Applied Composite Materials (v.23, #3)

A Joint Numerical-Experimental Study on Impact Induced Intra-laminar and Inter-laminar Damage in Laminated Composites by A. Riccio; F. Caputo; G. Di Felice; S. Saputo; C. Toscano; V. Lopresto (219-237).
The investigation of the mechanical response of fibre-reinforced composite laminates under impact loads can be very difficult due to the occurrence of simultaneous failure phenomena. Indeed, as a consequence of low velocity impacts, intra-laminar damages, like fibre and matrix cracking, and inter-laminar damages, such as delaminations, can take place simultaneously. These damage mechanisms can lead to significant reductions in strength and stability of the composite structure. In this paper a joint numerical-experimental study is proposed which, by means of non-destructive testing techniques (Ultra-sound and thermography) and non-linear explicit FEM analyses, aims to completely characterise the impact induced damage in composite laminates under low velocity impacts. Indeed the proposed numerical tool has been used to improve the understanding of the experimental data obtained by Non-Destructive Techniques. Applications on samples tested according to the AECMA (European Association of Aerospace Manufacturers) prEn6038 standard at three different impact energies are presented. The interaction between numerical and experimental investigation allowed to obtain an exhaustive insight on the different phases of the impact event considering the inter-laminar damage formation and evolution.
Keywords: Laminate; Impact behaviour; Finite element analysis (FEA); Damage mechanics; Non-destructive testing

The Sink Term to Different Kinds of Fibrous Mat During the Unsaturated Filling Process by Yongjing Lee; Shilin Yan; Dequan Lee; Fei Yan (239-253).
The fibrous pre-form of resin transfer molding is a dual-scale porous medium with two distinct scales of pores, i.e., pores in intra- and inter-tow, which produce an unsaturated infiltration phenomenon during filling. A sink term representing the delayed flow rate from the inter-tow gap into the intra-tow one is introduced to establish governing equations. This study mainly analyzes the sink term by tow saturation during the microscopic flow. First, fiber-tow permeability is calculated by FLOTRAN of ANSYS, Second, periodic unit cells are built according to different structures, and the concrete expression of the sink term is indirectly obtained through the numerical simulation and date fitting of tow saturation under different pressure and viscosity conditions. Results indicate that: the FLOTRAN module can be used to calculate the permeability of fiber tow in two directions; Moreover, the filling time and infiltration process for diverse unit cells with the same volume fraction are different; under the same injection condition, different unit cells have different parameters for the sink term.
Keywords: Unsaturated flow; RTM; Dual-scale; Sink term; Tow saturation rate

In this paper, a new numerical method that combines a surface-based cohesive model and extended finite element method (XFEM) without predefining the crack paths is presented to simulate the microscopic damage evolution in composites under uniaxial transverse tension. The proposed method is verified to accurately capture the crack kinking into the matrix after fiber/matrix debonding. A statistical representative volume element (SRVE) under periodic boundary conditions is used to approximate the microstructure of the composites. The interface parameters of the cohesive models are investigated, in which the initial interface stiffness has a great effect on the predictions of the fiber/matrix debonding. The detailed debonding states of SRVE with strong and weak interfaces are compared based on the surface-based and element-based cohesive models. The mechanism of damage in composites under transverse tension is described as the appearance of the interface cracks and their induced matrix micro-cracking, both of which coalesce into transversal macro-cracks. Good agreement is found between the predictions of the model and the in situ experimental observations, demonstrating the efficiency of the presented model for simulating the microscopic damage evolution in composites.
Keywords: Polymer-matrix composites (PMCs); Debonding; Matrix cracking; Finite element analysis (FEA); Transverse cracking

A Static Burst Test for Composite Flywheel Rotors by Stefan Hartl; Alexander Schulz; Harald Sima; Thomas Koch; Manfred Kaltenbacher (271-288).
High efficient and safe flywheels are an interesting technology for decentralized energy storage. To ensure all safety aspects, a static test method for a controlled initiation of a burst event for composite flywheel rotors is presented with nearly the same stress distribution as in the dynamic case, rotating with maximum speed. In addition to failure prediction using different maximum stress criteria and a safety factor, a set of tensile and compressive tests is carried out to identify the parameters of the used carbon fiber reinforced plastics (CFRP) material. The static finite element (FE) simulation results of the flywheel static burst test (FSBT) compare well to the quasistatic FE-simulation results of the flywheel rotor using inertia loads. Furthermore, it is demonstrated that the presented method is a very good controllable and observable possibility to test a high speed flywheel energy storage system (FESS) rotor in a static way. Thereby, a much more expensive and dangerous dynamic spin up test with possible uncertainties can be substituted.
Keywords: Flywheel energy storage systems; Polymer-matrix composites; Finite element analysis; Filament winding

Design and Manufacture of Conical Shell Structures Using Prepreg Laminates by Regina Khakimova; Florian Burau; Richard Degenhardt; Mark Siebert; Saullo G. P. Castro (289-312).
The design and manufacture of unstiffened composite conical structures is very challenging, as the variation of the fiber orientations, lay-up and the geometry of the ply pieces have a significant influence on the thickness imperfections and ply angle deviations imprinted to the final part. This paper deals with the manufacture of laminated composite cones through the prepeg/autoclave process. The cones are designed to undergo repetitive buckling tests without accumulating permanent damage. The aim is to define a process that allows the control of fiber angle deviations and the removal of thickness imperfections generated from gaps and overlaps between ply pieces. Ultrasonic scan measurements are used to proof the effectiveness of the proposed method.
Keywords: Prepreg; Buckling; Finite element modelling; Lay-up

An analytical method has been developed to investigate the effect of interface wear on the tensile strength of carbon fiber − reinforced ceramic − matrix composites (CMCs) under multiple fatigue loading. The Budiansky − Hutchinson − Evans shear − lag model was used to describe the micro stress field of the damaged composite considering fibers failure and the difference existed in the new and original interface debonded region. The statistical matrix multicracking model and fracture mechanics interface debonding criterion were used to determine the matrix crack spacing and interface debonded length. The interface shear stress degradation model and fibers strength degradation model have been adopted to analyze the interface wear effect on the tensile strength of the composite subjected to multiple fatigue loading. Under tensile loading, the fibers failure probabilities were determined by combining the interface wear model and fibers failure model based on the assumption that the fiber strength is subjected to two − parameter Weibull distribution and the loads carried by broken and intact fibers satisfy 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 corresponding to multiple fatigue peak stress levels and different cycle number have been analyzed.
Keywords: Ceramic − matrix composites (CMCs); Tensile strength; Interface wear; Fibers failure; Matrix multicracking; Interface debonding

In this paper, the relationship between hysteresis dissipated energy and temperature rising of the external surface in fiber-reinforced ceramic-matrix composites (CMCs) during the application of cyclic loading has been analyzed. The temperature rise, which is caused by frictional slip of fibers within the composite, is related to the hysteresis dissipated energy. Based on the fatigue hysteresis theories considering fibers failure, the hysteresis dissipated energy and a hysteresis dissipated energy-based damage parameter changing with the increase of cycle number have been investigated. The relationship between the hysteresis dissipated energy, a hysteresis dissipated energy-based damage parameter and a temperature rise-based damage parameter have been established. The experimental temperature rise-based damage parameter of unidirectional, cross-ply and 2D woven CMCs corresponding to different fatigue peak stresses and cycle numbers have been predicted. It was found that the temperature rise-based parameter can be used to monitor the fatigue damage evolution and predict the fatigue life of fiber-reinforced CMCs.
Keywords: Ceramic-matrix composites (CMCs); Fatigue; Hysteresis loops; Temperature rising

The damage evolution of unidirectional C/SiC ceramic-matrix composite (CMC) under cyclic fatigue loading has been investigated using a hysteresis loss energy-based damage parameter at room and elevated temperatures. The experimental fatigue hysteresis modulus and fatigue hysteresis loss energy versus cycle number have been analyzed. By comparing the experimental fatigue hysteresis loss energy with theoretical computational values, the interface shear stress corresponding to different cycle number and peak stress has been estimated. The experimental evolution of fatigue hysteresis loss energy and fatigue hysteresis loss energy-based damage parameter versus cycle number has been predicted for unidirectional C/SiC composite at room and elevated temperatures. The predicted results of interface shear stress degradation, stress–strain hysteresis loops corresponding to different number of applied cycles, fatigue hysteresis loss energy and fatigue hysteresis loss energy-based damage parameter as a functions of cycle number agreed with experimental data. It was found that the fatigue hysteresis energy-based parameter can be used to monitor the fatigue damage evolution and predict the fatigue life of fiber-reinforced CMCs.
Keywords: Ceramic-matrix composites (CMCs); Fatigue; Damage evolution

This paper presents a design methodology for optimizing the energy absorption under blast loads of cellular composite sandwich panels. A combination of dynamic finite element analysis (FEA) and simplified analytical modeling techniques are used. The analytical modeling calculates both the loading effects and structural response resulting from user-input charge sizes and standoff distances and offers the advantage of expediting iterative design processes. The FEA and the analytical model results are compared and contrasted then used to compare the energy response of various cellular composite sandwich panels under blast loads, where various core shapes and dimensions are the focus. As a result, it is concluded that the optimum shape consists of vertically-oriented webs while the optimum dimensions can be generally described as those which cause the most inelasticity without failure of the webs. These dimensions are also specifically quantified for select situations. This guidance is employed, along with the analytical method developed by the authors and considerations of the influences of material properties, to suggest a general design procedure that is a simple yet sufficiently accurate method for design. The suggested design approach is also demonstrated through a design example.
Keywords: Blast loads; Composite structures; Sandwich structures; Energy dissipation; Structural design; Dynamic structural analysis.

Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57–70 2014) to include delamination and simulated additional [45/−45/0/90]s and [02/90n]s {n = 1,2,3} CFRP laminates and a [0/903]s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90n/0] laminates that as the number of 90° ply increases past n = 2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.
Keywords: Fracture; Crack density; Finite element analysis (FEA); Composite materials

Liquid resin is injected into the tapered injection chamber through the injection slots to completely wetout the fiber reinforcements in a resin injection pultrusion process. As the resin penetrates through the fibers, the resin also pushes the fibers away from the wall towards the centerline causing compaction of the fiber reinforcements. The fibers are squeezed together due to compaction, making resin penetration more difficult; thus higher resin injection pressures are required to effectively penetrate through the fibers and achieve complete wetout. Fiber volume fraction in the final pultruded composite is a key to decide the mechanical and/or chemical properties of the composite. If the fiber volume fraction is too high, more fibers are squeezed together creating a fiber lean region near the wall and fiber rich region away from the wall. Also, the design of the injection chamber significantly affects the minimum injection pressure required to completely wet the fibers. A tapered injection chamber is considered such that wetout occurs at lower injection pressures due to the taper angle of the injection chamber. In this study, the effect of fiber volume fraction on the fiber reinforcement compaction and complete fiber wetout for a tapered injection chamber is investigated.
Keywords: Pultrusion; Fiber volume fraction; Resin viscosity; Fiber compaction; Fiber wetout

A line spring model is developed for analyzing the fracture problem of cracked metallic plate repaired with the double-sided adhesively bonded composite patch. The restraining action of the bonded patch is modeled as continuous distributed linear springs bridging the crack faces provided that the cracked plate is subjected to extensional load. The effective spring constant is determined from 1-D bonded joint theory. The hyper-singular integral equation (HSIE), which can be solved using the second kind Chebyshev polynomial expansion method, is applied to determine the crack opening displacements (COD) and the crack tip stress intensity factors (SIF) of the repaired cracked plate. The numerical result of SIF for the crack-tip correlates very well with the finite element (FE) computations based on the virtual crack closure technique (VCCT). The present analysis approaches and mathematical techniques are critical to the successful design, analysis and implementation of crack patching.
Keywords: Adhesively bonded composite repair; Cracked plate; SHIE; SIF; VCCT; FE analysis

This study proposes to simulate the deep drawing on carbon woven composites in order to reduce the manufacturing cost and waste of composite material during the stamping process, The multi-scale anisotropic approach of woven composite was used to develop a finite element model for simulating the orientation of fibers accurately and predicting the deformation of composite during mechanical tests and forming process. The proposed experimental investigation for bias test and hemispherical deep drawing process is investigated in the G1151 Interlock. The mechanical properties of carbon fiber have great influence on the deformation of carbon fiber composites. In this study, shear angle–displacement curves and shear load–shear angle curves were obtained from a bias extension test. Deep drawing experiments and simulation were conducted, and the shear load–displacement curves under different forming depths and shear angle–displacement curves were obtained. The results showed that the compression and shear between fibers bundles were the main deformation mechanism of carbon fiber woven composite, as well as the maximum shear angle for the composites with G1151 woven fiber was 58°. In addition, during the drawing process, it has been found that the forming depth has a significant influence on the drawing force. It increases rapidly with the increasing of forming depth. In this approach the suitable forming depth deep drawing of the sheet carbon fiber woven composite was approximately 45 mm.
Keywords: Carbon fiber woven; Bias test; Shear angle; Anisotropic approach; Finite elements modelling; Forming

This article proposes a model which takes the effect of matrix cracking into consideration and analyzes the mechanical behaviors of unidirectional ceramic matrix composites under stress-oxidation environment. The change in the rules of mass loss ratio, residual modulus and residual strength of unidirectional C/SiC composite under different stress, oxidation time, temperature and fiber volume fraction with the temperature varying from 400 to 900 °C have been discussed in this paper. The comparison between the predicted residual mechanics properties and the experiment results demonstrates that the predicted results have a good agreement with the experiment results, which means that the model is feasible to simulate mechanical behaviors of unidirectional C/SiC composite under stress oxidation environment.
Keywords: Unidirectional C/SiC; Under stress-oxidation environment; Matrix cracks; Mechanical behaviors

The computationally efficient simulation of the progressive damage behaviour of continuous fibre reinforced plastics is still a challenging task with currently available computer aided engineering methods. This paper presents an original approach for an energy based continuum damage model which accounts for stress-/strain nonlinearities, transverse and shear stress interaction phenomena, quasi-plastic shear strain components, strain rate effects, regularised damage evolution and consideration of load reversal effects. The physically based modelling approach enables experimental determination of all parameters on ply level to avoid expensive inverse analysis procedures. The modelling strategy, implementation and verification of this model using commercially available explicit finite element software are detailed. The model is then applied to simulate the impact and penetration of carbon fibre reinforced cross-ply specimens with variation of the impact speed. The simulation results show that the presented approach enables a good representation of the force-/displacement curves and especially well agreement with the experimentally observed fracture patterns. In addition, the mesh dependency of the results were assessed for one impact case showing only very little change of the simulation results which emphasises the general applicability of the presented method.
Keywords: Laminates; Fracture; Computational modelling; Damage mechanics