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。      

3D constitutive model of anisotropic damage for unidirectional ply based on physical failure mechanisms

A 3D anisotropic continuum damage model is developed for the computational analysis of the elastic–brittle behaviour of fibre-reinforced composite. The damage model is based on a set of phenomenological failure criteria for fibre-reinforced composite, which can distinguish the matrix and fibre failure under tensile and compressive loading. The homogenized continuum theory is adopted for the anisotropic elastic damage constitutive model. The damage modes occurring in the longitudinal and transverse directions of a ply are represented by a damage vector. The elastic damage model is implemented in a computational finite element framework, which is capable of predicting initial failure, subsequent progressive damage up to final collapse. Crack band model and viscous regularization are applied to depress the convergence difficulties associated with strain softening behaviours. To verify the accuracy of the damage model, numerical analyses of open-hole laminates with different lay-up configurations under tension and compression were performed. The numerical predictions were compared with the experimental results, and satisfactory agreement was obtained.     

Healing of low-velocity impact damage in vascularised composites

This research has sought to characterise damage formation and self-healing efficiency within vascularised carbon fibre reinforced polymer (CFRP) laminates over a range of low velocity impact energies. Using ultrasonic C-scanning and compression after impact (CAI) analysis, vascularised laminates were shown to conform to the same damage size to residual compression strength relationship established for conventional laminates. The damage tolerance level of the host laminate was carefully determined, an important consideration in selection of the most appropriate vascule spacing for a reliable self-healing system. The healing functionality imparted full recovery of post impact compression strength over the range of impact energies tested (2.5–20 J), via healing of matrix cracking and delamination damage. The successful implementation of this technology could substantially enhance the integrity, reliability and robustness of composite structures, whilst offering benefits through reduced operational costs and extended lifetimes. However, establishing the benefits of such novel systems to existing design criteria is challenging, suggesting that bespoke design tools will be required to fully attain the potential benefits of self-healing technologies.     

Numerical analysis of intralaminar failure mechanisms in composite structures. Part I: FE implementation

This paper presents a three-dimensional continuum damage mechanics-based material model which was implemented in an implicit finite element code to simulate the progressive intralaminar degradation of fibre reinforced laminates. The damage model is based on ply failure mechanisms and uses seven damage variables assigned to tensile, compressive and shear damage at a ply level. Non-linear behaviour and irreversibility were taken into account and modelled. Some issues on the numerical implementation of the damage model are discussed and solutions proposed. Applications of the methodology are presented in Part II [1].     

层间混杂复合材料板的拉伸强度预报

采用更为合理的分散度系数表达式改进了玻/碳层间混杂复合材料板断裂应变混杂效应系数公式,结合该混杂效应系数公式与复合材料强度混合定律,提出了层间混杂复合材料单向板的拉伸强度预报方法。将该混杂效应系数公式引入复合材料多向板渐近损伤有限元分析模型,修正了低延伸率纤维单层板的拉伸强度值,在此基础上提出了层间混杂复合材料多向板拉伸强度预报方法,并讨论了刚度退化方案。结果表明,模型预报值与实验均吻合较好,尤其考虑混杂效应的预报值与实验情况更加接近;基体退化系数大的刚度退化方案与实验更为吻合。     

Progressive damage analyses of angle‐ply laminates exhibiting free edge effects using continuum damage mechanics with layer‐wise finite element method

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi‐static, monotonic increasing loading are investigated using three‐dimensional (3D) CDM implementation in a finite element method that is based on the layer‐wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle‐ply composite laminates under quasi‐static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted.     

Numerical analysis of damage progression and strength of countersunk composite joints

A numerical investigation is conducted into the damage progression and strength of bolted joints between fibre-reinforced composite laminates using countersunk fasteners. Experimental tests were previously conducted on a bearing test specimen and countersunk fastener single-lap joints. In this work, computational models are developed for Abaqus/Explicit, with continuum shells employed to model in-plane ply failure. The bolt-nut assembly is modelled with rigid elements, and the models account for bolt torque and frictional contact. The material properties required in the computational model are determined from standard tests, with the compression fracture toughness of composite plies calibrated against experimental data from the bearing test. The analysis approach captures the load-carrying capability of all configurations, and provides reasonable accuracy in predicting damage patterns. The effects of bolt torque, clearance and countersink height ratio are investigated, and the analysis results compare well with experimental findings. Furthermore, the analysis provides rich insight into the damage progression and joint behaviour at the ply level, with the in-plane and through-thickness damage patterns mapped for increasing applied load. Delamination is incorporated using a cohesive element layer at the start of the countersunk region, though has minimal influence on damage progression and load-carrying capability, which agrees with the experimental results.     

Characterization of damage onset in glass-ceramic matrix composite angle-ply laminates

The tensile mechanical properties of a series of model [0/θ/0] glass-ceramic matrix composite angle-ply laminates have been measured at room temperature in an attempt to characterize the onset of damage in this class of material as a function of fibre orientation. The material selected for this study was a silicon carbide fibre-reinforced calcium aluminosilicate composite. The experimentally determined values of composite elastic modulus, strength and first ply failure stress have been compared with those predicted from classical laminate theory. Work carried out to date has shown that at high angles of θ, the damage onset of [0/θ/0] laminates is accurately predicted by the Tsai-Hill first ply failure stress whilst at low angles of θ the onset of damage is in reasonable agreement with that predicted by the Aveston-Cooper-Kelly model for multiple fracture (with the Tsai-Hill failure criterion predicting the ultimate strength of the composite). However, these models give no account of the mechanisms by which failure occurs and assume well-defined and single-valued failure strengths. In reality, glass-ceramic matrices have a distribution of strengths as a result of the inherent flaws within them and an attempt to quantify this has been made by mechanical and structural evaluation of the monolithic matrix material.     

Influences of artificial pre-stressing on ply stresses and tensile properties of Vinylon fibre-reinforced aluminium laminates (VIRALL)

A simple micromechanical model based primarily upon the rule-of-mixtures is developed which allows prediction of the effects of fibre preload on the ply stresses (i.e., the initial residual stresses of fibre, adhesive and matrix) induced within VIRALL laminates, and the tensile stress-strain curves and mechanical properties of VIRALL laminates. The analysis of the ply stresses of VIRALL laminates indicates that pre-stressing will dramatically influence the ply stresses. The predicted tensile stress-strain curves of VIRALL laminates are in good agreement with the experimental curves and the results show that the stress-strain curves of VIRALL laminates move upwards when the prestress increases. The predicted tensile mechanical properties of VIRALL laminates at room temperature show good agreement with those obtained experimentally; both show that prestress can improve the tensile properties (i.e., elastic limit strength, 0.2% yield strength and failure strength) of VIRALL laminates.     

An experimental and numerical investigation into the damage mechanisms in notched composites

Investigations of the effect of size on the tensile strength of composite laminates containing circular holes show that there is a large difference both in failure stress and mechanism due to changes in test configuration. This is particularly true of the ply and laminate thickness, and hole diameter. Interrupted tests have been performed on open hole tensile specimens at different load levels to determine the progressive damage development, evaluated through non-destructive testing (X-ray and C-scanning). The tests were also analysed using a novel Finite Element Modelling technique. This was able to accurately predict the wide range of ultimate strengths measured with variation in test parameters, principally through incorporation of the sub-critical damage in the analysis. A significant damage mechanism was seen to be delamination at the hole edge which generally occurred at a lower stress for a smaller hole diameter to ply block thickness ratio. Delaminations allowed damage to join up through the thickness of the laminate and propagate. In ply-level scaled specimens, the delamination propagation was the ultimate failure mode of most of the specimens. In sub-laminate level scaled specimens, localised damage relieved stress in the 0° fibres at the hole edge, delaying the onset of fibre failure. Less damage was seen for larger holes, thus leading to a decreasing failure stress with increasing hole diameter.     

Tensile behavior of epoxy based FRP composites under extreme service conditions

A well established technique for strengthening reinforced concrete (RC) members is based on the use of externally bonded (EB) FRP composites. Nevertheless, limited knowledge is available on the mechanical properties of FRP composites at extreme service environments. The performance of structural members strengthened with EB-FRP laminates exposed to extreme service temperatures or freeze–thaw cycles is mainly associated to either the bond between the FRP laminate and concrete substrate, or the mechanical properties of the laminates. This paper focuses on the latter aspects and presents results on a series of tensile tests of glass and carbon FRP (GFRP and CFRP) coupon specimens exposed to temperatures ranging between ?15 and +70 °C, or after freeze–thaw cycles, including FRP specimens with different number of plies. The experimental results for GFRP specimens indicate a low influence of ply number on FRP mechanical properties, and a minor reduction of axial tensile strength and strain with increasing the temperature. Results for CFRP specimens subjected to extreme service temperatures reflect a significant reduction of mechanical properties, while freeze–thaw cycles do not significantly influence the mechanical performance.     

Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates

The fracture process of composite laminates subjected to static or fatigue tensile loading involves sequential accumulation of intra- and interlaminar damage, in the form of transverse cracking, splitting and delamination, prior to catastrophic failure. Matrix cracking parallel to the fibres in the off-axis plies is the first damage mode observed. Since a damaged lamina within the laminate retains certain amount of its load-carrying capacity, it is important to predict accurately the stiffness properties of the laminate as a function of damage as well as progression of damage with the strain state. In this paper, theoretical modelling of matrix cracking in the off-axis plies of unbalanced symmetric composite laminates subjected to in-plane tensile loading is presented and discussed. A 2-D shear-lag analysis is used to determine ply stresses in a representative segment and the equivalent laminate concept is applied to derive expressions for Mode I, Mode II and the total strain energy release rate associated with off-axis ply cracking. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

缝合复合材料层板低速冲击及冲击后压缩实验研究

通过对缝合复合材料层板进行低速冲击和冲击后压缩实验, 研究了不同类型的缝合复合材料层板的冲击损伤特性及冲击后压缩的剩余强度。实验研究表明: 基体损伤和分层是缝合层板与未缝合层板低速冲击的主要损伤模式, 缝合层板具有更好的抗冲击性能, 更高的冲击后压缩强度。缝合密度越大的层板其抗冲击性能越好, 冲击后压缩强度越高。缝合方向为0°的缝合层板较缝合方向为90°的缝合层板具有更好的抗冲击性能和更高的冲击后压缩强度。增加0°方向铺层, 减少45°、-45°方向铺层, 可以提高缝合层板的抗冲击性能和冲击后压缩强度。     

Numerical analysis of intralaminar failure mechanisms in composite structures. Part II: Applications

A three-dimensional continuum damage mechanics-based material model was implemented in an implicit Finite Element code to simulate the progressive intralaminar degradation of fibre reinforced laminates based on ply failure mechanisms. This paper presents some structural applications of the progressive failure model implemented. The focus is on the non-linear response of the shear failure mode and its interaction with other failure modes. Structural applications of the damage model show that the proposed model is able to reproduce failure loads and patterns observed experimentally.     

Stiffness and fracture analysis of laminated composites with off-axis ply matrix cracking

Matrix cracks parallel to the fibres in the off-axis plies is the first intralaminar damage mode observed in laminated composites subjected to static or fatigue in-plane tensile loading. They reduce laminate stiffness and strength and trigger development of other damage modes, such as delaminations. This paper is concerned with theoretical modelling of unbalanced symmetric laminates with off-axis ply cracks. Closed-form analytical expressions are derived for Mode I, Mode II and the total strain energy release rates associated with off-axis ply cracking in [0/θ]_s laminates. Stiffness reduction due to matrix cracking is also predicted analytically using the Equivalent Constraint Model (ECM) of the damaged laminate. Dependence of the degraded stiffness properties and strain energy release rates on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is also discussed.     

纤维增强复合材料层板高速冲击损伤数值模拟

推导了复合材料应变率相关三维本构关系, 并将其用于复合材料层板高速冲击损伤的数值模拟。该模型在复合材料层间引入界面单元模拟层间分层, 结合三维Hashin失效准则进行单层板面内损伤识别, 引入材料刚度退化, 采用非线性有限元方法, 研究了复合材料层板高速冲击的破坏过程及层板的损伤特性。数值分析结果表明, 剩余速度预报结果与实验结果吻合较好, 层板的主要损伤形式是层间分层、 基体微裂纹和纤维断裂, 减小弹体直径、 增大铺层角度和层板厚度能够有效降低层板损伤面积。      

Matrix crack-induced delamination in composite laminates under transverse loading

Fibre-reinforced multidirectional composite laminates are observed in experiments under transverse static or low-velocity impact loading to suffer considerable delamination damage. The intensity of this damage depends on the difference in the ply angles above and below the interface. In this paper a fracture mechanics model is presented for investigating the role of matrix cracks in triggering delaminations and the influence of ply angles in adjacent plies on delamination cracking. The fracture mechanics analysis shows that for a graphite fibre-reinforced composite laminate containing a transverse intraply crack, the crack-induced largest interfacial principal tensile stress is a maximum when the difference between the ply angles across the interface is 90 °, and it attains a minimum when the difference is 40 °. When the crack tips touch the interfaces, the minimum mode II stress singularity, which is weaker than the usual square-root type, appears when the difference between the ply angles is about 45 ° for one glass fibre-reinforced laminate and three graphite fibre-reinforced laminates. These results are in agreement with the experimental observation that the largest delaminations appear at the interface across which the difference between the ply angles is the largest i.e. 90 °.     

Numerical investigation of matrix cracking propagation in cross‐ply laminated composites subjected to three‐point bending load using concurrent multiscale model

The purpose of the present study is to analyze fiber‐matrix debonding and induced matrix cracking formation as two major micromechanical damage modes in cross‐ply composite laminates using a two‐dimensional numerical approach. To this aim, the cross‐ply laminates containing 90‐degree layers are modeled, where the fibers are arranged randomly in transverse plies. Damage modes in this numerical model are simulated by the cohesive surface method. The performed analyses reveal that in the laminates with 90‐degree layers located in the outer positions, the primary micro damage mode is micro matrix cracking which is initiated from the fiber‐matrix debonding damage mode and will be followed by matrix cracking. The main benefit of the present study in comparison to other numerical methods is proposing a virtual test method for damage analysis of different cross‐ply laminates in which, the matrix cracking formation will emerge physically in a random and antisymmetric pattern similar to the experimental observations.     

A computational continuum damage mechanics model for predicting transverse cracking and splitting evolution in open hole cross‐ply composite laminates

The present study focuses on a computational constitutive model which predicts the matrix cracking evolution and fibre breakage in cross‐ply composite laminates with open hole under in‐plane loading. To consider the effects of matrix cracking on the nonlinear response of laminates, a simplified crack density based model is applied which evaluates the representative damage parameters of matrix cracking. Furthermore, a developed subroutine based on continuum damage mechanics concepts is applied in ANSYS code which is capable to consider the transverse cracking/splitting evolution and predict the final failure load of mentioned laminate under monotonic loading in a progressive damage analyses. It is shown that the obtained stress–strain behaviours and the damage evaluation of considered laminates are in good agreement with the available experimental results.     

复合材料层合板准静压损伤的数值模拟

从层合板准静压损伤机制出发, 根据渐进累积损伤原理, 建立了复合材料层合板准静压损伤的有限元模型, 合理地描述了复合材料层合板内部不同形式的损伤及其累积过程, 进而讨论了在相同的层合板厚度下, 单向铺层厚度对层合板准静压损伤的影响。结果表明, 单层厚度的增加会加大层合板的基体开裂损伤以及分层损伤的程度, 但有利于抑制纤维断裂的发生。