Fracture mechanisms and failure processes at stiffener run-outs in polymer matrix composite stiffened elements

This paper describes the fractographic analyses of three stringer run-out designs which had been loaded to failure in tension. The main aims of the investigation were to deduce the failure processes in the elements, and to characterise the effect of local geometry of the stringer run-out on the failure process. The analysis showed that the critical failure mechanism in the elements was the development of +45° ply splitting at the skin surface, initially under mode I dominated intralaminar fracture. However, as these splits grew beneath the stringer foot, the mode II component increased. This led to mixed-mode delamination growth, extending parallel to the +45° ply, at the skin/adhesive interface. Subsequently, the delamination migrated through the skin via ply splits, ultimately reaching the interface between the second and third (−45°/0°) plies, in which it remained until catastrophic failure.

Extending and tapering the stringer foot led to shifting of the site of the +45° ply splitting; this was attributed to in-plane tensile stresses in the skin being inhibited in the modified designs. The reduced out-of-plane support on the stiffener foot in the modified designs led to an increase in the mode I component at the delamination from the stringer tip. It also led to an increase in the degree of multi-plane delamination growth. Based on the fractographic observations, recommendations for modelling the elements were suggested.     

Local fracture mechanics analysis of stringer pull-off and delamination in a post-buckled compression panel

This paper describes some of the current global/local testing and analysis approaches to evaluating the design of composite structure. A case study for the local, fracture mechanics analysis of failure in a 4- stringer compression panel is described in detail. The analysis investigates the variation of strain energy release rate G with debond length using a 2-D plane strain finite element analysis (FEA) of one of the stringers. The boundary conditions on the local model were determined from a global shell element model of the panel. Delamination was also modelled in the cap of the stringer using FEA and a closed form solution. The values of G for these two damage modes were compared with the material's fracture toughness. Using this analysis, the load to initiate the stringer debond and to cause edge delamination of the cap may be determined.     

Mixed-mode quasi-static failure criteria for adhesively-bonded pultruded GFRP joints

The strain energy release rates of adhesively-bonded pultruded GFRP joints were determined experimentally. The crack propagated in the adherend along paths outside the symmetry plane accompanied by fiber bridging. A new method, designated the “extended global method”, was introduced to facilitate mode partitioning in the mixed-mode experiments. Non-linear finite element models were developed in order to quantify the effect of the observed fiber bridging on crack propagation. An exponential traction-separation cohesive law was used to model the fiber bridging zone and calculate the energy release rate due to the fiber bridging, while the virtual crack closure technique was used for calculation of the fracture components at the crack tip. Experimental, analytical and numerical analyses were used to establish quasi-static mixed-mode failure criteria for crack initiation and propagation. The derived mixed-mode failure criteria can be used for simulating progressive crack propagation in other joint configurations comprising the same adhesive and adherends.     

Evaluation of energy release rate for delamination defects at the skin/stringer interface of a stiffened composite panel

This paper deals with numerical investigation on a stiffened composite panel under longitudinal compression load, in presence of artificial delamination defects between skin/stringer interface layers.At first, both the experimental and numerical non-linear equilibrium paths were determined, until the failure load value of the structure was reached. Then local evaluation of the energy release rate parameter was performed at defect front, by means of a hybrid (FEM/analytical) procedure based on a particularized virtual crack closure technique. The same FE shell model was used to perform both global and local calculations by means of a single analysis.     

复合材料机身曲板环向弯曲加载试验及失效机制

对复合材料机身曲板进行了环向弯曲加载试验,采用四点弯加载方式对考核段进行纯弯加载,设计一种加强连接方式避免加载段提前破坏,通过试验对机身曲板的环向稳定性和破坏模式进行了分析。同时,建立了基于内聚力单元的考虑长桁与蒙皮粘接界面损伤的有限元模型,分别使用Quads准则和Hashin准则作为界面和层合板的失效判据分析曲板结构的失效机制,计算结果与试验结果吻合较好。试验及有限元分析结果表明,长桁帽底蒙皮的局部屈曲引起长桁与蒙皮粘接的R区出现初始开裂,并最终扩展为长桁脱粘。随着蒙皮屈曲及长桁脱粘的扩大,蒙皮由局部屈曲变为整体失稳而失去承载能力,最终导致隔框承载过大而发生断裂。根据初始损伤模式,采取了长桁帽内全包工艺改进设计,改进后的曲板结构稳定性和承载能力分别提高了21.9%和16.8%。      

A robust numerical approach for the simulation of skin–stringer debonding growth in stiffened composite panels under compression

In this paper, a numerical study on skin–stringer debonding growth in stiffened composite panels has been carried out. A novel numerical methodology is proposed here to investigate the compressive behaviour of a stiffened composite panel in the presence of skin–stringer partial separation. The novel numerical methodology, able to overcome the mesh size and time increment dependency of the standard Virtual Crack Closure Technique (VCCT), is an evolution of a previously developed and tested numerical approach for the circular delaminations growth. The enhancements, with respect to the previously developed approach, rely mainly in the capability to deal with the different defect shapes characterising a skin–stringer debonding. The proposed novel methodology has been implemented in a commercial finite element platform and tested over single stiffener composite panels. The effectiveness of the suggested numerical methodology, in predicting the compressive behaviour of stiffened panels with skin stringer debondings, has been preliminary confirmed by comparisons, in terms of load versus applied displacement and debonding size at failure, with literature experimental data and numerical results obtained with the standard VCCT approach.     

Prediction of post-buckling strength of stiffened laminated composite panels based on the criterion of mixed-mode stress intensity factors

An analytical investigation is conducted to predict the post-buckling strength of laminated composite stiffened panels under compressive loads. When a stiffened composite panel buckles, the skin would deform into a sinusoidal mode shape, and hence induces additional moments and forces near the skin-stiffener interface region. These induced loads would cause the existing small edge delamination cracks to propagate along the skin-stiffener interface, and this in turn would lead to the global failure of the stiffened panel. To reduce the cost of the analytical investigation, the failure of the stiffened panel under post-buckling loads is modeled in two stages: a global analysis to model the post-buckling behavior of the stiffened panel; and a local analysis to model the onset of propagation of the edge delamination crack at the skin-stiffener interface. The results from this study are compared with an experimental investigation conducted by Starnes, Knight, and Rouse (1987). It is found that for the eight different specimens that are considered in this study, the calculated critical energy release rate for the propagation of the edge delamination crack in each specimen differs substantially from those for the others; hence it may be concluded that the total energy release rate would not be a suitable fracture parameter for predicting the post-buckling strength of the stiffened panels. On the other hand, using the fracture criterion based on the critical mixed-mode stress intensity factors, the predicted post-buckling strength of the stiffened panels compares quite favorably with the experimental results and the standard deviation of the error of prediction is less than 10%. Furthermore, by applying the criterion of critical mixed-mode stress intensity factors on a simple damage model, the present analysis is able to predict the significant reduction in the post-buckling strenght of stiffened panels with a damage due to a low-speed impact at the skin-stiffener interface region.This work is supported by ONR, with Dr. Y. Rajapakse as the program official.     

A shell/3D modeling technique for the analysis of delaminated composite laminates

A shell/3D modeling technique was developed for which a local three-dimensional solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a plate or shell finite element model. Multi-point constraints provided a kinematically compatible interface between the local three-dimensional model and the global structural model which has been meshed with plate or shell finite elements. Double cantilever beam (DCB), end notched flexure (ENF), and single leg bending (SLB) specimens were modeled using the shell/3D technique to study the feasibility for pure mode I (DCB), mode II (ENF) and mixed mode I/II (SLB) cases. Mixed mode strain energy release rate distributions were computed across the width of the specimens using the virtual crack closure technique. Specimens with a unidirectional layup and with a multidirectional layup where the delamination is located between two non-zero degree plies were simulated. For a local three-dimensional model, extending to a minimum of about three specimen thicknesses on either side of the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures modeled with plate elements, the shell/3D modeling technique offers a great potential for reducing the model size, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.     

Critical discussion of the single-fibre pull-out test: does it measure adhesion?

With a comprehensive finite-element model the interface failure process of the single-fibre pull-out test, for the measurement of fibre/matrix adhesion, is investigated on the basis of a fracture-mechanics debonding criterion. Special emphasis is placed on the interface local mixed-mode load, which is shown to have an important influence on the debonding process and is taken into account by a fracture ellipsoid criterion. Additional features investigated are residual thermal stresses, specimen geometrical details (wetting meniscus, drop shape) and a simplistic model of fibre/matrix interfacial friction. For medium debonding lengths the energy release rate runs through a plateau range that can be approximated by a simple analytical approach and can be observed experimentally with a very stiff loading configuration. The mixed-mode state in the plateau range is uniform and dominated by mode 2, but its actual value is quite uncertain. From experimental experience the actual adhesion failure is closely connected with the interface local normal load, while local shear load induces submicroscopic friction and matrix inelasticity which strongly reduce the interface sensitivity, resulting in G_1c<G_2c. G_1c seems to be more significant for adhesion. The interpretation of the plateau range may provide the total critical energy release rate, G_c, for the debonding process, but from a region where mode II prevails. G_c will therefore be far from G_1c, reducing the significance of the tests results for characterization of adhesion.     

复合材料“T”形长桁压缩性能研究

压缩性能是飞机中央翼用“T”长桁上壁板的重要指标。为验证有限元分析方法模拟“T”形长桁压缩破坏过程的合理性,本文选取单根“T”形长桁作为试验件,并根据铺层和尺寸的不同将试验件分为4种。运用工程算法计算了长桁的局部屈曲载荷、压损载荷；用有限元算法计算了长桁的屈曲载荷、压损载荷；通过试验获得长桁的局部屈曲载荷、屈曲载荷和压损载荷。比较分析上述3种方式得到的结果,可以发现:工程计算结果与试验结果误差偏大,误差达到8%~50%,且全部偏于保守；有限元计算结果与试验结果较接近,误差在10%以内；利用有限元模拟试验件的压缩破坏过程得到的载荷-位移曲线与试验结果比较一致。研究结果表明,有限元计算分析方法可实际工程应用,为设计人员提供设计依据。     

Characterisation of impact damage in skin-stringer composite structures

In studies aimed at understanding the impact performance of structures made from carbon-fibre composites, effects of structural geometry, material type and impact location have been investigated in skin-stringer panels representative of aircraft structure. Effects were investigated for low-velocity impacts to the skin in the bay between stringers, over a stringer foot, and over a stringer centreline. Detailed studies of the impact damage at these locations were investigated using ultrasonic techniques, and optical and electron microscopy. The damage characteristics were explained in terms of the proportion of energy absorbed through damage, such as delamination, and elastic effects, such as structural response of the panel.     

Strain energy release rate determination of prescribed cracks in adhesively-bonded single-lap composite joints with thick bondlines

An analytical model for determining the strain energy release rate due to a prescribed crack in an adhesively-bonded, single-lap composite joint with thick bondlines and subjected to axial tension is presented. An existing analytical model for determining the adhesive stresses within the joint is used as the foundation for the strain energy release rate calculation. In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory. In order to simulate the thick bondlines, the field equations of the adhesive are formulated using the linear elastic theory to allow non-uniform stress distributions through the thickness. Based on the adhesive stress distributions, the equivalent crack tip forces are obtained and the strain energy release rate due to the crack extension is determined by using the virtual crack closure technique (VCCT). The specimen geometry of ASTM D3165 standard test is followed in the derivation. The system of second-order differential equations is solved to provide the adherend and adhesive stresses using the symbolic computational tool, Maple 7. Finite element analyses using J-integral as well as VCCT are performed to verify the developed analytical model. Finite element analyses are conducted using the commercial finite element analysis software ABAQUS™. The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses. It can be seen that the same prescribed crack has a higher strain energy release rate for the joints with thicker bondlines. This explains the reason that joints with thick bondlines tend to have a lower load carrying capacity.     

Numerical simulation of strain-rate dependent transition of transverse tensile failure mode in fiber-reinforced composites

This study numerically simulates strain-rate dependent transverse tensile failure of unidirectional composites. The authors’ previous study reported that the failure mode depends on the strain rate, with an interface-failure-dominant mode at a relatively high strain rate and a matrix-failure-dominant mode at relatively low strain rate. The present study aims to demonstrate this failure-mode transition by a periodic unit-cell simulation containing 20 fibers located randomly in the matrix. An elasto-viscoplastic constitutive equation that involves continuum damage mechanics regarding yielding and cavitation-induced brittle failure is used for the matrix. A cohesive zone model is employed for the fiber–matrix interface, considering mixed-mode interfacial failure. For the results, the relationship between failure modes and the strain rate is consistent with the authors’ previous studies.     

Behaviour of multiple composite plates subjected to ballistic impact

An experimental and numerical investigation has been carried out to study the behavior of single and multiple laminated panels subjected to ballistic impact. A pressurized air gun is used to shoot the impactor, which can attain sufficient velocity to penetrate all the laminates in a multiple laminated panel. The incidental and residual velocity of the impactor is measured to estimate the energy absorption in the impact process. The commercially available code ABAQUS has been used for the numerical simulation where the impactor has been modeled as a rigid body and the laminates have been modeled with a simple shell element. A user material model based on a continuum damage mechanics concept for failure mechanism of laminated composites has been implemented. Experimental tests showed that the numerical model could satisfactorily predict the energy absorption. Most interestingly, it has clearly demonstrated a feasible phenomenon behind counterintuitive experimental results for the multiple laminated panels.     

Designation of Mode Mix in Orthotropic Composite Delamination Problems

In interfacial fracture modeling of composite delamination, mode mix is typically specified in terms of energy release rates. Other near-tip quantities can be used to designate mode mix, however. This paper considers the designation of mode mix in terms of energy release rates, stress intensity factors, stresses ahead of the crack tip and crack face displacements and the consequences of using different near-crack-tip quantities to designate mode mix in analyzing composite delamination. The problem addressed is two-dimensional debonding between plies or ply groups modeled as in-plane orthotropic materials; however, the conclusions discussed apply to general composite delamination problems. It is shown that use of different quantities to designate mode mix can give significantly different results in matching composite applications to mixed-mode toughness tests. For cases where measured interfacial toughness increases with increasing mode II deformation, it is demonstrated that use of a mode mix designation based on energy release rates could be non-conservative. Based on these findings, it is suggested that practitioners consider the differences in failure load predictions that would result if different near-tip quantities were used to relate composite applications to measured toughnesses. To this end, methods for converting mode mix designations in terms of energy release rates into designations in terms of other fracture quantities are outlined and applied. This revised version was published online in August 2006 with corrections to the Cover Date.     

湿热环境下复合材料的混合型层间断裂特性研究

采用混合型挠曲(MMF)试件,研究了材料吸湿和环境温度对T300/5405复合材料混合型层间断裂韧性的影响。给出了在不同温度下,不同吸湿含量试件分层临界扩展时的Ⅰ型分量和Ⅱ型能量释放率分量散点图。结果表明:在吸湿和温度的综合作用下,分层尖端存在塑性变形;常温下,吸湿对材料的层间断裂韧性影响不明显,在高温环境中,随吸湿量增加,层间断裂韧性显著增加;温度对干态材料的断裂韧性影响较小,试件吸湿后,随温度升高,韧性增强。      

A new indentation model for sandwich circular panels with gradient metallic foam cores

A new analytical model is presented to predict indentation behavior of the sandwich circular panel with gradient foam cores under a flat-end cylindrical indenter. In the model, a displacement field of the upper face sheet of the sandwich panel is assumed to be a cosine function and plateau stress of the gradient foam core varies with the mass density along the thickness direction of the sandwich panel. The sandwich panel is modeled as an infinite, isotropic, plastic membrane on a rigid-plastic foundation. The explicit solutions of the relation between the indentation force and maximum plastic regions of the upper face sheet are derived based on the principle of minimum work. The analytical results are validated using the finite element code ABAQUS^®. The influences of the gradient foam core on the maximum plastic region, the indentation force and the plastic strain energy of the sandwich panel are also investigated.     

Dynamic micromechanical modeling of textile composite strength under impact and multi-axial loading

Micromechanical finite element modeling has been employed to define the failure behavior of S2 glass/BMI textile composite materials under impact loading. Dynamic explicit analysis of a representative volume element (RVE) has been performed to explore dynamic behavior and failure modes including strain rate effects, damage localization, and impedance mismatch effects. For accurate reflection of strain rate effects, differences between an applied nominal strain rate across a representative volume element (RVE) and the true realized local strain rates in regions of failure are investigated. To this end, contour plots of strain rate, as well as classical stress contours, are developed during progressive failure. Using a previously developed cohesive element failure model, interfacial failure between tow and matrix phases is considered, as well as classical failure modes such as fiber breakage and matrix microcracking. In-plane compressive and tensile loading have been investigated, including multi-axial loading cases. Highly refined meshes have been employed to ensure convergence and accuracy in such load cases which exhibit large stress gradients across the textile RVE. The effect of strain rate and phase interfacial strength have been included to develop macro-level material failure envelopes for a 2D plain weave and 3D orthogonal microgeometry.     

Crack propagation on helicopter panel: Experimental test and analysis

Aerospace structures need excellent structural efficiency and damage tolerant behaviour to avoid critical failure in presence of small defects and repeated small loads typical of contingent loads. With the aim of improving the performance of the structures, new materials have been developed. Such materials, as the Al–lithium alloy, are designed with the purpose of optimizing stress/strain vs. weight. Considering the distinct advantage, but also the disadvantage, of this innovative material, it is important to verify the damage tolerant behaviour of the component and this is the aim of the present work.With this aim, some tests have been performed on full scale panel specimens representative of a rear helicopter frame. Dedicated test equipment has been designed and built in order to apply the effective service loads on artificial damaged panels. During the tests, the propagation of the crack, started from an artificial damage, has been monitored until the progressive failure of the panel reaches one or more stringers. Moreover, each specimen has been instrumented with several strain gauges to obtain a strain map during the crack propagation. The crack parameters and the strains recorded during the propagation have been compared with the results from a detailed FE model and an analytical model, with a good correlation. In addition, a detailed FE submodel of the bolted joint (stringer and skin in the crack propagation path zone) has been constructed to obtain the crack parameter of a particular panel specimen whose test has also been carried out in the stringer bolted joint.     

A Study on Skin Delaminations Growth in Stiffened Composite Panels by a Novel Numerical Approach

In this paper, a study on skin delamination growth in stiffened composite panels made of carbon fibres reinforced polymers and subjected to compressive load is presented. A robust (mesh and time step independent) numerical finite elements procedure, based on the Virtual Crack Closure Technique (VCCT) and on the fail release approach, is used here to investigate the influence of skin delamination size and position on the damage tolerance of stiffened composite panels. Four stiffened panels configurations with skin delaminations differently sized and positioned are introduced. Bay delaminations and delaminations under the stringer foot are considered. The novel numerical procedure has been used to simulate the delamination growth for all the investigated panel configurations and to evaluate the influence of the delaminations’ geometrical parameters on the growth development. As a confirmation of the applicability and effectiveness of the adopted numerical tool, the numerical results, obtained for all the analysed configurations, in terms of grown delaminated area, displacements and strains measured in various panel locations, have been compared with experimental data available in literature.