Fatigue damage mechanisms and residual properties of graphite/epoxy laminates

Damage mechanisms and accumulation, and associated stiffness and residual strength reductions were studied in cross-ply graphite/epoxy laminates under cyclic tensile loading. Stress-life data were fitted by a two-parameter wearout model and by a second-degree polynomial on a log-log scale. The fatigue sensitivity is highest for the unidirectional laminates and it decreases for the crossply laminates with increasing number of contiguous 90° plies. Five different damage mechanisms were observed: transverse matrix cracking, dispersed longitudinal cracking, localized longitudinal cracking, delaminations along transverse cracks, and local delaminations at the intersection of longitudinal and transverse cracks. Failure patterns vary with cyclic stress level and number of cycles to failure. Under monotonie loading, failure is brittle-like and concentrated. At high stress amplitudes and short fatigue lives failure results from few localized flaws, whereas at lower stress amplitudes and longer fatigue lives failure results from more dispersed flaws. The residual modulus shows a sharp reduction initially, followed by a more gradual decrease up to failure. The residual strength showed a sharp reduction initially, followed by a plateau or even some increase in the middle part of the fatigue life, and a rapid decrease in the last part of the fatigue life. A tentative cumulative damage model is proposed based on residual strength and the concept of equal damage curves.     

Mixed-mode interlaminar fracture and damage characterization in woven fabric-reinforced glass/epoxy composite laminates at cryogenic temperatures using the finite element and improved test methods

The present research examines experimentally and analytically the mixed-mode interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates at cryogenic temperatures. The mixed-mode bending (MMB) tests were performed with the improved test apparatus, at room temperature, liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). The energy release rates at the onset of delamination crack propagation were evaluated for the woven GFRP specimens using both beam theory and finite element analysis. The fracture surfaces were also examined to verify the fracture mechanisms. In addition, the initiation and growth of damage in the specimens were predicted by a damage analysis, and the damage effect on the mixed-mode interlaminar fracture properties at cryogenic temperatures was explored.     

Modeling of permeation and damage in graphite/epoxy laminates for cryogenic tanks in the presence of delaminations and stitch cracks

Composites are extensively used for various aerospace applications and one of its important potential uses is as cryogenic fuel tank material for crew launch vehicles. Composites offer high specific strength and stiffness, and therefore are preferred over many other materials. However under structural mechanical loads and/or thermal loads, transverse micro-cracks develop in the polymer matrix. These cracks along with interlaminar delaminations produced at the crack tips, lead to permeation of cryogenic fuel permeation through the laminates. In this study, mathematical models have been proposed to determine the delaminated crack opening displacement (DCOD) for each ply of a damaged laminate and the permeability associated with it. In addition, a stitch crack model has been proposed to address experimental observations. The through-thickness DCOD distribution for a damaged composite under the action of thermal and/or mechanical load is predicted using a five-layer model which is developed based on first order shear deformation theory. The DCOD predicted by this mathematical model, with and without stitch cracks, shows good agreement with two dimensional finite element analysis. The DCOD values predicted for IM7/5250-4 laminate of lay-up [0/45/−45/90]_S were used to predict permeability using Darcy’s law for fluid flow through porous media. The analysis results were benchmarked using test data from Air Force Research Laboratory. A parametric study for permeability conducted with varying stitch crack lengths shows that the permeability of the composite is sensitive to this form of damage in individual plies.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

The role of microdamage in tensile failure of graphite/epoxy laminates

Damage development during quasistatic tensile loading of several laminates of graphite/epoxy material is examined and compared to damage development in laminates of a similar graphite/epoxy material subjected to tension-tension fatigue loading. Emphasis is placed upon following damage development at the microstructural level. Evidence of the important role of off-axis ply cracks in localizing and controlling fiber fracture in adjacent load-bearing plies for both loading modes is resented. The relationship between fiber fracture density and static load level is presented for tensile loading of unidirectional and cross-ply laminates by direct observation of fiber fracture in situ. The frequencies of occurrence of multiple adjacent fiber fractures are also reported. The cross-ply laminate results are compared with those from fatigue testing. Significant differences are described and discussed.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

Damage tolerance of glass mat/epoxy laminates hybridized with flexible resin under static and impact loading

This study deals with the impact property and damage tolerance of matrix hybrid composite laminates with different laminate constitution. The matrix hybrid composite laminates consisted of the laminae with a conventional epoxy resin and the laminae with a flexible epoxy resin modified from the conventional resin to avoid the interlaminar delamination. The impact energy absorption ratio greatly depended on the matrix resin placed at the impact face. The energy absorption was almost constant if the conventional resin was placed at the impact surface layer, while it increased exponentially with the increasing fraction of the flexible resin if the flexible resin was placed at the impact face. The impact energy was absorbed by the damage development and propagation in the laminate with conventional resin laminae as the impacted face, while it was absorbed by both the recoverable deformation of the flexible resin and the damage propagation in the laminate with flexible resin laminae as the impacted face.     

Statistical analysis for fatigue life evaluation of woven E-glass/epoxy composite laminates containing off-centre interacting circular holes

Mechanics of Time-Dependent Materials - Fatigue behaviour of woven E-glass/epoxy composite laminates containing off-centre interacting circular holes was determined under sinusoidal loading in...     

Experimental observations and finite element modelling of damage initiation and evolution in carbon/epoxy non-crimp fabric composites

Damage in carbon/epoxy non-crimp stitched fabric (NCF) reinforced composites, produced by the resin transfer moulding (RTM) process is described. Formation of the stitching loop results in a certain disturbance of the uniform placement of the fibres. These deviations in fibre placement produce resin-rich zones that can influence the mechanical behaviour of the composite part. Tensile tests on quadriaxial (45°/90°-45°/0°)_s laminates are performed accompanied by acoustic emission (AE) registration and X-ray imaging. Early initiation of damage (matrix cracking) in plies with different fibre orientation has been detected. Damage sites correlate with the resin-rich zones created by the stitching. Finite element (FE) analysis is carried out to develop a model that describes damage of the NCF composites. Numerical multi-level FE homogenization is performed to obtain effective elastic orthotropic properties of NCF composite at micro (unit cell of unidirectional tow) and meso (fabric unit cell) levels. A hierarchical sequence of FE models of different scales is created to analyze in detail the 3D stress state of the NCF composite (meso unit cell). A multi-level submodeling approach is applied during FE analysis. Zones of matrix-dominated damage are predicted. A comparison of non-destructive testing results with computational model is performed. Fracture mechanics parameters of matrix crack are computed and cracks growth stability is studied.     

A damage evolution study of E-glass/epoxy composite under low velocity impact

To predict the behavior of composites in case of low velocity impact, various material models are available in the literature. Damage evolves exponentially or linearly with strain in these models. These models are using either characteristic length ‘L_c’ or material exponent parameters, ’m’ to solve the problem of strain localization. A method to relate these parameter to each other is suggested here. The choice of material exponent, ‘m’ for a particular mesh size is also discussed. Low velocity impact simulations for E-glass/epoxy composite are performed using continuum damage mechanics based material model and compared with the experiments. The damage observed through the light projected area on the laminate, contact forces and displacement plots with respect to time were studied and compared with finite element analysis results to demonstrate the effectiveness of the model. Digital Image Correlation (DIC) technique is used for experimentation to obtain displacement on the surface of the plate.     

Low-velocity impact damage response of fiberglass/magnesium fiber-metal laminates under different size and shape impactors

Low-velocity impact tests are performed on fiberglass/AZ31B-H24 magnesium fiber-metal laminates (FMLs) with various configurations in order to gain a better understanding of the effect of an impactor's features on the response of this type of FML. For that, impactors with two different shapes (hemispherical and sharp-edged) and sizes are used to impact the specimens. The impact response data, such as the deformation of the contact location and energy absorption, is obtained directly during the impact tests through the impact equipment, while mechanical sectioning was carried out to establish the extent of delaminated area and post-impact residual deformation. While the sharp-edged impactor caused the development of cracks on the metal constituent, and delamination within the specimens, the hemispherical ones imposed more influence over the residual deformation. Noticeable differences are observed in response of FML specimens made with two and three layers of magnesium, especially with respect to the energy absorption capacity. Moreover, finite-element analysis, as a major part of this study, has been employed to simulate the low-velocity impact response of FML specimens. The behavior of specimens has been simulated using the commercial finite-element code ABAQUS. The results imply that there is a good agreement between the experimental and numerical results.     

The influence of hygrothermal conditions on the damage processes in quasi-isotropic carbon/epoxy laminates

The effects of hygrothermal conditions on damage development in quasi-isotropic carbon-fiber/epoxy laminates are described. First, monotonic and loading/unloading tensile tests were conducted on dry and wet specimens at ambient and high temperatures to compare the stress/strain response and damage development. The changes in the Young's modulus and Poisson's ratio were obtained experimentally from the monotonic tensile tests. The critical stresses for transverse cracking and delamination for the above three conditions are compared. The delamination area is measured by using scanning acoustic microscopy (SAM) at various loads to discuss the effects of delamination on the nonlinear stress/strain behavior. Next, the stress distributions under tensile load including hygrothermal residual stresses are computed by a finite-element code and their effects on damage initiation are discussed. Finally, a simple model for the prediction of the Young's modulus of a delaminated specimen is proposed. It is found that moisture increases the critical stresses for transverse cracking and delamination by reducing the residual stresses while high temperature decreases the critical stresses in spite of relaxation of the residual stresses. The results of the finite-element analysis provide some explanations for the onset of transverse cracking and delamination. The Young's modulus predicted by the present model agrees with experimental results better than that predicted by conventional models.     

Tensile behavior of glass/epoxy laminates at varying strain rates and temperatures

In the present work tensile tests at different strain rates and temperatures were performed in glass fiber reinforced polymer (GFRP). It is observed that such kind of composite presents an elasto–viscoplastic behavior – the rate dependency only occurs for loading levels above a given elasticity limit. Strain rate strongly affects the ultimate tensile strength (σ_u) and the modulus of elasticity is almost insensitive to it while temperature only influences the modulus. Analytical expressions to predict the modulus of elasticity and (σ_u) as a function of the temperature and strain rate are proposed and compared with experimental data showing a reasonable agreement.     

A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates

 A new numerical technique combining the finite element method and strip element method is presented to study the scattering of elastic waves by a crack and/or inclusion in an anisotropic laminate. Two-dimensional problems in the frequency domain are studied. The interior part of the plate containing cracks or inclusions is modeled by the conventional finite element method. The exterior parts of the plate are modeled by the strip element method that can deal problems of infinite domain in a rigorous and efficient manner. Numerical examples are presented to validate the proposed technique and demonstrate the efficiency of the proposed method. It is found that, by combining the finite element method and the strip element method, the shortcomings of both methods are avoided and their advantages are maintained. This technique is efficient for wave scattering in anisotropic laminates containing inclusions and/or cracks of arbitrary shape. Received 2 February 2001     

Application of the substructured finite element/extended finite element method (S-FE/XFE) to the analysis of cracks in aircraft thin walled structures

The substructured finite element/extended finite element (S-FE/XFE) approach is used to compute stress intensity factors in large aircraft thin walled structures containing cracks. The structure is decomposed into a ‘safe’ domain modeled with classical shell elements and a ‘cracked’ domain modeled using three-dimensional extended finite elements. Two applications are presented and discussed, supported by validation test cases. First a section of stiffened panel containing a through-thickness crack is investigated. Second, small surface cracks are simulated in the case of a generic ‘pressure membrane’ with realistic crack configurations. These two semi-industrial benchmarks demonstrate the accuracy, robustness and computational efficiency of the substructured finite element/extended finite element approach to address complex three-dimensional crack problems within thin walled structures.     

Fatigue damage in thin film Al interconnects at ultra high frequency: A finite element analysis approach

In order to investigate the behavior of thin metal films under high cyclic stress surface acoustic waves (SAW) test devices with frequencies up to several GHz can be used. Resulting from the microstructural damage formation a significant degradation in form of a shift of the resonance frequency in SAW test devices takes place. In the present paper, we analyze the influence of the amount of damage on the observed frequency shift in detail. It is shown that Finite Element (FEM) calculations simulate very well the sensitivity of the resonance frequency to the damage formation in the form of cracking, voiding and extrusion growth. The experimentally observed linear correlation between damage density and frequency shift is reproduced by the FEM model. Furthermore, the FEM simulations predict a significant deviation from the linear correlation for very high damage densities.     

An automated finite element analysis of the initiation and growth of damage in carbonfibre composite materials

The analysis and prediction of the development of damage in composite materials up to the point of final failure is important in the assessment of whether composite structures and components are fit for their purpose. Progressive damage modelling, using finite element analysis, has demonstrable potential as a tool for this.

If this approach is to be of real value, it needs to be automated so that the application of specialist knowledge is minimized. The ABAQUS finite element (FE) code has been used to develop fully-automated, threedimensional modelling of damage development in carbon fibre composites under tensile loading.

This paper describes the approach used in the development of these models. It covers work on the development of suitable FE meshes, the identification of suitable criteria to control the onset and effects of local damage, and the extension of the methodology to real component geometries.     

Failure criterion for laminated glass under impact loading and its application in finite element simulation

A failure criterion for laminated glass in case of impact is presented. The main idea of this criterion is that a critical energy threshold must be reached over a finite region before failure can occur. Afterwards crack initiation and growth is based on a local Rankine (maximum stress) criterion. The criterion was implemented in an explicit finite element solver. Different strategies for modeling laminated glass are also discussed.To calibrate the criterion and evaluate its accuracy, a wide range of experiments with plane and curved specimens of laminated glass were done. For all experiments finite element simulations were performed. The comparison between measured and simulated results shows that the criterion works very well.     

Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms, elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate the efficiency of the algorithm.