Cohesive Crack Propagation Research Articles

A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation

A three-phase hydro-mechanical model for hydraulic fracturing is proposed. Three phases include: porous solid, fracturing fluid and host fluid. Discontinuity is handled using extended finite element method (XFEM) while cohesive crack model is used as fracturing criterion. Flow through fracture is defined as one-dimensional laminar flow, and flow through porous medium (host reservoir) is defined as two-dimensional Darcy flow. Coupling between two fluids in each space, fracture and pore, is captured through capillary pressure–saturation relationship, while the identical fluids in fracture and pore are coupled through a so-called leak-off mass transfer term. Coupling between fluids and deformation is captured through compatibility of volumetric strain of fluids within fracture and pore, and volumetric strain of the matrix. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. The model is verified against analytical solutions available from literature. The leaking of fracturing fluid into the medium and suction of porous fluid into the fracture around the tip, are investigated. Sensitivity analyses are carried out for cases with slow and fast injection rates. It is shown that the results by single-phase flow may underestimate the leak-off.

XFEM–dislocation dynamics multi-scale modeling of plasticity and fracture

An extended three-dimensional multi-scale framework is presented to model plasticity in precipitate containing materials in the presence of cracks. The present framework is constructed in two scales. At the micro scale, plasticity is computed via the line dislocation dynamics (DD) methodology in which the penetrable and impenetrable precipitates are modeled. At the macro scale, application of the extended finite element method (XFEM) allows for accurate analysis of mixed-mode cohesive crack propagation without the need for any remeshing procedure. This is a significant improvement especially when two different scales are involved. While the former simulations have so far been limited to the study of only mode-I crack propagation to avoid the expensive remeshing procedure, in the present work, the effects of loading rates and precipitate density on general crack propagations are studied by utilizing the XFEM–DD multi-scale framework to illustrate the efficiency and capability of the proposed approach.

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM

SummaryThe aim of this paper is to propose a continuous–discontinuous computational homogenization–localization framework to upscale microscale localization toward the onset and propagation of a cohesive discontinuity at the macroscale. The major novelty of this contribution is the development of a fully coupled micro–macro solution strategy, where the solution procedure for the macroscopic domain is based on the extended finite element method. The proposed approach departs from classical computational homogenization, which allows to derive the effective stress–strain response before the onset of localization. Upon strain localization, the microscale is characterized by a strain localization band where damage grows and by two adjacent unloading bulk regions at each side of the localization zone. The microscale localization band is lumped into a macroscopic cohesive crack, accommodated through discontinuity enriched macroscale kinematics. The governing response of the continuum with a discontinuity is obtained numerically based on proper scale transition relations in terms of the traction–separation law and the stress–strain description of the continuous surrounding material at both sides of the discontinuity. The potential of the method is demonstrated with a numerical example, which illustrates the onset and propagation of a macroscale cohesive crack emerging from microstructural damage within the underlying microstructure. Copyright © 2015 John Wiley & Sons, Ltd.

다중점 구속조건을 이용한 응집요소의 선택적 활성화 기법

본 논문에서는 응집영역 모델링 방법에 의한 균열전파 해석에서 발생하는 연성추가문제의 효과적인 해결방법으로 사용자 부프로그램 UMPC를 이용한 응집요소의 선택적 활성화 기법을 연구 하였다. 먼저 균열의 발생 및 전파가 예상되는 지역의 일반요소들 사이에 응집요소를 삽입하고 응집요소를 구성하는 절점에 다중점 구속조건을 적용함으로써 응집 요소를 비활성화 시킨 상태로 해석을 시작한 후, 해석 도중에 특정 조건을 만족하는 절점들에 대해서만 다중점 구속조건을 해제하여 응집요소를 선택적으로 활성화하는 전략을 사용하였다. 응집요소의 초기강성 및 다중점 구속조건 해제 지표가 균열전파 거동 및 계산시간에 미치는 영향을 체계적으로 조사하였다. In this paper, a selective activation strategy of cohesive elements using user subroutine UMPC was studied as an efficient solution for the added compliance problem in cohesive zone model crack propagation analyses. The cohesive elements were inserted between every bulk elements in region where cracks were expected to initiate and propagate, but initially not activated by tying the cohesive nodes using multi-point constraints. During analyses, the cohesive elements for which specified criterion was met were selectively activated by releasing the constraints. The effect of initial cohesive stiffness and the release criterion on the crack propagation behavior was carefully investigated.

Analysis of cohesive cracking in saturated porous media using an extrinsically enriched EFG method

The subject of this study is to investigate propagation of cohesive cracks under various mixed mode conditions in saturated porous media. The mesh-free EFG algorithm, which uses the MLS shape functions for approximating both displacement and pressure fields, is used. An enrichment approach similar to XFEM, which exploits the Heaviside step function as the enrichment function for representing the crack surfaces is adopted. Basic formulations are developed for saturated fully coupled porous media, and a series of benchmark problems are assessed through the enriched EFG formulations. Both cases of uncoupled and fully coupled formulations for the solid displacements and the water pressure are presented. For the fully coupled case, the effect of mass exchange through the fracture and the surrounding undamaged media is examined. The results predicted by the present numerical framework are in good agreement with existing solutions in the literature.

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.

3D modeling of cohesive crack growth in partially saturated porous media: A parametric study

In this paper, the 3D cohesive crack propagation is presented in partially saturated porous media. The double-nodded zero-thickness cohesive interface elements are employed to capture the mixed mode fracture behavior. In order to describe the behavior of fractured media, two balance equations are applied similar to those employed for the mixture of solid–fluid phase in semi-saturated media, including: the momentum balance of fractured media, and the balance of fluid mass within the fracture. Crack permeability is modified based on the data obtained from experimental results to consider the roughness of fracture walls effect.

Solution of the Periodic Problem of Propagation of Cohesive Cracks Under Longitudinal Shear

UDC 539.375 We consider a punched body weakened by surface cohesive cracks under the conditions of longitudinal shear. The solution of the problem of equilibrium of this body is reduced to the solution of an infinite algebraic system of equations and one singular integral equation with Cauchy-type kernel.

A domain decomposition method for the simulation of fracture in polysilicon MEMS

To overcome the computational burden associated to the three-dimensional finite element simulation of fracture phenomena in polysilicon MEMS during dynamic loading, like e.g. impacts, a domain decomposition technique is used. The approach extends a method developed for linear elastic materials, by including cohesive crack propagation and it allows for the simulation of inter and trans-granular fracture initiation and propagation in polycrystals and it is a step forward in the construction of a complete simulation tool for the description of fracture phenomena in microsystems. Applications to critical MEMS details show encouraging results in reproducing local failure mechanisms.

A multi-scale approach to bridge microscale damage and macroscale failure: a nested computational homogenization-localization framework

This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE2) towards a discontinuity enriched framework. The classical homogenization approaches typically rely on the separation of scales principle, which is violated as soon as a strain localization band develops within a microstructural volume element (MVE). The newly developed scheme resolves this limitation by considering the bifurcation of the microscale deformation into a continuum ‘bulk’ part and a localization related part. The most distinct feature of the proposed framework is that both, the local macroscale traction-opening response of the cohesive crack and the stress-strain response of the surrounding ‘bulk’, are obtained from a single MVE analysis. The discontinuity enriched macroscale description is formulated to accommodate for the micro-macro coupling. The macroscale boundary value problem and the corresponding implementation are detailed for the use within the embedded discontinuities approach. The presented multi-scale method is demonstrated on a numerical example of a cohesive crack propagation in a macroscopic double notch specimen, with underlying voided microstructure.

Automatic modelling of cohesive crack propagation in concrete using polygon scaled boundary finite elements

An automatic cohesive crack propagation modelling methodology for quasi-brittle materials using polygon elements is presented. Each polygon is treated as a subdomain that is modelled by the scaled boundary finite element method (SBFEM). Generalised stress intensity factors (SIFs) based on matrix power function solutions of singular stress fields obtained from the SBFEM following standard finite element stress recovery procedures is used to evaluate the crack propagation criterion and determine the crack propagation direction. Interface elements model the fracture process zones and are automatically inserted into the polygon mesh as the crack propagates. A shadow domain procedure couples the polygons and interface elements. It computes the load–displacement response and crack propagation criterion, taking into account the cohesive tractions on the crack edges that are modelled as side-face tractions in the SBFEM. Cracks are propagated using a simple, yet flexible local remeshing procedure that can remesh any arbitrary polygon. Only minimal changes are made to the global mesh structure each time the remeshing algorithm is called. Five cohesive crack propagation benchmarks are modelled to validate the developed method and demonstrate its salient features.

Dynamic cohesive crack propagation modelling using the scaled boundary finite element method

ABSTRACTThis study develops a scaled boundary finite element method (SBFEM)‐based approach for modelling fast cohesive crack propagation in quasi‐brittle materials subjected to transient dynamic loadings. In this approach, the elastic bulk material is modelled by SBFEM subdomains and the cracks by nonlinear cohesive interface finite elements that are automatically inserted by a remeshing procedure. The global equation system is solved using an implicit time integration algorithm. Because all the solutions (displacements, stresses, velocities, accelerations) are semi‐analytical in an SBFEM subdomain, this approach offers a few advantages over other methods, such as accurate calculation of dynamic stress intensity factors and T‐stress without using fine crack‐tip meshes, simpler remeshing, more accurate and efficient mesh mapping, and the need of much fewer degrees of freedom for the same accuracy. The approach is validated by modelling two concrete beams under impact, subjected to mode‐I and mixed‐mode fracture, respectively.

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

SUMMARYIn this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.

Predictions of crack propagation using a variational multiscale approach and its application to fracture in laminated fiber reinforced composites

Predictions of crack propagation is a valuable resource for ensuring structural integrity and damage tolerance of aerospace structures. Towards that end, a variational multiscale approach to predict mixed mode in-plane cohesive crack propagation is presented here. To demonstrate applicability and to provide validation of the finite element based predictive methodology, a comparative study of the numerical results with the corresponding experimental observations of crack propagation in laminated fiber reinforced composite panels is presented.

A numerical investigation on the size effect of fiber-reinforced concrete specimens in crack propagation

The paper addresses a numerical investigation on the size effect in fiber-reinforced concrete specimens that is based on an alternative approach for cohesive crack propagation. A discrete version of the Hellinger---Reissner variational principle manages mode I crack growth in the case of piece-wise linear cohesive softening equations. A three-point bending test is investigated according to the mechanical properties of fiber-reinforced mixtures that have been characterized in the experimental literature. The achieved results point out that each segment of the considered cohesive laws plays an important role in the control of the size effect, depending on the dimension of the specimen.

A semi-analytic method for crack kinking analysis at isotropic bi-material interfaces

Interface delamination is a key failure mechanism in numerous applications. Microscopic analysis reveals that macroscopic delamination may contain both adhesive and cohesive cracking. As a result, the fracture pattern at this microscopic scale is inherently dependent not only on the adhesive interface properties but also on the cohesive properties of the bulk materials surrounding the interface. For this reason, this paper focuses on the competition between adhesive and cohesive crack propagation of an initial interface crack. A computationally efficient semi-analytic approach is presented to predict this competition. First, crack kinking theory is thoroughly reviewed explaining the use of solution coefficients to relate the energy release rate of an interface crack and a kinking crack. It is found that previously tabulated values of the imaginary part of the solution coefficients given for negative Dundurs’ parameters should be of opposite sign. Also, solution coefficients are calculated in a finite element framework based on recent literature. This method is validated by applying it to different geometries and loading conditions. In addition, the method is generalized for any arbitrary material combination by providing solution coefficients through Response Surface Modeling. This enables the semi-analytic approach, i.e. the analytic calculation of energy release rates for kinking cracks at interfaces solely based on the finite element results for the interface crack itself. The accuracy of this method is validated by comparison to detailed finite element simulations. Finally the relative size effect of the sample dimensions is scrutinized.

Accurate simulation of mixed-mode cohesive crack propagation in quasi-brittle structures using exact asymptotic fields in XFEM: an overview

The extended finite element (XFEM) enriches the standard local FE approximations with known information about the problem, with the use of the partition of unity. This allows the use of meshes that do not conform to a discontinuity and avoids adaptive re-meshing as the discontinuity grows as required with the conventional FEM. When the crack tip asymptotic field is available and used as the enrichment function, XFEM is more accurate than FEM allowing the use of a much coarser mesh around the crack tip. Such asymptotic fields have been known for a long time for traction-free cracks (the Williams expansions) but have only recently been derived for cohesive cracks (Karihaloo–Xiao expansions). In this paper an overview of latter expansions is given for a range of cohesive laws and their usefulness in the simulation of cohesive crack propagation is demonstrated on two examples of concrete and fibre-reinforced concrete flexural members.

Strength assessment of adhesively bonded tile claddings

A simplified analytical approach for the assessment of bonding strength in tiled flooring is formulated and discussed. The approach is conceived for application to a specific type of failure mechanism, usually activated by differential elongation/shortening between tiles and substrate, of the type induced by thermal gradients or fresh concrete maturation. It is discussed how the failure mechanism, promoted by eccentric tile compression, can be studied as a Mode I cohesive crack propagation through the adhesive layer and a closed form estimate of the ultimate tile compression is provided. Based on closed-form solutions for the problem of stress transfer between substrate and tile through shear of the adhesive, simple formulas for the estimation of the tile compression are also derived.

Fracture properties of high performance carbon foam sandwich structures

This paper investigates the fracture properties of high performance sandwich structures based on tough carbon fiber reinforced polyetheretherketone (PEEK) skins bonded to a carbon foam core. Single cantilever beam tests on pre-cracked samples indicated that an excellent level of adhesion can be achieved between the skin and core materials. In all specimens, the crack propagated within the carbon foam providing an additional in situ evaluation of the fracture properties of the core material. Single edge notched bend (SENB) testing was performed and revealed that both test procedures yielded similar values of fracture toughness. Three point bend (3 PB) testing on simple supported beams highlighted the excellent load bearing capabilities offered by these lightweight multifunctional structures. Optical examinations revealed that failure modes such as localized indentation; collapse and densification of the carbon foam core and cohesive bi-material crack propagation contributed to the excellent load bearing characteristics offered by these systems.

Modelling crack propagation in reinforced concrete using a hybrid finite element–scaled boundary finite element method

A previously developed hybrid finite element–scaled boundary finite element method (FEM–SBFEM) is extended to model multiple cohesive crack propagation in reinforced concrete. This hybrid method can efficiently extract accurate stress intensity factors from the semi-analytical solutions of SBFEM and is also flexible in remeshing multiple cracks. Crack propagation in the concrete bulk is modelled by automatically inserted cohesive interface elements with nonlinear softening laws. The concrete–reinforcement interaction is also modelled by cohesive interface elements. The bond shear stress–slip relation of CEB-FIP Model Code 90 and an empirical confining stress–crack opening relation are used to characterise slip and split failure at the concrete–reinforcement interface, respectively. Three RC beams were simulated. The numerical results agreed well with both experimental and numerical results available in the literature. Parametric studies demonstrated the importance of modelling both slip and split failure mechanisms at the concrete–reinforcement interface.