Crack Interaction Research Articles

Interactions of cracks and inclusions in homogeneous elastic media

The work is devoted to static problems of elasticity for an infinite homogeneous medium containing planar parallel cracks and heterogeneous inclusions of arbitrary shapes. Cracks and inclusions occupy a finite region of the medium that is subjected to arbitrary external forces. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for the stress tensor in the region. Gaussian approximating functions are used for discretization and efficient numerical solution of this system. Such functions are centered at the nodes of a regular node grid that covers all the inclusions and the crack surfaces. For Gaussian functions, the elements of the matrix of the discretized system have forms of standard integrals that can be tabulated and calculated fast. The matrix of the discretized system is not sparse but it has Teoplitz’s structure, and the number of independent matrix elements is much smaller than the total number of the elements. In addition, fast Fourier transform technique can be used for calculation matrix-vector products with such matrices. It accelerates substantially the process of iterative solutions of the discretized system. The method is mesh free. Examples of numerical solutions of the problems for planar circular cracks and spherical inclusions are presented and compared with analytical and numerical solutions available in the literature.

Analysis of Microdamage in Thermally Aged CF/Polyimide Laminates

Microdamage in the layers of CF Thornel® T650 8-harness satin-weave composites with a thermosetting NEXIMID® MHT-R polyimide resin, designed for high service temperatures, is analyzed. After cooling down to room temperature (RT), a multiple intrabundle cracking due to tensile transverse thermal stresses was observed in the [(+45/–45)/(90/0)]2s laminates studied. Then, the composite was subjected to two ramps of thermal cycling quantifying the increase in crack density in its layers. A comparison of two ramps with the same lowest temperature showed that the highest temperature in the cycle where thermal stresses were low had a significant detrimental effect on the thermal fatigue resistance of the composite. The effect of holding it at 288°C for 40 days was also studied: many new cracks formed in it after cooling down to RT. During the time at the high temperature, the mechanical properties degraded with time, and the crack density versus aging time was measured at RT. Then, both aged and nonaged specimens were tested in uniaxial quasi-static tension quantifying the damage development in layers of different orientation. Cracking in the layers was analyzed using fracture mechanics arguments and probabilistic approaches: a) a simple one, not considering crack interaction; b) Monte Carlo simulations. It is shown that cracking in the off-axis layers which are not in contact with the damaged 90°-layer can be predicted based on the Weibull analysis of the 90°-layer, whereas in the off-axis layer contacting the 90°-layer, the crack density is much higher due to the local stress concentrations caused by cracks in the 90°-layer. The thermal treatment degraded the cracking resistance in the surface and adjacent layer, whereas the composite close to the midplane was not changed.

Elastic-plastic fracture response of multiple 3-D interacting cracks in offshore pipelines subjected to large plastic strains

Multiple cracks may be initiated in offshore pipelines due to imperfect manufacturing processes. Under complicated loading conditions, small closely cracks can grow and coalesce into a large one that may pose threats to the integrity and safety of the structures. One of the severe loading conditions is the large strain-controlled loading which exceeds the yield stress considerably. In this case, the existing codes such as the BS7910:2013 code will not be accurate in providing the failure assessment for re-characterized multiple cracks since they are derived based on the load-controlled method. Therefore, this study focuses on the nonlinear elastic-plastic fracture responses of a flawed pipeline with the interactions of a circumferential semi-elliptical surface crack and an elliptical embedded crack under the large plastic strains. It systematically explores the influence of the crack parameters and makes the comparison with the BS7910:2013 code. New strain-based CTOD estimation schemes are proposed with a user-friendly flowchart that could be helpful to easily perform the failure assessment of the 3-D multiple cracks in offshore pipelines.

A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

Failure of brittle materials containing embedded three dimensional pre-cracks and subjected to uniaxial compressive and tensile loading is considered here. The sliding crack (wing-crack) model of Ashby and Sammis (1990) is extended and further developed to formulate a 3D anisotropic continuum damage model.First, a frictional sliding condition of pre-cracks is formulated in three dimensions and a crack interaction function is proposed. To introduce inelastic strains due to cracking, crack opening displacements are derived from Castigliano's second theorem. Finally, a strain–stress relation is obtained from the Gibbs energy density equation.The model was implemented in Abaqus/Explicit finite element software. Material inhomogeneity was considered assuming that the pre-cracks are lognormally distributed between integration points.While testing the proposed model against experimental results of granular ice, the numerical simulations were in good agreement both under uniaxial compression and tension as a function of grain size and temperature-dependent kinetic friction. The model was able to predict qualitatively and quantitatively the brittle failure modes and strength both under compression and under tension. Due to the modelled inhomogeneity, the scatter in simulated strengths corresponded to that of the test results. Besides non-simultaneous and non-uniform damaging, the model revealed important phenomena observed during the experiments; e.g. under compression the sliding of the pre-cracks resembled “stick-slip” motion, and secondary cracks were observed to grow in a jerky manner. The effect of specimen end conditions on both the failure stress and failure mode was addressed in the simulations.

Lattice Element Models and Their Peculiarities

This paper presents the lattice element models, as a class of discrete models, in which the structural solid is represented as an assembly of one-dimensional elements. This idea allows one to provide robust models for propagation of discontinuities, multiple cracks interaction or cracks coalescence. Many procedures for computation of lattice element parameters for representing linear elastic continuum have been developed, with the most often used ones discussed herein. Special attention is dedicated to presenting the ability of this kind of models to consider material disorder, heterogeneities and multi-phase materials, which makes lattice models attractive for meso- or micro-scale simulations of failure phenomena in quasi-brittle materials, such as concrete or rocks. Common difficulties encountered in material failure and a way of dealing with them in the lattice models framework are explained in detail. Namely, the size of the localized fracture process zone around the propagating crack plays a key role in failure mechanism, which is observed in various models of linear elastic fracture mechanics, multi-scale theories, homogenization techniques, finite element models, molecular dynamics. An efficient way of dealing with this kind of phenomena is by introducing the embedded strong discontinuity into lattice elements, resulting with mesh-independent computations of failure response. Moreover, mechanical lattice can be coupled with mass transfer problems, such as moisture, heat or chloride ions transfer which affect the material durability. Any close interaction with a fluid can lead to additional time dependent degradation. For illustration, the lattice approach to porous media coupling is given here as well. Thus, the lattice element models can serve for efficient simulations of material failure mechanisms, even when considering multi-physics coupling. The main peculiarities of such an approach have been presented and discussed in this work.

Evaluation of multiple cracks interaction effect subjected to biaxial tension under creep regime

Under creep regime, the multiple cracks would remarkably deteriorate the service life of the component with respect to the case of a single crack due to the higher C* values induced by the interaction and coalescence of the adjacent cracks. In this paper, the creep interaction effect of two identical coplanar surface flaws in a plate subjected to biaxial tension loads were calculated under various crack configurations, creep properties and biaxial stress ratios. The results revealed that the creep interaction level was greatly dependent on crack depth, crack distance, creep exponent and biaxial stress ratio whereas crack shape had little influence. In addition, the creep interaction factor determined by the average C* values along the crack front could better represent the multiple cracks interaction under biaxial stress state. Finally, an empirical equation for the creep interaction factor was established on the basis of the comprehensive finite element analyses and the size of the equivalent single crack replacing the interacted multiple cracks should be determined by the creep interaction factor.

Application of the second mixed boundary value solution for an interaction of an edge crack and an internal crack of a half plane subjected to uniform traction

The purpose of the present paper is an application of the solution of the second mixed boundary value problem for a doubly connected region with symmetry. As a demonstration, a half plane with an edge and internal cracks in the axis of symmetry subjected to the uniform traction is analyzed. The analytical stress function can be derived; therefore, it is easy to calculate stress distribution and stress intensity factor. The stress distribution is depicted. The stress intensity factors are precisely calculated and are investigated for the crack extension.

Special issue on interaction of multiple cracks in materials—Volume 1 and 2

Special issue on interaction of multiple cracks in materials—Volume 1 and 2

Interactions of double slanted cracks under mode I loading

This paper presents numerical analysis of double slanted central cracks in square plates under mode I tension stress. ANSYS finite element program is used to model and solve the problem of slanted cracks where the stress intensity factor is determined according to J-integral approach. Three relative crack length, a/W = 0.1, 0.2 and 0.3 is used while relative spacing between the cracks, s/2a are ranged between 0.1 to 0.6. In order to study the roles of slanted cracks on the stress intensity factor, several slanted angles are used such as 0°, 15°, 30°, 45°, 60° and 75°. According to the numerical analysis, all parameters above played an important role in determining the stress intensity factors. As expected, longer crack produced higher stress intensity factor. For the cracks with a/W ≤ 0.2, insignificant crack interaction is observed however when crack reached a/W=0.3, the interaction is gradually increased. Increasing the slanted angles slightly increased the interaction factor however the effect of relative crack spacing became insignificant.

Interaction factors for two elliptical embedded cracks with a wide range of aspect ratios

The value of stress intensity factor may be increased through the interaction of multiple cracks that are in close proximity to one another. We investigated the interaction factors of two equal elliptical cracks with a wide range of aspect ratios. Finite element analysis for a linear elastic solid was used to obtain the interaction factor for embedded cracks in an infinite model subjected to remote tension loading. Relationships between interaction factors and dimensionless distances between the cracks were discussed. The results demonstrated that the interaction factors depend on the crack aspect ratio, whose effect is related to the dimensionless distance. Thus, it is suggested that interaction factors can be reasonably characterized using different dimensionless distances depending on the aspect ratio. Finally, we provide a simple empirical formula for obtaining the interaction factors for embedded cracks.

Multiple crack initiation and propagation in weldments under fatigue loading

The work aims at addressing the modelling and implementation of criteria for multiple crack propagation, including interaction and coalescence, for a more reliable fracture mechanics-based prediction of stress-life curves for weldments.A large experimental work is presented in which micro-cracks have been made visible by heat-tinting at successive stages of fatigue life of the welded specimens. Here the correlation between the number of initiation sites and the applied stress level has been also investigated.The criteria have been implemented in in-house software, which allows multiple fatigue crack propagation, and validated against selected experimental tests. The results have shown that the modelling of multiple crack propagation and interaction is crucial for the prediction of the fatigue strength of weldments, both in finite and infinite life regime.

A computational framework for modelling impact induced damage in ceramic and ceramic-metal composite structures

When ceramic or ceramic-metal composite structures are subjected to impact loading, they undergo various deformation phases such as plastic yielding, pulverization, fragmentation, tensile spalling, interface debonding, penetration etc. In order to study these phenomenological characteristics and produce insightful observation, numerical simulation is inevitable. Apart from reasonably accurate constitutive model, a numerical scheme must also accommodate any possible loss (in the case of fragmentation and material separation) of the continuum nature of the problem domain. This is generally difficult to achieve through mesh-based methods. In this study a computational framework based on smoothed particle hydrodynamics (SPH), a particle-based method, is explored and revamped. Damage growth and localized cracks are modelled through a pseudo-spring analogy, wherein particle-interactions are modulated based on material strength reduction after damage initiation. Different material models are coupled in this analogy for investigating different paradigms of penetration mechanics in ceramic and ceramic-metal composites. The computational framework is first validated through experimentally obtained results of flyer plate tests on Silicon Carbide (SiC) disc. Subsequently the framework is explored in simulating more complex failure mechanisms involving multiaxial crack interaction and fragmentation in ceramic-metal composite target system.

Invariant integrals of crack interaction with an inhomogeneity

The crack growth can be shielded or anti-shielded by a specific inhomogeneity occurring in materials. This can be estimated from the change of the crack tip invariant Jk-, M-, L-integrals due to the presence of inhomogeneity. The closed-form solutions of the change of invariant integrals are derived for a crack interacting with the near crack-tip inhomogeneity by using the concept of material configurational forces. Two simple problems such as a phase transformation or an inhomogeneous inclusion interacting with a main crack in two-dimensional solids are solved in explicit form. The present formulations and methods are validated by the alternative weight functions or finite element analysis. It is concluded that the total components of configurational forces given by integration over the inhomogeneity can be used to evaluating the shielding or anti-shielding effect of various inhomogeneities e.g., inclusion, plasticity, dislocation, phase transformation, residual strain, on the crack growth in fracture mechanics.

Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM

The present work aims at saving computational cost of multiscale simulation on major crack/minor crack interaction problems. The multiscale extended finite element method (MsXFEM) used for the numerical simulation is developed on multiscale projection technique which enables different scale decomposition, and transition of field variables between different scales. Both macroscale and microscale problems are solved independently and alternatively, in the framework of XFEM. The improvement made in this paper is to employ corrected XFEM on the macroscale level, so that a more accurate boundary condition can be obtained for the microscale problem. The modification leads to a reduced necessary microscale domain size, meanwhile a solution of higher accuracy and enhanced convergence rate can be achieved. The numerical examples of minor cracks near a major one are studied, which show that the effect of minor cracks on major crack can be efficiently captured.

Multiscale characterization of White Etching Cracks (WEC) in a 100Cr6 bearing from a thrust bearing test rig

A common cause for premature bearing failures in wind turbine gearboxes are the so-called White Etching Cracks (WEC). These undirected, three-dimensional cracks are bordered by regions of altered microstructure and ultimately lead to a cracking or spalling of the raceway. An accelerated WEC test was carried out on a FE8 test rig using cylindrical roller thrust bearings made of martensitic 100Cr6 steel. The resulting WECs were investigated with several characterisation techniques. Ultrasonic measurements showed the WEC were mainly located in the region of the overrolled surface in which negative slip occurs, which agrees with hypotheses based on an energetic approach for a prognosis. SEM orientation contrast imaging of the area around WEC revealed an inhomogeneous structure with varied grain sizes and a large amount of defects. Microstructure characterization around the WEA using EBSD showed significant grain refinement. Atom probe tomography showed the microstructure in the undamaged zone has a plate-like martensitic structure with carbides, while no carbides were detected in the WEA where the microstructure consisted of equiaxed 10nm grains. A three dimensional characterisation of WEC network was successfully demonstrated with X-ray computerized tomography, showing crack interaction with unidentified inclusion-like particles.

Multiscale GFEM with superposition of crack enrichment functions driven by finite fracture mechanics: Theory, first computation and open problems

This work presents a direct extension of the multiscale GFEM (MS-GFEM) where damage and fracture mechanisms are now taken into account. Using a pattern-based description of the microscale, the construction of the model falls into two main parts: the modeling of a multiphase composite yarn, and the modeling of crack events inside the microstructure. The classical difficulties associated with the implementation and computation cost of the GFEM are dealt through a multiscale approach based on the Saint–Venant principle. This multiscale vision enables the microstructure and the microkinematics to be handled on the scale of the pattern independently of the macroscale discretization. Additionally, numerical enrichment functions are superimposed between the existing enrichment functions in a local computational domain. These enrichment functions deliver accurate solutions of crack interactions among local features, like inclusions, voids, etc, and are specifically appealing to evolution type problems like the crack events defined under the finite fracture mechanics framework. Different crack patterns can be introduced at different positions in the global domain when certain fracture criteria are met. The multiscale approach is implemented inside the finite element software Cast3M in order to use the existing infrastructure of the object oriented code for the development of MS-GFEM.

Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach

This article presents a parallel algorithm to model the nonlinear dynamic interactions between ultrasonic guided waves and fatigue cracks. The Local Interaction Simulation Approach (LISA) is further developed to capture the contact-impact clapping phenomena during the wave crack interactions based on the penalty method. Initial opening and closure distributions are considered to approximate the 3-D rough crack microscopic features. A Coulomb friction model is integrated to capture the stick-slip contact motions between the crack surfaces. The LISA procedure is parallelized via the Compute Unified Device Architecture (CUDA), which enables parallel computing on powerful graphic cards. The explicit contact formulation, the parallel algorithm, as well as the GPU-based implementation facilitate LISA’s high computational efficiency over the conventional finite element method (FEM). This article starts with the theoretical formulation and numerical implementation of the proposed algorithm, followed by the solution behavior study and numerical verification against a commercial finite element code. Numerical case studies are conducted on Lamb wave interactions with fatigue cracks. Several nonlinear ultrasonic phenomena are addressed. The classical nonlinear higher harmonic and DC response are successfully captured. The nonlinear mode conversion at a through-thickness and a half-thickness fatigue crack is investigated. Threshold behaviors, induced by initial openings and closures of rough crack surfaces, are depicted by the proposed contact LISA model.

WITHDRAWN: Computational modeling of fracture in rock using an improved cracking particles method

Computational modeling of fracture in rock remains a challenging problem. The interaction between existing faults and emerging cracks is one difficulty which does not exist in other man-made materials. In this study, I present an approach which can handle interacting cracks in a natural manner. This method belongs to the class of cracking particle method. The fracture surface is described by a set of crack segments that pass the domain of influence. The representation of the crack surface is hence extremely simple and crack interactions are a natural outcome of the simulation. No additional criteria as in the extended finite element method or cohesive element method is needed. While the original cracking particle method, the crack path is discontinuous, I present an efficient and simple improvement so the crack path can be nearly continuous. This improvement can be implemented with ease in any existing cracking particles code.

Vzaimodeystviya treshchin v uprugom bimateriale pod deystviem antiploskogo sdviga

Vzaimodeystviya treshchin v uprugom bimateriale pod deystviem antiploskogo sdviga

The Combination of Probabilistic Method and Fracture Mechanics Model in Multiple Cracks Analysis

Probabilistic method and fracture mechanics model were combined to analysis the failure probability of structure with multiple site cracks. Comparing the result with probabilistic model showed that, accounting the actual failure mode and the interaction of cracks, combination of probabilistic method and fracture mechanics model get better approaching to determine failure probability during structural integrity analysis.