复杂载荷下复合材料对称层合板的椭圆形分层屈曲

应用Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ法对含有单个椭圆形分层的复合材料对称层板在压剪载荷联合作用下的脱层屈曲问题进行了分析计算。给出相应于不同的椭圆长短半轴之比ａ／ｂ值下及不同椭回主轴的偏角时，脱层屈曲的临界应变值。此计算考虑了层板的拉伸剪切藕合刚度影响及子层本身弯曲－扭转耦合刚度，和拉伸－弯曲耦合刚度的影响，给出有工程参考价值的计算结果。     

An experimental study of dynamic delamination of thick fiber reinforced polymeric matrix composites

Dynamic delamination of thick fiber reinforced polymeric matrix composite laminates is investigated using optical techniques and high-speed photography. The laminates used in this work are graphite/epoxy fiber reinforced, 65 percent fiber volume fraction, composite plates consisting of 48 plies (6 mm plate thickness). Two different laminate layups are tested: a quasi-isotropic arrangement and a unidirectional arrangement. The experimental setup consists of 152 mm×152 mm square plates impact loaded in an outof-plane configuration using a high-speed gas gun. Impact speeds range from 1 m/s to 30 m/s. Real-time imaging of the laminate out-of-pane displacement is performed using the lateral shearing interferometer of coherent gradient sensing (CGS) in conjunction with high-speed photography. Onset of dynamic delamination can be observed, and quantities such as delamination speeds (in some cases up to 1800 m/s) are measured and reported. A brief comparison is made with dynamic fracture experiments of the same material conducted in a separate study.     

A novel model of delamination bridging via Z-pins in composite laminates

A new micro-mechanical model is proposed for describing the bridging actions exerted by through-thickness reinforcement on delaminations in prepreg based composite materials, subjected to a mixed-mode (I–II) loading regime. The model applies to micro-fasteners in the form of brittle fibrous rods (Z-pins) inserted in the through-thickness direction of composite laminates. These are described as Euler–Bernoulli beams inserted in an elastic foundation that represents the embedding composite laminate. Equilibrium equations that relate the delamination opening/sliding displacements to the bridging forces exerted by the Z-pins on the interlaminar crack edges are derived. The Z-pin failure meso-mechanics is explained in terms of the laminate architecture and the delamination mode. The apparent fracture toughness of Z-pinned laminates is obtained from as energy dissipated by the pull out of the through-thickness reinforcement, normalised with respect to a reference area. The model is validated by means of experimental data obtained for single carbon/BMI Z-pins inserted in a quasi-isotropic laminate.     

A novel technique for time-resolved detection and tracking of interfacial and matrix fracture in layered materials

A novel experimental technique is developed for time-resolved detection and tracking of damage in the forms of delamination and matrix cracking in layered materials such as composite laminates. The technique is non-contact in nature and uses dual or quadruple laser interferometers for high temporal resolution. Simultaneous measurements of differential displacement and velocity at individual locations are obtained to analyze the initiation and progression of interfacial fracture and/or matrix cracking/delamination in a polymer matrix composite laminate system reinforced by graphite fibers. The measurements at multiple locations allow the speeds at which interfacial crack front (mode-I) or matrix cracking/delamination front (mode-II dominated) propagates to be determined. Experiments carried out use three-point bend configurations. Impact loading is achieved using a modified Kolsky bar apparatus with a complete set of diagnostics for load, deformation, deformation rate, and input energy measurement. This technique is used to characterize the full process of damage initiation and growth. The experiments also focused on the quantification of the speed at which delamination or damage propagates under primarily mode-I and mode-II conditions. The results show that the speed of delamination (mode-I) or the speed of matrix cracking/delamination (primarily mode-II) increases linearly with impact velocity. Furthermore, speeds of matrix failure/delamination under primarily mode-II conditions are much higher than the speeds of mode-I crack induced delamination under mode-I conditions.     

大开口复合材料层合板强度破坏研究

复合材料层合板的各向异性及非均质,使得复合材料层合板内部的破坏形式非常复杂.在复合材料结构的设计中,为满足制造及使用功能上的需求,在复合材料层合板承力结构件上不可避免地需要设计各种开口.然而,含大开口复合材料层合板的强度破坏问题变得更为复杂,使得现有的强度理论面临新的挑战.针对碳纤维增强复合材料大开口层合板受单向拉伸载荷作用下的强度破坏问题进行了数值分析和实验研究.首先,根据Hashin准则和刚度退化模型,对含不同圆形开口尺寸的[0]_(10)单向铺层、[0/90]_5和[±45]_5正交铺层的层合板,进行了单向拉伸载荷作用下渐进失效的数值模拟分析,获得了对应结构的极限载荷和破坏模式.在此基础上,采用数字图像相关方法,进行复合材料大开口层合板强度破坏的实验研究.研究结果表明,大开口复合材料层合板在单向拉伸加载下主要呈现脆性破坏形式,破坏起始位置处于应力集中区.此外,破坏强度和失效模式与复合材料铺层方式和开口尺寸大小密切相关.其中[±45]_5铺层的开口层合板承载能力最弱,分层破坏最严重.开口尺寸越大,结构的极限载荷值越低.同实验测试结果相比,数值模拟对复合材料层合板的损伤失效分析略显不足,往往很难全面分析复合材料层合板破坏失效过程中的各种因素的影响.     

Generalized layerwise mechanics for the static and modal response of delaminated composite beams with active piezoelectric sensors

A coupled linear layerwise laminate theory and a beam FE are formulated for analyzing delaminated composite beams with piezoactuators and sensors. The model assumes zig-zag fields for the axial displacements and the electric potential and it treats the discontinuities in the displacement fields due to the delaminations as additional degrees of freedom. The formulation naturally includes the excitation of piezoelectric actuators, their interactions with the composite laminate, and the effect of delamination on the predicted sensory voltage. The quasistatic and modal response of laminated composite Gr/Epoxy beams with active or sensory layers having various delamination sizes is predicted. The numerical results illustrate the strong effect of delamination on the sensor voltage, on through the thickness displacement and on the stress fields. Finally, the effect of delamination on modal frequencies and shapes are predicted and compared with previously obtained experimental results.     

基于树脂层强度预测分层萌生载荷

 轴向拉伸下的层合板在自由边缘附近存在奇异应力场，容易产生分层萌生进而导致结构破坏．而大多数基于材料力学方法的分层萌生研究对强度参数的确定有较强的主观性，缺乏合理解释．本文通过在层间插入一定厚度的树脂层，将分层萌生视为层间树脂层在三维应力状态下的强度破坏，根据有明确试验标准的树脂强度和Mohr 判据判断是否发生分层萌生．采用Pipes-Pagano 的均匀轴向拉伸模型计算应力场，对层间应力与树脂层面外应力进行了对比．取临界长度为4 个单层板厚度对T800/914 层合板的分层萌生进行了预测，结果表明预测值与实验值吻合良好．     

Strain and Fracture of Glass-Fiber Laminate Containing Metal Layers

This paper describes an experimental study on strain and fracture of plane samples made of glass-fiber laminate and fabric-based laminate with surface and inner aluminum layers. It is shown that the presence of these layers reduces the strength of glass-fiber laminate under static and low-cycle loading. This can be explained by the fact that the stretching of a hybrid composite along the layers is accompanied by the formation of localized tensile regions of glass-fiber laminate across the layers. As a result, both the hybrid composite and its glass-fiber laminate component are stratified.     

A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites

An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating interface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the frictionless contact condition.The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum approach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction.     

缝合复合材料层间开裂的试验和数值研究

缝合复合材料层合板中贯穿厚度方向的缝线,能有效增强层合板的抗分层能力。本文对一种碳纤/环氧缝合复合材料层板进行了短梁三点弯试验,测得了压头的载荷-位移曲线,并观察了层间裂纹的扩展,证实了缝线对层间裂纹的阻滞作用。建立了三维有限元模型模拟了上述试验,模型中相邻的铺层之间布置了一层初始无厚度的界面单元,界面单元的失效自然模拟层间开裂,而缝线简化为面积等效的梁单元,数值结果与试验观测吻合。     

Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter.     

The use of stereo X-ray and deply techniques for evaluating instability of composite cylindrical panels with delaminations

The buckling loads of eight-ply AS4/3501-6 graphite/epoxy cylindrical panels with delaminations were determined experimentally. The delaminations fabricated into the laminate with Mylar and Teflon inserts, represent the effect of low-velocity projectile impact damage. The Mylar was found to cause partial delamination while the Teflon inserts caused total delamination. Two types of insert positions were considered; eccentric or off-midsurface, and midsurface. The eccentric delaminations were placed progressively through the thickness of the laminate. STAGSC-1 finite-element computer code results for undelaminated composite panels were compared to the experimental results to obtain a percent strength degradation. The experimental testing was accomplished by the Air Force Flight Dynamics Laboratory. The test device provided boundary conditions of clamped top and bottom edges and simply supported vertical sides. Two destructive techniques, stereo X-ray and deply, were used to determine the total delaminated areas and locations. Based in part on these results, one equivalent delamination was obtained corresponding to the total area of the multiple partial delaminations. The panels with multiple delaminations were found to be approximately five-percent weaker than a single delaminated area of the same total size. Paper was presented at the 1987 SEM Spring Conference on Experimental Mechanics held in Houston, TX on June 14–19.     

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions and plate thickness. As expected, the natural frequencies and the critical buckling load of the plates with delaminations decrease with increase in delamination length. Increase in delamination length also causes instability regions to be shifted to lower parametric resonance frequencies. The effect of edge delamination on the static and dynamic stability as well as of delamination growth is investigated.     

Energy release rates for delamination of composite beams

This paper deals with the formulation of a mechanical/numerical model for analyzing the delamination effects of layered composite beams. The laminate is modelled through a multiple-beam model and interfacial constitutive laws are obtained by introducing interlaminar bilateral and unilateral springs. Delamination growth is described by employing the classical energy release rate criterion. A path-following procedure with delamination growth control is presented for the numerical analysis of the given model. Numerical results on delamination buckling and growth in compressed beams are given and comparisons with simplified theories are established.     

大、中等质量冲头冲击下支持跨度对复合材料层压板冲击的影响分析

基于ABAQUS软件建立三种支持跨度的层压板三维有限元模型,分别计算在两种质量冲头冲击下的响应和损伤。结果表明,在判断支持跨度对冲击结果的影响时,要考虑冲头质量与板质量的比;在大质量冲头冲击的情况下,层压板的响应呈现准静态特征,层压板支持跨度的变化对,最大接触力、冲击持续时间、分层损伤面积等参数的影响较为简单明确;对于中等质量冲头情况,冲击接触时间减小,层压板振动明显,导致冲头与层压板在冲击过程中会脱离接触。在这种情况下不同跨度下板的响应差异也较为明显,冲击力的大小和损伤情况要依据具体的分析。从冲击接触时间和层压板固有振动周期的角度分析了冲头质量水平对冲击响应的影响。     

Response and Damage Tolerance of Composite Sandwich Structures under Low Velocity Impact

The deformation and failure response of composite sandwich beams and panels under low velocity impact was reviewed and discussed. Sandwich facesheet materials discussed are unidirectional and woven carbon/epoxy, and woven glass/vinylester composite laminates; sandwich core materials investigated include four types of closed cell PVC foams of various densities, and balsa wood. Sandwich beams were tested in an instrumented drop tower system under various energy levels, where load and strain histories and failure modes were recorded for the various types of beams. Peak loads predicted by spring-mass and energy balance models were in satisfactory agreement with experimental measurements. Failure patterns depend strongly on the impact energy levels and core properties. Failure modes observed include core indentation/cracking, facesheet buckling, delamination within the facesheet, and debonding between the facesheet and core. In the case of sandwich panels, it was shown that static and impact loads of the same magnitude produce very similar far-field deformations. The induced damage is localized and is lower for impact loading than for an equivalent static loading. The load history, predicted by a model based on the sinusoidal shape of the impact load pulse, was in agreement with experimental results. A finite element model was implemented to capture the full response of the panel indentation. The investigation of post impact behavior of sandwich structures shows that, although impact damage may not be readily visible, its effects on the residual mechanical properties of the structure can be quite detrimental.     

Energy release rate analysis of delamination in laminates

Delamination growth caused by local buckling of delaminated laminate under compression may lead the structure to failure. In this paper, a two-dimensional model of delaminated laminates was studied using a combination of post-buckling theory and fracture mechanics. The delaminated laminate under compression is first analysed by the first-order deformable plate thoery. Then, the energy release rateG at every point along the delamination front is derived by means of a variation problem with a moving boundary. Finally, the near-surface elliptical delamination is also discussed. There is a large variation of energy release rateG along the delamination front, the direction in which delamination growth may occur depends upon the delamination aspect ratio, the state of applied load and the orientation of plies.Supported by the Chinese Science Foundation of Aeronautics     

CONTACT ANALYSIS FOR FIBER-REINFORCED, DELAMINATED LAMINATES WITH KINEMATIC NONLINEARITY

A macro-micro analytical approach for the anti-penetrating contact problem at the interfaces of the delamination in symmetrically cross-plied,fiber-reinforced rectangular laminates is presented in this paper.The laminate is simply supported and subjected to a uniform transverse load with a through-width delamination buried at the center position.A contact factor is defined to characterize the contact efect and determined using the micro-mechanics of composite material.By analyzing the kinematics of nonlinear deformation at the interfaces of the delamination,the contact force is derived.Asymptotic solutions from perturbation analysis are presented.It is found that the deformation of the laminate involves a global deflection and a local buckling.The antipenetrating contact efects are characterized by the local buckling and are intrinsic properties of the laminates,relying only on the geometries of the delamination and the material properties.Parametric analyses show that the location and size of the contact areas and the distribution of the contact force are hardly afected by the aspect ratio.     

Delamination initiation of laminates with pin-loaded holes

A finite element analysis is conducted to determine the three-dimensional stress field in a composite laminate with a pin-loaded hole. The accuracy of computation is established by comparison with the strain gauge measurements near and away from the hole boundary. An acoustic emission technique was used to determine the initial failure load as the specimen was subjected to a quasi-static loading rate. Specimens were examined between the load steps using radiography and micrography in order to detect delamination initiation. The delamination initiation site and the corresponding load level are predicted by applying the strain energy density criterion. The critical parameters were extracted from the experimental measurements and finite element analysis of a double cantilever beam specimen. The analysis predictions indicate that delaminations could initiate close to the free surface at the interface between layers with a fiber orientation of ±45° relative to the load direction. These predictions confirm the experimental observations.