A damage mechanics tool for laminate delamination

A simplified method based upon damage mechanics for the delamination analysis of carbon-resin composites is presented. In the neighbourhood of a laminate structure quasi-straight edge, damage is taken concentrated on the interface between layers. The finite element code EDA, acting as a post-processor of an elastic laminate shell computation, allows the onset and propagation forecast of delamination. First numerical simulations of delamination are given and compared with experimental results from literature.     

Identification of embedded interlaminar flaw using inverse analysis

The integrity of a composite laminate can be greatly affected by an existence of embedded interlaminar flaw. In general, identification of such a flaw often requires expensive tools and tedious processes. The aim of the present work is to develop a novel method with the aid of an intelligent post-processing scheme, thereby not relying on those sophisticated experiments. Essentially the proposed procedure utilizes an inverse analysis to estimate unknown delamination parameters from limited measurements. The procedure first constructs approximate functions relating the delamination parameters to measurement parameters. Then, a multi-dimensional minimization technique is adopted to search for the best estimates of unknown parameters corresponding to the lowest value of error objective function. In the present verification and simulation analyses, surface strains at discrete locations on a composite laminate under three-point bending are selected as the input measurements. Although reasonable estimates are obtained with these measurements, to increase their accuracy, the deflection at load point is also included as measurement input. Additional improvements are observed when those measurements under multiple loading conditions are included. A detailed error sensitivity analysis is also carried out to confirm the methods robustness. These results suggest the current method to be one of the alternate identification approaches for detecting a single embedded delamination in composite laminates.     

基于反平面剪切模型的含分层双金属板片条合成能量解法及其与有限元解的比较

基于反平面剪切模型, 求解得到受出面载荷含分层双金属梁的位移解答, 利用片条合成能量解法构造含分层双金属板附加位移模态, 得到闭合解。利用有限元软件ANSYS建立含对称、非对称矩形分层双金属板有限元模型, 采用接触元模拟非对称分层区, 得到有限元解。结果表明, 与弯曲型闭合解相比, 反平面剪切型闭合解与有限元解更接近。      

含矩形内部分层的复合材料层板的 状态分解-片条合成能量解法

根据叠加原理将含有矩形内部分层的层板在横向载荷作用下的受力状态进行分解, 从而 将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析, 并据此 建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于边界的切片, 将切片视为 含分层的层合梁, 其位移模态以相应层合梁的附加位移模态来表示。这样, 可构造层板分层区内满 足位移边界条件的位移场。最后, 应用最小势能原理确定位移幅值的闭合解。计算结果表明, 挠度 幅值远远大于中面位移幅值, 且与由双三角级数能量解法所得挠度幅值吻合很好。      

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.     

Self-healing of delamination cracks in mendable epoxy matrix laminates using poly[ethylene-co-(methacrylic acid)] thermoplastic

This paper investigates the self-healing repair of delamination cracks in a carbon fibre–epoxy laminate using the mendable thermoplastic poly[ethylene-co-(methacrylic acid)] (EMAA). The effects of different types (fibres or particles) and concentrations of the mendable EMAA agent on the self-healing efficiency was measured using mode I interlaminar fracture toughness testing and fractographic analysis. The EMAA was effective in healing delamination damage and increasing the fracture toughness compared to the original laminate. High healing efficiency was achieved by the wide area flow of EMAA (increase of ～25 times) through delamination cracks under the pressure delivery mechanism. High recovery in the fracture toughness was achieved after healing by the formation of large-scale EMAA-bridging ligaments along the delamination, which is a toughening mechanism unique to this type of self-healing material. EMAA proved effective for the multiple repairs of delamination cracks with some loss in the self-healing efficiency of the mendable laminates.     

Numerical analysis of delamination buckling and growth in slender laminated composite using cohesive element method

In this article, the finite element method (FEM) using cohesive element is applied to predict the delamination buckling and growth in slender laminated composite with embedded delamination under compressive load. In particular, the study is focused on the significant effects of delamination buckling for various parameters in slender composite laminate, such as model length–width ratio, delamination shape, delamination size, and delamination depth position. Furthermore, the delamination growth is assessed to investigate the influence of some key parameters (delamination size and delamination depth position) on the delamination growth load, growth shape and direction.     

Development of smart composite structures with small-diameter fiber Bragg grating sensors for damage detection: Quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing

The authors and Hitachi Cable, Ltd. have recently developed small-diameter optical fiber and its fiber Bragg grating (FBG) sensor for embedment inside a lamina of composite laminates without strength reduction. The outside diameters of the cladding and polyimide coating are 40 and 52 μm, respectively. First, a brief summary is presented for applications of small-diameter FBG sensors to damage monitoring in composite structures. Then, we propose a new damage detection system for quantitative evaluation of delamination length in CFRP laminates using Lamb wave sensing. In this system, a piezo-ceramic actuator generates Lamb waves in a CFRP laminate. After the waves propagate in the laminate, transmitted waves are received by an FBG sensor attached on or embedded in the laminate using a newly developed high-speed optical wavelength interrogation system. This system was applied to detect interlaminar delamination in CFRP cross-ply laminates. When the Lamb waves passed through the delamination, the amplitude decreased and a new wave mode appeared. These phenomena could be well simulated using a finite element analysis. From the changes in the amplitude ratio and the arrival time of the new mode depending on the delamination length, it was found that this system could evaluate the delamination length quantitatively. Furthermore, small-diameter FBG sensors were embedded in a double-lap type coupon specimen, and the debonding progress could be evaluated using the wavelet transform.     

Perforation of flexible laminates by projectiles of different geometry

This paper investigates the response of flexible laminates to ballistic impacts by projectiles of various geometries, namely, flat-ended, hemispherical, ogival (CRH 2.5) and conical (30° half-angle) projectiles. The laminate of interest is Spectra Shield^® comprising [0°/90°] extended chain polyethylene filaments embedded in a thermoplastic resin. Ballistic tests show that flat-ended projectiles cut the laminate through a shearing action, effectively punching a circular hole in the laminate whereas hemispherical projectiles perforate the laminates by stretching the Spectra filaments to failure resulting in a rectangular hole in the laminates. While the manner in which they are perforated are different, many similarities are observed in specimens perforated by flat ended and hemispherical projectiles such as the formation of a generator strip, the extent of delamination, the creasing of the laminate, tearing of the laminate at the edges, etc. Ogival and conical projectiles, on the other hand, perforate the laminates with minimal delamination and tearing of the specimens. Interestingly, the region of the specimens affected by the projectiles appears to increase in size instead of becoming more localised at higher impact velocities as often reported for most ballistic impacts events, including the ballistic perforation of woven fabric. This suggests flexible laminates are more effective in dissipating energy than woven fabric in the application of flexible armour.     

The influence of ply sequence and thermoelastic stress field on asymmetric delamination crack growth behavior of embedded elliptical delaminations in laminated FRP composites

The influence of ply lay up and the interaction of residual thermal stresses and mechanical loading on the interlaminar asymmetric embedded delamination crack growth behavior have been investigated. Two sets of full three-dimensional thermo-elastic finite element analyses have been performed for the interlaminar elliptical delaminations, which may be due to manufacturing defects or other reasons and are located symmetrically with respect to the midplane in a quasi-isotropic FRP composite laminate lay up. Depending upon the through-the-thickness location of the embedded elliptical delaminations, four different laminate configurations have been considered. Strain energy release rate (SERR) procedures have been employed to assess the delamination crack growth characteristics at the interfaces. It is found that the individual fracture modes exhibit asymmetric and non self-similar crack growth behavior along the delamination front depending upon the location of the interfacial delaminations; ply sequence and orientation and thermo-elastic anisotropy of the laminae.     

复合材料层合板三维分层问题的断裂力学分析

对复合材料层板中椭圆分层的断裂力学问题进行了研究。根据层板平面剪切型分层和反平面剪切型分层尖端附近位移场、应力场与应力强度因子的关系,利用法向切片法,得到椭圆分层前缘应力强度因子与能量释放率的关系。结合由附加位移所确定的总位能,确定了能量释放率和应力强度因子沿分层前缘分布的表达形式。数值计算给出了二者随分层区形状、载荷以及各层厚度比等参数变化的分布情况。     

Energy-release-rate evaluation for delamination growth prediction in a multi-plate model of a laminate composite

In this paper, numerical methods for the evaluation of the energy-release-rate along a delamination periphery under conditions of local buckling of the delaminate, as well as global buckling of the entire laminate, are presented. A multi-plate model, using independent Reissner-Mindlin plate models for each of the delaminated and undelaminated plies, with Reissner-Mindlin constraints for relating the degrees of freedom of the delaminated plates to those of the undelaminated plate at the crack front, is used to model the laminate with embedded delaminations. Explicit expressions, in terms of finite element nodal or Gauss-point variables, are derived for the pointwise energy release rate in terms of the J-integral and the Equivalent Domain Integral in the context of a typical multi-plate model for characterising the delamination growth. A finite element method with a 3-noded quasi-conforming shell element, and an automated post-buckling solution capability, is used for conducting the numerical analyses in this paper. Using these numerical results, mechanisms of multiple buckling modes and their effect on the propagation of embedded delaminations in plates, are studied.This work has been supported by a grant from FAA to the Center of Excellence for Computational Modeling of Aircraft Structures, Georgia Institute of Technology. The first author also acknowledges the support by the INDO-US Science and Technology Fellowship under the auspices of US Agency for International Development.     

含椭圆形分层层板的状态分解-片条合成能量解法

根据叠加原理将含有椭圆形非穿透分层的层板在横向载荷作用下的受力状态进行分解,从而将分层问题归结为在分层表面上的附加剪切载荷作用下层板附加位移与附加应力的分析,并据此建立了一个仅包含分层区的力学模型。进而在层板分层区中切取平行于坐标平面的切片,将切片视为含分层的层合梁,其位移模态以相应层合梁的附加位移模态来表示。这样,可构造层板分层区内满足位移边界条件的位移场。最后,应用最小势能原理确定位移幅值的闭合解。计算结果表明,挠度幅值远远大于中面位移幅值,且与由双三角级数能量解法所得挠度幅值吻合很好。      

Fatigue crack growth and delamination behaviours of advanced Al‐Li alloy laminate under single tensile overload

In this paper, fatigue crack growth and delamination behaviours of a new fibre metal laminate (FML) named as Al‐Li alloy laminate were tested under different single tensile overloads and compared with those of glass laminate aluminium reinforced epoxy. The results indicate that the crack growth rate of Al‐Li alloy laminate after overload applied can quickly get back to its original level when the crack grows outside of the overload plastic zone. The overload has no influence on the delamination shape and size of Al‐Li alloy laminate. These results are obviously different from those found in the present study for GLARE, in which the crack growth rate cannot recover after overload, even though the crack is far beyond the overload plastic zone. A kink nearby the location of overload applied was found in the obtained delamination shape. This study provides some new results for better understanding the damage tolerance mechanism of FMLs.     

复合材料层板损伤过程的刚度分析

本文对典型铺设的[0₂/±45₂/90₂]_s碳/环氧复合材料层板中的典型损伤状态进行了实验观察,测定出损伤对层板刚度引起的下降率.建立了横向裂纹扩展、分层伴以横向裂纹扩展的三维有限元分析模型,计算出对层板刚度引起的下降率,并与实验值进行了比较.结果表明,横向裂纹和分层是层板的主要损伤型式,分层损伤扩展是一个主导性的稳定的损伤扩展过程,是导致刚度下降的主要因素.     

Prediction of Mode I interlaminar fracture toughness of stitched flax fiber composites

This paper aims to propose a simulation procedure to predict the interlaminar fracture toughness of stitched flax fiber composites through a virtual double cantilever beam test. The proposed procedure is constituted of two steps. First, the interlaminar failure of unstitched flax fiber laminate, as the parent laminate, is modeled using cohesive elements with a nonlinear softening law in order to model the large-scale fiber bridging occurred during delamination. The experimental results are used to calibrate the parameters of the cohesive law. Second, two-node beam elements are superposed onto the cohesive interface of the parent laminate at a prescribed stitch density and distribution to model the bridging stitches present in the validation samples. The stitch material behavior and properties are obtained from the tensile test of impregnated stitch fibers. The out-of-plane flax yarn stitching was found to generate a twofold increase in the delamination resistance of the composite laminate at a medium stitch density. The FE analysis results agreed well with the experimental results, where a good fit between the predicted and experimental R-curves was achieved.     

Delamination monitoring of CFRP laminate using the two-stage electric potential change method with equivalent electric conductivity

Carbon fiber reinforced plastics laminate (CFRP) has a high specific strength and stiffness compared to conventional metals, although it is very sensitive to impact. A low impact leads to a delamination and results in the deterioration of the structural reliability. The present study employs a two-stage electric potential change method (EPCM) to identify delamination. In the methods, delamination is estimated using response surfaces, which require numerous experiments. An equivalent electric conductivity method is introduced to reduce this number. Delaminations are successfully estimated using response surfaces based on the results of the finite element method with equivalent electric conductivity.     

Enhanced delamination initiation stress and monitoring sensitivity of quasi-isotropic laminates under in-plane tension by interleaving with CNT buckypaper

Delamination initiation and the corresponding in-situ monitoring method have been investigated for a T300/epoxy quasi-isotropic laminate. Interfaces of the laminate, in which the delamination tends to occur under in-plane tensile load, have been interleaved with porous carbon nanotube (CNT) buckypapers. Both sectional loading to the delamination initiation and full tension to the fracture of specimens were performed to evaluate the reinforced effect and self-sensing properties of the CNT buckypapers on the laminates. As expected, enhanced delamination initiation stress level was obtained, improved by 7.7% compared with that of the base laminate. Simultaneously, electrical resistance and acoustic emission (AE) responses of the laminates were also measured and used to determine the initiation of delamination. The tests have exhibited that the CNT buckypapers have significant influence on the resistance change of the laminate, showing potential to be used as a detector. This study has preliminarily demonstrated that the CNT buckypapers can serve as both sensing and strengthening constituent.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

含分层损伤缝合复合材料层板的剩余压缩强度

基于渐进损伤方法,研究了含单脱层缝合复合材料层板在压缩载荷下的剩余强度。通过商用软件ABAQUS建立了含单脱层缝合复合材料层板剩余压缩强度计算模型,考虑了子层屈曲和分层扩展对剩余强度的影响。通过UMAT子程序实现了层板失效、层间失效和缝线失效的模拟。通过嵌入式杆单元结构模拟了缝线桥联作用及失效。采用Hashin准则及刚度折减法对纤维拉压、基体拉压失效进行了模拟。通过渐进损伤分析,揭示了缝合情况下含单脱层复合材料层板的失效机理,讨论了缝合参数对剩余压缩强度的影响。所预测的破坏模式和剩余强度结果与实验能较好地吻合。分析表明缝合可以明显提高含分层损伤复合材料层板的子层屈曲载荷,抑制分层扩展,并提高层板的剩余压缩强度。