The prediction of R-curves and notched tensile strength for composite laminates

A new model is proposed to explain the cracking and fracture of notched composite laminates. It is based on the energy absorption associated with the micromechanisms of fracture. Crack-growth resistance curves (R-curves) are predicted for a wide range of laminate constructions and materials, and the corresponding notched strengths deduced. Both R-curve and notched strength predictions are in good agreement with published data. The effect of improved fibre-matrix bonding on laminate notched strength is investigated in a case-study, and is successfully predicted using the model.     

Progressive failure analysis of 2/2 twill weave fabric composites with moulded-in circular hole

Micromechanical three-dimensional finite element models of 2/2 twill weave T300 carbon/epoxy woven fabric composite panels with moulded-in circular hole are established for stress analysis. In these models, the streamline equation is used as a shape function to simulate the fibre configuration. A progressive failure analysis together with a newly developed ‘maximum notched strength method’ are also proposed to predict the failure modes and notched strengths of the fibre dominated laminate with moulded-in hole. Perforated specimens of different hole sizes are prepared using a special procedure. Tension tests are performed to evaluate the stress–strain and failure characteristics. An increase in tensile strength with increasing hole size is observed within the experimental data range. Numerical results from progressive failure analysis provide good prediction to the failure phenomena of the fractured specimens. The notched strengths from the proposed numerical procedure are slightly higher than the experimental results.     

平面编织复合材料层合板低速冲击后的拉伸性能

对两种不同铺层形式的平面编织复合材料层合板低速冲击后拉伸性能进行了实验研究,在此基础上建立了有限元损伤扩展仿真模拟。在所建立的有限元模型中,将低速冲击损伤等效为形状规则的软化夹杂,并针对两种铺层形式采用不同的损伤判据和模量衰减准则。研究结果表明:该有限元模拟结果与实验结果符合,说明该模型能够准确地预测低速冲击后平面编织复合材料层合板的损伤扩展规律和剩余拉伸强度;不同铺层形式的平面编织复合材料层合板在低速冲击后拉伸的损伤扩展规律不同;它们的冲击后拉伸强度降均>50%,在复合材料结构设计中应该受到重视。      

Failure assessment on central-sharp notched carbon/epoxy laminates

Fracture models to predict the strength of laminated composites having sharp notches demand the un-notched strength and the critical damage size ahead of the notch. The critical damage size, in general, depends on the material, geometry of the specimen and size of the sharp notch. The extraordinary success of a fracture model lies in its ability to combine a theoretical framework with experimentally measured quantities. Modifications are made in one of the stress-fracture criteria known as the point stress criterion for accurate prediction of notched tensile strength of composite laminates containing sharp notches. To examine the adequacy of these modifications, fracture data of central-sharp notched carbon/epoxy composite laminates with various lay-ups are considered. The notched strength estimates are found to be close to the test results. The modified point stress criterion is very simple and accurate in predicting the notched tensile strength of laminated composites.     

A micromechanics-based strength prediction methodology for notched metal-matrix composites

An analytical micromechanics-based strength prediction methodology was developed to predict failure of notched metal-matrix composites. The stress/strain behaviour and notched strength of two metal-matrix composites, boron/aluminium (B/Al) and silicon carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three-dimensional finite element analysis of a notched specimen to a micromechanical model of a single fibre. In the B/Al laminates, a fibre failure criterion based on the axial and shear stress in the fibre accurately predicted laminate failure for a variety of lay-ups and notch-length-to-specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fibre failure criterion based on the axial stress in the fibre correlated well with experimental results for static and post-fatigue residual strengths when fibre/matrix debonding and matrix cracking were included in the analysis. The micromechanics-based strength prediction methodology presented here offers a direct approach to strength prediction by modelling behaviour and damage on a constituent level, thus explicitly including matrix non-linearity, fibre/matrix interface debonding and matrix cracking.     

3D finite element analysis of tensile notched strength of 2/2 twill weave fabric composites with drilled circular hole

This paper presents the micromechanical three-dimensional finite element models of the 2/2 twill weave T300 carbon/epoxy woven fabric composite laminates with drilled circular holes of different sizes. A fiber breakage failure criterion for predicting the ultimate tensile notched strength of fiber dominated composites is also proposed. It is found that the location of failure initiation for laminates with large hole size is different from those for laminates with smaller holes while the stress concentration may not occur at the notch roots for the fiber dominated laminates. Based on the uniaxial, shear and von Mises stress distributions in the yarn and matrix, the influence of hole-size on the stress distributions and stress concentration is discussed. Standard tensile tests with modifications are performed for this particular type of woven fabric composites. The apparent strain concentration factors and notched strengths determined by experiments are presented and the finite element models are verified by satisfactory correlation between prediction and experiment.     

Progressive damage analysis of composite bolted joints with liquid shim layers using constant and continuous degradation models

The structural behaviour of a single-lap, single-bolt composite joint is investigated using a three-dimensional finite element model. In contrast to previous investigations the influence of a liquid shim layer, added between the two laminates, on strength and structural behaviour of the joints is investigated by virtual testing. The finite element model is validated with experimental data. The experiments point out that the structural behaviour of these joints is dominated by progressive damage. Therefore, as a first approach, progressive damage is considered using Hashin’s three-dimensional failure criterion and a constant degradation model. It is shown that this combination yields very conservative results. As a second approach the model is improved by a continuous degradation model. Considering continuous degradation, the numerical results show very good correlation with the experimental data.     

基于ANSYS环境的平面编织层合板拉伸破坏数值仿真

以ANSYS为平台编制了具有可移植性的APDL程序, 建立了损伤累积模型, 对平面编织层合板的损伤破坏行为进行了数值仿真。该模型对适合于单向铺层的Hanshin判据和Reddy刚度衰减方法进行了相应的修正。为验证模型的有效性, 对G803/5224平面编织光滑板、 孔板进行了相应的试验研究。结果表明, 该模型仿真结果与试验结果吻合, 并且比较简单直观, 为平面编织层合板的损伤扩展与破坏的研究提供了便于工程应用的数字化手段。      

A size effect law for notched tensile strength of woven carbon/epoxy laminates

Specimen-size effect and notch-size effect on the tensile strength of woven fabric carbon/epoxy laminates are evaluated and modeled. For two different layups of [(0/90)₁₂] and [(±45)₂/(0/90)₅]_S, respectively, static tension tests were performed on two-dimensional geometrically similar unnotched and double-edge notched specimens scaled to three different sizes. Experimental results demonstrate that the notched strength of the woven CFRP laminates depend on the size of specimen as well as the size of notch. The ratio of notched strength to unnotched strength decreases as the length of notch increases, regardless of the size of specimen. For a given size of notch, the notch strength ratio becomes larger with decreasing size of specimen. A notch-size effect law is derived by means of the Neuber interpolation method. A specimen-size effect is embedded into the notch sensitivity parameter involved by the notch-size effect law to establish a size effect law that can cope with these two kinds of size effect. The engineering size effect law proposed can adequately describe the specimen-size effect as well as notch-size effect on the tensile strength of the woven CFRP laminates. It is also demonstrated that the size effect law allows determining the size independent fracture toughness on the basis of notched strengths of small specimens that fail in a quasi-brittle manner.     

Effect of damage on the interlaminar shear properties of hybrid composite laminates at cryogenic temperatures

This paper presents the experimental and numerical characterization of the interlaminar shear failure of hybrid composite laminates at cryogenic temperatures. Cryogenic short beam shear tests were performed on hybrid laminates consisting of woven glass fiber reinforced polymer (GFRP) composites and polyimide films to evaluate their interlaminar shear strength. Microscopic observations of damage accumulation and failure mechanisms were also made on failed specimens. In addition, a progressive damage analysis was conducted to predict the initiation and growth of damage in the specimens, and the interlaminar shear strength was determined from the maximum shear stress in the failure region. The damage effect on the interlaminar shear properties of hybrid laminates at cryogenic temperatures was examined based on the experimental and numerical results.     

The effect of fibre length on fracture toughness and notched strength of short carbon fibre/epoxy composites

The effect of radius of curvature on the tensile notched strength of random short carbon fibre/epoxy composites containing 1, 5 and 15 mm length fibres is studied. The strength of all laminates showed a sensitivity to the radius of curvature, with the tensile strength decreasing at smaller radii of curvature. A model is developed to predict notched strength based on assumed evolution and propagation of damage from the tip of the notch. The predictions of the model depend principally on two material properties: the unnotched tensile strength and fracture toughness. Reasonable agreement is achieved between the predicted notched strength and experimental data.     

Experimental and numerical investigation of the tension and compression strength of un-notched and notched quasi-isotropic laminates

Un-notched and notched (in the form of through-thickness open holes), quasi-isotropic AS4/3501-6 laminate coupons were tested in tension and compression. Basic lamina properties were also determined experimentally. Numerical analyses using linear elastic and progressive damage approaches were conducted. The linear elastic model either significantly underestimated (first-ply failure approach) or overestimated (last-ply failure approach) the strength of un-notched laminates. The progressive damage approach was able to predict accurately the un-notched strength, providing that the non-linear shear behaviour was accounted for and appropriate failure criteria used. It was also demonstrated that the progressive damage approach could be implemented, with satisfactory accuracy and efficiency, for open-hole strength prediction using basic material degradation laws, a shell element model and widely available commercial FEM software (ABAQUS). This is of practical use for industrial applications. In addition, for the purpose of comparison, a characteristic distance approach was also applied to the open-hole strength problem. It was found that using a linear analysis with a properly defined secant shear modulus this approach gave an accurate prediction, however at least one measured value of notched strength is still required for calibration using this approach.     

Notch sensitivity of thermoset and thermoplastic laminates loaded in tension

Inplane tensile fracture of unnotched and notched thermoset graphite-epoxy and thermoplastic graphite-PEEK composite laminates is examined. Both fibre-dominated quasi-isotropic and matrix dominated ±45 angle-ply layups were investigated.Classical lamination theory predictions of elastic and strength properties of unnotched specimens are compared with experiments. Several notched geometries, i.e. centre-notched, double-edge notched and open-hole specimens subjected to tensile loading to fracture were examined. The notched strength of the quasi-isotropic laminates was analysed by a damage zone model, where damage around the notch is represented by an equivalent crack with cohesive force acting between the crack surfaces.Good agreement between experimental and calculated strength was observed for the graphite-epoxy laminates which failed in a collinear manner. For the graphite-PEEK laminates discrepancies between predicted and experimental strength are related to observed deviations from collinear crack growth. The angle-ply graphite-PEEK laminates showed larger notch sensitivity than the corresponding graphite-epoxy, probably due to less degree of stress relieving damage formation around the notch.     

Effect of fibre/matrix adhesion on residual strength of notched composite laminates

Effects of fibre/matrix adhesion and residual strength of notched polymer matrix composite laminates (PMCLs) and fibre reinforced metal laminates (FRMLs) were investigated. Two different levels of adhesion between fibre and matrix were achieved by using the same carbon fibres with or without surface treatments. After conducting short-beam shear and transverse tension tests for fibre/matrix interface characterisation, residual strength tests were performed for PMCLs and FRMLs containing a circular hole/sharp notch for the two composite systems. It was found that laminates with poor interfacial adhesion between fibre and matrix exhibit higher residual strength than those with strong fibre/matrix adhesion. Major failure mechanisms and modes in two composite systems were studied using SEM fractography. The effective crack growth model (ECGM) was also applied to simulate the residual strength and damage growth of notched composite laminates with different fibre/matrix adhesion. Predictions from the ECGM were well correlated with experimental data.     

Influence of Fibre Architecture on Impact Damage Tolerance in 3D Woven Composites

3D woven composites, due to the presence of through-thickness fibre-bridging, have the potential to improve damage tolerance and at the same time to reduce the manufacturing costs. However, ability to withstand damage depends on weave topology as well as geometry of individual tows. There is an extensive literature on damage tolerance of 2D prepreg laminates but limited work is reported on the damage tolerance of 3D weaves. In view of the recent interest in 3D woven composites from aerospace as well as non-aerospace sectors, this paper aims to provide an understanding of the impact damage resistance as well as damage tolerance of 3D woven composites. Four different 3D woven architectures, orthogonal, angle interlocked, layer-to-layer and modified layer-to-layer structures, have been produced under identical weaving conditions. Two additional structures, Unidirectional (UD) cross-ply and 2D plain weave, have been developed for comparison with 3D weaves. All the four 3D woven laminates have similar order of magnitude of damage area and damage width, but significantly lower than UD and 2D woven laminates. Damage Resistance, calculated as impact energy per unit damage area, has been shown to be significantly higher for 3D woven laminates. Rate of change of CAI strength with impact energy appears to be similar for all four 3D woven laminates as well as UD laminate; 2D woven laminate has higher rate of degradation with respect to impact energy. Undamaged compression strength has been shown to be a function of average tow waviness angle. Additionally, 3D weaves exhibit a critical damage size; below this size there is no appreciable reduction in compression strength. 3D woven laminates have also exhibited a degree of plasticity during compression whereas UD laminates fail instantly. The experimental work reported in this paper forms a foundation for systematic development of computational models for 3D woven architectures for damage tolerance.     

双轴载荷下缝合层板的强度预测

基于缝合层板单层单胞细观力学模型,研究了单层板在拉、压、剪下的力学特性。根据经典层板理论建立了缝合层板在双轴载荷下的强度模型,并考虑了缝合造成表面层和内部层刚度和强度的差异。通过有限元软件ABAQUS分析了双轴载荷多种工况下缝合层板的损伤演化过程,揭示了缝合层板的失效机理,获得了缝合层板在双轴载荷下的失效包络线以及对应比率载荷下的应力应变曲线。所预测的失效模式和失效强度与实验取得了较好的吻合。通过分析表明缝合层板单层在剪切载荷下表现出一定的非线性特性。多轴多向层板在双轴载荷下表现出较强的耦合性。     

Unification of strength scaling between unidirectional,quasi-isotropic,and notched carbon/epoxy laminates

An investigation into size effects and notch sensitivity in quasi-isotropic carbon/epoxy laminates was carried out. The purpose is to draw a complete picture of the strength scaling in unidirectional, quasi-isotropic, and notched carbon/epoxy laminates. A link was established between the strength scaling of the unidirectional and quasi-isotropic laminates. Efforts were made to understand the relationship between unnotched and open-hole strengths. For very small holes, the notched strengths approach the unnotched strength limit. A scaling law based on Weibull statistics was used to predict the unnotched laminate strengths. For very large holes, the same scaling law in conjunction with a detailed 3D ply-by-ply FE analysis with matrix cracks in the 90° plies and delamination cohesive interface elements was used to predict the large notched strengths. A good agreement between the modelling and experimental results was achieved. The effects of 90° matrix cracks on unnotched and notched strengths were also studied.     

基于细观结构的2.5维机织复合材料强度预测模型

采用经纱矩形截面及纬纱六边形截面假设,将经纱的屈曲轨迹简化为折线形式,建立了2.5维机织复合材料单胞几何模型。以单胞为研究对象,引入改进的三维Hashin失效准则和Mises准则作为组分材料的失效判据,采用不同的刚度退化方式来表征不同的失效模式,建立了基于逐渐损伤理论的强度预测模型。利用有限元分析（FEA）技术,开发了相应的参数化2.5维机织复合材料逐渐损伤分析程序,预测了浅交弯联结构不同机织参数2.5维机织复合材料的拉伸强度,并模拟了经向拉伸和纬向拉伸的损伤扩展过程。与静拉伸试验结果相比,拉伸强度的预测误差在10%以内;模拟的失效模式与试验结果吻合较好。     

复合材料层合板多尺度交互渐进损伤分析

纤维增强复合材料强度的准确表征是复合材料力学性能研究的核心问题之一。该文以碳纤维增强树脂基复合材料层合板为研究对象,基于宏观-细观多尺度分析方法,根据复合材料的物理失效模式分别给出了基体和纤维的细观失效准则,同时考虑基体失效对复合材料层合板纤维轴向力学性能的影响。提出了新的刚度退化方式,可准确表征复合材料层合板的损伤演化过程,开展了复合材料层合板四点弯模型的多尺度交互渐进损伤分析和试验验证。结果表明:基于多尺度方法的复合材料层合板宏-细观交互渐进损伤分析结果与试验结果吻合较好,新的刚度退化方式可以准确模拟层合板的失效过程。