The effect of using thin plies to increase the bearing strength of composite laminates has been investigated. A series of 5 laminates of theoretically identical stiffness with varying proportions of thin plies were manufactured using a single material system. Four specimens from each plate were tested for bearing strength and damage was subsequently characterized using an optical microscope. The results show that performance in terms of bearing stiffness, strength at onset of damage, and ultimate bearing stress increase proportionally with the increasing amount of thin plies within the stack. Shifting from a 100% conventional ply laminate to a 100% thin-ply laminate gave an increase of 47% in the strength at onset of damage. Placement of the thin plies within the stack was also shown to be important for strength at initial onset of damage. Microscopic examination of the failure modes for all samples showed fiber kinking, localized to the center of the hole, to be the dominant failure mode regardless of the stacking sequence. © 2020 The Authors

This paper presents a new discrete parametrization method for simultaneous topology and material optimization of composite laminate structures, referred to as Hyperbolic Function Parametrization (HFP). The novelty of HFP is the way the candidate materials are parametrized in the optimization problem. In HFP, a filtering technique based on hyperbolic functions is used, such that only one design variable is used for any given number of material candidates. Compared to state-of-the-art methods such Discrete Material and Topology Optimization (DMTO) and Shape Function with Penalization (SFP), HFP has much fewer optimization variables and constraints but introduces additional non-linearity in the optimization problems. A comparative analysis of HFP, DMTO and SFP are performed based on the problem of maximizing the stiffness of composite plates under a total volume constraint and multiple manufacturing constraints using various loads, boundary conditions and input parameters. The comparison shows that all three methods are highly sensitive to the choice of input parameters for the optimization problem, although the performance of HFP is overall more consistent. HFP method performs similarly to DMTO and SFP in terms of the designs obtained and computational cost. However, HFP obtains similar or better objective function values compared to the DMTO and SFP methods. © 2021 The Author(s)

We propose a new deterministic robust design optimization method for composite laminate structures under worst-case material uncertainty. The method is based on a simultaneous parametrization of topology and material and combines a design problem and a material uncertainty problem into a single min–max optimization problem which provides an efficient approach to handle variation of material properties in stiffness driven design optimization problems. An analysis is performed using a design problem based on a failure criterion formulation to evaluate the ability of the proposed method to generate robust composite designs. The design problem is solved using various loads, boundary conditions and manufacturing constraints. The designs generated with the proposed method have improved objective responses compared to the worst-case response of designs generated with nominal material properties and are less sensitive to the variation of material properties. The analysis indicates that the proposed method can be efficiently applied in a robust structural optimization framework. © 2023 The Author(s)

We propose a method to analyze effects of material uncertainty in composite laminate structures optimized using a simultaneous topology and material optimization approach. The method is based on computing worst-case values for the material properties and provides an efficient way of handling variation in material properties of composites for stiffness driven optimization problems. An analysis is performed to evaluate the impact of material uncertainty on designs from two design problems: Maximization of stiffness and minimization of a failure criteria index, respectively. The design problems are solved using different loads, boundary conditions and manufacturing constraints. The analysis indicates that the influence of material uncertainty is dependent on the type of optimization problem. For compliance problems the impact on the objective value is proportional to the changes of the constitutive properties and the effect of material uncertainty is consistent and predictable for the generated designs. The strength-based problem shows that material uncertainty has a significant impact on the response, and the effects of material uncertainty is not consistent and changes for different design requirements. In addition, the results show an increase of up to 25% of the maximum failure index when considering the worst-case deviation of the constitutive properties from their nominal values. © 2022 The Author(s)

The degradation of the elastic properties of composite laminates with intralaminar cracks is caused by reduced stress in the damaged layer which is mainly due to two parameters: the crack opening displacement (COD) and the crack sliding displacement (CSD). In this paper these parameters are measured experimentally providing laminate stiffness reduction models with valuable information for validation of used assumptions and for defining limits of their application. In particular, the displacement field on the edges of a [0/ +704/ -704]s glass fiber/epoxy laminate specimens with multiple intralaminar cracks is studied and the COD and CSD dependence on the applied mechanical load is measured. The specimen full-field displacement measurement is carried out using ESPI (Electronic Speckle Pattern Interferometry). By studying the displacement discontinuities, the crack face displacements were measured. A comparison between the COD and the CSD (for the same crack) is performed

The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated. 

The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.

Intralaminar cracking in relatively thick 90-plies of [(Formula presented.)]s laminates is analyzed using experimental data for two Glass fiber/Epoxy (GF/EP) material systems. Weibull parameters for transverse failure stress of the 90-ply are obtained from experimental intralaminar crack density versus applied strain data, showing that a reliable analysis requires sufficient amount of data in so called noninteractive crack density region. Monte Carlo simulations of cracking were performed using stress distribution between two cracks calculated using two models: Hashin’s model and a novel model that ensures that the average stress is exactly the same as in FEM solution. Due to its features, the Hashin’s model predicts too low intralaminar crack density (it predicts too strong interaction between cracks). The results emphasize the importance of having a proper stress distribution model when performing Monte Carlo simulations. Simulations were used not only to simulate intralaminar cracking in high and very low crack density regions but also for improving the procedure of Weibull parameter determination.

Laminates with ultra-thin plies is a promising new development for polymeric composite materials expected to provide superior resistance to intralaminar crack propagation. The ply thickness effect on the crack initiation stress that according to some theoretical studies on fiber/matrix debonding does not depend on the ply thickness was investigated. Ultra-thin ply carbon fiber/epoxy cross-ply laminates subjected to tensile loading at room, –50, and –150°C temperatures relevant for cryogenic fuel storage, aeronautical, and aerospace applications were studied. The stochastic nature of the crack initiation stress in the 90°-plies was analyzed using Weibull strength distribution. The results obtained show delayed transverse crack initiation only in the thinnest plies with a clear trend that the scale parameter is much larger. This thickness effect on initiation is different than that for crack propagation which is observable in much larger ply thickness range. Regarding crack propagation, it was found that in most cases even at very high applied strain levels (1.5%) only a few transverse cracks have propagated from the specimen edges to its middle. 

The bending stiffness of carbon/epoxy and glass/epoxy cross-ply laminates with intralaminar cracks in the surface 90° plies and local delaminations were studied experimentally using 4-point bending tests. The bending stiffness is defined as the slope of the relation between the applied bending moment and the corresponding midplane curvature. To measure the midplane curvature of laminates with different damage states, the digital image correlation system was used. The reduction in the bending stiffness with increasing density of transverse cracks and delamination length was also analyzed using a 3-D FEM model. The analysis and optical microscopy observations showed that, in the initial stage of damage evolution, local delaminations were small, but with increasing load, the delaminations grew rapidly from the tips of existing and newly created cracks, enhancing the bending stiffness degradation. As an alternative to the 3-D FEM modelling of the test, analytical approaches in conjunction with the classical laminate theory were suggested. The analytical approach was based on the concept of the “effective stiffness of damaged ply,” where the initial stiffness of the damaged ply was replaced by the effective stiffness depending on the damage state. In the present work, two routines were used to determinate the effective stiffness of the damaged ply: a) back-calculation from the difference in the stiffnesses of damaged and undamaged laminates employing the FEM model of the representative volume element; b) simple analytical fitting functions. It is shown that the analytical approach suggested is accurate and convenient for predicting the degradation of bending stiffness of a laminate with an evolving microdamage. 

During the last decade new models for bending stiffness prediction of damaged composite laminates have been proposed in the literature advancing the earlier developed engineering approaches in accuracy and in complexity. However, experimental data for validation of complex analytical or engineering models are almost non-existent in the literature. In the present work a detailed experimental study was performed to investigate the bending stiffness reduction of composite cross-ply laminates with evolving micro-damage. Intralaminar cracks and local delaminations in the bottom surface 90-degree layer of carbon/epoxy and glass/epoxy cross-ply laminates were introduced in 4-point bending tests. Digital Image correlation (DIC) technique was used to experimentally determine the midplane curvature. The accuracy of beam theory for bending stiffness determination was assessed. The measured bending stiffness reduction with respect to transverse crack density was also compared with FEM predictions. The results show that the beam theory gives slightly underestimated curvature at low deflections, whereas at large deflections the beam theory overestimates the curvature and the moment–curvature relation becomes nonlinear. Nevertheless, the overall agreement between beam theory and DIC-based results is still very good, which leads to conclude that beam theory based data reduction schemes have sufficient accuracy for predicting bending stiffness even for highly damaged laminates. © 2022, The Author(s)

In the present work an experimental study of bending stiffness reduction was conducted on carbon/epoxy cross-ply laminates with surface 90° layers with different thicknesses. The initially undamaged laminate samples were statically loaded in 4-point bending by running loading-unloading steps with increasing maximum displacement levels, eventually leading to multiple transverse cracking in the surface 90° layers as well as formation of delaminations at the interface between the surface 90° layer and neighbouring 0° layer. Density of transverse cracks was quantified and presence of delaminations was qualitatively inspected after each loading-unloading step using optical microscopy. Digital image correlation (DIC) system was used to measure the complete displacement distribution of the laminate in the middle region between the load application points ensuring accurate determination of the laminate mid-plane curvature and the bending stiffness. The experimental results of bending stiffness reduction and the mid-plane curvature were compared with 3-D FEM calculation results, where a 4-point bending test of a laminate with parametrically variable transverse crack density and delamination length was simulated. The experimental and numerical results were also compared with analytical model based on Classical Laminate Theory (CLT), where the damaged layer in the laminate is homogenized and replaced by an undamaged layer with effective (reduced) stiffness properties. In the analytical model the effective properties of a damaged layer at any given transverse crack density and delamination length are back-calculated using the in-plane stiffness properties of a representative volume element (RVE) with and without damage. The calculated effective properties of the damaged layer are then used in CLT to predict the reduction of laminate bending stiffness. The predictions of bending stiffness reduction obtained with the analytical CLT based model yield good agreement with experimental and 3-D FEM results for the tested cross-ply laminate configurations. 

Simple approach based on Classical Laminate Theory (CLT) and effective stiffness of damaged layer is suggested for bending stiffness determination of laminate with intralaminar cracks in surface 90-layers and delaminations initiated from intralaminar cracks. The effective stiffness of a layer with damage is back-calculated comparing the in-plane stiffness of a symmetric reference cross-ply laminate with and without damage. The in-plane stiffness of the damaged reference cross-ply laminate was calculated in two ways: (1) using FEM model of representative volume element (RVE) and (2) using the analytical GLOB-LOC model. The obtained effective stiffness of a layer at varying crack density and delamination length was used to calculate the A, B and D matrices in the unsymmetrically damaged laminate. The applicability of the effective stiffness in CLT to solve bending problems was validated analyzing bending of the damaged laminate in 4-point bending test which was also simulated with 3-D FEM.

Simple approach based on Classical Laminate Theory (CLT) and effective stiffness of damaged layer is suggested for bending stiffness determination of laminate with intralaminar cracks in surface 90-layers. The effective stiffness of layer with cracks as a function of crack density is back-calculated comparing in-plane stiffness of laminates with and without damage. The accuracy of the CLT and effective stiffness approach is demonstrated comparing with bending stiffness results from FEM simulated 4-point bending test on laminate with damage. Analytical model for damaged laminate stiffness is presented which gives similar values for effective stiffness as FEM calculations for unit cell. Effect of local delaminations initiated from transverse cracks is analyzed.

Experimental and numerical studies were carried out to characterize hybrid thin- and thick-ply composite laminates and assess modelling capabilities. Five different composite laminates were manufactured using a single material system with varying proportions of thin plies (0%, 50%, and 100% thin-ply). Bearing tests were performed and the results from the tests were investigated. The results showed that performance, in terms of bearing strength at onset of damage and ultimate bearing stress, increased proportionally with the increasing amount of thin plies within the laminate. Microscopic examination of the failure modes for all laminates was performed at the center of the hole to determine the dominant failure mode. The numerical investigation uses a highly detailed mesoscale model previously validated for crash simulations but never used successfully to bearing damage areas. The results showed a good correlation regarding both the load response and the morphology of damage. 

Lightweight Production Technology (LWPT) is today a well-established technology in the automotive industry. By introducing light weight fixtures manufactured from Carbon Fiber Reinforced Plastics (CFRP) in aeronautical applications, new challenges as well as possibilities of in-situ health monitoring emerges. The present paper present results from experimental investigations using optical fibers with multiplex Bragg gratings (FBG) as strain gauges in an industrial CFRP fixture. Fixtures were manufactured of laminates made from CFRP. Measurements have been performed on a single CFRP beam with dimensions (8000 × 500 × 500 mm), used as a structural part in a larger assembly (9000 × 4000mm). The optical fibers were placed in between two laminates on two sides of the beam. The measurement data from the FBGs were compared and correlated to the measured displacements of the beam and the applied loads. The results show that for an eight meter long CFRP beam, it is possible to measure and detect displacements of 0.12 mm (load = 36kg), and resolve a displacement of 0.02 mm (Δload = 4.75kg). The experimental results were also compared to FEM calculations on the displacement of the beams when subject to the same load. Here measurements and calculations showed very good agreement. Overall the results imply that FBGs show a high potential as a suitable in-situ health monitoring of lightweight fixtures for the aeronautic industry as well as other applications.

The concept of the effective stiffness of a unidirectional layer with intralaminar cracks is revisited performing 3-D FEM parametric analysis of symmetric and balanced laminates with damaged 90-layer. The effective stiffness of the damaged layer is obtained from the difference between damaged and undamaged laminate stiffness. The effective longitudinal modulus and Poisson's ratio of the layer are equal to their initial values. A very simple expression for the effective transverse modulus change with normalized crack density has sufficient accuracy and generality to be used in laminate theory to predict macroscopic elastic property change with crack density in laminates with very different lay-ups and made of different UD composites.

The old concept of the effective stiffness of a 90-layer with intralaminar cracks is revisited performing 3-D FEM parametric analysis of symmetric and balanced laminates. It is shown, focusing on the effective transverse modulus, that the expected dependence of this property on composite elastic properties and laminate lay-up is very weak and follows very simple rules. Calculations show that the effective longitudinal modulus and Poisson’s ratio of the layer are not affected at all by intralaminar cracking. Simple fitting curve for effective transverse modulus change with normalized crack density is obtained from analysis of GF/EP cross-ply laminate. It is shown, comparing with FEM results and experimental data, that this expression can be used as a ‘master curve’ in laminate theory to predict macroscopic elastic property change with crack density in laminates with very different lay-ups and made of different unidirectional composites.