A simplified approach to the damage tolerance design of asymmetric tapered laminates. Part II: Methodology validation

An analytical approach for the computation of the energy release rates associated with ply drop-offs has been presented in Part I of this study; the methodology is based on the Euler–Bernoulli theory applied to layered beams, together with orthotropic rescaling. The analytical approach accounts for both thick and thin section delaminations, as well as for variable tapering angles. This paper presents the validation for the analytical methodology which has been developed in Part I. The validation is carried out via: (1) comparison with finite element solutions in terms of energy release rates versus delamination length; (2) prediction of delamination onset load in experimentally characterized tapered samples under combined tension and bending.     

Prediction for delamination initiation around holes in symmetric laminates

The purpose of this paper is to present an analytical technique for predicting the delamination initiation load and delamination location for balanced symmetric laminates containing a hole. Basically, this approach includes two phases. First, the stress distribution around the hole region is calculated by the authors' recently developed efficient method. Second, the delamination initiation load and delamination location are predicted by using an average stress failure hypothesis together with the Hashin-Rotem delamination criterion. A computer program was developed to calculate the delamination initiation load and location for notched laminates with different ply orientations, different material properties and different stacking sequences. Numerical results for (θ/ – θ/0°)_s and (0°/90°)_s composite laminates generated by the current approach are compared with existing solutions. The results show that the present method is very efficient and useful for the purpose of engineering design.     

含内埋矩形脱层板屈曲分析的传递函数方法

研究了含任意内埋矩形脱层复合材料层合板的屈曲问题。采用一种基于Mindlin一阶剪切理论的条形传递函数方法,将含内埋矩形脱层的复合材料层合板分成含脱层和不含脱层的两种矩形超级单元,然后由各超级单元之间连接结点处的位移连续和力平衡条件得到脱层板屈曲的特征方程,进而得到脱层板的屈曲载荷和屈曲模态。进行参数分析发现,脱层大小、深度、位置以及脱层板的边界条件和复合材料铺层方向对脱层板屈曲载荷的影响较显著。     

Numerical simulation of delamination in laminated composite components – A combination of a strength criterion and fracture mechanics

An approach for the numerical treatment of delamination in laminated composite components is presented. A first ply failure criterion is employed to predict delamination initiation, while delamination propagation is analyzed using linear elastic fracture mechanics. The combination of initiation and propagation criteria yields a conservative estimation of the load earring capacity of a structure. Furthermore, the growth stability, the sensitivity of the results with respect to a change in the interface properties, and the non-linear structural response caused by the delamination growth process are determined. Two structures are investigated, which show the capability of the proposed approach, a curved laminate and a double lap shear test specimen.     

Quantification of flexural fatigue life and 3D damage in carbon fibre reinforced polymer laminates

Carbon fibre reinforced polymer (CFRP) laminated composites have become attractive in the application of wind turbine blade structures. The cyclic load in the blades necessitates the investigation on the flexural fatigue behaviour of CFRP laminates. In this study, the flexural fatigue life of the [+45/−45/0]_2s CFRP laminates was determined and then analysed statistically. X-ray microtomography was conducted to quantitatively characterise the 3D fatigue damage. It was found that the fatigue life data can be well represented by the two-parameter Weibull distribution; the life can be reliably predicted as a function of applied deflections by the combined Weibull and Sigmodal models. The delamination at the interfaces in the 1st ply group is the major failure mode for the flexural fatigue damage in the CFRP laminate. The calculated delamination area is larger at the interfaces adjacent to the 0 ply. The delamination propagation mechanism is primarily matrix/fibre debonding and secondarily matrix cracking.     

Experimental study on delamination migration in composite laminates

The transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, was investigated experimentally. The test method used promotes delamination growth initially along a 0/θ ply interface, which eventually migrates to a neighbouring θ/0 ply interface. Specimens with θ = 60° and 75° were tested. Migration occurs in two main stages: (1) the initial 0/θ interface delamination turns, transforming into intraply cracks that grow through the θ plies; this process occurs at multiple locations across the width of a specimen, (2) one or more of these cracks growing through the θ plies reaches and turns into the θ/0 ply interface, where it continues to grow as a delamination. A correlation was established between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses.Overall, the experiments provide insight into the key mechanisms that govern delamination growth and migration.     

A mechanical model of damage and delamination in corrugated board during folding

The mechanical behavior of a layered paper structure subjected to a combined load of bending and tension is studied. A finite element analysis is performed to include a gradient enhanced continuum damage theory since a non-local theory has to be used when stress gradients are present. Despite the anisotropic nature of paper materials, each layer is modeled as isotropic and homogenous where material parameters are estimated from the in-plane properties of the paper sheet. The two failure modes, material failure and delamination between top and base layer is analyzed within the frameworks of fracture and continuum damage mechanics. Delamination is assumed to be in shearing mode since the crack surfaces are predominantly sliding and crack opening is vanishing. An analytic solution for the fracture energy release rate is derived utilizing engineering beam theory assuming small deformations. Different combinations of stiffness and thickness ratios between the top and base layer are examined in order to judge the risk for having material failure or delamination failure of the multi-ply linerboard. Having a thick and weak top layer, compared to the base layer, increases the probability to obtain through-thickness damage failure in favor of delamination. On the other hand, having a stiff and thin top layer, compared to the base layer, increases the probability to obtain delamination prior to rupture of the top layer. Experiments performed on two-ply linerboards consisting of one ply of mainly virgin fibers and one ply of recycled fibers confirm the predictions made by the model.     

Strength improvement to composite T-joints under bending through bio-inspired design

This paper shows that a bio-inspired design methodology is an effective method to strengthen composite T-joints under bending loading. The ply angles in the laminate of a carbon/epoxy T-joint were tailored using an optimisation program mimicking the evolutionary process of adaptive growth in which the wood microfibril orientation in and around the tree branch-trunk joint is tailored to the prevailing bending loading condition. A single objective optimisation program with four ply angle input variables was used to compute the optimal design of the ply stacking pattern which minimised the interlaminar tensile stress in composite T-joints where delamination damage is initiated. FEA and experimental testing were performed to compare the structural properties of the bio-inspired T-joint against a base-line T-joint with a quasi-isotropic ply stacking pattern. The bio-inspired T-joint exhibited a higher bending failure initiation load (improved by 40%) and elastic strain energy capacity (increased by 75%) than the base-line T-joint.     

Failure analysis of multiple delaminated composite plates due to bending and impact

The present work aims at the first ply failure analysis of laminated composite plates with arbitrarily located multiple delaminations subjected to transverse static load as well as impact. The theoretical formulation is based on a simple multiple delamination model. Conventional first order shear deformation is assumed using eight-noded isoparametric quadratic elements to develop the finite element analysis procedure. Composite plates are assumed to contain both single and multiple delaminations. For the case of impact, Newmark time integration algorithm is employed for solving the time dependent multiple equations of the plate and the impactor. Tsai-Wu failure criterion is used to check for failure of the laminate for both the cases. To investigate the first ply failure, parametric studies are made for different cases by varying the size and number of delaminations as well as the stacking sequences and boundary conditions.     

PNF增韧层对CFRP复合材料分层影响的数值分析

尼龙无纺布增韧层能在保证良好工艺性能的前提下,显著提高纤维复合材料(carbon fiber reinforced polymer,CFRP)的断裂韧度,但其机制还不明晰。引入一种反映尼龙无纺布增韧层(polyamide non-woven fabric,PNF)厚度和力学特性的内聚力模型,建立PNF/CFRP复合材料分层损伤产生与扩展的力学模型,通过双悬臂梁弯曲实验和验证,得到如下结论:增韧层的厚度对复合材料Ⅰ型分层的峰值载荷几乎没有影响,增韧层厚度为20μm时,复合材料分层扩展阻力最大;界面最大法向应力分布可有效反映裂纹扩展前沿形貌,分层扩展开始后,其前沿形貌保持一致;在相同的外力载荷下,随着PNF/CFRP复合材料铺层从[012/012]变化到[012/9012],其Ⅰ型分层的峰值载荷和扩展距离不断减小。     

Preliminary design of composite riser stress joints

The objective of this paper is to investigate the technical feasibility of using hybrid carbon and glass-fibre reinforced epoxy composite tubes as production risers for a tension leg oil platform tethered in 1000 m of water. The axial forces and bending moment distributions applied to the riser were calculated by hydrodynamic finite element analysis, taking into consideration the extreme environmental conditions, large displacements, waves, currents and platform motions, which could occur in a 100 year recurrent storm. Loads induced by pre-tensioning the riser, the weight of the riser, external water pressure and the internal pressure that could arise in the event of a blow-out in the well were also considered.The riser was of 220 mm internal diameter and the walls were reinforced with layers of carbon-fibre wound at ±20° to the tubes axis, sandwiched between circumferentially wound glass-fibre reinforced epoxy layers on the inner and outer surfaces. The thickness of the carbon-fibre reinforced layers tapered along the 24 m lengths of the top and bottom sections of the riser, which are described as tapered joints. The strengths at various sections of the composite tubes were calculated using orthotropic, laminated, thick cylinder theory and progressive failure analysis. The wall thicknesses were chosen by comparing the predicted first failure load and 1/3rd final failure load envelopes with the various combinations of axial tensile and bending loads and internal and external pressures that the tubes could encounter. The possibility of delamination occurring at the ply drop-offs in the walls of the tapered joints was investigated using finite element methods and fracture mechanics.The composite riser was shown to satisfy all the design requirements and to weigh less than half the weight of an equivalent steel component.     

Progressive Failure Analysis of Laminated Beams and Arches Undergoing Large Rotations

A geometrically nonlinear finite-element formulation based on the total Lagrangian approach is used to predict the onset of various failure modes in laminated composite beams and arches. Some of the failure modes considered include matrix cracking, fiber breakage, and delamination. Numerical examples of beam and arch geometries are analyzed statically to observe the characteristics of large displacements and large rotations considering these failure modes. Large strain effects on load displacement characteristics are studied. Load-carrying capabilities of the composite beam and arch structures, after the first ply failure, are discussed.     

Adaptive delamination analysis

A methodology aimed at addressing computational complexity of analyzing delamination in large structural components made of laminated composites is proposed. The classical ply‐by‐ply discretization of individual layers may increase the size of the problem by an order of magnitude in comparison with the laminated shell or plate element meshes. The paper features delamination indicators that pinpoint the onset and propagation of delamination fronts with striking accuracy. Once the location of delamination has been identified, the discrete solution space of the classical laminated plate/shell element is hierarchically enriched by a combination of weak and strong discontinuities to adaptively track the evolution of delamination fronts. The so‐called adaptive s‐method proposed herein is equivalent in terms of approximation space to the extended finite element method but offers sparser matrices and added flexibility in transitioning from weak to strong discontinuities. Numerical examples suggest that despite an overhead that comes with adaptivity, the adaptive s‐method is computationally advantageous over the classical ply‐by‐ply discretization, especially as the problem size increases. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of delamination–migration and core crushing in a CFRP sandwich structure

Following the onset of damage caused by an impact load on a composite laminate structure, delaminations often form propagating outwards from the point of impact and in some cases can migrate via matrix cracks between plies as they grow. The goal of the present study is to develop an accurate finite element modeling technique for simulation of the delamination–migration phenomena in laminate impact damage processes. An experiment was devised where, under a quasi-static indentation load, an embedded delamination in the facesheet of a laminate sandwich specimen migrates via a transverse matrix crack and then continues to grow on a new ply interface. Using data from this test for validation purposes, several finite element damage simulation methods were investigated. Comparing the experimental results with those of the different models reveals certain modeling features that are important to include in a numerical simulation of delamination–migration and some that may be neglected.     

Energy-based delamination theory for biaxial loading in the presence of thermal stresses

This paper addresses the issue of using energy balance methods and crack closure concepts to predict the growth of delaminations associated with ply cracks during the progressive loading of cross-ply laminates subject to a combination of in-plane biaxial stresses and thermal residual stresses. When the effective applied stresses and the temperature are held fixed during delamination growth, and there is negligible interaction of the delamination tips with the ply cracks, very simple analytical formulae for the energy release rate can be derived for unconstrained and generalised plane strain conditions, which are exact when the ply crack separation tends to infinity.     

含环向贯穿脱层的轴压圆柱层壳屈曲分析:II——算例分析

脱层的存在将会大大降低层合结构的屈曲载荷。利用含环向贯穿脱层壳的屈曲分析模型,对各种算例进行分析。首先通过与经典理论和一阶剪切理论结果的比较,验证了分析模型的正确性,指出了它们各自的适用范围。考虑了脱层壳的三种不同屈曲模态。分析了不同径厚比、边界条件及脱层长度、深度、位置对脱层壳屈曲载荷的影响。最后给出了正交各向异性脱层壳的屈曲分析以及铺层角度对脱层壳屈曲载荷的影响。     

GLARE层板挤压渐进损伤分析

对GLARE36/5层板进行挤压性能试验研究,采用超声C扫描、断口微距拍摄和扫描电子显微镜等方法观测GLARE层板挤压渐进损伤过程和最终破坏模式。结果表明:GLARE层板挤压起始损伤为铝合金塑性变形;损伤扩展阶段,0°纤维主要承受挤压正应力,铝合金塑性变形增大,铺层间分层起始并扩展;0°纤维屈曲折断后层内纤维基体损伤和分层损伤急剧扩展,层板最终发生挤压破坏。将GLARE层板挤压失效分为层内失效和层间失效,采用应变描述的Hashin准则和界面单元方法并引入金属塑性建立GLARE层板挤压渐进损伤数值模型,数值模型对层板损伤起始位置、分层产生位置、损伤演化过程、最终破坏模式及破坏载荷进行了预测,计算结果与试验结果吻合较好,说明该计算方法能够有效模拟GLARE层板挤压渐进损伤性能。      

The role of delamination in failure of fibre-reinforced composites

The mechanisms by which delamination contributes to the failure of fibre-reinforced composites are reviewed. Through-thickness failure owing to interlaminar stresses is considered first, and the effect of delamination in impact and compression after impact. The way in which in-plane failure can occur by delamination and matrix cracks joining up to produce a fracture surface without the need to break fibres is considered next. Examples of quasi-isotropic laminates loaded at different off-axis angles, and with different numbers and thicknesses of ply blocks show large differences in unnotched tensile strength controlled by delamination from the free edge. Similar mechanisms determine the strength of notched specimens and give rise to the hole size effect, whereby tensile strength increases with decreasing hole diameter owing to increased delamination and splitting. Open hole tension and over-height compact tension tests with constant in-plane dimensions show a transition in failure mode with increasing ply block thickness from fibre-dominated fracture to complete delamination. In all these cases, the critical factor controlling strength is the relative propensity to delaminate.     

含面芯界面缺陷的蜂窝夹芯板侧向压缩破坏模式

为了对含面芯层间脱胶缺陷的蜂窝夹芯板在侧向压缩载荷作用下的典型破坏模式进行数值预报, 建立了基于蔡-希尔破坏准则和粘结模型的计算模型。该计算模型是建立在对蜂窝夹芯板的双悬臂梁(DCB)和单臂梁(SLB) 试验中所发现的一种新的破坏模式的分析基础之上的。对蜂窝夹芯板的侧向压缩破坏行为的数值预报中, 发现一种新的破坏模式: 位于脱胶区域的面板首先发生局部屈曲失稳, 随后面板内部靠近芯子的45°/0°层间出现分层, 与此同时最靠近芯子的45°铺层发生断裂, 伴随着45°/0°层间分层的扩展, 面板发展成为对称性整体屈曲失稳。与侧向压缩试验测试结果对比发现, 计算模型模拟中所预报的破坏模式在实验测试中也得到了很好的验证。      

Suppression of initial failure at tapered end-closure sandwich panel joint by taper angle change

To examine the configuration of CFRP face plates/foamed plastic core sandwich panel joints, a tapered end-closure-type joint is selected and studied. In this type of joint, the sandwich panel is tapered to form a solid laminate comprising two face plates near the joint, and the two panels to be joined are mechanically fastened at the solid laminate with a splice plate. This type of joint may be suitable for aircraft panels because a flat surface can be obtained at the joint, which is advantageous from an aerodynamic viewpoint. However, in a previous study on such a joint, it was found that a delamination crack initiated from the tapered core end and propagated through the interface between the two face plates as an initial failure mode at a much lower tensile load than the final failure load in a tensile strength test. In this study, the angle of the tapered panel was focused on and the effect of changing the taper angle on suppressing the initial failure was investigated through experiments and numerical analysis. It was found that a smaller taper angle is more effective for suppressing the initial failure.