Effects Of Thermal Residual Stresses Research Articles

Micromechanical analysis of layered systems of MMCs subjected to bending––effects of thermal residual stresses

A three-dimensional finite element micromechanical model is presented to study the effects of manufacturing process thermal residual stresses on the mechanical behavior of layered systems of metal matrix composites subjected to four point bending. The presented model contains layered systems, consisting of layers of monolithic titanium alloy (IMI834) and unidirectional fiber reinforced titanium metal matrix composite (SiC/Ti). A representative volume element (RVE) was defined and appropriate boundary conditions were imposed to apply bending and temperature change simultaneously on the model. In an agreement with experimental data, the model is able to predict asymmetric behavior of the composite in tension and compression on the bottom and top surfaces of the beam. This is due to the existence of a high level of thermal residual stresses arising from cool-down from manufacturing temperature. As a result of this asymmetric behavior, the neutral axis of the beam during bending moves from the mid-surface through the compressive part of the beam.

Micromechanical modeling of interface damage of metal matrix composites subjected to transverse loading

A three-dimensional finite element micromechanical model was developed to study effects of thermal residual stress, fiber coating and interface bonding on the transverse behavior of a unidirectional SiC/Ti–6Al–4V metal matrix composite (MMC). The presented model includes three phases, i.e. the fiber, coating and matrix, and two distinct interfaces, one between the fiber and coating and the other between coating and matrix. The model can be employed to investigate effects of various bonding levels of the interfaces on the initiation of damage during transverse loading of the composite system. Two different failure criteria, which are combinations of normal and shear stresses across the interfaces, were used to predict the failure of the fiber/coating (f/c) and coating/matrix (c/m) interfaces. Any interface fails as soon as the stress level reaches the interfacial strength. It was shown that in comparison with other interface models the predicted stress–strain curve for damaged interface demonstrates good agreement with experimental results.

Effect of the critical size of initial voids on stress-induced migration

The stress-induced migration phenomenon is one of the problems related to the reliability of metal interconnections in semiconductor devices. This phenomenon causes voids and fractures in interconnections. The basic feature of this phenomenon is vacancy migration to minute initial voids. Expanding initial voids grow into larger voids and fractures. The purpose of this work is to theoretically clarify the effects of residual thermal stress and void surface stress on the behavior of the initial voids which exist immediately after a passivation process. Using a spherical metal sample with a spherical void under external stress, vacancy absorption or emission was investigated between the void surface and the sample surface. The behavior of vacancies and atoms was also investigated in interconnections under residual thermal stress. We show that the void or sample surface becomes a vacancy sink or source, depending on the mutual relationship between the surface stress due to the surface-free energy and the residual thermal stress. We also reveal that the initial voids, which exist immediately after a passivation process, grow into larger voids and fractures when the size of the initial voids exceeds the critical size. If the size of the initial void can be controlled to below the critical size, voids and fractures do not occur.

Elastic–plastic stress transfer in short fibre-reinforced metal–matrix composites

The classical shear lag model was modified to study the elastic–plastic stress transfer in short fibre-reinforced metal–matrix composites. The effect of the matrix plastic deformation on the stress transfer in the elastic range was analysed by introducing a plastic strain. The stress transfer in the overall plastic range was analysed by using the incremental form of the stress and strain relation. The expressions for the fibre stress and the interfacial shear stress in a cylindrical unit cell including the fibre end region were derived with the use of the technique of adding imaginary fibre. The modified model was then used to study the effects of thermal residual stresses on the tensile and compressive stress–strain responses of the composite. It was demonstrated that the stress transfer efficiency in the elastic range is reduced due to the matrix local plastic deformation. In the presence of thermal residual stresses, different variations of the matrix plastic strain result in asymmetric tensile and compressive stress–strain responses. The model predictions exhibited very good agreements with the experimental results in a SiCw/Al–Li composite.

Effects of thermal residual stresses on effective elastoplastic behavior of metal matrix composites

During the fabrication processes of particle-reinforced metal-matrix composites, thermal residual stresses are normally developed due to the difference of the coefficients of thermal expansion between the matrix and the reinforcement. The effect of thermal residual stresses is analytically investigated on the elastoplastic behavior of the composites. Micromechanical stress and strain fields are calculated due to the combination of applied external loads and prescribed thermal mismatch eigenstrains. Ensemble-volume averaging procedures are then employed to derive the effective yield function of the composites. It is shown that the residual stresses result in a combined kinematic hardening and isotropic hardening effect. Comparisons between the analytical predictions and experimental data are performed to illustrate the capability of the proposed model.

The effect of residual thermal stresses on the fatigue crack growth of laser-surface-annealed AISI 304 stainless steel: Part I: computer simulation

The effect of residual thermal stresses on the fatigue crack growth of the laser-surface-annealed AISI 304 stainless steel, especially the effect of stress redistribution ahead of the crack tip was extensively evaluated in the study. Based on the finite element simulation, the longitudinal residual tensile stress field has a width of roughly 20 mm on the laser-irradiated surface and was symmetric with respect to the centerline of the laser-annealed zone (LAZ). Meanwhile, residual compressive stresses distributed over a wide region away from the LAZ. After introducing a notch perpendicular to the LAZ, the distribution of longitudinal residual stresses became unsymmetrical about the centerline of LAZ. High residual compressive stresses exist within a narrow range ahead of notch tip. The improved crack growth resistance of the laser-annealed specimen might be attributed to those induced compressive stresses. As the notch tip passed through the centerline of the LAZ, the residual stress ahead of the notch tip was completely reverted into residual tensile stresses. The existence of unanimous residual tensile stresses ahead of the notch tip was maintained, even if the notch tip extended deeply into the LAZ. Additionally, the presence of the residual tensile stress ahead of the notch tip did not accelerate the fatigue crack growth rate in the compact tension specimen.

Flexural strength of a composite cylinder incorporated with thermal residual stresses

Continuous fiber reinforced composite cylinders are frequently fabricated at higher than working temperatures and are used as a primary load-carrying element in general. The purpose of this paper is to investigate the ultimate bending strength of a polymer composite cylinder and to compare the estimated results with and without thermal residual stresses incorporated. In order to figure out the progressive bending failure process generated in the cylinder, it is discretized into a number of lamina layers with different widths and is analyzed as a laminated structure. Whereas the failure of an individual lamina ply with combined flexural load and thermal residual stress effect can be understood in terms of the bridging microsmechanics model, a critical deflection condition has to be employed to determine the ultimate failure and thus the ultimate bending strength of the cylinder. An experiment has been carried out to measure the load–deflection of a polymer composite cylinder subjected to three-point bending until ultimate failure. The measured results have been used as benchmark to validate the analysis accuracy. It has been found that the present thermal residual stresses only had a marginal effect on the later part of the load–deflection curve of the composite cylinder. By ignorance of them, however, the prediction was less accurate.

Size effects in the fiber pullout test

In this paper, a numerical simulation method is used to study the effect of specimen size on interfacial behavior of the specimen in fiber pullout tests. Interfacial shear stress and normal stress are analyzed for different sizes of the test specimen. The interface between fiber and matrix is assumed to be bonded perfectly. For simplicity, all materials are assumed to be linear and elastic solids, and the effects of thermal residual stress and friction between crack faces are ignored. The effects on interfacial behavior of both length of the fiber embedded in the matrix and thickness of the matrix around the fiber are studied using the finite element approach. Furthermore, the effect of the specimen size on the interfacial crack growth is also studied by way of energy release rate. The study shows that the size of the test specimen can influence interfacial stresses and fracture characteristics dramatically.

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.

Prediction of plastic deformation of fiber-reinforced copper matrix composites

Copper alloys have been considered as a structural material for the heat sink of the actively cooled plasma facing components due to its high thermal conductivity. However, the decrease of strength at elevated temperatures and their large thermal expansion are detrimental aspects. The fiber-reinforced copper matrix composites (FRCMC) can be a potential candidate as heat sink material. In this article, the non-linear constitutive behavior of the FRCMCs reinforced with continuous SiC fibers is predicted. To this end, a simulation tool was developed using analytical micro-mechanics theory. The effects of thermal residual stress and of the matrix flow stress are estimated. The results show that these composites have a significantly increased work-hardening rate compared to the unreinforced matrix metals. The thermal residual stress has a marked influence on the initial yield surface as well as on the stress–strain curve showing asymmetry in tension and compression.

횡방향 등방성을 고려한 단섬유 인장 실험 모델링

Single fiber pull-out technique has been commonly used to characterize the mechanical behavior of interface in fiber reinforced composite materials. An improved analysis considering the effects of transversely isotropic properties of fiber and the effects of thermal residual stresses in both radial and axial directions along the fiber/matrix interface is developed for the single fiber pull-out test. Although the stress transfer properties across the interface is not much affected by considering the transversely isotropic properties of fiber, interfacial debonding is notably encouraged by the effect. The interfacial shear stress that plays an important role in interfacial debonding is very much affected by the component of axial thermal residual stress in the bonded region, which can induce a two-way debonding mechanism.

Analysis of Delamination Growth in Laminated Composites with Consideration for Residual Thermal Stress Effects

This paper presents the results of a buckling and postbuckling analysis and modeling of embedded delaminations, and the prediction of delamination growth in laminated composites with consideration for residual thermal stresses. The distribution of the local strain energy release rate along the delamination front is obtained via the virtual crack closure technique applied to three-dimensional (3D) finite element models of circular delaminations embedded in woven and nonwoven composite laminates. In each case, the delamination is embedded at a different depth along the thickness direction of the laminates. The fibre orientation of the plies bounding the delamination significantly influences the distribution of the local strain energy release rate. There is general qualitative agreement between the predicted directions of delamination growth and C-scan results of the embedded delaminations. It is found that residual thermal stresses have a significant effect on the onset of buckling of the delaminated sublaminate, but negligible influence on the distribution of the local strain energy release rate in the postbuckled regime. Furthermore, the effect of residual thermal stresses is more pronounced for delaminations that are closer to the surface. A method for the prediction of delamination areas and directions using fatigue growth criteria derived from test coupon data is also presented. It is found that growth criteria based on components of the strain energy release rate predict the rate of delamination growth much better than those based on the total strain energy release rate.

Effect of thermal residual stress on the reflection spectrum from fiber Bragg grating sensors embedded in CFRP laminates

When FBG sensors are embedded in CFRP laminates, the reflection spectrum from the FBG sensors splits into two peaks because of the non-axisymmetric thermal residual stress. This deformation of the spectrum will lead to misreading in strain measurements or crack detection in the laminates. In the present research, three types of FBG sensors: uncoated normal, polyimide-coated normal, and polyimide-coated small-diameter FBG sensors, were embedded in CFRP cross-ply laminates, and reflection spectra from the sensors were measured during the fabrication process of the laminates. Through the comparison of results obtained for the three FBG sensors, it was found that the effect of thermal residual stress on the reflection spectrum could be decreased when the optical fiber was coated with polyimide and its diameter was small in the present laminate configuration and embedment position. Furthermore, these changes of the spectra during the curing process could be simulated by theoretical calculation considering the birefringence effect.

Improved modeling of the effects of thermal residual stresses on single fiber pull-out problem

The single fiber pull-out technique has been commonly used to characterize the mechanical behavior of fiber/matrix interface in fiber reinforced composite materials. In this study, an improved analysis considering the effect of thermal residual stresses in both radial and axial directions is developed for the single fiber pull-out test. It is found to have the pronounced effects on the stress transfer properties across the interface and the interfacial debonding behavior.

Effect of Thermal Stresses on the Thermal Expansion and Damping Behavior of ZA-27/Aluminite Metal Matrix Composites

When the fabrication of a metal matrix composite (MMC) involves its cooling from a high temperature, plastic-elastic residual deformation fields can be generated within and around the particle due to the differential thermal expansion between the particle and matrix metal. The present investigation is concerned with the effect of thermal residual stresses on the thermal expansion and damping behavior of aluminite particulate-reinforced ZA-27 alloy MMCs. Composites were prepared by the compocasting technique with 1, 2, 3, and 4 wt.% of aluminite reinforcement. Thermal expansion and damping properties have been studied experimentally as a function of temperature over a temperature range 30 to 300 °C both in the heating and cooling cycle. The thermal expansion studies exhibited some residual strain, which increased with the increase in the weight percent of the reinforcement. The damping capacity of both the composites and matrix alloy is found to increase with the increase in temperature during the heating cycle, whereas in the cooling cycle, damping behavior exhibits a maximum, which becomes more pronounced with the increase in the weight percentage of the reinforcement. The appearance of the maximum may be linked with dislocation generation and motion as a result of plastic deformation of the matrix at the metal/reinforcement interface. This phenomenon is attributed to the thermal stresses generated as a result of coefficient of thermal expansion (CTE) mismatch between the composite constituent phases. The thermal stresses have been estimated in both the cases using simple models.

Optimization of the buckling load for composite structures taking thermal effects into account

This paper deals with optimization of the buckling load for laminated composite structures. A new methodology has been developed where thermal residual stresses introduced in the manufacturing process are included in the buckling analysis. The thermal effects are also included in the calculation of the buckling load sensitivities, and it is therefore possible to "tailor" the thermal residual stresses in order to increase the buckling load. Rectangular plates and circular cylindrical shells subjected to axial compression are considered. The structures are optimized twice; the first time the thermal residual stresses are ignored in the optimization, and the second time the thermal residual stresses are included in the optimization. These two sets of optimizations give two important results. Firstly, it is possible to increase the buckling load for the structures significantly when the thermal residual stresses are taken into account. Secondly, structures which have been optimized ignoring the effects of thermal residual stresses, may have a buckling load which is much less than expected when the effects of the thermal residual stresses are included.

Dynamic penetration of alumina/aluminum laminates: experiments and modeling

The effects of structural layering and thermal residual stresses on impact resistance of alumina/aluminum laminated structures were investigated. Two multilayered structures of different layer thicknesses were manufactured. Two different bonding techniques were used to bond these laminates producing four different structures. One bonding process was cured at room temperature, and the other was cured at a high temperature to induce thermal residual stresses in the alumina layers. Laminates were impact tested between 100 and 300 m/s. Dynamic impact experiments showed that the thick layer laminates allowed less penetration than the thin layer laminates. The effect of thermal residual stresses on impact performance was minor. Finite element models using ABAQUS/Explicit successfully simulated the impact, and several parametric studies were completed. The performance of the laminates was highly dependent on the yield strength of the aluminum layers. At increased velocity the thick layer laminate continued to outperform the thin layer laminate in the finite element simulations.

Influence of residual stress on the elastic-plastic deformation of composites with two- or three-dimensional randomly oriented inclusions

Based on the secant moduli framework with second-order moment of stress and the elastic micro-mechanical method proposed by Ponte Castaneda and Willis [8], a micro-mechanical method is proposed to consider the effects of thermal residual stress on the elastic-plastic deformation of composites. The micro-structural parameters like the volume fraction, shape, orientation, and distribution of inclusions are taken into account, and their influences on the macroscopic properties of the composites in the presence of thermal residual stress are analyzed. The computed results show that the presence of thermal residual stress induces asymmetric behavior in tension and compression. This depends intimately on the micro-structural parameters of the composite. Finite element calculations are also performed to predict the secant thermal dilatation coefficient and stress-strain relations in tension and compression for unidirectional composites. The proposed analytical method is found to compare favorably with the finite element results.

Fracture mechanics analysis of coating/substrate systems: Part I: Analysis of tensile and bending experiments

A finite fracture mechanics model is used to predict the development of multiple cracks in the coating layer of coating/substrate systems. The stresses in a cracked coating are evaluated by a variational mechanics approach. These stresses are then used to calculate the total energy released due to the formation of a complete crack in the coating layer. The analysis can handle tensile loads or bending loads and includes the effect of residual thermal stresses. By assuming the next coating crack forms when the energy released due to the formation of a complete microcrack equals the in situ fracture toughness of coating, it is proposed that one can predict the number of coating cracks as a function of applied strain. Alternatively, it is proposed that experimental data for number of cracks vs. strain can be fit to the fracture analysis and be used to determine an in situ coating fracture toughness.

Effect of thermal residual stress on the high temperature toughening behaviour of TiB 2/SiC w composites

SiC-whisker-reinforced TiB 2 composite was produced by hot pressing techniques. The composite exhibited superior mechanical properties at room temperature compared to those of monolithic TiB 2, especially in respect of the fracture toughness, K IC, which was approximately 115% higher than that of TiB 2 ceramic without SiC whiskers, the maximum values of the fracture toughness and flexural strength being 7.3 MPa m and 640 MPa, respectively. Considerable improvement in the high-temperature fracture toughness of the composite was observed up to 1200°C. Based on the thermal residual stress analysis and fracture surface observations, the fracture toughness at high temperature was correlated with the change in inequality between the whisker fracture strength and the compressive clamping forces on the whiskers caused by thermal expansion mismatch between the whiskers and the matrix. The results showed that the number of whiskers pulled out depends greatly on the test temperature, the whisker aspect ratio and the interfacial friction coefficient. At high temperature the whiskers are mainly pulled out, whilst at low temperature the whiskers are mainly fractured.