Cleavage Fracture Model Research Articles

Multilevel Model of Cleavage Fracture in Brittle Rocks in Compression

Multilevel Model of Cleavage Fracture in Brittle Rocks in Compression

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.

Analysis and improvement of local cleavage fracture models at elevated loading rates

Brittle fracture has to be excluded in safety-relevant components such as nuclear reactor pressure vessels. Recent work has indicated that brittle failure under dynamic loading cannot be assessed reliably by macroscopic methods such as the Master Curve concept (ASTM E1921). This finding is strongly connected to adiabatic heating processes and local crack arrest events in the crack tip region. However, a detailed study involving the assessment at elevated loading rates with local cleavage fracture models is not available to this point. The present work deals with the application of a local model to various dynamic loading conditions, as well as a proposed model adjustment to improve the analysis results. It was found that existing local concepts are not capable of describing fracture behavior adequately. Though the explicit numerical consideration of heat generation and conduction at elevated loading rates allows a better estimation of failure compared to the Master Curve concept, this still poor assessment quality can also be obtained by simply utilizing the adjusted “dynamic” Master Curve with an increased exponent of p = 0.030 /°C. It is therefore concluded that this exponent adjustment approximates the impact of heat effects quite well. The shortcomings of the numerical model were observed to correlate strongly with the documented amount of local crack arrest events on the fracture surface. This leads to a micromechanically-motivated adjustment of a local approach model to incorporate this mechanism. This modification ensures a more satisfying physical background of the local approach model. Moreover, it significantly improves model analysis accuracy for all examined testing conditions.

A Physically Based Model Predicting the Degradation of Hydrogen on Crack Growth Critical Stress Intensity Factor of Metals

A simple, physically based model is developed to quantitatively predict the degradation of hydrogen on the crack growth critical stress intensity factor (CSIF) of metals. The model is formulated by combining a microscopically shielded Griffith criterion (MSGC) model for plasticity-induced cleavage fracture and thermodynamics decohesion (TDD) theory for hydrogen-enhanced interface decohesion. The hydrogen-influenced CSIF is described as a function of the intrinsic CSIF (hydrogen-free), initial hydrogen concentration (solubility), hydrogen trap binding energy and crack tip stress. All parameters in the model can be determined with a physical basis and the model is successfully validated by comparison with published experimental data.

Micromechanics driven design of ferritic–austenitic duplex stainless steel microstructures for improved cleavage fracture toughness

Ferritic–austenitic duplex stainless steels are known to offer favorable combinations of good mechanical properties and corrosion resistance to be used for structural purposes. Lean duplex grades have already been introduced for consideration to replace standard 18–8 austenitic stainless steels in various industrial applications. Ferrite and austenite represent different deformation behaviors and contribute to the resulting fracture toughness characteristics. Micromechanical crystal plasticity based assessment of this cleavage fracture behavior is the subject area of current work. The objective is to bridge cleavage fracture models to full field crystal plasticity imaging based modeling of microstructures of ferritic–austenitic duplex stainless steels. The goal is to introduce means to computationally assess the effects of different multi-phase microstructural morphologies to cleavage fracture toughness and develop both the respective constitutive and cleavage fracture modeling capabilities. Such means can be used as an aid to develop better cleavage resistant, while in the current context lean, steel grades. Three different steels are investigated with differing austenite phase morphologies, and their behavior with respect to fracture mechanical response evaluated by micromechanical modeling. The effect of austenite fraction and morphology in terms of improving fracture toughness, a critical parameter concerning these steel grades and improvement of their cleavage fracture properties, is investigated. Deleterious features such as large ferrite grain size and microstructural property mismatching are identified and their implications to fracture toughness and development of applicable modeling capabilities for ferritic–austenitic duplex steels discussed. Simple design task of varying the austenite phase fraction is performed using synthetic microstructural modeling and the results evaluated with respect to their influence on the fracture toughness ductile-to-brittle transition.

Validation of Monte Carlo Simulation Technique for Calibration of Cleavage Fracture Model Parameters, With the Calibrated Values From Experimental Results for Reactor Pressure Vessel Material 20MnMoNi55 Steel in the Lower Self of Ductile-to-Brittle Transition Region

Abstract In the earlier work done by the author for the reactor pressure vessel (RPV) material 20MnMoNi55 steel, Monte Carlo simulation technique is shown as an effective statistical technique to calibrate Weibull modulus “m” and Weibull scale parameter “σu” for temperatures −100 °C, −110 °C, −120 °C, −130 °C, and −140 °C by performing only six fracture toughness tests instead of (30 × 5 = 150) number of tests. But it lacks validation with the experimental work. So, in this paper, huge numbers of fracture toughness tests (minimum 30 for each temperature) are performed experimentally at −100 °C, −110 °C, and −130 °C in the lower self of the ductile-to-brittle transition (DBT) region for the RPV material 20MnMoNi55 steel. Then, linear regression analysis of the experimental data is performed to calibrate Weibull modulus m and Weibull scale parameter σu of Beremin (a cleavage fracture model) for the above mentioned temperatures. The calibrate values show a matching trend with that of experimental calibrated values and justify the prediction capability of Monte Carlo simulation to predict the Beremin model parameters with the help of only six fracture toughness tests. This statistical simulation procedure can be considered as an effective technique for the proper calibration of Beremin model parameters for any material.

Study on the Size Dependence of Calibration Parameters of the New Local Approach Model for Cleavage Fracture

This paper investigates whether the Weibull parameters of the new local approach model for cleavage fractures are affected by the geometric size of the specimen. Based on the fracture test data of A508-C steel, low temperature round notched bar tensile specimens of A508-C steel with two different notch sizes are numerically simulated by using finite element analysis software ABAQUS, and the stress distributions are obtained. The Weibull parameters of two notched bars are calibrated by linear regression method. The results show that the Weibull parameters of the specimens with different notch sizes are different. This suggests that the calibration parameters are dependent on the notch size.

Stress triaxiality effect on cleavage fracture stress

In this work the effect of stress triaxiality on cleavage fracture stress was investigated by means of micromechanical modelling. A unit-cell model was used to determine macroscopic conditions for brittle fracture, in accordance with the slip-induced cleavage fracture model, because of included particle fracture and consequent crack initiation in the matrix. This approach allowed to correlate the critical fracture stress to the particle strength and the ability of the matrix to undergo plastic deformations. Numerical simulations results indicate that the critical fracture stress is strongly dependent on the stress triaxiality, which justify the variability observed in experiments on different specimen geometry. Additionally, the unit-cell modelling allowed to establish a simple relationship between the expected cleavage fracture stress and stress triaxiality, also considering temperature and strain rate. Finally, the use of the plastic constrain factor (defined as the ratio of the critical fracture stress and the yield stress) allows to obtain a master curve that can be used to predict the expected critical fracture stress at different stress triaxiality, temperature and strain rate in different steel grades and alloys.

Fracture simulation model for API X80 Charpy test in Ductile-Brittle transition temperatures

This paper presents a method to simulate fracture patterns of interacting ductile and cleavage fracture and experimental validation using API X80 Charpy test data. For ductile fracture, the stress modified fracture strain damage model is used, whereas for cleavage fracture, the maximum principal stress criterion is proposed. By combining ductile and cleavage fracture models, a numerical method to simulate interacting ductile and cleavage fracture is proposed. The proposed numerical method is validated by comparing with experimental Charpy test data at ductile-brittle transition temperatures. Comparison of fracture surfaces and impact energies shows good agreements.

Observations of cleavage initiation in ferritic steel

Local Approach (LA) to cleavage fracture models have been under development since the 1980s with the aim of predicting cleavage fracture, including accounting for the effects of temperature, crack-tip geometry and irradiation. This work presents observations of particle behaviour and micro-crack nucleation under stress conditions similar to those ahead of a crack-tip, achieved by testing bespoke tensile specimens with a highly constrained volume at temperatures in the material’s ductile to brittle transition region. This region was examined post-test using a scanning electron microscope to identify and characterise micro-cracks and micro-crack initiation defects, such as particles. Supporting finite element analyses were performed to predict the mechanical fields acting on the defects. The results suggested that:• micro-cracks nucleated in the form of damaged, spherical regions around the initiation particle with a cloud of crack-tips, rather than as single penny shaped cracks as assumed in LA models;• these damaged regions can be much larger than the initiating particle;• nucleation was more often caused by failure of the particle-matrix interface than particle cracking.

Micromechanical modeling of cleavage fracture for a ferritic-pearlitic steel

Despite efficient computational capability of phenomenological macromechanical models to predict cleavage fracture, they still lack microstructure sensitive information for material design. Therefore, a microstructure-based micromechanical modeling approach is proposed to predict cleavage fracture for a steel of grade AISI 1045 at different stress states. For the micromechanical modeling, virtual experiments are performed on an artificial microstructure model to derive the plasticity and cleavage damage initiation strain for the investigated material at −196 °C. The predicted microcrack initiation strains of cleavage fracture at two different states (plane strain tension and equibiaxial tension) agree well with the calibrated results of macromechanical modeling, illustrating the validity and predictive capability of the proposed approach. Furthermore, the approach is applied to a microstructure sensitivity study on artificial microstructure models with different microstructure constitutes to investigate the influence of microstructure on the behavior of cleavage fracture. Therefore, the new approach is contributing to the material design directly.

A generalized probabilistic model for cleavage fracture with a length scale – Influence of stress state and application to surface cracked experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture with a material related length scale is further developed in this study. A new generalized effective stress measure is proposed, based on a normal stress decomposition of the stress tensor, capable of describing a state of normal stress in the range from the mean stress to the maximum principal stress. The effective stress measure associated with a material point is evaluated from the stress tensor averaged over the material related length scale. The model is shown to be well capable to predict both the fracture toughness at loss of both in-plane and out-of-plane constraint by model application to two different datasets from the open literature. The model is also shown to be well capable of predicting the probability of failure of discriminating experiments on specimens containing semi-elliptic surface cracks. A comparison where the master curve methodology is used to predict the probability of failure of the experiments is also included.

A simplified method for parameters calibration of the new local approach model for cleavage fracture in a ferritic steel

This work presents a simplified method for parameters calibration of the new local approach model (NLAM) for cleavage fracture in a ferritic steel. Based on the Beremin model, a NLAM was recently proposed by Lei (2016) to calculate the Weibull parameters. Although the above NLAM proves to be mathematically and physically self-consistent, yet there are still no reliable and convenient methods to calibrate the model parameters. Considering the plastic volume is determined by the threshold coefficient of fracture process zone λ, we adopt four different values of λ in this work to calculate the plastic volume so as to obtain four groups of calibrated Weibull parameters. The material used in this study is the pressure vessel steel 20MnMoNi55 with some published strength data under two subzero temperatures. And the finite element analysis FEA) software ABAQUS is employed to obtain the stress distributions, then the calibration results for four different values of λ are compared and analyzed. These efforts show that taking λ=1.5 is a more reasonable and reliable choice.

A semi-empirical fracture model for silicon cleavage fracture and its molecular dynamics study

In micro scale, the capability of conventional fracture models is limited due to lacking of micro scale information. In this work, by incorporating crystal information and equivalent transformation, a semi-empirical fracture model for silicon single crystal is constructed. To verify the semi-empirical model, the fracture process is tested by molecular dynamics simulations and theoretical values. The result shows a good agreement between the semi-empirical fracture model and molecular dynamics simulations. And the fracture stresses and fracture toughness can be easily predicated by this model. It provides a link between micro and macro scale fracture for brittle material. And after the equivalent transformation, the fracture of brittle material can be calculated by this semi-empirical model without using conventional crack related parameters.

Phase stability and mechanical properties of ternary transition elements X(X = Cu,Zn,Ag) in Al3Hf intermetallic from first-principles calculations

Site preference, phase stability and brittle vs ductile behaviors of ternary transition elements Cu, Zn and Ag in Al3Hf intermetallic are investigated by using of first-principles calculations. It is found that it has a phase transition from D023 phase to L12 phase for Al3Hf due to the strong Al site preference for Cu, Zn and Ag addition. It is shown that the role of activated antiphase boundaries on 〈110〉(001) plane is the key factor for the phase transition. Elasticity modulus show that ternary elements can effectively improve the ductility of Al3Hf due to the phase transition. Finally, cleavage fracture model and slip fracture model were used to give a prediction of brittle to ductile transition mechanism based on Griffith fracture theory. The energetic results show that the improved ductility is due to the activated dislocation emission but suppressed crack propagation in materials.

Experimental evaluation of effective surface energy for cleavage microcrack propagation across grain boundary in steels

Fracture tests and finite element analysis were conducted to evaluate the temperature dependence of the effective surface energy γmm corresponding to microcrack propagation across the grain boundary of steels. Steels containing coarse cementite particles were prepared to enable γmm evaluation. The critical fracture stress of microcrack propagation across the grain boundary is considered larger than the critical fracture stress of microcrack propagation across the interface between a cementite particle and a ferrite grain in these steels because of the large cementite particles; therefore, local fracture stress estimated by finite element analysis and fracture initiation site obtained by fractography reflect the critical fracture stress of microcrack propagation across the grain boundary. Thus, the accuracy of γmm calculated from local fracture stress is observed to be enhanced by employing the steels prepared for the present study. In addition, the effect of nickel on γmm was studied using steels containing different concentrations of nickel. Values of γmm were evaluated considering both the direction of a neighboring facet relative to the crack initiation facet and the mixed mode stress intensity factors. The authors proposed a new temperature dependence ofγmm. Additionally, the negligible effect of nickel addition on γmm was observed. The results of the present study can be used effectively to develop a probabilistic cleavage fracture model based on microstructural information.

On the temperature independence of statistical model parameters for cleavage fracture in ferritic steels

The work relates to the effect of temperature on the model parameters in local approaches (LAs) to cleavage fracture. According to a recently developed LA model, the physical consensus of plastic deformation being a prerequisite to cleavage fracture enforces any LA model of cleavage fracture to observe initial yielding of a volume element as its threshold stress state to incur cleavage fracture in addition to the conventional practice of confining the fracture process zone within the plastic deformation zone. The physical consistency of the new LA model to the basic LA methodology and the differences between the new LA model and other existing models are interpreted. Then this new LA model is adopted to investigate the temperature dependence of LA model parameters using circumferentially notched round tensile specimens. With the published strength data as input, finite element (FE) calculation is conducted for elastic-perfectly plastic deformation and the realistic elastic-plastic hardening, respectively, to provide stress distributions for model calibration. The calibration results in temperature independent model parameters. This leads to the establishment of a ‘master curve’ characteristic to synchronise the correlation between the nominal strength and the corresponding cleavage fracture probability at different temperatures. This ‘master curve’ behaviour is verified by strength data from three different steels, providing a new path to calculate cleavage fracture probability with significantly reduced FE efforts.

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.

Simulating toughness properties under varying temperatures with micromechanical and phenomenological damage models

The sustainable and efficient use of high-strength micro-alloyed steels is of particular interest in today’s industry. Using modern steels with high strength and excellent toughness enables thinner constructions, for example in infrastructure applications, for pressure vessels or pipelines. Sufficient toughness is of special importance to avoid catastrophic brittle failure. Yet, the simplified, conventional design rules prevent a full exploitation of the properties of modern high strength steels. Modern simulation models are able to represent the actual failure characteristics of high strength steels and thereby help to fully exploit the potential of these materials. To include toughness properties, it is essential that the models are able to describe the transition behavior of these steels. The materials’ behavior in the transition region is characterized by a competition of ductile and cleavage failure mechanisms. To simulate the corresponding behavior, it is necessary to adapt damage mechanics models for considering both effects. While numerous studies on the simulation of either ductile or cleavage failure exist, only a limited selection is available on investigations in the transition range. Therefore, the presented study investigates two representatives of the most popular groups of ductile failure models. The Gurson-Tvergaard-Needleman model (GTN) is investigated as a micromechanical model while the Modified-Bai-Wierzbicki model (MBW) is selected as a phenomenological model. Both are combined with the Orowan cleavage fracture model. Investigations are performed on a thermomechanical rolled S355, for which the cleavage fracture stress and the parameters for the ductile failure models were experimentally determined. The study compares simulations of Charpy impact toughness tests to experimental results to determine which model class delivers results that are more accurate. The focus of the investigation is hereby set on the simulation of the lower shelf and the lower transition area. In addition, the efficiency of the simulations performed is also evaluated.

Investigation and Modeling of Local Crack Arrest in Ferritic-Bainitic Steels Under Dynamic Loading

Local crack arrest is usually irrelevant under quasi-static loading conditions in the ductile to brittle transition region. Elevated loading rates, however, allow cleavage fracture due to the dynamic embrittlement also at higher testing temperatures compared to static loading. This behavior is generally accompanied by local crack arrest events. In addition, adiabatic heating processes in the crack tip region increase local temperature as well, which further promotes crack arrest. This complex interaction between crack initiation and crack arrest at elevated loading rates substantially changes macroscopic fracture behavior, whereas its investigation is the core of this work. An experimental database of dynamic fracture mechanics experiments for the reactor pressure vessel steel 22NiMoCr3-7 is examined in this work that was previously tested at crack tip loading rates of about 103 to 105 MPa√m /s. Recent fractographic examinations and statistics regarding the occurrence and characteristics of local crack arrest incidences are shown for different loading rates and testing temperatures. Furthermore, an existing local probabilistic cleavage fracture model is used to describe macroscopic fracture behavior for the provided experimental database, and also compared to other assessment methods (i.e. Master Curve). The shortcomings in the numerical assessment methods can be linked to the amount of observed local crack arrest incidences, and a micromechanically motivated model modification is proposed to consider the mechanism of local crack arrest. The agreement between experimental results and numerical cleavage fracture assessment can be significantly increased by using the modified model.