A Point‐wise Approach to the Analysis of Complex Composite Structures Using Digital Image Correlation and Thermoelastic Stress Analysis

Thermoelastic stress analysis (TSA) and digital image correlation (DIC) are used to examine the stress and strain distributions around the geometric discontinuity in a composite double butt strap joint. A well‐known major limitation in conducting analysis using TSA is that it provides a metric that is only related to the sum of the principal stresses and cannot provide the component stresses/strains. The stress metric is related to the thermoelastic response by a combination of material properties known as the thermoelastic constant (coefficient of thermal expansion divided by density and specific heat). The thermoelastic constant is usually obtained by a calibration process. For calibration purposes when using orthotropic materials, it is necessary to obtain the thermoelastic constant in the principal material directions, as the principal stress directions for a general structure are unknown. Often, it is assumed that the principal stress directions are coincident with the principal material directions. Clearly, this assumption is not valid in complex stress systems, and therefore, a means of obtaining the thermoelastic constants in the principal stress directions is required. Such a region is that in the neighbourhood of the discontinuities in a bonded lap joint. A methodology is presented that employs a point‐wise manipulation of the thermoelastic constants from the material directions to the principal stress directions using full‐field DIC strain data obtained from the neighbourhood of the discontinuity. A comparison of stress metrics generated from the TSA and DIC data is conducted to provide an independent experimental validation of the two‐dimensional DIC analysis. The accuracy of a two‐dimensional plane strain finite element model representing the joint is assessed against the two experimental data sets. Excellent agreement is found between the experimental and numerical results in the adhesive layer; the adhesive is the only component of the joint where the material properties were not obtained experimentally. The reason for the discrepancy is discussed in the paper.     

Residual stresses due to gas arc welding of aluminum alloy joints by numerical simulations

This study deals with the numerical simulation of the gas arc welding process of Aluminum tee joints using finite element analysis and evaluation of the effect of welding parameters on residual stress build up. The 3D simulations are performed using ABAQUS code for thermo-mechanical analyses with moving heat source, material deposition, solid-liquid phase transition, temperature dependent material properties, metal elasticity and plasticity, and transient heat transfer. Quasi Newton method is used for the analysis routine and thermo-mechanical coupling is assumed; i.e. the thermal analysis is completed before performing a separate mechanical analysis based on the thermal history. The residual stress build up and temperature history state in a three-dimensional analysis of the tee joint is then compared to experimental results. Hole drilling method is used for measuring the residual stress, while temperature history is measured by thermocouples. After carrying out numerical simulations, the effects of voltage/current, welding speed, material thickness and size of electrode on residual stress build-up and resulting distortions are evaluated.     

Variational-asymptotic modeling of the thermoelastic behavior of composite beams

This paper deals with steady state thermoelastic problems in composite beam structure by using variational-asymptotic method. First, the original three-dimensional heat conduction problem is reduced to be a two-dimensional thermal cross-sectional analysis along with an optional one-dimensional heat conduction analysis. The one-dimensional heat conduction analysis exists only if the temperature is not prescribed at any point of the cross-section along the span except the end surfaces. Then we reduce the one-way coupled, three-dimensional thermoelasticity problem into a two-dimensional, one-way coupled thermoelastic cross-sectional analysis and a one-dimensional, one-way coupled, thermoelastic beam analysis. The present theory is implemented into the computer program, variational-asymptotic beam sectional analysis (VABS). Several examples are studied using the present theory and the results from VABS are compared with available analytical solutions and the three-dimensional analysis using the commercial finite element package ANSYS.     

Investigation on a Two-dimensional Generalized Thermal Shock Problem with Temperature-dependent Properties

The dynamic response of a two-dimensional generalized thermoelastic problem with temperature-dependent properties is investigated in the context of generalized thermoelasticity proposed by Lord and Shulman. The governing equations are formulated, and due to the nonlinearity and complexity of the governing equations resulted from the temperature-dependent properties, a numerical method, i.e., finite element method is adopted to solve such problem. By means of virtual displacement principle, the nonlinear finite element equations are derived. To demonstrate the solution process, a thermoelastic half-space subjected to a thermal shock on its bounding surface is considered in detail. The nonlinear finite element equations for this problem are solved directly in time domain. The variations of the considered variables are obtained and illustrated graphically. The results show that the effect of the temperature-dependent properties on the considered variables is to reduce their magnitudes, and taking the temperature-dependence of material properties into consideration in the investigation of generalized thermoelastic problem has practical meaning in predicting the thermoelastic behaviors accurately. It can also be deduced that directly solving the nonlinear finite element equations in time domain is a powerful method to deal with the thermoelastic problems with temperature-dependent properties.     

Numerical simulation of the dynamic thermostructural response of a composite rocket nozzle throat

The finite element method, in the form of the commercial finite element code ADINA, is used to investigate the dynamic thermostructural response of a composite rocket nozzle throat. ADINA’s thermoelastic analysis capability is validated by the comparison of its solution for the thermoelastic response of a thick, homogeneous, cylindrically orthotropic tube heated internally, to an analytical one. The spatially reinforced Carbon–Carbon nozzle throat examined here forms part of a low-erosion solid rocket motor nozzle model that is subjected to structural and thermal loading, with the effects of material ablation being neglected. An initial transient quasi-static thermostructural analysis is performed to determine the validity of the nozzle design, following which, an uncoupled dynamic thermostructural analysis of the nozzle’s throat and entrance section for the initial transient phase of the nozzle’s operation, is carried out. The results of this analysis are then compared to those of the equivalent transient quasi-static analysis to assess the degree of variance in either solution. It is found that the dynamic response oscillates about the quasi-static response in all cases, and that, in general, the variance in stress magnitudes between the two solution techniques is significant.     

Characterization of the Mechanical Stress–Strain Performance of Aerospace Alloy Materials Using Frequency-Domain Photoacoustic Ultrasound and Photothermal Methods: An FEM Approach

Determining and keeping track of a material’s mechanical performance is very important for safety in the aerospace industry. The mechanical strength of alloy materials is precisely quantified in terms of its stress–strain relation. It has been proven that frequency-domain photothermoacoustic (FD-PTA) techniques are effective methods for characterizing the stress–strain relation of metallic alloys. PTA methodologies include photothermal (PT) diffusion and laser thermoelastic photoacoustic ultrasound (PAUS) generation which must be separately discussed because the relevant frequency ranges and signal detection principles are widely different. In this paper, a detailed theoretical analysis of the connection between thermoelastic parameters and stress/strain tensor is presented with respect to FD-PTA nondestructive testing. Based on the theoretical model, a finite element method (FEM) was further implemented to simulate the PT and PAUS signals at very different frequency ranges as an important analysis tool of experimental data. The change in the stress–strain relation has an impact on both thermal and elastic properties, verified by FEM and results/signals from both PT and PAUS experiments.     

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.     

某低温压力容器失效机理研究

针对某液氮预冷设备的结构进行了研究,通过有限元分析得到结构的应力集中位置与最大等效应力,并分析得到其失效原因为底部三通在低温下发生脆性破坏。根据分析结果更换了3 mm壁厚316L材质的三通,并进行了冷冲击试验进行验证,解决了容器失效的问题。     

A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.     

Thermoelastic wave characteristics in a hollow cylinder using the modified wave finite element method

This paper represents a modified formulation of the wave finite element (WFE) method for propagating analysis of thermoelastic waves in a hollow cylinder without energy dissipation. The 2D-high-order spectral element with the Gauss–Legendre–Lobatto integration is applied into the WFE method, which produces the diagonal mass matrix. Based on the assumption of harmonic displacement fields by Fourier series expansion, the general discretization wave equation is simplified from the 3D problem to 2D. Dispersion properties of elastic wave propagation in the hollow cylinder are computed considering the choice of the spectral element orders, and the results indicate the high efficiency and high accuracy of the modified formulation compared with that of the software Disperse. Then, using the modified formulation, the thermoelastic dynamic equation of the cylinder is derived from the generalized thermoelasticity theory. The propagation of the thermoelasticwave (including two kinds of wave modes) in the cylinder without energy dissipation is discussed in differentcases. Finally, wave structures along the radial direction of thermoelastic wave modes are shown at thenondimensional frequency 1.25, which can be used for the recognition of different modes.     

A finite element formulation for thermoelastic damping analysis

We present a finite element formulation based on a weak form of the boundary value problem for fully coupled thermoelasticity. The thermoelastic damping is calculated from the irreversible flow of entropy due to the thermal fluxes that have originated from the volumetric strain variations. Within our weak formulation we define a dissipation function that can be integrated over an oscillation period to evaluate the thermoelastic damping. We show the physical meaning of this dissipation function in the framework of the well‐known Biot's variational principle of thermoelasticity. The coupled finite element equations are derived by considering harmonic small variations of displacement and temperature with respect to the thermodynamic equilibrium state. In the finite element formulation two elements are considered: the first is a new 8‐node thermoelastic element based on the Reissner–Mindlin plate theory, which can be used for modeling thin or moderately thick structures, while the second is a standard three‐dimensional 20‐node iso‐parametric thermoelastic element, which is suitable to model massive structures. For the 8‐node element the dissipation along the plate thickness has been taken into account by introducing a through‐the‐thickness dependence of the temperature shape function. With this assumption the unknowns and the computational effort are minimized. Comparisons with analytical results for thin beams are shown to illustrate the performances of those coupled‐field elements. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of material and geometry variations on the behaviour of bonded tee connections in FRP ships

This paper is concerned with the design of tee connections in single skin FRP ships and boats. A brief review of the problem is first presented and reference is made to current practice towards the design of such joints. Areas of principal interest, especially those with most influence on joint behaviour, are identified. These are used in a systematic manner in physical and numerical modelling of the joint. Load/deflection graphs from the mechanical tests are presented and physical characteristics of the joint under load are noted. Numerical finite element models have then been used to provide an insight into the internal load dissipation and failure mechanisms. The modelling is used to highlight significant influences of geometry and material variations on the performance of the tee joints.     

高温压力管道三通接头的应力应变分析及仿真

高温压力管道的爆管事故通常需要实时监控高温管道的薄弱部位的应力应变状况.选取高温管道的典型薄弱部位"三通接头"作为分析对象,在理论分析建模的基础上,运用有限元AYASYS分析软件,对三通接头高温管道稳态运行时的热应力应变状况进行了分析计算,确定出其高温工作时的应力分布状况以及最大应力部位.并相应地给出了二维应变花结构的高温应变片安装方案.     

Thermal and geometrically non-linear stress analyses of an adhesively bonded composite tee joint

Adhesive bonding technique is used successfully for joining the carbon fibre reinforced plastics to metals or composite structures. A good design of adhesive joint with either simple or more complex geometry requires its stress and deformation states to be known for different boundary conditions. In case the adhesive joint is subjected to thermal loads, the thermal and mechanical mismatches of the adhesive and adherends cause thermal stresses. The plate-end conditions may also result in the adhesive joint to undergo large displacements and rotations whereas the adhesive and adherends deform elastically (small strain). In this study, the thermal and geometrically non-linear stress analyses of an adhesively bonded composite tee joint with single support plus an angled reinforcement made of unidirectional CFRPs were carried out using the non-linear finite element method. In the stress analysis, the effects of the large displacements were considered using the small displacement–large displacement theory. The stress states in the plates and the adhesive layer of the tee joint configurations bonded to a rigid base and a composite plate were investigated. An initial uniform temperature distribution was attributed to the adhesive joint for a stress free state, and then variable thermal boundary conditions, i.e. air flows with different velocity and temperature were specified along the outer surfaces of the tee joints. The thermal analysis showed that a non-uniform temperature distribution occurred in the tee joints, and high heat fluxes took place along the free surfaces of the adhesive fillets at the adhesive free ends. Later, the geometrical non-linear thermal-stress analysis of the tee joint was carried out for the final temperature distribution and two edge conditions applied to the edges of the vertical and horizontal plates (HP). High stress concentrations occurred around the rounded adherend corners inside the adhesive fillets at the adhesive free ends, and along the adhesive–composite adherend interfaces due to their thermal–mechanical mismatches. The most critical joint regions were adhesive fillets subjected to high thermal gradients, the middle region of HP, the region of the vertical plate corresponding to the free end of the vertical adhesive layer–left support interface. In addition, the support length had a small effect of reducing the peak stresses at the critical adherend and adhesive locations.     

Calculation of stress intensity factors based on mode I crack opening integral parameters

We present stress intensity factor assessment using nodal displacements of the crack surfaces determined by the finite element method for cracked bodies. The equation is solved by expanding the crack opening displacement in the Chebyshev function, where crack front asymptotic behavior corresponds to the regulations of the linear elastic fracture mechanics. Results of the stress intensity factor calculations are obtained for test problems with analytical solution. Crack opening displacements are defined with the help of the 3D SPACE software package designed to model mixed variational formulation of the finite element method for displacements and strains of the thermoelastic boundary value problems. Translated from Problemy Prochnosti, No. 6, pp. 122–127, November–December, 2008.     

Fatigue life prediction of friction stir spot welds based on cyclic strain range with hardness distribution and finite element analysis

The main aim of the present study is to investigate the fatigue behavior of single friction stir spot welds (FSSW) using strain-based modified Morrow’s damage equation. The correlation between microhardness, cyclic material constants, and mechanical strength of different zones around the FSSW are assumed to be proportional to the base material hardness. Experimental fatigue tests of friction stir spot welded specimens have been carried out using a constant amplitude load control servo-hydraulic fatigue testing machine. ANSYS finite element code has been used to simulate a single tensile shear friction stir spot welded joint, and non-linear elastic-plastic finite element analysis has been employed to obtain the values of local equivalent stress and strain near the notch roots of the joints. The results based on the numerical predictions have been compared with the experimental fatigue test data. It has been shown that the strain-based approach does a very good job for estimating the fatigue life of friction stir spot welded joints.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

Progressive failure predictions for rib-stiffened panels based on multicontinuum technology

An ongoing challenge within the structural analysis community is to accurately predict damage and progressive failure in large-scale structural components composed of composite materials. Multicontinuum technology (MCT) provides a means to produce constituent (fiber and matrix) level stress and strain information within the framework of commercial finite element analysis. Constituent level stress/strain information forms the basis for a progressive failure algorithm that has successfully been used to predict coupon failure in a wide range of composite materials and laminate configurations.

In this paper, MCT is used to analyze the failure of rib-stiffened panels associated with advanced composite grid-stiffened structure (AGS) designs. More specifically, MCT is used to predict and analyze the separation of the rib to skin interface for comparison with tee pulloff and tee bend test data. Predictions for the initial and final separation of the rib to skin interfaces are shown to be in good agreement with experimental test data. The results also lend insight into design and manufacturing considerations that are key to the strength and performance of the rib to panel interface.     

Material forces in micromorphic fracture mechanics

Abstract

The physical foundation, the balance laws and the constitutive relations of microcontinuum field theories are briefly reviewed. The concept of material forces, which may also be referred as Eshelbian mechanics, is extended to micromorphic theory. The balance law of pseudo‐momentum is formulated. The detailed expressions of Eshelby stress tensor, pseudo‐momentum, and material forces are derived. It is found that, for micromorphic thermoelastic solid, the material forces are due to (1) body force and body moment, (2) temperature gradient, and (3) the material inhomogeneities in density, microinertia, and elastic coefficients. It is shown that, at the crack front, material forces are reduced to generalized vectorial J‐integral. The calculation of material forces, due to the presence of inhomogeneities or cracks, by finite element analysis and meshless analysis is discussed. Finite element analysis is performed for a multiphase material which is composed of randomly distributed and oriented grains and in between the grain boundaries in its amorphous phase. Each grain is modeled as a single crystal by specialized micromorphic theory. The grain boundaries are modeled with a thin and finite width by classical continuum mechanics. Numerical results, including Cauchy stresses, Eshelby stresses, and material forces, for a thin film of silicon subjected to thermal and/or mechanical loadings are obtained and discussed.     

Torsional buckling and post-buckling of composite geodetic cylinders with special reference to joint flexibility

Curved (geodetic) composite frameworks are being considered for battledamage tolerant helicopters. In a previous paper by the authors it was shown that it was necessary to use curved, twisted beam elements to numerically predict the correct stiffness. Unfortunately the predicted torsional buckling load of a carbon cylinder was still 30% too high. Upon further detailed experimental testing of isolated geodetic joints it was realised that joint flexibility is an important factor in the overall behaviour of the shell.

When this joint flexibility is incorporated in the finite element models of the geodetic joint test specimens the differences between experiment and theory are dramatically reduced. This is also true for the complete shell where the buckling torque, calculated from linear finite element analysis, now exceeds the experimental value by about 12%, while for the non-linear analysis the discrepancy is reduced to below 7%.

Compression tests of the cylindrical geodetic shell confirm that the finite element model incorporating joint flexibility produces much better results for the compression stiffness.