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.     

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.     

Thermographic stress analysis of composite materials

Several critical aspects of stress measurements in composite materials by thermographic stress analysis (TSA; also SPATE method) have been investigated. The emphasis is on the observed effects of thermal-expansion coefficients with positive and negative signs, thickness of surface coating, and absolute temperature increases in the material due to cyclic loading. Heat transfer and mean stress effects are also discussed.     

Image enhancement and stress separation of thermoelastically measured data under random loading

Traditional thermoelastic stress analysis (TSA) presupposes that the structure being analyzed is cyclically loaded at a constant amplitude and frequency. This approach typically has been used to satisfy the adiabatic reversible assumptions. The authors employ an alternative signal analysis technique that enables one to evaluate the magnitude of the individual components of stress in a component subjected to a loading that is random in both frequency and magnitude. However, the nature of the measured information does not change; i.e., data are inherently noisy, and edge information is unreliable. The latter two aspects have caused many thermoelastic stress analyses to be more qualitative than quantitative. The present paper emphasizes developing the TSA technique into a practical, noncontacting quantitative method for stress analyzing actual engineering structures that are randomly loaded. In particular, ability to determine the individual stresses thermoelastically under random loading is demonstrated.     

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.     

Reproducibility and reliability of the response from four SPATE systems

The SPATE (stress pattern analysis by thermal emissions) system is currently the standard equipment for thermoelastic stress analysis (TSA). A carefully designed test program that studied the behavior of four independent SPATE systems over an 8-month period is described. The response of each system is compared with the response of the other systems in the study.     

Thermography Applied to the Study of Fatigue Crack Propagation in Polycarbonate

Thermography was used to study the propagation of fatigue cracks during cyclic loading of pre-cracked SAE keyhole polycarbonate specimens. A micro-bolometer infrared camera (FLIR A655sc) and a commercially available software program (DeltaTherm2) were employed. The stress intensity factors were determined using a hybrid thermoelastic stress analysis (TSA) technique. The crack growth rate was determined via thermography using two different approaches. The first approach used the output of the crack-tip position from the developed TSA algorithm and the number of cycles between data sets. The second approach used temperature measurement as a new way to determine da/dN (crack growth rate) directly. As a result, da/dN vs ΔK (stress intensity factor range) graphs were plotted and fitted using Paris’ law. A comparison between the resultant da/dN vs ΔK curves and results found in the literature, as well as curves from the finite element method (FEM) simulations showed good agreement. The conclusion was that thermography is a very powerful tool that can detect, measure and monitor fatigue cracks in polycarbonate.     

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.     

Prestressing effect of twisted fiber yarn in composites

By utilizing the behavior of twisted fiber yarn, prestressing composites can be made. In unloading, the matrix of the prestressing composite is applied in compression. If tensile load acts on the composite, the value of the tensile stress acting on the materials may decrease greatly. By twisted fiber yarn, therefore, the tensile strength of the composites can be improved. An analysis for extension of continuous fiber yarns is made here and residual stress after curing is taken into account. The prestressing intensity in the composite depends on the twist of fiber yarn. The photoelastic test and the analysis of electron micrograph are performed, and the theoretical method for calculating prestressing effect is presented in this paper.     

复合材料中加捻纤维束的预应力效应

利用加捻纤维束的力学性能,可以制成预应力复合材料.在不受外力的情况下,这种复合材料的基体受压应力的控制.当有拉伸力作用的时候,材料所受的拉应力值会大大减少,这样,利用这种现象可以提高纤维增强复合材料的抗拉强度.本文将分析连续的加捻纤维束受拉状况并考虑到材料固化后产生的残余应力的影响.这种方法所产生的预应力取决于纤维束的加捻程度.本文将给出计算这种预应力的方法,而且还提供加捻纤维束产生预应力的光弹测试结果以及这种纤维预应力复合材料的纤维破坏的特征.     

Three-dimensional stress analysis of textile composites: Part I. Numerical analysis

Three-dimensional stress analysis in a unit-cell of a plain-woven composite was performed by using B-spline displacement approximation. The spline approximation provides continuity of displacement and stress components within each yarn and matrix subregion. Two types of unit-cell problems with and without inter-yarn delamination were considered. A penalty function approach along with a contact surface characteristic function was used to obtain a full-field numerical solution for the frictionless contact problem between delaminated yarn surfaces.Yarn interfaces at yarn-crossover locations represent three-material wedge-type regions resulting in singular stress behavior. In the case of unit-cells with perfect bonding between the yarn interfaces, the numerical values of the inter-yarn normal stress did not exhibit trends typical for unbounded stress behavior, whereas the inter-yarn shear stress components displayed discontinuous behavior typical for numerical results in the vicinity of the stress singularity. In the presence of the delamination, both the inter-yarn normal and shear stress components exhibited unbounded behavior near the singularity. Notably, the inter-yarn normal stress showed signs of singular behavior in both cases of open and closed delaminations. Due to the stress singularity that exists at yarn-crossover locations containing three materials (yarn–yarn–matrix) interface intersections, the full-field numerical solution, even with high-order approximation functions, was not able to capture the directional nonuniqueness of the stress values in the vicinity of the singularity, and therefore calls for incorporation of the asymptotic singular stress analysis, which will be given in a follow-on paper [Sihn and Roy, International Journal of Solids and Structures (accepted for publication)].     

Residual stress analysis of functionally gradient materials

Functionally gradient materials (FGM) are new engineering materials without fully understanding. One important aspect in mechanical analysis of FGM is to determine a gradient distribution that finally results in maximum thermal stress relaxation. In this paper, numerical analysis by finite element method and experimental analysis by Moire interference method were carried out to study the stress distribution in FGM. Much attention was paid on the edge effect stresses in the coating/substrate structures, and their dependence on the different gradient distribution of the new kind of composite materials.     

基于试验与有限元耦合技术的延性材料全程单轴本构关系获取方法

摘 要: 材料拉伸直至断裂的全程单轴本构关系对材料大变形和断裂机理研究具有重要意义。传统拉伸试验获取的材料真应力-真应变曲线在试样颈缩后不可测。借助可以精确测量三维变形的DIC(Digital image correlate) 技术和有限元分析技术(Finite element analysis),本文提出了基于漏斗试样拉伸试验获取材料全程单轴本构关系的新方法,即TF(Test and FEA)方法。该方法将TF方法获取的材料全程单轴应力应变关系曲线作为有限元软件中的材料本构关系对漏斗试样拉伸变形过程进行模拟,其模拟载荷-位移曲线、漏斗根部直径-位移曲线和漏斗变形轮廓线等均与试验结果吻合良好,试样表面模拟应变也与DIC测试结果吻合, 根据不同半径漏斗试样模拟获得的全程真应力-真应变曲线保持良好一致性。最后,还对试样颈缩断面的力学行为进行了讨论,并给出了304不锈钢、汽轮机叶片材料2Cr12Ni4Mo3VNBN和 1Gr12Ni3Mo2VN、汽轮机转子材料30Cr2Ni4MoV的全程单轴本构关系模型参数、破断应力和破断应变。     

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.     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。     

多物理场下FCBGA焊点电迁移失效预测的数值模拟研究

随着微电子封装技术的快速发展, 焊点的电迁移失效问题日益受到关注. 基于有限元法并结合子模型技术对倒装芯片球栅阵列封装(flip chip ball grid array, FCBGA)进行电-热-结构多物理场耦合分析, 详细介绍了封装模型的简化处理方法, 重点分析了易失效关键焊点的电流密度分布、温度分布和应力分布, 发现电子流入口处易产生电流拥挤效应, 而整个焊点的温度梯度较小. 基于综合考虑“电子风力”、温度梯度、应力梯度和原子密度梯度四种电迁移驱动机制的原子密度积分法, 并结合空洞形成/扩散准则及失效判据, 分析FCBGA焊点在不同网格密度下的电迁移空洞演化过程, 发现原子密度积分算法稳定, 不依赖网格密度. 采用原子密度积分法模拟真实 工况下FCBGA关键焊点电迁移空洞形成位置和失效寿命, 重点研究了焊点材料和铜金属层结构对电迁移失效的影响. 结果表明, 电迁移失效寿命随激活能的增加呈指数级增加, 因此Sn3.5Ag焊点的电迁移失效寿命约为63Sn37Pb的2.5倍, 有效电荷数对电迁移寿命也有一定的影响;铜金属层结构的调整会改变电流的流向和焊点的应力分布, 进而影响焊点的电迁移失效寿命.      

增强相形态对复合材料微区力学状态影响的有限元分析

采用三维有限元方法模拟了非连续增强金属基复合材料的应力场，得到了不同长径比的椭球形增强体周围的最大主应力场和应力球张量场的分布，分析了增强体长径比对非连续增强金属基复合材料的应力场、应力集中、界面应力过渡及材料内部最危险位置的影响。与仅适用于稀疏夹杂的Eshelby单夹杂模型相比，本文模型(体积分数约为20％—60％)与工程实际更加接近，所得的椭球状增强体内部应力分布并不均匀的计算结果与Eshelby的经典解析解有所不同。     

Biothermomechanics of skin tissues

Biothermomechanics of skin is highly interdisciplinary involving bioheat transfer, burn damage, biomechanics and neurophysiology. During heating, thermally induced mechanical stress arises due to the thermal denaturation of collagen, resulting in macroscale shrinkage. Thus, the strain, stress, temperature and thermal pain/damage are highly correlated; in other words, the problem is fully coupled. The aim of this study is to develop a computational approach to examine the heat transfer process and the heat-induced mechanical response, so that the differences among the clinically applied heating modalities can be quantified. Exact solutions for temperature, thermal damage and thermal stress for a single-layer skin model were first derived for different boundary conditions. For multilayer models, numerical simulations using the finite difference method (FDM) and finite element method (FEM) were used to analyze the temperature, burn damage and thermal stress distributions in the skin tissue. The results showed that the thermomechanical behavior of skin tissue is very complex: blood perfusion has little effect on thermal damage but large influence on skin temperature distribution, which, in turn, influences significantly the resulting thermal stress field; the stratum corneum layer, although very thin, has a large effect on the thermomechanical behavior of skin, suggesting that it should be properly accounted for in the modeling of skin thermal stresses; the stress caused by non-uniform temperature distribution in the skin may also contribute to the thermal pain sensation.     

Dynamic Analysis of Multi-Beam MEMS Structures for the Extraction of the Stress-Strain Response of Thin Films

Freestanding MEMS structures made of two long connected beams from different materials are fabricated and released in order to extract the stress-strain properties of thin films. The first material, named actuator, contains a high internal tensile stress component and, when released, pulls on the other beam. The strain in the beams is calculated based on the measurement of the displacement with respect to the reference configuration using scanning electron microscopy. The stress is estimated using two different methods. The first method, already reported, is based on the displacement of the actuator and the knowledge of its internal stress. The method which constitutes the novelty of the present study is based on the dynamic analysis of the multi-beam structures, and the determination of the stress value that corresponds to the measured resonance frequencies. The dynamic analysis is performed via two different methods: (i) the modified Rayleigh–Ritz technique and (ii) the Euler–Bernoulli beam dynamics. Results are provided for palladium thin films which deform plastically and for monocrystalline silicon thin films, exhibiting a purely elastic behavior. The results show the higher accuracy of the dynamic measurements for the estimation of the stress compared to the static method. The dynamic measurements also show that the Rayleigh–Ritz technique tends to give a higher bound for the resonance frequencies compared to the Euler–Bernoulli technique. This dynamic method extends the potential of this on-chip material testing technique which can also be adapted to stress controlled sensors applications.