Crack Growth Instability Research Articles

Characteristics of allowable axial cracks for pressurized pipes governed by limit load criteria

When axial cracks were detected in pressurized pipes, failure stresses for high-toughness ductile pipes are estimated using the Limit Load Criteria. The allowable stresses for the cracked pipes are derived from the combination of the failure stresses and safety factors. Then, the allowable sizes of crack depths and lengths are determined from the allowable stresses. From the comparison of the allowable and failure stresses for through-wall cracks, the allowable cracks are not uniform. The allowable crack sizes can be separated into different characteristics of leak-before-break (LBB) and crack growth stability. Inspectors and users should pay special attention to allowable cracks with non-LBB and crack growth instability characteristics to prevent unexpected failure, particularly for thin-wall pipes. The boundaries of allowable crack depths and lengths that require special attention can be expressed by appropriate equations.

Experimental investigation on mechanical properties and deformation mechanism of soft-hard interbedded rock-like material based on digital image correlation

The soft-hard interbedded rocks are often encountered in rock engineering such as mining engineering, tunnel engineering, and natural gas engineering. In this study, the horizontal soft-hard interbedded composite rock-like material (HSHC) specimens were prepared with different thickness ratios of rock-like layers, and a series of uniaxial compression tests were performed by using a self-designed loading mold. A parameter R was defined for the HSHC specimens, which is related to the thickness ratio of the soft and hard rock-like layers, the length-width ratio, and the mechanical parameters of the soft and hard rock-like materials. R was regarded to characterize the strength properties of the HSHC specimens. The test results showed that the axial strength of the HSHC specimens decreases first and then tends to be constant with increasing of R. Digital image correlation (DIC) technique was used to investigate the strain evolution and crack propagation process of the HSHC specimens. The displacement variation trend of the specimen can be roughly divided into three stages: stable deformation stage, rapid crack growth stage and instability failure stage. The failure mode of the HSHC specimens was mainly splitting tensile failure along the bedding plane. Meanwhile, a simplified mechanical model of laminated rock mass under uniaxial compression is established. The strength variation trend predicted by this model is consistent with the experimental results. The present study can reveal the failure mechanism of soft-hard interbedded rock mass at the bottom of the tunnel under the action of large horizontal stress after excavation.

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part II, Pipes subjected to bending moment

If cracks are detected in power plant pipes and the cracks are allowable, the plants can continue operating without the need for repair/replacement. The allowability of cracks is determined by means of allowable stresses, based on failure stresses. Failure bending stress at crack penetration is estimated by applying the Local Approach of Limit Load Criteria, which is based on the net-section stress approach. Using the stress at crack penetration, the allowable bending stress can be calculated for a pipe with a circumferential part-through crack. The allowable bending stress decreases with increasing crack depth and angle, as expected. However, the allowable bending stress can have one of three characters, depending on crack size: i) leak-before-break (LBB) and crack growth stability, ii) non-LBB and crack growth stability, and iii) non-LBB and crack growth instability. Character iii) represents a severe crack, and special attention needs to be paid to such a crack, even if it is allowable. Frequent non-destructive inspection and precise calculation of subcritical crack growth are recommended in order to prevent unexpected failure, especially for small-diameter thin-walled pipes. The boundaries of leak-before-break and crack growth stability can be successfully expressed by appropriate equations.

J - Integral Tearing Modulus Analysis for Cracked Plates under Biaxial Bending.(Dept.M)

This paper presents a J - integral - tearing modulus analysis for thick plates containing uniform through cracks and subjected to biaxial bending stresses. The solutions are derived for various crack length ratios and applied stress conditions. They are useful for predicting stability of crack propagation in plates with limited plasticity in the vicinity of crack tip. The results are then applied to a carbon steel plate to predict the onset of crack growth instability. Similar applications may be made for other materials, plate geometry and stress conditions.

Damage tolerant analysis of corner cracks in small nozzle process penetration of the CAREM-25 reactor pressure vessel

This paper presents a damage tolerant approach assessment of corner cracks in small nozzle process penetrations in the pressure vessel of the small modular reactor CAREM-25 subjected to mechanical and thermal shock loadings during certain operation events. Fracture mechanics analyses were performed following ASME XI guidelines considering a representative geometry and specific loading conditions. Stress distributions in the uncracked component were calculated by finite element techniques, while fracture driving forces were estimated using closed form solutions. Maximum allowable corner crack sizes were calculated using linear elastic fracture mechanics and failure assessment diagram (FAD) approaches. The onset of stable crack growth and crack instability were considered as failure conditions. Additionally, fatigue crack growth estimations during the service life were performed integrating a Paris law up to the maximum allowable crack sizes. The results indicate that it seems unlikely that pre-existing cracks reach allowable sizes during the reactor's service life.

Failure Mechanism of Brass with Three V‐Notches Characterized by Acoustic Emission in In Situ Three‐Point Bending Tests

The purpose of this study is to characterize the V pre‐notched specimens with different relative depth ratio and the relative distance ratio by the AE signals in in situ three‐point bending tests. Simultaneously, during the bending process, the V pre‐notched specimen is in situ monitored by the opto‐digital microscope. In order to analyze the depth of V‐notch and the distance between the side V‐notches and the middle V‐notch effect on the specimens, a finite element analysis model is built by ABAQUS. Combining the in situ images, the AE signals and the finite element analysis (FEA) results, it is found that the experiment results are consistent with the FEA results. It is demonstrated that the amplitude of AE signals can effectively characterize the crack initiation, crack growth, and crack fast instability fracture.

Analysis of the various processes downstream cathodic hydrogen charging, IV: detailed mechanism of sulfide stress cracking

The diabolic subtlety of the SSC mechanism is that for its occurrence on a smooth surface, crack initiation actually requires a superficial compressive strain, in order to get exactly the same combination of shear strain, dislocation glide and hydrogen drag as what is explained by fracture mechanics for a notch. This compressive strain is produced by the universal contraction induced by any tensile stress in the perpendicular direction, expressed by Poisson’s ratio, but never accounted for in simplified 1D or 2D calculations, whereas the hydrogen drag is much more powerful when it is directly fed by the raw charging flux in the few cropping out grains with the appropriate orientation. This new “evidence” results from a holistic approach analysing all the numerous questions remained unanswered since 70 years, and previously listed in Part III. Consequently, they were all explained, and to begin with, the basic relationship between SSC sensitivity and high strength or high hardness. It also occurs that the actually four stages of crack nucleation, crack growth, crack propagation and final instability have already been experimentally confirmed by acoustic emission. A new SSC severity diagram is finally proposed, both safer and less conservative than that of ISO 15156.

Crack growth instability studied by the strain energy density theory

The strain energy density theory has successfully been used to address the problem of material damage and structural failure in problems of engineering interest. The theory makes use of the strain energy density function, dW/dV, and focuses attention in its stationary values. The directions of crack growth and yielding are determined from the minimum and maximum values of dW/dV, respectively, along the circumference of a circle centered at the point of failure initiation. Failure by crack growth or yielding takes place when these values of dW/dV become equal to their critical values which are material constants. In the present work the basic principles of the strain energy density theory were reviewed. Furthermore, this theory was used to study three problems of structural failure, namely the problem of slow stable growth of an inclined crack in a plate subjected to uniaxial tension, the problem of fracture instability of a plate with a central crack and two notches, and the problem of unstable crack growth in a circular disc subjected to two equal and opposite forces. The results of stress analysis were combined with the strain energy density theory to obtain the whole history of crack growth from initiation to instability. A length parameter was introduced to define the fracture instability of a mechanical system. Fracture trajectories were obtained for fast unstable crack propagation.

Crack growth instability studied by the strain energy density theory

Crack growth instability studied by the strain energy density theory

Self-similarity and crack growth instability in the correlation between the Paris’ constants

In this note the question about the existence of a correlation between the parameters C and m of the Paris’ law is re-examined. According to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter C to m and to the governing variables of fatigue is derived. Then, from the observation that the Griffith–Irwin instability must coincide with the Paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. A fair good agreement is found between the proposed theory and extensive experimental data.

107 熱弾性効果に起因する温度勾配下における一方向き裂成長の不安定性(OS3-2,OS3 実験力学と可視化技術,学術講演)

107 熱弾性効果に起因する温度勾配下における一方向き裂成長の不安定性(OS3-2,OS3 実験力学と可視化技術,学術講演)

Stability of crack fronts under Griffith criterion: a computational approach using integral equations and domain derivatives of potential energy

This paper deals with the numerical study of stability and instantaneous extension of cracks under Griffith criterion, within the classical linear fracture mechanics framework. First- and second-order domain derivatives of the potential energy W in crack extensions play a central role in the mathematical formulation of such situations. The proposed solution strategy (called the θ-integral method, by reference to the FEM-based θ-method) possesses the following main characteristics: (i) it is based on a symmetric Galerkin boundary integral formulations; and (ii) explicit expressions for the domain derivatives of W are established using Lagrangian formulas (so that the derivations do not increase crack front singularities). The numerical solution procedure for the extension velocity problem, including all domain derivative evaluations, is entirely supported by the boundary element mesh of the current crack configuration; numerical differentiation is avoided. Numerical examples for an isolated crack in a 3-D unbounded elastic body show that in practice an excellent accuracy can be achieved for the energy release rate, the second-order domain derivatives of W and the prediction of stability or instability of crack growth.

Effect of inertial loadings on the criterion for stable growth of a crack in a piping system

In the research on the effect of circumferential cracks in piping, the International Piping Integrity Research Group (IPIRG) has shown that inertial loadings are more conducive to crack growth instability than displacement controlled loadings. In applying the results to an an actual piping system that is subjected to a seismic event, when both types of loading occur simultaneously, it was inferred that the two types of loading are likely to behave differently as regards unstable crack growth leading to a double-ended guillotine pipe break. However, it is important to appreciate that the two configurations used in experiments of separate effects are completely different; displacement-controlled loadings were simulated by displacement-controlled four-point bending, while inertial loadings were simulated by actuating a beam with masses at its free ends. This latter situation is particularly susceptible to instability and is not reproducible in a piping system that is built-in at its end points. The present paper argues that, with an actual piping system and provided the deformation at the cracked section proceeds primarily by bending, then the two types of loading can be treated in the same way, as regards their effects on the crack growth stability criterion.

Tearing modulus analysis for cracked plates under biaxial bending

This paper presents a tearing modulus analysis for thick plates containing uniform through cracks and subjected to biaxial bending stresses. The solutions are derived for various crack length ratios and applied stress conditions. They are useful for predicting stability of crack propagation in plates with limited plasticity in the vicinity of the crack tip. The results are then applied to a carbon steel plate to predict the onset of crack growth instability. Similar applications may be made for other materials, plate geometry and stress conditions. A set of design curves, which predict the critical crack length which corresponds to a given loading condition, is presented.

Bi-parametric criterion applied to brittle and quasi-brittle fracture

The bi-parametric criterion applied to mixed mode brittle and quasi-brittle fracture is based on the principle that the initiation of crack growth instability occurs when the maximum value of strain energy density, evaluated along the initial elastic-plastic boundary around the crack tip, is equal to the elastic component of the specific fracture energy in the uniaxial tension test for the smooth specimen. Therefore the crack initiation depends not only on the fracture toughness K Ic but also on the parameter ω when the inelastic deformation ahead of the crack tip before fracture is considered. ω is the ratio of fracture stress to yield strength.

Displacement control crack-growth instability in an elastic-softening material

The paper formulates a general criterion for the displacement control instability of a crack in an elastic-softening solid, with attention being focused on the situation where the softening zone size is small in relation to the solid's characteristic dimension. The instability criterion is expressed in terms of the material's softening behaviour and the solid's geometrical parameters

Displacement control crack-growth instability in an elastic-softening material

The criterion for crack growth instability in an elastic-softening material that is subjected to displacement control loading conditions is examined. A theoretical analysis of the model of a solid containing two symmetrically situated deep cracks and with tensile loading of the remaining ligament, defines the criterion for crack growth instability. The criterion is expressed in terms of the material's softening characteristics and the solid's geometrical parameters. The analysis covers the complete spectrum of material behaviour from the case where the softening zone is very small to the case where instability does not occur until the softening zone traverses the ligament between the crack tips.

Displacement control crack-growth instability in an elastic-softening material

The criterion for a cusp catastrophe type of crack-growth instability in an elastic-softening material that is subjected to displacement control loading conditions has been investigated. Attention was focused on the behaviour of a material whose softening-zone size was very small in comparison with a solid's characteristic dimensions, because this facilitates a simple linear elastic analysis. Special consideration was given to the behaviour of an edge-cracked solid that was subjected to bending deformation, and the results complement those obtained by Carpinteri, who analysed the behaviour of an elastic-softening material which had a very large softening-zone size.

Tearing stability analysis of an axial surface flaw in thick-walled pressure vessels

This paper presents two fracture mechanics models for evaluation of an axial surface flaw in pressure vessels. The surface flaw is located on the outside surface of the vessel. The first model assumes yielding of the remaining ligament directly ahead of the flaw. The second model assumes contained yielding ahead of the flaw and uses a linear elastic fracture mechanics solution. The former model is suitable for cases where the combination of material toughness, flaw size, and load is such that initiation of flaw growth follows ligament yielding. The latter model is suitable for low-toughness materials where initiation of crack growth and potential tearing instability may occur prior to the yielding of the ligament. Both models are suitable for thick-walled vessels. The paper discusses the applicability regime for both models. The models are then applied to a test vessel and the predicted failure pressure is compared against the pressure attained in the test. Results show that both models can be applied successfully. In particular, the contained yielding model when used with the plane-stress assumption can give reasonable predictions even for cases that involve yielding of the ligament.

The instability of circumferential crack growth in pipes—V. The effect of multiple restraints on the instability criterion

This paper presents the results of a study of the effect of multiple restraints on the instability of growth of a through-wall circumferential crack in a pipe that is subjected to bending deformation. Particular attention is focussed on the way in which the effects of multiple restraints are coupled, and how they are beneficial with regards to the stability of circumferential crack growth.