Fatigue life simulation of multi-axial CFRP laminates considering material non-linearity

The objective of an on-going DFG research project is to investigate the effect of non-linear stress–strain curves (e.g. τ₁₂–γ₁₂) on the fatigue life simulation of carbon fiber reinforced polymer (CFRP) laminates under variable amplitude cyclic loading. Based on the critical element concept of Reifsnider and Stinchcomb appropriate models including a secant modulus iteration for the non-linear stress analysis, the evaluation of inter-fiber fracture effects applying a fracture plane criterion, and appropriate continuum mechanics based stiffness degradation algorithms to treat both inter-fiber cracking and ply delamination were implemented into an existing fatigue life prediction software. Using this software the fatigue life of a quasi-isotropic vinylester/urethane/carbon fiber composite laminate subjected to miniTWIST variable amplitude loading was analyzed and compared to experimental data.     

Behaviour of unidirectional and crossply ceramic matrix composites under quasi-static tensile loading

Experimental results are presented for the quasi-static tensile behaviour of unidirectional, (0/90)_s, (0₂/90₄)_s and (0/90)_3s silicon carbide fibre (Nicalon) reinforced calcium aluminosilicate glass-ceramic matrix laminates. The stress-strain behaviour and associated damage development is described in detail for each laminate. The damage development is quantified by counts of crack density (in both the longitudinal and transverse plies) and stiffness reduction as functions of applied strain. The damage initiation and growth (and its effect on residual properties) are discussed with reference to the Aveston-Cooper-Kelly (ACK) theory for unidirectional ply cracking and crossply laminate shear-lag (originally developed for polymer matrix composites) to describe the transverse ply cracking behaviour.     

Off-axis Fatigue Crack Growth and the Associated Energy Release Rate in Composite Laminates

Stable matrix crack growth behaviour under mechanical fatigue loading hasbeen studied in a quasi-isotropic (0/90/-45/+45)_s GFRPlaminate. Detailed experimental observations were made on the accumulationof cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finiteelement model of the damaged laminate has been constructed. This model hasbeen used to relate the energy release rate of growing cracks to the crackgrowth rate via a Paris relation.     

Thermo-mechanical behaviour of wood and wood products

The dynamic mechanical behaviour of solid wood, fibreboard, and wood laminates has been examined in the temperature range –100 to +150° C. Two events are apparent in the response of the solid wood, a low-temperature (–50° C) transition which is interpreted as being associated with the onset of movement of bound water, and a higher temperature (40 to 120° C) thermal softening process. With fibreboard, the relationship between the shear storage modulus and density is shown to be described by a simple packing efficiency factor applicable over a wide range of temperature. The behaviour of the laminates is strongly dependent upon the orientation of the outer ply. A model is proposed which analyses the response of the laminate in terms of its constituent plies and allows calculation of numerical values of the component shear storage moduli. With both the fibreboard and the laminates the binder, urea-formaldehyde resin, is shown to have a significant influence on the absolute values of tan observed.     

On transverse matrix cracking in cross-ply laminates loaded in simple bending

A one-dimensional analysis of a cross-ply laminate, containing cracked transverse plies, loaded in flexure is presented. Simple bending theory is used in conjunction with a shear-lag analysis, to calculate the degraded longitudinal modulus of a cracked transverse ply, enabling the flexural modulus of the laminate to be determined. The solution is shown to agree well with a more sophisticated stress transfer model in the literature. The analysis is then extended to calculate the applied bending moment at transverse crack onset under flexural loading using a fracture mechanics approach. The results suggest that the in situ transverse ply stress at which matrix cracking commences for the beam loaded in flexure is very close to the stress level at which the same ply would crack if the laminate were loaded in tension.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

An acoustic emission energy analysis and its use to study damage in laminated composites

A new technique which uses the output of a true RMS voltmeter to measure the acoustic emission energy output of a transducer is presented. To demonstrate its use in a typical case, this procedure is used to measure acoustic emission energy during tensile tests on [0°/±30°/90°]_s glass-epoxy laminate uniaxial and 10° off-axis tensile coupons. The test results were compared with numerical predictions of laminate response and acoustic emission energy. The experiments indicate that acoustic emission energy can be used to indicate the onset of ply and interlaminar failure.     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

Thermal expansion of selected graphite-reinforced polyimide-, epoxy-, and glass-matrix composites

The thermal expansion of continuous carbon-fiber reinforced composites with epoxy-, polyimide-, and borosilicate glass-matrices has been measured and compared. The expansion of a rubber-toughened epoxy-matrix/P75S carbon-fiber composite was very different from the expansion of two different single-phase epoxy-matrix/P75S composites, although all three had the same stacking sequence. Reasonable agreement was obtained between measured thermal expansion data and results from classical laminate theory. Microdamage in the graphite/polyimide laminate, induced by 250 cycles between –156 and 121°C, caused a 53% decrease in the coefficient of thermal expansion. The thermal expansion of the graphite/glass laminate was not changed after 100 thermal cycles from –129 to 38°C; however, a residual strain of about 10×10^–6 was observed for the laminate tested.     

Transverse ply cracking strains in (0°/90°) and (±θ°/90°) laminates

Comparisons have been made between experimental data on transverse ply cracking in various types of (0°/90°) and (°/90°) laminates and the predictions of the constrained cracking and strain field theory. Generally it is observed that the predictions of the strain field theory are in closer agreement with the experimental data over a wider range of experimental conditions than those of the constrained cracking model. It is shown that reasonable agreement with the observed transverse ply cracking strains of various laminates produced from similar material can be obtained through the use of a standard set of material property values.     

Experimental characterization of damage behavior in polycyanate CFRP laminates under high temperature atmospheric exposure

This study focuses on the experimental characterization of damage behavior due to thermo-oxidative-induced matrix shrinkage in carbon fiber reinforced plastics (CFRP) with polycyanate ester. To investigate the effects of laminate configuration on matrix shrinkage behavior, [90]₈ and [0]₈ unidirectional laminates, [±45]_2S angle ply laminates, and [45/0/–45/90]_3S quasi-isotropic laminates were exposed to high temperature atmospheric environment at 180 °C to analyze matrix shrinkage up to 2000 h. These samples were removed from convection oven to observe sample side surface changes. The thermo-oxidative-induced matrix shrinkage was measured on the side surface of CFRP sample by confocal laser microscopy. The results suggested thermo-oxidative-induced matrix shrinkage depended on aged hours, fiber-to-fiber distance, and fiber orientation angle. The matrix shrinkage coefficient could be calculated with a tensorial transformation and empirical formula. The model can predict matrix shrinkage tendency of the 45° intra-lamina layer in quasi-isotropic laminate using the data of 0° and 90° matrix shrinkage in the quasi-isotropic laminates.     

Fatigue life prediction of composite laminates by FEA simulation method

This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation.     

Effect of curing stresses on the behaviour of fibre reinforced plastic composites under biaxial loading

Residual stresses are induced in fibre reinforced plastic (FRP) composites during fabrication and environmental exposure. The curing residual stresses induced during fabrication are mainly due to the thermal expansion mismatch of the constituents. The residual stresses can be either microresidual or macroresidual stresses. Macroresidual stresses in 0° plies and 90° plies of [90/0]_s symmetric cross-ply laminates are calculated starting with ply elastic and thermal properties for different material systems. The calculated curing stresses in Kevlar49/Epoxy unidirectional tape plies in the transverse direction are more than the transverse strength of the corresponding ply. First ply failure (FPF) envelopes are plotted using classical lamination theory and Tsai-Wu quadratic failure theory with and without considering the curing residual stresses. There is a significant effect of residual stresses on the FPF envelopes.     

Toughness,flexural, damping and interfacial properties of hybridized GFRE composites with MWCNTs

As the improved damping in fiber-reinforced composites can affect the other mechanical properties, therefore, the aim of this work is to investigate the effect of multiwall carbon nanotube (MWCNT) on the interfacial bond strength, flexural strength and stiffness, toughness and damping properties of hybridized glass-fiber reinforced epoxy (GFRE) composites. Nanophased epoxy resin was used to hybridize unidirectional and quasi-isotropic GFRE composites with [0/±45/90]_s and [90/±45/0]_s stacking sequences. Results from the interfacial characterizations of the hybridized composites showed improvement up to 30% compared to the control laminates. Hybridization of GFRE laminates with MWCNTs leads to decreasing the flexural and storage moduli, increasing flexural strength, toughness, natural frequencies and damping ratio. A high correlation coefficient of 0.9985 was obtained between static flexural and dynamic storage moduli. The highest flexural strength, flexural and storage moduli and natural frequency of quasi-isotropic laminate were observed for [0/±45/90]_s stacking sequence and vice versa for damping ratio.     

Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear

The aim of present investigation is to study the buckling and postbuckling response and strengths under positive and negative in-plane shear loads of simply-supported composite laminate with various shaped cutouts (i.e., circular, square, diamond, elliptical-vertical and elliptical-horizontal) of various sizes using finite-element method. The FEM formulation is based on the first order shear deformation theory which incorporates geometric nonlinearity using von Karman’s assumptions. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. The effect of cutout shape, size and direction of shear load on buckling and postbuckling responses, failure loads and failure characteristics of quasi-isotropic [i.e., (+45/−45/0/90)_2s] laminate has been discussed. In addition, the effect of composite lay-up [i.e., (+45/−45/0/90)_2s, (45/−45)_4s and (0/90)_4s] has also been reported. It is observed that the cutout shape has considerable effect on the buckling and postbucking behaviour of the quasi-isotropic laminate with large size cutout. It is also observed that the direction of shear load and composite lay-up have substantial influence on strength and failure characteristics of the laminate.     

Mechanical properties of vanadium beryllide,VBe12

The mechanical properties of VBe₁₂, both at room and elevated temperatures (up to 1200°C), have been measured. Room-temperature properties, including Young's modulus, flexural strength, and fracture toughness are reported. The material behaved elastically at room temperature but became plastic at temperatures above 1000°C. Creep properties of VBe₁₂ were also studied in temperature ranges from 1000–1200°C and applied stress ranges from 33–58 MPa. At low strain rates (approximately < 10^–5s^–1), the stress exponent was about 4, suggesting deformation was controlled by dislocation climb. Microstructural examination indicated that fracture was initiated from grain boundaries subjected to tensile stresses. The creep behaviour of VBe₁₂ is briefly compared with that of other intermetallics.     

Damage and residual strength of laminated carbon–epoxy composite circular plates loaded at the centre

The research dealt with the characterization of damage in quasi-isotropic carbon fibre reinforced epoxy resin laminate loaded at the centre. Load was applied by means of a servo hydraulic machine and it was supposed to simulate a low velocity impact. The acoustic emission (AE) technique was used to detect damage progression. Tensile resistance after indentation was investigated and correlated with acoustic emissions parameters. This was been done for different lamination sequences on specimens cut from the damaged plates.A numerical model to predict both the first ply failure (FPF) and the ultimate ply failure (UPF) of the laminate was developed by means of the ANSYS^® software.     

The thermal expansion of carbon fibre reinforced plastics

Measurements of the principal linear thermal expansion coefficients of a tridirectional (–45°, 0°, +45°) carbon fibre reinforced plastics laminate are reported in the approximate temperature range 90 K to 500 K. A quantitative evaluation of the in-plane results in thermoelastic terms has yielded an agreement with these results consistent with the approximations and uncertainties involved. The qualitative agreement with expectations based upon the behaviour of unidirectional and bidirectional laminates is also demonstrated. The account concludes with an examination of some effects which are peculiar to multidirectional laminates.