Hybrid Thermoelastic Stress Analysis of a Pinned Joint

Mechanical joints such as bolted or pinned connections are commonly used to fasten mechanical or structural members together. Inadequate knowledge of the stresses at the edge of the loaded holes can render it difficult to stress analyze such mechanical fasteners theoretically or numerically. Thermoelastic stress analysis (TSA) is utilized here to analyze a plane-stressed pin-loaded plate. The approach combines the recorded temperature information with an Airy stress function, plus imposes the traction-free conditions on the non-contacting edge of the hole and on the external boundaries of the plate. Individual components of stress are determined full-field as well as on the pin-plate interface. In addition to agreeing with the frequently assumed interface contact stresses in mechanical connections having zero clearance, the TSA results satisfy force equilibrium, are compatible with residual markings on the contacted surfaces of the pin and the hole, and correlate with FEM predictions. Significant advantages of TSA here include neither needing to know the elastic modulus nor to differentiate the recorded information.     

具有中心孔的正交复合材料板在双轴载荷下的应力分析

本文研究了具有中心孔的正交复合材料板在双向载荷下的应力,建立了有限校核系数和双轴率以及之间板宽率的关系,并得到孔边的应力集中系数.这些结果对研究具有中心孔的正交复合材料板在双向载荷下的强度预测和应力分析具有重要的作用.     

The General Solution for a Finite Thermopiezoelectric Plate Containing a Hole and a Crack

By application of complex variables and conformal transformation, the general solution to multiply connected domains of two dimensions is constructed in terms of multiple Laurent series for thermopiezoelectric materials. Three typical boundaries, i.e., a rectangular contour, a curvilinear hole, and a line crack are considered in the paper. Though the Green’s function of an arbitrarily shaped hole still remains unknown for anisotropic materials, the approximate solutions both for thermal and electro-mechanical fields are obtained in explicit form by the least square method. The accuracy of the approximation are investigated upon each boundary contours. It is found that the local error on the crack surface diminishes below 10⁻⁷% by adopting only 20 terms of related power series. For a rectangular plate, the precision is enhanced up to the level of 99.99% on its boundary contour by adding the supplementary function, due to the rectangular corners, into the complex solution. Considering that the singular character of a crack is retained in the solution, the stress and electric displacement intensity factors influenced by the hole width and plate size are exhibited herein.     

Thermoelastic Stress Analysis of Structures Under Natural Vibrations

The paper focuses on stress analyses of structures subjected to excitation forces operating at resonant frequencies. The structures are analysed experimentally using the Thermoelastic Stress Analysis (TSA) technique. Experiments are carried out for fixed-free beams of different dimensions and materials, and also for a steel rectangular plate with clamped edges. These structures are excited by a shaker via a stinger. For materials with low thermal conductivity, the agreement between the theory, numerical results and experimental results is excellent. As the thermal conductivity of the material is increased, the correspondence is not as close. This is because of non-adiabatic behaviour. The implications of these results are discussed in detail in the paper and a means of deriving the severity of heat transfer is provided. Other factors that influence the TSA results from structures under natural loading are also discussed.     

热电材料孔边周期裂纹问题的热电弹分析

论文研究了均匀电流密度和能量流作用下,热电材料中带4k个周期径向裂纹的圆形孔口问题.考虑非渗透型电和热边界条件,运用复变函数理论和保形映射方法,得到了热电材料中电流密度、能量密度和应力场的精确解.依据断裂力学理论,运用Cauchy积分公式得到了周期裂纹的电流、能量和应力强度因子.数值结果分析了场强度因子随各个参数的变化...     

Thermoelastic Stress and Damage Analysis Using Transient Loading

Thermoelastic stress analysis (TSA) is often regarded as a laboratory based technique due to its requirement for a cyclic load. A modified methodology is proposed in which only a single transient load is used for the TSA measurement. Two methods of imparting the transient load are validated against calculations and the conventional TSA approach. Specimens with different damage severities are tested and it is shown that the modified TSA method has the potential to be applied in the field as a non-destructive evaluation tool.     

开孔热塑性复合材料的三维弹塑性面内应力分析

本文利用一单参数三维塑性模型对AS4/PEEK热塑性复合材料的塑性行为进行表征。利用有限元程序生成系统FEPG,将复合材料的三维单参数塑性模型引入该系统中,编制了相应的有限元程序。通过将本文的有限元计算结果与文献实验结果进行对比,证明了所生成程序的精确性。并对AS4/PEEK热塑性复合材料层合板[0/90]s的面内应力进行了计算与分析。给出了0°层与90°层的面内应力。0°层的最大应力σx大约是90°层相应值的20倍,这主要是由于热塑性复合材料AS4/PEEK的纵向和横向模量存在很大的不同,并且具有明显的弹塑性行为所造成的。     

A Dual Phase Lag Model on Thermoelastic Interaction in an Infinite Fiber-Reinforced Anisotropic Medium with a Circular Hole

The model of generalized thermoelasticity proposed by dual phase lag (DPL), is applied to study the thermoelastic interactions in an infinite fiber-reinforced anisotropic medium with a circular hole. A decaying with time thermal field on the boundary of the hole, which is stress free, causes the thermoelastic interactions. The solutions for displacement, temperature, and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress, and displacement are studied. The exact solution in the case of isotropic medium is discussed explicitly. The accuracy of the finite element method validated by comparing between the finite element and exact solutions for absence the reinforcement.     

Thermoelastic Determination of Individual Stresses in Vicinity of a Near-Edge Hole Beneath a Concentrated Load

Thermoelastic data are combined with an Airy stress function to determine the individual stresses on and near the boundary of a circular hole which is located below a concentrated edge-load in a plate. Coefficients of the stress function are evaluated from the measured temperatures and the local traction-free conditions are satisfied by imposing s_rr = t_rq = 0 {sigma_{r{rm{r}}}} = {tau_{rtheta }} = 0 analytically on the edge of the hole. The latter has the advantage of reducing the number of coefficients in the stress function series. The method simultaneously smoothes the measured input data, satisfies the local boundary conditions and evaluates individual stresses on, and in the neighbourhood of, the edge of the hole. Attention is paid to how many coefficients to retain in the stress function series. Although the presence of high stress concentration factors, together with a hole-diameter-to-plate-thickness ratio of only two, result in some three-dimensional effects, these are relatively small and the agreement between the thermoelastic values, those from recorded strains and FEM-predicted surface stresses is good.     

Assessment of Non-adiabatic Behaviour in Thermoelastic Stress Analysis of Composite Sandwich Panels

Thermoelastic stress analysis (TSA) is used to derive the surface stresses in large sandwich structure panels with honeycomb core and carbon fibre face sheets. The sandwich panels are representative of those used for secondary aircraft structure. The panels were subjected to a pressure load, similar to that experienced in-service, using a custom designed test rig. To achieve the necessary adiabatic conditions for TSA, cyclic loading is regarded as an essential feature. As the panels were full-scale, the maximum loading frequency that could be imparted to the panels by the rig was 1 Hz, which is below the usual range recommended to achieve adiabatic behaviour. To assess the effectiveness of TSA at low frequencies two approaches to calibration are investigated and compared with the stress distribution obtained from independently validated FE models. The thermoelastic response was calibrated into stress data using thermoelastic constants derived experimentally from tensile strips of the sandwich panel face sheet material. It is shown that by using thermoelastic constants obtained from the tensile strips manufactured with the same lay-up as the sandwich panel face sheets, and at the same cyclic load frequency used in the full-scale tests, quantitative stress metrics can be derived from the TSA data. More significantly, a deeper insight into the importance of the thermal characteristics in TSA of laminated materials is provided. It is demonstrated that, for the material used in this work, it is possible to use the global material behaviour to obtain quantitative results when adiabatic conditions do not prevail.     

圆筒结构动态特性全场激光扫描试验研究

利用全场激光扫描仪对圆筒结构开展了动态特性试验研究,准确获得了结构的模态参数,结果与有限元计算相比最大相对偏差仅为3.5%,且全场激光扫描能在短时间内完成信号瞬态采集、实时显示与处理,整个扫描测量不引入额外电噪声,并能提高测试准确度.     

Assessment of Non-Adiabatic Behaviour in Thermoelastic Stress Analysis of Small Scale Components

The classical thermoelastic equation and the generalized heat conduction equation are developed to deal with a non-adiabatic response in thermoelastic stress analysis. A FE simulation procedure is set up to solve the heat conduction equation over a range of loading frequencies. A small disc (20 mm diameter) loaded under three-point diametric compression is used to examine the effect of in-plane heat conduction. As the disc has regions of zero, moderate and high stress gradients it is an ideal component for this analysis. A regime is developed that provides a basis for an assessment of the nature of the response and allows a minimum loading frequency to be identified so that adiabatic behaviour is obtained. This validity of this approach is demonstrated on steel disc of 20 mm diameter. A special loading device has been designed to obtain the three-point loading and a recently introduced Instron Electropuls test machine is used to achieve the high levels of cyclic loading required for the adiabatic conditions.     

功能梯度平板的二维热弹性分析

本文研究正交各向异性功能梯度平板的二维热弹性问题.该平板在y方向无限长,x方向对边简支且温度恒定.从热弹性力学的基本方程出发,假设材料参数沿板厚方向(z方向)按同一函数规律变化,基于状态空间法,在板的上下表面作用机械荷载和热荷 载的情况下,获得了功能梯度平板二维热弹性问题的Peano-Baker级数解.通过算例,验证了Peano-Baker级数解的正确性;同时也分析了材料参数沿板厚方向不同的幂函数分布对平板响应的影响.     

Phase Shifting Full-Field Interferometric Methods for Determination of In-Plane Tensorial Stress

A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.     

The Potential for Assessing Residual Stress Using Thermoelastic Stress Analysis: A Study of Cold Expanded Holes

Thermoelastic stress analysis (TSA) is a well established tool for non-destructive full-field experimental stress analysis. In TSA the change in the sum of the principal stresses is derived, usually when a component is subjected to a cyclic load. Therefore the mean stress or any residual stress in a component cannot be obtained from the thermoelastic response. However, modifications to the linear form of the thermoelastic equation that incorporate the mean stress may provide a means of establishing the residual stresses. It has also been shown that the application of plastic strain modifies the thermoelastic constant in some materials, causing a change in thermoelastic response, which may also be related to the residual stress. The changes in response due to plastic strain and mean stress are of the order of a few mK and are significantly less than those expected to be resolved in standard TSA. Recent developments in infra-red detector technology have enabled these small variations in the thermoelastic response to be identified, leading to renewed interest in the use of TSA for residual stress analysis in realistic components. The component studied in this work is an aluminium plate that contains a cold expanded hole, hence providing an opportunity to examine any changes in thermoelastic response caused by the residual stress in the neighbourhood of the hole. The variations in thermoelastic response due to residual stress are shown to be measurable and significant; validation of the residual stress field is provided by laboratory X-ray diffraction. The potential for a TSA based approach for residual stress analysis is revisited, and the feasibility of applying it to components containing realistic residual stress levels is assessed.     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

含孔边非均匀材料圆环的无限大薄板的应力集中系数

对于含圆孔及孔边非均匀材料圆环的无限大薄板，假设非均匀材料的弹性模量沿径向按照指数函数变化，而泊松比为常数，分别导出了双轴拉伸和纯剪切作用时孔边及界面处的应力集中系数的解析解．通过数值算例详细分析了非均匀材料圆环的弹性模量的变化对无限大薄板的孔边及界面处的应力集中系数的影响．研究结果表明，合理选择孔边非均匀材料圆环的材料性能变化参数可有效地缓解薄板的孔边应力集中程度．本文的研究结果可为含圆孔的薄板的设计提供一定的参考．     

High-speed Photoelastic Stress Analysis of Axially-impacted Finite Column

In an earthquake occurring directly under a city, such as the Hanshin–Awaji great earthquake, the first axial longitudinal impact induced from the source may create fatal damage to the architectural columns. This phenomenon has been confirmed by a theoretical analysis based on elastic wave propagation in columns fixed at both ends. In this paper, the stress intensification behavior in the columns under axial impact is verified by the high-speed photoelastic experiments in combination with semiconductor strain gage and by the theoretical analysis of the longitudinal stress wave analysis method.