Singular Stress Field Research Articles

A powerful matrix formalism for stress singularities in anisotropic multi-material corners. Homogeneous (orthogonal) boundary and interface conditions

A computational code based on a semianalytic procedure for the determination of the characteristic exponents and the singular stress and displacement fields in multi-material corners is developed. Linear elastic anisotropic materials under generalized plane strain state are considered. This code is a universal computational tool able to analyze both open and closed (periodic) corners, composed of one or multiple materials with isotropic, transversely isotropic or orthotropic constitutive laws, covering both mathematically non-degenerate and degenerate materials in the framework of Stroh formalism. In multi-material corners, material junctions with perfectly bonded or frictionless sliding interfaces can be studied. The considered homogeneous boundary conditions cover stress free and fixed faces, or faces with some restricted or allowed direction of displacements, defined either in the reference frame aligned with the cylindrical coordinate system or in an inclined reference frame. The code is developed in MATLAB and it is based on the Stroh matrix formalism for anisotropic elasticity, the concept of transfer matrix for single material wedges, and on the matrix formalism for homogeneous (orthogonal) boundary conditions. The comparison of the characteristic exponents obtained by the present code and by the solution of closed-form eigenequations available in the literature, has a two-fold objective, first to exhaustively check the general computational implementation of the matrix formalism presented, and second to check the closed-form expressions of eigenequations for relevant specific cases published in the literature.

Analysis of stress singularity in adhesive joints using meshless methods

Recent years saw a rise in the application of bonding techniques in the engineering industry. This fact is due to the various advantages of this technique when compared to traditional joining methods, such as riveting or bolting. The growth of bonding methods demands faster and more powerful tools to analyze the behavior of products. For that reason, adhesive joints have been the subject of intensive investigation over the past few years. Recently, a fracture mechanics based approach emerged with great potential to evaluate joint behavior, called Intesity of Singular Stress Fields (ISSF), similar to the Stress Intensity Factor (SIF) concept. However, it allows the study of multi-material corners and does not require an initial crack. This approach was not yet tested with meshless methods. The present work intends to fill this gap, resorting to the Radial Point Interpolation Method (RPIM). With this purpose, adhesive joints with four different overlap lengths (LO) bonded with a brittle adhesive were studied. The interface corner's stresses were also evaluated. The predicted strengths were compared with the experimental data to assess the accuracy of the applied methods. In conclusion, the ISSF criterion proved to be applicable to meshless methods, namely the RPIM.

Fracture analysis of cracked magneto-electro-elastic functionally graded materials using scaled boundary finite element method

This paper develops the scaled boundary finite element method to analyse fracture of functionally graded magneto-electro-elastic materials. Polygon meshes are employed to discretize the domain. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required to calculate the intensity factors. When the material gradients of the coefficients in the constitutive matrix are expressed as a series of power functions of the scaled boundary coordinates, the stiffness matrices can be integrated analytically. The formulation enables the generalized intensity factors of stress, electric displacement and magnetic induction fields along the radial direction to be represented analytically. This permits the calculation of the generalized intensity factors directly from the scaled boundary finite element solution of the singular stress, electric displacement and magnetic induction fields by following the standard stress recovery procedures in the finite element method. Several numerical benchmarks are presented to validate the proposed technique with the results reported in the literature.

Examination of plastic region size and two singular stress field on the ISSF adhesive strength evaluation method

In an adhesive joint under certain conditions, the adhesive joint strength is larger than the bulk adhesive strength. In this study, the fracture of adhesive joints by using the elastic-plastic behavior is considered. Then, the validity of evaluating the adhesive strength by two ISSFs based on the elastic analysis is discussed. Even when the butt joint strength is larger than the bulk adhesive strength, the small-scale yielding is occurred. Therefore, it is shown that the ISSF strength evaluation method is appropriate.

Residual Notch Stress Intensity Factor assessment via 3D welding numerical simulation: influence of power input

In fusion welded joints fatigue crack originates from the weld toe or weld route due to geometrical discontinuities inducing high stress concentration. This holds true even in presence of residual stress which was found to follow the same asymptotic distribution theorized first by Williams and then, in the elastic-plastic filed, by Hutchinson, Rice and Rosengren. Solid state phase transformations play a fundamental rule in determining the sign of the singular residual stress field. This obviously will influence the crack initiation life in the high cycle fatigue regime where plastic effects at the weld toe can be neglected. In this scenario, the influence of process parameters on the residual asymptotic stress distribution is not yet investigated using a 3D numerical modeling of the welding process. This work is aimed at filling this gap. Computational welding mechanics and the peak stress method are combined to calculate the residual Notch Stress Intensity Factors (R-NSIF) as a function of power input. Results are summarized in terms of heat input and discussed in view of a future guidelines proposal addressed to designers who are going to face a welding process optimization for fatigue life improvement.

Intensity of singular stress field for bonded body with dissimilar adherends

In this study, the intensities of the singular stress field (ISSFs) at the interface corner and interface edge in 3D BJ models with similar/dissimilar adherends are calculated by changing the adhesive layer thicknesses by the proportional method. The differences between the ISSFs for the 3D BJ models with similar/dissimilar adherends are discussed. The ISSF for the BJ with dissimilar adherends is larger than that for the BJ with similar adherends. The differences between the ISSFs for the 3D BJ models with similar/dissimilar adherends increase as the adhesive layer thickness decreases. When the adhesive layer thickness is 0.05 mm, the ISSF at the interface corner in the BJ with dissimilar adherends is about 1.7 as large as that for the BJ with similar adherends. Then, the remarkable differences between the singular stresses at the interface corner and along the interface edge in the BJ with dissimilar adherends are found.

An Over-deterministic Method Based on Atomistic Stress Fields: Higher Order Terms of the Williams power expansion

The investigation of the atomistic near crack-tip stress fields under Mixed Mode loading via molecular dynamics method implemented in a flexible classical molecular dynamics method software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is presented. The molecular dynamics modelling is applied for evaluation of the coefficients of higher-order terms of the Williams’ expansion -based approximation for the near crack tip fields in isotropic linear elastic materials. Fracture mechanics parameters such as stress intensity factors, higher-order coefficients of the Williams power-series for a copper plate with a central crack under Mode I and Mixed Mode (Mode I+Mode II) loadings are obtained by atomistic simulations. All computational experiments are realized in LAMMPS with the Embedded Atom Method (EAM) potential. The atomistic values of higher-order coefficients of the Williams series expansion are computed by the over-deterministic method and liken to the values obtained from classical continuum fracture mechanics solutions. It is demonstrated that the conventional continuum fracture theory successfully describes fracture quantities at extremely limited singular stress field of only several nanometers.

A convenient evaluation of intensity of singular stress field at the interface corner in single lap joint with fillet

A convenient evaluation of intensity of singular stress field at the interface corner in single lap joint with fillet

Stress Intensity Factors of Continuum Fracture Mechanics at the Nanoscale

The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum fracture mechanics parameters. Stress intensity factors for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated with the help of atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors are compared with the values obtained from continuum fracture mechanics considerations. It is shown that the continuum fracture theory successfully describes fracture even at extremely confined singular stress field of only several nanometers.

Parametric features of an UIC60 rail at weld bottom crack in transverse direction under weld-wheel contact forces

In this study, the stress fields of a welded beam track under the influence of a wheel-rail weld force are explored using a finite element model assembly of a weld wheel contact system which has been built on ANSYS space-claim. Practical observations have been shown that semi-elliptical type of cracks are most of the reason to failure of a weld thus a 3-D semi-elliptical type of crack has been induced on the bottom of the rail having transverse direction propagation. Simulation was performed using singular elemental method with ANSYS mechanical workbench for stress field singularity and transverse pattern of crack propagation on the bottom of the rail weld has been observed. The crack analysis and simulation tool in ANSYS workbench provides three modes of stress intensity factors where Mode-I factor KI shows increase in its value with increase in wheel force on its rail-weld contact under each type of forces i.e. vertical, lateral and longitudinal, and if there is an increase in the lateral force the KI took its maximum value. Now if we increase the vertical force the rest of two intensity factors KII and KIII shows a decreasing tendency. It has been observed also that if the longitudinal and lateral forces raised simultaneously both KII and KIII increases in magnitude. The amplitude of KI at the tip side of crack on welds outer edge is greatest within the Stress Intensity Factor of the crack tip, whereas the peak of KII and KIII on the crack-tip of weld centerline seems the highest in the range of Stress Intensity Factor.

Crack singular field evaluation with characteristic tensor considering residual stress

ABSTRACT To accurately evaluate the fracture behaviour and fatigue life of welded structures, it is necessary to consider welding residual stress in addition to the stress produced by the applied loads. Characteristic tensor, which has a proportional relationship to stress intensity factor (SIF), is one new approach to evaluate stress singularity caused by a crack. Characteristic tensor is the tensor that is easily calculated by integrating stresses in a simple sphere zone around a crack tip using coarse mesh without special limitation in the mesh division, even under general cases like mixed-mode loading conditions. In this study, the stress singularity in the welded plate is evaluated by characteristic tensor and its effectiveness with the residual stress field is verified. Firstly, the residual stress distribution in butt-welded plates is calculated by the finite element method. Secondly, the singular stress field is obtained by introducing a single straight crack in the welded plates. A crack with different lengths and the crack tip located at different residual stress states are considered in reproducing the stress singularity. In each case, SIF is estimated from the characteristic tensor calculated from stress distribution nearby a crack tip and compared to those from the Green’s function or virtual crack extension method. Additionally, the stress singularity caused by the external load is evaluated in the same manner. The estimated SIFs with coarse mesh are in good agreement with the conventional methods. The results suggest that characteristic tensor provides a practical approach to evaluating stress singularity in welding structures.

A strain gradient enhanced model for the phase‐field approach to fracture

AbstractPhase‐field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that the total energy of fracture in the classical phase‐field formulations includes the strain energy density from the linear elasticity theory resulting in singular stresses at the crack tip. Recently, we have demonstrated that integrating the strain gradient elasticity into the conventional phase‐field fracture formulations may improve the final results by alleviating the effects of a singular stress field around the crack tip [1]. The current contribution focuses on a more general formulation of strain gradient elasticity.

On the three-dimensional singular stress field near the corner front of revolution-shaped inclusions

On the three-dimensional singular stress field near the corner front of revolution-shaped inclusions

Meshless analysis of the stress singularity in composite adhesive joints

Adhesives are an exceptionally well-suited method for joining composites. Unlike other methods, such as bolting or riveting, adhesives do not introduce holes in their joining material. This is a significant advantage in the case of composites because the holes required by bolting or riveting induce stress concentrations and can also lead to tears, burrs or delamination. A point of concern in adhesive joints is the adhesive/adherend interface corner where a stress singularity occurs, and failure usually initiates. Thus, it is crucial to study this stress singularity to better understand adhesive joints’ mechanical behaviour.The goal of this work is to validate the application of the Intensity of Singular Stress Fields (ISSF) criterion to meshless methods, in this case, the Radial Point Interpolation Method (RPIM). With this purpose, eight overlap lengths (LO) in single-lap joints (SLJ) composed of Carbon Fibre Reinforced Polymer (CFRP) and bonded with a brittle adhesive were experimentally and numerically tested. Furthermore, an extrapolation based method is implemented to determine the critical stress singularity components (Hc) necessary for the strength predictions. In the end, the experimental and numerical results are compared to assess the suitability of the method. It was found that the ISSF criterion can be accurately applied to meshless methods and composite materials successfully, given the simplicity of the method applied.

Emergence of non-trivial polar topologies hidden in singular stress field in SrTiO3: topological strain-field engineering

Discovery of non-trivial topological structures in condensed matters holds promise in novel technological paradigms. In contrast to ferromagnetics, where a variety of topological structures such as vortex, meron, and skyrmion have been discovered, only few topological structures can exist in ferroelectrics due to the lack of non-collinear interaction like the Dzyaloshinskii–Moriya interaction in ferromagnetics. Here, we demonstrate that polarization structures with a wide range of topological numbers (winding number n from −3 to +1) can be mechanically excited and designed by the mode-I singular stress field formed near the crack-tip in incipient ferroelectric SrTiO3. Our phase-field simulations based on Ginzburg–Landau theory successfully reveals that the near-tip polar topology is driven by the flexoelectric coupling with intense strain gradient at the tip, while a variety of the far-field topological structures is triggered by a collaboration between the electrostrictive and flexoelectric effects. The strain (gradient) field analysis further shows that the unexpected topological characters are implied in the singular stress field, which develops a variety of polar topologies near the crack tip. Therefore, our work provides a novel insight into the unusual interplay between mechanical- and ferroelectric-topologies, i.e. ‘topological strain-field engineering’, which paves the way to the mechanical design of functional topologies in the matter.

Crack-tip Stress Fields on Anisotropic Plate

The basic equation of elastic mechanics has been established according to the anisotropic material properties. The crack-tip stress problem has been investigated for the mixed loading condition. In order to determine the stress fields in an anisotropic plate, the pan-complex variable means must be utilized. Typical analytic function including the material parameter was analyzed fully. The special functions have been determined to be satisfactory for the stress boundary conditions. The pan-complex variable means as well as polar coordinate transform method were adopted so as to solve the mixed loading problems on cracked anisotropic plate. Finally, the explicit expressions of the singular stress fields were obtained with the real variables. The means in the paper ought to be of benefit to the stress fields and fracture character analysis of anisotropic plates.

Analysis of Intensity of Singular Stress Field at the Stepped-Lap Joint

Analysis of Intensity of Singular Stress Field at the Stepped-Lap Joint

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

AbstractThe plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

Investigation of the Near-Tip Stress Field of a Notch Terminating at a Bi-Material Interface.

The article deals with the problem of a sharp corner, the tip of which is located on the bi-material interface. The paper presents a qualitative and quantitative description of singular stress fields occurring in the tip area of such a stress concentrator. The qualitative description was obtained by solving the problem of the plane theory of elasticity with appropriately defined boundary conditions. To obtain a quantitative description, it was necessary to determine the values of generalised stress intensity factors (GSIFs). The GSIFs were determined using the developed analytical-numerical method. The calculations were made for various load variants (uniaxial/biaxial tension load, shear load) and notch positions (single/double edge-notched plate, centre-notched plate). Additionally, the impact of notch geometry (height and opening angle) and relative stiffness (Young’s moduli ratio of both components of bi-material) on GSIFs was investigated. It has been noticed that with a decrease in the relative stiffness and an increase in the notch angle or its height, the normalised GSIFs values increased. The obtained results were compared with the data available in the literature and their satisfactory agreement with those presented by other scientists was found.

Mode-I stress intensity factors for cracked R-fluted shells under complex loads

Based on the conservation law and bending theory, a technique to determine complicated stress intensity factors on three-dimensional components is proposed, A series of closed form expressions of stress intensity factor are derived for cracked shells under different loads, such as bending, tension. The method requires the geometric relationship between multiple singular stress fields from the crack section, and the relationship between the stress at different crack tips can be estimated. In the expression of the stress intensity factor K, K is proportional to the stress σ at the crack tip, and we can get the supplementary equation of between different stress fields K according to the ratio of the stress at the crack tip, then use the J-integral method to calculate the stress intensity factors of different stress fields. In order to verify the feasibility of this method, a cracked R-fluted shells model was constructed. Under the action of the bending moment, the corner crack propagation is simulated through the reserved corner crack, and two crack tips with different stress fields are generated during the simulation. The research result indicates that the proposed method is effective for cracked R-fluted shells, and has universal applicability for solving complex stress intensity factors on three-dimensional components.