A linear finite element model to predict processing-induced distortion in FRP laminates

Manufacturing processes for laminated composites often produce parts whose dimensions do not match the mold from which they were made. This distortion is commonly referred to as ‘spring-in’. The amount of spring-in can depend on many factors including the manufacturing process (cure temperature, resin bleed, and applied pressure), the part (geometry, material, thickness, cure shrinkage, thermal expansion and layup sequence), and the tool (surface, thickness and thermal expansion). Much of the current work devoted to spring-in relies on extensive resin characterization. While this approach has been reasonably successful, it does little to assist the designer using material systems that have not been fully characterized (which is not always possible or feasible). This study considers the ability of a linear elastic finite element model to describe and quantify many of the factors contributing to spring-in. The aim of this study is to show that spring-in can be accurately predicted without a complete resin characterization. Numerical predictions based on relatively simple mechanical tests were observed to compare favorably with experimental measurements. Spring-in was dominated by thickness shrinkage, which contributed approximately 3/4 of the measured distortion. The mold stretching contribution diminished with thickness and was negligible for parts thicker than 2.5 mm (0.1 in.). While the material system at hand did not exhibit a fiber volume fraction gradient, its effects were included in the formulation of the model. For materials that have reported a gradient, it was found to account for approximately 10% of the part spring-in.     

Stress distribution modeling for interference-fit area of each individual layer around composite laminates joint

The discussion about nonuniform stress distribution around interference-fit joint is particular significance in the design of composite laminates structures. In order to investigate the stress distribution of interference-fit area around composite laminates joint, an analytical model is developed for stress distribution based on the Lekhnitskii's complex potential theory. The normal and tangential stresses of contact are achieved by the relationship of deformation between pin and hole. The effects of ply orientation and interference percentage on stress components distributions of each individual layer around symmetrical laminates joint are discussed. In order to verify the validity of the analytical model, extensive 3D finite element models are established to simulate the stress components of laminates interference-fit joint. The results show that the analytical model is valid, and the laminate property and ply orientation have a significant effect on stress distribution trend while interference percentage mainly affects stress magnitude.     

A composite cost model for the aeronautical industry: Methodology and case study

This paper presents a novel composite production cost estimation model. The strength of the model is its modular construction, allowing for easy implementation of different production methods and case studies. The cost model is exemplified by evaluating the costs of a generic aeronautical wing, consisting of skin, stiffeners and rib feet. Several common aeronautical manufacturing methods are studied. For studied structure, hand layup is the most cost-effective method for annual volumes of less than 150 structures per year. For higher production volumes automatic tape layup (ATL) followed by hot drape forming (HDF) is the most cost-effective choice.     

Determination of ply level residual stresses in a laminated carbon fibre-reinforced epoxy composite using constant,linear and quadratic variations of the incremental slitting method

Measurement of residual stresses in FRP composites is by no means a trivial task and there are no commonly applied or standardised methods currently available. As a result, characterisation of residual stresses is often avoided, resulting in the use of conservative safety margins, which has consequently resulted in structures being overdesigned. In the work described here, the incremental slitting method has been demonstrated to be a technique suitable for measuring residual stress in thin (∼0.3 mm) plies of a [0°₂/90°₂]_4s carbon fibre-reinforced epoxy laminate. The stresses measured using a constant stress approximation approach provided the best agreement with measurements obtained using the layer removal technique and stresses predicted using a semi-coupled transient-thermal and structural model.     

Nesting effect on the mode I fracture toughness of woven laminates

The fracture toughness of two woven laminates is evaluated for different nesting/shifting values between advanced layers. The analysed woven composites are manufactured using the same resin-reinforcement and same architecture, but have a different tow size (3K/12K). Three different nesting/shifting configurations are applied to the plies at the fracture surface: zero shifting, middle shifting and maximum shifting. Before being tested, the internal geometry of the material is evaluated and any shifting error is measured. For all these configurations mode I fracture tests are carried out. The differences obtained between 3K and 12K cases can be explained by fibre bridging, but not the differences between the nesting configurations. Depending on the nesting/shifting value the delaminated surface waviness is different, and consequently the fracture toughness is also influenced.     

Guidelines for flexural resistance of FRP reinforced concrete slabs and beams in fire

Several building codes are currently available for the design of concrete structures reinforced with fiber-reinforced polymer (FRP) bars. Nevertheless, there is little information provided about structural behavior in case of fire and no reliable design methods are available for FRP reinforced concrete (RC) members in fire. The goal of this paper is to provide guidelines for the calculation of the resistant bending moment of FRP-RC members exposed to fire in compliance with the provisions of Eurocodes, based on studies recently carried out by the authors. The paper provides a conceptual approach to fire safety checks for bending moment resistance of FRP-RC members. With reference to thermo-mechanical analysis, a simplified design method (for both thermal and mechanical analyses) for sagging bending moment resistance of FRP-RC slabs in fire situations is finally suggested.     

Characterisation of inter-ply shear in uncured carbon fibre prepreg

Understanding the inter-ply shear behaviour of uncured carbon fibre prepreg is fundamental to avoiding process-induced defects during manufacturing of large-scale components. Shear tests for AS4/8552 are compared to a one-dimensional viscoelastic–plastic model for inter-ply shear. The paper presents a methodology capable of determining the parameters of temperature, rate and pressure required for minimum resistance to movement of a prepreg. Investigating the joint strength and friction values individually shows that friction increases with temperature, contrary to previous work, and that the new value of joint strength is predominant at lower temperatures. Rate dependent variables are strongly linked to the resin behaviour, confirming the need for a viscoelastic model. Simple application to industrial scenarios is discussed along with more complex process modelling.     

Suitability of optimized truss model to predict the FRP contribution to shear resistance for externally bonded FRP strengthened RC beams without internal stirrups

Shortcoming in the current design guidelines on externally bonded FRP shear strengthened members has initiated a motivation to relook the whole shear design approach. It is understood that effective FRP strain models used in present design guidelines are basically calibrated from the experimental data based on the conservative and unrealistic 45-deg truss model. This paper is intended to propose an optimized truss model that derived from the principle of minimum total strain energy theorem to improve the present 45-deg truss model. The proposed optimized truss model is characterized with limiting failure criteria that reflects truly to the actual FRP strengthened beam behaviour. One of the most important failure criteria is the FRP debonding failure. To characterize it, limiting effective FRP strain ε_frp,e model is incorporated into the optimized truss model. Six most recent effective strain models are chosen for the analysis, included three of the international design guidelines. Performance of each effective strain model will be evaluated along with the optimized and 45-deg truss models in order to assess their respective accuracy in predicting the FRP contribution to the shear strength. The validation of optimized truss model is done through comparing with experimental test results collected from the literature. The results obtained indicated that the optimized truss model is indeed more viable representative to the actual internal stress distribution and accurate than existing 45-deg truss model. So it might have a great potential to be used in the derivation of a new effective FRP strain model that can be implemented in the current design guidelines.     

Investigation on the spring-in phenomenon of carbon nanofiber-glass fiber/polyester composites manufactured with vacuum assisted resin transfer molding

Process-induced residual stress arises in polymer composites as a result of mismatched resin contraction and fiber contraction during the cure stage. When a curved shell-like composite part is de-molded, the residual stress causes the spring-in phenomenon, in which the enclosed angle of the part becomes smaller than the angle of its mold. In this paper, a new approach is presented to control and reduce the spring-in angle by infusing a small amount of carbon nanofibers (CNFs) together with liquid resin into the glass fiber preform using vacuum assisted resin transfer molding (VARTM) process. The experimental results showed that the spring-in angles of the L-shaped composite specimens were effectively restrained by the CNFs. An analytical model and a 3-D FEA model were developed to predict the spring-in phenomenon and to understand the role of CNFs in reducing the spring-in angle. The models agreed with the experimental results reasonably well. Furthermore, the analytical model explains how the CNF-enhanced dimensional tolerance control is accomplished through the reductions in the matrix’s equivalent coefficient of thermal expansion and linear crosslinking shrinkage.     

A continuum damage model for glass/epoxy laminates in tension

The present work is concerned with the study of the damage behaviour of a composite material based on glass fibre reinforced polymer (GFRP). The main goal is to predict the rupture force using model equations that combine enough mathematical simplicity to allow their usage in engineering problems with the capability of describing a complex nonlinear mechanical behaviour. A model for tensile developed within the framework of Continuum Damage Mechanics that accounts for the effect of the load rate and temperature of the system is proposed and analyzed. The predicted values of tensile stress for different values of the load rate and temperature are compared with experimental data, showing a good agreement.     

An approach to the positioning of FRP provisions in vaulted masonry structures

In the paper, one starts from a theoretical formulation aimed at analysing masonry vaults by selecting, in an inverted approach, families of load shapes that may be equilibrated by sets of admissible solutions, in order to develop an operative method for the positioning of FRP reinforcements in masonry vaulted constructions. On the basis of this premise a strategy is outlined for identifying the areas of the vault to be selected for introducing the FRP provisions. As shown in the numerical investigation, higher intensities of the stress state are then allowed by the introduction of the reinforcement and the local relaxation of some of the constraints of the problem is possible.     

Harsh environments effects on the axial behaviour of circular concrete-filled fibre reinforced-polymer (FRP) tubes

Concrete-filled fibre-reinforced polymer (FRP) tubes (CFFTs) are becoming an attractive system for structural elements proposed to harsh environments. FRP tube provides a corrosion resistant element, reinforcement, confinement for the concrete core, and a stay-in-place formwork. Harsh environments may affect the mechanical performance of the FRP tube, which consequently affect the structural response of the CFFT members. This project investigates the environmental degradation and the durability of concrete cylinders unconfined and confined by filament-wound glass-FRP tubes. Standard plain concrete cylinders and CFFT cylinders were immersed in pure water, salt and alkaline solutions, and exposed to 200 freeze–thaw cycles, between −40 °C and +40 °C. Then, the cylinders were tested under uniaxial compression test to evaluate their performance by comparing the stress–strain behaviour and their ultimate load capacities. Test results indicated that the FRP tube, in CFFTs, is significantly qualified as a sustainable coating material to resist the harsh environments attacks. Theoretical predictions using long term confinement models from CSA and ACI codes are presented.     

Forming induced wrinkling of composite laminates: A numerical study on wrinkling mechanisms

When manufacturing composite aircraft components consisting of uni-directional prepreg laminates, Hot Drape Forming (HDF) is sometimes used. One issue with HDF is that, in contrast to hand lay-up where normally only one ply is laid up at a time, multiple plies are formed together. This limits the in-plane deformability of the stack, thus increasing the risk of out-of-plane wrinkling during forming. In this paper mechanisms responsible for creating different types of wrinkles are explained. It is shown through simulations how the wrinkles are created as a result of interaction between two layers with specific fibre directions or due to compression of the entire stack. The simulations are compared to experimental results with good agreement.     

Prediction of residual strength of CFRP after impact

It was found that the residual strength of CFRP after impact decreases as the impact energy increases when the energy is larger than the threshold impact energy. If the impact energy is sufficiently large, the influence of the mass of an impactor on the residual strength of the composite materials can be disregarded. Also, when the specimen is placed on a rigid plane, it was seen that the residual strength decreases as the diameter of the impactor nose increases. The residual strength after impact can be estimated by measuring the size of the permanent impression on the surface of composite materials after impact and applying the prediction equation for the residual strength proposed in this study.     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

A stochastic approach to model material variation determining tow impregnation in out-of-autoclave prepreg consolidation

Material variations are always present even though out-of-autoclave prepregs are machine-made. They strongly determine the consolidation and may eventually lead to voids within the final part, depending on applied process conditions. To capture any contingencies, stochastic differential equations are derived to describe various interacting phenomena in OoA consolidation. In a second step the probabilistic space is discretized using the Karhunen–Loève truncation and the Probabilistic Collocation method is applied in order to use deterministic solvers for flow and compaction problems. The initial degree of impregnation is represented by an Ornstein–Uhlenbeck process and calibrated with CT-images.     

Nesting effect on the mode II fracture toughness of woven laminates

The mode II fracture toughness is evaluated for carbon fibre T700-epoxy reinforced woven laminates using the end notch flexure set-up. The analysed woven composites have a different tow size (3K/12K). Three different nesting/shifting configurations are applied to the plies at the fracture surface. Corrected Beam Theory with effective crack length method (CBTE) and Beam Theory including Bending rotations effects method (BTBE) are evaluated for obtaining mode II fracture toughness. During data post-processing, the importance of the bending angle of rotation and the test configuration is observed to be important. The results show that crack propagation under mode II is more stable if the matrix is evenly distributed on the surface. The nesting does not significantly affect mode II fracture toughness values, although a greater presence of matrix on the delaminated area increases its value.     

Vacuum bag only co-bonding prepreg skins to aramid honeycomb core. Part I. Model and material properties for core pressure during processing

A process model was developed for the honeycomb core pressure during sandwich panel manufacturing. The model predicted the inflow of moisture from the cell walls into the cell void space using by Fick’s law, and the outflow of moist air through the bag-side skin was governed by Darcy’s law. The model required the core moisture content and honeycomb skin through-thickness air permeability to be experimentally measured. A partially saturated out-of-autoclave woven prepreg was used as the skin material in this study. In-order to accurately apply Darcy’s law during elevated temperature processing, an incremental temperature measurement technique was proposed to maintain constant skin thickness during air permeability characterization. Micro-CT imaging was performed on cure quenched samples to confirm that the proposed characterization technique maintained the impregnation dynamics of the target cure cycle. Model predictions using the characterized material properties are compared to in-situ core pressure measurements in Part II.     

Gas permeability of various graphite/epoxy composite laminates for cryogenic storage systems

Experiments were performed to investigate the effect of cryogenic cycling on the gas permeability of various composite laminates for cryogenic storage systems. Textile composites have lower permeability than laminated composites even with increasing number of cryogenic cycles. Nano-particles dispersed in one of the ply-interfaces in tape laminates do not show improvement in permeability. Micrographs of sections of various specimens provide some insight into formation of microcracks, and damage before and after cryogenic cycling. In laminated tape composites microcracks in various layers connect and form an easy path for gas leakage. Composites wherein plies of different orientations are dispersed rather than grouped show excellent performance even after cryogenic cycling. In textile composites the damage is restricted to regions contained by the weave yarns and hence the permeability does not increase significantly with cryo-cycling.