizes the temperature invariant, random distribution of microcrack sizes in the material. Direct calibration of σ_u values at temperatures over the DBT region requires extensive sets of fracture toughness values. A more practical approach developed here utilizes the so-called Master Curve standardized in ASTM Test Method E1921-02 to provide the needed temperature vs. toughness dependence for a material using a minimum number of fracture tests conducted at one temperature. The calibration procedure then selects σ_u values that force the Weibull stress model to predict the Master Curve temperature dependence of K_Jc values for the material. At temperatures in mid-to-upper transition, the process becomes more complex as fracture test specimens undergo gradual constraint loss and the idealized conditions of high-constraint, small-scale yielding assumed in E1921-02 gradually degenerate. The paper develops the σ_u calibration process to incorporate these effects in addition to consideration of threshold toughness effects and the testing of fracture specimens with varying crack-front lengths. Initial illustrations of the calibration process for simpler conditions, i.e. 1T crack-front lengths, use the temperature dependent flow properties and a range of toughness levels for an A533B pressure vessel steel. Then using the extensive fracture toughness data sets for an A508 pressure vessel steel generated recently by Faleskog et al. [Engng. Fract. Mech., in press], the paper concludes with calibrations of both m and σ_u over the DBT region and assessments of the Master Curve calibration approach developed here.     

Loading rate effects on parameters of the Weibull stress model for ferritic steels

This study investigates the effects of loading rate on parameters of the Weibull stress model for prediction of cleavage fracture in a low strength, strongly rate-sensitive A515-70 pressure vessel steel. Based on measured, dynamic fracture toughness data from deep- and shallow-cracked SE(B) specimens, the calibrated Weibull modulus (m) at shows little difference from the value calibrated previously using static toughness data. This newly obtained result supports the hypothesis in an earlier study [Gao X, Dodds RH, Tregoning RL, Joyce JA. Weibull stress model for cleavage fracture under high-rate loading. Fatigue Fract Engng Mater Struct 2001;24:551-64] that the Weibull modulus likely remains rate independent for this material over the range of low-to-moderate loading rates. Additional experimental and computational results for higher rates show that a constant m-value remains applicable up to the maximum loading rate imposed in the testing program . Rate dependencies of the scale parameter (σ_u) and the threshold parameter (σ_w-min) are computed using the calibrated m, and the results indicate that σ_u decreases and σ_w-min increases with higher loading rates. The predicted cumulative probability for cleavage fracture exhibits a strong sensitivity to small changes in σ_u. Consequently, σ_u must be calibrated using dynamic fracture toughness data at each loading rate of interest in an application or selected to make the Weibull stress model predict a dynamic master curve of macroscopic toughness for the material.     

Temperature dependence of Weibull stress parameters: Studies using the Euro-material

This work demonstrates the temperature invariance of the Weibull stress modulus, m, for a 22Ni-MoCr37 pressure vessel steel through calibrations at two extreme temperatures of the ductile-to-brittle transition. This temperature invariance reflects the characterization of microcrack size distribution in the material described by the modulus. The calibrations performed here also demonstrate the clear dependence of the Weibull scale parameter, σ_u, on temperature. The increase of σ_u with temperature reflects the increase in microscale toughness of ferritic steels. The calibration procedure employs a three-parameter Weibull stress model which includes the effects of a minimum (threshold) toughness, K_min. The calibrations suggest that K_min increases gradually with temperature. Finally, an engineering procedure is presented to enable practical applications of the Weibull stress model for defect assessments. This procedure combines the demonstrated temperature invariance of m, a recently developed method for predicting the variation of σ_u with temperature using the Master Curve, and calibration of the Weibull stress parameters at one temperature. The (calibrated) temperature invariant m and the estimated σ_u as a function of temperature are used to predict the cumulative probability of fracture for several large datasets without direct calibration.     

Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components

This paper presents a procedure for transferring the CTOD fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components, taking constraint loss into account. The Weibull stress criterion is applied to correct the CTOD for constraint loss, which leads to an equivalent CTOD ratio, β, defined as β = δ/δ_WP, where δ and δ_WP are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress. The CTOD ratio β is intended to apply to the fracture assessment of ferritic steel components to stress levels beyond small-scale yielding. Nomographs are given to determine the β-value as a function of the crack type and size in the component, the yield-to-tensile ratio of the material and the Weibull shape parameter m. Examples of the fracture assessment using β are shown within the context of a failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reduced reasonably by applying the equivalent CTOD ratio, β.     

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress. Part I: Methodology using the equivalent CTOD ratio

This part I of a two-part paper presents a method of assessing the effects of welding residual stress and constraint loss on the cleavage fracture of a wide plate subjected to membrane stress based on the Weibull stress criterion. It has been found that the Weibull stress criterion is efficient for evaluating the fracture instability of wide plates with and without a welding residual stress field. The concept of an equivalent crack-tip opening displacement (CTOD) ratio β_r under a welding residual stress field is introduced for assessment of constraint loss effects on CTOD fracture toughness of wide plates. The equivalent CTOD ratio β_r is defined as the ratio of the CTOD in the standard fracture toughness specimen to the CTOD in a wide plate with a welding residual stress at the same level of the Weibull stress. Fracture assessment procedures using β_r for wide plates are shown within the framework of the failure assessment diagram. It has been found that the excessive conservatism observed in the conventional procedure can be reduced reasonably by applying the proposed method. The companion part II of the paper presents applications of the CTOD toughness correction method using β_r to the fracture test data of welded joints and verifies the proposed method in the ductile-brittle transition temperature region.     

Prediction of prestraining effect on fracture toughness of high strength structural steel by local approach

In the present study, the tension and fracture toughness tests on high strength structural steel of Q420 were carried out in different conditions of non-prestraining and prestraining. The results indicated that the prestrain increased the yield stress and tensile strength, but decreased the fracture toughness. Meanwhile, the local parameters m and σ_u controlling the brittle fracture were obtained using finite element method (FEM) analysis. Based on the Weibull stress fracture criterion, the prestraining effect on the fracture toughness was predicted from fracture toughness results of the virgin material by the local approach. The prediction was in good agreement with the experimental results. It certified that the critical Weibull stress obeys the two-parameter Weibull distribution in the local approach, and the fracture behaviour of the material with prestrain can be characterised well by the local approach.     

Large scale testing and statistical analysis of dynamic fracture toughness of ductile cast iron

The present paper deals with the experimental determination and statistical analysis of dynamic fracture toughness values of ductile cast iron. K_Id data from 140 mm thick single edge bend specimens of two dynamic fracture toughness test series on ductile cast iron from heavy-walled castings were analysed.At first, the statistical analysis of data at −40 °C was done based on ASME Code Case N-670 using a two-parameter Weibull distribution function. Weibull analyses of three samples covering different pearlite contents (?4%, ?9%, ?20%) were performed and characteristics of the distribution functions as well as two-sided confidence intervals were calculated. The calculated characteristics show that K_Id of ductile cast iron decreases with increasing pearlite content.In a second step, the applicability of the Master curve procedure according to ASTM E 1921 to ductile cast iron materials was investigated and it was formally used for statistical analysis of ductile cast iron dynamic fracture toughness data. Although the Master curve method was originally introduced for static fracture toughness data of ferritic steels, the successful individual analyses performed here support the engineering way taken to apply the method to ductile cast iron materials too. The results of both methods, the Master curve procedure and the ASME Code Case N-670, show acceptable congruity. At the same time, it is concluded from the present study that further investigations and experiments are required to improve precision and for verification before the results could be applied within component safety analyses.     

A K0‐based calibration procedure for the Weibull stress cleavage model

This paper presents a simplified calibration procedure for the microscopic Weibull stress model to estimate the cumulative probability of cleavage fracture for ferritic steels. The proposed method requires two discrete values of the macroscopic Weibull scale parameter (K₀) in contrast to the two sets of statistically significant fracture toughness data mandated in previous calibration schemes. The proposed approach predicates on the fundamental assumption that the macroscopic toughness, for specimens dominated by cleavage mechanisms, follow the three‐parameter Weibull model outlined in the testing standards. The calibration procedure thus generates two sets of fictitious toughness data corresponding to two sets of specimens with marked differences in crack‐front constraints. The calibrated Weibull parameters agree closely with the calibration results based on the conventional approach for the Euro steels. The proposed calibration also leads to an improved method to determine a limiting load level, beyond which extensive plastic deformation propagates in the specimen.     

Constraint loss correction for assessment of CTOD fracture toughness under welding residual stress - Part II: Application of toughness correction methodology

This part II paper presents the verified results of the toughness correction methodology for welded joints of wide plates. The equivalent CTOD ratio, β_r, is applied to the fracture data of the welded joints from lower to upper ductile-brittle transition temperature region. In the part I paper, β_r is defined as the ratio of CTOD in the standard fracture toughness specimen to CTOD in the wide plate with welding residual stress at the same level of the Weibull stress. In this part II paper, the equivalent CTOD ratio, β_r, under the welding residual stress field has been verified for assessment of constraint loss effects on CTOD fracture toughness of wide plate. Fracture assessments have been conducted by applying the methodology for “After Weld Notch” and “Before Weld Notch” type welded joints. It has been found that an excessive conservatism observed in the conventional procedure is reasonably reduced by applying the proposed methodology.     

Fracture toughness of M2 and H13 alloy tool steels

Abstract

The influence of microstructural variations on the fracture toughness of two tool steels having compositions (wt-%) lC–4Cr–5Mo–2V–6W (AISI M2 high-speed steel) and 0·35C–5Cr–1·5Mo;amp;#x2013;1V (AISI H13 hot-work steel) was investigated. In the as-hardened condition, the H13 steel has a higher fracture toughness than M2 steel, and the latter steel is harder. In the tempered condition, the H13 steel is again softer and has a higher fracture toughness than M2. There is a decrease in fracture toughness and an increase in hardness when the austenitizing temperature is above I050°C for M2 steel and above 1100°C for H13 steel, in both the as hardened and hardened and tempered conditions. The fracture toughness of both steels was enhanced by reducing the grain size and increasing the overall carbide volume in the matrix. The steel samples of average grain diameter ≥40μm exhibit 2–3 MN m ^?3/2 lower fracture toughness than samples of average grain diameter ≤15 μm. A high content of retained austenite appears to raise the fracture toughness of as-hardened M2 steel. Tempering improved the fracture toughness of M2 and H13 steels. The present results are explained using observations of changes in the microstructure and the modes of fracture.

MST/468     

Micromechanics of fracture in a NiCrMo alloy

In a NiCrMo steel, quenched and tempered at various temperatures, the critical stress and strain at fracture have been computed in the SEN bending fracture toughness specimens and the effect of triaxiality factor on the fracture ductility has been studied. The experimental investigation included the tensile and fracture toughness (K_Ic, COD, J_Ic) tests, quantitative microscopy for statistical size distribution analysis of inclusions, and the quantitative fractography. An attempt has been made to identify the effective inclusion size to characterize the microfracture process under uniaxial and triaxial loading situations and the mechanics of void expansion has been investigated. A quantitative relationship between the process zone size and material microstructure as well as fractographic features has been presented for the cleavage and the microvoid coalescence mode of fracture.     

Temperature dependence of fracture toughness J IC and ductility for BCC materials in the transition region

The temperature dependence of ductility, strength and fracture toughness for a BCC material undergoing predominantly linear elastic behavior at low temperatures and elastic-plastic behavior at higher temperatures is examined. A model, based on ductile fracture mechanisms involving void nucleation followed by cavity growth and void coalescence, is developed to relate the fracture toughness parameter J _IC with temperature. Two general equations for linear elastic and elastic plastic regimes of J _IC versus temperature T, are obtained. Applications of this model to experimental data obtained on a carbon steel show that J IC varies with T ² at low temperatures and with T at higher temperatures, thus defining a transition temperature.     

Gouge assessment for pipes and associated transferability problem

The purpose of this work is to assess a gouge defect in a pipe submitted to internal pressure. To do that a method based on failure assessment diagram and more precisely on a Modified Notch Failure Assessment Diagram (NMFAD) which has been proposed as a mesofracture approach. The safety factor has been determine under conservative conditions i.e. for a X52 pipe steel having a relatively low fracture toughness and a severe gouge defect with high aspect ratio and high constraint. In addition a mesofracture approach of the fracture toughness transferability problem has been proposed. The crack (K–T) methodology has been modifying to create the (K_ρ–T_ef) two parameters fracture resistance criterion.     

Fracture behaviour of dynamically loaded ship building plate material

The fracture toughness values of ship building mild steel measured over a temperature range ? 196°C to 28°C and crack tip strain rates ranging from 10^?5/sec to 10^?1/sec are examined in the light of the models recently proposed by Malkin and Tetelman. The effect of a change in inclusion morphology brought about by electroslag refining on the fracture toughness of the steel is also evaluated. It is found that the stress-induced fracture criterion ofthe model applies for the case where the ratio $\text{σ}{}^1{}_{\mathrm{f}}\text{σ}{}_{\mathrm{YS}}\text{? 3.94}$. This ratio is independent of the strain rate. In the strain induced fracture region of the model, the critical strain near the crack tip, ?_f(Rβ) is a function of the yield stress irrespective of temperature and strain rate. Electroslag refining reduces significantly the size and volume fraction of the inclusions and changes their shape from prolate ellipsoid to spherical. Apparently the electroslag refining does not improve fracture toughness significantly if the fracture toughness of the as received material measured with the major axis of the inclusions perpendicular to the crack front, is taken as a basis of comparison.     

Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing

A new method has been developed involving direct measurement of the load-line displacement during instrumented Charpy testing. The method uses a laser interferometer to measure displacement in addition to the load-line displacement derived from the load signal. Tests were conducted using fatigue precracked and V-notched test pieces in the temperature range +23°C to −80°C on a conventional ship grade steel, a pressure vessel steel and two welded joints. Good correlation was found between the J_0.2 initiation fracture toughness determined by the multi-specimen method and the J_i fracture toughness determined from single specimens using the new method to detect ductile fracture initiation.     

Fracture characterisation of a nuclear vessel steel under dynamic conditions in the transition region

The Master Curve (MC) methodology, originally proposed by Kim Wallin, is a standardised engineering tool for analysing the fracture toughness of ferritic steels in the ductile to brittle transition (DBT) region by means of the reference temperature T₀. This temperature is normally estimated from quasi-static fracture toughness tests, nevertheless, it has been recently extended to the determination of dynamic fracture toughness. The aim of the present contribution is to characterise the fracture resistance in the DBT region under high strain rate conditions by applying the MC methodology to the steel of the Santa María de Garoña Spanish nuclear power plant (NPP). In this sense, 15 Charpy instrumented tests were performed on pre-cracked specimens from the surveillance program of the plant. The dynamic reference temperature, T_0,dyn, was obtained and compared with the quasi-static reference temperature, T_0,sta. The reliability of a semi-empirical formula proposed by Wallin to obtain T_0,dyn from T_0,sta has been analysed for this material.     

Comparison of ASME K IR curve and dynamic master curve in determining ductile–brittle transition temperature of A48P2 steel

Abstract

The ductile–brittle transition temperature (DBTT) of grade A48P2 steel is characterised based on the American Society of Mechanical Engineers (ASME) fracture toughness K _IR curve and dynamic master curve approaches. The indexing parameter for the K _IR curve, reference temperature RT_NDT, is determined from drop weight and Charpy tests to be ?45°C. The dynamic master curve is constructed following ASTM standard E1921 guidelines; however, instead of precracked tests, the dynamic fracture toughness K _Jd is determined from Charpy V notch tests using a modified Schindler's procedure. A Weibull plot is constructed using the K _Jd data, and it is found that the points comply reasonably with the forced fit line of slope 4. The reference temperature for constructing the dynamic master curve, termed T^dy,Sch₀, thus determined is ?56°C. The ASME K _IR curve is shown to be conservative compared with the dynamic master curve constructed using T^dy,Sch₀.     

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.     

Statistical scatter of fracture toughness in the ductile-brittle transition of a structural steel

The statistical scatter of fracture toughness in the ductile-brittle transition temperature range was experimentally examined on a 500 MPa class low carbon steel. Fracture toughness tests were replicatedly performed at −60 °C, −20 °C and −10 °C. The tests at −60 °C resulted in a single modal Weibull distribution with a shape parameter of 4 for the critical stress intensity factor converted from J-integral, whereas the Weibull distributions of the critical stress intensity factor at −20 °C and −10 °C showed a bilinear pattern with an elbow point, which caused a wider scatter than that at −60 °C. Such scatter transition behavior was discussed with reference to stable crack initiation. A model of the statistical scatter transition has been proposed in this work and the model reasonably explains the experimental results.     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.