Crack Interaction Research Articles

Interaction between interfacial damage and crack propagation in quasi-brittle materials

A thermodynamically consistent phase field formulation for modeling the interactions between interfacial damage and bulk brittle fracture is presented. A regularization scheme is considered for both the interface and the crack phase field. A coupled exponential cohesive zone law is adopted to model the interface which has the contributions of both normal and tangential displacement jump components. A novel nonlocal approach is devised to evaluate the smoothened values of jump at the regularized interface using element-specific geometric information. Such a description of the interface allows a more realistic mechanical response of any composite system in terms of accurately representing failure modes such as matrix/bulk cracking, deflection and or branching of crack at interface, through thickness penetration at interface, and delamination. The possibility of these would depend on modulus mismatch, inclination of the interface, length of the interface and relative fracture toughness of the interface to the bulk. Several numerical examples are solved to validate the performance of the proposed model by peel test, crack interaction with an inclined interface, crack at a bimaterial interface, and stiff-soft interface crack interaction.

Constraint-based failure assessment for pipelines with coplanar circumferential cracks under biaxial loading

The presence of coplanar or multiple cracks emerges as a common problem in many engineering structures, e.g., at the toe of circumferential welds of pipelines subjected to cyclic actions and in other piping systems for the nuclear power plants. The failure assessment diagram provides a convenient means to examine the competing failure between the fracture failure and plastic collapse failure, often for structural components with a single crack. The existing failure assessment diagram relies on the leading term characterizing the near-tip stress solutions, and ignores the geometry or plasticity-induced constraint variations. This paper aims to integrate the crack interaction effect between two coplanar cracks, measured by a constraint-based crack interaction factor, into the option 3 failure assessment curve in the engineering standard. This study examines three types of circumferential coplanar cracks in a pipe: two coplanar embedded cracks; two coplanar surface cracks; and a surface crack interacting with an embedded crack. Using a modified J solution based on a proposed crack interaction factor, this investigation quantifies the plasticity-driven increase in the near-tip opening stress for coplanar cracks. The stress field estimated based on this modified J solution agrees closely with the numerically computed stress field near the coplanar crack tips at large deformation levels. This work subsequently integrates the modified J solution into the failure assessment diagram. The failure assessment diagram based on the equivalent crack size recommended in BS7910 appears to be un-conservative for a number of coplanar cracks considered in this study.

Interaction of magnetoelastic shear waves with a Griffith crack in an infinite strip

In this research paper, the diffraction of a Griffith crack, situated in an infinite strip of finite thickness, due to magnetoelastic shear wave propagation has been analyzed. The effect of magnetic field on the Griffith crack interaction has been studied. Fourier transform is used to reduce the mixed boundary value problem to the dual integral equations. Finally, with the help of Abel’s transform the integral equations have been converted to Fredholm integral equation of 2nd kind. Fox and Goodwin method is used to solve the integral equation numerically. The analytical expression of Stress Intensity Factor at the crack tip has been illustrated graphically for the cases with magnetic effect and without magnetic effect.

Interaction of a finite crack with shear waves in an infinite magnetoelastic medium

The aim of this paper is to investigate the interaction of a finite crack with shear waves in an infinite magnetoelastic medium. Fourier integral transformation is applied to convert the boundary value problem for a homogeneous, isotropic elastic material to the Fredholm integral equation of second kind. The integral equation is solved by the perturbation method and the effect of magnetic field interaction on the crack is discussed. The stress intensity factor at the crack tip is determined numerically and plotted for low frequencies. Moreover, shear stress outside the crack, crack opening displacement, and crack energy are evaluated and shown by means of graphs.

Hydro-mechanical coupling behaviors in the failure process of pre-cracked sandstone

The interaction of cracks and water significantly affects the fracture mechanism of rocks. In this study, laboratory tests were conducted using sandstone samples containing a single fissure to explore the hydro-mechanical behaviors in the failure process of pre-cracked rocks. The internal crack characteristics were also analyzed using X-ray CT scanning. The results show that the confining pressure has the greatest effect on the mechanical properties (e.g., strengths, elastic modulus, and Poisson's ratio), followed by the fissure inclination and water pressure. At a lower fissure inclination, the confining pressure may control the type main cracks that form, and an increase in the water pressure increases the number of anti-wing cracks and the length of wing cracks and branch cracks. However, the fracture behaviors of samples with a higher fissure inclination are only slightly affected by the confining pressures and water pressures. The effect of fissure inclination on the internal crack area is reduced with the propagation from the fissure tips to the sample ends. The fissure inclination mainly affects the value of permeability but not affect the trend. The impact of pre-existing fissure on permeability is smaller than that of confining pressure and water pressure.

Study on fracture propagation and interaction mechanism during hydraulic fracturing

With the widespread application of hydraulic fracturing technology, the corresponding numerical simulation methods have been rapidly developed, and we have a deep understanding about the fracture propagation trajectory during hydraulic fracturing at the same time. However, the fracture interference mechanism during hydraulic fracturing is still insufficiently understood. Based on linear elastic fracture mechanics and relevant fracture criterion, a simulation model was established to simulate the fracture propagation by using boundary element method. The interaction mechanisms between fractures are studied. Results show that hydraulic fractures will change distribution direction of formation stresses during propagation process, and asymmetric fractures tend to merge together during propagation. The reverse propagation phenomenon between two fractures in numerical simulation rarely exists in the actual formation. The analysis and research on the mechanism of crack propagation and interaction can provide a theoretical basis for the trajectory control of hydraulic cracks in the later period.

Study of Chaotic and Regular Modes of the Fractional Dynamic System of Selkov

The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benettin-Wolf algorithm. It is shown that the existence of chaotic regimes is possible. In particular, the spectrum of the maximum Lyapunov exponents of the order of the fractional derivative contains positive values, which indicates the presence of a chaotic regime. Phase trajectories were also constructed to confirm these results. It was also confirmed that the orders of fractional derivatives are responsible for dissipation in the system under consideration.

Three-dimensional fields in an infinite transversely isotropic magneto-electro-elastic space with multiple coplanar penny-shaped cracks

This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions, which assume a crack to be electrically permeable (or impermeable) and magnetically permeable (or impermeable), are adopted, and all the possible combinations of these electro-magnetic crack boundary conditions are considered. An approximate three-dimensional solution of the field variables and expressions of some important fracture mechanics quantities are proposed, by virtue of Kachanov’s method and the generalized potential theory method. Numerical examples for some particular configurations of cracks are presented. Based on a two-crack system, the validity of the present solution is checked by comparing the results with their counterparts from a finite element simulation. Interaction of cracks is investigated as well, by taking the crack size and distance between two cracks as factors. From the phenomena shown in the numerical examples, a reduced solution and an empirical method for evaluating generalized stress intensity factors are proposed.

Numerical Investigation of an Orthotropic Plate with Interactions of Crack, Inclusions and Voids under Uniaxial Tensile Loading by XFEM

This work is focused to investigate the effect of various discontinuities like cracks, inclusions and voids for an orthotropic plate, to evaluate the normalized mixed-mode stress intensity factors (NMMSIFs) by implementing the extended finite element method (XFEM) under uniaxial tensile loading though considering the various numerical examples. The NMMSIFs are investigated with the interaction of crack, single- and multi-inclusions/voids for an orthotropic plate. The effect of NMMSIFs is analyzed for an orthotropic plate with several orthotropy axis orientations by changing the position of single- and multi-inclusions/voids while aligned, above and away with respect to an edge crack of the plate and for the both side inclusions/voids aligned the center crack. It is also investigated for the effect of various shapes of inclusions/voids for an edge crack orthotropic plate under uniaxial tensile loading using XFEM.

Transient response of several cracks in a nonhomogeneous half-layer bonded to a magneto-electro-elastic coating

In this study, we examine the fracture analysis of a non-homogeneous half-layer reinforced by a magneto-electro-elastic (MEE) coating with multiple interface and embedded cracks in a non-homogeneous substrate under impact loadings. Material properties of the functionally graded (FG) orthotropic substrate are assumed to vary exponentially in the thickness direction of the half-layer. First, the analytical solution is developed by considering a dynamic mechanical dislocation with time-dependent Burgers vector be situated at the substrate and interface by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the medium containing embedded and interface cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the dynamic stress intensity factors (DSIFs). The effects of crack spacing, the length and position of the cracks and FGM exponent as well as crack interaction are studied.

Improved Probabilistic Modeling of Multi-Site Fatigue Cracking

The purpose of this paper is to investigate the effect of fatigue, in the presence of neighboring cracks, and to integrate that into a model that could be used to predict crack growth. A total of 20 fatigue experiments were performed at different loading conditions using dog-bone samples of API-5L grade B carbon steel containing neighboring cracks. The impact of the neighboring cracks dimensions and the loading conditions on the interaction, coalescence and growth of cracks were investigated. A design of experiment approach to study neighboring cracks interactions and growth in carbon steel materials is also presented. Simulation efforts were performed to assess the Stress Intensity Factor (SIF) around neighboring cracks. Models discussing how the SIF of single semi-elliptical crack could be corrected to account for the neighboring cracks interaction were discussed in order to better understand the fatigue behavior. A combination of these models was integrated to find the SIF values necessary for the probabilistic life prediction modeling purposes. Finally, a multi-site fatigue crack growth rate model was developed and its parameters including their uncertainties were estimated. A Bayesian approach was adopted to perform uncertainty characterization and model validation.

Transgranular fracturing of crystalline rocks and its influence on rock strengths: Insights from a grain-scale continuum–discontinuum approach

The aim of this study is to understand the effects of micro-heterogeneity, such as grain size, morphology and mineralogy, on the initiation, propagation and coalescence of microcracks in heterogeneous materials. A multiscale grain-breakable continuum–discontinuum model incorporating realistic micro-heterogeneity reproduction method is proposed to investigate the fracturing behaviours and confinement mechanism of rocks. Crack initiation and damage stresses are intrinsic properties of rocks determined by grain-scale heterogeneity. Intergranular tensile cracks are primarily initiated as a result of local stress heterogeneity along grain boundaries. The subsequent generation of transgranular shear cracks implies a rapid proliferation of grain-crossing fractures, leads to large-scale crack interaction and coalescence. The effect of confinement inhibits crack extension and increases the appearance of shear-induced grain pulverizations. Furthermore, the effects of grain size, grain morphology and mineralogy on macro mechanical properties, including crack initiation stress, crack damage stress, uniaxial compression strength and elastic modulus, are discussed. The simulated results indicate that the larger grain size contributes to stronger local stress heterogeneity, which results in a lower failure strength of rocks. The crack initiation stress is determined by local heterogeneity and is less affected by the change in average grain size. Grain morphology plays an important role in grain interlocking while a reduction in grain size variance leads to a more homogeneous stress field. The mineralogy is evaluated with the aid of a quartz-mica-feldspar diagram, and the quantitative relationships between mineralogy and the macro-scale mechanical properties of rocks are discussed.

Fatigue crack growth in micro specimens as a tool to measure crack–microstructure interactions

AbstractThe process of short fatigue crack growth plays a significant role for the lifetime of materials in the high and very high cycle regimes. Fatigue crack growth is strongly influenced by interactions with microstructural obstacles, such as grain boundaries or phase boundaries, requiring a better understanding of these interactions to enhance the lifetime in these load regimes and improve lifetime calculations. Although it is possible to obtain crack growth rates from fatigue cracks in the lower micrometre range, further information like the exact position and type of the obstacle are mostly unavailable during the experiment. To overcome this issue, we propose a testing methodology of fatigue crack growth in micro specimens, which allows for an exact positioning of the crack relative to the obstacles and for monitoring the crack behaviour in a scanning electron microscope. The capabilities of this method are demonstrated for the interaction of fatigue cracks with grain boundaries.

Extended finite element modeling of fatigue crack growth microstructural mechanisms in alloys with secondary/reinforcing phases: model development and validation

Light structural metals have been extensively applied throughout the transportation sector in recent years with greater impetus to reduce vehicle weight and enhance energy efficiency. However, their use is restricted by the engineering challenge of fatigue crack growth and the need to understand, simulate, and predict crack propagation mechanisms with respect to materials’ microstructure. To address this need, a comprehensive computational methodology has been developed using the extended finite element method to predict fatigue crack interaction mechanisms with characteristic microstructural features. Mathematical formulations and algorithmic development are rigorously addressed, with specific emphasis on the incorporation of relevant physical phenomena of plasticity and particle debonding/fracture. This approach is validated by comparison with analytical models and experiments on cast aluminum–silicon alloys using digital image correlation. The proposed methodology constitutes a framework for the successful development, application, and advancement of computational design of materials. Ultimately, this contributes to material/process selection and design for structural integrity by enabling rapid assessment of fatigue crack growth resistance without prior testing, thereby reducing of the extent of costly experimental investigations.

Fatigue crack growth simulation of interacting multiple cracks in perforated plates with multiple holes using boundary cracklet method

AbstractIn this study, the recently developed boundary cracklet method (BCM) is used to model the fatigue crack propagation (FCP) in complex geometries in two‐dimensional domain. Several benchmark examples of FCP are analysed to show the effectiveness of BCM. Calculated stress intensity factors and crack paths show good agreement with reference studies. BCM is further used to simulate the multiple cracks interaction in a perforated plate with multiple holes having different cases of precracks emanating from edges of the plate and outer periphery of holes under fatigue loading. FCP is assumed to follow Paris–Erdogan law, and the maximum tangential stress criteria are used to predict the direction of propagation in each step. Moreover, to describe the computational efficiency of a numerical method in fatigue problems, a new parameter is introduced: Yavuz's fatigue computational efficiency factor (YCF), which is the number of computed million cycles per hour (CPU time).

Multi-scale interface design of strong and damage resistant hierarchical nanostructured materials

Synthesis of damage resistant nanostructured materials with high strength and fracture toughness is a challenging task. In this work, multi-scale interfaces were implemented into a hierarchical TiN/SiOx microstructure to mimic stepwise crack growth behaviour of the hard and damage resistant bivalve mollusc Saxidomus purpuratus shell. In situ micromechanical testing in scanning and transmission electron microscopes revealed multi-scale crack deflection events at grain boundaries of individual alternately-tilted TiN crystallites, at kinks of their repeatedly tilted columnar grains as well as crack interaction with perpendicular interfaces of elastic amorphous SiOx layers. These events induced an increase in the crack surface area, reduction of the crack driving force and dissipation of local stress and energy at the crack tip with subsequent crack slow-down or arrest, resulting in fracture toughness exceeding by ~200% the toughness of monolithic TiN nanoceramics. By this perspective biomimetic microstructural design, catastrophic failure of brittle ceramics may be turned into a predictable and controllable process increasing reliability of strong materials in various challenging safety-critical engineering applications. It also shows potential paths for the development of strong and simultaneously tough materials with high mechanical and thermal stability.

Stress intensity factor and interaction analysis of offset parallel cracks in brittle solids

The analytical solutions for the mode-I and mode-II stress intensity factor (SIF) of arbitrary distributed offset parallel cracks in brittle solids were generated based on the Kachanov method and superposition principle. By analyzing the SIF ratio, effects of the horizontal interval, vertical interval, crack inclination angle and crack length on the interaction of offset parallel cracks were estimated, and the interference area of the crack was determined theoretically. Numerical models were established using the finite element method (FEM) to show the performance of the present method, and the relationship between crack propagation and crack interaction was discussed. The results show that the SIFs obtained from the present method agree well with the accurate ones. The interaction of offset parallel cracks contains three types, i.e. reinforcing effect, shielding effect and null-effect, which can convert mutually with the change in interval, crack inclination angle and crack length. The interference area of the crack can be divided into reinforcing, shielding area and null-effect area which are symmetric about the crack. The reinforcing effect facilitates crack propagation while the shielding effect inhibits crack propagation.

Temperature effect on the material removal mechanism of soft-brittle crystals at nano/micron scale

Soft-brittle crystals, e.g. KH2PO4 (KDP), are difficult-to-cut due to their high brittleness which can easily generate crack during the machining process. The conventional method to machine this kind of material is by inducing ductile cutting mechanism at room temperature with ultra-precision machining, which can only remove materials at nanoscale level and hence yields very low material removal rate. While some thermal-assisted processes have been recently attempted to improve the machinability of some difficult-to-cut materials, e.g. ceramics, there is no systematic understanding of the temperature effect on material removal mechanism of soft-brittle KDP crystals yet. In this work, the temperature effect on the material removal mechanism has been investigated for the first time using nano-scratch technique. While a decreased hardness and elastic modulus have been observed with the increase of temperature, an increase of fracture toughness has been revealed with a contradictory tendency, indicating a higher capacity of plastic deformation at elevated temperature. In contrast to the almost totally brittle scratch at room temperature (RT) caused by crack propagation and edge chipping, the scratch at 170 °C can achieve more ductile-regime surfaces with a larger critical undeformed cutting depth (3.61 μm), e.g. a significant increase of 8.60 times compared with that at RT (0.42 μm). Moreover, the TEM analysis on the subsurface microstructures shows that a great number of nano grits was generated in the subsurface at RT as the result of crack propagation and interaction, while at elevated temperature some crystallographic lattice misaligned structures (LMS) and nano crystals have been brought about due to the nucleation and evolution of thermal-activated dislocations, which explains the higher plasticity of KDP at elevated temperature. The results present in this paper are of great significance for understanding the specific temperature effect on the brittle-to-ductile transition of the cutting mechanism for future designing thermal-involved processes to machine soft-brittle materials.

Interaction of multiple straight cracks and elliptical inclusions in a finite plate due to mismatched thermal expansion

The purpose of this paper is to study the interaction between multiple elliptical inclusions and straight cracks in a finite plate due to a uniform temperature change. In this solution, Eshelby’s equivalent inclusion method involving both interior Eshelby’s tensor and exterior Eshelby’s tensor is applied to calculate the thermal stress fields of an infinite plate containing multiple elliptical inclusions under a uniform temperature change first. Then the multiple cracks and the boundary are modeled by continuous distributions of dislocation densities in an infinite plate. Based on the stress boundary conditions of the cracks and boundary, a system of singular integral equations with Cauchy kernels are obtained. After solving the singular integral equations with Gauss–Chebyshev numerical quadrature, the stress intensity factor of each crack can be calculated. Besides, the finite element method is employed to examine the accuracy and efficiency of the presented method. Finally, the effects of the material and geometric parameters on the normalized stress intensity factors of the cracks are studied.

Impacts of natural fractures on hydraulic fracturing treatment in all asymptotic propagation regimes

Hydraulic fracturing is a technique in which pressurized fluid is pumped into the well to induce fracture propagation in the rock formation. The treatment aims at enhancing permeability and well-reservoir connectivity. However, the presence of natural fractures can impact the hydraulic fracture propagation, increasing the complexity of the hydraulic fracturing treatment, and affect the final configuration of the fracture network. Furthermore, different propagation regimes can develop depending on field conditions, properties of the porous matrix, fractures, the injection fluid, and time. This work introduces a robust fully coupled hydro-mechanical approach to investigate the impacts of natural fractures on hydraulic fracturing in four limiting propagation regimes: toughness-storage, toughness-leak-off, viscosity-storage, and viscosity-leak-off dominated. The proposed approach is based on the finite element method and incorporates the coupling of pore pressure/stress within the permeable rock formation and fracture propagation. An innovative mesh fragmentation technique with an intrinsic pore-cohesive zone approach is implemented in the in-house multiphysics framework to simulate fracture propagation with complex crack patterns. Cohesive Zone Model (CZM) represents the initiation and propagation of hydraulic fractures while a contact model with the Mohr–Coulomb criterion is used to represent the normal closure/opening and friction/shear dilation of natural fractures. The results of the new approach are compared against analytical and numerical solutions. Moreover, the influence of parameters such as rock permeability, fluid viscosity, initial stress state, and intercepting angle on the hydraulic and natural fracture is also investigated. The robustness of the presented methodology is demonstrated by simulating crossing with an offset, branching, fracture propagation from the tip of a natural crack, and interaction of multiple cracks. These results can provide guidance for a better understanding of the complex process of hydraulic fracturing.