Fracture Of Ferritic Steels Research Articles

On modeling fracture of ferritic steels due to hydrogen embrittlement

Experimental studies in the literature show that the fracture of ferritic steels in the presence of hydrogen occurs primarily perpendicular to the direction of the maximum principal tensile stress, is transgranular in nature, and has fracture surfaces which show “quasi-cleavage” features. Such features are cleavage-like but not along any known cleavage plane or grain boundaries. While the precise micromechanisms which lead to a transition from regular plastic deformation of the steel to “quasi-brittle” fracture are at present unclear, in this paper we have formulated a continuum theory for the diffusion of hydrogen coupled with the elastic-viscoplastic response of metals, together with a simple model which leads to quasi-brittle fracture in the presence of hydrogen. We assume that when an internal variable φ of the theory reaches a critical value φcr, then the inelastic deformation transitions from (a) a volume-preserving plastic stretching which occurs in the direction of the stress deviator — as in standard Mises-type plasticity, to (b) a different form of inelastic stretching which occurs in the direction of the maximum principal stress, and which is dilational in nature. We call this latter form of inelastic deformation craze inelasticity. We view the strain produced due to crazing as a “quasi-brittle” form of inelastic deformation. We allow only a small amount of inelastic craze-strain before the process of craze-breakdown and fracture sets in. To model craze-breakdown we introduce a damage variable d∈[0,1]; if d=0 at a point then that point is intact, while if d=1 at some point then that point is fractured. With the aim of “regularizing” the strain-softening behavior during craze-breakdown, and to avoid mesh-dependency related issues during finite element simulations, we develop a damage theory which depends not only on d but also its gradient ∇d, which is considered to be a measure of the spatial inhomogeneity of the damage during the craze-breakdown process. We have numerically implemented our coupled diffusion-deformation-damage theory in a finite element program, and we present representative numerical examples which show the ability of the simulation capability to qualitatively replicate the process of fracture due to hydrogen embrittlement in some technically relevant geometries.

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.

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.

Coupled porous plasticity – Continuum damage mechanics approaches for modelling temperature driven ductile-to-brittle transition fracture in ferritic steels

Following; (a) the observation that micro-void and micro-crack driven failure mechanisms co-exist in metallic alloys and (b) the two damage state variable definition given in Chaboche et al. (2006), two coupled porous plasticity and continuum damage mechanics approaches to assess temperature driven ductile-to-brittle transition fracture in ferritic steels have been developed. Based on hypo-elastic formulation of Gurson-Tvergaard-Needleman (GTN) thermoplasticity to account for ductile failure following void growth, continuum damage mechanics formalism have been coupled in order to account for micro-crack driven brittle fracture. Keeping GTN thermoplasticity as a basis for ductile fracture, Leckie-Hayhurst creep rupture criterion has been modified and proposed to account for brittle damage, thus cleavage, in the first model. The second approach, which is proposed following the motivation that plasticity exists in and below the lower transition region, replaces Leckie-Hayhurst model with plasticity driven damage evolution law of Lemaitre et al. (2000). Unlike commonly used cleavage models such as Ritchie et al. (1973) and Beremin (1983), both of the proposed models have been aimed to take into account blended effects of micro-voids and micro-cracks in order to capture energy dissipation and softening accompanying and prior to brittle fracture. Numerical implementation has been done for ABAQUS/Explicit and uses staggered solution based on plastic flow-damage correction structure, while its validation has been performed modeling Small Punch Fracture Experiments for P91 ferritic steel, published by Turba et al. (2011).

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.

A general method for coupling microstructural response with structural performance

The paper sets out the general principles of a method of coupling finite element for the representation of the structural response with array of cellular automata to encompass the associated microstructural behaviour. For the purpose of this paper, cellular automata is a discrete time–discrete space system consisting of cells which may take one of several states. The state of a cell depends on the states of the neighbouring cells as well as on some macroscopic field variables. The paper goes on to show how these principles can be used, by applying them to problems of oxide scale cracking and of dynamic recrystallization during the hot working of steel, and to the ductile-to-brittle transition in the fracture of ferritic steels.

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.

Multiscale modeling of the brittle to ductile transition

A recently introduced method of crack representation as a distribution of three-dimensional Volterra dislocations is used in conjunction with two-dimensional dislocation dynamics simulations to study the brittle to ductile transition behavior of Ferritic Steels. The crack-tip plasticity zone is represented as an array of discrete dislocations emitted from crack-tip sources. The dislocations shield the crack and result in an increase of the applied stress intensity for fracture from the pure Griffith value. The crack system responsible for fracture in Ferritic Steels is modeled by a macrocrack and a microcrack in its field. Crack-tip plasticity of microcrack is also modeled by arrays of emitted dislocations. The simulations are performed for different friction stresses corresponding to different yield stresses or temperatures. The brittle to ductile transition fracture toughness curve is obtained and compared to experiments.

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.

Models to describe brittle and ductile fracture in ferritic steels

Models to describe brittle and ductile fracture in ferritic steels

Models to describe brittle and ductile fracture in ferritic steels

Abstract Theoretical models have been developed to describe the various fracture mechanisms that occur in polycrystalline α-iron and ferritic steels over a range of temperature which spans the duct...

Effect of prior creep cavitation on brittle fracture in heat affected zone of ferritic steel weldments

Many components used by a range of industries, such as electrical power generation, operate at temperatures where creep damage is accumulated during the service life. In this process the materials undergo a range of microstructural changes including accumulation of cavities on grain boundaries oriented predominantly normal to the direction of the maximum principal stress. A theoretical model has been developed to consider the influence of such prior creep cavitational damage on subsequent brittle fracture of ferritic steels. The model allows the modes of transgranular cleavage and intergranular fracture to be quantified. It shows that if there is less than ~20% of cavitated boundaries they have little effect on the nature of the fracture process or the fracture strength. Material encompassing the heat affected zone has been removed from a region of a manual metal arc weldment in a CrMoV steel containing creep cavities arising from stress relief heat treatment. Fracture toughness tests using reconstituted Charpy geometry specimens were undertaken at a temperature of 170 K to assess the effect of this damage on the lower shelf fracture toughness. The results are discussed with respect to the predictions of the theoretical model.

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

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

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.