Search

Copyright of Journal of Shanghai University / Shanghai Daxue Xuebao is the property of Journal of Shanghai University (Natural Sciences) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The determination of eigenstrain from residual stress is a crucial aspect in process predicting and optimizing of laser peen forming. However, direct measurement of eigenstrain is not possible, and therefore an indirect method based on the Fredholm integral equation is proposed for determining eigenstrain from residual stress. The residual stress of full-coverage laser shock peening (LSP) is analyzed, and the governing equation of eigenstrain is derived from the elastic deformation of a linear elastic plate under full-coverage LSP. The governing equation is a second-kind Fredholm integral equation, which can be solved analytically using the weight function method. Since residual stress is difficult to measure accurately in LSP, an inverse method based on the integral governing equation is proposed for determining eigenstrain from an incomplete set of measurements. The validity of this method is demonstrated through simulation and experimental results, highlighting its high efficiency and engineering application value. [ABSTRACT FROM AUTHOR]

• The dissimilar material and the crack are treated as inhomogeneities of different elastic modulus based on the EIM. • A semi-analytical model for two joined dissimilar materials with interfacial cracks is established and validated. • Parametric analysis on rupture performance of joined materials with interfacial cracks are carried out. Existing interfacial cracks in two joined dissimilar materials play a crucial role in determining the stress concentration and its further propagation, which severely affects the interfacial strength of the bi-materials, even leading to its debonding failure under external loading. This study proposes a semi-analytical method (SAM) to analyze the elastic field of two joined dissimilar materials with interfacial cracks. One of the two dissimilar materials is treated as an inhomogeneity having different material properties from the other and the crack is regarded as a line inhomogeneity whose elastic modulus equals to zero, hence the problem for the two joined dissimilar materials with an interfacial crack is converted to a homogeneous half space material problem with the assistance of the well-known Eshelby equivalent inclusion method (EIM). The results obtained with the SAM agree very well with those with the finite element method (FEM), providing a verification for the proposed method. Cases studies are conducted to explore the influences of the material mismatch, the length and the depth of the crack, the friction coefficient and the loading location on the elastic field of the two joined dissimilar materials, demonstrating that this work has potential in the analysis of joined dissimilar materials with interfacial cracks. [ABSTRACT FROM AUTHOR]

The objective of this paper is to validate a measurement-driven, model-based approach to estimate residual stress (RS) in samples machined from quenched aluminum stock. Model input is derived from measurement of RS in the parent stock. Validation is performed for prismatic T-sections removed from bars at different locations. We find RS predicted agrees with RS measured, by contour and neutron diffraction methods, with root-mean-square model-measurement difference of 22 MPa. Follow-on work (in Part 2) applies the RS estimation to samples representative of aircraft structures and examines the effects of RS on fatigue crack growth in the RS-bearing samples.

This paper assesses the accuracy of fatigue crack growth (FCG) predictions for high-strength aluminum samples containing residual stress (RS) and complex two-dimensional cracks subjected to constant amplitude load. FCG predictions use linear-elastic, multi-point fracture mechanics. A first prediction includes RS estimated by the model described in Part 1; a second prediction includes RS measured by the contour method. FCG test data show a significant influence of RS. Ignoring the RS results in a +60% error in predicted FCG life (non-conservative). Including RS improves predictions of crack growth significantly (errors better than +26% (estimated RS) and −14% (measured RS)).

Laser peen forming (LPF) is promising to form large-scale metal sheets in various applications. Understanding the bending deformation of the LPF process is of particular importance for accurate shape prediction and process planning elaboration. This study established a simplified eigenstrain-based finite element (FEM) model by incorporating loading sequence and geometric non-linearity to explore the bending deformation and shape prediction of the LPF process. The simplified eigenstrain was inversely determined based on the arc heights of plates subjected to full-covered LPF. The above model incorporating loading sequence and geometric non-linearity was verified by the comparison of experimental results, and it improved shape prediction accuracy considerably compared to the common beam bending analytical model. Moreover, the bending deformation processes and mechanisms of LPF plates were elucidated. It was found that biaxially curved surfaces were formed for thick plates with 5 mm or larger thickness, in which the geometric non-linearity and flattening effects played significant roles on their formation. On the other side, monoaxially curved surfaces were obtained for thin plates with 4 mm or smaller thickness after the LPF process. Three stages, i.e., forward bending, reverse flattening, and buckling, occurred and contributed to the formation of the monoaxially curved surface. With the increase in the eigenstrain amplitude and side length, and the decrease in plate thickness, the LPF plates transit from a biaxially curved shape to a monoaxially curved one. [ABSTRACT FROM AUTHOR]

The compressive residual stress distribution in shot peening can be simulated using the nonlinear elastic–plastic finite element method (FEM) or obtained using various measurement methods; however, a simple and efficient prediction is desirable for practical applications. The residual plastic strain component produced by shot peening, known as the inherent strain or Eigenstrain, has a simple distribution and can be used to predict the residual stress via linear elastic analysis. In this study, the residual stress distributions in aluminum–magnesium alloy plates due to various shot velocities and shot diameters were simulated using the nonlinear FEM; further, the residual stress distributions were verified using the X-ray diffraction method. The inherent strain was identified using these results as datasets, and the strain distribution was quantitatively expressed using a simple equation. Finally, an analytical method for shot peening residual stress prediction using inherent strain and plate bending theory was developed. The residual stress distributions predicted from the inherent strain determined for 5 -mm-thick plate were consistent with the experimentally measured and numerical simulated results for 2-, and 1 -mm-thick plates with different shot blasting machines and shot diameters. [ABSTRACT FROM AUTHOR]

• A novel homogenization model for elastic periodic multiphase composites is presented. • The model construction is based on the eigenstrain concept. • Composites with arbitrary number of phases and shapes of inclusions can be considered. • The model performance is evaluated by comparison with other homogenization techniques. This paper presents a novel micromechanical procedure for the linear elastic homogenization of composites with periodic microstructures. The procedure is developed for composites with arbitrary number of phases and geometric shapes of the inhomogeneities, in contrast with most existing homogenization approaches. Also, no restriction is made in relation to the mismatch between the properties of the phases and volume fractions of the inhomogeneities. The proposed procedure is based on the Eshelby equivalent inclusion approach and extends a model originally derived for evaluating the effective elastic moduli of periodic two-phase composites. The procedure represents the fluctuating elastic fields within each multiphase repeating unit cell (RUC) using Fourier series, resulting in Lippmann-Schwinger integral equations governing the unknown eigenstrain fields of the inclusions. Unlike traditional iterative algorithms used in Fast Fourier Transform (FFT)-based approaches, the procedure solves the integral equations straightforwardly from a scheme of partition of the domain of each inclusion. The efficiency of the proposal procedure is demonstrated through applications to composites with different arrays of coated fibers and constituent materials. [ABSTRACT FROM AUTHOR]

Inverse eigenstrain (inherent strain) analysis methods are shown to be effective for the reconstruction of residual stresses in plane eigenstrain problems (continuously processed bodies) while conversely residual stress reconstruction in discontinuously processed bodies is extremely challenging and necessitates the use of complex regularizing assumptions. Herein, a new generic inverse eigenstrain method suitable for the reconstruction of residual stresses along with residual elastic strains and displacements in discontinuously processed bodies is introduced. The proposed method uses the superposition of eigenstrain radial basis functions together with a set of limited experimental data for model‐free (unconstrained) determination of unknown eigenstrain fields. This approach eliminates the limitations introduced by global basis functions such as polynomials. The novel point of this method is the ability to account for all six components of strain in an isotropic body without using regularizing assumptions. By lifting complex guiding formulation, the fidelity of full‐field eigenstrain reconstruction becomes directly related to the quality of experimental data and proper discretisation of the model domain. The FEniCS implementation has been validated using the experimental data of pointwise high‐energy synchrotron X‐ray diffraction measurements from a bent titanium alloy bar. A hybrid high throughput computing approach is also introduced for effective parallel computing. [ABSTRACT FROM AUTHOR]

Eshelby’s seminal work on the ellipsoidal inclusion problem leads to the conjecture that the ellipsoid is the only inclusion possessing the uniformity property that a uniform eigenstrain is transformed into a uniform elastic strain. For the three-dimensional isotropic medium, the weak version of the Eshelby conjecture has been substantiated. The previous work (Ammari et al., 2010) substantiates the strong version of the Eshelby conjecture for the cases when the three eigenvalues of the eigenstress are distinct or all the same, whereas the case where two of the eigenvalues of the eigenstress are identical and the other one is distinct remains a difficult problem. In this work, we study the latter case. To this end, firstly, we present and prove a necessary condition for an inclusion being capable of transforming a uniform eigenstress into a uniform elastic stress field. Since the necessary condition is not enough to determine the shape of the inclusion, secondly, we introduce a constraint that is concerned with the material parameters, and by introducing the concept of dissimilar media we prove that there exist combinations of uniform eigenstresses and the elastic tensors of dissimilar isotropic media such that only an ellipsoid can have the Eshelby uniformity property for these combinations simultaneously. Finally, we provide a more specifically constrained proof of the conjecture by proving that for the uniform strain fields constrained to those induced by an ellipsoid from a set of specified uniform eigenstresses, the strong version of the Eshelby conjecture is true for a set of isotropic elastic tensors which are associated with the specified uniform eigenstresses. This work makes some progress towards the complete solution of the intriguing and longstanding Eshelby conjecture for three-dimensional isotropic media. [ABSTRACT FROM AUTHOR]

• An analytical warpage model is developed based on eigenstrain mismatch. • A process-dependent parameter "Eigenstress" is proposed as the fundamental cause of warpage. • Eigenstress is experimentally obtained by measuring the curvature of standard plate. • Adding a compensation layer on the warped substrate effectively reduces warpage. Warpage resulting from the deposition of films on substrates remains a persistent challenge that significantly impacts the application of numerous advanced devices. To precisely evaluate warpage in multilayer thin film/substrate systems, we employ the eigenstrain method in the warpage analysis. An analytical model is developed to predict warpage and residual stress in multilayer film/substrate system based on classical laminate theory. We introduce a novel concept termed "Eigenstress", which serves as the fundamental cause of warpage and characterizes the influence of the manufacturing process on warpage. Theoretical analysis and simulation demonstrate that warpage is entirely determined by eigenstress and other process-independent parameters. This model also explains that there is little interaction between thin films deposited on the same substrate. An experimental method is studied for measuring eigenstress using a standard plate. The measured eigenstress differs significantly from the corresponding thermal stress. We also propose a critical condition and its governing equation for warpage in multilayer film/substrate systems. Experimental results confirm that adding a compensation layer on a warped substrate can considerably reduce warpage. The warpage model based on "Eigenstress" provides a theoretical foundation for accurately predicting and controlling warpage in multilayer thin film/substrate systems. [Display omitted] [ABSTRACT FROM AUTHOR]

Measurements of lattice strain at high spatial resolution are becoming accessible and routine, owing to advances in imaging techniques such as 4D Scanning Transmission Electron Microscopy. This has the potential to enhance materials characterisation, but the data are difficult to interpret. We present a procedure for extracting local concentrations of isotropic defects, such as vacancies, from a spatially fluctuating strain field. The local dilatation is related to the defect concentration at the same point; strain fluctuations are directly proportional to concentration fluctuations by a factor determined by the Poisson ratio of the material. The inversion of strains to isotropic defect concentrations is demonstrated in molecular dynamics and finite element simulations of vacancy distributions in bcc W and fcc Au. • A recipe to extract concentrations of isotropic defects, such as vacancies in cubic metals, from spatially varying strain. • The dilatation produced by defects in an elastically isotropic material is related locally to the defect concentration. • The recipe for extracting vacancy concentration profiles is demonstrated via molecular statics and finite element methods. [ABSTRACT FROM AUTHOR]

In linear elasticity, universal displacements for a given symmetry class are those displacements that can be maintained by only applying boundary tractions (no body forces) and for arbitrary elastic constants in the symmetry class. In a previous work, we showed that the larger the symmetry group, the larger the space of universal displacements. Here, we generalize these ideas to the case of anelasticity. In linear anelasticity, the total strain is additively decomposed into elastic strain and anelastic strain, often referred to as an eigenstrain. We show that the universality constraints (equilibrium equations and arbitrariness of the elastic constants) completely specify the universal elastic strains for each of the eight anisotropy symmetry classes. The corresponding universal eigenstrains are the set of solutions to a system of second-order linear PDEs that ensure compatibility of the total strains. We show that for three symmetry classes, namely triclinic, monoclinic, and trigonal, only compatible (impotent) eigenstrains are universal. For the remaining five classes universal eigenstrains (up to the impotent ones) are the set of solutions to a system of linear second-order PDEs with certain arbitrary forcing terms that depend on the symmetry class. [ABSTRACT FROM AUTHOR]

Cold expansion (CX) is a material processing technique that has been widely used in the aircraft industry to enhance fatigue life of structural components containing holes. CX introduces compressive hoop residual stresses that slow crack growth near the hole edge. The objective of this paper is to predict residual stresses arising from cold expansion using two different finite element (FE) approaches, and compare the results to measurement data obtained by the contour method. The paper considers single-hole, double-hole, and triple-hole configurations with three different edge margins. The first FE approach considers process modeling, and includes elastic-plastic behavior, while the second approach is based on the eigenstrain method, and includes only elastic behavior. The results obtained from the FE models are in good agreement with one another, and with measurement data, especially close to the holes, and with respect to the effect of edge margin on the residual stress distributions. The distribution of the residual stress and equivalent plastic strain around the holes is also explored, and the results are discussed in detail. The eigenstrain method was found to be very useful, providing generally accurate predictions of residual stress.

Through the multi-phase field method, this research explores microstructure evolution within the Al–Cu–Ni system comprising Al-rich FCC, Al 2 Cu, and Al 3 Ni intermetallic compounds (IMCs). Notably, the Al 3 Ni exhibits substantial growth due to its higher free energy magnitude, while the Al 2 Cu phase diminishes within the FCC matrix. Additionally, this study investigates the impact of heterogeneous elastic effects on these microstructural changes. Density functional theory calculations were employed to determine temperature-dependent elastic tensor at a simulation temperature of 723 K. Initially both cases, simulations with elastic constants at 0 K and 723 K, start with identical grain areas. But by 21.45 ms, deviations notably intensify to 18.18% for single grains, underlining the importance of temperature-calibrated elastic tensor in the phase evolution driven by elastochemical effects. [Display omitted] • Temperature dependence of elasticity investigated via first principle calculations. • Bridging the scales with DFT-informed phase field model. • Elastochemical effects alter the evolution trajectories of Al 2 Cu, Al 3 Ni, and FCC phases. [ABSTRACT FROM AUTHOR]

Eigenstrain is a distributed strain field considered in mechanics that is particularly helpful in evaluating residual stress fields in the finite element method, and estimating the stress intensity factor due to residual stress in cracked components. The objective of this paper is to provide a solution for a simple eigenstrain problem in a two-dimensional rectangular domain that can serve as a benchmark for validation of fracture mechanics analysis methods. The solution provides residual stress fields and the stress intensity factor for a single edge crack as a function of crack size. Documenting the benchmark provides opportunities to demonstrate the correlation of different means to determine the stress intensity factor and to highlight details in implementing stress intensity factor calculations.

The contour method (CM) was applied to obtain residual stress field in the round-rod titanium alloy specimen fabricated by laser power bed fusion additive manufacturing. In order to improve the accuracy of CM, two methods were investigated. One employed a steel block glued to the specimen to shift the surface stress uncertainties. The other is to reconstruct the stress based on the eigenstrain inverse analysis method. Results show that both methods can improve the measurement accuracy on the surface layer stress to a certain extent. Attaching steel block would affect the cutting process and cause new test errors. The stress reconstruction method requires surface stress results and eigenstrain basis function with an order of at least 10. [ABSTRACT FROM AUTHOR]

In this paper a new boundary-only based damage modeling is presented. Despite the damage occurred inside the problem domain, the solution procedure requires boundary-only discretization of the problem. A few additional points are located at damage places. The Eshelby equivalent inclusion theory is coupled with the direct boundary integral equation method to predict the damage patterns. The relevantment like damage stiffness matrix which is obtained directly in a condensed form at degrees of freedom along the problem boundary. A nonlinear incremental–iterative solution procedure is implemented. Several numerical examples are presented to demonstrate the validity of the proposed technique. [ABSTRACT FROM AUTHOR]

The paper presents a general solution of the isotropic elasticity problem for the sandwiched inclusion in an elastic cylinder and having axially varying eigenstrain. This problem is relevant in considerations of a cylinder with axially varying thermal expansion coefficient or a nanowire having an axial inhomogeneity of the crystal lattice parameter due to growth and processing conditions. The technique of the solution and the results for the elastic fields and energies of dilatational inclusions with different distribution of eigenstrain, namely, constant, trapezoidal, and diffusion-like, along the axis of the cylinder, are given in full details. The technique explores the axial superpositions of infinitely thin dilatation disks inserted in the cylinder, the elastic fields of which are found in analytical form. In addition, the energies of interfaces separated domains with constant eigenstrains in the cylinder are given. It is demonstrated that the blurring of the eigenstrain in the transition region leads to a decrease in interface energy. [ABSTRACT FROM AUTHOR]

The M waves introduced by Burridge and Willis (1969, "The Self-Similar Problem of the Expanding Crack in an Anisotropic Solid," Math. Proc. Cambridge Philos. Soc., 66(2), pp. 443-468) are emitted by the surface of a self-similarly expanding elliptical crack, and they give Rayleigh waves at the corresponding crack speed. In the analysis for the self-similarly expanding spherical inclusion with phase change (dynamic Eshelby problem), the M waves are related to the waves obtained on the basis of the dynamic Green's function containing the contribution from the latest wavelets emitted by the expanding boundary of phase discontinuity, and they satisfy the Hadamard jump conditions for compatibility and linear momentum across the moving phase boundary of discontinuity. In the interior of the expanding inclusion, they create a "lacuna" with zero particle velocity by canceling the effect of the P and S. It is shown that the "lacuna" and Eshelby properties are also valid for a Newtonian fluid undergoing phase change in a self-similarly expanding ellipsoidal region of a fluid with different viscosity. [ABSTRACT FROM AUTHOR]

The present study carries out systematic thermodynamics analysis of Grain Boundary (GB) segregation and relaxation in Nano-Grained (NG) polycrystalline alloys. GB segregation and relaxation is an internal process towards thermodynamic equilibrium, which occurs naturally in NG alloys without any applied loads, causes deformation and generates internal stresses. The analysis comprehensively investigates the multiple coupling effects among chemical concentrations and mechanical stresses in GBs and grains. A hybrid approach of eigenstress and eigenstrain is developed herein to solve the multiple coupling problem. The analysis results indicate that the GB stress and grain stress induced by GB segregation and relaxation can be extremely high in NG alloys, reaching the GPa level, which play an important role in the thermal stability of NG alloys, especially via the coupling terms between stress and concentration. The present theoretic analysis proposes a novel criterion of thermal stability for NG alloys, which is determined by the difference in molar free energy between a NG alloy and its reference single crystal with the same nominal chemical composition. If the difference at a temperature is negative or zero, the NG alloy is thermal stable at that temperature, otherwise unstable. [ABSTRACT FROM AUTHOR]

This work presents force and shape control strategies for adaptive structures subjected to quasi-static loading. The adaptive structures are designed using an integrated structure-control optimization method developed in previous work, which produces minimum “whole-life energy” configurations through element sizing and actuator placement optimization. The whole-life energy consists of an embodied part in the material and an operational part for structural adaptation during service. Depending on the layout, actuators are placed in series with the structural elements (internal) and/or at the supports (external). The effect of actuation is to modify the element forces and node positions through length changes of the internal actuators and/or displacements of the active supports. Through active control, the stress is homogenized and the displacements are kept within required limits so that the design is not governed by peak demands. Actuation has been modeled as a controlled non-elastic strain distribution, here referred to as eigenstrain. Any eigenstrain can be decomposed into two parts: an impotent eigenstrain only causes a change of geometry without altering element forces while a nilpotent eigenstrain modify element forces without causing displacements. Four control strategies are formulated: (C1) force and shape control to obtain prescribed changes of forces and node positions; (C2) shape control through impotent eigenstrain when only displacement compensation is required without affecting the forces; (C3) force control through nilpotent eigenstrain when displacement compensation is not required; and (C4) force and shape control through operational energy minimization. Closed-form solutions to decouple force and shape control through nilpotent and impotent eigenstrain are given. Simulations on a slender high-rise structure and an arch bridge are carried out to benchmark accuracy and energy requirements for each control strategy and for different actuator configurations that include active elements, active supports and a combination of both.

Evolution equations, or equations of motion, of moving defects are the balance of the “driving forces”, in the presence of external loading. The “driving forces” are defined as the configurational forces on the basis of Noether’s theorem, which governs the invariance of the variation of the Lagrangean of the mechanical system under infinitesimal transformations. For infinitesimal translations, the ensuing dynamic J integral equals the change in the Lagrangean if and only if the linear momentum is preserved. Dislocations and inclusions are “defects” that possess self-stresses, and the total driving force for these defects consists only of two terms, one expressing the “ self-force” due to the self-stresses, and the other the effect of the external loading on the change of configuration (Peach–Koehler force). For a spherically expanding (including inertia effects) Eshelby (constrained) inclusion with dilatational eigenstrain (or transformation strain) in general subsonic motion, the dynamic J integral, which equals the energy-release rate, was calculated. By a limiting process as the radius tends to infinity, the driving force (energy-release rate) of a moving half-space plane inclusion boundary was obtained which is the rate of the mechanical work required to create an incremental region of eigenstrain (or transformation strain) of a dynamic phase boundary. The total driving force (due to external loading and due to self-forces) must be equal to zero, in the absence of dissipation, and the evolution equation for a plane boundary with eigenstrain is presented. The equation applied to many strips of eigenstrain provides a system to solve for the position/ evolution of strips of eigenstrain.

Investigation of residual stresses is of crucial importance due to their effect on the performance of engineering components. Recently, inverse methods have been developed for determination of the residual stresses. Inverse eigenstrain method is one of the mentioned inverse methods. The inverse eigenstrain method, which is based on the eigenstrain theory, uses limited measurements of residual elastic strains obtained from the experimental tests. In this study, effective parameters on result accuracy obtained from the 2D inverse eigenstrain method in residual stresses measurement were investigated using numerical experiment. The results indicated that in the inverse eigenstrain method the accuracy of the results increases with increasing the basis functions order and the number of the points where displacement is measured. Additionally, the result accuracy increases selecting the appropriate basis functions. Moreover, in this paper the inverse eigenstrain method was applied for an actual part. The results showed that in the real conditions too, accurate results can be obtained by selecting the appropriate parameters of the inverse eigenstrain method.

Ericksen's problem consists of determining all equilibrium deformations that can be sustained solely by the application of boundary tractions for an arbitrary incompressible isotropic hyperelastic material whose stress-free configuration is geometrically flat. We generalize this by first, using a geometric formulation of this problem to show that all the known universal solutions are symmetric with respect to Lie subgroups of the special Euclidean group. Second, we extend this problem to its anelastic version, where the stress-free configuration of the body is a Riemannian manifold. Physically, this situation corresponds to the case where nontrivial finite eigenstrains are present. We characterize explicitly the universal eigenstrains that share the symmetries present in the classical problem, and show that in the presence of eigenstrains, the six known classical families of universal solutions merge into three distinct anelastic families, distinguished by their particular symmetry group. Some generic solutions of these families correspond to well-known cases of anelastic eigenstrains. Additionally, we show that some of these families possess a branch of anomalous solutions, and demonstrate the unique features of these solutions and the equilibrium stress they generate. [ABSTRACT FROM AUTHOR]

Background: The integral method of incremental hole-drilling is used extensively to determine the residual stress distribution in isotropic materials. When used with Tikhonov regularization, the method is robust and produces accurate results with minimal uncertainty. Alternatively, an optimal hole depth distribution can be found using the method of Zuccarello to improve the conditioning of the calibration matrices. If substantial measurement noise or a steep variation in stress exists, however, considerable uncertainty in, or distortion of, the calculated residual stress distribution can occur. Series expansion offers an alternative solution, but it has been reported to become unstable before meaningful accuracy can be achieved. Objective: Investigate the use of series expansion to determine a rapidly changing throughthickness residual stress distribution in an aluminium alloy 7075 plate subjected to laser shock peening treatment. Methods: Power series expansion of eigenstrains is used in finite element modelling to calculate the calibration coefficients. Monte Carlo simulation is used to determine robust uncertainties in the residual stress distributions. This allows the series order with the lowest RMS uncertainty in stress to be selected from those series orders that have converged. The best estimate of the residual stress distribution is thereby obtained. Results: Series expansion is shown to be stable up to 8th order and convergence to a stress solution can be found before instability dominates. The method is insensitive to measurement errors due to the least-squares approach employed by the inverse solution. Conclusions: The use of series expansion reduces the RMS uncertainty in stress when compared to the regularized integral and Zuccarello methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai University / Shanghai Daxue Xuebao is the property of Journal of Shanghai University (Natural Sciences) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper describes an improved data reduction scheme for the deep-hole method of residual stress measurement. The deep-hole method uses the changes in diameter of a reference hole, drilled through the thickness of a component, to determine residual stress. The diameter changes result from the removal of a cylindrical core from the component, where the core is larger than and concentric with the reference hole. The new data reduction seeks to determine the unknown eigenstrain distribution that gives rise to the residual stress state and to the reference hole deformations; once the eigenstrain distribution is found, it is input to an elastic finite element analysis to provide the residual stress distribution in the original component. The new data reduction relies on expressing the unknown eigenstrain field in a polynomial basis, and finding the unknown basis function amplitudes from the measured reference hole diameter changes. The new data reduction is compared with the current technique, and it is shown that the proposed scheme offers several advantages to the current method of data reduction.

The Eshelby inhomogeneity problem plays a crucial role in the micromechanical analysis of the effective mechanical behaviour of inhomogeneous media since it provides a mechanism to predict interior fields associated with ellipsoidal inhomogeneities. In the context of linear elasticity, Eshelby showed that given an isolated elliptical (two dimensions) or ellipsoidal (three dimensions) inhomogeneity embedded in a homogeneous material of infinite extent, then for any uniform strain or traction imposed in the far field, the induced strain inside the inhomogeneity is also uniform. In the case of non-uniform far-field conditions, Eshelby showed that if the loading is a polynomial of order n, the associated interior field is characterized by a polynomial of the same order. This is often called 'Eshelby's polynomial conservation theorem'. Since then, the problem has been studied by many, but in most cases for the uniform loading scenario, i.e. when strains or tractions in the far field are uniform. However, in many applications, e.g. permittivity, conductivity, elasticity, etc., the case of non-uniform conditions is also of interest and furthermore, methods to deal with non-elliptical and non-ellipsoidal inhomogeneities are required. In this work, for prescribed non-uniform polynomial far-field conditions, we introduce a method to approximate interior fields for isolated inhomogeneities of elliptical shape. This subproblem is relevant for approximating effective properties of numerous composites since constituent inhomogeneities are often of this form, or limiting forms, e.g. layered and fibre reinforced composites. We verify that the obtained results agree with the polynomial conservation property and with results determined using conformal mappings or the classical circle inclusion theorem. We close with a discussion of how the method can be straightforwardly extended to the case of non-elliptical inhomogeneities. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of a new methodology to design adaptive structures. This design method synthesises structural configurations that are optimum hybrids between a passive and an active structure. An optimisation scheme searches for an optimal material distribution and actuation layout to minimise the structure whole-life energy which consists of an embodied part in the material and an operational part for structural adaptation. Instead of using more material to cope with the effect of loads, here, strategically located active elements redirect the internal load path to homogenise the stresses and change the shape of the structure to keep deflections within required limits. To ensure the embodied energy saved this way is not used up to by actuation, the adaptive solution is designed to cope with ordinary loading events using only passive load-bearing capacity whilst relying on active control to deal with larger events that have a smaller probability of occurrence. The design methodology has been implemented for statically determinate and indeterminate reticular structures. However, the formulation is general and could be implemented to other structural types. Numerical simulations on a truss system case study confirm that substantial savings up to 50% of the whole-life energy can be achieved by the adaptive solution compared to a passive solution designed using state of the art optimisation methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalised continuum theory possesses a weak nonlocal character with two internal material lengths and provides a mechanics of defects without singularities. Gradient elasticity of bi-Helmholtz type gives a natural and physical regularisation of the classical singularities of defects, based on higher order partial differential equations. Point defects embedded in an isotropic solid are considered as eigenstrain problem in gradient elasticity of bi-Helmholtz type. Singularity-free fields of point defects are presented. The displacement field as well as the first, the second and the third gradients of the displacement are derived and it is shown that the classical singularities are regularised in this framework. This model delivers non-singular expressions for the displacement field, the first displacement gradient and the second displacement gradient. Moreover, the plastic distortion (eigendistortion) and the gradient of the plastic distortion of a dilatation centre are also non-singular and are given in terms of a form factor (shape function) of a point defect. Singularity-free expressions for the interaction energy and the interaction force between two dilatation centres and for the interaction energy and the interaction force of a dilatation centre in the stress field of an edge dislocation are given. The results are applied to calculate the finite self-energy of a dilatation centre. [ABSTRACT FROM AUTHOR]

• Repeated slitting safe distance (RSSD) which determines the region where the material undergoes residual stress relief is defined. • The introduced RSSD parameter determines the minimum safe distance between consecutive slitting experiments to get accurate results. • The presented method reduces the run-time and slitting experiment expenses for low thickness specimens significantly. • The proposed method to repeat the slitting method on a single part was validated for an isotropic aluminium beam and for a transversely isotropic laminated composite. The slitting method is a destructive procedure whereby the residual stresses are determined throughout the thickness of the specimen. One should repeat this experiment to ascertain the uncertainties of the obtained results. However, performing the slitting experiment relieves the residual stresses around the cut which influences the results of the next experiments. In this paper the repeated slitting safe distance (RSSD) parameter was introduced which determines the proper distance between slitting experiments to guarantee the validity of the next ones. This method also contributes to reducing the calculation process and experiment costs especially for specimens with low thicknesses. The RSSD was obtained by two different methods including the eigenstrain based method and supplemental stress analysis. First, this distance was verified numerically for both isotropic and composite materials. Next, the slitting experiment was conducted for these materials and it was shown that the proposed method was successful to determine a proper distance to exclude the effects of the previous cuts. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the numerical simulation of coil sagging. This problem arises within the framework of the steel making industry where strips are wound on themselves for storage. Coil sagging is a major defect that can occur for recent grades undergoing phase transitions during the coiling process. The detailed mechanisms leading to coil sagging are still not well understood, making this phenomenon very difficult to prevent. The coil is a multilayer hollow cylinder where sliding takes place at each interface and significantly contributes to the overall deformation. However, a detailed numerical simulation addressing the contact problem, considering both pressure and sliding is difficult to perform under non-axisymmetric conditions. This paper presents a simplified approach considering an orthotropic hollow cylinder instead of a multilayer coil. The anisotropy is due to contact roughness that tends to decrease the radial stiffness. The hollow cylinder is subjected to gravity and an eigenstrain representing thermal expansion, phase transitions and transformation induced plasticity. Sliding at each interface is taken into account through a continuous plastic-like shear strain that is determined through an energetic principle. The proposed solution relies on analytical developments so that computation time is compatible with parametric studies. Results are addressed in order to give a better understanding of mechanisms and conditions under which coil sagging occur. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a fast method of solving 3D contact problems when one of the mating bodies has an elastic-damageable behavior. The damage model is implemented in a semi-analytical model using Eshelby' s equivalent inclusion method in the contact solver. The proposed technique can be seen as an enrichment technique for which the effect of heterogeneous inclusions is surimposed on the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to a massive use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space and with the same elastic properties are surimposed. The damage model affects the elastic properties of the cuboidal inclusions. The emphasis is put on the effects of the fretting regimes on the contact pressure and damage evolution. [ABSTRACT FROM AUTHOR]

Highlights • An anisotropic elastic–plastic model was developed for predicting rafting behavior. • Variation in mismatch degree has a strong effect on rafting in the elastic stage. • Variation in mismatch degree has very slight impact on rafting in the plastic stage. • Three elastic-constant differences have different influences on rafting behavior. Abstract An anisotropic elastic–plastic model was developed to investigate the rafting behavior of Ni-based single crystal superalloys. This model was developed by introducing the plastic constitutive equation of face-centered cubic (FCC) single crystal in the framework of Eshelby's equivalent inclusion theory. The Hill's equivalent stress was calculated when applying a tensile or compressive loading along the [001] direction. The calculated results successfully predict the rafting direction for alloys with a positive or negative mismatch, consistent with pervious experimental and theoretical studies. Moreover, based on this model, the mismatch degree and the elastic-constant differences of the matrix and precipitate phases and their effects on the speed of rafting are carefully discussed. Regardless of a positive or negative mismatch alloy, the larger absolute value of mismatch degree can more effectively accelerate the process of rafting in Ni-based single crystal superalloys. However, when the alloys enter the plastic deformation stage, the variation in mismatch degree slightly affects the speed of rafting. For the elastic-constant differences (C 11 r ′ − C 11 r , C 12 r ′ − C 12 r ,and C 44 r ′ − C 44 r), the smaller the value of C 11 r ′ − C 11 r , or the greater the value of C 12 r ′ − C 12 r , the more effective the acceleration of γ′ rafting; whereas the value of C 44 r ′ − C 44 r has no effect on the rafting of alloys. The research results provide a new theory and method for studying the rafting behavior and its influencing factors for Ni-based single crystal superalloys. Graphical abstract Fig. Material model of Ni-based single crystal superalloys and representative volume element (RVE) for micromechanical analysis. (a) Original material microstructure: Cubical γ′ precipitates are uniformly embedded in the γ matrix, and the volume fraction of γ′ phase is 70%. (b) Simplified material model. (c) RVE for micromechanical analysis. (d) Variations in Hill's equivalent stress with the external tensile stress. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Highlights • The least squares method for implementing the unit pulse functions and the Tikhonov regularization technique were developed for determining the residual stresses using the slitting method. • The developed least squares and Tikhonov regularization techniques were validated by reproducing a known residual stress field inside an aluminum beam using the four-point bending experiment. • Laminated composite specimens were subjected to thermal loading and the induced residual stresses were determined by the slitting method and utilizing the developed least squares and Tikhonov regularization techniques. • The present methods significantly decreased the noise and uncertainty in the experimental measurements of both metals and composites. Abstract One of the challenges of measuring the residual stresses in metals and composites is the adverse effect of the noise and error on final results. The least squares and the Tikhonov regularization methods are the two available techniques for the noise reduction of the residual stress measurement in materials. In the present paper, the least squares method was developed for the residual stress measurement in metallic and laminated composites. Moreover, the application of the Tikhonov regularization method was extended for the eigenstrain based method and used for the measurement of residual stresses in laminated composites. The proposed methods were validated by performing experiments on an aluminum beam and a laminated composite plate using the slitting method. It was illustrated that the present methods diminished the uncertainty and sensitivity to noise of the final results successfully. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

To deal with the problems encountered in the large scale numerical simulation of three dimensional (3D) elastic solids with fluid-filled pores, a novel computational model with the corresponding iterative solution procedure is developed, by introducing Eshelby's idea of eigenstrain and equivalent inclusion into the boundary integral equations (BIE). Moreover, by partitioning all the fluid-filled pores in the computing domain into the near- and the far-field groups according to the distances to the current pore and constructing the local Eshelby matrix over the near-field group, the convergence of iterative procedure is guaranteed so that the problem can be solved effectively and efficiently in the numerical simulation of solids with large numbers of fluid-filled pores. The feasibility and correctness of the proposed computational model are verified in the numerical examples in comparison with the results of the analytical solution in the case of a single spherical fluid-filled pore under uniform pressure in full space and with the results of the subdomain BIE in a number of other cases. The overall mechanical properties of solids are simulated using a representative volume element (RVE) with a single or multiple fluid-filled pores, up to one thousand in number, with the proposed computational model, showing the feasibility and high efficiency of the model. The effect of random distribution of fluid-filled on overall properties is also discussed. Through some examples, it is observed that the effective elastic properties of solids with a large number of fluid-filled pores in random distributions could be studied to some extent by those of solids with regular distributions. [ABSTRACT FROM AUTHOR]

Abstract Tungsten is the main candidate material for plasma-facing armour components in future fusion reactors. Bombardment with energetic fusion neutrons causes collision cascade damage and defect formation. Interaction of defects with helium, produced by transmutation and injected from the plasma, modifies defect retention and behaviour. Here we investigate the residual lattice strains caused by different doses of helium-ion-implantation into tungsten and tungsten‑rhenium alloys. Energy and depth-resolved synchrotron X-ray micro-diffraction uniquely permits the measurement of lattice strain with sub-micron 3D spatial resolution and ~10−4 strain sensitivity. Increase of helium dose from 300 appm to 3000 appm increases volumetric strain by only ~2.4 times, indicating that defect retention per injected helium is ~3 times higher at low helium doses. This suggests defect retention is not a simple function of implanted helium dose, but strongly depends on material composition and presence of impurities. Conversely, analysis of W-1 wt% Re alloy samples and of different crystal orientations shows that both the presence of rhenium, and crystal orientation, have a comparatively small effect on defect retention. These insights are key for the design of armour components in future reactors where it will be essential to account for irradiation-induced dimensional change when predicting component lifetime and performance. Graphical abstract Unlabelled Image Highlights • Helium-implantation causes large strains likely to reduce longevity of plasma-facing tungsten armour in fusion reactors. • Non-linear defect retention (ten times dose increase only increases strain three times) suggests saturation regime onset. • Little grain-orientation dependence means texture of tungsten armour can be optimised for other performance aspects. • Not all transmutation elements strongly affect defect retention, e.g. 1% Re causes little increase in defect retention. [ABSTRACT FROM AUTHOR]

This paper presents an evaluation method of residual stresses in large welded thin-walled structures based on eigenstrain analysis and small sample residual stress measurement. In this method, small samples containing weld and heat-affected zones are firstly cut from large thin-walled structures, then residual stress in the small samples are measured to determine the welding-induced eigenstrains using a finite element-aided inverse solution. Finally, residual stress in large thin-walled structures are evaluated based on the obtained eigenstrain distribution. The feasibility of the proposed method was validated by evaluating residual stresses in welded plates with different lengths or widths. The method was then applied to evaluating residual stress in a welded skin-stiffener panel. Good agreement between the evaluated residual stress and measurement by diffraction technique has demonstrated the practicability of the method. [ABSTRACT FROM AUTHOR]