Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

The Effect of Crack Spacing Distribution on Stiffness Reduction of Cross-ply Laminates

The effect of transverse crack distribution on the effective mechanical properties of cross-ply laminates is considered. Young’s modulus and Poisson’s ratio dependence on the transverse ply crack density is obtained experimentally for glass fiber/epoxy laminates of lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s subjected to uniaxial tensile loading. Crack spacing distributions at the edge of the specimen are also measured at a predefined applied strain. Mechanical property reduction is evaluated for two crack spacing distributions: uniform spacing routinely considered in theoretical derivations and the experimental crack spacing distribution; the results are compared with test data.     

Damage evolution of angle-ply SCS-6/Ti composites under static and fatigue loading

The effect of fibre orientation and laminate stacking sequence on the tensile and fatigue behaviour of SCS-6/Ti 15-3 composites were investigated. The laminates used in this study were: (90)₆, (0/ ± 45)_s, (0/90)_s, and (90/ +-45)_s. The initiation and progression of microstructural damage at various stress levels was thoroughly characterized. It was found that fatigue life at high applied stresses were controlled by fibre fracture; progressive damage involving fibre fracture, interfacial debonding and matrix cracking became dominant at low applied stresses. Observation of the damage mechanisms in the angle-ply laminates under cyclic loading suggests that increasing the fibre-matrix bonding strength may improve the load carrying capability and fatigue life of laminates containing off-axis plies.     

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0₂/90₂]_s, [0/90₂]_s, and [0/90₄]_s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.     

Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth

A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension–compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0_n, ?_m]_s with severed central plies [?], and of stacking order [0₂, +45, 0₂, ?45, 0, 90]_s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.     

Modeling of facesheet crack growth in titanium-graphite hybrid laminates. Part II: Experimental results

Titanium-graphite hybrid composite laminates exhibit a coupled damage growth mode of facesheet cracking and delamination. Part I of this work modeled the growth of the coupled damage mode. Fatigue experiments were conducted on single edge notch tension specimens to measure the crack growth rate. This paper compares the model predictions with experimental data. The three-dimensional finite element model successfully captured the damage growth behavior for two of the lay-ups ([Ti/0/90/0₂]_s and [Ti/90/0/90₂]_s) in the experimental program. However, in a third lay-up, [Ti/0/90/±30]_s, the underlying damage modes were found to be sufficiently different than the other two lay-ups and the model did not capture the steady-state growth behavior. The effects of temperature and specimen size were also investigated for TiGr laminates. Except for the effects of the load ratio, elevated temperatures did not affect the crack growth rate significantly. For wider specimens, the steady-state fatigue crack growth behavior was similar to the narrow specimens, indicating that the steady-state facesheet crack growth behavior is independent of specimen size.     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

Damage Assessment of CFRP [90/±45/0] Composite Laminates over Fatigue Cycles

The present paper develops a stiffness-based model to characterize the progressive fatigue damage in quasi-isotropic carbon fiber reinforced polymer (CFRP) [90/±45/0] composite laminates with various stacking sequences. The damage model is constructed based on (i) cracking mechanism and damage progress in matrix (Region I), matrix-fiber interface (Region II) and fiber (Region III) and (ii) corresponding stiffness reduction of unidirectional plies of 90°, 0° and angle-ply laminates of ±45° as the number of cycles progresses. The proposed model accumulates damages of constituent plies constructing [90/±45/0] laminates by means of weighting factor η ₉₀, η ₀ and η ₄₅. These weighting factors were defined based on the damage progress over fatigue cycles within the plies 90°, 0° and ±45° of the composite laminates. Damage model has been verified using CFRP [90/±45/0] laminates samples made of graphite/epoxy 3501-6/AS4. Experimental fatigue damage data of [90/±45/0] composite laminates have fell between the predicted damage curves of 0°, 90° plies and ±45°, 0/±45° laminates over life cycles at various stress levels. Predicted damage results for CFRP [90/±45/0] laminates showed good agreement with experimental data. Effect of stacking sequence on the model of stiffness reduction has been assessed and it showed that proposed fatigue damage model successfully recognizes the changes in mechanism of fatigue damage development in quasi-isotropic composite laminates.     

Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction

A fatigue life to the initiation of transverse cracks in cross-ply carbon fiber-reinforced plastic (CFRP) laminates has been predicted using properties of the fatigue strength of unidirectional CFRP in the 90° direction. In the experiments, unidirectional [90]₁₂ laminates were used to obtain a plot of maximum stress versus number of cycles to breaking, and two types of cross-ply laminates of [0/90₄]_S and [0/90₆]_S were used to evaluate the initiation and multiplication of transverse cracks under fatigue loading. Transverse cracks were studied by optical microscopy and soft X-ray photography. Analytical and experimental results showed good agreement, and the fatigue life for transverse crack initiation in cross-ply laminates was predicted successfully from the fatigue strength properties of the unidirectional CFRP in the 90° direction. The prediction results showed a conservative fatigue life than the experimental results.     

Nonlinear constant fatigue life diagrams for carbon/epoxy laminates at room temperature

Exploration of a full shape of constant fatigue life (CFL) diagram and development of an efficient CFL diagram-based fatigue life prediction method are attempted for multidirectional CFRP laminates. On three kinds of CFRP laminates of [45/90/−45/0]_2s, [0/60/−60]_2s and [0/90]_3s lay-ups, tension–tension, tension–compression and compression–compression fatigue tests are performed at room temperature for two different stress ratios each. Experimental results clearly show that a stress ratio has a significant influence on the fatigue behavior of those CFRP laminates, and the CFL diagrams delineated using alternating stress and mean stress become asymmetric about the alternating stress axis. The alternating stress component of fatigue load for a given constant value of fatigue life turns maximum in the case of fatigue loading at a critical stress ratio that is nearly equal to the ratio of compressive strength to the tensile one. The shape of CFL diagrams progressively changes from a straight line to a nonlinear curve as a given constant value of fatigue life increases. A new and efficient method for accurately predicting an asymmetric nonlinear CFL diagram is then developed which is based on the static strengths in tension and compression and the reference S–N relationship fitted to the fatigue data for the critical stress ratio. The theoretical CFL diagram constructed following the proposed procedure agrees well with the experimental CFL diagram, regardless of the type of CFRP laminate. It is also demonstrated that the S–N relationships predicted using the proposed CFL diagram-based fatigue life prediction method adequately coincide with the experimental results for fatigue loading with a variety of different stress ratios in the range of fatigue life up to 10⁶ cycles.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

An investigation into the damage development and residual strengths of open-hole specimens in fatigue

An extensive experimental program was carried out to investigate and understand the sequence of damage development throughout the life of open-hole composite laminates loaded in tension–tension fatigue. Quasi-isotropic carbon/epoxy laminates, with stacking sequence [45₂/90₂/−45₂/0₂]_S, [45/90/−45/0]_2S and [45/90/−45/0]_4S were examined. These were selected on the basis that under quasi-static loading the [45₂/90₂/−45₂/0₂]_S configuration exhibited a delamination dominated mode of failure whilst the [45/90/−45/0]_2S and [45/90/−45/0]_4S configurations showed a fibre dominated failure mode, previously described as “pull-out” and “brittle” respectively. Specimens were fatigue loaded to 1 × 10⁶ cycles or catastrophic failure, which ever occurred first. A number of tests were interrupted at various points as the stiffness dropped with increasing cycles, which were inspected using X-ray computed tomography (CT) scanning. A static residual strength program was carried out for run-out specimens of each configuration.     

Damage response of stitched cross-ply laminates under impact loadings

The impact response of stitched graphite/epoxy laminates was examined with the aim of evaluating the efficiency of stitching as a reinforcing mechanism able to improve the delamination resistance of laminates. The investigation, which focussed on two classes of cross-ply stacking sequences ([0₃/90₃]_s and [0/90]_3s), showed that the role of stitches in controlling damage progression of laminates and their capability to reduce the impact sensitivity of specimens are greatly dependent on the impact behaviour of base (unstitched) laminates. In [0₃/90₃]_s laminates, in particular, stitching is able to reduce damage area, on condition that the impact energy is higher than a threshold level and delaminations are sufficiently developed. In [0/90]_3s laminates, on the other hand, stress concentration regions generated by the stitching process appear to promote the initiation and propagation of fibre fractures, thereby inducing a decrease in the penetration resistance of the laminate.     

Simulation of multiple delaminations in impacted cross-ply laminates using a finite element model based on cohesive interface elements

The paper investigates the capability of a finite element model based on cohesive interface elements to simulate complex three-dimensional damage patterns in composite laminates subjected to low-velocity impact. The impact response and the damage process of cross-ply laminated plates with grouped ([0₃/90₃]s and [90₃/0₃]s) and interspersed ([0/90]₃s) ply stacking was simulated using a FE model developed by the authors in a previous study and the numerical results were compared to experimental observations. The model provided a correct simulation of size, shape and location of the principal fracture modes occurring in impacted [0₃/90₃]s and [90₃/0₃]s laminates. In [0/90]₃s laminates, characterized by a complex spatial damage distribution, the model was able to predict the approximately circular shape of the overall projected damage area and to capture the typical shape features of individual delaminations; significant discrepancies between experiments and predictions were however observed in terms of delamination sizes at single interfaces. Further investigations are needed to clarify the main reasons of these discrepancies.     

Bearing damage evolution of a pinned joint in CFRP laminates under repeated tensile loading

A mechanical pinned joint in the CFRP laminates such as [0/±45/90]_3S, [90/±45/0]_3S, [0/±45/90]_2S and [90/±45/0]_2s is loaded statically and cyclically to finally obtain the critical condition for fatigue. It is derived that in the static loading, the critical damage that yields shear matrix crack is kink and the critical condition to the final failure is the appearance of kink in every inner 0° layer and that in the fatigue loading within the moderate load, the critical damage that yields shear matrix crack is almost always kink-like damage along the collapse front and at high load it is rather kink. Next, the non-elastic elongation of a joint at the maximum load subtracted by the one at 10th cycle is focused on and its capability is figured out for various stacking sequences. The critical value U_NE,F^* for the elongation rate change to the final fatigue failure is around 50–65 μm in the present material. The critical condition to the final fatigue failure and corresponding to U_NE,F^* is roughly the appearance of mostly kink-like damage in every inner 0° layer.     

A critical evaluation of theories for predicting microcracking in composite laminates

We present experimental results on 21 different layups of Hercules AS4 carbon fibre/3501-6 epoxy laminates. All laminates had 90 ° plies; some had them in the middle ([(S)/90 _n ] _s ) while some had them on a free surface ([90 _n /(S)] _s ). The supporting sublaminates, (S), where [0 _n ], [±15], or [±30]. During tensile loading, the first form of damage in all laminates was microcracking of the 90 ° plies. For each laminate we recorded both the crack density and the complete distribution of crack spacings as a function of the applied load. By rearranging various microcracking theories we developed a master-curve approach that permitted plotting the results from all laminates on a single plot. By comparing master-curve plots for different theories it was possible to critically evaluate the quality of those theories. We found that a critical-energy-release-rate criterion calculated using a two-dimensional variational stress analysis gave the best results. All microcracking theories based on a strength-failure criteria gave poor results. All microcracking theories using one-dimensional stress analyses, regardless of the failure criterion, also gave poor results.     

Mechanical properties of cross-ply and quasi-isotropic composite laminates processed using aligned multi-walled carbon nanotube/epoxy prepreg

This study examined the processing and mechanical properties of cross-ply and quasi-isotropic composite laminates processed using aligned multi-walled carbon nanotube/epoxy prepreg sheets. Three kinds of CNT/epoxy laminates, ([0°/90°]s, [60°/0°/?60°]s, [0°/45°/90°/?45°]s) were successfully fabricated using aligned CNT/epoxy prepreg sheets. The CNT volume fraction was approximately 10%. No visible void or delamination was observed in composite laminates, and the thickness of each layer was almost equal to that of the prepreg. To evaluate the elastic moduli, E₁₁, E₂₂, and G₁₂, of each ply in the laminates, on-axis and off-axis tensile tests (0°, 45°, 90°) were conducted of aligned CNT/epoxy lamina specimens. The Young’s modulus of CNT/epoxy cross-ply and quasi-isotropic laminates agreed with the theoretical values, which were calculated using classical laminate theory and elastic moduli of CNT/epoxy lamina. The respective failure strains of [0°/90°]s, [60°/0°/?60°]s, and [0°/45°/90°/?45°]s laminates are 0.65, 0.92, 0.63%, which are higher than that of 0° composite lamina (0.5%). Results suggest that the failure strain of 0° layer in composite laminates is improved because of the other layers.     

Fiber direction and stacking sequence design for bicycle frame made of carbon/epoxy composite laminate

According to the maximum stress theory and the results of strength-to-stress ratios, the fiber direction and stacking sequence design for the bicycle frame made of the carbon/epoxy composite laminates have been discussed in this paper. Three testing methods for the bicycle frame, i.e. torsional, frontal, and vertical loadings, are adopted in the analysis. From the finite element results, the stacking sequences [0/90/90/0]_s and [0/90/45/−45]_s are the good designs for the composite bicycle frames. On the contrary, the uni-directional laminates, i.e. [0/0/0/0]_s, [90/90/90/90]_s, [45/45/45/45]_s and [−45/−45/−45/−45]_s, are the bad designs. In addition, weak regions of failure occur at the fillets and connections of the frame, i.e. the stress concentration regions. All weak points occur at the inner or outer layer of the laminated composite tube. The 0°-ply and 90°-ply located on the inner and outer layer of the tube can effectively resist the higher stress at its location.     

Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements

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 [0₂/90_n]_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 [0/90_n/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.