A generalized method for photoelastic studies of transient thermal stresses

This paper describes the apparatus and experimental method which was developed for generalized studies of transient thermal stresses in photoelastic models of many different shapes under a variety of steady-state or transient temperature conditions. It explains how the desired temperature gradients are established in the models and how rapidly changing temperature and stress profiles are monitored during a test. The experimental method is used to study the stresses in a three-dimensional photothermoelastic model subjected to three different temperature sequences. These are: symmetrical cooling of both faces of a thick plate initially at a uniform temperature; heating of one face only of a thick plate initially at a uniform temperature; and heating of only the cold face of a thick plate with an initial linear temperature gradient through its thickness. The last sequence generated temperature profiles which relate to conditions where internal heating is present. The resultant temperature and stress histories for each case are presented graphically and similarity scales are applied to give correct time-stress relations for a typical steel prototype. The magnitude and time of occurrence of the peak stresses on the boundary, as well as in the interior of the plate are found. These stresses are very high and occur comparatively late in each test, at a time when the temperature of the central plane has already started to respond to the changing conditions at the surface. The model was of the sandwich-type construction used by previous investigators, which has a built-in polariscope to isolate a transverse plane for viewing.     

Nonlinear transient response of strain rate dependent composite laminated plates using multiscale simulation

The effects of strain rate dependency and inelasticity on the transient responses of composite laminated plates are investigated. A micromechanics model which accounts for the transverse shear stress effect, the effect of strain rate dependency and the effect of inelasticity is used for analyzing the mechanical responses of the fiber and matrix constituents. The accuracy of the micromechanics model under transverse shear loading is verified by comparing the results with those obtained using a general purpose finite element code. A higher order laminated plate theory is extended to capture the inelastic deformations of the composite plate and is implemented using the finite element technique. A complete micro–macro numerical procedure is developed to model the strain rate dependent behavior of inelastic composite laminates by implementing the micromechanics model into the finite element model. Parametric studies of the transient responses of composite plates are conduced. The effects of geometry, ply stacking sequence, material models, boundary conditions and loadings are investigated. The results show that the strain rate dependency and inelasticity influence the transient responses of composite plates via two significantly different mechanisms.     

Accelerated aging of unidirectional hybrid composites under the long-term elevated temperature and moisture concentration

Despite their high performances, composites with polymer matrix are very sensible to the increase in temperature and moisture concentration. During long years of services, both phenomena cause a critical transient hygrothermal transverse stresses, particularly at first-ply; i.e. at two edges of the composite plates. Therefore, significant degradation of hygrothermal characteristics and ultimate strengths of materials are occurred. To get an explicit relation between the durability and the damage probability of the composite, quadratic failure criterion in stress space is used. This criterion enables us to find a direct relation between transient hygrothermal stresses produced by the increase in temperature and moisture concentration and the ultimate strengths. It is necessary to calculate the strength ratio R from initial to saturation time for each condition imposed of temperature and moisture concentration. The strength ratio gives a point of view on the damage probability of the composite plates, where the rupture occurs if R = 1. In order to limit the consequences of simultaneous effects of temperature and moisture concentration, unidirectional hybrid composites in graphite epoxy was proposed. To reach this aim, hygrothermal transverse stresses are calculated through the thickness of unidirectional hybrid plate. Finally, the strength ratio was evaluated along of the plate with a gradual increase in temperature and moisture concentration.     

Thermally induced vibration and stability of laminated composite plates with temperature-dependent properties

This paper presents a study on the buckling and vibration of initially stressed composite plates with temperature-dependent material properties in thermal environments. The initial stress is taken to be a combination of a pure bending stress and an axial stress. The temperature distribution in the plate is assumed to be uniform and linear in the transverse direction. The governing equations including the transverse shear deformation effects are established using the variational method. The effects of various parameters on the buckling and vibration behaviors of laminated plates with respective temperature-dependent and temperature-independent material properties are investigated. The buckling load and natural frequency are sensitive to the thermal stresses and initial stresses. Numerical results reveal that temperature-dependent material properties should be considered in the buckling and vibration analysis for laminated plates under thermal conditions.     

Damage of hybrid composites under long term hygrothermal loading and stacking sequence

The exposure of polymeric composite matrix to a cyclic moist environment produces transient residual stresses extremely important at the edges of the laminated plates, particularly at first times. In cases of critical cyclic environmental conditions, the damage of composites becomes very probable, so durability is intensively reduced. To avoid the damage probability, and to reduce the transient hygrothermal stresses, in our paper the hybrid composites with optimal stacking sequences are used. The first aim of this paper is the determination of hygrothermal characteristics for balanced stacking sequences [θ/−θ]_nS. Therefore, in order to locate the favourite directions of each stacking sequence, the polar representation method is adopted. The suitable choice of hygrothermal characteristics, allows thereafter, the reduction of transient hygrothermal stresses. By using the quadratic failure criterion in stress space, the transient strength ratio is evaluated at first ply of the hybrid plate for each sequences [θ/−θ]_nS from initial time until saturation time. Avoid the damage probability is reached by the reduction of transient hygrothermal stresses along the thickness of the hybrid plate. To locate the minimal and maximal stresses, a progressive variation of the relationship between the thicknesses h₁ and h₂ of hybrid composites constituents AS3501 and T300/5208 was carried out. In this way five cases are proposed, on which, the thickness of each material varies gradually, but the total thickness of our plate remains constant. This procedure permits us to find the best configuration which will offer favourable conditions of services, i.e., to predict a considerable reduction of hygrothermal transverse stresses at both edges of the hybrid plate.     

Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al–SiC composite cylinder

The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.     

湿热环境对挖补修理后复合材料层合板振动特性的影响

通过对湿热环境下阶梯挖补胶接修理后碳纤维/双马树脂(T300/QY8911)层合板振动特性的分析,探究了挖补修理后碳纤维/双马树脂层合板在不同湿热效应下的振动特性。基于Mindlin-Reissner板理论与最小势能变分原理,在考虑湿热效应前提下,推导了正交各向异性复合材料层合板的本构关系及四边简支条件下的自由振动控制方程;其次,利用ABAQUS软件建立了三维黏弹性有限元挖补修理模型,应用Fortran语言将湿热耦合下的应力-应变本构关系编入UMAT二次开发文件中,采用三维八节点五自由度等参单元进行了离散。通过与参考文献对照,验证了胶接修理后T300/QY8911层合板有限元模型和编译的湿热环境下UMAT子程序的合理性与有效性。算例结果表明:湿热环境对挖补修理后层合板固有频率的影响比对完整层合板严重;温度对材料性能的影响大于湿度;相比于材料性能变化对振动特性的影响,湿热残余应力对胶接修理后层合板振动特性的影响占主导;参考环境下,胶接修理后层合板的固有频率增大;湿应力对层合板固有频率的影响大于热应力。     

Natural frequencies of composite plates with tailored thermal residual-stresses

Thermal residual-stresses introduced during manufacture and their effect on the natural frequencies and vibration modes of stringer stiffened composite plates is investigated. The principal idea in the work is to include stiffeners on the perimeter of a composite plate in which the laminate design of the stiffeners and plate are different. Such an arrangement yields manufacturing induced thermal residual-stresses; these stresses result from the difference in manufacturing and operating temperatures as well as the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. The analysis is based on an enhanced Reissner–Mindlin plate theory and involves two separate calculations. In the first, the thermal residual-stress state is determined for an unconstrained plate. In the second, the free vibration problem is solved; thermal effects from the first calculation are included by way of nonlinear membrane-bending coupling which in turn defines the free vibration reference state. The problem is solved using a 16-node bi-cubic Lagrange element in a finite element formulation. Three different plate-stiffener geometries are used to illustrate the effects of stringer size, stringer placement and temperature difference. Two principal results are obtained: first, it is shown that thermal residual-stresses can have a significant effect on the natural frequencies; secondly, thermal residual-stresses can be tailored to increase natural frequencies. Therefore it is concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design of this class of composite structures.     

Sensitivity analysis of the thermomechanical response of welded joints

A computational procedure is presented for evaluating the sensitivity coefficients of the thermomechanical response of welded structures. Uncoupled thermomechanical analysis, with transient thermal analysis and quasi-static mechanical analysis, is performed. A rate independent, small deformation thermo-elasto-plastic material model with temperature-dependent material properties is adopted in the study. The temperature field is assumed to be independent of the stresses and strains. The heat transfer equations emanating from a finite element semi-discretization are integrated using an implicit backward difference scheme to generate the time history of the temperatures. The mechanical response during welding is then calculated by solving a generalized plane strain problem. First- and second-order sensitivity coefficients of the thermal and mechanical response quantities (derivatives with respect to various thermomechanical parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility. Numerical results are presented for a double fillet conventional welding of a stiffener and a base plate made of stainless steel AL-6XN material. Time histories of the response and sensitivity coefficients, and their spatial distributions at selected times are presented.     

Three-dimensional thermomechanical deformations of functionally graded rectangular plates

Three-dimensional thermomechanical deformations of simply supported, functionally graded rectangular plates are studied by using an asymptotic method. The locally effective material properties are estimated by the Mori–Tanaka scheme. The temperature, displacements and stresses of the plate are computed for different volume fractions of the ceramic and metallic constituents, and they could serve as benchmark results to assess two-dimensional approximate plate theories.     

Photothermoelastic study of stress concentrations in a plate with internal heating

This paper describes a photothermoelastic method for simulating, in a three-dimensional model, the temperature gradients that occur in structural parts subjected to internal heating such as is frequently encountered in certain areas of nuclear-reactor design. The method is applied to a plate which has a step change in thickness and sustains a nonlinear temperature gradient through its thickness. The shapes of the gradients simulate internal heating of the plate material. The values for the highest stresses on the free surfaces of the plate, within the thickness of the plate, and at the root of the step are presented in graphical form for a range of internal heat-generated conditions. Thermal-stress-concentration factors are presented for a step change in the thickness of a plate under this type of heating. Its design significance is discussed. The same stress and stress-concentration values are shown to also apply to nonnuclear problems. During shut-down in conventional thermal plants, when the walls sustain linear steady-state temperature drops across their thicknesses, temperature profiles exactly analogous to those presented in this paper occur. The stresses can then be computed from the values presented here.     

Lamb mode stresses as means of identifying voids in the adhesive zone of bilaminates

Lamb wave technique has emerged as a reliable tool in the nondestructive testing of laminated plates. Some current studies to identify the specific Lamb modes that can characterize different kinds of defects in layered plates using Lamb waves have shown that the modes for which high stresses and low displacements occur in the interface indicate the presence of defects like pores or voids whereas the modes for which the displacements are high show the presence of harder inclusions. In this context this paper tests an earlier analytical model developed to facilitate NDT of porosity in the adhesive zone of bilaminates.The model tested treats the pore infested thin adhesive region as a linear elastic material with voids (LEMV). For certain parametric values of the LEMV adhesive layer the influence of these voids on dispersion and stresses carried by the first few Lamb modes in glass/glue/glass (G/g/G) bilaminate is traced in the range 0–10 MHz. The frequency–phase velocity points experimentally obtained by Kundu and Maslov are seen to fall very close to the present dispersion. The stresses traced using the present model in G/g/G plate at these experimentally tallied points show an easily discernable rise in the central region of adhesive, as observed by Kundu and Maslov.The model appears to be useful as a good first approximation to detect voids in adhesive zone of composite structural elements.     

Transient dynamic response of debonded sandwich plates predicted with finite element analysis

Dynamic transient response of a composite sandwich plate with a penny-shaped debonded zone has been studied by using the finite element analysis within the ABAQUS/Explicit code in this paper. In order to accurately predict the response of the debonded sandwich plate to impulsive loading, contact–impact and sliding conditions along the damaged skin-to-core interface were imposed in the model through a kinematic predictor/corrector contact algorithm. The accuracy of the finite element (FE) model used was verified by comparing between numerical predictions and experimental data known in literature for the frequency spectrum of a cracked polycarbonate laminated beam containing a delamination. By analyzing nonlinear aspects of the transient dynamics of the sandwich plate, it is shown that the presence of the debond significantly alters its short-term response. In this respect, a considerable influence of contact events within the debonded region on the plate’s global dynamic response was found out. These results were presented in both time and frequency domains. The predictions performed also showed that the FE model applied would be useful for nondestructive evaluation of defects in composite sandwich plates, and for studying dynamic response of such plates to impact.     

采用包络-准则法优化考虑瞬态传热的薄板结构

刚度和强度是薄板结构的两个主要性能。在瞬态传热过程中,考虑热-力耦合,随时间和空间变化的非均匀温度场在结构中会引起热变形和热应力,温度场随时间变化的规律和空间分布依赖于板的厚度变化,进而影响板的刚度和强度。因此,考虑瞬态传热的薄板优化问题具有更强的非线性,更加难以求解。本文给出一种包络-准则方法处理这类结构优化问题。首先,针对外力荷载,进行一个结构柔顺性的优化设计;以这一设计为基础,通过瞬态热-力耦合分析及优化准则,计算多个时刻的优化设计变量并取其包络,对上述优化结果进行迭代修正,以消除瞬态温度场作用下较高的局部应力。优化算例表明,该方法对于考虑瞬态传热薄板优化问题有效。     

ANALYSIS OF INTER-LAMINAR STRESSES FOR COMPOSITE LAMINATED PLATE WITH INTERFACIAL DAMAGE

A constitutive model for composite laminated plates with the damage effect of the intra-layers and inter-laminar interface is presented. The model is based on the general six-degrees-of-freedom plate theory, the discontinuity of displacement on the interfaces are depicted by three shape functions, which are formulated according to solutions satisfying three equilibrium equations, By using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated plates with two different damage models are derived. Then, considering a simply supported laminated plate with damage, an analytical solution is presented using finite difference method to obtain the inter-laminar stresses.     

????-FGM-???EFBF?????????????

为研究金属-FGM-陶瓷 EFBF 复合板的稳态热应力,从热传导规律出发,结合热应力计算公式,建立了该复合板稳态热应 力的研究模型,用有限元和辛普生法分析了T_a=500K和T_b=1800K时,该 复合板的稳态热应力分布并与无梯度两层复合板的结果进行了比较. 结果表明：FGM梯度层的厚度、组分和孔隙率对该EFBF复合板的热应力有不同程度的影响, 此外,有梯度三层复合板的热应力比较缓和,最大拉应力减小29.18%. 此结果为该复合板的设计和应用提供了准确的计算依据.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.     

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.     

作大范围运动矩形板的动力学建模理论研究

研究了初应力法的作大范围运动矩形板的建模理论。根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性板刚-柔耦合动力学方程。从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程。通过引入准静态概念,把其结构动力学方程转化为准静态方程。对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项;并对此非惯性系下作大范围运动柔性板的结构动力学方程进行数值仿真,验证了采用初应力法柔性板的动力学建模方法来计算经历大范围运动的不规则柔性板的动力学响应是可行的,体现了初应力法对柔性板建模的优越性。     

用高阶位移模式分析复合材料层合板的自由振动

建立一种新的高阶位移模式：分层假设复合材料层合板的位移场，利用各层间应力及位移的连续性条件，导出了作为整体的层合板控制微分方程。最后，采用这一高阶剪切理论来分析复合材料矩形层合板的自由振动。数值计算采用有限差分法，并编制了计算程序，计算得出了六种不同边界条件、不同铺层、不同宽厚比工况下的矩形层合板的自振频率。同经典理论解进行比较，可以看出本文方法简便易行，且精度较高，可以在微机上实用。