Measurement of thermal expansion coefficients of composites using strain gages

The measurement of the coefficients of thermal expansion (CTEs) of composite materials using electrical resistance strain gages is addressed. Analytical expressions for the CTEs of an orthotropic lamina are derived, accounting for the effects of transverse sensitivity and possible misalignment of the gages. Experiments are performed for the characterization of the thermal expansion behavior of a fiber-glass-reinforced epoxy unidirectional lamina using an invar specimen as reference material. Preliminary training cycles are performed for the determination of an optimal heating rate for the measurements, which ensures thermal equilibrium conditions. Three measurement cycles yield the principal CTEs of the lamina α₁, α₂ and α₁₂ with repeatability within ±0.34×10⁻⁶, ±0.85×10⁻⁶ and ±2.8×10⁻⁶/°C, respectively. It is noted that inhomogeneity of the specimen and variation in thermomechanical properties of the gages can cause a noticeable spead in the measurements.     

Le jet libre immergé d'un fluide viscoélastique

Résumé Les auteurs étudient le jet libre laminaire bidimensionnel d'un fluide viscoélastique obéissant à une loi de comportement semiempirique. Ils appliquent la méthode de raccordement des développements asymptotiques afin de déterminer le profil de vitesses à l'intérieur du jet, et l'entraînement du fluide extérieur. Les résultats obtenus illustrent l'influence de l'élasticité sur le champ de vitesse et la présence d'un gradient de pression à l'intérieur du jet. Les lignes de courant obtenues montrent que le fluide externe est aspiré vers l'axe du jet.

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Summary A two-dimensional laminar free jet of a viscoelastic fluid following a semiempiric constitutive equation is studied. The method of matching asymptotic expansions is applied to determine the velocity profiles inside the jet and the entrainment of the external fluid. The results thus obtained highlight the influence of elasticity on the velocity field and the presence of a pressure gradient inside the jet. The streamlines obtained show that the external fluid is sucked in towards the axis of the jet.

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Zusammenfassung Es wird der laminare zweidimensionale Freistrahl einer viskoelastischen Flüssigkeit, die einem halbempirischen Stoffgesetz folgt, untersucht. Asymptotische Entwicklungen werden aneinandergefügt, um die Geschwindigkeitsverteilung in der Strahlströmung und die Ansaugkraft der äußeren Flüssigkeit zu bestimmen. Die erzielten Ergebnisse zeigen den Einfluß der Elastizität auf die Geschwindigkeitsverteilung und das Bestehen eines Druckgradienten innerhalb der Strahlströmung. Die abgeleiteten Stromlinien zeigen weiter, daß die äußere Flüssigkeit zur Strahlachse hin angesaugt wird.

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A ₁;A ₂;A ₃ tenseurs de Rivlin-Ericksen - A constante définie par [27] - D domaine d'écoulement - f ₁();f ₀() fonctions définies par la transformation [20] - I tenseur unité - J nombre adimensionnel [12] - L longueur de référence - M flux total d'impulsion [19]m: µ/ - N _Re nombre de Reynolds - N _w nombre de Weissenberg - n indice de comportement - p pression - s indice de comportement «élastique» - T tenseur des contraintes - U ₀ vitesse de référence - u, v composantes du vecteur vitesse - x, y coordonnées cartésiennes - Y coordonnée de «couche limite» [9] - Z variable complexe - angle entre les parois de la fente - paramètre de perturbation - variable affine [20] - () fonction définie par [2c] - coefficient d'élasticité - fonction de viscosité [2a] - µ indice de consistance - masse volumique - ; fonctions de courant - fonction définie par [2b] - 2ème invariant principal du tenseurA ₁ Avec 7 figures     

The stick-slip problem for a round jet

Summary The stick-slip problem for a round jet studied in Part I gives a good approximation for the swell of a low speed jet when the surface tension is large but it fails when the surface tension is small. In this paper a new stick-slip problem (II) is defined and solved using matched eigenfunction expansions. The new problem reduces to that solved in Part I when the surface tension is large and gives good results in the case of zero and small surface tension.With 18 figures     

实现金属环动态拉伸的电磁加载技术研究

描述了实现金属环动态拉伸的电磁膨胀环实验方法,改进了快速放电和短路开关两个实现自由膨胀的关键问题,为研究材料本构关系、动态断裂和破碎提供了一条简单而实用的加载途径。主回路电流由Rogowski线圈测量获得,金属环的膨胀速度由狭缝扫描相机测量得到,并由电动力学方程可计算出金属环中的流动应力、应变、应变率以及温升等动态力学参数。     

剪切模量是幂函数的成层土的地震随机反应

基于改进的一维剪切梁模型，对剪切模量是其深度的某一幂函数的成层非均质土层，得到其稳态动力响应的封闭型解析表达式。首次证明了这种土层振型函数的正交性，然后利用随机振动理论，并基于基岩输入地震加速度的功率谱密度函数：白噪声谱和过滤白噪声谱。研究了该土层对地震的随机动力响应问题。计算结果表明，1)在基岩输入地震加速度的功率谱为白噪声谱的情况下，土层的最大期望反应均有别于过滤白噪声谱时的相应值；2)平稳输入与输出过高地估计了土层的随机响应。     

Weight functions for interface cracks in dissimilar anisotropic materials

Bueckner‘s work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials. The difficulties in separating Stroh‘s six complex arguments involved in the integral for the dissimilar materials are overcome and then the explicit function representations of the integral are given and studied in detail. It is found that the pseudo-orthogonal properties of the eigenfunction expansion form (EEF) for a crack presented previously in isotropic elastic cases, in isotopic bimaterial cases, and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases. The relation between Bueckner‘s work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stressdisplacement state. Finally, some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.     

POST-BUCKLING AND IMPERFECTION SENSITIVITY OF A COLUMN WITH AN EQUILATERAL TRIANGULAR CROSS-SECTION IN THE PLASTIC RANGE

The asymmetric initial post-buckling corresponding to the lowest bifurcation load andthe imperfection sensitivity are analysed in detail for a compressed simply supported column with anequilateral triangular cross-section in the plastic range.The effect of elastic unloading is taken into ac-count in the analysis.The asymptotic relations,including high order terms,among the load,the am-plitude of imperfection and the amplitude of the bifurcation mode are realized.The results show thatthe maximum supported load is very sensitive to imperfection.     

Non-linear normal modes,invariance, and modal dynamics approximations of non-linear systems

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates

A modified shear-lag analysis, taking into account the concept of stress perturbation function, is developed and applied to evaluate the effect of transverse cracks on the effective thermal expansion coefficient of aged angle-ply composites laminates. Effects of number of 90° layers and number of θ° layers in the outer angle-ply laminates on the reduction of the effective axial coefficient of thermal expansion have also been studied. The results of this paper represent well the dependence of the reduction of the effective axial coefficient of thermal expansion on the hygrothermal conditions, the fibre orientation angle of the outer layers, the number of cracked cross-ply layers and the number of un-cracked outer θ° layers in laminate.