This paper describes a thermodynamics based model for viscoelastic composites with damage and illustrates its use in characterization of viscoelastic response of polymer matrix woven fabric composites subjected to loading at high temperatures. The characterization is conducted by an experimental method aided by finite element (FE) modeling. The experimental characterization is based on creep data obtained under constant loads of different magnitudes and at different temperatures, and on recovery data collected after unloading. A carbon fiber/polyamide resin woven composite with glass transition temperature (Tg) of around 380 °C was used in the experimental program. A FE model was developed to determine the non-linear viscoelastic response by implementing incremental constitutive relations into an ABAQUS® code. The laminate viscoelastic properties were obtained by finite element micromechanics analysis using the neat resin data as input. Comparing its results with creep-recovery test data at different temperature and stress levels validated the FE model. There are several factors affecting the viscoelastic behavior of polymer matrix composites such as temperature, moisture and stress level. Accordingly, a large number of tests need to be performed to characterize the viscoelastic response experimentally for each fiber-matrix combination. For this purpose an efficient and systematic experimental procedure was used to understand the effects of temperature and stress level on the viscoelastic response, to clarify the damage-viscoelasticity coupling and to determine the viscoelastic properties of the material system

We propose a mechanistic model which is capable of describing the evolution of transverse cracking in cross ply laminates subjected to cyclic tension in the longitudinal direction. The key feature of the model is that it incorporates delamination associated with transverse cracks in a manner that induces further formation of transverse cracks as delamination grows in fatigue. A variational approach is taken to estimate the stresses in the region between transverse cracks, and these are found to be accurate away from the crack planes when comparison is made with finite element computations. The evolution of transverse crack density and the associated overall elastic moduli changes predicted by the model are in agreement with experimental results

The current practice, as well as the hitherto proposed models, for assessment of fatigue life of composite laminates rely largely on experimental fatigue life data. In this paper, we propose a methodology for fatigue life prediction that utilizes a micromechanics based evaluation of damage evolution in conjunction with a semi-empirical fatigue failure criterion. The specific case treated is that of cross ply laminates under cyclic tension. The predicted results are compared with experimental data for several glass/epoxy and carbon/epoxy laminates, and good agreement is found. Published by Elsevier Science S.A. The current practice, as well as the hitherto proposed models, for assessment of fatigue life of composite laminates rely largely on experimental fatigue life data. In this paper, we propose a methodology for fatigue life prediction that utilizes a micromechanics based evaluation of damage evolution in conjunction with a semi-empirical fatigue failure criterion. The specific case treated is that of cross ply laminates under cyclic tension. The predicted results are compared with experimental data for several glass/epoxy and carbon/epoxy laminates, and good agreement is found.

Three epoxy systems of interest as composite matrix materials are examined for their yielding and failure behavior under uniaxial, biaxial and triaxial stress states. Yield criteria applicable to glassy polymers, i.e. accounting for the hydrostatic stress effect on the deviatoric stress to yielding, are assessed. It is found that under stress states resembling those in matrix constrained between fibers, e.g. equibiaxial and equitriaxial tension, yielding is suppressed while brittle failure, presumably caused by crack growth from cavitation, occurs. A criterion for this mode of failure is proposed as the critical dilatational strain energy density. Experimental data are found to support this criterion.

Failure initiation in polymer-matrix composites loaded transverse to the fibers is investigated by a numerical parametric study where the effects of constituent properties, interphase properties and thickness are examined. Failure initiation in the matrix only is studied, interfacial debonding not being considered. Two modes of failure - yielding and cavitation-induced brittle failure - are examined. A criterion for the cavitation-induced brittle failure has been proposed previously and failure prediction based on this criterion was found to agree with experimental data for a glass-fiber-reinforced epoxy. The present study shows that the elastic modulus of fibers has a large effect on the stress and strain to failure initiation. A rubbery interphase material is found in most cases to have a beneficial effect. The site at which failure initiates and the governing mode of failure initiation are also affected by the fiber modulus and the interphase properties

A study has been conducted of failure in unidirectionally-reinforced fiber composites loaded in tension normal to the fibers. The case considered is when this failure is governed by failure of the matrix rather than fiber/matrix debonding. Both yielding and cavitation-induced brittle failure of the matrix are considered. The latter mode of failure was suggested previously as the likely mode to occur in epoxies under stress states that are purely or nearly hydrostatic tension. Three fiber packing arrangements (square, hexagonal and square-diagonal) with different fiber volume fractions were studied numerically by a finite element method to determine the local stress states. It is found that cavitation-induced brittle failure occurs much before yielding in all cases. Experimental data taken from the literature support this finding.

A framework is presented for analyzing the inelastic behavior and fracture of polymer matrix composites. Physics-based viscoplastic constitutive equations are used and supplemented with a matrix cracking model and an energy-based debonding model. The capabilities of the framework are illustrated by finite-element solutions of boundary-value problems under plane strain conditions using the unit-cell concept. In the application, focus is centered on the effect of manufacturing induced voids on local modes of fracture under both tension and compression

A framework is presented for analyzing the low-temperature inelastic behavior of a class of amorphous polymers with full account taken of finite deformations and inertial effects. Viscoplastic constitutive equations are used and supplemented with a new model for craze initiation, growth and breakdown. The capabilities of the framework are illustrated by finite element solutions of initial/boundary-value problems under plane strain conditions. Three illustrative benchmark problems are used to evaluate the proposed implementation: shear band formation and propagation under compression, dynamic response under impact and quasi-static response of a polymer composite unit-cell subject to uniaxial tension transverse to fibers.

A limiting property governing the thermomechanical behavior of composites is the strength transverse to the fibers. The present study investigates the dependence of this property on the distribution of fibers in the cross-section of a unidirectional composite. The approach taken is to consider actual distributions, which are arbitrary and are not necessarily described by random or periodic distributions. A fundamental issue in studying non-uniform distributions is the size of a representative volume element (RVE). By the use of an actual radial distribution function obtained for a ceramic-matrix composite by quantitative stereology in conjunction with a simulation technique developed in this study, the RVE size is investigated with respect to initiation of debonding and radial matrix cracking - two basic mechanisms governing the transverse strength of composites. Tensile loading transverse to the fibers and residual stresses induced by thermal cooldown are considered separately as loading modes for transverse failure. The results provide some useful insight into the importance of non-uniformity of fiber spatial distribution with regard to the transverse failure of composites. A limiting property governing the thermomechanical behavior of composites is the strength transverse to the fibers. The present study investigates the dependence of this property on the distribution of fibers in the cross-section of a unidirectional composite. The approach taken is to consider actual distributions, which are arbitrary and are not necessarily described by random or periodic distributions. A fundamental issue in studying non-uniform distributions is the size of a representative volume element (RVE). By the use of an actual radial distribution function obtained for a ceramic-matrix composite by quantitative stereology in conjunction with a simulation technique developed in this study, the RVE size is investigated with respect to initiation of debonding and radial matrix cracking - two basic mechanisms governing the transverse strength of composites. Tensile loading transverse to the fibers and residual stresses induced by thermal cooldown are considered separately as loading modes for transverse failure. The results provide some useful insight into the importance of non-uniformity of fiber spatial distribution with regard to the transverse failure composites.

Quantitative microscopy in conjunction with finite element analysis is used to study the effects of fiber distribution on damage initiation in the transverse direction of a [0]8 NicalonTM/MAS-5 glass-ceramic composite. Fiber centroid locations in a transverse cross-section of the composite are collected and stored and used to evaluate the second order intensity function, K(r), and the radial distribution function g(r). The g(r) yields several representative volume elements (RVEs) of the composite, where each element represents one statistical realization of the actual fiber distribution. Potential damage initiation sites are identified by applying a simple failure criterion to the stress distribution in each RVE

A framework is presented for analyzing the low temperature inelastic behavior of amorphous glassy polymers with full account taken of finite deformations and inertial effects. Two classes of viscoplastic constitutive equations are explored: rate-sensitive Drucker-Prager type models and an elaborate macromolecular model. These constitutive equations are integrated using a forward gradient time integration scheme. The capabilities of the framework are illustrated by finite element solutions of initial/boundary-value problems under plane-strain conditions. The discretized equations of motion are integrated using a Newmark algorithm. Three illustrative benchmark problems are used to evaluate the proposed implementation: dynamic shear band formation and propagation in a polymer under compression, dynamic response of a polymer under impact and quasi-static response of a polymer composite plate with a hole under uniaxial tension along fibers

The finite deformation response of a planar block of polymer material subject to impact loading is analyzed using two constitutive models for glassy polymers, a reference Drucker-Prager type model and a physics-based macromolecular model, supplemented by a phenomenological model for craze initiation and widening. Full transient finite element analyses are carried out using a Lagrangian formulation of the field equations. The analyses allow an assessment of possible failure mechanisms under dynamic loading and the ability of the different models to predict such behavior. The results highlight the effect of the stress-strain behavior of polymers, notably the post-yield softening and large strain hardening, on localization of plastic flow. This behavior is adequately captured only by the macromolecular model.

This paper presents results of a computational study focused on examining the role of manufacturing-induced voids in the initiation and growth of damage at the microstructural level in polymer matrix composites loaded in tension normal to fibers. The polymer deformation is described by an improved macromolecular constitutive model accounting for strain-rate-, pressure-, and temperature-sensitive yielding, isotropic hardening before peak yield, intrinsic postyield softening, and rapid anisotropic hardening at large strains. A new craze model that accounts for craze initiation, growth, and breakdown mechanisms is employed. An energy-based criterion is used for cavitation induced cracking that can lead to fiber/matrix debohding. The role of voids is clarified by conducting a comparative study of unit cells with and without voids. The effects of strain rate and temperature are investigated by a parametric study. The overall composite stress-strain response is also depicted to indicate manifestation of microlevel failure on macroscopic behavior

initial honors offerings have subsequently become UPTs for the recitation sections. The RW-E project funding includes support for an assistant professor and a PhD level graduate student from the College of Education and Human Resources. These two project participants have drafted a training program for the UPTs and GTAs to be held prior to each semester, and they convene the instructional team on a weekly basis to share experiences, share additional learning resources and discuss plans for the following week. They assist the engineering professors in charge of the course to incorporate student-centered learning strategies in line with design principles of the How People Learn1 framework. They also conduct research on the course design and its effectiveness in achieving learning goals, emphasizing critical thinking, effective communication skills, learning from peers, and issues awareness. The RW-E project is highly beneficial to development of the ENGR 101 course. Involving learning scientists in the course design and planning has greatly enhanced its value to students

This paper reports a study of the initiation of the first failure event in unidirectional composites subjected to transverse tension. Two energy based point failure criteria – critical dilatational energy density and critical distortional energy density – are considered. The manufacturing induced disorder in the fiber distribution in the composite cross section is described in terms of the degree of nonuniformity, which is quantified and for which an algorithm is developed. The nonuniformity is captured in a representative volume element (RVE) whose minimum size is determined based on statistics of nearest fiber distance distribution. Several realizations of the RVE for three fiber volume fractions and three degrees of nonuniformity are analyzed using a finite element model. A parametric study of the effect of matrix/fiber stiffness ratio on the damage initiation is also conducted. Significant effects of the fiber distribution nonuniformity on the strain to onset of damage are found.

The fatigue life behaviour and the underlying micromechanisms have been studied in two different Types of unidirectional carbon-fibre-reinforced plastics loaded in tension-tension along the fibre direction. The carbon fibres (AS4) were the same in the two composite systems. One thermoplastic matrix (polyetheretherketone, PEEK) and one thermosetting matrix (epoxy toughened with a thermoplastic additive) were used. The macroscopic fatigue behaviour was characterised by fatigue life diagrams. Surface replicas were taken intermittently during the course of the fatigue tests to monitor the active fatigue damage micromechanisms. The thermoset based composite showed a higher fatigue resistance with few microcracks initiated at distributed fibre breaks growing at a decelerating rate. The thermoplastic composite had a more pronounced fatigue degradation with a steeper fatigue life curve, which was caused by widespread propagating debonds and matrix cracks. The use of a tougher and more ductile matrix results in an inferior fatigue life performance, due to a more widely distributed accumulation of damage that propagates at a higher rate.

An acousto-ultrasonic technique was used to monitor damage initiation and development in (0, 90//2)//s, (0, plus or minus 45)//s, and (0, 90, plus or minus 45)//s graphite epoxy laminates. The laminates were either loaded in quasi-static tension or were fatigued with tension-tension loading cycles. At a number of intermediate stages (strain levels for quasi-static tests and load cycles for the fatigue tests), the loading was halted and the acousto-ultrasonic measurements were made on the specimens. Several quantitative parameters, which include moments and ratios of moments of the frequency spectrum, were found to correlate extremely well with the stiffness change and the stress-strain behavior of the specimens.

In the current study, a variational model is developed for predicting stress transfer due to ply cracking in general cross-ply laminates subject to out-of-plane bending and biaxial in-plane loading. The model is valid for multiple ply laminates that can be nonsymmetric. Using the principle of minimum complementary energy, an optimal admissible stress field is derived that satisfies equilibrium, boundary, and traction continuity conditions. Natural boundary conditions are derived from the variational principle to overcome the limitations of the existing variational methods on the analysis of cracked general cross-ply laminates. Comparing laminates of glass/epoxy and graphite/epoxy with the available finite element results shows that stress components are in very good accordance with the analytical results. It is also shown that the existing variational models are specific cases of the current formulation. In the next step, the obtained stress field is used in conjunction with the principle of minimum complementary energy to get the effective stiffness modulus of a cracked general cross-ply laminate. It is indicated that the method provides a lower bound for the stiffness modulus of a cracked laminate.

Voids are one of the most common types of manufacturing process induced defects in composite materials that have detrimental effect on the material properties. The void content can be reduced by carefully chosen process parameters, such as pressure and temperature, but often at the price of higher cost. A quantitative relationship between void characteristics and material properties would allow the trade-off between the cost and the desired product performance. The characteristics of interest include volume fraction, size, shape, and spatial distribution. In this paper, methods for determining effective elastic constants of unidirectional continuous fiber reinforced composites containing voids of various characteristics are presented. Finite element analysis (FEA) is performed on a representative volume cell based on observed void microstructure to determine the effective elastic constants. Analytical method based on Mori-Tanaka theory is also utilized for comparison. The predictions by FEA and the analytical method are compared with each other as well as with available experimental data. Overall good agreement is found. A parametric study reveals that the void content has severe impact on the out-of-plane modulus, while the in-plane properties are less significantly affected. For a given void content, the shape of the voids has different effect on different moduli. Flat voids are benign for in-plane moduli but undesirable for out-of-plane stiffness. Long voids reduce significantly the out-of-plane shear modulus, but have little effect on the in-plane properties

This paper presents a numerical simulation based analysis of micro-cracking in short fiber reinforced polymer composites. For this case, the conventional linear elastic fracture mechanics approach is shown not to be useful; instead, the Rice-Tracey ductile fracture model is shown to work well in the framework of the local approach to fracture. The model is first applied to the case of matrix cracking from the broken fiber end in a fiber fragmentation test of a single-fiber reinforced composite. The model predicts the measured conical crack path successfully, including the crack initiation angle and the kink formation as the crack propagates away from the fiber. Furthermore, the predicted dependence of the crack length on the nominal strain is found to be in qualitative agreement with measured data. Next the model is applied to micro-cracking in an aligned short fiber composite. The analysis predicts propagation of a matrix crack from the debonded fiber end towards the neighboring fiber at an oblique angle to the fiber axis. Before reaching the neighboring fiber, the crack is found to divert gradually towards the fiber axis. This behavior explains the so-called fiber-avoidance cracking mode reported in the literature. A parametric study is performed to reveal the dependence of the locally-averaged failure stress/strain on the fiber length and volume fraction

A previously developed statistical model for transverse cracking in cross ply laminates is extended to oblique cracking in multidirectional laminates. The oblique cracks are assumed to form in a ply when the local in-plane tensile stress normal to fibers exceeds the transverse strength of the ply. This strength is assumed to have a statistical distribution given by a two-parameter Weibull function. The model is applied to a glass-epoxy [0/602/0/-602]s laminate in which cracking evolution of the four -600 plies in the middle of the laminate is examined. The local stress field in the cracked -600 plies is calculated by a three-dimensional finite element method based on a unit cell construction developed by Li et al. [1]. The measured crack density is found to agree well with that calculated by the statistical model

We present a statistical analysis based methodology for making assessment of the manufacturing quality of cross ply composite laminates as it relates to its effect on transverse cracking evolution. Assuming a two-parameter Weibull distribution of tensile strength of the transverse plies to represent randomly distributed manufacturing defects, multiple crack formation in the plies is simulated in the non-interactive and interactive regimes of cracking using the local stress fields calculated by a variational analysis. The statistical methodology is demonstrated on crack density evolution in cross ply laminates manufactured by four different processing routes and loaded in monotonic tension in the axial direction. The differences in the crack density evolution, supposedly due to different defect population induced by the four manufacturing conditions, could be described by the proposed statistical simulation method.

Damage in composite laminates affects its overall viscoelastic response. Constitutive equations have been developed for composite laminates considering a fixed damage state. A complete description, however, requires suitable damage evolution laws. This paper is focused on studying damage evolution in viscoelastic laminates using a cohesive finite element approach. A two dimensional, four nodded finite element is developed incorporating a rate-independent traction-displacement cohesive law. This element is used in conjunction with plane strain bulk elements behaving in a linear viscoelastic manner to simulate crack evolution between two existing transverse cracks in symmetric cross-ply laminates. The effects of loading strain-rate, ply constraint and initial crack density are studied. This study shows expected trends in the behavior and indicates the suitability of cohesive zone modeling to study damage evolution in viscoelastic composite materials.

Damage in composite laminates affects their overall viscoelastic response. Previous research has been focused on developing constitutive equations for these materials considering a fixed state of damage. A complete description, however, requires suitable damage evolution laws. This paper is focused on studying damage evolution in viscoelastic laminates using a computational micromechanics approach. We use cohesive finite elements to study nucleation and subsequent growth of a transverse crack between two existing cracks in the 90° layer of a linear viscoelastic cross-ply laminate. The effect of loading rate, thickness of 90° ply and initial crack density on the evolution of a new crack is investigated.

This paper presents a constitutive model for linear viscoelastic orthotropic solids containing a fixed level of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Use is made of the correspondence principle for linear viscoelastic solids to define a pseudo strain energy function in the Laplace domain. This function is then expressed as a polynomial in transformed strain and tensorial damage variables using the integrity bases restricted by the initial orthotropic symmetry of the material. The constitutive relationships derived in the Laplace domain are then converted to the time domain by using the inverse Laplace transform. The model is applied to the specific case of cross-ply laminates with transverse matrix cracks. The material coefficient functions appearing in the model are determined by a numerical (finite element) method for one cross-ply laminate configuration at one damage level. Predictions of the viscoelastic response are then made for the same laminate at other damage levels and for other cross-ply laminate configurations at different damage levels. These predictions agree well with independently determined time variations of properties by an analytic method (Kumar and Talreja, 2001, Linear viscoelastic behavior of matrix cracked cross-ply laminates. Mechanics of Materials 33 (3), 139-154) as well as with the numerically calculated values. Extension of the model to incorporate effects of transient temperature, physical aging and moisture is outlined

The linear viscoelastic behavior of matrix cracked symmetric cross-ply laminates is studied. A lower bound solution and an approximate 3D solution to the properties are obtained by using the elastic-viscoelastic correspondence principle. The accuracy of Schapery's approximate Laplace inversion technique in the solution procedure is discussed

Fatigue testing of 5-harness satin woven laminates indicates damage in the form of matrix cracking in transverse bundles and internal delamination at the tip of these cracks. These damage entities reduce the overall elastic properties of the laminate. The woven laminate is modeled by approximating it to an equivalent cross-ply laminate. The evolution of cracks during constant amplitude fatigue loading is explained by modeling both the cracks and internal delamination and assuming frictional stresses at the delaminated interface

Approximate analytical solutions based on a variational approach are presented for stresses in two cross-ply laminates, [90m/0n]s and [0m/90n]s, with matrix cracks in the 90° layers, subjected to bending. The analysis assumes a plane stress state in longitudinal sections of the laminate and accounts for the lack of symmetry caused by partially closed crack planes or by cracks present on one side of the laminate mid-plane. Comparisons with finite element analysis for laminates of glass/epoxy and graphite/epoxy show that the stress components in the cracked layers in the regions of interest are in good agreement with analytical results. The model is therefore suitable for predicting matrix crack multiplication in addition to estimating the residual flexural stiffness. The results obtained show that the transverse normal stress at the 0/90 interface is compressive for [0/90]s laminate, while this stress is tensile in regions of the interface closer to the crack for the [90/0]s laminate. Thus the analysis suggests that delamination is possible under bending in the [90/0]s laminate.

While low-order measures of damage have sufficed to describe the stiffness of bodies with distributed voids or cracks, such as the void volume fraction or the crack density tensor of Vakulenko, A.A., Kachanov, M., 1971., addressing the growth of distributed defects demands a more comprehensive description of the details of defect configuration and size distribution. Moreover, interaction of defects over multiple length scales necessitates a methodology to sort out the change of internal structure associated with these scales. To extend the internal state variable approach to evolution, we introduce the notion of multiple scales at which first and second nearest-neighbor effects of nonlocal character are significant, similar to homogenization theory. Further, we introduce the concept of a cutoff radius for nonlocal action associated with a representative volume element (RVE), which exhibits statistical homogeneity of the evolution, and flux of damage gradients averaged over multiple subvolumes. In this way, we enable a local description at length scales below the RVE. The mean mesoscale gradient is introduced to reflect systematic differences in size distribution and position of damage entities in the evolution process. When such a RVE cannot be defined, the evolution is inherently statistically inhomogeneous at all scales of reasonable dimension, and the concept of macroscale gradients of internal variables is the only recourse besides micromechanics. Based on a series of finite element calculations involving evolution of 2D cracks in brittle elastica arranged in random periodic arrays, we examine the evolution of the mean mesoscale gradients and note some preliminary implications for the utility of such an approach.

The effect of damage patterning on elastic moduli and damage evolution in ideal brittle cracked solids is examined. Key limitations associated with typical continuum damage mechanics approaches are addressed. Critical shortcomings arising from the use of spatially-averaged damage descriptors in the evaluation of effective moduli and thermodynamic forces are investigated using numerical simulations of evolving two-dimensional crack systems. Fundamental elements of a higher-order continuum description of damage based on distribution functions are discussed, which directly include damage interaction effects.

Recent micromechanically inspired phenomenological theories using internal state variable (ISV) representations of damage have been used to predict the thermomechanical behavior of microcracked solids. These models do not, in an explicit manner, account for distributions of microcracks in a representative volume element (RVE) and have been used success-fully only to determine the effective moduli of damaged solids. It has been demonstrated that while the distribution and interaction of damage entities within an RVE generally have a minor effect on the effective moduli, it has a significant effect on the evolution of damage and failure at the macroscale. Damage evolution rates, in general, cannot be described adequately by such theories because of their inability to account for interactions between damage entities in an arbitrary distribution. Key issues pertaining to the development of viable damage evolution equations using a continuum damage mechanics approach are addressed. In particular, limitations associated with the use of ISVs that can be expressed either in terms of macroscopically measurable quantities or through a spatial average of the geometric features of individual damage entities are discussed. Numerical simulations of evolving crack systems in two-dimensional perfectly brittle solids indicate that "effective stress" models may have difficulty in characterizing damage evolution in brittle microcracked solids when the damage consists of cracks of variable size or spatial distributions. An argument for implementing ISVs based on higher-order moments of the damage distribution within an RVE is presented.

A methodology is proposed for the construction of a representative volume element (RVE) for analysis of laminated composites containing two arrays of ply cracks running in different directions. The only requirement is that the cracks in any ply are uniformly spaced, and if more than one ply of a given orientation is cracked, then the crack spacing of individual plies must only be in exact multiples of each other. The spacing of cracks in the two directions can be fully independent. The RVE is constructed through a systematic consideration of translational symmetries present in the cracked laminate. As a result, the boundary conditions on the RVE can be imposed without compromising accuracy. Examples of the application of the RVE methodology are given to illustrate its broad capability and a finite element (FE) stress analysis is performed for these cases to illustrate results such as the crack surface displacements, local stress fields and RVE-averaged elastic properties. For one case, the average properties are compared with experimental results, showing good agreement.

The buckling behavior of a face layer debonded locally from the core of a sandwich panel is analyzed by considering a Euler beam on Winkler foundation with debonds subjected to in-plane compression. Exact closed form solutions of the buckling load and mode shape are obtained, and corresponding numerical results are given to illustrate the solution. Results indicate that the wrinkling wavelength of the perfectly bonded face layer can be used as an appropriate characteristic length for normalizing the debond length of a relatively long face layer. The effects of length and location of debonds and the end constraints of the face layer on the load carrying capacity are discussed. Interactive effects due to two debonds and the overlapping of debond faces are also studied. A master curve based on a classical solution is developed by employing the new normalization of the debond length. A modification to the usual Winkler foundation constants is made for an isotropic core, and it agrees very well with published results of a finite element analysis.

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic-viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.

Polymer-based composites are used in novel designs of jet engine fan blade containment cases. The performance of these structures is directly affected by its behavior under impact during a blade-out event. Here, we develop the basic ingredients of a multiscale modeling methodology, which includes a polymer model capable of accounting for intrinsic softening, tension-compression asymmetry, rate-sensitivity, thermal softening and kinematic-like hardening, as well as models of matrix cracking and fiber debonding. Material and fracture parameters are identified using epoxy data for various temperatures and strain rates. Results of unit-cell calculations are presented to discuss damage initiation and progression modes

Polymers and their composites are increasingly sought for applications where impact resistance constitutes an important design specification. One example of practical significance is the use of polymer-based composites in novel designs of fan blade containment cases (BCCs) of jet engines. During a blade-out event, a failed blade may penetrate the BCCs, but damage has to be contained within the composite. Here, we develop the basic ingredients of a multiscale modeling methodology with focus on the scale of the basic structural unit, where polymeric matrix and reinforcements are explicitly modeled. The polymer model accounts for nonlinear behavior, finite strains, intrinsic softening, tension- compression asymmetry, rate-sensitivity, thermal softening and kinematic-like hardening associated with macomolecular mechanisms of chain reorientations. In addition to the polymer model, models of matrix cracking and fiber debonding are used. The material parameters entering the macromolecular model are identified based on tests conducted on an untoughened epoxy resin for a wide range of temperatures and strain rates. Results from unit-cell calculations are presented to discuss damage initiation and progression as well as competition between modes of failure

Purpose - To provide a basis for making assessment of the safety of adhesively bonded joints after they have been de-painted by a dry abrasive method or a wet chemical method. Design/methodology/approach -Stress analysis by a finite element method has been conducted for metal/composite and composite/composite joints in a single lap configuration. The effects of degradation of composite and adhesive, separately or combined, on the stresses in the adhesive layer bonding the two components are studied. Effects of wet and dry conditions of de-painting are included in the study. It is assumed that in the composite these conditions affect only the laminae close to the surface from which the paint coating is removed. Findings - The locations and values of the maximum peel and shear stresses in the adhesive are determined for both joints under different assumed conditions of degradation caused by de-painting. Research limitations/implications - Experimental data indicating the extent of surface damage caused by de-painting is not available. Originality/value - Extensive literature study did not show any investigation of composite surface damage and adhesive property degradation on integrity of adhesively bonded joints. Results reported here will be of use in assessing effects of de-painting on the structural performance of adhesively bonded joints.

In this work an experimental investigation on damage initiation and evolution in laminates under cyclic loading is presented. The stacking sequence [0/θ2/0/-θ2]s has been adopted in order to investigate the influence of the local multiaxial stress state in the off-axis plies and the possible effect of different thickness between the thin (2-plies) and the thick (4-plies) layers. Results are presented in terms of S–N curves for the initiation of the first cracks, crack density evolution, stiffness degradation and Paris-like curves for the crack propagation phase. The values of the off-axis angle θ has been chosen in order to obtain local multiaxial stress states in the off-axis plies similar to those in previous studies for biaxially loaded tubes. Results concerning damage initiation and growth for these two specimen configurations are shown to be consistent for similar local multiaxial stress states

In this work an experimental investigation on damage initiation and evolution in laminates under cyclic loading is presented. The stacking sequence [0/θ2/0/−θ2]s has been adopted in order to investigate the influence of the local multiaxial stress state in the off-axis plies and the possible effect of different thickness between the thin (2-plies) and the thick (4-plies) layers. Results are presented in terms of S–N curves for the initiation of the first cracks, crack density evolution, stiffness degradation and Paris-like curves for the crack propagation phase. The values of the off-axis angle θ has been chosen in order to obtain local multiaxial stress states in the off-axis plies similar to those in previous studies for biaxially loaded tubes. Results concerning damage initiation and growth for these two specimen configurations are shown to be consistent for similar local multiaxial stress states

A thorough analysis of fatigue of composite laminates under multiaxial loading is presented. A large body of experimental data taken from the literature is examined to delineate the influence on the fatigue strength of factors such as biaxiality ratios and off-axis and out-of-phase angles. The data are found to clearly suggest that the ply-level shear biaxiality ratio, defined as the ratio of the shear stress amplitude to the largest normal stress amplitude, is the governing factor. The multiaxial fatigue criteria are examined next. The empirical method proposed by Ellyin and co-workers, based on the assumed log-linear fatigue life relationship, is compared with data. The Tsai-Hill and Smith-Pascoe quadratic polynomial criteria are also scrutinised. Finally, a mechanisms-based approach to multiaxial fatigue is outlined and proposed as the way to developing a reliable life prediction methodology

The paper presents a methodology for evaluating the effects of voids on the fracture behaviour of woven fabric composites. The particular model studied consists of a double cantilever beam (DCB) in which voids are placed ahead of the crack tip and the Mode I Strain Energy Release Rate (SERR) is calculated. The standard beam-on-elastic-foundation theory is modified to account for shear compliance and material orthotropy, and the new formulation is used to evaluate the deformed shape, elastic deformation energy and SERR. The presence of the voids is simulated as an unsupported zone in the elastic-foundation. The validation of the new analytical model, in terms of the deformed shapes and SERR values, is successfully carried out by suitable 2D finite element (FE) analyses. The effect of size, location and shape of the voids is investigated by a parametric study that showed that the enhancement of SERR increases with the size of the voids and the proximity to the crack tip and that elongated (elliptical) voids are more critical than the circular voids. Finally, the influence of more complex void distributions on the fracture toughness is evaluated by FE analysis.

This paper reports an experimental study of transverse cracking in 90(0) plies of (+/-theta(0)/90(2)(0))s laminates of graphite/epoxy. The constraint to this cracking process is varied by varying the angle theta to have the discrete values of 0(0), 15(0), 30(0) and 40(0). The evolution of crack density and the associated stiffness changes of the laminates are studied. The crack densities are measured in tensile specimens at increasing stress levels by examining the edge replicas under an optical microscope and the continuity of these cracks between the specimen edges is ascertained by X-ray radiography. The stiffness changes ate reported here and the stiffness-damage relationships are analyzed in a separate study.

This study examines the effect of manufacturing induced voids on failure of adhesive joints. A single lap joint with preexisting crack between the adherend and the adhesive is considered and the crack growth behavior is studied in the presence of a void in the adhesive. The analysis conducted is numerical using finite elements and a revised virtual crack closure technique for calculating the energy release rate of the interface crack. After verifying the numerical model for a case where analytical solution exists, it is used to gain insight into the failure of the adhesive joint by conducting a parametric study where the size, shape and location of the void with respect to the crack tip are varied. The case of two preexisting cracks on opposite interfaces in the presence of a void is also examined.

Damage in composite materials initiates at the length scale of one or a few fiber diameters, governed by the local stress fields. Further progression of the failure events is governed by conditions existing in a material volume representative of geometrical aspects such as fiber orientation and thickness of the plies, as well as the extent of stress field perturbations caused by damage entities. Failure of a composite structure occurs at attainment of a critical state in its response related to the designed functionality. Assessment of failure must therefore involve analyzing failure events from initiation until the relevant criticality state, with proper account of the length scales at which the respective failure mechanisms occur. Approaches for this purpose are necessarily of a multiscale nature. This chapter discusses a particular approach that incorporates the micro-, meso-, and macroscales in one single framework and is aimed at describing the deformational response of multidirectional composite laminates with multiple cracking in different orientations.