Crack Interaction Research Articles

Crack Propagation Through Interfaces in a Borosilicate Glass and a Glass Ceramic

Dynamic crack propagation across an adhesive interface in a borosilicate glass and a glass ceramic was studied to understand the interactions of cracks with the interface. Specimens were manufactured by attaching a notched plate to a rectangular plate using an epoxy adhesive. A plastic projectile was impacted on the notched edge to initiate a single crack at the notch tip in the first plate. The propagation of the crack in the first plate and the crack patterns after the interface in the second plate were recorded using a high‐speed camera. For borosilicate glass, a single crack propagated to the adhesive interface and arrested for a certain time. Cracks re‐initiated in the second plate, and crack patterns were observed to depend on the thickness of the adhesive interface. The crack developed a higher number of branches, and the branching angle increased as the interface thickness was increased. For the glass ceramic, the notch‐initiated crack branched in the first plate and did not penetrate through to the second plate regardless of the various adhesive thicknesses studied.

Behavioral Simulation Model for SFRC and Application to Flexural Fatigue in Tension

A fatigue behavioral simulation for steel fiber reinforced concrete (SFRC) subjected to high cycle repetition of loads is presented. The fatigue constitutive models for normal strength concrete developed in the past decades are extended to those for SFRC with regard to tension, compression and shear transfer along dispersed cracking. The hysteretic path-dependency of SFRC is extensively focused on as well as post-cracking tension softening, because it greatly affects the stress-strain amplitudes of SFRC inside structures. The interaction of multi-directional cracks is taken into account based upon the fixed crack approach for enabling the damage evolution under the principal stress rotation. The rate effect on the stress and strain relation is also formulated to take into account the nonlinearity related to both loading rates and numbers of cycles. These proposed models for SFRC are experimentally verified in view of S-N diagrams of flexural tension for practical use.

Multiple Crack Interactions in Bi-Material Plates under Mode I Tension Loading

The solution of stress intensity factor (SIF) for central edge crack embedded in bi-material plate can be found in open literature. Instead of a single edge crack, some researches on the multiple crack problems can also be found. However, the solutions of SIFs for multiple edge cracks in bi-material plates are difficult to obtain. In this paper, such problems are solved numerically using ANSYS finite element program. There are three important parameters that are used namely, relative crack depth, a/W, relative offset distance, b/h and modulus ratio, E1/E2. Both materials are assumed to be perfectly bonded and fulfill the plain strain condition. It is found that all variables used play an important role in determining the SIFs. However, when b/h is large enough, it has no significant effect on the SIF where it converged to an almost single value. The same situation does not occur for mode II SUFs where the SIFs diverged when the parameters used are increased.

Improved Probabilistic Remaining Useful Life Estimation in Structures: Modeling Multi-site Fatigue Cracking in Oil and Gas Service Structures

The purpose of this research is to develop a multi-site damage probabilistic life prediction model that could be used to assess the integrity of engineering structures susceptible to fatigue in presence of neighboring cracks. Both experiments and simulation were used to produce the data required for the model development. The experiments were performed to investigate the interaction of two adjacent semi-elliptical cracks under cyclic loading. A series of tests at different loads and for different crack aspect ratios were conducted under uniaxial constant amplitude fatigue loads on API-5L grade B steel samples. Crack growth rate of two initial semi-elliptical cracks was investigated both on the sample surface and in the depth direction. Moreover, Crack growth and interaction was investigated using a simulation technique that incorporates the stress intensity factor of a single crack with an existing cracks interaction correction factor models from the literature. Finally, a Bayesian inference modeling technique is adopted to estimate the life prediction model parameters, assess any model bias and uncertainty and validate it.

A probabilistic method for determining the volume fraction of pre-embedded capsules in self-healing materials

Autonomous healing of cracks using pre-embedded capsules containing healing agent is becoming a promising approach to restore the strength of damaged structures. In addition to the material properties, the size and volume fraction of capsules influence crack healing in the matrix. Understanding the crack and capsule interaction is critical in the development and design of structures made of self-healing materials. Assuming that the pre-embedded capsules are randomly dispersed we theoretically model flat ellipsoidal crack interaction with capsules and determine the probability of a crack intersecting the pre-embedded capsules i.e. the self-healing probability. We also develop a probabilistic model of a crack simultaneously meeting with capsules and catalyst carriers in two-component self-healing system matrix. Using a risk-based healing approach, we determine the volume fraction and size of the pre-embedded capsules that are required to achieve a certain self-healing probability. To understand the effect of the shape of the capsules on self-healing we theoretically modeled crack interaction with spherical and cylindrical capsules. We compared the results of our theoretical model with Monte-Carlo simulations of crack interaction with capsules. The formulae presented in this paper will provide guidelines for engineers working with self-healing structures in material selection and sustenance.

Theoretical and experimental study of fatigue growth of interacting cracks

Life assessment of structures weakened by interacting cracks represents an important and very challenging problem. Subsequently, the main objective of this paper is to address this problem by developing a new computational technique. It is based on the classical strip-yield model and plasticity-induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle-by-cycle calculations of the effective stress intensity factors and crack increments. The modelling results are validated against an experimental study focusing on fatigue behaviour of two closely spaced collinear cracks in wide plates with different thicknesses. It is confirmed that non-linear effects associated with crack interaction have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components.

On the effect of interactions of inhomogeneities on the overall elastic and conductive properties

A simple method of estimating the effect of inhomogeneity interactions on the overall properties (elastic and conductive) is developed. It is formulated in terms of property contribution tensors that give the contribution of an inhomogeneity to the overall properties. The method can be viewed as further development of the approach of Rodin and Hwang (1991) and Rodin (1993) that generalized the method of analysis of crack interactions (Kachanov, 1987) to inhomogeneities. We also extend the method to the conductive properties. Considering the effect of interactions on the property contribution tensors on the example of pores we find that this effect is generally moderate, at most (even when pores touch one another) – in contrast with the effect on local fields. On example of two spheres, we compare the interaction effects on the elastic and the conductive properties, and discuss the impact of interactions on the cross-property connections.

Numerical and analytical investigation on the dynamic buckling behavior of glass columns under blast

Current applications in buildings of structural glass elements often require design rules and formulations able to provide acceptable predictions for phenomena complex to describe, which generally depend on combination of several geometrical and mechanical aspects. The estimation of the buckling resistance of glass elements, for example, represents a topic of large interest for researchers, due to typical high slenderness ratios, limited tensile strength and brittle material behavior. In the paper, the buckling response of glass columns under impulsive orthogonal pressures (e.g. blast) and combined static compressive vertical loads (e.g. gravity loads or further service loads) is investigated. The dynamic buckling behavior of columns in out-of-plane bending is primarily analyzed. Advanced numerical nonlinear dynamic simulations are then performed on various laminated columns, by means of 3D numerical FE-models able to take into account the interaction of simultaneous loads and possible glass cracking. Analytical calculations are also carried-out by means of single-degree-of-freedom (SDOF) formulations derived from structural dynamics theories, in order to properly estimate blast and second-order effects on maximum deflections and corresponding tensile stresses. Finally, based on the rather good correlation generally found between numerical and analytical calculations, a design approach is proposed for practical estimation of buckling strength of glass elements in the analyzed loading and boundary conditions.

Percolation of the interacting elastic stress fields of aligned cracks as an alternative explanation of critical crack densities

Abstract The concept that the lithosphere is in a general critical, or near-critical, mechanical state has previously assumed spatial intersection of fractures at the critical point. This paper provides an initial basis for an alternative mechanism in which elastic interactions between aligned, open, spatially separated (micro-)cracks in rock can, by themselves, lead to a continuous phase change at a critical threshold of crack density lower than that required for crack coalescence. The existence of a critical density of aligned cracks is first demonstrated on a regular 2D hexagonal grid when subjected to a central stress perturbation; at this critical density the elastic tensile stress interactions have a long-range effect. From the results of those calculations an approximation of the tensile stress field around a crack in 3D is provided. The percolation behaviour of such 3D bodies is discussed and a critical crack density in 3D for elastic interaction of 0.035 is deduced. This falls within the range of crack densities (0.015–0.045) interpreted from observations of shear-wave splitting in many different rocks. The possibility that critical crack interactions can be mostly elastic provides one explanation of the long-range nature of correlations in flowrate fluctuations in oilfields without large-scale seismicity.

New Stress Activation Method for Kerfless Silicon Wafering Using Ag/Al and Epoxy Stress-Inducing Layers

The SLIM-cut technique provides a way to obtain thin silicon foils without a standard sawing step, thus avoiding kerf losses. This process consists of three steps: depositing a stress-inducing layer on top of the silicon surface; stress activation by heating and cooling, resulting in crack propagation in the silicon and detachment of a thin silicon layer; and a chemical cleaning to remove the stress-inducing layer. This paper describes a new stress activation method using Ag/Al and epoxy stress-inducing layers. The crack propagation is controlled along the sample length in order to avoid unwanted additional crack formation and interaction with other crack fronts. Silicon foils with thickness ranging between 50 and 130 μm were obtained with effective lifetimes between 1 and 81 μs.

Fracture development on a weak interface ahead of a fluid-driven crack

This paper is aimed at modelling of mechanical interaction of a fluid-driven crack (FDC) with a weak natural interface in a rockmass. FDC may be thought as a magma-filled crack (dyke) typical for volcanic edifices or as a hydraulic fracture artificially induced in oil and gas bearing reservoirs. The main focus of this study is the investigation of the development of delaminating and shear zone on the interface caused by the stresses produced by the FDC that precede the FDC branching and bifurcation when crossing the interface. The mechanism of generation of a network of the connected open-shear cracks is also discussed on the basis of formulation of the problem for the case when the delamination on the interface occurs over a part of the longer shear crack. The method of complex integral equations is used to study two configurations of the fracture pattern developing ahead of the FDC.

Numerical study on interaction of surface cracking and interfacial delamination in thermal barrier coatings under tension

The interaction of surface cracking and interfacial delamination in thermal barrier coatings under tension is investigated by using a cohesive zone finite element model. It is found that the surface crack density has a significant effect on the initiation and propagation of interfacial delamination. The interfacial delamination length decreases with increase of the surface crack density. The influence of ceramic coating thickness and interfacial adhesion parameters on surface cracking and interfacial delamination is discussed. It is shown that the saturated crack densities decrease with increase of the ceramic coating thickness and interfacial delamination length, and the critical surface crack density without interfacial delamination decreases as the interfacial adhesion energy increases. The results imply that the larger the surface crack density and interfacial adhesion energy are, the less the probability of interfacial delamination.

Distributed non-singular dislocation technique for cracks in strain gradient elasticity

AbstractThe mode III fracture analysis of a cracked graded plane in the framework of classical, first strain gradient, and second strain gradient elasticity is presented in this paper. Solutions to the problem of screw dislocation in graded materials are available in the literature. These solutions include various frameworks such as classical elasticity, and the first strain and second strain gradient elasticity theories. One of the applications of dislocations is the analysis of a cracked medium through distributed dislocation technique. In this article, this technique is used for the mode III fracture analysis of a graded medium in classical elasticity, which results in a system of Cauchy singular integral equations for multiple interacting cracks. Furthermore, the technique is modified for gradient elasticity. Owing to the regularization of the classical singularity, a system of non-singular integral equations is obtained in gradient elasticity. A plane with one crack is studied, and the stress distribution in classical elasticity is compared with those in gradient elasticity theories. The effects of the internal lengths, introduced in gradient elasticity theories, are investigated. Additionally, a plane with two cracks is studied to elaborate the interactions of multiple cracks in both the classical and gradient theories.

Damage and fracture evolution of hydraulic fracturing in compression-shear rock cracks

Compression-shear fractured rock under high pore fluid pressure was studied to determine an appropriate model for describing the Initial Cracking Law and the Evolution Law of the stress intensity factor at the tip of a wing crack. Considering the interaction of wing cracks and the additional stress caused by rock bridge damage, this paper proposes an intensity factor Evolution Equation of multiple rock cracks which combines the action of compression-shear stress and pore fluid pressure. The interaction of multiple wing cracks resulting in rock bridge damage makes the stress intensity factor at the crack tip larger than that of a single wing crack, and wing crack propagation under high pore fluid pressure takes a turn from stable expansion to unstable expansion. Based on the rock fracture mechanics criterion, the damage fracture mechanical models of a compression-shear rock mass are established when the rock bridge happens axial transfixion failure, tension-shear combined failure, or wing crack shear connection failure under the combined action of compression-shear stress and high pore fluid pressure. This theory provides the basis for the quantitative investigation of the hydraulic fracturing process.

Fracture failure in crack interaction of asphalt binder by using a phase field approach

Fracture failure in crack interaction of asphalt binder has always been one serious problem in the pavement industry. In the state of the art research of asphalt cracking, single mode cracking has been studied by many researchers but there lacks theoretical and experimental research on the crack interaction of asphalt binder, which is more reasonable and realistic. The traditional way is to use the Griffith’s theory which is complex and complicated. In this paper, the phase field method (PFM) is presented for modeling, which describes the whole cracking system using a phase-field variable that assumes negative one in the void region (crack) and positive one in the solid region (intact). The fracture toughness is then considered as a material property and modeled as the surface energy stored in the diffuse interface between the intact solid and crack void. The non-conserved Allen–Cahn equation is adopted as the system governing equation to evolve the phase field variable to account for the growth of cracks. The energy based formulation of the phase-field method handles the competition between the growth of surface energy and release of elastic energy of crack interaction in a natural way: the crack propagation is a result of the energy minimization in the direction of the steepest descent. Both the linear elasticity and phase-field equation are solved in a unified finite element frame work, which is implemented in the commercial software COMSOL. Two cracking experiments, namely, direct tension test and double edge notch tension test are then performed for validation. It is discovered that the critical load of crack interaction by PFM agrees very well with both experiment results.

A fatigue crack growth model for interacting cracks in a plate of arbitrary thickness

ABSTRACTFatigue and fracture assessment of structures weakened by multiple site damage, such as two or more interacting cracks, represents a very challenging problem. A proper analysis of this problem often requires advanced modelling approaches. The objective of this paper is to develop a general theoretical approach and investigate the fatigue behaviour of two interacting cracks. The developed approach is based on the classical strip yield model and plasticity induced crack closure concept. It also utilises the 3D fundamental solution for an edge dislocation. The crack advance scheme adopts the cycle‐by‐cycle calculations of the effective stress intensity factors and crack increments. The modelling results were validated against experimental data available in the literature. Further, the nonlinear effects of the crack interaction and plate thickness on the crack opening stresses and crack growth rates were studied with the new approach for the problem geometry. It was demonstrated that the both effects could have a significant influence on fatigue life and cannot be disregarded in life and integrity assessments of structural components with multiple site damage.

An efficient augmented finite element method for arbitrary cracking and crack interaction in solids

SUMMARYThis paper presents an augmentation method that enables bilinear finite elements to efficiently and accurately account for arbitrary, multiple intra‐elemental discontinuities in 2D solids. The augmented finite element method (A‐FEM) employs four internal nodes to account for the crack displacements due to an intra‐elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single bilinear element that employs standard external nodal DoFs only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piece‐wise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A‐FEM's high‐fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous, and heterogeneous solids have been demonstrated through several challenging numerical examples. It is shown that the proposed A‐FEM, empowered by the new elemental condensation procedure, is numerically very efficient, accurate, and robust. Copyright © 2014 John Wiley & Sons, Ltd.

Microstructural Barriers against Fatigue Crack Growth

Fatigue induced fracture is the number one reason for failure of technical systems. However, in the stage of small crack growth grain or phase boundaries lead to a fluctuating crack propagation rate near the obstacle. Sometimes the cracks stop completely for a large number of cycles resulting in an additional number of life time cycles. However, so far it is not clear, what actually determines the resistance of a grain boundary against fatigue cracks. Therefore we developed a systematic experimental technique based on in-situ imaging in the scanning electron microscope and focused ion beam (FIB) crack initiation which gives detailed information on the interaction of short fatigue cracks with microstructural elements. We investigated the mechanisms of crack transmission in the neighbouring grain on the microscopic scale and identified different useful aspects of the interaction between microcracks and microstructural barriers. The 3D-tomographs revealed by serial sectioning an FIB give information about the transition process from one grain to the neighbouring one. The result is a purely geometrical consideration leading to a quantitative description of the blocking effect of grain boundaries on short fatigue crack growth. The results include useful aspects for fatigue life calculation and to make materials more fatigue resistant.

Elastodynamic Interaction of Two Offset Interfacial Cracks in Bonded Dissimilar Media With a Functionally Graded Interlayer Under Antiplane Shear Impact

The impact response of bonded media with a functionally graded interlayer weakened by a pair of two offset interfacial cracks is investigated under the condition of antiplane deformation. The material nonhomogeneity in the graded interlayer is represented in terms of power-law variations of shear modulus and mass density between the dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the crack problem to solving a system of Cauchy-type singular integral equations in the Laplace domain. The crack-tip behavior in the physical domain is recovered through the inverse Laplace transform to evaluate the dynamic mode III stress intensity factors as a function of time. As a result, the transient interaction of the offset interfacial cracks spaced apart by the graded interlayer is illustrated. The peak values of the dynamic stress intensity factors are also presented versus offset crack distance, elaborating the effects of various material and geometric parameters of the bonded system on the overshoot characteristics of the transient behavior in the near-tip regions, owing to the impact-induced interaction of singular stress fields between the two cracks.

Recent efforts toward modeling interactions of matrix cracks and delaminations: an integrated XFEM-CE approach

This paper presents a novel integrated approach using the extended finite element method (XFEM) and cohesive elements (CEs) for modeling three-dimensional (3D) delaminations, matrix cracks, and their interactions in progressive failure of composite laminates. In the proposed XFEM-CE approach, the matrix cracks are explicitly modeled by the XFEM through nodal enrichment and element partition, and the inter-ply delaminations are modeled by cohesive elements through traction–separation law. An XFEM-based cohesive element enrichment scheme is developed in order to properly model the interactions between the delaminations and matrix cracks. It is critical to enrich the cohesive elements at the local juncture where cracks meet, in order to obtain the correct crack path interactions. Examples are presented for failure analysis of double-cantilever-beam and end-notch-flexure laminates with different layups. The results show strong explicit matrix crack–delamination interactions in these laminates. This work presents another significant development of a computational platform for realistic modeling of progressive damage in composites.