Applied Composite Materials (v.22, #6)

An analytical methodology has been developed to investigate the effect of fiber Poisson contraction on matrix multicracking evolution of fiber-reinforced ceramic-matrix composites (CMCs). The modified shear-lag model incorporated with the Coulomb friction law is adopted to solve the stress distribution in the interface slip region and intact region of the damaged composite. The critical matrix strain energy criterion which presupposes the existence of an ultimate or critical strain energy limit beyond which the matrix fails has been adopted to describe matrix multicracking of CMCs. As more energy is placed into the composite, matrix fractures and the interface debonding occurs to dissipate the extra energy. The interface debonded length under the process of matrix multicracking is obtained by treating the interface debonding as a particular crack propagation problem along the fiber/matrix interface. The effects of the interfacial frictional coefficient, fiber Poisson ratio, fiber volume fraction, interface debonded energy and cycle number on the interface debonding and matrix multicracking evolution have been analyzed. The theoretical results are compared with experimental data of unidirectional SiC/CAS, SiC/CAS-II and SiC/Borosilicate composites.
Keywords: Ceramic matrix composites (CMCs); Matrix cracking; Interface debonding

Modelling Strategies for Predicting the Residual Strength of Impacted Composite Aircraft Fuselages by Frederic Lachaud; Christine Espinosa; Laurent Michel; Pierre Rahme; Robert Piquet (599-621).
Aeronautic Certification rules established for the metallic materials are not convenient for the composite structures concerning the resistance against impact. The computer-based design is a new methodology that is thought about to replace the experimental tests. It becomes necessary for numerical methods to be robust and predictive for impact. Three questions are addressed in this study: (i) can a numerical model be “mechanically intrinsic” to predict damage after impact, (ii) can this model be the same for a lab sample and a large structure, and (iii) can the numerical model be predictive enough to predict the Compression After Impact (CAI)? Three different computational strategies are used and compared: a Cohesive Model (CM), a Continuous Damage Model (CDM) coupling failure modes and damage, and a Mixed Methodology (MM) using the CDM for delamination initiation and the CM for cracks propagation. The first attempts to use the Smooth Particle Hydrodynamics method are presented. Finally, impact on a fuselage is modelled and a numerical two-stage strategy is developed to predict the CAI.
Keywords: Composite Materials; Delamination; Crack Propagation; Mixed Mode; Compression After Impact; Smooth Particle Hydrodynamics

Investigation of Buckling Behavior of Composite Shell Structures with Cutouts by Mariano A. Arbelo; Annemarie Herrmann; Saullo G. P. Castro; Regina Khakimova; Rolf Zimmermann; Richard Degenhardt (623-636).
Thin-walled cylindrical composite shell structures can be applied in space applications, looking for lighter and cheaper launcher transport system. These structures are prone to buckling under axial compression and may exhibit sensitivity to geometrical imperfections. Today the design of such structures is based on NASA guidelines from the 1960’s using a conservative lower bound curve generated from a database of experimental results. In this guideline the structural behavior of composite materials may not be appropriately considered since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. It is clear that with the evolution of the composite materials and fabrication processes this guideline must be updated and / or new design guidelines investigated. This need becomes even more relevant when cutouts are introduced to the structure, which are commonly necessary to account for access points and to provide clearance and attachment points for hydraulic and electric systems. Therefore, it is necessary to understand how a cutout with different dimensions affects the buckling load of a thin-walled cylindrical shell structure in combination with other initial geometric imperfections. In this context, this paper present some observations regarding the buckling load behavior vs. cutout size and radius over thickness ratio, of laminated composite curved panels and cylindrical shells, that could be applied in further recommendations, to allow identifying when the buckling of the structure is dominated by the presence of the cutout or by other initial imperfections.
Keywords: Shell buckling; Cylinder with openings; Knock-down factor; Thin-walled structures; Composite materials; Finite element model

The reliability of composite structures depends, among other damage mechanisms, on their ability to withstand delaminations. In order to have a better understanding of the cohesive zone method technique for delamination simulations, a complete analysis of the multiple parameters influencing the results is necessary. In this paper the work is concentrated on the cohesive zone method using cohesive elements. First a summary of the theory of the cohesive zone method is given. A numerical investigation on the multiple parameters influencing the numerical simulation of the mode I and mode II delamination tests has been performed. The parameters such as the stabilization method, the output frequency, the friction and the computational efficiency have been taken into account. The results will be compared to an analytical solution obtained by linear elastic fracture mechanics. Additionally the numerical simulation results will be compared to the experimental results of a glass-fibre reinforced composite material for the mode I Double Cantilever Beam (DCB) and to a carbon fibre 5-harness satin weave reinforced polyphenylene sulphide composite for the mode I DCB and mode II End Notched Flexure (ENF).
Keywords: Composites; Critical strain energy release rate; Double cantilever beam (DCB); End notched flexure (ENF); Failure mode; Delamination

Experimental Tests on the Composite Foam Sandwich Pipes Subjected to Axial Load by Feng Li; QiLin Zhao; Kang Xu; DongDong Zhang (669-691).
Compared to the composite thin-walled tube, the composite foam sandwich pipe has better local flexural rigidity, which can take full advantage of the high strength of composite materials. In this paper, a series of composite foam sandwich pipes with different parameters were designed and manufactured using the prefabricated polyurethane foam core-skin co-curing molding technique with E-glass fabric prepreg. The corresponding axial-load compressive tests were conducted to investigate the influence factors that experimentally determine the axial compressive performances of the tubes. In the tests, the detailed failure process and the corresponding load–displacement characteristics were obtained; the influence rules of the foam core density, surface layer thickness, fiber ply combination and end restraint on the failure modes and ultimate bearing capacity were studied. Results indicated that: (1) the fiber ply combination, surface layer thickness and end restraint have a great influence on the ultimate load bearing capacity; (2) a reasonable fiber ply combination and reliable interfacial adhesion not only optimize the strength but also transform the failure mode from brittle failure to ductile failure, which is vital to the fully utilization of the composite strength of these composite foam sandwich pipes.
Keywords: Composite foam sandwich pipe; Compressive performance; Experimentation; Failure mode; Ultimate bearing capacity; Axial load

Long-Term Viscoelastic Response of E-glass/Bismaleimide Composite in Seawater Environment by Zhao Yian; Wang Zhiying; Seah Leong Keey; Chai Gin Boay (693-709).
The effect of seawater absorption on the long-term viscoelastic response of E-glass/BMI composite is presented in this paper. The diffusion of seawater into the composite shows a two-stage behavior, dominated by Fickian diffusion initially and followed by polymeric relaxation. The Glass transition temperature (Tg) of the composite with seawater absorption is considerably lowered due to the plasticization effect. However the effect of water absorption at 50 °C is found to be reversible after drying process. The time-temperature superposition (TTS) was performed based on the results of Dynamic Mechanical Analysis to construct the master curve of storage modulus. The shift factors exhibit Arrhenius behavior when temperature is well below Tg and Vogel-Fulcher-Tammann (VFT) like behavior when temperature gets close to glass transition region. As a result, a semi-empirical formulation is proposed to account for the seawater absorption effect in predicting long-term viscoelastic response of BMI composites based on temperature dependent storage modulus and TTS. The predicted master curves show that the degradation of storage modulus accelerates with both seawater exposure and increasing temperature. The proposed formulation can be applied to predict the long-term durability of any thermorheologically simple composite materials in seawater environment.
Keywords: Water diffusion; Bismaleimide; Time-temperature superposition; Viscoelasticity

Interaction mechanism between the intralaminar damage and interlaminar delamination of composite laminates is always a challenging issue. It is important to consider the progressive failure and strain softening behaviors simultaneously during the damage modeling and numerical simulation of composites using FEA. This paper performs three-dimensional finite element analysis of the progressive failure and strain localization of composites using FEA. An intralaminar progressive failure model based on the strain components is proposed and the nonlinear cohesive model is used to predict the delamination growth. In particular, the nonlocal integral theory which introduces a length scale into the governing equations is used to regularize the strain localization problems of composite structures. Special finite element codes are developed using ABAQUS to predict the intralaminar and interlaminar damage evolution of composites simultaneously. The carbon fiber/epoxy composite laminates with a central hole demonstrates the developed theoretical models and numerical algorithm by discussing the effects of the mesh sizes and layups patterns. It is shown the strain localization problem can be well solved in the progressive failure analysis of composites when the energy dissipation due to the damage of the fiber, matrix and interface occurs at a relatively wide area.
Keywords: Composite laminates; Progressive failure; Strain localization; Cohesive model; Finite element analysis (FEA)

The matrix multicracking evolution of cross-ply ceramic-matrix composites (CMCs) has been investigated using energy balance approach. The multicracking of cross-ply CMCs was classified into five modes, i.e., (1) mode 1: transverse multicracking; (2) mode 2: transverse multicracking and matrix multicracking with perfect fiber/matrix interface bonding; (3) mode 3: transverse multicracking and matrix multicracking with fiber/matrix interface debonding; (4) mode 4: matrix multicracking with perfect fiber/matrix interface bonding; and (5) mode 5: matrix multicracking with fiber/matrix interface debonding. The stress distributions of four cracking modes, i.e., mode 1, mode 2, mode 3 and mode 5, are analysed using shear-lag model. The matrix multicracking evolution of mode 1, mode 2, mode 3 and mode 5, has been determined using energy balance approach. The effects of ply thickness and fiber volume fraction on matrix multicracking evolution of cross-ply CMCs have been investigated.
Keywords: Ceramic matrix Composites (CMCs); Cross-ply; Matrix cracking; Energy balance approach

This paper investigates the elastic and failure behavior of textile composite laminates by using an analytical multi-scale correlating approach. The analyses are performed under the four scale levels, i.e. the laminate scale, representative unit cell (RUC) scale, tow architecture scale and fiber/matrix scale levels. The correlation between different scales is derived based on the continuum mechanics and homogenization method from which the stress and strain fields in multiple scales can be obtained concurrently. Effective modulus and ultimate failure strengths of different textile composite (plain weave, twill weave and satin weave) laminates are predicted solely from the corresponding constituent properties, braid geometrical parameters and lay-up. The damage and failure mechanisms at the constituent level are also determined by the micromechanical failure criteria. All the predicted results compare favorably with available experimental data. Parametric studies are also performed to examine the effect of various mechanical and geometrical parameters on the resulting mechanical properties.
Keywords: Textile composites; Multi-scale modeling; Analytical; Mechanical properties; Strength

The stress–strain curves of fiber − reinforced ceramic − matrix composites (CMCs) exhibit obvious non-linear behaviour under tensile loading. The occurrence of multiple damage mechanisms, i.e., matrix multicracking, fiber/matrix interface debonding and fibers fracture, is the mainly reason for the non-linear characteristic. The micromechanics approach has been developed to predict the tensile stress–strain curves of unidirectional, cross-ply and woven CMCs. The shear-lag model was used to describe the micro stress field of the damaged composite. The damage models were used to determine the evolution of micro damage parameters, i.e., matrix crack spacing, interface debonded length and broken fibers fraction. By combining the shear-lag model with damage models and considering the effect of transverse multicracking in the 90° plies or transverse yarns in cross-ply or woven CMCs, the tensile stress–strain curves of unidirectional, cross-ply, 2D and 2.5D woven CMCs have been predicted. The results agreed with experimental data.
Keywords: Ceramic − matrix composites (CMCs); Stress–strain curve; Matrix cracking; Interface debonding; Fiber failure

For certification, novel fuselage concepts have to prove equivalent crashworthiness standards compared to the existing metal reference design. Due to the brittle failure behaviour of CFRP this requirement can only be fulfilled by a controlled progressive crash kinematics. Experiments showed that the failure of a twin-walled fuselage panel can be controlled by a local modification of the core through-thickness compression strength. For folded cores the required change in core properties can be integrated by a modification of the fold pattern. However, the complexity of folded cores requires a virtual design methodology for tailoring the fold pattern according to all static and crash relevant requirements. In this context a foldcore micromodel simulation method is presented to identify the structural response of a twin-walled fuselage panels with folded core under crash relevant loading condition. The simulations showed that a high degree of correlation is required before simulation can replace expensive testing. In the presented studies, the necessary correlation quality could only be obtained by including imperfections of the core material in the micromodel simulation approach.
Keywords: Crash; Explicit simulation; Sandwich structures; Foldcore; Energy absorption

The curing stresses in a newly proposed bi-axial residual stress testing configuration are studied using a chopped strand mat glass/epoxy specimen. In-situ monitoring of the curing is conducted using dielectric and fibre Bragg grating sensors. It is confirmed that a bi-axial residual stress state can be introduced in the specimens during curing and a quantification of its magnitude is presented. An alternative decomposition method used for converting the dielectric signal into a material state variable is proposed and good agreement with models found in the literature is obtained. From the cure cycles chosen it is suggested that any stress build up in the un-vitrified state is relaxed immediately and only stress build up in the vitrified state contributes to the residual stress state in the specimen.
Keywords: Polymer-matrix composites; Residual/internal stress; Process monitoring; Thermal analysis

Experimental data for Carbon/Carbon (C/C) constituent materials are combined with a three dimensional steady state heat transfer finite element analysis to demonstrate the average in-plane and out-of-plane thermal conductivities (TCs) of C/C composites. The finite element analysis is carried out at two distinct length scales: (a) a micro scale comparable with the diameter of carbon fibres and (b) a meso scale comparable with the carbon fibre yarns. Micro-scale model calculate the TCs at the fibre yarn scale in the three orthogonal directions (x, y and z). The output results from the micro-scale model are then incorporated in the meso-scale model to obtain the global TCs of the 3D C/C composite. The simulation results are quite consistent with the theoretical and experimental counterparts reported in references. Based on the numerical approach, TCs of the 3D C/C composite are calculated from 300 to 2500 K. Particular attention is given in elucidating the variations of the TCs with temperature. The multi-scale models provide an efficient approach to predict the TCs of 3D textile materials, which is helpful for the thermodynamic property analysis and structure design of the C/C composites.
Keywords: Carbon/Carbon composite; Thermal conductivity; Multiscale modeling; High temperature; Manufacturing defects

Experimental quasi-static tests were performed on center notched carbon fiber reinforced polymer (CFRP) composites having different stacking sequences made of G40-600/5245C prepreg. The three-dimensional Digital Image Correlation (DIC) technique was used during quasi-static tests conducted on quasi-isotropic notched samples to obtain the distribution of strains as a function of applied stress. A finite element model was built within Abaqus to predict the notched strength and the strain profiles for comparison with measured results. A user-material subroutine using the multi-continuum theory (MCT) as a failure initiation criterion and an energy-based damage evolution law as implemented by Autodesk Simulation Composite Analysis (ASCA) was used to conduct a quantitative comparison of strain components predicted by the analysis and obtained in the experiments. Good agreement between experimental data and numerical analyses results are observed. Modal analysis was carried out to investigate the effect of static damage on the dominant frequencies of the notched structure using the resulted degraded material elements. The first in-plane mode was found to be a good candidate for tracking the level of damage.
Keywords: Carbon fiber; Digital image correlation; Finite element modeling; Open-hole composites

The paper presents an homogenised core model suitable for use in the analysis of fuselage sandwich panels with folded composite cores under combined loading conditions. Within a multiscale numerical design process a failure criterion was derived for describing the macroscopic behaviour of folded cores under combined loading using a detailed foldcore micromodel. The multiscale modelling method was validated by simulation of combined compression/bending failure of foldcore sandwich panels.
Keywords: Computational modelling; Damage mechanics; Sandwich; Multiscale

Meshing Preprocessor for the Mesoscopic 3D Finite Element Simulation of 2D and Interlock Fabric Deformation by A. Wendling; J. L. Daniel; G. Hivet; E. Vidal-Sallé; P. Boisse (869-886).
Numerical simulation is a powerful tool to predict the mechanical behavior and the feasibility of composite parts. Among the available numerical approaches, as far as woven reinforced composites are concerned, 3D finite element simulation at the mesoscopic scale leads to a good compromise between realism and complexity. At this scale, the fibrous reinforcement is modeled by an interlacement of yarns assumed to be homogeneous that have to be accurately represented. Among the numerous issues induced by these simulations, the first one consists in providing a representative meshed geometrical model of the unit cell at the mesoscopic scale. The second one consists in enabling a fast data input in the finite element software (contacts definition, boundary conditions, elements reorientation, etc.) so as to obtain results within reasonable time. Based on parameterized 3D CAD modeling tool of unit-cells of dry fabrics already developed, this paper presents an efficient strategy which permits an automated meshing of the models with 3D hexahedral elements and to accelerate of several orders of magnitude the simulation data input. Finally, the overall modeling strategy is illustrated by examples of finite element simulation of the mechanical behavior of fabrics.
Keywords: Woven fabrics; Unit-cell model; Mesoscopic scale; 3D finite element simulations; 3D hexahedral mesh

An analytical method has been developed to investigate the effect of interface wear on fatigue hysteresis behavior in carbon fiber-reinforced ceramic-matrix composites (CMCs). The damage mechanisms, i.e., matrix multicracking, fiber/matrix interface debonding and interface wear, fibers fracture, slip and pull-out, have been considered. The statistical matrix multicracking model and fracture mechanics interface debonding criterion were used to determine the matrix crack spacing and interface debonded length. Upon first loading to fatigue peak stress and subsequent cyclic loading, the fibers failure probabilities and fracture locations were determined by combining the interface wear model and fiber statistical failure model based on the assumption that the loads carried by broken and intact fibers satisfy the global load sharing criterion. The effects of matrix properties, i.e., matrix cracking characteristic strength and matrix Weibull modulus, interface properties, i.e., interface shear stress and interface debonded energy, fiber properties, i.e., fiber Weibull modulus and fiber characteristic strength, and cycle number on fibers failure, hysteresis loops and interface slip, have been investigated. The hysteresis loops under fatigue loading from the present analytical method were in good agreement with experimental data.
Keywords: Ceramic-matrix composites (CMCs); Fatigue; Hysteresis loops; Interface wear; Matrix multicracking; Interface debonding

An analytical method has been developed to investigate the effect of oxidation on the tensile strength of carbon fiber − reinforced ceramic − matrix composites (CMCs). The Budiansky − Hutchinson − Evans shear − lag model was used to describe the micro stress field of the damaged composite considering fibers failure. The statistical matrix multicracking model and fracture mechanics interface debonding criterion were used to determine the matrix crack spacing and interface debonded length. The fiber strength degradation model and oxidation region propagation model have been adopted to analyze the oxidation effect on tensile strength of the composite, which is controlled by diffusion of oxygen gas through matrix cracks. Under tensile loading, the fibers failure probabilities were determined by combining oxidation model and fiber statistical failure model based on the assumption that fiber strength is subjected to two-parameter Weibull distribution and the loads carried by broken and intact fibers statisfy the global load sharing criterion. The composite can no longer support the applied load when the total loads supported by broken and intact fibers approach its maximum value. The conditions of a single matrix crack and matrix multicrackings for tensile strength considering oxidation time and temperature have been analyzed.
Keywords: Ceramic − matrix composites (CMCs); Tensile strength; Oxidation; Fibers failure; Matrix Cracking; Interface debonding

In this paper, the fatigue hysteresis loops of fiber-reinforced ceramic-matrix composites (CMCs) under multiple loading stress levels considering interface wear has been investigated using micromechanical approach. Under fatigue loading, the fiber/matrix interface shear stress decreases with the increase of cycle number due to interface wear. Upon increasing of fatigue peak stress, the interface debonded length would propagate along the fiber/matrix interface. The difference of interface shear stress existed in the new and original debonded region would affect the interface debonding and interface frictional slipping between the fiber and the matrix. Based on the fatigue damage mechanism of fiber slipping relative to matrix in the interface debonded region upon unloading and subsequent reloading, the interface slip lengths, i.e., the interface debonded length, interface counter-slip length and interface new-slip length, are determined by fracture mechanics approach. The fatigue hysteresis loops models under multiple loading stress levels have been developed. The effects of single/multiple loading stress levels and different loading sequences on fatigue hysteresis loops have been investigated. The fatigue hysteresis loops of unidirectional C/SiC composite under multiple loading stress levels have been predicted.
Keywords: Ceramic-matrix composites (CMCs); Fatigue; Hysteresis loops

This paper follows on from the earlier study (Part I) which investigated the fatigue behavior of unidirectional, cross-ply and 2.5D C/SiC composites at room and elevated temperatures. In this paper, a micromechanics approach to predict the fatigue life S−N curves of fiber-reinforced CMCs has been developed considering the fatigue damage mechanism of interface wear or interface oxidation. Upon first loading to fatigue peak stress, matrix multicracking and fiber/matrix interface debonding occur. The two-parameter Weibull model is used to describe fibers strength distribution. The stress carried by broken and intact fibres on the matrix crack plane under fatigue loading is determined based on the Global Load Sharing (GLS) criterion. The fibres failure probabilities under fatigue loading considering the degradation of interface shear stress and fibres strength have been obtained. When the broken fibres fraction approaches critical value, the composite would fatigue fail. The fatigue life S−N curves of unidirectional, cross-ply and 2.5D C/SiC composites at room and elevated temperatures have been predicted. The predicted results agreed with experimental data.
Keywords: Ceramic-matrix composites (CMCs); S−N curve; Life prediction; Fatigue; Hysteresis loops; Matrix multicracking; Interface debonding