Free-edge Effects Research Articles

Random vibration-based progressive fatigue damage monitoring in thermoplastic coupons: a preliminary investigation

In recent years there has been an increasing trend towards the utilization of composites, particularly thermoplastics, in various components of aerostructures. The prelusion of such materials has underscored the significance of investigating their fatigue behavior and developing reliable methods for detecting fatigue damage. In this context, vibration-based techniques hold significant potential as they leverage the inherent excitation provided by in-flight noise and turbulence. This study aims at assessing the progressively accumulated fatigue damage in thermoplastic coupons via random vibration signals while accounting for operational and inter-structural uncertainties. The experimental process consists of preliminary tension and fatigue tests, interrupted fatigue tests, C-Scan inspection tests, and non-contact random vibration tests. Consecutive fatigue states are obtained by performing fatigue tests at intervals of 10 000 cycles for a population of 7 coupons. At each interruption, ultrasonic C-Scan and vibration inspection tests are performed, allowing for the visualization of fatigue damage and random vibration signal analysis. Welch Power Spectral Density estimates are employed and are shown to have good potential for distinguishing among different fatigue states despite the inevitable population and experimental uncertainty. Furthermore, fatigue damage is found to progress symmetrically and laterally along the free edges of the test coupons, which is explained by the free edge effect.

A micropolar modelling framework for interfacial free-edge effects of heterogeneous laminates

A micropolar modelling framework for interfacial free-edge effects of heterogeneous laminates

Experimental and simulation study on compressive failure evolution of multidirectional laminates with different dimensions

The composite strength refers to the ultimate local value rather than the average value of local strength, thus the effect of size effect needs to be considered. In this study, experimental and numerical approaches are used to evaluate the influence of size effect on the compressive characteristics and failure process of multidirectional carbon fiber reinforced composites. The representative failure modes of specimens with different thicknesses are described. The reasons for the difference in failure modes are analyzed by microstructure analysis, and the crack propagation process of specimens with different gauge lengths is identified. The simulation results and microscopic mechanism analysis reveal that with the increase of specimen thickness, the final failure mode develops from longitudinal cracking to multidirectional delamination, and finally evolves into shear failure through the thickness. Influenced by the free edge effect, the specimen thickness significantly affects the final failure mechanism by influencing the location of the initial cracking, and the size of the gauge section affects the site of matrix compression failure leading to a change in the final failure mode. These findings provide some helpful guidance for the design and fabrication of thick composite structures.

Free-edge effects at circular holes in composite laminates under hygrothermomechanical load

In this paper, the free-edge effects which play an important role in the failure analysis of composite laminates are studied. Pure temperature change and its combination with biaxial tension are investigated for a composite plate with a centric circular hole that is adequately small in comparison to the dimension of the plate. Moreover, the laminate is assumed to be thin, the temperature change of all points of the plate is identical and the biaxial tensile load is applied far from the center of the hole. For this purpose, a semi-analytical method based on a two-dimensional thermoelastic boundary layer theory and a minimum potential energy principle is proposed. It is shown that the present method predicts the interlaminar peeling and shear stresses surrounding the hole with good agreement compared to the results obtained by FEM analysis.

Free-edge effect on the tensile properties of 3D woven composites

Free-edge effect is one of the factors affecting the mechanical properties of three-dimensional woven composites under tensile load. However, current research is relatively poorly understood regarding the effect of free-edge on the stiffness and strength of the material. This paper aims at examining the influence of free-edge effect on the mechanical properties of 3D woven composites under tension through experimental and simulation methods. The three-dimensional digital image correlation (DIC) technique is used to collect the full-field strains on the specimen surface during the test, and the stress-strain differences in different regions in the width direction are analyzed, and the overlap of the curves in each region is found to be high, indicating that the boundary effect has a small influence on the tensile properties of 3D woven composites. Experimental studies are conducted on specimens of different widths (within the range of 15–20 mm), and the results indicate that the differences in mechanical properties of 3D woven composites under tension loading in this width range are not significant. A progressive damage finite element model is developed for calculation and compared with experimental results. It is found that the tensile properties of the material decreased when the width of the specimen is less than twice the size of the single cell. This study can provide certain data support for the study of the mechanical properties of 3D woven composites and enable the subsequent more in-depth study to provide a certain foundation.

A particular manner to observe free-edge effects in hybrid elastomer/composites plates

Hybrid elastomer/composite sandwich plate structures are typically used where simultaneously both lateral stiffness and shear flexibility are required. In these hybrid structures, however infinitesimal strains take place in laminated composite layers, but elastomer layer is under hyper-elastic strains. The present work aims to adapt an individual two-step technique to examine three-dimensional stress field in this plate to observe free-edge effects in composite layers. For this purpose, at the first step, employing elastic equivalent properties for the composite layers and nonlinear elastic properties for elastomer layer, large deformation finite element analysis is performed for the hybrid structure by ameliorate an available open source code named FLagSHyp. This analysis provides the load distribution at elastomer-composite interface. Next, using this external load distribution on composite layers, based on Kantorovich technique a detail analysis is proposed to study free edge effect in composite layer. The results are verified numerically and/or experimentally and vital observations involving free-edge effects are reported.

Stress evaluation of TBCs with inclined film-cooling hole considering CMAS penetration-induced change of thermo-mechanical properties

CaO-MgO-Al2O3-SiO2 (CMAS) penetration is an essential factor leading to the failure of thermal barrier coatings (TBCs), especially around the film-cooling hole structure of high-temperature gas turbine components. The complex temperature distribution and the free-edge effect around the cooling holes aggravate the influence of CMAS penetration on the failure of the TBCs. In this study, a three-dimensional (3D) model of a TBC-film cooling system considering CMAS attack is presented based on the observation of a retired turbine blade. CMAS penetration-induced change of thermo-mechanical properties of the ceramic top coat (TC) was considered. The thermal gradient around a cooling hole and the uneven growth of the thermally grown oxide (TGO) on the stress distribution in TBCs were investigated. The results showed that the thermal insulation performance of TBCs declined considerably under CMAS penetration, and the induced maximum increase in the temperature at the TC/bond coat (BC)interface reached 60 K. CMAS penetration also led to a considerable stress increase in the TBC-film system. We therefore conclude that CMAS penetration accelerates the crack initiation at the TC/TGO and TGO/BC interfaces.

Thickness variation effect on compressive properties of ultra-thick CFRP laminates

As ultra-thick laminates are widely used in the field of aerospace and marine as the main load-bearing structure, extreme service conditions lead to increasing thickness of composite structures. However, the effect of the increase in thickness on the compressive properties of ultra-thick laminates is still unclear. Herein parameters including fiber volume fraction, fiber waviness, void content and free edge effect that affect the compressive strength with increasing thickness are studied. The results show that the fiber volume fraction of ultra-thick laminates does not change significantly with the increase of thickness due to the adoption of the zero-bleeding process, while the fiber waviness and void contribute to the thickness effect on compressive strength. On the other hand, the high interlaminar stress of the free edge contributes to the premature delamination of the specimen, which dominates the compressive strength of the ultra-thick laminate. Finally, compared with the thin laminate (2 mm), the compressive strength of ultra-thick laminate drops sharply (nearly 28%), but when the thickness increases from 30 to 70 mm, the drop of compressive strength is not obvious (only 10%). When the material and curing process are consistent, the weak interlaminar properties of ultra-thick laminates does not change significantly with the increase of thickness, which leads to the insignificant decrease in compression strength of ultra-thick laminates with the increase of thickness. The proposed empirical relationship between the compressive strength and thickness of quasi-isotropic laminates can provide important theoretical basis and experimental reference for the design of ultra-thick composite structures.

Control of multi-scale cracking for improvement of the reliability of carbon/carbon composites via design of interlaminar stress

Controlled cracking at micro/mesoscale is crucial for decreasing the strength scatter and improving the reliability of carbon/carbon composites (C/Cs). In this work, the controlled cracking is realized by a designed interlaminar residual thermal stress (RTS), which is introduced inside the C/Cs by the alternate stacking of two types of C/C plies with different coefficients of thermal expansion. Firstly, multiscale finite element (FE) modeling is performed to capture the interlaminar RTS induced by the alternate stacking and evaluate the risk of delamination due to the free edge effect. Secondly, mechanisms responsible for the controlled cracking are elaborated with the aid of the FE modeling and experimental characterizations, and the controlled deflections and bifurcations of the crack strongly shield the influence of multiscale flaws. Finally, by adopting this strategy, the flexural strength of the C/Cs increases by 66% while the statistical Weibull modulus also increases from 4.9 to 8.3, verifying the simultaneously improved strength and reliability of the C/Cs.

Experimental and Numerical Study on the Bending Behavior of Satin-Woven SiCf/SiC Composites

The present research intends to explore the progressive failure in the case of five-harness SiCf/SiC satin-woven sheet composites consisting of twelve layers using a combination of numerical and experimental methods. For derivation and characterization of the bending behavior, a three-point bending procedure was used under conditions of atmospheric temperature. A charge-coupled device (CCD) camera was used to monitor the initiation and evolution of the failures. Variations in the strain fields were quantified following the digital image correlation (DIC) approach, whereas the resultant failure markings were elucidated by conducting microscopic assessments. The 3D finite element modeling (FEM) of the experiment was accomplished via ABAQUS/Explicit, thereby reproducing the material performance. A 3D-modified theory of the Tsai-Wu failure initiation was executed by exploiting the VUMAT subroutine. The evolutionary rule was used to study the complementary failure. A cohesive zone element of the composite interlayer was utilized to mimic the intra-deformation interfacial damage. The DIC-based experimental values of the strain fields agreed favorably with the numerical computations and the strength value error was less than 10%. An in-depth investigation was performed concerning the advantage of the 3D modeling approach to study the applicability of the method for the foreseeable distribution of the complex field parameters (e.g., progressive failure deposition and free edge effect) inside the critical specimen section.

Experimental and Numerical Analysis of Progressive Damage of SiCf/SiC Composite under Three-Point Bending

Satin SiCf/SiC composite has a wide range of applications; it is necessary to study its mechanical properties. The progressive failure of five-harness five-layer satin weave SiCf/SiC plate composites was explored experimentally and numerically in this research. The bending properties were derived and elucidated at ambient temperature through a three-point bending experiment. The generation and progression of damage was observed by CCD camera. For quantitative analysis of the strain field evolution, DIC (digital image correlation) was adopted, while the microscopic analyses were performed for the description of the derived failure markings. With the aid of ABAQUS/Explicit, the experiment was subjected to 3D finite element modeling for the reproduction of the material behavioral, where the VUMAT subroutine was used to implement a 3D-altered criterion of the Hashin damage initiation and the progression law of its complementary damage. Intra-deformation interface failure was simulated with a composite interlayer cohesive zone element. The experimentally derived DIC-based strain fields were well-consistent with the numerical outcomes. Deeper investigation was made into the superiority of the 3D modeling, which is ascribed to the predictability for distribution of complex field variables like the free-edge effect and progressive failure accumulation within the critical sample section. The damage mechanism of the satin weave composite was explored in depth and it provides useful guidance for the practical application of the composite.

Experimental investigation of the modified butterfly notch shear specimen with PMCs

An experimental study of the modified butterfly shear sample was undertaken for polymer matrix composites using three quasi-isotropic IM7/977-3 laminates. This study used 3D digital image correlation (DIC) to observe and quantify the severe shear strain concentrations developed by compressively loading the modified butterfly geometry laminates. Interrupted X-Ray computed tomography (X-Ray CT) was used to understand the failure mechanisms present in the region of shear strain. By choosing to conduct interrupted testing, the progressive nature of the damage could be observed. At ultimate failure, extensive damage in the region of high shear strain was observed using post testing inspection with X-Ray CT. The mechanical testing was accompanied by numerical simulations for each laminate. The damage predicted by the numerical simulations was shown to be consistent with the damage observed with the post failure inspection via X-Ray CT. Stress components caused by free-edge effects were also quantified, and shown to have a minimal impact on the failure mode in the region of interest.

Free-Edge Effects in Composite Laminates—A Review of Recent Developments 2005–2020

AbstractThe design and analysis of composite structures in the form of layered plates or shells is often driven by stress concentration phenomena that occur due to geometric or material discontinuities. One prominent example is the so-called free-edge effect that manifests itself in the form of significant localized interlaminar stress fields in the vicinity of free laminate edges and that is given rise to due to the mismatch of the elastic properties of the individual laminate layers. The free-edge effect has been under scientific investigation for more than five decades, and this paper aims at providing an overview of recent developments and scientific advances in this specific field wherein an emphasis is placed on investigations that were published in the time range between the years 2005 and 2020. This paper reviews closed-form analytical methods as well as semi-analytical and numerical analysis approaches and summarizes the recent state of the art concerning the investigation of stress singularities and experimental characterization of free-edge effects. This paper also reviews advanced problems such as free-edge effects in curved laminated structures and in piezoelectric laminates as well as in the vicinity of holes and other geometric discontinuities, and two new aspects in the field of free-edge effects, namely, the development and application of a new semi-analytical method (the so-called scaled boundary finite element method (SBFEM)) and the fracture mechanical strength assessment, also by novel approaches such as finite fracture mechanics, are also discussed. This paper closes with a summary and an outlook on future investigations.

Hygrothermomechanical analysis of the free-edge stress fields in cylindrical cross-ply laminated shells

The present work introduces two novel semi-analytical methods for the three-dimensional stress analysis of thick, circular cylindrical cross-ply laminated shells subjected to hygrothermomechanical loadings under consideration of the free-edge effect. Comparisons with full-scale three-dimensional finite element computations and existing semi-analytical approaches from literature confirm the good accordance of the numerical results. Furthermore, parametric studies, wherein the influence of various hygrothermomechanical loading conditions on the free-edge stress fields are investigated, revealed that the interlaminar stresses in laminated shells are impacted significantly by the orientation of the load introduction and can even be reduced when the composite laminate is exposed to humidity.

Reduction of free-edge effects around a hole of a composite plate using a numerical layup optimization

The stacking sequence has a great influence on the performance of composite structures especially when it comes to stress concentration effects. In the current research, various orientation angles and layups for a composite plate with a central hole are investigated and the optimized layup is determined for the desired thickness. The objective of the optimization is the minimization of the interlaminar peeling stress around the hole. Failure strength around the hole is the basis of the constraint incorporating Hashin’s failure criteria for each lamina individually. For this purpose a two-step analysis is carried out: Primarily a finite element analysis is performed using ABAQUS to determine the constraint for orientation angles. Then, the pattern search method is utilized to obtain the optimized layup using the interaction of MATLAB and ABAQUS software. Moreover, a sensitivity analysis is carried out to determine the effect of the material properties, the size of the hole and the initial guess applied for the pattern search solution upon the optimal layup sequence.

Core Cracking in Advanced Organic Substrates Due to Free Edge Effect at Cold Temperatures

Advanced FPGAs utilizing substrates with thick organic core showed substrate core cracking after thermal cycling. These substrates are laminate structures with a core made from stacked layers of glass fiber and resin with routing layers made of copper and dielectric build-up polymer. This type of cracking typically occurs on the glass fiber-resin interface, can penetrate several millimeters and across thru-vias to cause electrical failure, and was found on several test vehicles, four of which are detailed here. This work observed numerous examples to identify the characteristics of the cracking and notes the best observation practices. We hypothesize this cracking is due to free edge effect at cold temperature. Since the free edge cannot have normal stress, a large out-of-plane stress exists at the edge and concentrates at the corner. Models were built to study the effects of various package parameters on the failure mode. The primary contributions to the free edge effect are the low-CTE glass fiber, the high-CTE resin, and the high-CTE build-up layers. The trend toward lower CTE substrates has demanded lower CTE glass fiber material, which exacerbates this problem. Increasing complexity of routing demands additional layers, which also increases the out-of-plane stress at the corner. Other less significant factors that increase the stress include lower resin CTE, higher build-up CTE, and decreasing core thickness. Thru-via placement and dicing optimization had small impact and substrate had negligible impact.

Evaluation of fracture toughness of VN hard coatings: Effect of preferred orientation

The objectives of this study were to evaluate the fracture toughness (Gc) of vanadium nitride (VN) hard coatings using internal energy-induced cracking (IEIC) method, and investigate the effect of preferred orientation on the fracture toughness. VN coatings were deposited on Si (100) substrates by unbalanced magnetron sputtering. Two different nitrogen flow rates were used to prepare coatings with different textures. The fracture toughness of the specimens were assessed using the IEIC method. The results showed that fracture toughness of the VN coatings was texture-dependent, and the Gc values for specimens with random texture and (200) texture were 11.2±0.7 and 19.2±1.2 J/m2, respectively, which were in between those of TiN and ZrN. The higher Gc for the VN coatings with (200) texture was consistent with the higher residual stress in the coatings. The fracture morphology and crack propagation path were examined using a focused ion beam and electron beam system. The fracture morphology of the coatings was similar regardless of random or (200) texture, where the crack path consisted of horizontal (R1) and zigzag (R2) regions. Since the VN coatings possessed a relatively uniform stress gradient, crack initiation may occur inside the coating ahead of the specimen edge due to the edge stress acting at local defects. Similar to the fracture behavior in ZrN coatings, the stress distribution due to free edge effect could move with the crack front and consequently drive the main crack to propagate stepwise.

Implications of free-edge effect at thin plain-woven carbon fiber reinforced plastic laminates with out-of-plane waviness under cyclic loading

The onset of damage caused by the free-edge effect in plain-woven carbon fiber reinforced plastic (CFRP) specimens with an out-of-plane waviness under tension-tension fatigue loading is investigated. Numerical calculations show that interlaminar and intralaminar stresses close to the out-of-plane waviness are higher than the equivalent stresses at the surrounding edge regions. Using submodels, the influence of the chosen out-of-plane waviness can be better assessed. The free-edge effect of the considered specimens, which originates from stress gradients between plies of different orientation, is altered by the change in the stress field caused by the out-of-plane waviness. Large interlaminar stresses between plies of the same orientation are obtained, which contrasts with existing literature. In experimental fatigue testing it is found that cracks at the free edge appeared at the predicted locations, and after reaching crack saturation, in regions close to the out-of-plane waviness, interlaminar and intralaminar stresses lead to additional cracks along the whole free edges. The experimental tests are supported by a three dimensional image correlation system (3D-DIC), a thermal-imager and a digital photographic camera, which allows detailed examination of selected areas. Visual observation during fatigue testing and post-mortem inspection show good agreement between experimental data and numerical calculations in relation to the location of the damage initiation. As a result, out-of-plane waviness at free edges must be considered as an additional significant fatigue damage initiation location in laminate analysis.

Free-edge crack onset induced by thermal loading

In composite laminates the layer-wise material mismatch induces highly localized stress concentrations at the free edges. This is referred to as free-edge effect. As a consequence interlaminar crack initiation may occur in addition to the typically considered intralaminar failure modes. The stresses do not necessarily have to be caused by mechanical loads. Also temperature differences may induce significant interlaminar stresses. In the present study, delamination onset in symmetric angle-ply laminates caused by thermal stresses is investigated by means of the coupled stress and energy criterion within the framework of finite fracture mechanics on the basis of the well-known generalized plane strain state. Using this relatively young criterion, both failure load and the length of the initiated crack can be predicted. Besides the intrinsic material properties in terms of strength and fracture toughness, only the interlaminar stresses as well as the released energy during crack initiation are required for the evaluation of the coupled criterion. Since no analytical closed-form solution of the free-edge effect is known, the required field quantities are obtained by employing a finite element model. Effects as the influence of the thickness and the orientation of the individual layers on the failure temperature are studied. For that purpose, a dimensional analysis is performed allowing to scale the results of a certain boundary value problem to self-similar configurations yielding a significant reduction of the numerical effort. It is revealed that especially for thick angle-ply laminates with large fiber orientation angles and temperature differences as they may occur in aeronautical applications interlaminar crack initiation can be the predominant failure mode. For validation purposes the results obtained by the coupled criterion are compared to the widely-used cohesive zone model.

Predicting thermally induced edge-crack initiation using finite fracture mechanics

In temperature-loaded bi-material joints, highly localized stress concentrations occur at the bi-material junction at the free edge. This so-called free-edge effect may cause premature failure in form of an interface crack emanating from the free edge. In the present work, thermal crack initiation is investigated using a coupled stress and energy criterion within the framework of finite fracture mechanics by the example of a uniformly cooled epoxy–glass bi-material specimen. The mechanical analysis is based on the assumption of a plane-strain state, providing a simplified two-dimensional model. Interface stresses and the energy dissipation due to crack initiation are computed efficiently using the scaled boundary finite element method (SBFEM) and the effect of the layer thickness on crack initiation is studied. Dimensional analyses revealed that interface stresses and energy dissipation can be scaled to an arbitrary layer thickness such that only few model evaluations are required. For validation purposes, a finite element reference solution is provided and compared to the results obtained by the SBFEM approach. In addition, a cohesive zone model is applied to validate the predictions of the coupled stress and energy criterion.