Computational Fracture Mechanics Research Articles

Analysis of Surface Crack using Various Crack Growth Models

This research focusing on fatigue crack growth experiment and assessments of fatigue crack growth model. Fatigue has been considered as the most important phenomena in the engineering problems. It has been found to occur in every engineering field. Many methods were introduced to overcome fatigue problem. One of it is fatigue crack growth prediction models. Fatigue crack growth model prediction can determine the residual life of the mechanical component. Fatigue crack growth is an important parameter in engineering. It may begin from undamaged area and propagate afterwards. In this case, a mechanical component condition before an unstable crack still can be used until fatigue. With the study of fatigue crack growth, it can predict the crack life of the component and can reduce cost to repair the component. In this thesis, primary objective is to develop, test and provide computational fracture mechanics model that emphasized an uncertainties quantification for surface crack. Fracture and failure study that has been promoted by S-version finite element method is focus on the analysis of the surface-crack problem. In this project, a few limitations of the study have been implemented as to present a specific scope of the investigation. Both fatigue crack growth model is considered; Paris law model and modified Forman model. The specimen in this analysis is aluminium al 2024 T3. The effect of load on the fatigue crack growth rate is investigated on aluminium 2024 T3. It is concluded that modified Forman has a low exponent compared to the Paris law. Further the crack growth prediction based on modified Forman is lower than Paris law. Paris law only can predict the crack in the region II while modified Forman can predict the crack in region II and III. After finish setup the project based on the instruction, the project is proceeded and the data is collected. The result is analysed based on the objective by using data collected from the project. After that, conclusion is made based on the result of the project.

Numerical modeling of crack propagation with dynamic insertion of cohesive elements

One of the most challenging issues in computational fracture mechanics is the propagation of a crack through a finite element mesh for arbitrary crack paths. In this work, this problem is approached by means of an advanced remeshing technique that propagates a crack using cohesive elements. The crack direction is computed using the maximal energy release rate criterion which is implemented using finite elements and the Gθ method. The remeshing procedure used here is composed of two stages. In the first step, a conforming mesh is obtained in the computed crack direction, ensuring that edges are placed over the sought direction. In the second stage, cohesive elements are dynamically inserted at the conforming edges previously remeshed. The combination of this remeshing technique with dynamic insertion of cohesive elements, leads to a mesh-independent crack propagation method. The effects of different numerical and physical parameters regarding the crack path and fracture energy is investigated.

Lamellar architectures in stiff biomaterials may not always be templates for enhancing toughness in composites

The layered architecture of stiff biological materials often endows them with surprisingly high fracture toughness in spite of their brittle ceramic constituents. Understanding the link between organic–inorganic layered architectures and toughness could help to identify new ways to improve the toughness of biomimetic engineering composites. We study the cylindrically layered architecture found in the spicules of the marine sponge Euplectella aspergillum. We cut micrometer-size notches in the spicules and measure their initiation toughness and average crack growth resistance using flexural tests. We find that while the spicule’s architecture provides toughness enhancements, these enhancements are relatively small compared to prototypically tough biological materials, like nacre. We investigate these modest toughness enhancements using computational fracture mechanics simulations.

Nonlinear Fracture Mechanics Analysis Considering Material Inhomogeneity of Welded Joints

Professor Hiroshi Okada and his team from the Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Japan, are engaged in the field of computational fracture mechanics. This is an area of computational engineering that refers to the creation of numerical methods to approximate the crack evolutions predicted by new classes of fracture mechanics models. For many years, it has been used to determine stress intensity factors and, more recently, has expanded into the simulation of crack nucleation and propagation. In their work, the researchers are proposing new methods for fracture mechanics analysis and solid mechanics analysis.

NURBS-Based Isogeometric Analysis Method Application to Mixed-Mode Computational Fracture Mechanics

In this paper, unified shear deformation theory is used to analyze simply supported thick isotropic beams for the transverse displacement, axial bending stress, transverse shear stress and natural frequencies. This theory enables the selection of different in-plane displacement components to represent shear deformation effect. The numbers of unknowns are same as that of first order shear deformation theory. The governing differential equations and boundary conditions are obtained by using the principle of virtual work. The results of displacement, stresses, natural bending and thickness shear mode frequencies for simply supported thick isotropic beams are presented and discussed critically with those of exact solution and other higher order theories. The study shows that, while the transverse displacement and the axial stress are best predicted by the models 1 through 5 whereas models 1 and 2 are overpredicts the transverse shear stress. The model 4 predicts the exact dynamic shear correction factor (pi^2/12 = 0.822) whereas model 1 overpredicts the same.

Open issues in PTS assessment of WWER RPVs

The main aim of the paper is the critical review of the current methodologies of WWER RPV brittle fracture assessment from the practical point of view. Design rules PNAE-G-7-002-86 and three modern approaches (Ukrainian MT-D.0.03.391-09, Czech and EU VERLIFE and Russian MRKR-SKhR-2004) are considered. Main issues of the modern methodologies are divided into two parts, that are related to computational fracture mechanics and to fracture characteristics (Fracture Toughness curve and Ductile to Brittle Transition Temperature) of metal of RPV beltline zone as well.The misconceptions of current methodologies of RPV brittle fracture assessment are described as well as recommendations for they improvements are given. It is shown, that some of problems (for instance cladding integrity, modelling of weld residual stresses, Fracture Toughness curve modification) needs to be justificated, before they are considered as a part of good-practice methodology of RPV integrity assessment. In particular, unreasonable high level of conservatism of Fracture Toughness curves specified in modern methodologies is shown. And finally, for some of them such as VERLIFE’s probabilistic embrittlement trend curve generation and Master-Curve approach for both deterministic and probabilistic assessment, – engineering inapplicability is demonstrated. Some improvements, such as chemical factor consideration and transition temperature determination for radiation embrittlement assessment, probabilistic RPV brittle fracture assessment are developed by “IPP-Centre” LLC and briefly presented.

Elasto Plastic Crack Growth by XFEM: A Review

Abstract This paper presents a review on the applications of extended finite element method in the modelling of elastoplastic crack growth. This article presents an overview and recent progress of the extended finite element method in the analysis of crack growth. It summarizes the important milestones achieved by the finite element community in the arena of computational fracture mechanics. The work aims at discussing the basic ideas and methodologies of extended finite element method (XFEM). The advantage of the method is that the element topology need not conform to the surfaces of the cracks. XFEM models all types of cracks independent of the mesh chosen for analysis. Moreover, XFEM coupled with the level set method provides the accurate description of complex engineering geometries, which may otherwise be impossible to solve using the standard finite element method. The extended finite element method (XFEM) is an accurate and powerful numerical technique for modelling different types of discontinuities such as holes, cracks, inclusions and contact surfaces.

Computational fracture mechanics: An overview from early efforts to recent achievements

AbstractAn overview of the state of the art of computational fracture mechanics is presented, starting from early efforts and going all the way up to recent achievements. Some specific aspects of linear elastic and elastic plastic fracture mechanics problems have been discussed, including the fact that even for a static loading, numerical simulation is not a simple task because of complex geometries, material nonlinearity, and heterogeneity, and especially if crack growth is considered. Therefore, micromechanical modelling of elastic‐plastic crack growth is presented as new and promising approach to overcome some of the shortages of traditional approach. Besides static loading, couple of other important practical problems are tackled, like fatigue crack growth, with remaining life in the focus of investigation, using the empirical laws for crack growth rates. Numerical simulation of fatigue crack growth is inherently complex both because of complex material damage processes and lack of sound theoretical basis to define them. Therefore, combination of theoretical, experimental, and numerical approach is presented here to get reliable and efficient estimation of life under fatigue loading.

Computational Methods for Ductile Fracture Modeling at the Microscale

This paper is a state-of-the-art review of computational damage and fracture mechanics methods applied to model ductile fracture at the microscale. An emphasis is made on robust and stable methods that can handle heterogeneous structures, large deformations , and cracks initiation and coalescence. Duc-tile materials' microstructures feature brittle and duc-tile components whose heterogeneous behavior can give raise to cracks initiation due to stress concentration. Due to large deformations, cracks initiated by brittle components failure transform into large voids. These major voids interact and coalesce by plastic localiza-tion within ductile components and lead to final failure. This process can involve minor voids nucleated directly within ductile components at sub-micron scales. State-of-the-art discontinuous approaches can be applied to discretize accurately brittle components and model their failure, given that large deformations can be handled. For ductile components, continuous approaches are discussed in this review as they can model the homogenized influence of minor voids, hence alleviating the burden and computational cost overhead that an explicit discretization of those voids would require. Close to final failure, when major voids are coalesc-ing, and the influence of minor voids becomes comparable to that of major voids, the transition from a continuous damage process within ductile components to the initiation and propagation of discontinuous cracks within these components has to be modeled. This review ends with a discussion on computational methods that have successfully been applied to model the continuous-discontinuous transition, and that could be coupled to discontinuous approaches in order to model ductile fracture at the microscale in its full three-dimensional complexity. Keywords ductile fracture; heterogeneous structure; microstructure; computational fracture mechanics; computational damage mechanics Nomenclature 2D Two-Dimensional 3D

Mechanical integrity of nano-interconnects as brittle-matrix nano-composites

In this study, the mechanical integrity of advanced multilayer nano-interconnects, as metal/dielectric nano-composites, was investigated using a combination of analytical modelling, computational mechanics and experiments. A method for fast derivation of the effective orthotropic elastic moduli of complex multilayer nano-interconnects was demonstrated and corroborated using finite element modelling (FEM). Subsequently, the effective elastic properties were employed for homogenization and course-graining in computational fracture mechanics models. This allowed the model development and simulation time to be reduced drastically and also enabled the global delamination behavior in nano-interconnects to be predicted consistent with experimental results. The study identified the via layers integrated with ultra low-k (ULK) dielectrics as the delamination prone layers. Particularly, failure analysis following exposure to bump shear tests revealed that the via layer adjacent to the top stiff layers was the dominant fracture path. By using analytical and computational mechanics it is shown that the elasticity mismatch between the soft intermediate group of layers and the stiff top group of layers dictates this delamination mode. Detailed FE modeling, showed that when vias are uniformly distributed, increasing the via density by only a few percent will increase the mechanical integrity drastically. Delamination experiments revealed a statistically significant increase of critical fracture energy (Gc) of ULK dielectric films when their thickness is reduced. Thus, reducing the thickness of the via layers, will also increase their effective Gc. However, analytical modelling together with experiments indicate that this trend will apply down to an optimal via layer thickness of approximately 30 nm where the Gc is predicted to reach its theoretical maximum in the case of organosilicate glass ULK (OSG 2.55).

Three-dimensional fundamental thermo-elastic field in an infinite space of two-dimensional hexagonal quasi-crystal with a penny-shaped/half-infinite plane crack

In the present work, a penny-shaped/half-infinite plane crack problem is investigated in the framework of thermo-elasticity of two-dimensional quasi-crystals. In view of the symmetry with respect to the crack plane, the original problem is formulated by a mixed boundary-value problem defined in a half-space. The boundary integral equations are derived by virtue of the general solution and the method of generalized potential theory. For the crack subjected to a pair of point temperature loadings, the corresponding fundamental thermo-elastic field variables are exactly and explicitly obtained in terms of elementary functions. Furthermore, the physical quantities on the crack plane, which are important in fracture mechanics, are given. Numerical calculations are carried out to discuss the validity of the present solutions and to characterize the thermo-phonon-phason coupling effect. The present analytical solutions may serve as benchmarks for future computational fracture mechanics of QCs and as a guide for the infrared thermography techniques in non-destructive detection.

Identifying the crack path for the phase field approach to fracture with non-maximum suppression

The phase field method is proven to be a powerful tool in computational fracture mechanics in that it can predict crack nucleation and branching, in some cases, without explicitly tracking the crack path. However, in such applications as hydraulic fracturing or leakage, it is necessary or beneficial to have the crack geometry available. This paper presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples.

Massive parallelization of the phase field formulation for crack propagation with time adaptivity

The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turn restricts the maximum element size that can be used in a finite element mesh. In this work we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields. We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Finally, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom.

Cracking behavior of tungsten armor under ELM-like thermal shockloads II: A revised prediction for crack appearance map

In this work, the surface cracking features of tungsten armor under thermal shock loads by edge-localized mode (ELM) were investigated by means of computational fracture mechanics analysis. For the simulation it was assumed that a small crack was initiated at low temperature after the shut-off of thermal load in contrast to the previous studies where the presence of a crack before thermal loading was assumed. The threshold power density for surface cracking was predicted to range between 0.3 and 0.6GW/m2 while the threshold of base temperature lay between 200 and 400°C. The theoretically predicted damage map agreed well with the experimental data from electron beam irradiation tests. The current simulation model turned out to match better to the real experimental observation than the previous predictions where the threshold base temperature lies roughly between 400 and 600°C.

Local and Global Approaches to Fracture Mechanics Using Isogeometric Analysis Method

The present research investigates the implementations of different computational geometry technologies in isogeometric analysis framework for computational fracture mechanics. NURBS and T-splines are two different computational geometry technologies which are studied in this work. Among the features of B-spline basis functions, the possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric analysis method a suitable candidate for modeling discrete cracks. Also, the repetition of two different control points between two patches can create a discontinuity in and demonstrates a singularity in the stiffness matrix. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. T-splines constitute a type of computational geometry technology with the possibility of local refinement and with no topologically rectangular arrangement of control points. Therefore, T-splines can decrease superfluous control points which do not have any major effects on the geometry. Various numerical simulations demonstrate the suitability of the isogeometric approach in fracture mechanics.

Extended finite element method in computational fracture mechanics: a retrospective examination

In this paper, we provide a retrospective examination of the developments and applications of the extended finite element method (X-FEM) in computational fracture mechanics. Our main attention is placed on the modeling of cracks (strong discontinuities) for quasistatic crack growth simulations in isotropic linear elastic continua. We provide a historical perspective on the development of the method, and highlight the most important advances and best practices as they relate to the formulation and numerical implementation of the X-FEM for fracture problems. Existing challenges in the modeling and simulation of dynamic fracture, damage phenomena, and capturing the transition from continuum-to-discontinuum are also discussed.

A direct evaluation of stress intensity factors using the Extended Dual Boundary Element Method

We introduce an alternative method in computational fracture mechanics to evaluate Stress Intensity Factors (SIFs) directly using the Extended Dual Boundary Element Method (XBEM) for 2D problems. Like other enrichment approaches, the new approach is able to yield accurate results on coarse discretisations, and the enrichment increases the problem size by only two degrees of freedom per crack tip. The BEM equations formed by collocation at nodes are augmented by two additional equations that enforce continuity of displacement at the crack tip. The enrichment approach provides the values of SIFs KI and KII directly in the solution vector and without any need for postprocessing such as the J-integral. Numerical examples are used to compare the accuracy of these directly computed SIFs to J-integral processing of both conventional and enriched boundary element approximations.

Discontinuous Galerkin/extrinsic cohesive zone modeling: Implementation caveats and applications in computational fracture mechanics

Implementation of the hybrid discontinuous Galerkin/cohesive zone model method, which is a (volumetric) locking free single field yet highly scalable method for nonlinear fracture mechanics problems, is presented. In this method cohesive interface elements are placed at element surfaces prior to the simulation of which artificial compliance is removed by a discontinuous Galerkin formulation. The formulation is switched to a standard extrinsic cohesive crack model upon satisfaction of a failure criterion. We provide details on the computation of the internal force vector and the tangent stiffness matrix. Examples that consist of (in) compressible elasticity, microcracking of fiber reinforced composite materials and dynamic fracture are provided. This paper is addressed to researchers who would like to have a quick working implementation of the discontinuous Galerkin/cohesive zone model method.

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

One current challenge related to computational fracture mechanics is the modeling of ductile fracture and in particular the damage to crack transition. On the one hand, continuum damage models, especially in their non-local formulation which avoids the loss of solution uniqueness, can capture the material degradation process up to the localization of the damage, but are unable to represent a discontinuity in the structure. On the other hand cohesive zone methods can represent the process zone at the crack tip governing the crack propagation, but cannot account for the diffuse material damaging process.In this paper we propose to combine, in a small deformations setting, a non-local elastic damage model with a cohesive zone model. This combination is formulated within a discontinuous Galerkin finite element discretization. Indeed this DG weak formulation can easily be developed in a non-local implicit form and naturally embeds interface elements that can be used to integrate the traction separation law of the cohesive zone model. The method remains thus consistent and computationally efficient as compared to other cohesive element approaches.The effects of the damage to crack transition and of the mesh discretization are respectively studied on the compact tension specimen and on the double-notched specimen, demonstrating the efficiency and accuracy of the method.

Integrity analysis of reactor pressure vessels subjected to pressurized thermal shocks by XFEM

The integrity of an reactor pressure vessel (RPV) related to Pressurized Thermal Shocks (PTSs) has been widely studied. However, due to the difficulties associated with the crack modeling with the 3-D finite element method (FEM), it is preferred to use models with simple geometries and crack configurations. In the last years new improved FEMs were developed which include the singularities and discontinuities and simplify the computational fracture mechanics studies. One of those methods, the eXtended Finite Element Method (XFEM) relies on the introduction of the crack effect with an enrichment of the finite element approximation space. This paper introduces the use of XFEM to the structural analysis of an RPV subjected to PTSs. The analysis compares the stress intensity factor (SIF) calculated with XFEM with results obtained by conventional FEM calculations.