F. Mujika

Strain rate and temperature effects on the mechanical behaviour of epoxy mixtures with different crosslink densities

Abstract The microstructure and the flexural behaviour of two highly crosslinked mixtures have been investigated. Besides the usual α and β relaxations appearing for any epoxy mixture, an additional ω relaxation, located slightly above room temperature, was evident for the mixture with higher crosslink density. This relaxation, which seems to be related to microstructural variations originating in a free volume increase, permits us to explain the lower mechanical properties of the larger higher crosslinked mixtures in the temperature range between the β and α relaxations. Whilst at room temperature the flexural modulus did not show any significant variation upon testing rate and the strength slightly increased for both epoxy mixtures.

On the Displacement Field for Unidirectional Off-Axis Composites in 3-Point Flexure — Part 1: Analytical Approach:

The displacement field of a unidirectional off-axis specimen in 3-point flexure test is obtained in a new way, by applying the Second Castiglianos theorem and the unitarial load method. The displacement field is calculated for two cases: in the first one, lift-off between specimen and fixture support occurs caused by bending-twisting coupling, and specimen is supposed to contact with the test fixture support at two diagonally opposite points. In the second case, lift-off does not occur and specimen is supposed to contact with the fixture support at four corners. The limit between two cases is established by the calculation of the critical value of the span-to-width ratio for lift-off to occur. The displacement field calculated includes shear effects and satisfies displacements compatibility and equilibrium conditions, except in the vicinity of point reactions and applied load. Neither displacement field solutions for composite plates with point boundary conditions, nor solutions based on the Second Castiglianos theorem concerning composite plates have been encountered in the literature survey.

Off-axis Flexure Test: A New Method for Obtaining In-plane Shear Properties

Off-axis three-point flexure test for unidirectional composites is proposed as a new method for obtaining in-plane shear modulus and in-plane shear strength. The method of determination of the in-plane shear modulus GLT has been explained in a previous work where the displacement field of an off-axis flexure test was analyzed. In the present work, besides summarizing the calculation equations of GLT, the condition of small displacements is analyzed. Otherwise, an error analysis is carried out in order to study the influence of the calculated value of GLT on the other elastic parameters. Normal and shear stresses in the fiber–matrix interface change from point to point in the specimen depending on the fiber orientation angle and specimen geometry. A critical point of failure that depends on the fiber orientation angle is determined and optimum conditions for obtaining in-plane shear strength are discussed. Experiments for different fiber orientations and geometric conditions have been carried out for IM7/8552 epoxy matrix based carbon fiber reinforced unidirectional composite material.

A novel approach for the three-point flexure test of multidirectional laminates

The complementary energy of a multidirectional laminate is obtained as a function of mechanical and hygrothermal force and moment resultants. Three-point flexure is then analysed assuming that the specimen is in contact with the support rollers at four points. As this problem is statically indeterminate, the redundant force is obtained by applying Engessers second theorem. Lift-off at supports is assumed to occur when the redundant unknown is zero. The displacement field of a multidirectional laminate in three-point flexure is then obtained by applying Engessers first theorem, including transverse shear and hygrothermal effects. The displacements related to bending and twisting moments, hygrothermal effects and transverse shear forces are analysed separately.

On the displacement field for unidirectional off-axis composites in 3-point flexure - Part II: Numerical and experimental results

The displacement field calculated in Part I of this work is numerically analysed for specimens of IM7-8552 epoxy matrix based carbon fiber reinforced unidirectional composite material. Three-point tests have been performed in 5 specimens with different fiber orientation, using 10 spans for each specimen. Theoretical displacement fields obtained in Part 1 have been used for showing level curves on supports and load cylinder lines, in order to analyse the suitability of assumptions concerning boundary conditions and load application. Middle point load-displacement curve slopes obtained from displacement field equations and from Classical Laminated Beams Theory are compared with experimentally obtained results. On the other hand, in-plane shear modulus has been calculated in different ways, knowing the other elastic constants of the material and the experimental load-displacement curve slope. The agreement between numerical and experimental results is rather good in all cases.

45° flexure test for measurement of in-plane shear modulus

A new method to obtain the in-plane shear modulus GLT for unidirectional oriented composite materials is proposed. The method is based on an original analytic way for calculating middle point displacement in a 3-point flexure test. The bending–twisting coupling effects in such a test induce the lift-off of the specimen at the fixture supports for some geometrical conditions. Thereby, contact points are located at two opposite points of the specimen. Consequently, new bending moments along the width of the specimen and twisting moments appear. By supposing resultant moments and shear forces per unit length are uniformly distributed, these distributions are calculated for static conditions along longitudinal and transverse cross sections of the specimen. After having expressed strain energy as a function of resultant moments and resultant shear forces per unit length, Second Castigliano’s theorem is applied in order to calculate the middle point displacement. No similar analytic way has been encountered in classical laminated beams theory or in classical laminated plates theory. The displacement obtained in this work and the one obtained from classical laminated beams theory are particularised to the case of 45 fibre orientation. GLT expressions have been derived from those displacement expressions in three ways: two of them from the solution of this work, not considering and considering shear effects, respectively, and the third one from displacement obtained from classical laminated beams theory. Experiments have been made for different geometric conditions in order to test the influence of geometric parameters in experimental results. For span-to-width ratios up to two, the values obtained are quite constant and agree well with the in-plane shear modulus value obtained by the material manufacturer using 45 tensile test.

Determination of In-plane Shear Strength of Unidirectional Composite Materials Using the Off-axis Three-point Flexure and Off-axis Tensile Tests

The aim of this work is to compare from an experimental point of view the determination of in-plane shear strength of unidirectional composite materials by means of two off-axis tests: three-point flexure and tensile. In the case of the off-axis three-point flexure test, the condition of small displacements and the condition of lift-off between the specimen and the fixture supports have been taken into account. Some considerations regarding stress and displacement fields are presented. The in-plane shear characterization has been performed on a carbon fiber reinforced unidirectional laminate with several fiber orientation angles: 10°, 20°, 30°, and 45°. Test conditions for both off-axis experimental methods, in order to ensure their applicability, are presented. Off-axis flexure test is considered more suitable than off-axis tensile test for the determination of in-plane shear strength.

New Considerations on the Stress Field in an Off-axis Tensile Test

Two new analytical approaches are proposed for the off-axis tension test problem. Both of them are based on the Second Castigliano’s theorem. In the first one, a simple stress field that satisfies equilibrium conditions is used. In the second approach, integration constants of the stress field obtained by Pagano and Halpin are calculated directly, without the use of the displacement field. The first approach shows the points of maximum normal and shear stresses in a qualitative manner. The second approach, besides the fulfilment of equilibrium and compatibility conditions, minimizes the strain energy. Furthermore, both approaches give the same solution for bending moments and shear forces at specimen ends caused by coupling effects. After analyzing the stresses at critical points in the principal material directions, it is shown that the value of in-plane shear strength is usually underestimated. The effect of end constraints on the obtention of in-plane shear modulus is also analyzed.

Hygrothermal effects in composites: Influence of geometry and determination of transverse coefficient of thermal expansion

This work evaluates the influence of geometric properties, the length-to-width ratio, named Aspect Ratio, on curvatures in [θ − 90/θ]T carbon/epoxy composite laminates at room temperature due to thermal residual stresses. A new method to determine experimentally thermal residual curvatures in composites laminates by defining small-length increments on the surface of deformed plate has been exposed. [–454/454]T was considered to obtain a simple analytical expression of twisting curvature. A new way to determine transverse coefficient of thermal expansion α2 is proposed in squared laminates based on experimental values of twisting curvatures of [–454/454]T laminates.

Analysis of Thermal Stresses in Unsymmetric Cross-ply Composite Strips

An approach based on the hypotheses of the classical beam theory for determining thermal stresses in unsymmetric cross-ply strips has been developed. The material behavior is considered linear elastic, and viscoelastic effects are not considered. By supposing linear strain distribution in the cross-sections, the position of the neutral axis, the radius of curvature and the distribution of thermal stresses have been determined. The analysis is valid in the case of large displacements, since the curvature is constant and the deformed shape is an arc of circumference. Five different lay-up configurations of strip geometry specimens have been used for experimental verification. Mid-point deflections have been measured and compared with theoretical values, applying both the proposed approach and the classical laminated plates theory.