A study on the induced drilling stresses in the centre hole method of residual stress measurement

This paper aims at the improvement of the accuracy of the centre hole method of residual stress measurement by reducing the error caused by the drilling itself. Based on the results of an intensive experimental investigation, a new approach is proposed for the determination of the induced drilling stresses caused by the mechanical drilling process. In this study, the electric discharge machining (EDM) technique was utilised to obtain a stress free sample from the bulk material. As compared to the annealing heat treatment method for obtaining a stress free sample, it was found that the EDM technique does not cause the changes of the structures and machining properties of the parent material. Thus, the induced drilling stresses in centre hole method can be evaluated more accurately by using a stress free sample obtained by EDM technique than by using an annealed one.     

Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method

In this paper, we use a numerical method based on the boundary integral equation (BIE) and an application of the dual reciprocity method (DRM) to solve the second-order one space-dimensional hyperbolic telegraph equation. Also the time stepping scheme is employed to deal with the time derivative. In this study, we have used three different types of radial basis functions (cubic, thin plate spline and linear RBFs), to approximate functions in the dual reciprocity method (DRM). To confirm the accuracy of the new approach and to show the performance of each of the RBFs, several examples are presented. The convergence of the DRBIE method is studied numerically by comparison with the exact solutions of the problems.     

A new approach to triaxial residual stress evaluation by the hole drilling method

A new analysis technique is introduced to resolve the triaxial residual stress profiles from measurements using the conventional strain gauges for the hole drilling or ring core method extended with a displacement transducer to measure the out of plane displacement. The new technique uses an inverse formulation with wavelets.     

A New Method to determine Triaxial Non-Uniform Residual Stresses from Measurements using the Hole Drilling Method

A new integral analysis technique in combination with finite element calibration data is introduced to resolve the triaxial residual stress profiles of measurements performed with the hole drilling or ring core method. The new technique uses an inverse formulation with symmetrised trigonometric basis functions or wavelets.     

On the correction of plasticity effect at the hole edge when using the centre hole method for measuring high welding residual stress

Significant error caused by plasticity at the hole edge may arise when measuring sufficiently high welding residual stress by means of the hole drilling method. According to elastoplastic theory, a critical parameter of plastic deformation round the centre hole is obtained. On the basis of this critical parameter, a simple method is proposed to correct the stresses for the plasticity effect. It is shown in the experiments with welded joints that the correction method may improve the accuracy of high residual stress measurement.     

Structural shape and topology optimization using a meshless Galerkin level set method

This paper aims to propose a meshless Galerkin level set method for shape and topology optimization of continuum structures. To take advantage of the implicit free boundary representation scheme, the design boundary is represented as the zero level set of a scalar level set function, to flexibly handle complex shape fidelity and topology changes by maintaining concise and smooth interface. Compactly supported radial basis functions (CSRBFs) are used to parameterize the level set function and construct the shape functions for meshfree approximations based on a set of unstructured field nodes. The meshless Galerkin method with global weak form is used to implement the discretization of the state equations. This provides a pathway to unify the two different numerical stages in most conventional level set methods: (1) the propagation of discrete level set function on a set of Eulerian grid and (2) the approximation of discrete equations on a set of Lagrangian mesh. The original more difficult shape and topology optimization based on the level set equation is transformed into a relatively easier size optimization, to which many efficient optimization algorithms can be applied. The proposed level set method can describe the moving boundaries without remeshing for discontinuities. The motion of the free boundary is just a question of advancing the discrete level set function in time by solving the size optimization. Several benchmark examples are used to demonstrate the effectiveness of the proposed method. The numerical results show that the proposed method can simplify numerical process and avoid numerical difficulties involved in most conventional level set methods. It is straightforward to apply the proposed method to more advanced shape and topology optimization problems. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite strain fracture analysis using the extended finite element method with new set of enrichment functions

Nonlinear fracture analysis of rubber‐like materials is computationally challenging due to a number of complicated numerical problems. The aim of this paper is to study finite strain fracture problems based on appropriate enrichment functions within the extended finite element method. Two‐dimensional static and quasi‐static crack propagation problems are solved to demonstrate the efficiency of the proposed method. Complex mixed‐mode problems under extreme large deformation regimes are solved to evaluate the performance of the proposed extended finite element analysis based on different tip enrichment functions. Finally, it is demonstrated that the logarithmic set of enrichment functions provides the most accurate and efficient solution for finite strain fracture analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Depth-resolved residual stress analysis of thin coatings by a new FIB-DIC method

A new methodology for the measurement of depth sensitive residual stress profiles of thin coatings with sub-micrometer resolution is presented. The two step method consists of incremental focused ion beam (FIB) ring-core milling, combined with high-resolution in situ SEM-FEG imaging of the relaxing surface and a full field strain analysis by digital image correlation (DIC). The through-thickness profile of the residual stress can be obtained by comparison of the experimentally measured surface strain with finite element modeling using Schajer's integral method. In this work, a chromium nitride (CrN) CAE-PVD 3.0 μm coating on steel substrate, and a gold MS-PVD 1.5 μm on silicon were selected for the experimental implementation. Incremental FIB milling was conducted using an optimized milling strategy that produces minimum re-deposition over the sample surface. Results showed an average residual stress of σ = −5.15 GPa in the CrN coating and σ = +194 MPa in the Au coating. These values are in reasonable agreement with estimates obtained by other conventional techniques. The depth profiles revealed an increasing residual stress from surface to the coating/surface interface for both coatings. This observation is likely related to stress relaxation during grain growth, which was observed in microstructural cross sections, as predicted by existing models for structure-stress evolution in PVD coatings. A correlation between the observed stress gradients and the in-service mechanical behavior of the coatings is proposed. Finally, critical aspects of the technique and the influence of microstructure and elastic anisotropy on stress analysis are analyzed and discussed.     

Stress intensity factor evaluations for a curved crack in orthotropic particulate composites using an interaction integral method

This paper develops a domain-independent interaction integral (DII-integral) for extracting mixed-mode stress intensity factors (SIFs) for orthotropic materials with complex interfaces. The DII-integral does not require material property gradients, and moreover its validity is not affected by material interfaces. Combined with the extended finite element method (XFEM), the DII-integral is employed to investigate a straight crack in an orthotropic functionally graded plate and a curved crack in orthotropic particulate composites.     

A model for interface cracks in layered orthotropic solids: Convergence of modal decomposition using the interaction integral method

The mode‐partitioning problem for bimaterial interfaces is still not resolved by the classical fracture mechanics approach in a satisfactory manner. Stress oscillations and overlapping crack faces are a direct consequence of the rigorous solution of the elastic boundary value problem, if the constitutive law changes discontinuously across the interface. Conversely, continuously varying material properties, also referred to as functionally graded materials (FGM), avoid these physically not admissible drawbacks. In this case the crack tip fields are of the same nature as those known from homogeneous materials. Therefore, the well‐established stress intensity factor concept can be used without any changes. Following this motivation an FGM‐interface model for delaminated composite beam structures was developed and its characteristics with respect to the modal decomposition of the crack tip fields were investigated. The considered beam structures consisted of two orthotropic layers, each of a different material. The spatial variation of the material properties in the interface region was modeled by a tanh ‐function introducing one transition parameter that controlled the FGM‐gradient. Four load cases were analyzed for each structural configuration: either a unit normal force or a unit bending moment was imposed on each end of the split beam. Thus, any load case can be simply reconstructed from the presented results by means of superposition. The stress intensity factors for modes I and II were then evaluated using an interaction integral method along with the finite element method. The corresponding results are given depending on the mesh density of the interface region, the integration domain and the transition parameter. In this manner, the influence of the transition parameter on the mode ratio and on the convergence behavior of the modal decomposition scheme with respect to its integration domain was identified. Finally, the ability of the FGM‐interface model to represent bimaterial interfaces while still maintaining the advantages of crack analysis in homogeneous materials was highlighted. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of plasticity on the residual stress measurement using the groove method

The mechanical methods based on milling rectilinear or annular grooves on a component's surface and measurement of relaxed strains are some of the most used semi-destructive methods for the determination of residual stresses. These are evaluated from the relaxed strains by means of equations based upon the linear elastic theory. In this paper the errors due to yielding localised at the bottom of the groove have been investigated. The analyses were carried out by means of the finite element technique varying the most important parameters involved. The experimental results show a good agreement with the numerical ones.     

Elastic wave propagation in a functionally graded nanocomposite reinforced by carbon nanotubes employing meshless local integral equations (LIEs)

The transient dynamic analysis of displacement field and elastic wave propagation in finite length functionally graded nanocomposite reinforced by carbon nanotubes are carried out using local integral equations (LIEs) based on meshless local Petrov–Galerkin (MLPG) method. The distribution of the aligned carbon nanotubes (CNTs) is assumed to vary as three kinds of functionally graded distributions as well as uniform distribution (UD) through radial direction of axisymmetric reinforced cylindrical composites. The mechanical properties are simulated using a micro-mechanical model in volume fraction form. A unit step function is used as a test function in the local weak form, which leads to local integral equations (LIEs). The analyzed domain is divided into small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized. The 2D propagation of elastic waves through 2D domain is illustrated for various kinds of carbon nanotubes distributions. The time histories of displacement fields are studied in detail for various kinds of carbon nanotube distributions in reinforced cylindrical composites.     

Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method

In this paper a singular integral equation method is applied to calculate the distribution of stress intensity factor along the crack front of a 3D rectangular crack. The stress field induced by a body force doublet in an infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r ^–3. In solving the integral equation, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function, which expresses stress singularity along the crack front in an infinite body. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary.     

An extended equivalent domain integral method for mixed mode fracture problems by the p-version of FEM

A new path-independent contour integral formula is presented to estimate the crack-tip integral parameter, J-value, for two-dimensional cracked elastic bodies which may quantify the severity of the crack-tip stress fields. The conventional J-integral method based on a line integral has been converted to an equivalent area or domain integral (EDI) by the divergence theorem. It is noted that the EDI method is very attractive because all the quantities necessary for computation of domain integrals are readily available in a finite element analysis. The details and its implementation are extended to the p-version FE model with hierarchic elements using integrals of Legendre polynomials. By decomposing the displacement field obtained from the p-version finite element analysis into symmetric and antisymmetric displacement fields with respect to the crack line, the Mode-I and Mode-II non-dimensional stress intensity factors can be determined by using the decomposition method. The example problems for validating the proposed techniques are centrally oblique cracked plates under tensile loading. The numerical results associated with the variation of oblique angles show very good agreement with the existing solutions. Also, the selective distribution of polynomial orders and the corner elements for automatic mesh generation are applied to improve the numerical solution in this paper. © 1998 John Wiley & Sons, Ltd.     

Reliability assessment of a tanker using the model correction factor method based on the IACS-CSR requirement for hull girder ultimate strength

The model correction factor method (MCFM) is adopted to assess the reliability of a Suezmax oil tanker considering the ultimate vertical bending moment capacity of the hull girder as a limit state. The approach uses the incremental iterative method proposed by the International Association of Classification Societies (IACS) Common Structural Rules (CSR) to evaluate the hull girder ultimate strength as a response model that is calibrated iteratively at the design points calculated by the First Order Reliability method (FORM) by means of advanced non-linear Finite Element Analyses (FEA). The considered loads are the still water and the wave-induced bending moments in a typical seagoing operational condition of the oil tanker in the full load and ballast load conditions. First, the predictions of the hull girder bending capacities calculated by the IACS-CSR method and by non-linear FEA are compared and then the efficiency of the MCFM for hull girder reliability problems is illustrated. It is shown that using semi-empirical response models, which include the important mechanical features with respect to the bending capacity of the ship hull girder, the reliability evaluation can be performed with a limited number of non-linear FEAs (less than 10) promoting the application of advanced response and reliability methods to complex structures.     

Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real‐part dual BEM

It has been found recently that the multiple reciprocity method (MRM) (Chen and Wong. Engng. Anal. Boundary Elements 1997; 20 (1):25–33; Chen. Processings of the Fourth World Congress on Computational Mechanics, Onate E, Idelsohn SR (eds). Argentina, 1998; 106; Chen and Wong. J. Sound Vibration 1998; 217 (1): 75–95.) or real‐part BEM (Liou, Chen and Chen. J. Chinese Inst. Civil Hydraulics 1999; 11 (2):299–310 (in Chinese)). results in spurious eigenvalues for eigenproblems if only the singular (UT) or hypersingular (LM) integral equation is used. In this paper, a circular cavity is considered as a demonstrative example for an analytical study. Based on the framework of the real‐part dual BEM, the true and spurious eigenvalues can be separated by using singular value decomposition (SVD). To understand why spurious eigenvalues occur, analytical derivation by discretizing the circular boundary into a finite degree‐of‐freedom system is employed, resulting in circulants for influence matrices. Based on the properties of the circulants, we find that the singular integral equation of the real‐part BEM for a circular domain results in spurious eigenvalues which are the zeros of the Bessel functions of the second kind, Y (kρ), while the hypersingular integral equation of the real‐part BEM results in spurious eigenvalues which are the zeros of the derivative of the Bessel functions of the second kind, Y_n′(kρ). It is found that spurious eigenvalues exist in the real‐part BEM, and that they depend on the integral representation one uses (singular or hypersingular; single layer or double layer) no matter what the given types of boundary conditions for the interior problem are. Furthermore, spurious modes are proved to be trivial in the circular cavity through analytical derivations. Numerically, they appear to have the same nodal lines of the true modes after normalization with respect to a very small nonzero value. Two examples with a circular domain, including the Neumann and Dirichlet problems, are presented. The numerical results for true and spurious eigensolutions match very well with the theoretical prediction. Copyright © 2000 John Wiley & Sons, Ltd.     

Determination of ply level residual stresses in a laminated carbon fibre-reinforced epoxy composite using constant,linear and quadratic variations of the incremental slitting method

Measurement of residual stresses in FRP composites is by no means a trivial task and there are no commonly applied or standardised methods currently available. As a result, characterisation of residual stresses is often avoided, resulting in the use of conservative safety margins, which has consequently resulted in structures being overdesigned. In the work described here, the incremental slitting method has been demonstrated to be a technique suitable for measuring residual stress in thin (∼0.3 mm) plies of a [0°₂/90°₂]_4s carbon fibre-reinforced epoxy laminate. The stresses measured using a constant stress approximation approach provided the best agreement with measurements obtained using the layer removal technique and stresses predicted using a semi-coupled transient-thermal and structural model.     

Rapid evaluation of notch stress intensity factors using the peak stress method: Comparison of commercial finite element codes for a range of mesh patterns

The peak stress method (PSM) is an engineering, finite element (FE)‐oriented method to rapidly estimate the notch stress intensity factors by using the singular linear elastic peak stresses calculated from coarse FE analyses. The average element size adopted to generate the mesh pattern can be chosen arbitrarily within a given range. Originally, the PSM has been calibrated under pure mode I and pure mode II loadings by means of Ansys FE software. In the present contribution, a round robin between 10 Italian universities has been carried out to calibrate the PSM with 7 different commercial FE codes. To this aim, several two‐dimensional mode I and mode II problems have been analysed independently by the participants. The obtained results have been used to calibrate the PSM for given stress analysis conditions in (i) FE software, (ii) element type and element formulation, (iii) mesh pattern, and (iv) criteria for stress extrapolation and principal stress analysis at FE nodes.     

On the convergence analysis,stability, and implementation of meshless local radial point interpolation on a class of three‐dimensional wave equations

In this article, the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form subject to given initial and Dirichlet boundary conditions. The main difficulty of the great number of methods in full 3‐D problems is the large computational costs. In meshless local radial point interpolation method, it does not require any background integration cells, so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method with the help of radial basis functions is proposed to construct shape functions that have Kronecker delta function property. A weak formulation with the Heaviside step function converts the set of governing equations into local integral equations on local subdomains. A two‐step time discretization method is employed to evaluate the time derivatives. This suggests Crank‐Nicolson technique to be applied on the right hand side of the equation. The convergence analysis and stability of the method are fully discussed. Three illustrative examples are presented, and satisfactory agreements are achieved. It is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones. Copyright © 2015 John Wiley & Sons, Ltd.