Interaction Of Multiple Cracks Research Articles

Numerical method for predicting the nucleation and propagation of multiple cracks based on the modified extended finite element method

In practical engineering, structures will inevitably suffer from multiple cracks and require accurate numerical methods to calculate the structural behavior. Regarding the multi-crack problems, the nucleation of new cracks and the development of existing cracks will affect the subsequent structural responses. Therefore, the criterion for calculating crack nucleation and development is a critical factor influencing the numerical results. This paper presents a modified Extended Finite Element Method (XFEM) to predict the nucleation and development of multiple cracks in plane members focusing on the interaction of multiple cracks. In the proposed method, the crack competition criterion is based on the minimum total energy principle, which can ensure that the nucleation and development of cracks can achieve a maximum energy dissipation per unit length. The effectiveness and robustness of the presented method are verified by comparing the numerical results with experimental and/or other numerical simulations. The result shows that the proposed competition criterion can accurately judge the sequence of new-crack nucleation and existing-crack propagation.

Interaction and initiation mechanism of non-parallel multiple cracks by strain gauge method

The maximum stress intensity factors, KI,kmax(θ) and KII,kmax(θ), of three non-parallel oblique cracks were calculated to reveal the interaction mechanism of multiple cracks. The multiple crack initiation criterion was adopted to predict the non-parallel multiple crack initiation parameters. Uniaxial compression tests were performed on rock specimens (red sandstone) with three non-parallel oblique cracks, where the strain near the crack tips was monitored by the strain gauge measurement method to determine the crack initiation sequence. The results showed that the change of crack relative inclination angle had little effect on the fracture trajectory. Multiple crack tips were seldom initiated at the same time. The failure modes of red sandstone specimens with three non-parallel oblique cracks under uniaxial compression are divided into two types: wing crack penetration and wing crack–secondary crack penetration. All of the fracture mechanisms are Mode I (tensile) initiation. The predicted results coincided well with the test results, verifying the validity of the theoretical results.

Estimation of multiple cracks interaction and its effect on stress intensity factors under mixed load by artificial neural networks

One of the goals of fracture mechanics in the analysis of problems involving cracks is to investigate crack growth and propagation. Each crack grows and propagates in the environment based on its geometry and loading conditions, which can occur under pure mode or a combination of modes. The growth and propagation pattern of the crack in these conditions aligns with the fracture mode. In the presence of multiple cracks in the environment, the growth and propagation paths of these cracks differ from the isolated crack case, where they can either grow independently under certain conditions or merge together. Nowadays, extensive research has been conducted on cracks and their mathematical relationships with respect to the geometry and loading conditions of various components. Since in many cases, a large number of cracks may occur in proximity to each other, the intensification and protective effects of each crack on others and their impact on the overall behaviour of components are of great importance. This study focuses on investigating the behaviour of interaction and the stress intensity factor for an infinite plate with parallel adjacent cracks. Remote stress boundary conditions in the form of tensile and compressive stresses have been applied to this plate, and using the J-integral and the finite element method with the Abaqus finite element analysis software, this subject has been examined. The obtained results indicate that depending on the type of vertical and horizontal distances and the angle of their placement between the adjacent crack and the main crack in the first, second, and mixed modes, the adjacent crack can have intensifying, protective, or neutral effects. Furthermore, a good estimation of the secondary crack's influence on the main crack has been provided using a neural network method (MLP), which creates an appropriate weight function for the upcoming sample.

Reliability analysis of plate parts with multiple interacting hole-edge cracks using complex variable function

In this paper, a successive conformal mapping technique is used to propose an analytical method for solving the stress intensity factor (SIF) of asymmetrical hole-edge cracks on the basis of Muskhelishvili's complex variable function analysis method. Based on this analytical solution, the superposition method is used to get the SIF under the interaction of multiple cracks. Subsequently, according to the plastic collapse criterion, the residual strength under the interaction of two collinear asymmetric elliptical hole-edge cracks with different sizes on the side rail of a dumper's frame is analyzed through the method established. The failure probability of the plate part is obtained by the Kriging meta-model. This study provides a theoretical guide for the operation and maintenance plan of plate parts with multiple cracks.

Effective elastic properties of three-dimensional multiple crack problems with the isogeometric boundary element parallel fast direct solver

We propose an isogeometric boundary element (IGABEM) parallel fast direct solver based on OpenMP to solve three-dimensional multiple crack problems. In this paper, the orderly and randomly distributed cracks are studied to observe the influence of the multiple crack interaction on the effective elastic properties. This paper designs the parallel implementation of the matrix low rank approximation and the matrix assembly for the hierarchical off-diagonal low rank (HODLR) matrix. In the matrix low rank approximation, we propose the m-n tree to improve the accelerated hybrid algorithm to balance the CPU performance and memory usage. The numerical results show that the effective elastic properties can respond to the strong interaction to a certain extent, but the maximum stress intensity factors (SIFs) of multiple cracks still need to be calculated to diagnose the possible crack initiation points. On the other hand, the numerical results also show that the IGABEM parallel fast direct solver can greatly improve the computational efficiency on the premise of ensuring the computational accuracy.

Facilitation effect of multiple crack interaction on fatigue life reduction and a quantitative evaluation of interactions factor of two parallel Non-coplanar cracks

Synergistic/interaction action of the multiple cracks can be clearly observed from fracture topography of the post-fatigue test specimen. Based on experimental observations, the interactions of two parallel non-coplanar cracks mounted in double-edge crack specimens under tension loading are investigated. The stress intensity factor (SIF) for a wide range of crack configurations is established using three-dimensional finite element analysis (FEA), and the effects of multiple crack interactions on the SIF values are studied. The effects of crack interactions on the SIF are strongly dependent on the crack geometry. The greater the vertical distance between the two cracks, the more strongly the stress field at the tip of the main crack is impacted. The analytical solutions for calculating SIF under effect of the multiple crack interactions were derived in a matrix form and the accuracy of the estimated equation was confirmed.

Simulation of Surface Crack Interaction of Marine Solid Shaft

In the marine industry, an engine transmits power through a marine shaft, also called a propeller shaft, to a propeller drive. Almost all naval architects construct this shaft as a solid cylinder. When a crack shows up in the hub of a shaft, it is essential to take preventative measures. When solid cylinders are exposed to various mechanical stresses, cracking or fracturing is a typical failure, and most of the crack exists in single and multiple cracks. Owing to the possible interactions between fractures, they are likely to play a significant role in how the structure collapses. Consequently, this study is being conducted to address issues emerging from the interaction of multiple cracks during particular loading conditions. This paper will highlight the research conducted on various cracks interacting with parallel configurations on the cylinder's surface. Finite Element Software, AnsysTM has been employed through modelling and simulation to calculate the stress intensity factor (SIF) for various crack geometry features and separation distances under various types of loading. The dimension for length and diameter of the cylinder has been set as 200 mm and 50 mm, respectively. The values of crack depth ratio used is ranged from 0.1 to 0.4 with the increment of 0.1, while for crack aspect ratio is 0.6. The results from the SIFs are normalized for generalization to determine the interaction factor and the relationship between two cracks and a single crack.

Fracture of brittle material with two 3D parallel internal cracks under thermal stress: Experimental and numerical analysis

Many defects such as cracks are often present inside brittle solids, and most of the cracks do not appear in a single form. The fracture and failure of brittle solids are basically caused by the interaction and expansion of multiple cracks. Most of the traditional studies on this topic have focused on surface or penetration crack interaction under tensile and compressive loads, while there have been very few studies on the expansion characteristics and interaction of parallel internal cracks under temperature loading. This study applies the 3D internal laser-engraved crack (3D-ILC) method to fabricate parallel internal cracks inside the 3D cube. Physical tests and numerical simulations of parallel internal cracks of different sizes and single crack propagation under temperature fields are carried out, and the propagation characteristics of internal cracks and the interaction between parallel internal cracks of unequal size under temperature loading are investigated. The study results show that the big crack will inhibit and shield the expansion of the small crack. In addition, there are typical “anti-binary tree” mode III features on both sides of the parallel large crack and single large and small crack propagation surface, which are classified as mixed I-II-III crack, while the parallel small cracks are mode I-II. Compared with the quasi-static crack growth criterion, the simulation results of the subcritical crack growth criterion are more in line with the physical test results, and there is a subcritical growth phenomenon in the parallel crack propagation under the temperature load. The results provide experimental and theoretical references for the study of 3D bi-parallel cracks interaction of different sizes and the fracture of mode I-II-III crack under the temperature field.

Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method

A new method is presented to study the interaction of multiple cracks, especially for the areas near crack tips by using the extended finite element method. In order to track the cracks, a new geometric tracking technique is proposed to track enriched elements and nodes along the crack instead of using the narrow band level set method. This allows to accurately determine enriched elements and nodes and calculate enrichment values. A method is proposed for constructing a multicrack matrix, which involves numbering enriched nodes of multiple cracks and solving the global stiffness matrix. In this approach, the stress fields around multiple cracks can be studied. The interaction integral method is employed to study the crack propagation and its direction by calculating the stress intensify factor. The developed model has been coded in MATLAB environment and validated against analytical solutions. The application of the model in the crack interaction study is demonstrated through a number of examples. The results illustrate the influence of the interaction of multiple cracks as they approach each other.

Predicting growth and interaction of multiple cracks in structural systems using Dynamic Bayesian Networks

Digital twins have the potential to improve future health prognosis and operational safety of engineering structures. However, few studies have attempted to validate such twins with experimental data. In this work, two system-level digital twin models for structural capacity degradation are evaluated with experimental data from a four-crack structural fatigue specimen. Each twin model is based on a dynamic Bayesian network, but the two models differ in the complexity of the crack-to-crack interaction model. Using measured crack lengths from the experiment, the ability of each twin to predict the evolution of future crack size is assessed. For this specimen, a high level of crack-to-crack interaction must be captured for the twin to realistically trace the evolution of the system. The suitability of Bayesian network based twins for this type of problem is discussed.

Fatigue life estimation of additively manufactured Ti-6Al-4V: Sensitivity, scatter and defect description in Damage-tolerant models

Damage-tolerant models for fatigue life estimation rely on fracture mechanics principles to model fatigue crack initiation and growth. In Laser-Based Powder Bed Fusion (LPBF) produced Ti-6Al-4V defect populations present non-uniform in size, shape, and location within components. Considering defect populations in a statistical nature offers one method to characterise defects to be included in fatigue life modelling for AM parts. In this study a novel numerical fatigue life model is built upon which the sensitivity to input parameters, short crack growth mechanics, defect morphology and location for LPBF-produced Ti-6Al-4V is established. Furthermore, we introduce the potential for multiple crack initiation sites and crack interaction. Fatigue strength is shown to be more sensitive to selected threshold parameters and short crack growth mechanics. Furthermore, the introduction of multiple crack initiations and interaction results in distributions of fatigue strength estimates sensitive to defect number, illustrating the importance of its inclusion as a source of fatigue scatter in LPBF produced Ti-6Al-4V parts. Overall, this study establishes areas of nuance and criticality required in the design and modelling of fatigue life unique to AM produced components.

Interaction of multiple parallel cracks in a pre-stressed orthotropic elastic plane

Pre-stressed structures have been widely applied in aerospace, deep mining, and civil engineering fields. This paper presents a theoretical analysis of the interaction of multiple parallel cracks in a pre-stressed orthotropic elastic material. The pseudo-traction method and complex potential method are applied to solve an associated mixed boundary-value problem. First, we derive two kinds of fundamental solutions for a pair of normal and tangential concentrated forces acting at any point on an isolated crack. Then, with these solutions, a system of Fredholm integral equations are derived by superposition. The interaction of multiple parallel cracks in a pre-stressed orthotropic elastic plane is analyzed. Numerical results show that the pre-stress has little influence on the stress intensity factors when two cracks are collinear or two cracks are far away from each other (Dh>2a or Dv>5a). For closer two parallel cracks, KI decreases with increasing pre-stress σ0 under normal loading and KII increases with increasing pre-stress σ0 under shear loading.

The propagation and interaction of cracks under freeze-thaw cycling in rock-like material

In cold mountainous regions, the freeze-thaw cycling often leads to rock weathering, which might trigger spalling, significant landslides and rockfalls. In this work, we used combined experimental, theoretical and numerical approaches to investigate the mechanisms of frost cracking as a result of coupled effects of freeze-thaw cycling, confining stress and the interaction of multiple cracks. The experimental facility with a temperature cycling chamber and a high-pressure cell has been developed. We used rock-like materials (rock analogue samples made from cured cement and quartz-sand mixtures) to conduct the experiments. The rock-like samples contain pre-existing single or double initial cracks, which are then water filled and exposed to freeze-thaw cycling. The coupled thermal-hydro-mechanical modeling for analyzing fractures induced by freeze-thaw cycling was achieved by using a code that was previously developed named TOUGH-AiFrac. Good agreements between the TOUGH-AiFrac modeling and the laboratory experiments have been achieved including the exact paths of crack propagation. The experimental and numerical results show that the frost cracks tend to propagate in the direction of maximum principal stress. The results further show that the interaction effect between two frost cracks is significantly influenced by the position, orientation and offset of initial cracks, as well as the orientation of intact rock bridges between the cracks. At last, the stress shadow that was calculated by the TOUGH-AiFrac model between two cracks was discussed.

Dynamic mode III stress intensity factors of multiple axisymmetric interfacial cracks in an FGM coated orthotropic layer

In the present study, mode III dynamic stress intensity factors (DSIFs) for the multiple axisymmetric interfacial cracks in an orthotropic layer with FGM orthotropic coating under transient torsional loading are formulated. It is assumed that the mass density and the shear modulus of the FGM orthotropic coating vary exponentially and power-law form along the thickness of the layer. At first, the solution for Somigliana-type dynamic rotational ring dislocation in the layer and its coating is obtained by using the Laplace and Hankel transforms. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interfacial cracks, including penny-shaped and annular cracks. The integral equations are of Cauchy singular type, which are solved by Erdogan’s collocation method for dislocation density on the surface of interfacial crack and the results are used to determine DSIFs for axisymmetric interfacial cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of multiple interfacial cracks on the DSIFs.

Research on Taylor impact fracture behavior of ZrCuAlNiNb amorphous alloy

Under argon conditions, the Taylor impact test for ZrCuAlNiNb amorphous alloy with impact velocity range of 78.9-155 m/s was carried out, the failure fracture process of the material was recorded by high-resolution high-speed photography, and the fractured samples after fracture were recovered. The microscopic morphology of the section was observed by scanning electroscope, and the fracture behavior of the material at different impact speeds was analyzed. ZrCuAlNiNb amorphous alloy breaks from a single main shear band under low-speed impact to a multi-shear band break at high speed (≥ 150 m/s), and several secondary shear straps are formed along the axial direction of the sample. Its complex force leads to a variety of fractured forms, and dynamic temperature rise aggravates the thermal softening effect of the material. ZrCuAlNi crystal alloy is transmitted by axial cracks, which cause the crystal alloy to fracture under the interaction of multiple cracks, and the fractured morphology presents a river-like cleavage fracture. The study of the mechanical properties of ZrCuAlNiNb amorphous alloys and their failure behavior provide theoretical guidance and experimental basis for the application of ZrCuAlNiNb amorphous alloys.

Stress Intensity Factor of Double Cracks on Seabed-Spanning Pipeline Surface under the Spring Boundary

AbstractIn order to study the interaction of multiple cracks on the submarine spanning pipelines under a complex marine environment, the stress intensity factor (SIF) of double circumferential crac...

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).

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.

Influence of Different Types of Small-Size Defects on Propagation of Macro-cracks in Brittle Materials

The presence of defects in the structure requires noticeable attention and understanding of fracture mechanisms in brittle materials has to be established. Defects in the form of holes, macro- and micro-cracks are the main interest of this paper. This work investigates the dual role of holes and micro-crack arrays on toughening and degradation mechanisms in concrete structures. An ordinary state-based peridynamics (PD) model is utilized to analyse the fracture problem at the micro-level. The application of PD shows its advantage in crack-hole, macro- and micro-crack interaction problems since PD can accurately predict the contribution of defects on structural behaviour. The study of the three-point bending problem with five types of holes existing in the structure showed the crack arrest phenomena at the hole boundary and the “attraction” of the crack to propagate towards the hole. For the study of the macro- and micro-cracks interaction problem, various cases of the micro-crack distribution and inclination angles are considered and validated with analytical studies. The PD quasi-static simulations show good agreement with analytical solutions. Moreover, PD dynamic solutions show the capability of PD to capture complex crack propagation paths. It is observed that the presence of micro-cracks and holes ahead of the main crack can suppress its further propagation as well as have an influence on the crack propagation direction. The numerical results demonstrate the efficiency of the PD modelling of multiple crack interaction problems.