Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90 _n /0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.     

Damage in composite laminates: Effects of transverse cracks

Two different methods of solution are used to study the effects of transverse cracks in cross-ply composite laminates. The results of an approximate analytical solution are compared with those obtained using a finite element analysis in order to study the effects of transverse cracks on the degradation of elastic and thermal coefficients as well as stress distributions. In particular, it is shown that transverse cracks cause significant degradation of the Poisson's ratio and shear modulus of the laminates, and also affect some stress distributions in a peculiar manner. Theoretical results are compared with existing experimental results where appropriate.     

复合材料横向剪切弹性模量的识别与层间剪切强度的实验研究

本文提出一种测试复合材料横向剪切弹性模量的参数识别方法。该方法是将复合材料的横向剪切弹性模量视作横向剪应变的函数，由横向剪应变的测量值反演横向剪切弹性模量。剪应变与剪切弹性模量间的函数关系用有限单元法得到。文中给出了参数识别计算格式和一种玻璃布层压板的识别结果。同时，文中提出了用五点弯曲实验测试层间剪切强度的方法，给出了实验结果。     

On the transverse shear modulus of negative Poisson's ratio honeycomb structures

The transverse shear modulus of in-plane negative Poisson's ratio honeycombs is determined using numerical simulations. General honeycombs have theoretical upper and lower bounds of transverse shear moduli. The actual transverse shear modulus is an intermediate value, depending on the relative density and the gauge thickness ratio. The difference between upper and lower bounds is particularly significant for negative Poisson's ratio honeycombs. Finite element simulations confirm the theoretical trend, and show gauge ratio dependence different from that envisaged in the literature for conventional honeycombs. A modified approximate formula is thus proposed to predict the actual transverse shear modulus for honeycombs having in-plane negative Poisson's ratio values.     

Transverse shear modulus and strength of honeycomb cores

The transverse shear mechanical behavior and failure mechanism of aluminum alloy honeycomb cores are investigated by the single block shear test in this paper. The transverse shear deformation process of honeycomb cores may be approximately categorized into four stages, namely elastic deformation, plastic deformation, fracture of cell walls and debonding of honeycomb cores/facesheets. The elastic deformation of unit cell under transverse shear displacement is also investigated by the finite element method, and the result shows that the bending deformation of the cell walls is similar to that of the cantilever beam. In order to precisely predict the equivalent transverse shear modulus and strength, not only shear deformation but also bending deformation of cell walls should be considered. Therefore, in the present paper, the equivalent transverse shear modulus and strength are predicted by application of the cantilever beam theory and thin plate shear buckling theory in conjunction with simplifying assumption as to the displacement in the cores. It is concluded that the contribution of bending deformation of cell walls to equivalent transverse shear modulus and strength is obvious with the decreasing height of cell walls.     

Long-term thermal stability of carbon fibre-reinforced addition-type polyimide composite in terms of compressive strength

A previously developed carbon fibre-reinforced addition-type polyimide composite material was exposed to temperatures of 240, 270 and 300 °C in air for 3000 h to study its long-term stability in terms of its compressive strength. The in-plane shear modulus, compressive failure mode and transverse crack density were also evaluated to determine whether a degradation process induces a decrease in the compressive strength of a high-temperature polymer matrix composite having a laminated configuration of [90/0]_4s. The carbon fibre-reinforced polyimide composite exhibited excellent thermal stability in terms of its compressive strength after being subjected to ageing at 240 °C for 3000 h and at 270 °C for 2000 h, with degradation becoming significant at 300 °C. The compressive strength decreased only when the surface degradation caused the 90° plies sandwiching the 0° plies to degrade severely.     

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Micro-Mechanical Behavior of a Unidirectional Composite Subjected to Transverse Shear Loading

The effects of interphase between fibers and matrix on the micro-and macro-mechanical behaviors of fiber-reinforced composite lamina subjected to transverse shear load at remote distance have been studied. The interphase has been modeled by the compliant spring-layers that are linearly related to the normal and tangential tractions. Numerical analyses on composite basic cells have been carried out using the boundary element method. For undamaged composites the micro-level stresses at the matrix side of the interphase and effective shear modulus have been calculated as a function of the fiber volume fraction and the interphase stiffness. Results are presented for various interphase stiffnesses from perfect bonding to total debonding. For a square array composite results show that for a high interphase stiffness k > 10, an increase in a fiber volume fraction results in a higher effective transverse shear modulus. For a relatively low interphase stiffness k < 1, it is shown that an increase in the fiber volume fraction causes a decrease in the effective transverse shear modulus. For perfect bonding, the effective shear modulus for a hexagonal array composite is slightly larger than that for a square array composite. Also for the damaged composite with partially debonded interphase, local stress fields and effective shear moduli are calculated and a decrease in the effective shear modulus has been observed.     

Young's modulus and shear modulus of a composite shaft from resonance measurements

A simple method which uses axial and torsional vibration resonance for the measurement of Young's modulus, E, and shear modulus, G, of shafting is described. The moduli are used to calculate the resonance frequency of transverse vibration for comparison with a measured value. The agreement is extremely good so the measurements of E and G, and the theory used to calculate the transverse resonant frequency, must be precise.This method can be used in materials research but its simplicity also commends it for the quality control of composite material components in production.     

Ply cracking and property degradations of symmetric balanced laminates under general in-plane loading

The authors have previously proposed a method of using a resistance curve to characterize transverse crack multiplication in balanced symmetric laminates. The method was based on the concept of a through-the-thickness inherent flaw and energy balance principle. In the present paper, this model is further extended to shear and general in-plane loading conditions. The corresponding mechanical property degradations due to transverse ply cracking are also investigated. The effective longitudinal modulus and Poisson's ratio depend not only on the crack density but also on the thermal residual and applied stresses. The reason is that the cracks do not close tightly even upon unloading due to the residual stress. Experimental results for the mechanical property degradations correlate well with the analysis except for the shear modulus. The nonlinear behavior of the shear modulus should be considered for better correlation.     

The shear properties and deformation mechanisms of porous metal fiber sintered sheets

Porous metal fiber sintered sheets (MFSSs) are a type of layered transversely isotropic open cell materials with low relative density (i.e., volume fraction of fibers), high specific stiffness and strength, and controllable precision for functional and structural applications. Based on a non-contact optical full field strain measurement system, the in-plane and transverse shear properties of SMFFs with relative densities ranging from 15% to 34% are investigated. For the in-plane shear, the modulus and strength are found to depend linearly upon the relative density. The associated deformation is mainly due to fiber stretching, accompanied by the direction change of metal fibers. When the shear loading is applied in the transverse direction, the deformation of the material is mainly owing to fiber bending, followed by the separation failure of the fiber joints. Measured results show that the transverse shear modulus and strength have quartic and cubic dependence upon the relative density respectively and are much lower than their in-plane counterparts. Simple micromechanics models are proposed for the in-plane and transverse moduli and strengths of MFSSs in shear. The predicted relationships between the shear mechanical properties of MFSSs and their relative density are obtained and are in good agreement with the measured ones.     

Interface and impregnation relevant tests for continuous glass fibre-polypropylene composites

An experimental investigation was performed in order to compare the effect of the adhesive strength between fibres and matrix, contra the effect from the degree of impregnation on the mechanical properties of melt impregnated continuous glass fibre—polypropylene composites. Single fibre pull-out tests were performed in order to compare the interfacial bond strength. The degree of impregnation was measured using opacity and scattering from reflected light measurements of the prepregs. The testing included transverse tensile, ±45° tensile, double-notch shear, compression shear and double cantilever beam (DCB). These tests can to a certain degree be given interface relevance (InR) as well as impregnation relevance (ImR). With regard to InR sensitivity, the tests can be ranked in descending order according to prepreg transverse, laminate transverse, intralaminar, and interlaminar double-notch shear tests. With regard to ImR sensitivity, the tests can be ranked in descending order according to prepreg transverse, compressive interlaminar double-notch shear and laminate transverse tests. The measured shear and transverse modulus values showed limited relevance regarding the interface strength and degree of impregnation. The transverse and shear elastic modulus scored low regarding InR and ImR sensitivity. This was also true for the G_IC and G_ICPROP values.     

Instrumented indentation and ultrasonic velocity techniques for the evaluation of creep cavitation in silicon nitride

Instrumented indentation and ultrasonic wave velocity techniques combined with precise density change measurements and transmission electron microscopy (TEM) were used to investigate the changes of elastic moduli in silicon nitride after tensile deformation up to 3%. Linear dependencies on strain were also found for the degradation of the indentation modulus, longitudinal and transverse ultrasonic wave velocities, Young's, shear and bulk moduli and Poisson's ratio. The results obtained by indentation technique and ultrasonic method were essentially identical. TEM observation confirmed that multigrain junction cavities were responsible for the density changes and the elastic moduli degradation. The density changes were linearly proportional to tensile strain with the slope of 0.75. Thus, cavitation is the dominant creep mechanism in silicon nitride studied. Instrumented indentation and ultrasound velocity techniques are suitable for non-destructive monitoring of creep damage accumulation in ceramic components.     

Experimental determination of torsion and shear properties of sandwich panels and laminated composites by the plate twist test

A recently developed sandwich plate twist test is employed here for determination of the transverse shear modulus of the core and twist stiffness (D₆₆) of a sandwich panel consisting of a soft (H45 PVC foam) core and glass/vinylester face sheets. The shear modulus of the H45 PVC foam core extracted from the twist test was in good agreement with shear modulus obtained from ASTM plate shear testing of the foam core. D₆₆ values obtained from the sandwich twist test were in good agreement with predictions from classical laminated plate theory. In addition, the twist test was used to determine the in-plane shear modulus of glass/vinylester laminates isolated and as face sheets in sandwich panels with a stiff (plywood) core. The in-plane shear modulus of the face sheets, isolated and as part of a sandwich panel, was in good agreement with shear modulus determined using the Iosipescu shear test. The results point to the potential of the twist test to determine both in-plane and out-of-plane shear moduli of the constituents of a sandwich structure, as well as D₆₆.     

The lateral deformation of cross-linkable PPXTA fibres

The lateral deformation properties of oriented polymer fibres were examined by transverse compressive and torsional experiments. A modified interfacial test system machine was used to study the transverse compressive deformation behaviour of thermally cross-linkable poly(p-1,2-dihydrocyclobutaphenylene terephthalamide) (PPXTA) fibres and of a number of commercially available polymers (Nomex, nylon, Kevlar, Dacron) and ceramic (Nicalon and FP) fibres. The torsional (shear) modulus G of PPXTA and Kevlar poly(p-phenylene terephthalamide) (PPTA) fibres was measured by pendulum experiments. During both fibre torsion and transverse compression, the deformation involves materials slip on (h k 0) planes, in the [0 0 1] direction for the torsion and the [h k 0] directions for transverse compression. The intermolecular crosslinks in PPXTA did not significantly modify the elastic transverse modulus Et and caused only slight (13%) increase in shear modulus G. However, the plastic transverse properties of cross-linked PPXTA were significantly different than those of uncross-linked PPXTA. The stress at the proportional limit σp, determined from the transverse load–displacement curves, was substantially higher for the cross-linked fibres than for the uncross-linked fibres. In addition, the cross-linked PPXTA fibres exhibited a large strain recoverable response reminiscent of elastomers, whereas the PPTA and uncross-linked PPXTA fibres exhibited a large strain irreversible response. This revised version was published online in November 2006 with corrections to the Cover Date.     

The transverse moduli of fibre-composite material

The elastic moduli of uniaxial fibre-composite material are briefly reviewed. The transverse Young's modulus and the axial-transverse shear modulus are matrix dependent. A single formula is derived for their calculation. This formula accepts the Halpin-Tsai philosophy of the need for a simple equation but presumes to improve on Halpin-Tsai by eliminating an arbitrary constant varied for the cases of direct stress and shear stress. It draws attention to the variation of packing array with fibre volume fraction and demonstrates the concentration of strain at the points of minimum clearance between fibres. The accuracy of the new formula is shown, first by comparison with the two established formulae of Halpin and Tsai, and with Hewitt and Malherbe's modification of Halpin and Tsai's formula for shear. Secondly, its accuracy is shown by verifying its trends for the extremes of fibre volume fraction.     

复合材料圆管构件的等效模型研究

本文针对任意壁厚的复合材料圆管构件的等效弹性模量和剪切模量提出了高阶理论计算方法,它考虑了构件的横向剪切效应以及层合材料的三维本相关系,并且对三种缠绕方式的等效模量进行了预测,预测结果与经典层合报理论和实验的预测结果吻合较好,该方法可用于复合材料杆件结构的设计中。     

The transverse elastic properties of chiral honeycombs

This work describes the out-of-plane linear elastic mechanical properties of trichiral, tetrachiral and hexachiral honeycomb configurations. Analytical models are developed to calculate the transverse Young’s modulus and the Voigt and Reuss bounds for the transverse shear stiffness. Finite Element models are developed to validate the analytical results, and to identify the dependence of the transverse shear stiffness vs. the gauge thickness of the honeycombs. The models are then validated with experimental results from flatwise compressive and simple shear tests on samples produced with rapid prototype (RP)-based techniques.     

Thermoelastic composites with columnar microstructure and cylindrically anisotropic phases. Part II: One-parameter generalized self-consistent estimates

The effective transverse shear modulus of a transversely isotropic composite with columnar microstructure and with two cylindrically orthotropic phases is estimated by a one-parameter generalized self-consistent model. The equation characterizing the effective transverse shear modulus is a fourth-order polynomial equation instead of the quadratic one determined by the classical generalized self-consistent model. The result obtained in Part II of this work extends the relevant one of Hashin [Z. Hashin, Thermoelastic properties and conductivity of carbon/carbon fiber composites, Mech. Mater. 8 (1990) 293–308].     

Transverse cracking and Poisson's ratio reduction in cross-ply carbon fibre-reinforced polymers

Gradual damage development in carbon fibre-reinforced polymers (CFRP) and its effect on the mechanical properties have been important subjects of investigation for many years. Most authors have studied transverse matrix cracking in cross-ply lay-ups and used the longitudinal Young's modulus as an indicator of the extent of damage development. Reductions of typically only a few percent have been found at saturation crack spacing. Some authors have studied the effect of matrix cracking on Poisson's ratio. The results show large reductions, but few data are available on the evolution of Poisson's ratio throughout the process of gradual matrix cracking and on the influence of the 0°/90° ply thickness ratio. Moreover, none of the available models seems to accurately predict the quantitative evolution of Poisson's ratio. In this work the degradation of the longitudinal and the transverse properties of a number of cross-ply CFRP laminates due to transverse matrix cracking under longitudinal tension was studied. The longitudinal Young's modulus appeared to be less sensitive to damage development, in contrast to Poisson's ratio which exhibited significant reductions in all lay-ups. A micromechanical model, based on the shear lag theory, was developed to predict the evolution of Poisson's ratio and the effect of the 0°/90° ply thickness ratio. The correlation between experiment and theory was very satisfactory.