Interlaminar stresses in composite laminates: Thermoelastic deformation

An approximate elasticity solution for prediction of the displacement, stress and strain fields within the m-layer, symmetric and balanced angle-ply composite laminate of finite-width and subjected to uniform axial extension was developed earlier [4]. In the present paper, the authors have extended that solution to treat thermal stresses and deformations induced by a uniform change in laminate temperature. The results have revealed not only the complex fields within the laminate, but also inter-relationships between the lamina axial and shearing coefficients of thermal expansion and the effective laminate coefficients of thermal expansion. Further, the solution is shown to recover laminated plate theory predictions for thermally induced fields at interior regions of the laminate, thereby confirming the boundary layer nature of the interlaminar phenomena for the thermoelastic case. Finally, the results exhibit the anticipated response in congruence with the mechanical solution of Ref. [4] and the thermoelastic results satisfy the conditions of self-equilibration necessary for the finite-width laminate subjected to free thermal deformation. Integration of the stress σ_x over the laminate cross-section in the y–z plane is shown to converge to zero as the number of Fourier terms is increased. While the exact solution for mechanical loading is known to exhibit singular behavior, non-convergence of the interlaminar shearing strain is also seen to occur at the intersection of the free edge and planes between lamina of +θ and −θ orientation under thermal loading. The analytical results show excellent agreement with the finite-element predictions for the same boundary-value problem.     

Minimization of thermal expansion of symmetric, balanced, angle ply laminates by optimization of fiber path configurations

Optimal fiber path configurations that minimize the sum of the coefficients of thermal expansion (CTE) values along the principal material directions for a class of laminates are presented. Previous studies suggest that balanced, symmetric, angle ply laminates exhibit negative CTE values along the principal directions. Using the sum of the CTE values along the principal material directions as an effective measure of the coefficient of thermal expansion (CTE_eff), we have shown and provided a proof that the smallest value of CTE_eff is rendered by straight fiber path configurations. The laminates considered are sufficiently thin so as to neglect the thermal stresses induced through the thickness of the laminate. It is found that the minimal CTE_eff values occur for [+45/−45]_ns lay-ups. This result is supported by numerical studies that consider curvilinear fiber paths. The possibility of obtaining zero CTE values along both principal material directions and the conditions that render this situation are also examined.     

A non-local criterion for modelling unbalanced woven ply laminates with stress concentrations

A non-local ply scale criterion [Hochard C, Lahellec N, Bordreuil C. A ply scale non-local fibre rupture criterion for CFRP woven ply laminated structures. Compos Struct 2007;80:321–26] was previously developed for predicting the failure of balanced woven ply structures with stress concentrations. This non-local criterion was based on the mean values determined over a Fracture Characteristic Volume (FCV) corresponding to a cylinder with a circular area and the same thickness as the ply. This non-local approach along with a ply scale continuum damage behavioural model was implemented in the ABAQUS Finite Element Code. The behavioural model was developed from a classical Continuum Damage Mechanics (CDM) model [Ladevèze P. A damage computational method for composite structures. Comput Struct 1992;44:79–87]. In the present study, this approach was extended to the case of unbalanced woven ply. The FCV approach and the CDM behavioural model are presented and comparisons are made between the experimental data and the modelling predictions obtained on plates with open holes, notches and saw cuts.     

Fatigue life prediction of carbon fibre reinforced laminates by using cycle-dependent classical laminate theory

In this work a study about the adaption of the classical laminate theory for fatigue loads is presented. Cycle dependent stiffnesses of single UD 0°, UD 45° and UD 90° plies are implemented in order to calculate the fatigue-induced stiffness decrease of a multidirectional lay-up with the stacking sequence [0°/+45°/−45°/90°/90°/−45°/+45°/0°]. As second input alternative, UD 0°, UD 90° and ±45° plies are used. The calculated cycle-dependent stiffness parameters are compared to experimentally measured fatigue data of the multidirectional lay-up. The experimental test procedure used for the measurement of cycle-dependent stiffness parameters has been published previously. Results show that the experimentally measured stiffness decreases of the multidirectional lay-up can be estimated accurately based on the cyclic unidirectional input parameters.     

Acoustic structural health monitoring of composite materials : Damage identification and evaluation in cross ply laminates using acoustic emission and ultrasonics

The characterisation of the damage state of composite structures is often performed using the acoustic behaviour of the composite system. This behaviour is expected to change significantly as the damage is accumulating in the composite. It is indisputable that different damage mechanisms are activated within the composite laminate during loading scenario. These “damage entities” are acting in different space and time scales within the service life of the structure and may be interdependent. It has been argued that different damage mechanisms attribute distinct acoustic behaviour to the composite system. Loading of cross-ply laminates in particular leads to the accumulation of distinct damage mechanisms, such as matrix cracking, delamination between successive plies and fibre rupture at the final stage of loading. As highlighted in this work, the acoustic emission activity is directly linked to the structural health state of the laminate. At the same time, significant changes on the wave propagation characteristics are reported and correlated to damage accumulation in the composite laminate. In the case of cross ply laminates, experimental tests and numerical simulations indicate that, typical to the presence of transverse cracking and/or delamination, is the increase of the pulse velocity and the transmission efficiency of a propagated ultrasonic wave, an indication that the intact longitudinal plies act as wave guides, as the transverse ply deteriorates. Further to transverse cracking and delamination, the accumulation of longitudinal fibre breaks becomes dominant causing the catastrophic failure of the composite and is expected to be directly linked to the acoustic behaviour of the composite, as the stiffness loss results to the velocity decrease of the propagated wave. In view of the above, the scope of the current work is to assess the efficiency of acoustic emission and ultrasonic transmission as a combined methodology for the assessment of the introduced damage and furthermore as a structural health monitoring tool.     

Compressive response of Z-pinned woven glass fiber textile composite laminates: Experiments

In the first of this two part sequel, experimental results pertaining to the compressive response and failure of Z-pinned S-Glass fiber, plain-weave laminated composites are presented. These experiments are motivated by a need to understand the effect of Z-pinning on the strength and stiffness of these composites. A series of experiments are performed based upon density of the Z-pins and the diameter of the Z-pins. It is concluded that the damage zone around a Z-pin plays an important role in influencing the stiffness and strength of the Z-pin composite. In part 2 of this sequel, a 3D finite element (FE) based numerical model (based upon the composite microstructure acquired from scanning electron micrograph-SEM images) are used to capture details of the observed failure mechanisms and to provide predictions of the stiffness and strength of the composite.     

Mechanical property variability in FRP laminates and its effect on failure prediction

Results are presented from an experimental study for the modeling of stochastic behavior of a unidirectional Glass/Polyester composite. An analytical approach is developed for the prediction of failure under general in-plane loading including the variability of strength, stiffness and the thermal expansion coefficients. Monte Carlo simulation and the first-order reliability method are used for comparison and the new method is proved to be in good agreement. Following international design codes, a direct comparison is also presented for failure locii at a specific reliability level as derived by the various probabilistic approaches. Results reveal that a serious overestimation of the reliability of the composite structure is being made when the stochastic nature of the material elastic properties is not taken into account.     

Unit cell modelling of textile laminates with arbitrary inter-ply shifts

Deformation and failure mechanisms of textile laminates are strongly affected by mutual shift of the plies. To model arbitrarily stacked laminate within a traditional framework of multi-scale modelling, one must construct a representative volume element (RVE), which includes all the plies. This is a time consuming and computationally expensive work. As an alternative, the paper suggests a technique that allows setting problems on one unit cell of a single ply, i.e. a volume smaller than RVE of the laminate. The technique approximates the stress field in a ply by combination of stress fields obtained in two additional problems. Boundary conditions (BC) in these problems imitate the interaction of the unit cell with surrounding media. Once these problems are solved, the solution for arbitrary number of plies is composed analytically. The proposed technique respects inter-ply configurations, accounts for the number of plies, distinguishes the ply position, and reproduces the meso stress state with a good accuracy. The technique is validated against reference solutions obtained for the entire laminate.     

Characterization of microstructure in stitched unidirectional composite laminates

The internal geometry of stitched uniaxial multiply carbon-fiber preforms is investigated experimentally. The microstructure is parameterized by such four introduced parameters as distortion length, distortion width, minor axis and major axis. The quantificational measurements are performed for these parameters under different stitch densities and different stitch threads. A theoretical model, called fiber distortion model, is developed to describe the spatial distribution of in-plane fiber misalignment angle and inhomogeneous fiber volume fraction induced by stitching.     

Localised blast loading of fibre–metal laminates with a polyamide matrix

This paper presents the results of localised blast tests on fully clamped square fibre–metal laminate panels, manufactured using sheets of 2024-O aluminium alloy, woven glass–fibre reinforced polyamide and a polypropylene adhesive. The fracture properties of the composite–metal interface were determined using the single cantilever beam geometry and the measured interfacial fracture toughness was between values in the literature for thermosetting composites and aluminium/glass fibre polypropylene. Observations from blast experiments performed on panels with different stacking configurations are reported. Diamond and circular back face damage were observed, along with pitting, global displacement and tearing of the front face. Examinations of sectioned panels are presented and multiple debonding, plastic deformation and fibre fracture were identified within the panels.     

The role of temperature on impact properties of Kevlar/fiberglass composite laminates

This paper demonstrates results of an experimental study on Kevlar/fiberglass composite laminates subjected to impact loading at variable temperatures. The effect of temperature on maximum energy, elastic energy, maximum deflection, maximum impact force, ductility, and compression after impact was studied at several low velocity impact energy levels (8, 15 and 25 J). The temperatures considered were in the range of −50 to 120 °C. Results indicated that impact performance of these composites was affected over the range of temperature considered. Testing at ambient temperature is not fully sufficient and therefore additional testing must be performed for full understanding of composite laminate properties.     

Damage tolerance of fully orthotropic laminates in compression

The compression after impact (CAI) strength of fully orthotropic composite laminates with up to 21 plies is presented, as analysed by an existing strip model. Candidate layups, which can be symmetric, anti-symmetric or non-symmetric, are preselected to exhibit no elastic coupling response, with manufacturing rules applied. These criteria, along with the use of a simple surrogate sublaminate buckling model, were chosen to allow analysis of all feasible laminates in the design space without excessive computation time. Results indicate that although the inclusion of non-symmetric layups in the design space does not give benefits with respect to maximum achievable damage tolerance, these laminates can exhibit damage tolerance close to that of an anti-symmetric design for some ply counts, and better than symmetric solutions in most cases. It is also noted that in some instances increasing the number of plies in a laminate can actually reduce the highest achievable threshold load for damage tolerance, as a result of the large influence Poisson’s ratio has on sublaminate buckling. Average errors in the surrogate model were low in all cases, with maximum non-conservative errors less than 1%. The surrogate buckling model reduced computational time by over 99% when compared to the fully exhaustive search.     

Optimum laminate design by using singular value decomposition

In practice, a structure is subjected to given loads and boundary conditions, and a multitude of stress and strain states may exist in the structure; hence, optimal construction of a laminate in a structure cannot be sought by considering only a limited number of stress resultants in the existence of multiple load cases. Then, another design objective based on optimization of a laminate for the worst possible load case emerges which is formulated as a minimax problem whose solution is shown to be equivalent to singular value minimization problem. As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a composite material is equivalent to shaping the response of the material. As a novel approach, singular values are used for the layout optimization of laminate. In this method, the main idea is minimization of the largest singular value of the transfer function matrix between force/moment resultants and outputs stress/strain. Thus the overall optimization problem is reduced to a simple minimization problem. Numerical examples and finite element simulations are presented for several test problems. In particular, it is shown that the use of singular values and singular vectors is computationally advantageous in case of multiple load case.     

A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.     

Analytical and experimental studies on the low-velocity impact response and damage of composite laminates under in-plane loads with structural damping effects

In this paper, low-velocity impact response and damage of composite laminates under in-plane loads are analytically and experimentally investigated. The authors recently proposed a modified displacement field of plate theory, considering the effect of initially loaded in-plane strain, and used a finite element program to analyze the structural behavior of the composite laminate. In this study, the program is upgraded to account for the structural damping effect of the laminate. A pendulum type impact test system and an in-plane loading fixture are constructed for the experimental study. The analytical and experimental impact behaviors are compared at different impact energy levels for cases with an initial in-plane tensile load and a compressive load, as well as cases without the initial in-plane load. The results show good correspondence between the analytical and experimental impact force histories. The effect of the initial in-plane load reduces for higher impact energies. The numerical estimation of the damaged area is in good agreement with the results from C-scanning experiments.     

Analysis and design of RC structures strengthened with mechanically fastened FRP laminates: A review

The use of Mechanically Fastened Fiber Reinforced Polymer (MF-FRP) laminates is emerging as a viable alternative to adhesively bonded FRP laminates for the rehabilitation of reinforced concrete (RC) members such as beams and slabs. A recently published state-of-the-art review of the experimental research has demonstrated the viability and effectiveness of MF-FRP systems. This paper provides a state-of-the-art review of the analytical and numerical studies performed over the last decade with the aim of: (a) predicting the strength, the load-deformation response and the failure mode of rehabilitated RC members, and (b) accounting for the interfacial behavior between the concrete and the MF-FRP laminate. Ultimate strength models and constitutive models are critically reviewed based on their key assumptions and formulations and compares the analytical predictions with previously reported experimental results.