Geometry effects of substrate and coating layers on the thermal stress response of FGM structure

Summary Due to transient temperature change, the plane strain elastic-plastic problem for a functionally graded material (FGM) bonded to a homogeneous coating layer and a metal substrate is considered by the use of the finite element method (FEM). The substrate and the coating are assumed to be aluminum and partially stabilized zirconia, respectively. The FGM layer is a particulate composite of aluminum and partially stabilized zirconia with volume fractions continuously varying through the thickness. Generally in high temperature applications, the FGM system is sandwiched between a substrate layer and a coating layer. The coating layer increases the protection from heat but decreases the thermal shock resistance while the substrate layer increases the rigidity of the structure and decreases strength-related properties at high temperature. In order to compromise the thickness of both the coating and substrate layers, different values of the substrate and coating thickness are studied in order to evaluate their effects on the thermal stress response of the FGM structure. Since the main objective of the FGMs is using them in different applications with severe thermal loading conditions, the thermal stresses may be so high that some reinforcements may be fractured and/or debonded from the matrix giving a weakening effect instead of a reinforcing one. Hence, the behaviors of the reinforcements and the matrix are essential to be studied. In this regard, microscopic constitutive equations along with the temperature-dependent properties of the constituent materials are considered to enable us obtaining more realistic results of thermal stresses. Since the FGM structures are fabricated at high temperatures, thermal residual stresses are produced. In order to find out the importance of the consideration of the residual stresses arising from the fabrication process, the FGM structure with stress-free conditions is heated to the operating temperature, and its thermal stress response is compared with that one where the residual stresses are taken into account. Also, several functional forms of gradation of the constituents in the FGM layer are examined to reach the optimum profile giving the minimum stress level for the FGM structure under thermo-elasto-plastic behavior.     

Aspects of residual thermal stresses in continuous-fibre-reinforced ceramic matrix composites

An analytical model is presented that predicts the thermal stresses which arise from mismatch in coefficients of thermal expansion between a fibre and the surrounding matrix in a continuous fibre composite. The model consists of two coaxial isotropic cylinders. Stress transfer between the fibre and the matrix near an unstressed free surface has been modelled by means of a shear-lag analysis. Away from the free surface the theoretical approach satisfies exactly the conditions for equilibrium and continuity of stress at the fibre-matrix interface. Application of the model to a composite consisting of a glass-ceramic calcium alumino-silicate (CAS) matrix containing unidirectional Nicalon fibres points to a strong dependence of stress on fibre volume fraction. Surface effects are significant for depths of the order of one fibre diameter. Near-surface shear stresses resulting from cooling from the stress-free temperature are sufficiently high to suggest that a portion of fibre close to the surface is debonded at room temperature. Experimental results acquired with a scanning electron microscope (SEM) equipped with a heating stage are consistent with this prediction. Consequently, the model has been modified in a simple way to incorporate frictional slip at the interface, according to the Coulomb friction law. Although detailed measurements are limited by the resolution of the technique, experimental evidence suggests that the transfer length is within an order of magnitude of the model prediction.     

The effects of residual stresses and degradation on the response of viscoplastic functionally graded materials

Functionally graded materials (FGMs), having ceramic and metallic constituents, are commonly used for extreme temperature applications. Under extreme temperature changes, the mismatches in the thermo-mechanical properties of the ceramics and metallic constituents could cause pronounced thermal stresses and could lead to degradation in the properties of the constituents. High stresses in the metallic constituent lead to plastic deformations and high tensile stresses in the ceramic constituent induce cracking. An elastic–viscoplastic micromechanical model is formulated for analyzing residual stresses and strains and degradation in ceramic–metal FGMs undergoing temperature changes due to conduction of heat. A degradation parameter that depends on the temperature and strain is introduced in order to determine the level of material degradation in the ceramics and metallic constituents. The Perzyna viscoplastic model is considered for the metallic constituent while the ceramic constituent is assumed linear elastic. The material parameters in these constituents change with the degradation. The problem leads to time-dependent coupled thermal, deformation, and degradation behaviors. The micromechanical model is implemented in a displacement based finite element (FE), which is used to determine the performance of the viscoplastic functionally graded structures subject to external thermo-mechanical stimuli.     

Influence of thermal residual stresses on the composite macroscopic behavior

The influence of the thermal residual stress on the deformation behavior of a composite has been analyzed with a new micromechanical method. The method is based on secant moduli approximation and a new homogenized effective stress to characterize the plastic state of the matrix. It is found that the generated thermal residual stresses after cooling and their influence on the subsequent deformation behavior depends significantly on the aspect ratio of the inclusions. With prolate inclusions, the presence of thermal residual stresses generate a higher compressive hardening curves of the composite, but it is reversed with oblate inclusions. For particle reinforced composite, thermal residual stresses induce a tensile hardening curve higher than the compressive one and this is in agreement with experimental observations.     

Reduction of residual stresses in thick-walled composite cylinders by smart cure cycle with cooling and reheating

The nozzle parts of solid rocket motors must endure both the internal pressure generated by high temperature exhaust gas and the mechanical load generated by steering operation. Therefore, the nozzle parts of solid rocket motors are fabricated with thick carbon fiber phenolic resin composites. When the thick-walled phenolic composite cylinder is cooled down from the curing temperature of about 155 °C to the room temperature, thermal residual stresses are created due to the anisotropic thermal deformation of the composite structure.

In this paper, a smart cure method with cooling and reheating was developed to reduce residual stresses in thick-wound composite cylinders made of carbon phenolic woven composite. The optimal cure cycle was obtained to reduce the residual stresses without increasing processing time and applied to fabrication of the thick-walled composite cylinder. From the residual stresses measured by the radial-cut-cylinder-bending method, it was found that the residual stresses were reduced 30% by using the smart cure method.     

Evolution of phase stresses in Al/SiC_p composite during thermal cycling and compression test studied using diffraction and self-consistent models

In this work,the evolutions of stresses in both phases of the Al/SiCp composite subjected to thermal cycling during in situ compression test were measured using Time of Flight neutron diffraction.It was confirmed that inter-phase stresses in the studied composite can be caused by differences in the coefficient of thermal expansion for the reinforcement and matrix,leading to a different variation of phase volumes during sample heating or cooling.The results of the diffraction experiment during thermal cycling were well predicted by the Thermo-Mechanical Self-Consistent model.The experimental study of elastic-plastic deformation was carried out in situ on a unique diffractometer EPSILON-MDS(JINR in Dubna,Russia)with nine detector banks measuring interplanar spacings simultaneously in 9 orientations of scattering vector.For the first time,the performed analysis of experimental data allowed to study the evolution of full stress tensor in both phases of the composite and to consider the decomposition of this tensor into deviatoric and hydrostatic components.It was found that the novel Developed Thermo-Mechanical SelfConsistent model correctly predicted stress evolution during compressive loading,taking into account the relaxation of thermal origin hydrostatic stresses.The comparison of this model with experimental data at the macroscopic level and the level of phases showed that strengthening of the Al/SiCp composite is caused by stress transfer from the plastically deformed A12124 matrix to the elastic SiCp reinforcement,while thermal stresses relaxation does not significantly affect the overall composite properties.     

More on the effects of thermal residual and hydrostatic stresses on yielding behavior of unidirectional composites

The influence of manufacturing process thermal residual stresses and hydrostatic stresses on yielding behavior of unidirectional fiber reinforced composites has been investigated when subsequently subjected to various mechanical loadings. Three-dimensional finite element micro-mechanical models have been used. The results of this study reveal that the size of the initial yield surface is highly affected by the thermal residual and hydrostatic stresses. It was also found that effects of a uniform temperature change on the initial yield surface in the composite stress space is not equivalent to a solid translation of the surface in the direction of the hydrostatic stress axis. At the micro-level, magnitudes of various stress components within the matrix due to the thermal residual and hydrostatic stresses are different. However, at a macro-level, both temperature change and hydrostatic loading of composites show similar effects on the initial yield surface in the composite stress space. In an agreement with experimental data, results also show that residual stresses are responsible for asymmetric behavior of composites in uniaxial tension/compression in the fiber direction. This asymmetric behavior suggests that the existing quadratic yield criteria need modification to include thermal residual stress effects.     

Three dimensional exact solution of thermal stresses in rectangular composite laminate

Three-dimensional exact solutions for temperature distribution and thermal stresses in simply supported finite rectangular orthotropic laminate subjected to prescribed boundary conditions under combined thermal and mechanical loading, are presented which will be used to check the accuracy of more generalized numerical tools. The numerical results are presented for across-ply 3-layered 0/90/0. composite laminate. The numerical results help to draw the conclusion that the influence of the thermal field on deformations and stress is very predominant and induces high transverse normal stress at the interfaces which may cause the failure of the weak interlayer adhesive bond.     

A new viscoelastic method of calculation of low-temperature thermal stresses in asphalt layers of pavements

The paper presents a new method of calculation of thermal stresses in asphalt layers of pavements induced by cooling or heating. The method, developed by the author, is based on the analytical solution for the linear viscoelastic Burgers model extended numerically for the case of asphalt layers whose rheological parameters are strongly dependent on temperature. The coefficient of thermal expansion and Poisson’s ratio may optionally be taken either as constant or varying with temperature. Two equivalent numerical methods have been developed, named as ‘the incremental method’ and ‘the stress increase and relaxation method’. The computer program was developed for calculation of thermal stresses in several different cases of temperature impact, included constant rate cooling and heating, change of temperature and relaxation and a cycle of first cooling, relaxation and second cooling. What the most important practically, the solution for any change of temperature, modelling real winter changes in long period of time, was also developed. Several examples of calculations are presented. The results obtained with use of this method are promising and appear to be acceptable. The advantages of the new method in comparison with existing methods are that it takes fully into account the viscoelastic properties of a layer and the method is correct if the material does not meet the time–temperature superposition principle.     

一种新型复合相变材料导热性能的实验研究

针对相变材料在实际应用过程中交替存在升温液化和降温固化的复杂传热过程,采用JW-Ⅲ建筑材料热流计式导热仪,分别对升温和降温过程中处于固态、混合态、液态的新型复合相变材料导热性能进行了测试和分析。研究结果表明,复合相变材料在加热和冷却过程中的导热系数随温度的变化存在明显的规律性差异,导热系数在混合态时差值达到20%;升温过程中,复合相变材料在混合态和液态时的导热系数值相差不大,但与固态时相比有明显减小;降温过程中,在液-固相变的过程中导热系数随温度减小而增大,有利于加速相变材料的固化。     

The effect of oblique functional gradation to thermal stresses in the functionally graded infinite strip

Summary Thermal stresses in a functionally graded infinite strip (FGIS) which has an oblique boundary to its functional gradation are studied theoretically. The rigorous solution is derived by the use of the variable separation and the stress function methods. The material properties are assumed to be exponential functions of the position along the functional grading direction. Two types of boundary conditions are considered, one is the case of prescribed heat flux on the heating surface and the other is the case of prescribed temperature on the same surface. The numerical calculations are carried out for ZrO₂/Ti-6Al-4V functionally graded materials (FGMs). The numerical results of temperature and thermal stresses are illustrated in figures for different values of obliqueness angle θ. Numerical results show that the temperature curve leans to the ceramic-rich side and the values of compressive and tensile stresses drastically decrease when the obliqueness angle θ varies from 0 to 90 degrees. For the positions of the maximum compression and the maximum tension, after they shift to the left-hand side from the origin (X* = 0.0, θ = 0°), they shift to the right-hand side till θ = 90° passing the origin at 45°.     

梯度功能材料薄板瞬态热弹性弯曲有限元分析

用层合板有限元法分析了由ZrO2和Ti-6Al-4V组成的新型梯度功能材料薄板的瞬态热弹性弯曲应力问题,并对本方法的正确性进行了检验。讨论了加热、 冷却热边界条件以及两种力学边界条件(固支和简支)对梯度功能材料薄板的瞬态热弹性弯曲应力分布的影响。发现：(1) 在加热过程中,简支板低温金属侧出现较大压应力;在冷却过程中,简支板高温陶瓷侧出现较大拉应力; 且其拉、压应力会随着板上、下表面温差的增大而增大。(2) 无论是简支板还是固支板, 在冷却过程中,沿整个厚度板内部压应力均较大。(3) 在本文的相同条件下,固支板比简支板更适合高温、大温差的使用环境。     

Thermal shock and thermal fatigue study of ceramic materials on a newly developed ascending thermal shock test equipment

A test equipment was designed to study thermal shock and thermal fatigue of ceramic materials subjected to fast heating (ascending). The equipment was designed to generate thermal stress in a test specimen by heating one surface of it by an oxy-hydrogen flame while cooling the opposite surface. The sample cracked when thermal stress exceeded its mechanical strength. The in situ crack formation was detected by an acoustic emission system coupled to the set up. The hot zone temperature was measured by an infra red pyrometer. The equipment was also designed to run thermal fatigue test cycles in automatic mode between two selected temperatures. The temperature and thermal stress distribution in the test specimen were modelled using finite element software. The effect of temperature distribution of the top and bottom surfaces on thermal stresses was studied. It was observed that the thermal stress is very sensitive to the temperature distribution on the top surface and maximum near the periphery of the top surface. This was in agreement with the experimental results in which the cracks were originated from the periphery of top surface. It was also observed that the failure temperature was higher for thicker samples.     

On the matrix cracking stress and the redistribution of internal stresses in brittle-matrix composites

A concept is proposed to increase the matrix cracking stress of some brittle-matrix composites by taking advantage of the redistribution of internal stresses that occurs when a composite with phases that have dissimilar creep behavior is subjected to thermomechanical loading. The concept is elaborated through the stress analysis of a model unidirectional composite with constituents that exhibit linear viscoelastic behavior. It is shown that if a composite with a matrix that is less creep resistant than the fibers is subjected to a treatment involving both thermal and mechanical loading (e.g. creep test), stresses can be transferred from the matrix to the fibers, resulting in the stress–relaxation of the matrix. Furthermore, it is also shown that by the elastic recovery of the fibers, the matrix can be subjected to large compressive residual stresses at the end of the treatment. The conditions for the viability of this concept and the implications of fiber overloading and potential loss of composite-like behavior are discussed.     

Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates

Polymer matrix composites are relevant materials for future supersonic aircraft due to their high specific properties. However, in such aeronautical applications, the material is exposed to severe environmental conditions. The present paper aims at assessing an approximate model to evaluate hygrothermoelastic stress in composite laminated plates during moisture desorption taking into account the change of mechanical characteristics induced by the variation of temperature and moisture. The developed method permits us to calculate such stresses during desorption phase without the computation of the moisture concentration, through laminated plates. It observed through this study that the variation of elasticity modulus due to the temperature causes a stress relaxation. These stresses have to be taken into account for the design of composite structures submitted to a moist environment.

Through the presented study, we hope to contribute to the understanding of hygrothermal behaviour of composite laminated plates.     

Residual stresses in fibre- and whisker-reinforced aluminium alloys during thermal cycling measured by X-ray diffraction

Residual stresses have been determined using X-ray diffraction in two different metal matrix composites, viz. a squeeze-cast Al-2%Mg matrix with 10, 20 or 26 vol.% Al₂O₃ fibres and an extruded AA 6061 alloy with 25 vol.% SiC whiskers. The composites have been studied after thermal cycling between 240 or 250 °C and room temperature succeeded in some cases by quenching to liquid nitrogen temperature. On the squeeze-cast composite, stresses were measured at room temperature and in situ at 240 °C. X-ray stress determinations were compared with the stress values calculated by a modified Eshelby model for equivalent inclusions. By the model, the stresses can be accurately predicted for both composite systems. Thermally induced plastic relaxation reduces the residual stresses. The degree of reduction depends on the reinforcement volume fraction, the difference in coefficient of thermal expansion between the phases and the magnitude of the temperature drop. At elevated temperature the stresses are less responsive to reiterated quenching and heating.     

Thermal residual stresses in FSS layer-embedded composite plates in co-cure bonding

The residual stresses occur in the frequency selective surface (FSS)-embedded composite structures after co-curing due to mismatch between the coefficient of thermal expansions between the FSS and composite materials. It is well known that residual stress has a great influence on the strength and fatigue life of the FSS-embedded composite structures. Numerous researches have been reported about residual stresses in the composite structures. However, studies on the residual stresses in the FSS-embedded composite structure have not been widely investigated. Therefore, in this study, the thermal residual stresses of FSS-embedded composite structures were analyzed using finite element analysis, with considering the effect of FSS pattern and size. Various FSS patterns, such as square loop, gridded square loop, and double square loop, are considered in the analysis. The effects of dimensional change of design parameters of FSS pattern on the residual stresses in the hybrid composites were also investigated.     

热环境对FGM壳模态频率的影响

为了推动功能梯度材料(FGM)在高超音速飞行器热防护结构设计中的应用,旨在探讨不同温度场对热防护壳模态频率的影响,提供热防护壳动力学设计参考。从陶瓷金属基FGM的热物性参数模型入手,结合圆柱薄壳能量原理,建立FGM圆柱壳的模态方程。在此基础上,首先分析热物性参数变化规律对FGM壳模态频率的影响,然后探讨考虑热应力后不同热环境下FGM壳模态频率的变化规律。结果表明,FGM物性参数变化对模态频率的影响没有热力耦合影响明显;温度梯度300 K时,物性参数变化对模态频率起主导作用,反之温度梯度300 K时,热应力和热变形对模态频率起主导作用。     

复合材料层合板的固化残余应力和变形分析

本文采用非线性有限元方法研究了复合材料层合板在固化后期降温过程的残余应力和变形问题。考虑了材料的热物理与力学性质随温度的变化以及变化率和应力间耦合的影响。给出了一些有意义的结果。