Analytical modelling of thermal residual stresses in exponential functionally graded material system

An analytical model is developed for prediction of thermal residual stresses, arising from the fabrication of exponential functionally graded material (simply called E-FGM) systems. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness. Residual stresses were found to increase when fully ceramic and/or fully metal regions are included in the structure, adjoining the graded zone. The effects of temperature dependent elastic and thermal expansion characteristics of constituents on residual stress were found to be small.     

Piezo-spectroscopic characterization of alumina-zirconia layered composites

Ceramic monolithic and multilayered composites were produced by stacking water based green ceramic cast tapes. Two different mixtures of composites within the Al₂O₃/YTZP, system were investigated. The difference in the coefficient of thermal expansion (CTE) between the composites fabricated, resulted in the development of residual stresses when the same compositions were combined in a multilayered structure. The magnitude and the distribution of these residual stresses were assessed by the piezo-spectroscopic technique. The stress within the layers varied with a parabolic trend, with the highest values at the interfaces and a reduction toward the centre of the layers. The influence of symmetry of the multilayered laminate on the magnitude and distribution of the residual stresses within the structure are discussed.     

Analyses of thermal expansion behavior of intergranular two-phase composites

Both analytical modeling and numerical simulations were performed to analyze residual thermal stresses and coefficients of thermal expansion (CTEs) of intergranular two-phase composites in a two-dimensional sense. A composite-circle model was adopted for analytical modeling. Model microstructures consisting of square-array, hexagon-array, and brick wall-array of grains with an intergranular phase as well as an actual microstructure of random-array grains with an intergranular phase were adopted for numerical simulations. The results showed that in predicting CTEs, the simple analytical model represents the two-dimensional composite well except that with brick wall-array grains, which induced significant anisotropic CTEs in the composite. The residual thermal stresses in composites were also discussed.     

Effects of particle size on the thermal expansion behavior of SiCp/Al composites

The coefficients of thermal expansion (CTEs) of 20 vol% SiCp/Al composites fabricated by powder metallurgy process were measured and examined from room temperature to 450 °C. The SiC particles are in three nominal sizes 5, 20 and 56μm. The CTEs of the SiCp/Al composites were shown to be apparently dependent on the particle size. That the larger particle size, the higher CTEs of the composites, is thought to be due to the difference in original thermal residual stresses and matrix plasticity during thermal loading. At low temperature, the experimental CTEs show substantial deviation from the prediction of the elastic analysis derived by Kerner and rule of mixture (ROM), while the Kerner’s model agrees relatively well at high temperatures for the composite with the larger particle size.     

Influence of the particle size and phase type of zirconia on the fabrication and residual stress of zirconia/stainless-steel 304 functionally gradient material

Tetragonal zirconia polycrystal (TZP)/stainless steel 304 (SUS304)- and ZT [50 vol % monoclinic zirconia polycrystal (MZP) + 50 vol % TZP]/SUS304-functionally gradient material (FGM) were fabricated by pressureless sintering, and the sintering properties and residual stresses of this proposed FGM were compared with directly jointed material. The defects in the sintered specimens, such as warping, frustum formation, delamination, and cracking, which originated from the different shrinkage and sintering behavior of ceramic and metal, could be controlled by the adjustments in terms of the particle size and phase type of zirconia. The residual stresses induced on the ceramic and metal regions of FGM were characterized by the X-ray diffraction method, which were relaxed as the thickness and number of compositional gradient layers were increased. The residual stresses in TZP/SUS304-FGM show irregular patterns resulting from sintering defects and thermal expansion mismatch. In ZT/SUS304-FGM, compressive stress is induced on the ceramic regions by the volume expansion of MZP that resulted from the t m ZrO₂ phase transformation on cooling. Also, compressive stress is induced on the metal regions by the constraint of warping and frustum formation that must be created to the metal direction caused by the difference of the coefficient of thermal expansions. As a consequence, it has been verified that the residual stresses generated on FGM are dominantly influenced by the thickness and number of compositional gradient layers, and the sintering defects and residual stresses can be controlled by the decrease of the difference of the shrinkage and sintering behavior of each component.     

Carbon fiber-reinforced cyanate ester/nano-ZrW2O8 composites with tailored thermal expansion

Fiber-reinforced composites are widely used in the design and fabrication of a variety of high performance aerospace components. The mismatch in coefficient of thermal expansion (CTE) between the high CTE polymer matrix and low CTE fiber reinforcements in such composite systems can lead to dimensional instability and deterioration of material lifetimes due to development of residual thermal stresses. The magnitude of thermally induced residual stresses in fiber-reinforced composite systems can be minimized by replacement of conventional polymer matrices with a low CTE, polymer nanocomposite matrix. Zirconium tungstate (ZrW(2)O(8)) is a unique ceramic material that exhibits isotropic negative thermal expansion and has excellent potential as a filler for development of low CTE polymer nanocomposites. In this paper, we report the fabrication and thermal characterization of novel, multiscale, macro-nano hybrid composite laminates comprising bisphenol E cyanate ester (BECy)/ZrW(2)O(8) nanocomposite matrices reinforced with unidirectional carbon fibers. The results reveal that incorporation of nanoparticles facilitates a reduction in CTE of the composite systems, which in turn results in a reduction in panel warpage and curvature after the cure because of mitigation of thermally induced residual stresses.     

Design of multistable composites for application in adaptive structures

During the manufacturing process and operating conditions of multilayered fibre-reinforced composites with variable fibre orientations, residual stresses build up due to the directional expansion of the unidirectionally reinforced single layers. Dependent on the laminate lay-up, these inhomogeneous residual stresses, which are primarily caused by thermal effects, moisture absorption and chemical shrinkage, can lead to large multistable out-of-plane deformations in the case of unsymmetric laminates. Instead of avoiding these laminate's curvatures, they can be advantageously used for technical applications such as novel adaptive structures. In order to adjust the laminate deformations to technical requirements, a dimensioning tool based on a modified stability analysis in combination with a novel optimisation procedure has been developed and experimentally verified. Based on the theoretical investigations, an adaptive prototype of a multistable composite with integrated smart alloys has been designed and manufactured.     

The effect of thermal mismatch on Z-pinned laminated composite structures

Z-pinning is a method of improving the through-thickness properties of composite laminates by inserting a solid pin through the laminate prior to curing. The thermal expansion mismatch between the Z-pin and base laminate produces large residual stresses during the cure cycle. Finite element modelling has shown that these stresses are greater than the failure stress of standard resin systems indicating the resin around the Z-pin should fail. This was confirmed through microscopy, which showed cracking around the perimeter of the Z-pin. Changing the material properties and dimension of the model to represent different Z-pinning situations could not significantly reduce the residual stresses, indicating cracking should occur in all Z-pinned laminates. These results show that probably all published Z-pinning properties have been obtained from laminates that would have exhibited cracking, indicating that the improved through-thickness properties are due more to mechanical interlocking than bonding. Questions are raised about the suitability of using Z-pinned laminates in specific applications, and the effects of increased moisture ingress and long term durability.     

A method for measuring temperature-dependent stress and thermal expansion of coatings

Equations and a strain-gauge technique have been presented previously for the determination of the residual stresses in ceramic coatings. In the current work, the equations are rewritten in terms of simple form. The technique is extended to elevated-temperature environments. The stress-temperature relations of coated systems are modelled according to elastic and thermoviscoelastic theory. In addition, residual stress and thermal expansion coefficient measurements are performed on SiC coating-graphite substrate composites.     

Design of Si<Subscript>3</Subscript>N<Subscript>4</Subscript>-based ceramic laminates by the residual stresses

Ceramic laminates with strong interfaces between layers are considered a very promising material for different engineering applications because of the potential for increasing fracture toughness by designing high residual compressive and low residual tensile stresses in separate layers. In this work, Si₃N₄/Si₃N₄-TiN ceramic laminates with strong interfaces were manufactured by rolling and hot pressing techniques. The investigation of their mechanical properties has shown that the increase in apparent fracture toughness can be achieved for the Si₃N₄/Si₃N₄-20 wt.%TiN composite, while further increase of TiN content in the layers with residual tensile stresses lead to a formation of multiple cracks, and as a result, a significant decrease in the mechanical performance of the composites. Micro-Raman spectroscopy was used to measure the frequency shift across the Si₃N₄/Si₃N₄-20 wt.%TiN laminate. These preliminary Raman results can be useful for further analysis of residual stress distribution in the laminate.     

Strength estimation of ceramic–metal joints with various interlayer thickness

ABSTRACT Residual stresses generated by the mismatch of thermal expansion coefficients of ceramics and metals affect the strength of ceramic–metal joints. An interlayer metal can be inserted between the ceramic and metal in order to relax this stress. An analysis was carried out of the residual stresses produced during joint‐cooling and in 4‐point bending tests. The effects of interlayer thickness on ceramic–metal joint strength were then studied by considering a superimposed stress distribution of the residual stress and the bending stress. Finally, joint strength was estimated from fracture mechanics and strength probability analysis by considering the residual stress distribution, defect size and position of pre‐existing defects in the ceramic parts. As a result of this study, we suggest an optimum material selection and interlayer thickness for ceramic–metal joint structures. This approach is generally suitable for the design of electrical and mechanical structures.     

Measurement of residual stresses in Al2O3/Ni laminated composites using an X-ray diffraction technique

Using an X-ray diffraction technique, macro-residual stresses were measured in laminated composites consisting of alternating layers of -Al₂O₃ and nickel. The in-plane thermal mismatch stresses which develop during fabrication were found to be compressive and tensile in the -Al₂O₃ and nickel layers, respectively. The magnitude of the in-plane stresses was found to be 110 MPa. Models of laminate structures predict the stress state to be biaxial in the plane of the layers. However, substantial stresses were observed perpendicular to the plane of the laminate; this stress might be due to the hot-pressing procedure used to fabricate the samples. The stress on the side surface of a laminate was measured using the indentation method and the results were consistent with those obtained by the X-ray method. Three samples were heated to 700, 900 and 1000 °C, respectively, and then cooled to test the effect of stress relaxation of the residual stresses due to the thermal expansion. The heat treatments (700–1000 °C) had no effect on the measured stress states of the laminates.     

Joining MoSi2 to 316L stainless steel

The feasibility of joining MoSi2 to 316L stainless steel using active brazing techniques was investigated using two interlayer systems: cusil/Nb/cusil and cusil/Ni/cusil (where cusil is a commercially available Cu–Ag eutectic). Dense, uniform joints were obtained with the cusil/Nb/cusil interlayer system, because the coefficient of thermal expansion (CTE) of niobium closely matched that of MoSi2 over a wide temperature range. Matching the CTEs of MoSi2 and the interlayer material shielded the low-toughness MoSi2 from residual stresses formed during cooling from the joint-processing temperature (830°C). The cusil/Ni/cusil interlayer, however, failed to produce adequate joints because of the large CTE difference between nickel and MoSi2.     

Robust design and manufacturing of ceramic laminates with controlled thermal residual stresses for enhanced toughness

Boron carbide-silicon carbide ceramic composites are very promising armor materials because they are intrinsically very hard. However, their fracture toughness is not very high. Their ballistic performance could be significantly increased if the brittleness of these materials could be decreased. Here we report development of boron carbide-silicon carbide layered ceramics with controlled compressive and tensile stresses in separate layers. Such B₄C-SiC laminates with strong interfaces can provide high apparent fracture toughness and damage tolerance along with high protection capabilities. The theory of heterogeneous layered systems was used to develop optimal design parameters allowing the evaluation and maximization of apparent fracture toughness. The layered composites were designed in a way to achieve high compressive residual stresses in thin B₄C-SiC based layers and low tensile residuals stresses in thick B₄C layers. The residual stresses were controlled by the phase composition of layers and the layers thickness. The estimated apparent fracture toughness was calculated for both three layered and nine layered composites. B₄C-30 wt%SiC/B₄C laminates were made based on the optimized design for high apparent fracture toughness. Processing of laminates involved preprocessing of powders, forming green tapes and hot pressing. Work is in progress to measure fracture toughness of laminates, as well as their strength, hardness and the ballistic performance.     

Residual stresses in structures reinforced with adhesively bonded straps designed to retard fatigue crack growth

The residual stresses induced when adhesively bonding patches to a 7085 alloy SENT (side edge notched tension) specimen in order to produce fatigue crack growth retardation have been investigated. Knowledge of the induced residual stresses is important as they affect the beneficial bridging effect of the strap. The strap materials studied were: Titanium, GLARE (fibre metal laminate), GFRP (glass fibre reinforced polymer) and CFRP (carbon fibre reinforced polymer). The residual stresses were measured using neutron diffraction and are compared with those predicated by FE (finite element) simulation. The measured and modelled residual stresses were in reasonable correlation. Tensile residual stresses were found close to the strap, whereas small compressive residual stresses were found on the un-bonded side. The residual stresses were induced due to the mismatch in the coefficient of thermal expansion (ΔCTE) between the SENT and the strap. The magnitude of the stresses induced by the bonded crack retarders depend both on the ΔCTE and the stiffness ratio between the reinforced structure and the strap. For the straps studied, the magnitude of the peak residual stresses found were in the following descending order: CFRP, titanium, GFRP and GLARE.     

Thermal expansion of a novel hybrid SiC foam–SiC particles–Al composites

A new type of hybrid SiC foam–SiC particles–Al composites (V_SiC = 53, 56.2 and 59.9%) to be used as an electronic packaging substrate material were fabricated by squeeze casting technique, and their thermal expansion behavior was evaluated. The coefficients of thermal expansion (CTEs) of the hybrid composites in the range of 20–100 °C were found to be between 6.6 and 7.7 ppm/°C. The measured CTEs are much lower than those of SiC particle-reinforced aluminum (SiC_p–Al) composites with the same content of SiC because of the characteristic interpenetrating structure of the hybrid composites. A material of such a low CTE is ideal for electronic packaging because of the low thermal mismatch (and therefore, low thermal stresses) between the electronic component and the substrate. To achieve similar CTEs in SiC_p–Al composites, the volume fraction of SiC would be much higher than that in the hybrid composites.     

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.     

基于多尺度数值模型的复合材料各向异性热膨胀系数预测

依据复合材料内部纤维在基体内的排布规律及层合板铺层特性,基于多尺度方法,建立单层板和层合板代表性体积单元(RVE)模型,施加相应的边界条件,预测单层板的热膨胀系数和工程常数,进而预测复合材料层合板各向异性的等效热膨胀系数。通过与实验数据对比发现,基于正六边形单层板RVE模型预测的热膨胀系数,相比理论预测值,整体更接近实验值,其中预测的单向T300/5208碳纤维增强环氧树脂基复合材料、P75/934碳纤维增强环氧树脂基复合材料和C6000/Pi碳纤维增强环氧树脂基复合材料的横向热膨胀系数与实验结果的误差分别只有3%、1%和2%;采用单层板RVE预测的单向ECR/Derakane 510C玻璃纤维增强乙烯基酯树脂基复合材料的工程常数与实验值最大相差7.5%;层合板RVE模型预测的正交AS4/8552碳纤维增强环氧树脂基复合材料厚度方向的热膨胀系数与实验结果误差可以忽略,只有0.08%。最后以大型复合结构常用的正交铺层结构为研究对象,基于给出的单层板和层合板RVE模型预测了不同铺层复合材料烟道层合板的等效热膨胀系数,环向铺层比例对厚度方向的热膨胀系数影响较小。      

Impact of the non-homogenous temperature distribution and the coatings process modeling on the thermal barrier coatings system

The present study deals with a numerical investigation of the residual stresses arising during the plasma-sprayed coatings process and their effects on the final stress state of the thermal barrier coatings system (TBCs) during service. A new thermo-mechanical finite element model (FEM) has been designed to function using a non-homogenous temperature distribution. Several phenomena are taken into account in the model such as: residual stresses generated during the spraying of coatings, morphology of the top-coat/bond-coat interface, oxidation at the top-coat/bond-coat interface, thermal mismatch of the material components, plastic deformation of the bond-coat and creep of all layers during thermal cycling. These phenomena induce local stresses in the TBCs that are responsible of micro-crack propagation during cooling and thermal cycling, specifically near the ceramic/metal interface.     

Effect of thermal misfit stress on crack deflection at planar interfaces in layered systems

Deflection of a crack at a planar bi-material interface in a layered system was investigated by considering the effects of the in-plane residual thermal misfit stress. A new parameter based on strains due to mismatch of thermal expansion coefficients was introduced to describe residual stress state independent of length scale. From a numerical analysis, it was predicted that introducing compressive residual stress in the stiffer intact layers of a composite laminate ahead of a growing primary crack would favour crack deflection by allowing advantageous energetic conditions, which indicates that stronger interfaces can be introduced in layered systems this way to improve overall mechanical properties. It was also predicted that the residual stress effect is negligible if the intact layer is more compliant than the cracked layer supporting a previous analysis and discussion reported elsewhere.