Computation of transient hygroscopic stresses in unidirectional laminated composite plates with cyclic and asymmetrical environmental conditions

External variations in temperature and moisture are of primary importance for the long term behaviour of structures made of polymer matrix composites, because they induce residual stresses within laminated composite plates. It was shown (Hahn et al., 1978; Benkeddad et al., 1995, 1996; Tounsi et al., 2000, 2002, 2004; Adda-Bedia et al., 2001; Tounsi and Adda-Bedia, 2003a, b) that the heterogeneity and the anisotropy of such plates, have an influence on the distribution of transient hygroscopic stresses through the thickness of composite plates. The aim of the present paper is to present a simplified approach for the calculation of transient hygroscopic stresses within unidirectional laminates in the case where these latter are exposed to the cyclic and unsymmetric environmental conditions. Several examples are presented to assess such stresses and to demonstrate the efficiency of the used method. These stresses have to be taken into consideration for the design of composite structures submitted to a moist environment.     

Some observations on the evolution of transversal hygroscopic stresses in laminated composites plates: effect of anisotropy

The transient and non-uniform moisture concentration distributions in laminated composite plates give rise to transient and non-uniform stress fields [Composite Structures 30 (1995) 201; Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, 969; Composite Structures 55 (4) (2002) 393]. It was shown [Composite Structures 30 (1995) 201; Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, 969; Composite Structures 55 (4) (2002) 393] that the heterogeneity and the anisotropy of such plate, have an influence on the distribution of transient hygroscopic stresses through the thickness of composite plates. The purpose of this paper is to investigate the effect of anisotropy on the transverse residual stresses and strains in polymer composite systems under long term exposure to hygrothermal environments. The anisotropy is evaluated using the degree of anisotropy introduced from polar representation method of tensors [Communication au 12 journées nationales sur les composites, JNC12 (in French), 2000, p. 969; Composite Structures 55 (4) (2002) 393; Mechanical Behaviour, Design and Application, 1990, p. 29; Computer Aided Design in Composite Material Technology, 1988, p. 243; Proceeding of the seventh International Conference on Composite Materials, 1989, p. 358; Proceedings of the Fifth French Conference on Composite Materials, 1986, p. 267; Eighth International Conference on Composite Materials (ICCM-8), Honolulu (USA), 1991, p. 1; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; 12th International Conference on Composite Materials (ICCM-12), Paris, 1999; Découplage et quasi-homogénéité pour les stratifiés renforcés par tissus équilibrés”, JNC12, (in French), 2000, p. 265]. The principal objective of this study is to contribute to the understanding and predicting the behaviour of transversal hygroscopic stresses and strains in the studied composites as a function of the degree of anisotropy. The analysis has indicated that: (i) the reduction of degree of anisotropy favours the transversals hygroscopic stresses to be in tensile state, contrary to the thermal stresses where they become in compressive state; (ii) the values of the transverse residual stresses in laminates having the same degree of anisotropy are nearly identical; (iii) from certain value of in-plane degree of anisotropy which is about 38.5% for the used material in this study, the sensibility to the anisotropy is more felt. For inferior values, the transversal residual stresses are nearly identical to those of quasi-isotropic laminates.     

Reduction of hygrothermal transverse stresses in unidirectional hybrid composites under cyclic environmental conditions

When fiber-reinforced polymer plates are exposed to cyclic environmental conditions, polymer matrix absorbs or desorbs continuously the moisture due to the variation in service temperature and relative humidity. Both temperature and moisture concentration produce an important hygrothermal transverse stresses, which are maximum on both edges of the composite plates. These transverse stresses which are more important at first times of moisture diffusion, can produce a probable damage of composite plates. To extend the durability of our composite plate, interplay hybrid composites are adopted to reduce the transverse stresses on edges. Therefore, a variation of the relationship between thicknesses of unidirectional hybrid composites constituents AS/3501-5 and T300/5208 is carried out in order to find minimal transverse stresses. This thicknesses variation enables us to find the best configuration which gives favourable service conditions of our hybrid composite, i.e., to predict firstly a considerable reduction of hygrothermal transverse stresses at both edges of our hybrid plate, secondly to reduce or to attenuate the edge effect developed in 6 days and 6 weeks periods.     

Interaction between cyclic loading and residual stresses in titanium matrix composites

Metal matrix composites are gaining popularity for applications where high performance materials are needed. Titanium matrix composites (TMCs) continuously reinforced by silicon carbide fibres are under development for applications in aeroengines. Their use in blades, rings and shafts promises a significant weight reduction and performance improvement due to their high specific strength and stiffness. To obtain the whole capabilities of the material not only advanced processing techniques but also post-processing treatments are necessary. A detailed analysis of the residual stress development during cyclic loading leads to the necessity of residual stress modifications to optimise the fatigue behaviour of TMCs. Since the aerospace industry requires high reliability of the materials used, models for predicting failure and life time are of special interest. Predictive models based on the properties of the single constituents of the composite are most suitable to reduce the number of experiments and to develop methodologies to improve specific mechanical properties. Nevertheless, both experiments on the single constituents as well as on the composite are necessary to validate the model. A previously developed rheological model is used to assess different post-processing procedures to improve the fatigue behaviour of a titanium matrix composite. The usage of the model and experiments on the system SCS-6/Ti-6Al-2Sn-4Zr-2Mo are presented.     

Influence of the matrix constituent on mode I and mode II delamination toughness in fiber-reinforced polymer composites under cyclic fatigue

Mode I and mode II fracture behaviour under static and dynamic loading was analyzed in two composites made up of the same reinforcement though embedded in two different matrices. Specifically, the delamination energy under static and dynamic loading was obtained for both materials and both fracture modes, i.e. the number of cycles necessary for the onset of fatigue delamination. Subsequently, the crack growth rate (delamination rate) was obtained for different percentages of the critical energy rate. The main goal of the study was to ascertain the influence of the matrix on the behaviour of the laminate under fatigue loading.From the experimental results for the onset of delamination, similar fatigue behaviour was observed at a low number of cycles for both matrices and both fracture modes, while in fatigue at a high number of cycles, a higher fatigue limit was obtained in the composite with the modified resin (higher toughness) for both fracture modes. From the point of view of crack growth rate, both materials behaved similarly for different levels of stress under fatigue and the two fracture modes for small crack lengths (initial growth zone < 5 mm), although the growth rate increased for large crack lengths. This behaviour was the same in both loading modes.     

Influence of residual stresses and interfacial shear strength on matrix properties in fibre-reinforced ceramic matrix composites

Zircon matrix composites, uniaxially reinforced with a variety of SiC fibres were fabricated in order to create composites with different interfacial properties. Interfacial properties were varied by changing the nature of fibre coatings. The effect of changes in interfacial shear strength on important matrix properties, such as hardness and fracture toughness, was studied on a micro-scale using the microindentation technique. In addition, the relative orientation of the indented cracks with respect to the fibres was varied to investigate the existence of anisotropic behaviour of the matrix. The results indicated that the crack growth in the matrix was influenced by the presence of residual radial and axial stresses, such that relatively higher crack lengths were seen in certain directions in the matrix with respect to other directions. This asymmetric nature of the crack formation upon indentation was the reason for the observed anisotropic fracture toughness of the matrix. The residual stresses also led to anisotropic hardness and a critical load for crack initiation in the matrix.     

Intrinsic, thermal and hygroscopic residual stresses in thin gas-barrier films on polymer substrates

Intrinsic, thermal, and hygroscopic contributions to the in-plane residual stress in silicon nitride films on polyimide substrates are identified, based on iso-hygric thermal ramps and isothermal relative humidity jumps, combined with non-linear elastic modeling of the resulting dynamics of film curvature. This approach enables the thermal and hygroscopic properties of thin nitride films to be determined and provides useful input for material and process control.     

Thermo-viscoplastic residual stresses in metal matrix composites

A three-dimensional thermo-viscoplastic ideal method is presented to determine the interfacial and cellular stresses which arise during and from manufacturing of an ideal periodic continuous unidirectional graphite/aluminum metal matrix composite (MMC) lamina. The particular manufacturing process examined is a liquid-infiltrated cast MMC with temperature excursions from the matrix melting temperature of 933 K to room temperature. The final stress state of the aluminum matrix is found to be in the vicinity of its room temperature yield strength and essentially independent of fiber volume fraction. The interface has compressive normal tractions with an insignificant shear traction component present for fiber volume fractions less than 0·70, while for higher volume fractions, approximately one-half the interface experiences tensile normal tractions. Increased fiber volume fraction lowers fiber axial stresses and decreases the uniformity of the interfacial tractions. The magnitude of the residual stress state can be reduced from the value obtained from a constant cooling rate history by using an alternative cooling profile which has a rapid initial cooling rate of 0·75 K/s until 400 K, and a subsequent slower cooling rate of 0·2 K/min.     

The beneficial influence of matrix anisotropy in fiber composites

Summary It has been recently shown [1] that the stress concentrations in anisotropic materials with distinct complex or imaginary roots of the respective characteristic function are much higher than in materials with equal roots. It was further shown [2] that anisotropic materials with equal roots behave like quasi-isotropic materials. Modern carbon-carbon and metal-ceramic composites are intuitively using these facts to create much stronger materials by reinforcing the matrix properties.A theory is presented in this paper where the coupling of strongly anisotropic fibers along their axis with strongly anisotropic matrices along either the fiber direction or the transverse plane to the direction of the fibers, either deteriorates, or improves perceptibly the mechanical behavior of the composites. It was shown that anisotropy of the matrix, increasing its mechanical properties on the transverse isotropic plane of the composite, increased the transverse Poisson's ratio, whereas decreased the longitudinal shear modulusG _LC . This resulted in values of the eigenangle _c receding from the corresponding value _ic for the respective isotropic, case. This resulted in a deterioration of the mechanical performance of the composite since the material now has the tendency to develop higher stress concentrations for equivalent loadings.On the contrary, a strong anisotropic matrix along the direction of the fibers yielded the inverse results for the various moduli of the anisotropic composite. The most important result is the increase of the longitudinal shear modulusG _L , so that the ratioE _L /2G _L is consistently decreasing, thus yielding values of the eigenangle _c tending to approach the critical value _c for the isotropic material. This decrease of _c indicates the improvement of the quality of the composite, which develops relatively lower stress concentration factors approaching their respective isotropic values.This fact makes the anisotropic composite material to approach an equivalent state of quasi-isotropy and thus to improve the strength of the material by reducing considerably the eventual, anisotropic stress concentration factors of the respective structural elements.Examples with T300/N5208 Graphite-Epoxy composites and Borsic-1100 Aluminum metal-metal composites indicate clearly the beneficial effect of the anisotropy of their matrices.     

Influence of residual thermal stresses on fatigue crack growth life of discontinuous reinforcements in metal matrix composites

The fatigue life prediction model based on crack propagation from micro-structural features is derived and presented for planar and randomly oriented Discontinuous Reinforced Metal Matrix Composites (DRMMCs). The model contains the influence of micro-structural properties such as aspect ratio, volume fraction of particle/fibre and constraint between particle and the matrix. The effect of residual thermal stresses generated within the matrix during development of composite is considered. The particle/fibre plays a dominant role in the development of the cyclic plastic zone size ahead of the crack tip; moreover, it enhances the cyclic plastic deformation characteristics of DRMMC. The theoretical model-based evaluations for low cycle fatigue in DRMMCs are within the proximity of the experimental results.     

聚合物基导电复合材料研究进展

本文介绍了聚合物基导电复合材料的种类、用途及导电机理。并对碳系填料填充聚合物基导电复合材料及金属系填料填充聚合物基导电复合材料的研究进展进行了综述 ,最后展望了聚合物基导电复合材料的发展趋势。     

The role of carbon nanofibers on thermo-mechanical properties of polymer matrix composites and their effect on reduction of residual stresses

In this research, the effects of carbon nanofibers (CNFs) on thermo-elastic properties of carbon fiber (CF)/epoxy composite for the reduction of thermal residual stresses (TRS) using micromechanical relations were studied. In the first step, micromechanical models to calculate the coefficient of thermal expansion (CTE) and Young's modulus of CNF/epoxy and CNF/CF/epoxy nanocomposites were developed and compared with experimental results of the other researchers. The obtained results of the CTE and Young's modulus of modified Schapery and Halpin-Tsai theories have good agreement with the experimental results. In the second step, the classical lamination theory (CLT) was employed to determine the TRS for CNF/CF/epoxy laminated nanocomposites. Also, the theoretical results of the CLT were compared with experimental results. Finally, reduction of the TRS using the CLT for different lay-ups such as cross ply, angle ply, and quasi-isotropic laminates were obtained. The results demonstrated that the addition of 1% weight fraction of CNF can reduce the TRS that the most reduction occurred in the unsymmetric cross-ply laminate by up to 27%.     

Control of strength anisotropy of metal matrix fiber composites

Summary This paper examines theoretically the stress distribution around fiber breaks in a unidirectional reinforced metal matrix composite, subjected to axial loading when plastic yielding of the matrix is allowed to occur. The composites considered have a ductile interphase, bonding the matrix to the fiber. The likelihood of failure of a fiber adjacent to the existing broken fiber is considered. Detailed and systematic results are given for composites with a wide range of fiber volume fractions, Young's modulus of the fibers and the matrix, interphase properties and Weibull modulus for the strength of the fibers. The objective is the optimization of these material and geometric variables to ensure global load sharing among the fibers in the longitudinal direction, which will give the composite good longitudinal strength. Calculations are carried out for transverse loading of the composite to determine the effect of the ductile interphase on the yield strength. Characteristics of the ductile interphase are determined that will provide good longitudinal strength through global load sharing and a relatively high yield strength in the direction transverse to the fibers. This, in turn, will allow control of the strength anisotropy of uniaxially reinforced metal matrix composites.     

聚合物基导热复合材料研究进展

概述了聚合物基导热复合材料的应用开发背景,从理论上阐述了聚合物基导热复合材料的导热机理及导热理论模型.综述了国内外聚合物基导热复合材料研究开发状况,提出了今后的研究方向.     

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.     

Fabrication of polymer matrix composites reinforced with controllably oriented whiskers

Polyvinyl chloride (PVC) reinforced with controllably oriented potassium titanate whisker (PTW) has been prepared. The preparation includes wet-spinning a polymer solution that contains the whiskers, placing the resultant precursor fiber in a die and hot-pressing to form composite. The whiskers are highly aligned along the axis of the fiber as the result of extrusion and drawing in spinning. Therefore, the whisker orientation in the composite can be closely controlled through controlling the directions of the precursor. The degree of whisker alignment is found to depend strongly on drawing ratio, and a simplified mathematical relation is presented. The mechanical properties of the PTW reinforced PVC are reported. The applications of the composite processing technique described above in functional composites are also discussed.     

Investigation of mechanical stresses in strained solids on models of conducting polymer composites

A method for measuring mechanical stresses in the bulk of machine parts, which simplifies the known methods and does not require significant destruction of the test sample, is proposed. Pis’ma Zh. Tekh. Fiz. 25, 76–82 (June 26, 1999)     

Electro-thermo-mechanical coupling in carbon fiber polymer matrix composites

Field coupling in electric-current-carrying composites is studied. Governing equations describing electromagnetic, thermal, and mechanical field interactions in anisotropic materials and a corresponding two-dimensional approximation for transversely isotropic plates are discussed. A problem of electric current?Cinduced heating and the associated thermal stresses in the electrified carbon fiber polymer matrix composite plate is considered. A closed-form solution for the temperature distribution is obtained. It is shown that application of the electric current leads to a significant temperature gradient across the plate. This, in turn, results in a considerable rise of the in-plane compressive stresses in the direction transverse to the direction of the applied current.