Edge Crack Problem Research Articles

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

Galerkin finite block method with Lagrange multipliers method for cracked solids in functionally graded materials

This paper presents the application of the Galerkin Finite Block Method (GFBM) to address cracked solids associated with Functionally Graded Materials (FGMs), leveraging the foundational principles of the Galerkin method. The equilibrium equations pertinent to FGMs are articulated in their weak form. Employing Chebyshev polynomials as shape functions, the GFBM integrates mapping techniques to accommodate irregular finite or semi-infinite physical domains. Boundary and continuity conditions are enforced through the Lagrange Multiplier Method. The domain integrals are calculated through either analytical or numerical integration. The proposed method can easily solve the edge crack or diagonal crack problem by using the crack opening displacement method. The accuracy and convergence of the proposed method are illustrated through a selection of numerical examples. The obtained numerical solutions are verified with analytical solutions and the results from the Finite Element Method.

Inhibition Behavior of Edge Cracking in the AZ31B Magnesium Alloy Cold Rolling Process with Pulsed Electric Current

To solve the edge crack problem of AZ31B magnesium alloy cold rolling, a strong pulsed electric current was introduced to the cold rolling process. The influence of intensity, frequency, width of pulsed electric current and other parameters on edge cracking of AZ31B magnesium alloy plate cold rolling was analyzed based on the principle of a single variable. According to the experimental results, the assistance of pulsed electric current cut down edge cracking and the inhibition effect increased obviously with larger current parameters. When the parameters of pulsed electric current reached 4800 A, 500 Hz, 50 μs, zero edge cracking was achieved. Statistics of edge cracks, rolling load change, and microstructure analysis showed that the current thermal effect was not obvious and non-thermal effect played a more important role in the rolling process under pulse electric current. Edge cracks initiate at the shear bands. The addition of pulse current increases the number of shear bands and presents a blanket structure. Therefore, the amount of strain experienced by a single shear band decrease, which has a positive effect on inhibiting the formation of edge cracks. Furthermore, electroplastic rolling refines the grains and weakens the basal plane. As the current parameter increases, the hardness of the magnesium strip decreases and the yield and tensile strengths increase.

Multi-scale fracture analysis of fibre-reinforced composites

Fibre reinforced composite (FRC) have been widely used in engineering applications for the purpose of strengthening or lightening of the structures. Many modern applications such as aircraft structures, automotive components, ships, yacht, and infrastructures etc. are fabricated by FRC materials. Since the FRC is the homogenized mixture of fibre and resin (matrix). The structural performance of the FRC materials depends on the fibre arrangement in the matrix, as well as FRC constituents. Therefore, an accurate prediction of structural response of this material needs prior information of micro to macro-level material properties. This paper presents a multi-scale numerical approach to predict the fracture response of fibre reinforced composites. At the micro-level, analysis of representative volume element (RVE) using DIGIMAT software has been presented to describe the microstructure related material properties. In this analysis, fibre is described as a linear elastic material while the matrix phase is modelled by an exponential linear law. The unknown constitutive relationship at the macro-scale has been obtained by DIGIMAT-FE analysis. Further, the macro-scale constitutive relation is used to predict fracture behaviour of FRC. Virtual crack closure technique (VCCT) of Finite Element Method has been implemented to study fracture parameters of FRC. All presented computational results are obtained by DIGIMAT-FE analysis and ABAQUS software. In order to check the robustness and accuracy of the presented approach, few benchmark problems were solved at the multi-scale level and compared with the reference results. In addition, edge crack and centre crack problems were solved by the multi-scale approach to analyse the fracture response of FRC.

Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions

Response of an orthotropic half-plane subjected to transient anti-plane loading with multiple edge cracks

This study deals with the problem of multiple edge cracks in an elastic orthotropic half-plane under transient loading. The dislocation solution is utilized to derive integral equations for multiple interacting edge cracks in an orthotropic half-plane. These equations are solved numerically thereby obtaining the dislocation density function on the crack faces and stress intensity factors at crack tips. Numerical results are obtained to illustrate the variation of the dynamic stress intensity factors as a function of crack length and material properties.

Boundary Element Analysis for Piezoelectric Cracks by an Interaction Integral

In this paper, an interaction integral is applied to evaluate the crack-tip field intensity factors for piezoelectric cracks by using BEM. Based on this, the fracture parameters for different crack configurations and loading conditions are analyzed in details for both the center crack and edge crack problem. According to the present results, the path-independent behavior of the interaction integral is verified. The comparison of the I-integral results with those by the J-integral and the displacement interpolating methods shows a good agreement.

A new criterion for modeling multiple discontinuities passing through an element using XIGA

In this paper, a new criterion is proposed for the modeling multiple discontinuities i.e. crack, hole and inclusion passing through an element by XIGA. The modeling of multiple discontinuities passing through an element is done by imposing the additional degrees of freedom at the control points lying inside the influence of elements intersected by the discontinuities. In XIGA, the crack faces are modeled by discontinuous Heaviside jump functions, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The modeling of holes and inclusions is performed by Heaviside jump function and distance function respectively. The value of stress intensity factor is computed using domain form of interaction integral approach. Few static plane edge crack problems are analyzed in the presence of holes and inclusions to validate the proposed criterion. The results obtained by XIGA are compared with XFEM.

A micromechanical analysis of the fracture properties of saturated porous media

A two-dimensional single edge crack problem is employed to investigate the fracture behavior of saturated poroelastic media. The media are mimicked by a micromechanical model consisting of elastic matrix and square arrays of voids with prescribed uniform pore pressure. Finite element method is used to simulate the fracture responses of the model subject to remote stress and pore pressure loading. The stress extrapolation method is extended for the porous media to calculate the nominal stress intensity factor (SIF) from the crack tip stress field. By adopting the tensile strength criterion and assuming either brittle or ductile failure of the constituent solid skeleton of the porous media, lower and upper bounds of the fracture toughness are obtained. Theoretical expressions for the stress intensity factor and the toughness are derived, agreeing well with numerical results. The effects of the arrangement of pores and the non-uniform pore pressure on the cracking of porous media are discussed and are found to only have moderate effects on the obtained results.

Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension

It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering. However, the fracture mechanics studies of hole edge crack problems are not sufficient. The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated. Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors are provided. The stress distribution along the axes and the edge of the elliptical hole is given graphically. The numerical results show that there is obvious stress concentration near the hole and cracks, and the stresses tend to applied loads at distances far from the defect, which conform to Saint-Venant’s principle. Hence, the stress functions are proved to be right. Under special conditions, the present configuration becomes the Griffith crack, two symmetrical cracks emanating from an elliptical hole, two cracks of unequal length emanating from a circular hole, a crack at the edge of a circular hole, or a crack emanating from an elliptical hole. Compared with available results, stress intensity factors for these special shapes of ellipses and cracks show good coincidence. The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole. The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.

Oblique edge crack in an orthotropic material under thermal loading

An oblique edge crack in an orthotropic thermoelastic solid under thermal loading is analyzed, and thermally insulated and conductive cracks are considered. The thermal edge crack problem is formulated by the transformed function representation for linear thermoelasticity. The stress intensity factors and energy release rate induced by incompatible thermal strains are obtained, which are dependent on one geometric parameter and three orthotropic material parameters. The explicit dependence on one elastic orthotropic parameter is obtained by the orthotropy rescaling technique, and the influence of the other three parameters is examined numerically. The important influence of the material parameters on the stress intensity factors and energy release rate is discussed.

Numerical Simulation of Large Deformation Problems by Element Free Galerkin Method

In large deformation problems, the contribution of nonlinear terms is quite significant. Hence, components/structures involving large deformation must be analysed using non-linear theories. In this paper, element free Galerkin method (EFGM) has been applied to solve large deformation problems using updated Lagrangian approach. Geometrically nonlinear problems have been simulated assuming linear elastic material behaviour. The results obtained by EFGM have been compared with those obtained by FEM and analytical solutions. An elasto-plastic edge crack problem has been solved using nonlinear material behaviour and large deformation kinematics.

PARAMETER AND INTERACTION STUDY OF EDGE CRACK PROBLEM USING MESHFREE METHOD

In this work, element free Galerkin method (EFGM) has been used to obtain the solution of edge crack problem under mechanical loads as it provides a versatile technique to model static as well as moving crack problems without any requirement of remeshing. At first, some techniques are presented for enriching the EFG approximations near the crack tip such as extrinsic and intrinsic enrichment. Extrinsic enrichment involves the addition of solution form to the trial function, whereas the EFG basis is expanded to include few terms from crack tip solution in intrinsic enrichment. Apart from enrichment techniques, four basic techniques of smoothing meshless approximations near nonconvex boundaries are also presented such as diffraction, transparency, see through and wedge model. These techniques are then used for the parameteric analysis of an edge crack problem under mode-1 loading and results obtained using different approaches are compared with each other as well as with exact solution. Among these techniques, the extrinsic PU enrichment technique was found to be more accurate as compared to other approaches. Extrinsic PU enrichment technique has also been used for the analysis of a shear edge crack problem. In all these techniques, the value of mode-1 stress intensity factor and mode-2 stress intensity factor has been evaluated by interaction integral approach. Effect of crack orientation is also studied for different cases.

Single and double edge interface crack solutions for arbitrary forms of material combination

In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.

Thermoelectroelastic Solution for Edge Cracks Originating from an Elliptical Hole in a Piezoelectric Solid

Thermoelectroelastic solution is derived for the generalized two-dimensional problem of edge cracks originating from an elliptical hole in a piezoelectric solid based on complex variable method. First, the heat complex function is solved, and then the expressions for the complex potentials and field intensity factors are presented under the electrically impermeable boundary condition. Numerical analysis is also made to discuss the influences of crack length and heat flux on the electroelastic fields and fields intensity factors. It is found that the heat flux has great effect on the stress intensity factors for the mode II cracks, but its influence on the stress intensity factors for the mode I cracks and the intensity factors of electric displacements is not significant.

Numerical Solution of an Edge Cracked 2-D Piezoelectric Media Using Extended Finite Element Method

The numerical solution for an edge crack problem in a two-dimensional (2-D) finite piezoelectric media has been discussed using extended finite element method. The four-fold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors (IFs). The intensity factors as well as the mechanical energy release rate and the total energy release rate has been analyzed for different electro-mechanical boundary conditions. It is observed that the IFs results are coupled and contrary to analytic solution which shows uncoupled behaviour.

Edge-crack problem in a long cylindrical superconductor

In this work, the edge-crack problem is investigated for a long cylindrical high-temperature superconductor (HTS) under electromagnetic force. The distributions of the current density and the magnetic flux density in the cylinder are obtained analytically in the Kim critical state model. And then, based on the finite element method, the stress intensity factors at the crack tip for different magnetic fields and different lengths of the crack are obtained. The results obtained show that the applied field and the length of the edge crack have significant effects on the safety and validity of an HTS.

A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method

The extended finite element method is applied on the two-dimensional (2-D) finite piezoelectric media weakened by a crack. The fourfold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors. Four sequence of analysis, namely crack–mesh alignment, aspect ratio, mesh with local refinement and domain independency is done on the center and edge crack problems. These four analyses when combined together give an optimum result to study the finite specimen. It is observed that for smaller values of strip width to crack length ratio the finiteness of the specimen size affects the intensity factors.

A numerical study of crack interactions under thermo-mechanical load using EFGM

In this work, element free Galerkin method (EFGM) has been used to obtain the solution of various edge crack problems under thermo-mechanical loads as it provides a versatile technique to model stationary as well as moving crack problems without re-meshing. Standard diffraction criterion has been modified with multiple crack weight technique to characterize the presence of various cracks in the domain of influence of a particular node. The effect of crack inclination has been studied for single as well as two edge cracks, whereas the cracks interaction has been studied for two edge cracks lying on same as well as opposite edges under plane stress conditions. The values of mode-I and mode-II stress intensity factors have been evaluated by the interaction integral approach.

Mesh-Free Solution of Two-Dimensional Edge Crack Problems under Thermo-Mechanical Load

Abstract In this work, a mesh-free approach known as element free Galerkin method (EFGM) has been used to obtain the solution of two-dimensional edge crack problems in linear elastic fracture mechanics subjected to thermo-mechanical loads. The diffraction criterion has been modified with multiple crack weight technique to characterize the presence of all cracks in the domain of the influence of a node. The effect of crack orientation has been studied for two edge cracks lying on the same face as well as on opposite faces under plane stress conditions. The values of mode-I and mode-II stress intensity factors have been evaluated by domain based interaction integral approach. The results obtained by EFGM are compared with those obtained by finite element method.