Fracture Mechanics Problems Research Articles

Numerical Simulation of Three Dimensional Fracture Mechanics Problems of Functionally Graded Pipe and Pipe Bend Using XFEM

Numerical Simulation of Three Dimensional Fracture Mechanics Problems of Functionally Graded Pipe and Pipe Bend Using XFEM

Optimized Mesh-free Analysis for the Singularity Subtraction Technique of Linear Elastic Fracture Mechanics

In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since the representation of this singularity in a numerical model raises considerable numerical difficulties, the paper uses a strategy that regularizes the elastic field, subtracting the singularity from the stress field, known as the singularity subtraction technique (SST). In this paper, the SST is implemented in a local mesh-free numerical model, coupled with modern optimization schemes, used for solving two-dimensional problems of the linear elastic fracture mechanics. The mesh-free numerical model (ILMF) considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration. Since the ILMF model implements the singularity subtraction technique that performs a regularization of the stress field, the mesh-free analysis does not require a refined discretization to obtain accurate results and therefore, is a very efficient numerical analysis. Mesh-free numerical methods control the accuracy and efficiency of the model through the size of compact supports, the size of integration domains and the distribution of nodes in the body, which are usually heuristically determined through an expensive and time consuming calibration effort. The leading innovation of this paper is the automatic definition of these parameters and the nodal distribution by means of a multi-objective optimization, based on genetic algorithms (GA), with reliable and efficient objective functions. The optimization scheme effectively automates the whole pre-processing phase of a numerical analysis with mesh-free methods. Benchmark problems were analyzed to assess the accuracy and efficiency of the modeling strategy. The results presented in the paper are in perfect agreement with those of reference solutions and therefore, make reliable and robust this mesh-free numerical analysis, coupled with a multi-objective optimization,for linear elastic fracture mechanics problems.

Static and dynamic mechanical behaviors of cracked Mindlin plates in ordinary state-based peridynamic framework

An ordinary state-based peridynamic (PD) model based on the Mindlin plate theory is presented to deal with fracture mechanics problems. Static and dynamic stress resultant intensity factors regarded as the primary fracture parameters for plate structures are evaluated by the displacement extrapolation method. Owing to the PD surface effect, however, the accuracy of the displacement field near crack surfaces is significantly affected. Therefore, the arbitrary horizon domain method is adopted to correct the surface effect. It derives the variable PD parameters to properly describe mechanical behaviors for each material point. Several numerical examples are investigated to examine the performance of the presented method. It indicates that the PD Mindlin plate model incorporated with the arbitrary horizon domain method validly minimizes the influence of the PD surface effect and provides an effective approach to evaluate static and dynamic moment intensity factors.

MODELING THE EFFECT OF STOCHASTIC DEFECTS FORMED IN PRODUCTS DURING MACHINING ON THE LOSS OF THEIR FUNCTIONAL DEPENDENCIES

The article investigates the influence of hereditary defects formed in the surface layer of products from metals of heterogeneous structure on the quality of surfaces treated with finishing methods. The research is based on an integrated approach based on the results of the deterministic theory of defect development and methods of probability theory. The treated layer of the product is considered as a medium weakened by random defects that do not interact with each other, namely: structural changes, cracks, inclusions, the parameters of which are random variables with known laws of their probability distribution. The causes of structural changes, crack formation on the treated surface product depending on different types of probability distribution of dimensions are investigated: length, depth of defects, and their orientation. From these positions, technological possibilities of their elimination by definition of branch of combinations of the technological parameters providing necessary quality of the processed surfaces are considered. Modeling of thermomechanical processes in the treated surface containing hereditary defects is carried out based on thermoelastic equations with discontinuous boundary conditions in the places of their accumulation. The research used the apparatus of boundary value problems of mathematical physics equations, the method of singular integral equations for solving problems of fracture mechanics, Fourier-Laplace integral transformations for obtaining exact solutions, the method of constructing discontinuous functions. The dependences determining the intensity of stresses in the vertices of hereditary defects are obtained. A method for predicting the nature of crack formation depending on the probability distribution of defects, the values of heat flux entering the surface layer of the processed product has been developed. It is established that the increase in the homogeneity of the material leads to an increase in the value of heat flux, which corresponds to a fixed probability of failure.

On General List of References to the Monograph “Eight Non-Classical Problems of Fracture Mechanics”

On General List of References to the Monograph “Eight Non-Classical Problems of Fracture Mechanics”

Complex Fourier‐based stress intensity factor analysis of plane elasticity using boundary element theories

AbstractIn this article, the boundary element method is implemented for solving linear elastic fracture mechanics problems, using new complex Fourier shape functions which include constant and linear complex Fourier shape functions. They, unlike the classic Lagrange shape functions, can satisfy the exponential and trigonometric function fields in addition to the polynomial ones. Six numerical examples are provided to investigate the new shape functions and also, the stress intensity factors (SIF) are calculated for each so that the accuracy of the present study is illustrated. The results are compared with those obtained by classic Lagrange ones and the existing methods.

NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

Smoothed floating node method for modelling 2D arbitrary crack propagation problems

In this work, Floating Node Method (FNM), first developed for fracture modelling of laminate composites, is coupled with cell-wise strain Smoothed Finite Element Method (SFEM) for modelling 2D linear elastic fracture mechanics problems. The proposed method is termed as Smoothed Floating Node Method (SFNM). In this framework, FNM is used to represent the kinematics of crack and the crack front inside the domain without the requirement of remeshing and discontinuous enrichment functions during crack growth. For smoothing, a constant smoothing function is considered over the smoothing domains through which classical domain integration changes to line integration along each boundary of the smoothing cell, hence derivative of shape functions are not required in the computation of the field gradients. The values of stress intensity factor are obtained from the SFNM solution using domain based interaction integral approach. Few standard fracture mechanics problems are considered to check the accuracy and effectiveness of the proposed method. The predictions obtained with the proposed framework improves the convergence and accuracy of the results in terms of the stress intensity factors and energy norms.

Boundary element method for investigating large systems of cracks using the Williams asymptotic series

One of the main problems of fracture mechanics is to describe the behavior of media with cracks. At the same time, more and more attention is paid to the study of large systems, including periodic structures. For several cracks, the coefficient of influence is considered to be an important parameter. It is the ratio of the stress intensity factor calculated in the problem of a system of cracks to the stress intensity factor for a single crack under the same load. The paper proposes a method that allows to accurately determine the coefficients of influence for large systems of cracks, including the case of periodic structures, in which the number of cracks is infinite. The method is based on a numerical algorithm developed by the authors that uses the method of discontinuous displacements of a high order of accuracy and an asymptotic representation of stress fields at the crack tip (M. Williams). To verify the method, the results of the implemented algorithm are compared with known analytical solutions both for single cracks and for an infinite doubly periodic system of cracks.

Research on fracture behaviour of the adhesive sealant based on energy failure criterion for TFT-LCD

The adhesive sealant is a crucial structure connecting color filters and thin film transistors in liquid crystal panels. Research on the fracture progress of the connection structure is heavily needed in reliability evaluation engineering. In this work, three types of adhesive sealants with different widths were tested by the uniaxial tensile experiment to obtain their fracture process curves, which conformed to the brittle fracture characteristics described by the bilinear cohesion zone model. Then, according to the theory of engineering fracture mechanics, the Dugdale-Barenblatt plastic zone model was employed to analyze the adhesive sealant with hole defects, and it was simplified to mode ? fracture mechanics problem. Calculating with finite element numerical simulation, the numerical relationship between the stress field of the internal defect and the external stress of the material was obtained, and the brittle fracture behavior model was deduced as related to the defect size. Applying the model to the adhesive sealant, the average error of the model value after the correction was reduced from 7.98-12.13% to 6.84-7.53%, and the overall error was only within 15%. The model includes the material’s basic characteristics and the defect’s size that affect the fracture process, provides a theoretical basis for predicting the fracture of the sealant and improving the strength of bonded joints, thus is of great significance for material application and fracture analysis in engineering.

Machine learning RBF-based surrogate models for uncertainty quantification of age and time-dependent fracture mechanics

This paper proposes a machine learning strategy using radial basis function (RBF) as surrogate models for uncertainty quantification of age and time-dependent fracture mechanics problems. The RBF surrogate models are trained to replace the time-consuming evaluations of the mapping integral of the time-dependent energy release rate. The probabilistic problem considers input random variables of geometry, loading, and material parameters for a concrete plate section with the presence of an initial surface crack. The performance of the RBF surrogates was evaluated through cross-validation and Monte Carlo reference solutions that expensively evaluated the integrals. The results of mean square errors and the Kolmogorov-Smirnov goodness-of-fit tests on the predicted probability and cumulative density functions show that, the RBF surrogates reached good accuracy even for a small training set size, rather than second-order polynomial models which could reasonably perform only for bigger training set sizes. The RBF surrogates accurately predict even long-tail distributions for farther prediction times with relatively small training sets. The proposed RBF surrogate models presented the generalization capabilities to predict thousands of unseen data points from Monte Carlo simulations and successfully assess the uncertainty quantification of the time-dependent energy release rate.

A generalized 2D Bézier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets

In this study, a robust Bezier-based multi-step method is extended to accurately solve the governing fourth-order complex partial differential equation (PDE) in linear elastic fracture mechanics (LEFM) problems. The Bezier technique was first introduced by the authors to solve initial value problems in one dimension. Now, the method is further extended to simultaneously solve Boundary Value Problems (BVPs) in orthogonal directions. To examine the accuracy and performance of the present method, the first-mode normalized stress intensity factor (SIF) of a 2D epoxy resin plate having an initial edge crack and reinforced with randomly oriented graphene nanoplatelets (GnP) is determined and compared with the associated exact analytical solution using the Bayesian statistical analysis. Besides, the impact of GnP aspect ratio on the normalized crack opening displacement (COD) of the reinforced matrix is elaborated for the first time in the literature. Results of the present study suggest that GnPs with maximum aspect ratio are most effective to enhance elastic properties of the plate and potentially limit the edge crack propagation. Specifically, inclusion of 0.5 and 1.0% of needle-shaped GnPs in a notched epoxy resin plate decrease the maximum normalized COD by 33 and 50%, respectively, while for square-shaped GnPs, these reductions are limited to 20 and 37%, respectively.

Effect of Poroelastic Coupling and Fracture Dynamics on Solute Transport and Geomechanical Stability

AbstractThe coupling between solute transport and rock's geomechanical processes, for example, flow‐induced fracture activation, has emerged as an important hydrogeological challenge due to its role in applications such as underground waste disposal, carbon sequestration, contaminant remediation, enhanced oil recovery, and tracer‐based reservoir surveillance. Despite recent advances in modeling flow and geomechanics coupling, a holistic approach to capturing the synergy between fluid flow, solute transport, induced stresses, and fracture mechanics is lacking. This study investigates the rich interplay between these processes within a novel computational framework that is proposed to solve the coupled flow, transport, geomechanics, and fracture mechanics problem. The Embedded Discrete Fracture Modeling (EDFM) method is used to model the flow and transport processes in fractured porous media while an improved Bandis model is employed to capture the fracture mechanical response to flow‐induced stress perturbations. The role of transport‐geomechanics coupling in modulating the spreading and miscibility of a solute slug during viscously unstable flows is examined. We investigate how flow‐transport coupling, parameterized through the solute viscosity contrast and the fracture permeability, influences the stress state and fracture stability in the domain. A case study, inspired by a huff‐n‐puff tracer flowback study, is conducted to investigate the applicability of the proposed framework in the field. A sensitivity analysis is performed to evaluate the dependence of global transport characteristics, permeability evolution, and fracture stability on parameters dictating the strength of coupling between geomechanics, flow, and transport.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

Purpose It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity. Design/methodology/approach The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings. Findings The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy. Originality/value Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

Two- and Three-Dimensional Numerical Investigation of the Influence of Holes on the Fatigue Crack Growth Path

Problems in fracture mechanics are difficult when the appropriate analysis is unspecified, which is very common in most real-life situations. Finite element modeling is thus demonstrated to be an essential technique to overcome these problems. There are currently various software tools available for modeling fracture mechanics problems, but they are usually difficult to use, and obtaining accurate results is not an obvious task. This paper illustrates some procedures in two finite element programs to solve problems in two- and three-dimensional linear-elastic fracture mechanics, and an educational proposal is made to use this software for a better understanding of fracture mechanics. Crack modeling was done in a variety of ways depending on the software. The first is the well-known ANSYS, which is usually utilized in industry, and the second was a freely distributed code, called FRANC2D/L, from Cornell University. These software applications were used to predict the fatigue crack growth path as well as the associated stress intensity factors. The predicted results demonstrate that the fatigue crack is turned towards the hole. The fatigue crack growth paths are influenced by the varying positions and sizes of single holes, while two symmetrically distributed holes have no effect on the fatigue crack growth direction. The findings of the study agree with other experimental crack propagation studies presented in the literature that reveal similar crack propagation trajectory observations.

A new insight into analysis of linear elastic fracture mechanics with spherical Hankel boundary elements

In this research, the solution of linear elastic fracture mechanics problems when using spherical Hankel shape functions in the boundary element method is investigated. These shape functions benefit from the advantages of Bessel function fields of the first and second kind in addition to the polynomial ones, which makes them a robust and efficient tool for interpolation. Among the most important features of Hankel shape functions, the infinite piecewise continuity and the utilization of complex space with no influence on the imaginary part of the partition of unity property can be pointed out. The calculation of the stress intensity factors (SIFs) is carried out in five numerical examples so that the accuracy of the present study can be illustrated. Comparisons are made between the results of using spherical Hankel shape functions, the experimental ones, and those obtained by classical BEM with Lagrange shape functions. According to the results of these comparisons, the proposed spherical Hankel shape functions present more accurate and reliable results in comparison with the classic Lagrange ones.

Applications of the Trefftz method to the anti-plane fracture of 1D hexagonal piezoelectric quasicrystals

In terms of solving fracture mechanics problems of quasicrystals, the boundary element method known as Trefftz Method is used for the first time. In this paper, the collocation Trefftz method as an indirect Trefftz method has been demonstrated to be an excellent numerical method for the anti-plane fracture problems in quasicrystals plate, which can exactly satisfy the governing equations and approximately satisfy the boundary conditions. The algorithms of the collocation Trefftz method and the trial functions for the anti-plane fracture problems of piezoelectric quasicrystals are presented. The effects of the geometry size, the loadings and the materials properties on the fracture results are studied. For the materials with three dimensional constitutive relations, such as piezoelectric quasicrystals, the Trefftz method is an effective numerical method to solve the fracture problems.

Inverse problems with the digital image correlation: approach and applications

A viable approach to solve inverse problems in elasticity is proposed. It is based on regression algorithms to estimate materials and/or loading parameters by fitting the experimentally-evaluated displacement field to representative analytical solutions. Displacements are measured by the digital image correlation (DIC) technique and they are used as input for numerical procedures able to minimize the estimation errors of the unknowns and to quantify the unavoidable rigid body motions of the samples/components. In addition, thanks to ad-hoc developed iterative algorithms, non-linear phenomena related to high and localized stress/strain states, can be captured successfully. This latter represents a relevant novelty of the methodology as it allows to investigate plasticity-induced mechanisms in solid mechanics which are impossible to analyze with more traditional DIC-based approaches. Three different case studies are considered: 1) estimation of the stress intensity factor in fracture mechanics problems, 2) estimation of the elastic properties of a material by the Brazilian tests, 3) estimation of the contact pressure generated by thermally activated shape memory alloy (SMA) rings used for pipe coupling. The reliability and the accuracy of the method is demonstrated through systematic comparisons of the results with conventional techniques in experimental mechanics.

Knowledge extraction and transfer in data-driven fracture mechanics

Data-driven approaches promise to usher in a new phase of development in fracture mechanics, but very little is currently known about how data-driven knowledge extraction and transfer can be accomplished in this field. As in many other fields, data scarcity presents a major challenge for knowledge extraction, and knowledge transfer among different fracture problems remains largely unexplored. Here, a data-driven framework for knowledge extraction with rigorous metrics for accuracy assessments is proposed and demonstrated through a nontrivial linear elastic fracture mechanics problem encountered in small-scale toughness measurements. It is shown that a tailored active learning method enables accurate knowledge extraction even in a data-limited regime. The viability of knowledge transfer is demonstrated through mining the hidden connection between the selected three-dimensional benchmark problem and a well-established auxiliary two-dimensional problem. The combination of data-driven knowledge extraction and transfer is expected to have transformative impact in this field over the coming decades.