Perforation of FRP laminates under impact by flat-nosed projectiles

A theoretical study is performed herein on the perforation of fibre-reinforced plastic laminates subjected to impact by flat-nosed projectiles in a wide range of velocities. Ballistic impact on FRP laminates is a very complex problem and it can be generally classified into two categories, i.e. global deformation with local rupture and wave-dominated local failure. Simple analytical models for both global deformation failure as well as wave-dominated local failure are first given, and a shear failure criterion is employed to predict the perforation of FRP laminates which fail in global deformation mode. By combining the wave-dominated local failure model and the concept of Von Karman’s critical impact velocity, a condition for the transition of the above mentioned two failure modes is obtained. It is shown that the model predictions are in good agreement with available experimental observations in terms of ballistic limits and critical conditions for the transition of failure modes.     

A new fatigue failure theory for multidirectional fiber-reinforced composite laminates with arbitrary stacking sequence

Fatigue failure is one of the most important failure types of fiber-reinforced composites. In this paper, a new fatigue failure theory for multidirectional fiber-reinforced composite laminates with an arbitrary stacking sequence is developed, by combining nonlinear residual strength and residual stiffness models with the recently improved Puck’s failure theory which includes the in situ strength effect. This fatigue theory can predict the fatigue life, residual strength and residual failure envelope of fiber-reinforced composite laminates under multidirectional loadings. For these predictions it is necessary to recalculate the fatigue lives of laminae after each cycle since the stresses in the laminae change due to stiffness degradation. It is also necessary to account for the nonlinear accumulation of damage at the new stress level in the laminae resulting from stiffness degradation. This is achieved by using the concept of equivalent cycle. The theoretical predictions are in good agreement with available experimental results.     

Effect of off-axis ply orientation on 0°-fibre microbuckling

The aim of the present work is to study both experimentally and theoretically the compression failure mechanisms in multi-directional composite laminates, and especially the effect of the off-axis ply orientation on fibre microbuckling in the 0°-plies. The critical mechanism in the compressive fracture of unidirectional polymer matrix composites is plastic microbuckling/kinking. In multi-directional composites with internal 0°-plies, catastrophic failure also initiates by kinking of 0°-plies at the free-edges or manufacturing defects, followed by delamination. When 0°-plies are located at the outside, or in the case of cross-ply laminates, failure rather tends to occur by out-of-plane buckling of the 0°-plies. T800/924C carbon-fibre–epoxy laminates with a [(±θ/0₂)₂]_s lay-up are used here to study the effect of the supporting ply angle θ on the stress initiation of 0°-fibre microbuckling. Experimental data on the compressive strength of laminates with θ equal to 30, 45, 60 or 75° are compared to theoretical predictions obtained from a fibre kinking model that incorporates interlaminar shear stresses developed at the free edges at (0/θ) interfaces. Initial misalignment of the fibres and non-linear shear behaviour of the matrix are also included in the analysis.     

Transverse ply cracking strains in (0°/90°) and (±θ°/90°) laminates

Comparisons have been made between experimental data on transverse ply cracking in various types of (0°/90°) and (°/90°) laminates and the predictions of the constrained cracking and strain field theory. Generally it is observed that the predictions of the strain field theory are in closer agreement with the experimental data over a wider range of experimental conditions than those of the constrained cracking model. It is shown that reasonable agreement with the observed transverse ply cracking strains of various laminates produced from similar material can be obtained through the use of a standard set of material property values.     

Prediction of biaxial failure envelopes for composite laminates based on Generalized Method of Cells

Macro/micromulti-scale analysis based on the efficient implementation of the Generalized Method of Cells coupled with classical lamination theory was conducted to predict failure of composite laminates, applying failure criteria at the constituent level, including fiber, matrix and interface. Representative unit cells with different fiber arrays were constructed in order to study the effect of reinforcement architecture and failure criteria on strength prediction of composite laminates. In order to compare the micromechanics model’s accuracy with commonly-used macroscopic failure theories, the experimental data obtained from the Worldwide Failure Exercise (WWFE) was utilized, and a quantitative assessment method for failure envelopes was developed to evaluate the model’s performance. Finally, the types of representative unit cell architectures and failure theories which are applicable for different layups were identified. The results indicate that the predictive performance of the employed micromechanics-based model is closest to the three leading macroscopic failure criteria of Puck, Cuntze and Tsai–Wu, and better than all other microscopic-based failure criteria (Chamis, Mayes, Huang), employed in the WWFE study.     

Modeling damage and load redistribution in composites under tension–tension fatigue loading

A fatigue model developed for composite laminates and based on the cycle-by-cycle probability of failure has been modified to account for damage creation and evolution and its effect on cycles to failure. The residual strength of different parts of the laminate is determined during cyclic loading and damage such as matrix cracking is quantified along with its effect on load redistribution and cycles to failure of different parts of the laminate. The model does not require any curve fitting or experimentally measured data other than basic material static strength values and their associated experimental scatter. The model is applied to uni-directional and cross-ply laminates. A stress-based approach using energy minimization and calculus of variations is used. The model predictions range from fair to excellent.     

Experimental study of damage propagation in Over-height Compact Tension tests

This paper describes an experimental investigation into progressive damage development in notched fibre-reinforced composites laminates. The Over-height Compact Tension (OCT) test captures the behaviour of laminates typical of large structures and permits the stable formation of a process zone ahead of the crack tip. This allows a study of the influence of sub-critical damage on progression of fibre failure. A range of lay-ups have been tested using dispersed and blocked plies in the thickness direction. The load vs. pin opening displacement (POD) curve is used to characterise the progressive failure of specimens. A number of interrupted tests were performed for each lay-up to capture the sub-critical damage process before the onset of fibre fracture. Results show that dispersed plies promote fibre failure and crack growth whilst blocked plies promote a larger amount of splitting and delamination which in turn causes a larger process zone and ultimately a tougher laminate.     

Strength of composite laminates under biaxial loads

Five well known failure criteria and one simple progressive model have been used in conjunction with laminate theory, which allows for nonlinear lamina shear behaviour, to predict the initial and final failure strengths of filament wound composite tubes. The predictions have been compared with experimental leakage and fracture stresses for ±75°, ±55° and ±45° filament wound GRP tubes subjected to a wide range of biaxial stress systems including biaxial compression. In some cases the fracture strengths were a factor of 10 higher than the initial failure predictions. The simple progressive failure theory predictions gave the best agreement with the experimental results.©British Crown Copyright 1996, Defence Evaluation and Research Agency published by Kluwer Academic Publishers with permission.     

Modeling nonlinear rate dependent behaviors of composite laminates

Abstract

This study aims to propose a simple explicit model for predicting the nonlinear rate dependent behaviors of composite laminates. Using one parameter plastic potential to describe the flow rule, the viscoplasticity model is expressed as a single master effective stress‐effective plastic strain curve in the form of a power law with a rate dependent amplitude. Based on the viscoplasticity model together with the laminated plate theory, the incremental form of the constitutive formulation is derived to model the nonlinear rate dependent behaviors of composite laminates. Symmetric glass/ epoxy and graphite/epoxy composite laminates were tested at three different strain rates and the experimental results were then compared with the model predictions. It was indicated that the proposed constitutive model is effective in characterizing the nonlinear rate dependent behaviors of composite laminates at strain levels up to 1%.     

A strain-energy-based non-linear failure criterion: comparison of numerical predictions and experimental observations for symmetric composite laminates

A strain-energy-based model to predict non-linear stress/strain response, failure onset and progression in composite laminates was presented by Wolfe and Butalia (Compos. Sci. Technol. 1998, 58, 1107). This paper focuses on some of the critical issues relating to the development of that model. Several of the assumptions made in the model are relaxed or modified. A variety of unidirectional and symmetric laminates are studied. A comparison of numerical results obtained from the model and published experimental data (Supplied by Soden, Kaddour and Hinton (Compos. Sci. Technol., in press) is presented for four different material systems. The strain energy based failure theory predictions agree very well with many of the experimental observations for the material systems investigated in this study.     

Failure of Composite Materials

Abstract:  An overview is given of the state of the art of theories and procedures for predicting and analysing failure in composite materials. Of the scores of failure theories available, only those representative of each of the following categories are discussed: limit or noninteractive, interactive, and failure mode-based theories. The validity and applicability of the various theories are evaluated from the point of view of convenience of application and agreement with experimental results. Both lamina and laminate failures are discussed. In the case of ultimate laminate failure, a progressive damage scheme coupled with a failure mode-discriminating criterion is discussed. Special attention is given to textile composites where new three-dimensional experimental results are reported and a new interlaminar failure theory is proposed.     

Some tensile properties of metal-metallic glass laminates

The tensile properties of brass (Cu-30% Zn)-nickel base metallic glass (MBF-35 Metglas) laminates have been investigated. Laminates were prepared by soldering these constituents together with a Pb−Sn alloy. The metallic glass exhibited an enhanced tensile ductility in the metal matrix environments, and such enhanced ductility depended on the metal matrix strength and elongation. Multiple shear bands have been observed in the metallic glass ribbon with enhanced tensile ductility. The failure modes of the laminates have been analysed based on stress-strain concentration concepts, following failure of the glass. The results were consistent with the experimental observations.     

褶皱缺陷影响L型层合板失效行为:实验和数值研究

通过实验和数值分析相结合的方法开展了褶皱缺陷对L型复合材料层合板承载能力和失效过程影响的研究。实验方面,通过“横条法”人为引入褶皱缺陷,制备了含两种缺陷大小的L型层合板,研究了其在弯曲载荷作用下的承载能力和损伤扩展形式,并与无缺陷L型层合板进行对比分析。数值分析方面,基于3D Hashin失效准则的渐进损伤失效模型, 研究其失效过程中应力分布特征和失效模式,探求褶皱缺陷对L型层合板失效行为的影响机制。实验结果表明,褶皱缺陷会显著降低曲梁的承载能力,并使分层损伤演化的空间扩展特征从无褶皱试样的逐层扩展转变为褶皱区域的聚集式扩展。数值预测与实验现象吻合,并共同表明褶皱处横向应力和面法线应力的集中是导致结构提前失效的主导因素,且褶皱区域的应力集中改变了损伤过程中应力逐层重分配的趋势,导致含褶皱试样呈现出聚集式扩展的破坏特征。该工作可扩展应用于含褶皱缺陷L型层合板的安全性能评估及损伤容限设计。      

基于微观力学失效理论的CFRP多向层合板低速冲击行为预测

基于微观力学失效(MMF)理论对碳纤维增强复合材料(CFRP)多向层合板在低速冲击载荷下失效机制及损伤过程进行分析和预测。建立基于MMF理论的层合板结构冲击损伤行为分析方法。首先, 使用MMF理论对冲击过程中组分的失效类别进行判别; 然后, 根据组分失效的类别制定出相应的材料性能退化方案来实现对复合材料在低速冲击下的逐步失效分析;在ABAQUS平台上开发了基于显示分析的用户材料子程序(VUMAT), 即基于MMF理论的层合板冲击损伤分析程序;最后, 利用MMF理论冲击损伤行为分析方法, 对UTS50/E51碳纤维增强复合材料多向层合板在小能量低速冲击情况下的失效机制和损伤形貌进行预测, 并将预测结果与试验结果进行对比, 分析了利用MMF理论预测冲击损伤这一方法的准确性。结果表明理论预测的凹坑直径与试验测试的凹坑直径误差为4.8%, 预测的失效机制和损伤形貌与实际观察的一致。      

Two-dimensional strain-based interactive failure theory for multidirectional composite laminates

A 2-D strain-based interactive failure theory is developed to predict the final failure of composite laminates subjected to multi-axial in-plane loading. The stiffness degradation of a laminate during loading is examined based on the individual failure modes of the maximum strain failure theory, and a piecewise linear incremental approach is employed to describe the nonlinear mechanical behavior of the laminate. In addition, an out-of-plane failure mode normal to the laminate is also investigated to more accurately predict the failure of multidirectional laminates. The theoretical results of the failure model presented are compared with the experimental data provided by the World-Wide Failure Exercise, and the accuracy of the model’s predictive capabilities is investigated.     

The compressive failure of notched composites: the effects of geometry and microbuckling softening law

The compressive failure of notched composites is modelled from the basis of the understanding that has been reached with regard to the behaviour of cracked elastic softening solids that are subjected to tensile loadings. Particular attention is given to the effects of geometrical parameters and the softening law describing the behaviour of the microbuckling damage zone, and it is shown how the peak load can be related to a solid's geometrical parameters and the damage zone softening law via an analytical expression. The predictions are shown to be consistent with Sutcliffe and Fleck's numerical and experimental results for the compressive failure of centre notched panels of carbon fibre-epoxy laminates.     

层合板极限强度判据及其最大承载能力的工程设计

在研究层合板在复杂载荷下的极限强度时,提出了基于层合板基本强度和最佳应力比实验强度所确定的层合板张量型强度准则和层合板联合强度理论.通过建立新的层合板铺层刚度退化理论并用实验测定“均衡型刚度退化系数”,实现了LPF包络线预测;进而提出了层合板退化张量型强度准则.该准则是一种由单向板基本刚度、强度性能,辅助以均衡型刚度退化系数,预测各种铺层序列的层合板在复杂载荷下最大承载能力的强度判据和工程方法.上述强度准则与[±θ]s,层合板的单向拉伸,[±45]s、[0/90]s层合板平板拉剪,以及[0/90]s、[0/±45]s和[0/45]s层合管状件的双向载荷强度实验结果相当吻合.所提出的层合板极限强度判据和最大承载能力的估算方法,对玻纤复合材料层合结构的工程强度设计,具有实际的指导意义和实用价值.     

复合材料层板静压入破坏机制

建立一个有效的计算模型, 以分析复合材料层板在静压入过程中发生分层、 纤维断裂的现象。该计算模型基于有限元程序的三维逐渐损伤理论对层板的静压入全过程进行模拟, 对逐层逐个单元的损伤进行判断, 可以模拟任意角度、 铺层厚度的层板在递增载荷下的逐渐损伤破坏过程。对炭纤维增强环氧树脂基复合材料层板在静压入过程中发生的分层和纤维断裂现象进行预测,并与实验结果进行比较; 对炭纤维增强双马来酰亚胺树脂基复合材料层板在静压入过程中的分层损伤和最终破坏接触力的大小进行预测,并与低速冲击下的结果进行比较。数值仿真与实验结果吻合较好, 表明静压入分析方法是复合材料层板在低速冲击下产生损伤的可替换分析方法。      

The effect of the measurement frequency on the elastic anisotropy of fibre laminates

Static tests and ultrasonic measurements (2.25 MHz) have been carried out on a series of composite laminates of glass fibres in a polypropylene matrix. A range of angle ply laminates were prepared for this study, with laminate angles θ of ±0, 10, 20, 30 and 40^∘. The high frequency measurements were made using the ultrasonic immersion technique, which allows the determination of a complete set of the elastic constants of a material. The relationship between the ultrasonically determined elastic constants of the angle ply laminates was found to be in excellent agreement with theoretical predictions, as previously validated for carbon fibre/epoxy angle ply laminates. A comparison between the ultrasonic and statically measured values was made for two of the angle ply laminates (θ = 0 and 20^∘). It was found that the static values were lower than those measured at ultrasonic frequency, particularly those constants that were more matrix dominated (for example the transverse moduli of the laminates). Measurements on a pure polypropylene sample at both testing frequencies confirmed that the change in matrix properties with frequency was the cause of this difference. The change in properties with test frequency is likely to be much larger in this system than in other composite materials because the glass transition temperature of polypropylene is close to ambient temperature. Dynamic mechanical tests (1 Hz) were carried out on a sample of pure polypropylene to assess this effect. We also give an appropriate method of estimating the dependence of glass transition temperature on frequency. The results for polypropylene are compared with those for other commonly used polymer matrix materials: epoxy resin, nylon and polyetheretherketone (PEEK): DMTA measurements were also made on these samples. The effect of test frequency on matrix properties, for the glass/PP laminates, was further investigated by examining the relationship of the Poisson's ratios with laminate angle using a mixture of ultrasonic experiments and theoretical predictions. Previously we have shown that the degree of anisotropy between the reinforcing fibre and the matrix phase is paramount in determining whether the material will show a negative Poisson's ratio at a critical laminate angle. The ultrasonic measurements carried out in this study on the glass/PP laminates showed a minimum in one of the Poisson's ratio at a laminate angle of 32°, but the value did not become negative. However, theoretical predictions showed that for a static frequency measurement (1 Hz), where the matrix is softer and hence the anisotropy of each laminate ply is higher, the laminate will show a negative Poisson's ratio with a minimum at a laminate angle of around 28°.     

The impact resistance of polypropylene-based fibre–metal laminates

The high velocity impact response of a range of polypropylene-based fibre–metal laminate (FML) structures has been investigated. Initial tests were conducted on simple FML sandwich structures based on 2024-O and 2024-T3 aluminium alloy skins and a polypropylene fibre reinforced polypropylene (PP/PP) composite core. Here, it was shown that laminates based on the stronger 2024-T3 alloy offered a superior perforation resistance to those based on the 2024-O system. Tests were also conducted on multi-layered materials in which the composite plies were dispersed between more than two aluminium sheets. For a given target thickness, the multi-layered laminates offered a superior perforation resistance to the sandwich laminates. The perforation resistances of the various laminates investigated here were compared by determining the specific perforation energy (s.p.e.) of each system. Here, the sandwich FMLs based on the low density PP/PP core out-performed the multi-layer systems, offering s.p.e.’s roughly double that exhibited by a similar Kevlar-based laminate.A closer examination of the panels highlighted a number of failure mechanisms such as ductile tearing, delamination and fibre failure in the composite plies as well as permanent plastic deformation, thinning and shear fracture in the metal layers. Finally, the perforation threshold of all of the FML structures was predicted using the Reid–Wen perforation model. Here, it was found that the predictions offered by this simple model were in good agreement with the experimental data.