Cleavage Fracture In Ferritic Steels Research Articles

Validation of local approach‐based statistical models for cleavage fracture of ferritic steels in uniaxial tension

AbstractFive major local approach (LA)‐based statistical cleavage fracture models are evaluated in uniaxial tension. The focus is to inspect their mathematical conformity to the axiom of probability on normality and their physical adherence to the consensus that cleavage fracture occurs after plastic deformation. Only the LA model that incorporates a stress‐state and temperature dependent threshold satisfies both requirements. Two sets of experimental data in uniaxial tension are analyzed to support the arguments.

A new local approach model for cleavage fracture in ferritic steels and its validation

The paper discusses and applies a statistical approach to correlate the fracture behavior of a notched and fracture mechanics specimen. The method can be used for fatigue analysis. The random nature of cleavage fracture process determines that both the microscopic fracture stress and the macroscopic properties including fracture load, fracture toughness and the ductile to brittle transition temperature are all stochastic parameters. This understanding leads to the proposal of statistical assessment of cleavage induced notch toughness of ferritic steels according to a new local approach to cleavage fracture. The temperature independence of the two Weibull parameters in the new model induces a master curve to correlate the fracture load at different temperatures. A normalized stress combining the two Weibull parameters and the yield stress is proposed as the deterministic index to measure notch toughness. This proposed index is applied to compare the notch toughness of a ferritic steel with two different microstructures.

Statistical assessment of notch toughness against cleavage fracture of ferritic steels

AbstractThe work is an initial effort on adopting a statistical approach to correlate the fracture behavior between a notched and a fracture mechanics specimen. The random nature of cleavage fracture process determines that both the microscopic fracture stress and the macroscopic properties including fracture load, fracture toughness, and the ductile to brittle transition temperature are all stochastic parameters. This understanding leads to the proposal of statistical assessment of cleavage induced notch brittleness of ferritic steels according to a recently proposed local approach model of cleavage fracture. The temperature independence of the 2 Weibull parameters in the new model induces a master curve to correlate the fracture load at different temperatures. A normalized stress combining the 2 Weibull parameters and the yield stress is proposed as the deterministic index to measure notch toughness. This proposed index is applied to compare the notch toughness of a ferritic steel with 2 different microstructures.

Calibration of a new local approach to cleavage fracture of ferritic steels

A calibration method is proposed and proved feasible for implementing a new local approach to cleavage fracture of steels. The key is to adopt an elastic-perfectly plastic model to determine the maximum principal stress of each point at initial yielding as cleavage threshold stress for calculating the modified Weibull stress.

A cumulative failure probability model for cleavage fracture in ferritic steels

The fundamental physical assumption of plastic deformation as a prerequisite to the cleavage fracture event demands to rule out the contribution of elastic stress components to the occurrence of fracture from both the pure elastic zone and the elastoplastic zone. It also commands the threshold stress for cleavage fracture to be no less than the yielding stress. Based on this understanding, a model of the cumulative failure probability for cleavage fracture in ferritic steels is developed. Further, a self-consistent statistical model of cleavage fracture toughness is also derived. The Beremin model does not conform to the normality axiom of probability, as it defies the premise of plastic yielding before cleavage fracture by counting in the elastic stress components inside the plastic zone to calculate the cumulative probability. Examples are given in several homogeneous uniaxial and multiaxial loading conditions to highlight the differences between the Beremin model and the presented model in probability calculation, model calibration, and interpretation of the temperature and constraint dependence of microscopic cleavage fracture stress.

Prediction of cleavage fracture in ferritic steels by small punch tests with a modified Weibull stress model

In this paper, conventional small punch (SP) tests are carried out to determine the SP ductile-to-brittle transition temperature, TSP. The center holed small punch (CHSP) specimens are tested at TSP to determine the Weibull parameters with two different Weibull stress model. The relationship between temperature and the Weibull stress scale parameter, σu, is investigated. The result showed that a unique set of Weibull parameters for CHSP specimens and 0.4T SENB specimens is available by using the modified model not the original model. And the Weibull stress scale parameter, σu, is a power function of temperature.

Influence of grain size on arrest of a dynamically propagating cleavage crack in ferritic steels—micromechanics

Cleavage fracture in ferritic steels is controlled by several critical steps. First a microcrack must nucleate, grow and overcome barriers, such as grain boundaries. The latter is examined here by use of a periodic, axisymmetric model representing two grains. A microcrack nucleated at the center in one grain is driven by a constant remotely applied stress towards the second grain. The cleavage planes of the grain in which the microcrack is nucleated coincide with the principal loading direction. In the adjacent grain, due to misalignment in possible cleavage planes, the propagation direction changes and separation occurs in mixed mode, involving both normal and shear separations. The temperature dependence of the mechanical properties of the material is accounted for by use of a temperature dependent elasto viscoplastic material model. The largest grain size that can arrest a rapidly propagating microcrack is defined as the critical grain size. The effects of stress state and temperature on the critical grain size are examined. The influence of mismatch in lattice orientation between two adjacent grains in terms of a tilt angle is both qualitatively and quantitatively described. It is shown that the critical grain size is influenced by plastic geometry change and prestraining, which depend on the applied stress state. The results also show that a microcrack can be arrested in an adjacent grain under specific conditions.

Influence of crack deflection into the carbide/ferrite interface on cleavage fracture initiation in ferritic steels

In this and a companion study (Kroon, M., Faleskog, J., 2005. Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking. J. Mech. Phys. Solids 53, 171–196), the initiation of cleavage fracture in ferritic steels is studied. The initiation is modelled explicitly in the form of a microcrack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, in which the tractions are governed by a modified exponential cohesive law. The advancing microcrack, which has nucleated in the carbide, may either continue into the ferrite or deflect into the interface between the carbide and the ferrite. Special attention is given to the influence of the mode mixity factor β , which is defined as the ratio between the shear and tensile strength of the interface between the carbide and the ferrite. Crack growth in the interface occurs in shear mode and is driven by a fibre loading mechanism. For mode mixity values β ⩽ 0.2 , the crack deflects into the interface. The results indicate that crack growth in the interface can have a profound influence on the macroscopic fracture toughness of ferritic steels.

Development of the Local Approach to Fracture over the Past 25 years: Theory and Applications

This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic–plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.

Prediction of cleavage fracture in ferritic steels: a modified Weibull stress model

A modified three-parameter Weibull stress model is proposed in this paper, which considers the conjoint influences of plastic strain and stress triaxiality in the region of the crack tip. The model parameters are calibrated using two sets of fracture toughness data obtained from specimens exhibiting different constraint conditions at fracture, namely, deep-cracked compact tension specimens and shallow-cracked single-edge bending specimens. The master curve method is used to relate the fracture toughness data obtained at the different test temperatures. The calibrated Weibull stress model is then used to predict the cumulative failure probability of cleavage fracture for specimens containing surface cracks and loaded in varying combinations of tension and bending. The model predictions capture the measured toughness distributions for both bolt-loaded and pin-loaded specimens, while concurrently revealing a strong influence of the difference in crack tip constraint, due to different mode of loading, on probability of failure by cleavage. This effectively proves the applicability of the modified model for predicting cleavage-type fracture in ferritic steels.

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

ABSTRACTQuantification 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.

Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking

Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide.

The Role of Constraint and Warm Pre-Stress on Brittle Fracture in Ferritic Steels

This paper presents the results of an experimental and numerical study carried out to investigate the effect of warm pre-stressing on cleavage fracture in ferritic steels using cracked and notched specimens. It is shown that the local approach based on Weibull theory predicts the increase in toughness following warm pre-stressing in highly constrained geometries. The observed effect of pre-loading in low constraint specimens such as round notched bars is less. The local approach could not predict the differences and it is suggested that the variation of triaxiality factor, the ratio of hydrostatic stress to Von Mises, in the plastic zone, is a contributing factor.

Comparison of Global and Local Approaches to Predicting Warm Pre-Stress Effect on Cleavage Fracture of Ferritic Steels

Potentially both global and local approaches may be used to predicting the effect of loading history on cleavage fracture toughness distribution of ferritic steels. In this paper the dramatic increase in the apparent lower shelf fracture toughness of A533B steel following warm pre-stressing (WPS) has been predicted using these approaches. Extensive experimental evidence suggesting significant enhancement in fracture toughness of ferritic steels within the lower shelf temperatures following WPS are used to verify and compare the applicability and the extent of validity of the models. The global approach is based on the distribution of toughness data described by Wallin statistical model in conjunction with the Chell model for WPS effect. The local approach on the other hand is a Beremin type model that uses the Weibull stress to predict the WPS effect. Weibull stresses would essentially reflect the WPS effect on redistribution of stress-state around the crack tip. Predictions for apparent toughness using the two approaches are discussed in the light of the suggestion that residual stresses are the main cause of the enhancement, at least for the material and geometry used in this study.

Modelling the initiation of cleavage fracture of ferritic steels

The initiation of the cleavage fracture of ferritic steels at cracked grain boundary carbides situated in a plastic zone is modelled, using a 2D discrete dislocation simulation of the plastic zones associated with a microcrack under triaxial loading. Fracture is assumed to occur when the local stress intensity factor for the microcrack equals K IC. For microcracks in the size range 0.1–10 μm, the applied stress at fracture, σ F, is found to be independent of the yield stress (in the range 200–1600 MPa) and therefore of temperature. The dependence of σ F on the crack size deviates from a Griffith type relation. These predictions are consistent with experimental data on steels in the literature. The values of σ F predicted are in good agreement with the experimental values. The results suggest that only a small fraction of carbides are in configurations leading to fracture.

Deformation twins — probable inherent nuclei of cleavage fracture in ferritic steels

The vicinity of cleavage fracture of ferritic structural steels was analyzed. A strong tendency to deformation twinning was observed in the vicinity of the main cleavage crack. Numerous cleavage nuclei were revealed on the twins in the close vicinity of cleavage facets. It is concluded that deformation twinning represents an integral part of the deformation processes in the region of the propagating cleavage crack tip and that the deformation twins, which nucleate in front of the crack tip act as nucleation sites for cleavage fracture nuclei — pre-cleavage microcracks (PCMC). The size of PCMCs corresponds to that of the assumed inherent cleavage crack nuclei predicted by brittle/cleavage fracture theory. However, such nuclei have not hitherto been observed in ferritic materials.

Probabilistic modeling of weld fracture in steel frame connections part I: quasi-static loading

This study applies an advanced micro-mechanics model of cleavage fracture in ferritic steels to examine the nonlinear fracture behavior of welded, moment resistant steel frames of the type widely constructed prior to the 1994 Northridge earthquake. The Weibull stress model for cleavage, coupled with 3-D analyses of connections containing crack-like defects, provides a quantitative estimate of the cumulative failure probabilities with increasing beam moment. The 3-D models incorporate the complete geometry of a welded joint (access holes, shear tabs, continuity plate, weld geometry, backup bars). A set of previously conducted, 15 full-scale tests on T-connections of the pre-Northridge design (A36 beams, A572 columns, E70T-4 welds, backup bars left in place) provide fracture moments to calibrate parameters of the Weibull stress model. The present work considers quasi-static loading typically imposed in large-scale testing of the connections. Once calibrated, the model is used here to examine the importance of welding induced residual stresses in the lower-flange weld, the effects of stronger (A572) beams and modified access hole geometries, and a variety of proposed changes in the weld detail (backup bars, fillet reinforcements). The model predicts the cumulative failure probability as a function of beam moment for these various configurations. Using this same approach, the simplified “pull-plate” specimen is examined from a fracture mechanics viewpoint as a suitable replacement for full connection testing to evaluate alternative welding details.

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 $$(m,\sigma _u ) $$ . 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 $$(m,\sigma _u ) $$ 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 $$(m,\sigma _u ) $$ 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).

Loading rate effects on cleavage fracture of pre-cracked CVN specimens: 3-D studies

Specimen size and loading rate effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain key issues for the application of pre-cracked Charpy specimens. This investigation employs 3-D, nonlinear finite element analyses to assess crack-front stress triaxiality in quasi-static and impact-loaded pre-cracked CVN specimens, with and without side grooves. Crack-front conditions are characterized in terms of the Weibull stress which reflects the statistical effects on cleavage fracture. These 3-D computations indicate that a less strict size/deformation limit, relative to the limits indicated by previous plane-strain analyses, is needed to maintain small-scale yielding conditions at fracture under quasi-static and impact loading conditions. For impact toughness values which violate these size/deformation limits, a toughness scaling methodology is described to remove the effects of constraint loss. The new scaling model also enables prediction of the distribution of quasi-static fracture toughness values from a measured distribution of impact toughness values (and vice versa). This procedure is applied to experimental data obtained from a CrNiMoV pressure vessel steel and accurately predicts quasi-static fracture toughness values in 1T-SE(B) specimens from impact-loaded, pre-cracked CVN specimens. These 3-D analyses also yield η-total values for use in impact testing to infer thickness average and mid-thickness J-values from measured work quantities.

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.