Ply Cracks Research Articles

Efficient modelling of progressive damage due to quasi-static indentation on multidirectional laminates by a mesh orientation independent kinematically enriched continuum damage model

This work proposes a computationally efficient high-fidelity modelling framework for analysis of damage in composites subjected to quasi-static indentation. A ply-by-ply modelling approach is adopted, and a new semi-discrete continuum damage model is used for intra-ply cracking that allows for cracks to grow independent of the ply mesh pattern. This feature greatly simplifies the meshing effort since the requirement of a ply-oriented mesh and imposition of tie constraints at mesh-mismatched ply interfaces is eliminated. The model is further enhanced to realise kinematic interactions between the cracked and uncracked material domains at the constitutive level. Inter-ply delamination is simulated using cohesive elements. Through a challenging problem of static indentation on a quasi-isotropic laminate, it is shown that the model can capture solution-dependent multiple discrete ply cracks and detailed crack-delamination interaction, but with reduced computational time and complexity, compared to a reference model with ply-oriented mesh and pre-seeded cracks at known locations.

Building blocks towards progressive fatigue damage modeling of a whole wind turbine blade

This paper presents a concise summary of the recent fatigue damage modeling research in the Mechanics of Materials and Structures (MMS) research group at Ghent University, which utilizes physics-based models and microscopic experiments to develop components for a progressive fatigue damage model of laminated composite structures. The paper discusses the evolution of ply cracking and delamination under cyclic loading and highlights distinct modeling elements for stress analysis and fatigue damage evolution characterization. It also explores the experiments required for model calibration and validation, including the use of digital image correlation to quantify damage mechanisms. Additionally, the paper discusses the use of neural networks for efficient and robust modeling of damage effects and outlines the remaining steps required to develop a comprehensive fatigue design tool. Finally, the recent developments with the BladeMesher software of the research group provide a platform to integrate this fatigue design tool for complete wind turbine blades.

Simulation of acoustic emission in carbon fiber-epoxy matrix composite laminates due to transverse cracking: effect of ply stacking sequence

This work focuses on the numerical simulation of the AE due to transverse cracking in laminate composites. The objective of the work is the experimental characterization and numerical simulation of the influence of the ply thickness and stacking sequence on transverse matrix cracking induced acoustic emission. AE signals induced by transverse matrix cracking are simulated numerically using finite elements (FE) for composite laminates exhibiting different number of plies and stacking sequences. 3D FE models of the specimens are set-up using Abaqus™ Standard. Either [0n/90n/0n] or [90n/0n/90n] (n=1 or 3) composite laminates are modeled, one ply thickness is 0.3 mm. Matrix transverse cracking in 90 deg. inner or outer ply is simulated. The influence of the ply thickness on acoustic emission signals recorded at the crack epicenter is significative only for inner ply transverse cracking, whereas similar signals are obtained for outer ply cracking. The frequency content of signals induced by outer ply transverse cracking does not depend on the ply thickness. Contrary to outer ply cracking, the influence of the ply thickness on inner ply transverse cracking induced signals is significative, especially on the frequency content, and on the frequency centroid only close to the crack (Fig. 1). Outer ply cracking rather exhibits signals with a low frequency content, not depending much on the ply thickness, contrary to inner ply cracking, for which the frequency content is higher and more dependent on the ply thickness. Fig.1: Frequency centroid as a function of distance between the source and the sensor obtained numerically for [0n/90 n/0n] and [90n/0n/90n] stacking sequences (n=1 or 3). Results obtained without sensor effect, with a virtual perfect sensor. EWGAE 35, Ljubljana, Slovenia, 13th – 16th Sep. www.ewg

A variational approach for accurate prediction of stress and displacement fields and thermo-elastic constants in general symmetric laminates containing ply cracking and delamination under general triaxial loading

Delamination induced by ply cracking is an important damage mechanism that results in stress redistribution and degrades both the in-plane and out-of-plane laminate properties. In this work, a novel variational model is first developed that accurately predicts stress and displacement fields in arbitrary symmetric laminates, containing uniformly spaced ply cracks in a single orientation with delaminations on the interfaces between the plies at the tips of ply cracks, subject to general triaxial loading and thermal residual stresses. The model is then used to predict the dependence of the in-plane and out-of-plane laminate thermo-elastic properties on ply crack density and delamination length. The results are extensively compared with those obtained from refined finite element methods and available experiments, showing excellent accordance.

A three-dimensional micromechanical model for simulating ply crack formation in laminates under in-plane tensile loading

Micromechanical models were established to simulate ply cracking in [0/90/0] laminates under tension. A new user-defined material model was developed within a finite element framework to capture inelastic deformation of the matrix and local cavitation-induced and ductile failure. A damage model was used to capture corresponding post-peak behaviour. Representative volume elements (RVEs) of laminates were generated, where the fiber and matrix constituents were explicitly represented in the 90° ply. The experimentally verified simulations revealed local matrix failure onset was governed by brittle cavitation, while subsequent microcracking was influenced by local ductile failure. The model accurately captured the delay in first full ply crack formation for laminates with thinner plies. The role of thermal residual stress, ply constraints, and fiber volume fraction on ply crack formation were investigated. The associated effective energy release rate was predicted and can be used for predicting ply crack multiplication in meso- or macro-scale models.

Phenomenological constitutive modeling of the non-linear loading-unloading response of UD fiber-reinforced polymers

The matrix-dominated mechanical response of a unidirectional carbon/epoxy system is studied through experiments and constitutive modeling. Experiments were performed on off-axis specimens to characterize the main factors controlling material’s diverse response under different loading conditions, and to measure the irreversible deformations occurring along the potential yield plane. Assuming that shear bands are precursors of ply cracks, and keeping in mind the physical characteristics of the material, a simple constitutive relation is offered to describe the plastic strain evolution and appearance of hysteresis behavior during loading and unloading. The latter is done by introducing a third component of strain, which was found to have a correlation with the level of plastic deformations the material has experienced. The proposed framework is able to reproduce the nonlinear monotonic and loading–unloading response of fiber-reinforced polymers under tension and compression, while taking into account the effects of multiaxial loading and different shear behaviors in longitudinal and transverse directions. This paper presents a broad perspective on the main factors controlling the material nonlinearity within a simple constitutive model, nevertheless, the model predictions show good agreement with experimental data.

Effects of hybridization on the tension–tension fatigue behavior of continuous-discontinuous fiber-reinforced sheet molding compound composites

This study is focused on the fatigue of sheet molding compounds (SMC) with a discontinuous (DiCo) glass fiber-reinforced core and continuous (Co) unidirectional ([0/DiCo/0]) or cross-ply ([0/90/DiCo/90/0]) carbon fiber-reinforced face layers. Tension-tension tests were conducted on the constituents (i.e., DiCo and Co SMC) and hybrid specimens. Hybridization effects were larger under cyclic than under monotonic loading. Constraining effects resulted in enhanced high fatigue strength of the Co plies in [0/DiCo/0]. [0/90/DiCo/90/0] was more sensitive to fatigue than [0/DiCo/0] due to localized damage starting from 90°-ply cracks. The S-N behavior of the hybrid was approximated from the behavior of DiCo SMC.

Micromechanical assessment of local failure mechanisms and early-stage ply crack formation in cross-ply laminates

Three-dimensional computational micromechanical models are developed to study local failure mechanisms and early-stage ply crack formation in a carbon fiber/epoxy [0/90/0] cross-ply laminate under tensile loading. Pressure-dependent inelastic deformation of the epoxy is captured by a user-defined material model, where brittle cavitation and ductile failure are considered local failure mechanisms. Manufacturing-induced defects, including nonuniform fiber spatial dispersion and resin pockets, are represented in the 90° ply. The effects of ply constraints on the local distortional and dilatational energy densities in the matrix are evaluated. Brittle cavitation is found to be the first and dominating failure mechanism, while local inelastic deformation indirectly influences the number and location of cavitation sites. Inelastic deformation is deemed necessary for predicting the linkage of the microcracks that are induced by brittle cavitation. The study provides important insight into the early-stage formation of ply cracks, which is essential for analyzing the subsequent ply crack formation.

Transverse Cracking Induced Acoustic Emission in Carbon Fiber-Epoxy Matrix Composite Laminates.

Transverse cracking induced acoustic emission in carbon fiber/epoxy matrix composite laminates is studied both experimentally and numerically. The influence of the type of sensor, specimen thickness and ply stacking sequence is investigated. The frequency content corresponding to the same damage mechanism differs significantly depending on the sensor and the stacking sequence. However, the frequency centroid does not wholly depend on the ply thickness except for the inner ply crack and a sensor located close enough to the crack. Outer ply cracking exhibits signals with a low-frequency content, not depending much on the ply thickness, contrary to inner ply cracking, for which the frequency content is higher and more dependent on the ply thickness. Frequency peaks and frequency centroids obtained experimentally are well captured by numerical simulations of the transverse cracking induced acoustic emission for different ply thicknesses.

A computational study about the effects of ply cracking and delamination on the stiffness reduction of damaged lamina and laminate

Accurate prediction of stiffness degradation in the damaged plies (laminae) is a fundamental requirement for developing damage models for composite materials. In this study, a mesoscale analysis is proposed to predict all the effective thermo-elastic constants of damaged plies containing ply cracks and delaminations based on a numerical homogenization method. To do so, the in-plane and out-of-plane loading conditions are imposed on the three-dimensional representative volume elements (RVEs) using the periodic boundary conditions (PBCs). Considering the stress/strain fields obtained from the numerical simulations, the effective behavior of the damaged plies is evaluated. Moreover, the effects of various damage configurations, material properties, orientations of adjacent plies and ply thicknesses are studied to address the dependency of the effective elastic constants to those parameters. Numerical results reveal that the ply cracking and delaminations significantly reduce the in-plane and out-of-plane properties ([Formula: see text], [Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) of the damaged plies. Furthermore, to demonstrate the accuracy and capability of the developed homogenization method, the homogenized properties of the damaged plies are used in the intact laminates where the stiffness of such laminates are compared with direct FE simulation and available experimental data of the laminates containing ply cracks and local delamination.

Approach for analysing off-axis tunnelling cracks in biaxially loaded laminates

A novel approach is presented on how the growth of off-axis tunnelling cracks in a composite laminate subjected to biaxial loads can be studied on an equivalent laminate with an another off-axis angle under uniaxial load. The primary objective is to determine the off-axis angle of the equivalent laminate such that the mode mixity of tunnelling cracks is identical to that of the tunnelling cracks in the original biaxially loaded laminate. The situation of steady state cracking is considered for both the laminates and the stress state at the crack front is expressed in terms of the mode mixity and the steady state energy release rate, both averaged across the cracked ply thickness. The approach is based on an energy accounting method that uses the crack opening displacements, obtained from a finite element analysis, and the principle of superposition to account for biaxial loads. Results are presented in terms of average energy release rates and average mode mixity for an isolated crack in an arbitrary oriented off-axis ply subjected to uniaxial and biaxial loads. The design of the equivalent uniaxially loaded laminate is analysed with reference to the general off-axis laminates subjected to a range of biaxial load ratios. With respect to testing, the presented approach can replace a complex biaxial fatigue test method with a more simple uniaxial fatigue test.

A micro-mechanical constitutive model for cracked plies of laminated composites considering the constraint effect of the adjacent plies

Three types of representative unit cell (RUC) of [±θ/904]S composite laminates and cracked plies were created to obtain the constitutive model of the cracked plies and to compare their accuracy of the calculation. The RUCs represent the damaged laminates, cracked plies, and cracked plies with additional constraints. A correction factor was defined to improve the accuracy of transverse modulus estimation using the RUC of cracked plies with constraints. The correction factor and numerical results were discussed to illustrate the constraint effect of the adjacent plies on the cracked plies in terms of stiffness, orientation, and thickness.

Multi-phase-field modelling of the elastic and buckling behaviour of laminates with ply cracks

The phase-field theory is a well-known mathematical model for solving interface problems, including crack problems in fracture mechanics. In this study, the formula is derived by variational approaches based on the Reissner-Mindlin plate kinematics and the multi-phase-field theory for simulation of the buckling phenomenon in cracked laminates. Phase-field parameters are defined independently in different plies of laminate to capture the crack behavior of each ply. Simulation is carried out to numerically investigate the stiffness reduction and buckling behavior of transverse cracked laminated composite plates. This paper focuses on the consideration of laminated composite plates, which have a crack in each layer. Therefore, this work is more complicated than the case of the plate has one crack throughout the plate thickness. The significant advancement of the phase-field approach for laminated composite plates with complex crack geometries is demonstrated.

Prediction of matrix crack initiation and evolution and their effect on the stiffness of laminates with off-axis plies under in-plane loading

A model is described which allows the exact calculation of stresses in a cracked ply under combined state of strain. Closed form expressions for the stresses in each ply are combined in an energy density-based criterion to predict crack spacing and the resulting transverse modulus and shear modulus. Inelastic effects due to non-linearities of the ply-level shear stress-strain curve are accounted for through computation of the permanent shear strain in the ply. The model accounts for ply thickness, stacking sequence and load redistribution effects of a relatively broad class of laminates. Comparisons with test results for a variety of laminates and materials show very good to excellent agreement. The approach developed is extremely efficient and can easily be incorporated in numerical progressive failure analysis, where the stiffness properties of each element can be updated every time the crack pattern changes and in fatigue analysis where the stiffness of a ply or a laminate can be determined during every load cycle.

Automatic edge detection of ply cracks in glass fiber composite laminates under quasi-static and fatigue loading using multi-scale Digital Image Correlation

Digital image correlation is utilized to detect automatically crack density in glass/epoxy laminates with different lay-ups under quasi-static and fatigue loading conditions. The DIC setups used in the present work are 2D-DIC and 3D-DIC which are considered to be at meso-scale and macro-scale, respectively. The main objective of this work is to study whether the DIC technique is reliable in automatic crack detection and functional in calculation of crack density. Therefore, an optimization analysis is implemented to evaluate the resolution and the standard uncertainty in strain and displacement measurements. An optimized compromise is attained between the resolution and the uncertainty of both measurements to decide about the final configuration of the DIC setup. The setup is executed by acquiring in-situ images under quasi-static and fatigue experiments so that the images are synchronized with the data acquired from the testing machine. The crack detection analysis is attained by DIC analysis using strain and displacement fields in order to obtain optimum results. Then a semi-automatic program is created to evaluate the crack density and weighted crack density from the edge and top of the specimen, respectively. Moreover, a comparison is established between both strain and displacement fields in crack characterization. Consequently, the displacement field has proved to deliver better and more accurate results than strain fields in crack density calculation and individual crack characterization. Accordingly, the results obtained from DIC analysis are compared and validated by microscopic images which are acquired after performing each test.

Assessing the effects of ply constraints on local stress states in cross-ply laminates containing manufacturing induced defects

Computational micromechanics is employed to assess the influence of ply constraints on the early stages of 90° ply crack formation in a cross-ply laminate under tensile loading. Manufacturing induced defects, including nonuniform fiber spatial distribution, microvoids and microcracks, are explicitly simulated. Local distortion and dilatation energy density values in the matrix, associated with local yielding and brittle cavitation, are assessed within unconstrained and constrained 90° plies. The effects of ply constraints are found to emerge when pre-existing microvoids or microcracks are present, while dissimilar levels of constraining are observed in distinct regions of the ply, e.g. fiber clusters versus resin-rich zones. These important results reveal that for constrained plies variations in the local deformation fields within these regions and their interdependency directly influence crack nucleation and its subsequent evolution. Additional parametric studies show the influence of pre-existing microvoid and microcrack sizes on the degree of ply constraining. Furthermore, the effect of the constrained and adjacent ply thicknesses, ply interface resin-rich layer thickness, and post-cure thermal cooldown on the degree of constraining are also considered. The study provides an improved understanding of the early stages of ply crack formation in constrained plies, which is important for predicting damage evolution in laminates and for using the lowest damage thresholds for safe designs.

Analytical model for determining effective stiffness and mechanical behavior of polymer matrix composite laminates using continuum damage mechanics

The present paper proposes a new analytical model for predicting the effective stiffness of composite laminates with fiber breaks and transverse cracks. The model is based on continuum damage mechanics and the classical laminate theory. We derived damage variables describing stiffness reduction due to fiber breaks and its maximum value during ultimate tensile failure from the global load-sharing model. Furthermore, a simplified analytical model is presented for obtaining two damage variables for a cracked ply subjected to transverse tensile loading or in-plane shear loading. This model was developed assuming that the displacement field of the longitudinal direction can be expressed in the form of a quadric function by loosening the boundary condition for the governing differential equation. For verifying the developed model, the elastic constants of damaged composite laminates were predicted for cross-ply and angle-ply laminates and compared with the finite element analysis results. As for the appropriate expression of the effective elastic stiffness matrix of the damaged ply, we verified four types of effective compliance/stiffness matrices including the Murakami, Yoshimura, Li, and Maimí models. We found the Maimí model to be the most appropriate among these four models. Moreover, we successfully simplified the expressions for damage variables in the complicated infinite series obtained in our previous study. We also proved that this could contribute toward improving the accuracy of our analysis. After verifying the present model, the stress–strain response and failure strength of carbon- or glass-fiber-reinforced plastic cross-ply laminates were predicted using Maimí’s compliance model and the simplified damage variables.

Ultrahigh Resolution Pulsed Laser-Induced Photoacoustic Detection of Multi-Scale Damage in CFRP Composites

This paper presents a photoacoustic non-destructive evaluation (pNDE) system with an ultrahigh resolution for the detection of multi-scale damage in carbon fiber-reinforced plastic (CFRP) composites. The pNDE system consists of three main components: a picosecond pulsed laser-based ultrasonic actuator, an ultrasound receiver, and a data acquisition/computing subsystem. During the operation, high-frequency ultrasound is generated by pulsed laser and recorded by an ultrasound receiver. By implementing a two-dimensional back projection algorithm, pNDE images can be reconstructed from the recorded ultrasound signals to represent the embedded damage. Both potential macroscopic and microscopic damages, such as surface notches and delamination in CFRP, can be identified by examining the reconstructed pNDE images. Three ultrasonic presentation modes including A-scan, B-scan, and C-scan are employed to analyze the recorded signals for the representation of the detected micro-scale damage in two-dimensional and three-dimensional images with a high spatial resolution of up to 60 µm. Macro-scale delamination and transverse ply cracks are clearly visualized, identifying the edges of the damaged area. The results of the study demonstrate that the developed pNDE system provides a non-destructive and robust approach for multi-scale damage detection in composite materials.

Closed-form formulae for prediction of homogenized ply-properties and laminate thermo-elastic constants in symmetric laminates containing ply cracks in multiple orientations

The aim of this study is to develop a novel model for predicting homogenized properties of a cracked ply in a symmetric laminate using the crack density and thickness of the ply. In doing so, the periodic boundary conditions are applied to the RVEs in a three-dimensional finite element model to calculate the thermo-elastic constants of symmetric laminates containing uniformly and non-uniformly spaced cracks under in-plane and out-of-plane loading conditions. On the other hand, homogenized material properties of the cracked ply are explicitly determined by averaging procedures for both stress and strain components. Using computed results and nonlinear least square fitting, an analytical formula is proposed to describe the mechanical properties of the cracked ply, which takes into account the effect of ply thickness, material properties and crack density. Different cracked laminates are tested to indicate the potential of the developed method in analyzing complex crack geometries in multiple orientations. Moreover, the applicability and accuracy of the suggested model are verified by comparing the results with those of experiments, variational approach and finite element method.

Variational analysis of cracking in general composite laminates subject to triaxial and bending loads

A robust variational approach is first developed for predicting stress/displacement fields and effective thermo-elastic constants in a laminate with arbitrary lay-up, containing uniformly spaced ply cracks, subject to general triaxial and bending loads when the effects of thermal residual stresses are also considered. The methodology extends some previously developed variational approaches so that general non-symmetric lay-ups (not only cross-ply) under through-thickness loading conditions can be analyzed. Secondly, an approximate methodology is introduced which enables the approach to predict all effective thermo-elastic constants of laminates having non-uniformly spaced ply cracks, including new types of constant required to account for out-of-plane loading. Thirdly, some novel inter-relationships among effective thermo-elastic constants of cracked and uncracked general laminates are obtained showing that just three macroscopic parameters define the dependence of all relevant laminate constants (thirty five) on the state of cracking. The results are compared with those obtained from finite element methods, experiments and other high accuracy models.