A statistical approach for transferring fracture events across different sample shapes

The paper investigates the capability of a novel calibration method to predict accurately fracture events across different sample shapes at low temperatures. It is shown that the emergence of a threshold Weibull stress in the Weibull stress distribution is inherent in the fundamental assumptions of the Beremin model. The mathematical concept underlying the suggested calibration method is the correlation between the probability distributions of the fracture loads and the associated Weibull stresses. The calibration procedure is demonstrated using fracture data obtained in tests conducted at a test temperature of −150 °C on specimens fabricated of A533B ferritic steel. In contrast to the values found in the literature, the calibrated Weibull modulus is small and ranges from 2 to 4. The proposed methodology is straightforward to apply and yields reliable predictions of the failure probabilities of samples of different shapes.     

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.     

Effect of temperature on the mode I and mixed mode I/III fracture toughness of SA333 steel

The effect of temperature on tensile properties, mode I and mixed mode I/III fracture toughness of SA333 Grade 6 steel was investigated. The variation of ultimate tensile strength and strain hardening exponent with temperature as well as the appearance of serrations in the stress-strain plots indicated that dynamic strain aging regime in this steel is in the temperature range 175-300 °C at a nominal strain rate of 3 × 10⁻³ s⁻¹. Both mode I and mixed mode I/III fracture toughness values were found to exhibit a significant reduction in the DSA regime. The mixed mode I/III fracture toughness was found to be significantly lower than the mode I fracture toughness at all temperatures. However, the difference between the two toughness values was much higher prior to the onset of DSA. The results are explained on the basis of the nature of deformation fields under mode I and mixed mode I/III loading as well as the fracture mechanism prevalent in these steels at different temperatures.     

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.     

Development of carbon—Low alloy steel grades for low temperature applications

Low alloy steels are processed to fulfill the requirements of low temperature applications. Besides the chemical composition, the steel should receive a suitable heat treatment to ensure the targeted mechanical properties at low temperature. In other words, the steels are designed to delay the ductile to brittle transition temperature to resist dynamic loading at subzero temperatures. Steel alloys processed for liquefied gas pipeline fittings are examples for applications that need deep subzero impact transition temperature (ITT).The main purpose of the present work was to find a suitable heat treatment sequence for alloys LC2 and LC2-1. Further, it aimed to correlate the impact toughness with the microstructure and the fracture surface at different sub-zero temperatures.The steels under investigation are carbon-low alloy grades alloyed with Ni, Cr and Mo. LC2 steel alloy has been successfully processed and then modified to LC2-1 alloy by addition of Cr and Mo. Oil quenching from 900 °C followed by tempering at 595 °C was used for toughness improvements. Hardness, tensile and impact tests at room temperature have been carried out. Further impact tests at subzero temperatures were conducted to characterize alloys behavior. Metallographic as well as SEM fractographic coupled with XRD qualitative analysis are also carried out.Non-homogenous martensite-ferrite cast structure in LC2 was altered to homogeneous tempered martensite structure using quenching-tempering treatment, which is leading to shift the ITT down to −73 °C. Addition of Cr and Mo creates a very fine martensitic structure in LC2-1 alloy. Quenching-tempering of LC2-1 accelerates ITT to −30 °C. It is expected that the steel was subjected to temper embrittlement as a result of phosphorus segregation on the grain boundary due to Cr and Mo alloying, as it was concluded in reference no. [6].     

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.     

Residual stresses and fracture mechanics analysis of a crack in welds of high strength steels

This study presented the characteristics of residual stresses in welds of high strength steels (POSTEN60, POSTEN80) whose tensile strengths were 600 MPa and 800 MPa, respectively. Three-dimensional thermal elastic-plastic analyses were conducted to investigate the characteristics of welding residual stresses in welds of high strength steels through the thermal and mechanical properties at high temperatures obtained from the elevated temperature tensile tests. A finite element analysis method which can calculate the J-integral for a crack in a residual stress field was developed to evaluate the J-integral for a centre crack when mechanical stresses were applied in conjunction with residual stresses.The results show that the volumetric changes associated with the austenite to martensite phase transformation during rapid cooling after welding of high strength steels significantly influence on the development of residual stresses in the weld fusion zone and heat-affected zone. For a centre crack in welds of high strength steels where only residual stresses are present, increased tensile strength of the steel, increased the J-integral values. The values of the J-integral for the case when mechanical stresses are applied in conjunction with residual stresses are larger than those for the case when only residual stresses are present.     

A local approach to cleavage fracture in ferritic steels following warm pre-stressing

Quantification of the enhancement in cleavage fracture toughness of ferritic steels following warm pre‐stressing has received great interest in light of its significance in the integrity assessment of such structures as pressure vessels. A Beremin type probability distribution model, i.e., a local stress‐based approach to cleavage fracture, has been developed and used for estimating cleavage fracture following prior loading (or warm pre‐stressing, WPS) in two ferritic steels with different geometry configurations. Firstly, the Weibull parameters required to match the experimental scatter in lower shelf toughness of the candidate steels are identified. These parameters are then used in two‐ and three‐dimensional finite element simulations of prior loading on the upper shelf followed by unloading and cooling to lower shelf temperatures (WPS) to determine the probability of failure. Using both isotropic hardening and kinematic hardening material models, the effect of hardening response on the predictions obtained from the suggested approach has been examined. The predictions are consistent with experimental scatter in toughness following WPS and provide a means of determining the importance of the crack tip residual stresses. We demonstrate that for our steels the crack tip residual stress is the pivotal feature in improving the fracture toughness following WPS. Predictions are compared with the available experimental data. The paper finally discusses the results in the context of the non‐uniqueness of the Weibull parameters and investigates the sensitivity of predictions to the Weibull exponent, m, and the relevance of m to the stress triaxiality factor as suggested in the literature.     

Effects of preheating temperature on cold cracks,microstructures and properties of high power laser hybrid welded 10Ni3CrMoV steel

Laser hybrid welding has become one of the most promising welding methods for high strength low alloy steels due to combining the advantage of the laser and arc. A novel Y-groove cold cracking test adapted to laser hybrid welding is designed to assess the weldability of 10Ni3CrMoV steels at room temperature and different preheating temperatures. The experimental results show that the orientation of the predominant root cracks generally follows the contour of the fusion line. As the temperature increases from 25 °C to 150 °C, at first the root crack rate decreases and then slightly increases at 150 °C. The root crack rate obtained at 120 °C is the lowest. The fracture model changes from a brittle cleavage fracture to a mixture fracture with quasi-cleavage facets and dimples. The thermal cycle curves of laser hybrid welding obtained by temperature measurement systems are used to evaluate the crack resistance and microstructure transformation. The microstructures of welded joints obtained at different temperatures are analyzed by optical microscope (OM). The results reveal that the microstructures of the coarse grained region and the fusion zone at 120 °C have higher cold crack resistance and good impact toughness. Mechanical properties of the welded joint obtained at 120 °C and 150 °C are comprehensively evaluated by microhardness test, uniaxial tensile test and charpy V-notch impact test with side notches. Fractographs of the impact specimens are studied by scanning electron microscopy (SEM). The test results show that the welded joints obtained at 120 °C have satisfactory mechanical properties that can meet the technical requirements for shipbuilding industry.     

Calibration of Weibull stress parameters using fracture toughness data

The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36). This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical analysis of the effects of prior load on fracture

Collated fracture data for three steels, A533B, A508 and BS1501, and an Aluminium alloy, 2650, were examined to assess the statistical significance of the effect of prior loading on subsequent fracture. Weibull statistical and probabilistic analysis was used throughout. Two prior loading conditions were examined; one associated with warm pre-stress, and a second using pre-compression. For the former, prior loading resulted in an increase in the mean toughness together with an increase in the shape parameter and a decrease in variability compared to the as-received material. In contrast, when prior loading involved out-of-plane compressive loading (or side-punching) statistical evidence revealed that there was a reduction in toughness together with a decrease in the shape parameter and an increase in variability. Two numerical models were applied to steel data and were able to predict the overall trends obtained from the experiments, but could not reproduce accurately the experimental statistical distributions.     

Effects of short- and long-term thermal exposures on the stability of a Ni–Co–Cr–Si alloy

Long-term thermal stability is often needed for high temperature alloys used in a variety of industrial applications for extended operating lifetimes. In this paper, the effects of thermal exposures or aging on the mechanical properties and microstructure of a Ni–Co–Cr–Si alloy (HAYNES® HR-160® alloy) were studied. It includes both short- and long-term elevated temperature exposures ranging from 649 °C to 1093 °C (1200–2000 F) for duration of 6 min (0.1 h) to 6 years (50,000 h). The residual room temperature (RT) tensile and Charpy-V impact toughness properties were evaluated and correlated to microstructural changes as well as to fracture surfaces of the tensile tested samples. It was found that the RT ductility and impact toughness of the HR-160 alloy decreased continuously with time. A significant percentage of reduction in the ductility occurred in the initial 1000 h of exposure and the subsequent exposure led only to a minimal loss of ductility and impact toughness values. The concomitant microstructural changes were studied using optical metallography, SEM/EDS and X-ray diffraction of extracted residues. The results presented in this paper demonstrated that the HR-160 alloy exhibits good thermal stability characterized by >16% RT elongation after 50,000 h exposures at 649 °C, 760 °C, and 871 °C.     

Coatings with intrinsic stress profile: Refined creep analysis of (Ti,Al)N and cracking due to cyclic laser heating

A refined non-linear creep analysis of ceramic coatings has been performed by means of an improved substrate curvature technique in vacuum facilitating increased sensitivity by noise reduction. In this way the intrinsic stress profile may be derived from the time-dependent substrate curvature. Creep and stress parameters of 0.5 μm (Ti,Al)N-coatings have been found. At 500 °C the stress varies between − 1 GPa at the surface and + 0.2 GPa at the interface with the silicon substrate. From the onset of crack formation as observed in cyclic laser shock experiments a coating tensile strength of about 0.7 GPa is deduced. The number of cycles to cracking and delamination/spalling vs. maximum coating temperature as derived from creep simulation agrees quantitatively rather well with the experimental data. A rough estimate of the interface fracture toughness on WC/Co substrates yields 11 N/m as a lower bound.     

The influence of dynamic strain aging on resistance to strain reversal as assessed through the Bauschinger effect

The Bauschinger effect of three commercially produced medium carbon bar steels representing different microstructural classes with similar tensile strengths and substantially different yielding and work-hardening behaviors at low-strain was evaluated at room temperature and in situ at temperatures up to 361 °C. The influence of deformation at dynamic strain aging temperatures as a means to produce a more stable dislocation structure was evaluated by measuring the resistance to strain reversal during in situ Bauschinger effect tests. It was shown that the three medium carbon steels exhibited substantial increases in strength at dynamic strain aging temperatures with the peak in flow stress occurring at a test temperature of 260 °C for an engineering strain rate of 10⁻⁴ s⁻¹. Compressive flow stress data following tensile plastic prestrain levels of 0.01, 0.02 and 0.03 increased with an increase in temperature to a range between 260 °C and 309 °C, the temperature range where dynamic strain aging was shown to be most effective. The increased resistance to flow on strain reversal at elevated temperature was attributed to the generation of more stable dislocation structures during prestrain. It is suggested that Bauschinger effect measurements can be used to assess the potential performance of materials in fatigue loading conditions and to identify temperature ranges for processing in applications that utilize non-uniform plastic deformation (e.g. shot peening, deep rolling, etc.) to induce controlled residual stress fields stabilized by the processing at temperatures where dynamic strain aging is active.     

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.     

Correlation of austenite stability and ductile-to-brittle transition behavior of high-nitrogen 18Cr-10Mn austenitic steels

Ductile-to-brittle transition behavior of high-nitrogen 18Cr-10Mn austenitic steels containing different contents of Ni, Mo, Cu as well as nitrogen is discussed in terms of austenite stability and associated deformation-induced martensitic transformation (DIMT). Electron back-scattered diffraction and transmission electron microscopy analyses of cross-sectional area of the Charpy impact specimens fractured at −196 °C indicated that the brittle fracture planes were almost parallel to one of {1 1 1} slip planes and some metastable austenites near the fracture surface were transformed to α′-martensite by localized plastic deformation occurring during crack propagation. Quantitative evaluation of deformation-induced martensite together with characteristics of true stress-strain and load-displacement curves obtained from tensile and Charpy impact tests, respectively, supported that DIMT might take place in high-nitrogen austenitic steels with relatively low austenite stability. The occurrence of DIMT decreased low-temperature toughness and thus increased largely ductile-to-brittle transition temperature (DBTT), as compared to that predicted by empirical equations strongly depending on nitrogen content. As a result, the increased DBTT could be reasonably correlated with austenite stability against DIMT.     

Interaction of residual stress with mechanical loading in a ferritic steel

A well-defined residual stress field was introduced into modified single edge notched bend, SEN(B), specimens by the ‘in-plane compression’ procedure in order to investigate the interaction between residual stress and applied mechanical loading. Numerical predictions of the residual stress field arising from the in-plane compression procedure are given along with details of the numerical fracture modelling and experimental fracture test results made on A533B ferritic steel specimens in the lower transition region at −150 °C. Use was made of a recently developed finite element post-processor capable of determining path-independent J-integral values in the presence of residual stress fields. The paper compares the experimental results to predictions made using a probabilistic ‘global approach’ based on the conventional crack-tip parameters K and J and predictions made using a well-known structural integrity assessment code, R6 (Revision 4). It is shown that obtaining more accurate estimates of the crack driving force created by residual stresses leads to better correlation between experiments and predictions, and less conservatism in the assessment code.     

Intrinsic stress effect on fracture toughness of plasma enhanced chemical vapor deposited SiNx:H films

The apparent fracture toughness for a series of plasma enhanced chemical vapor deposition SiN_x:H films with intrinsic film stress ranging from 300 MPa tensile to 1 GPa compressive was measured using nanoindentation. The nanoindentation results show the measured fracture toughness for these films can vary from as high as > 8 MPa⋅√m for films in compression to as low as < 0.5 MPa⋅√m for the films in tension. Other film properties such as density, Young's modulus, and hydrogen content were also measured and not observed to correlate as strongly with the measured fracture toughness values. Various theoretical corrections proposed to account for the presence of intrinsic or residual stresses in nanoindent fracture toughness measurements were evaluated and found to severely underestimate the impact of intrinsic stresses at thicknesses ≤ 3 μm. However, regression analysis indicated a simple linear correlation between the apparent fracture toughness and intrinsic film stress. Based on this linear trend, a stress free/intrinsic fracture toughness of 1.8 ± 0.7 MPa⋅√m was determined for the SiN_x:H films.