Brittle Fracture Criterion Research Articles

A general mixed-mode brittle fracture criterion for cracked materials

In order to predict the fracture direction and fracture loadings of cracked materials under the general mixed-mode state, this paper presents a new general mixed-mode brittle fracture criterion based on the concept of maximum potential energy release rate (MPERR). This criterion can be easily degraded to the pure-mode fracture criterion, and can also be reduced to the commonly accepted fracture criteria for the mixed-mode I/II state. In order to validate the proposed criterion, we have carried out the experiments with aluminium alloy specimens under various mixed-mode loading conditions. The experimental results agree well with the predictions of the proposed criterion.

A stochastic model of damage accumulation in complex microstructures

A statistical approach for modeling fracture in brittle materials is presented. In particular, a microstructural-based finite element code called OOF is used in conjunction with a stochastic representation of failure that relies on the Weibull law. The OOF code, which maps materials microstructures onto finite element meshes, enables to calculate the local stress states; these stresses are used along with the statistical criterion for brittle fracture in order to determine microcrack formation and propagation. Computer simulations are performed on several microstructures of different materials types, e.g., laminates, particulate composites and polycrystals. The damage accumulation due to microcracking is characterized by the stereological measure of failed material and is investigated in order to assess the effect of microstructural features on the failure mechanism. Moreover, the approach allows to analyze the influence of the characteristic parameters for brittle materials on damage evolution.

Probabilistic definition of local criterion for brittle fracture under complex thermomechanical loading

The new local criterion for brittle fracture in probabilistic definition, which was used by the authors earlier for the KIc(T) prediction, is modified for the case of non-isothermal non-monotonic loading. An approach is put forward which allows predicting the brittle fracture probability for cracked elements under complex thermomechanical loading typical, for example, of the case of emergency cooldown of a reactor pressure vessel. The approach has been verified by comparing the calculated and experimental data of assessment of the influence of various thermomechanical pre-loading modes on the fracture toughness of reactor pressure vessel steels.

Steadiness and stop of brittle fracture driven by the forces in different distances

Based on the principle of fracture mechanics, the stop criterion of brittle fracture is proposed and the equation of minimal crack stop is given. By using the zero frequency Green function, the steadiness and stop of brittle fracture driven by the concentrated force and simple distributed forces in different locales are analyzed. The critical loading, unsteady boundary line and location of stop points under some typical conditions are calculated. The steady growth caused by the near forces is significant in interpreting the creep and the forming of some tectonics. Whereas the unsteady propagation caused by the forces in different distances from the crack is significant in interpreting the occurring and stop of earthquakes. It is suggested that the strong earthquakes may be the result of compound of the near-field and far-field forces. The results of this paper are also valuable for investigation of the mechanism of induced earthquake.

A crack at the interface of anisotropic bodies. Singularities of the elastic fields and a criterion for fracture when the crack surfaces are in contact

Novozhilov's quasistatic brittle fracture criterion is used to determine the direction angle of the branch of a crack with closed surfaces at the interface of two anisotropic bodies. The asymptotic form of the elastic fields near the crack tip is investigated and corollaries of Novozhilov's criterion are derived in an asymptotic formulation. Normalizations of the singular solutions, which have been adapted to the force and deformation fracture criteria, are discussed. In particular, it is established that, in the case of general anisotropy, there is no oscillation of the crack surfaces which can appear in the solution of the linear problem for an open crack.

Prediction of Brittle Failure of Notched Graphite and Silicon Nitride Bars

High stress gradients occur at metal-to-ceramic joints due to the different thermal and mechanical properties of the materials. In some cases, the magnitude of the highly localized stresses lead to failure thus compromising the structural integrity of such joints. The study of notched ceramic bars with high stress gradients can assist with the prediction of failure of metal ceramic joints. Experiments and fracture mechanics analysis were performed on notched and un-notched POCO E.D.M 3 graphite and AS800 Silicon Nitride bars with different notch parameters. The twoparameter, multi-axial Weibull statistics method and a brittle fracture criterion based on the average stress over an area approach were used to predict the failure of the bars and the results obtained were compared with experimental results. The brittle failure criterion appears to give much better correlation with experimental results than the multi-axial Weibull statistics approach. The findings also appear to highlight the limitations of the Weibull’s statistics method in cases involving very high stress gradients.

Prediction of brittle fracture of RPV steels under complex loading on the basis of a local probabilistic approach

A new local criterion of brittle fracture used to produce a probabilistic model for the temperature dependence of fracture toughness has been modified for non-isothermal and non-monotonic loading. An approach is proposed which allows calculation of the brittle fracture probability for cracked components under complex loading typical, for example, of that in pressurised thermal shock of a reactor pressure vessel. The proposed approach has been verified by comparison of calculated and experimental results for various warm pre-stressing conditions in reactor pressure vessel steels.

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K H IC for a single hydride platelet at the crack tip has been also estimated.

An Energy Gradient Fracture Criterion Based on Virtual Crack Vector Model with Application to T-Stress Problem

A virtual crack vector model is proposed in this paper to simulate the branched crack propagation and simplify its calculation of energy release rate. An energy gradient fracture criterion is constructed based on this model. It can take account of the effects of biaxial loads or T-stress on brittle mixed mode fracture and agrees well with the test data of biaxial tensile fracture and the specially conducted experiment of the influences of ox on the mixed mode fracture of plexiglas. Considering its advantage of predicting initial propagation angle and critical fracture stress independently without the determination of the core region radius, it can be used as a practical fracture criterion for brittle mixed mode fracture under biaxial tension.

Analysis of structure integrity of RPV on the basis of brittle fracture criterion: new approaches

Based on the Master curve conception, the condition for fracture toughness is formulated for a heterogeneous distribution of stress intensity factor along a crack front and non-monotonic, non-isothermal loading. This formulation includes an elaborated procedure for taking into account the effects of shallow cracks and biaxial loading on fracture toughness.

その場観察型２軸曲げ試験機の開発とガラスの混合モード下におけるき裂成長挙動観察

An attempt was made to investigate the crack growth behavior in soda-lime glass under mixed mode loading. Mixed mode crack growth tests under monotonic increasing biaxial loading were carried out by using the newly developed in-situ observation type biaxial bending testing machine. Biaxial stresses were applied by “saddle shape bending” for square plate. Crack extension from the residual stress free indentation-induced precrack were observed by a scanning laser microscope. The mode I and mode II stress intensity factors were calculated by Yoda's method. The major results of this study are summarized as follows:(1) Kinked cracks were initiated from indentation-induced precrack. With a crack growth, crack growth direction gradually approached to the direction perpendicular to the maximum principal stress.(2) When crack growth rate was arranged by mode I stress intensity factor KI, the threshold stress intensity KIth under mixed mode tends to decrease with decreasing in the stress mixing ratio R.(3) The criteria in which the crack starts to grow under mixed mode condition was expressed by similar equation for the brittle fracture criteria.(4) The stress intensity factor Keq, which is obtained by combining KI and KII, is useful to discuss a crack growth behavior under mixed mode condition.

Electron theory in materials modeling

This paper addresses four different areas of research that were of interest to the early readers of Acta Metallurgica, namely the Engel–Brewer theory for structural prediction, the CALPHAD methodology for phase diagram prediction, the 2γ-state hypothesis for the magnetic properties of fcc iron, and the Griffith criterion for brittle fracture. We discuss how the advent of density functional theory during the past 50 years has helped provide not only quantitative input into these areas, but also a firm framework for qualitative conceptual models.

A fracture mechanics interpretation of the DNV brittle fracture criteria for ships and mobile offshore units

ABSTRACT Design procedures against brittle fracture are either based on empirical experience based methods or theoretical fracture mechanics based methods. Frequently, the fracture mechanics based assessment procedures are suspected to be tools by which to get acceptance for poor quality. In reality, these suspicions are somewhat unfounded, since the manufacturing standards, implicitly, also assume some specific defect size. The standards contain specific inspection criteria, which in themselves lead to some specific possible accepted defect size. The problem has been that the manufacturing standards have not been evaluated based on an advanced fracture mechanics analysis. Here the Det Norske Veritas (DNV) rules for ships and mobile offshore units are analysed, applying the state‐of‐the‐art fracture mechanics assessment method SINTAP. Based on the assessment, the consistency of the DNV rules, with respect to strength level and inspection criteria is revealed. The assessment, also creates the possibility to extend the rules to thinner and higher strength steels.

Rheology of PVC Plastisol—VI: Criteria for Yielding and Fracture of an Immobilized Layer

PVC plastisol exhibits pseudo-plastic flow in steady shear; that is, viscosity decreases with the increasing shear rate. At higher shear rates viscosity reaches a minimum and then increases, i.e., dilatant behavior. Previously, pseudo-plastic behavior was explained by a mechanism in which the suspended particles partition into an immobilized layer and a mobile phase. The development of the immobilized layer with the increase in shear rate was shown to quantitatively account for pseudo-plastic behavior. In higher shear rates dilatation of the immobilized layer was shown to be the cause of dilatacy. At even higher shear rates the immobilized layer fractures. In this paper the viscosity minimum was interpreted as the yielding of the immobilized layer. Subsequently, data in the literature were analyzed to find criteria for the yielding and fracture of the immobilized layer. Yielding was found to obey Coulomb's criterion, from which the coefficient of friction and the cohesive strength of the immobilized layer were evaluated. These properties were controlled by the nature of particle assembly in the immobilized layer and the plasticizer type had only a minor effect. The value of the coefficient of friction was on the lower side and within the range of values found in the literature for other materials. There were two modes of fracture of the immobilized layer, one with low strength, low strain to break, and the other with high strength, high strain to break. The former is analogous to the brittle fracture of solids and the latter ductile failure. The strength of brittle fracture was somewhat higher than cohesive strength, which was evaluated from yielding data. This is akin to Griffith's criterion for brittle fracture of a solid. Ductile failure occurred when the shear stress exceeded normal stress.

On probabilistic fatigue models for composite materials

The general purpose of this article is to review the main ideas in fatigue analysis of composites in the context of the application of probabilistic methods, both theoretical and computational. That is why most deterministic concepts of composite materials fatigue are summarized together with stochastic approaches. The application of the perturbation based Stochastic Finite Element Method (SFEM) to fatigue analysis of homogeneous and heterogeneous media is shown. Further, homogenization method in its effective modules approach is proposed below for application in fatigue processes modeling of linear elastic periodic random composites. Considering stochastic character of the analysis, the reliability tools appropriate to multicomponent materials are presented together with the specially adopted brittle and ductile fracture criteria.

Verification of brittle fracture criteria for elements with V-shaped notches

In this paper an analysis of crack initiation in plane elements with V-shaped notches under biaxial loading (mode I and II) was presented. The following fracture criteria were used to evaluate the critical loads and directions of crack initiation: strain energy release rate criterion; strain energy density criterion; modified McClintock's stress criterion; non-local stress criterion. Results of numerical analysis obtained using the boundary element method and path independent H and J integrals were compared with experimental data.

Failure stress of a disordered three-dimensional spring network

This paper concentrates on the failure stress of a disordered three-dimensional spring network. In particular, we investigate the effects of several fracture criteria and of the connectivity at the nodes in the network. A node cannot be connected with another node if its relative distance is larger than a certain cutoff radius or a so-called connectivity threshold. In our modeling approach, the spring networks were loaded in compression and the network configuration with the lowest energy was calculated after each increment of force. Subsequently, the mechanical properties of the relaxed network structures were investigated using various fracture criteria. The largest threshold value of displacement was set to the commonly used criterion for brittle fracture, i.e., a fraction criterion of 1%, but also lower values (0.75%, 0.50%, and 0.25%) were examined. In addition, for each of these fracture criteria the stress calculations were repeated with different connectivity thresholds. From this investigation it is concluded that it is not sufficient to examine only the fracture strain. In particular, the connectivity, i.e., the connectivity threshold ${C}_{0},$ which controls the spring entanglement between the nodes, has a substantial effect on the crack morphology. Larger ${C}_{0}'\mathrm{s}$ result in smaller fragments caused by crack branching.

Criterion of Brittle Fracture of Materials under Single Loading

Criterion of Brittle Fracture of Materials under Single Loading

Prediction of the Brittle Fracture Toughness of Neutron-Irradiated Reactor Pressure Vessel Steels. Part 2

We apply the proposed model to study the effect of irradiation on the temperature dependence of brittle fracture toughness of 15Kh2MFA steel. We analyze also the influence of irradiation and the content of phosphorus and copper on the brittle fracture toughness. It is demonstrated that the probabilistic model, which is based on a new formulation of the brittle fracture criterion, allows an adequate prediction of the irradiation effect on the fracture toughness of reactor pressure vessel steels. Alternative models of prediction of fracture toughness are discussed.

A note on a proposed general criterion for brittle and ductile fracture in materials and structures

A material endures elastic–plastic deformation to the point where the mean stress reaches the maximum sustainable equi-cohesive bonding stress. In this note a proposed new ductile fracture criterion is developed from the theory of fracture toughness under different mean stress from that of the tensile test. Brittle fracture occurs during elastic deformation, which latter is induced by variation in the mean stress.