XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.     

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 °.     

Fracture simulation of CFRP laminates in mixed mode bending

This paper analyses the progressive mixed mode delamination failure in unidirectional and multidirectional composite laminates using fracture experiments, finite element (FE) simulations and an analytical solution. The numerical model of the laminate is described as an assembly of damageable layers and bilinear interface elements subjected to mixed mode bending. The analytical approach is used to estimate the total mixed mode and decomposed fracture energies for laminates with different stacking sequences, which is also validated through experiments. It is concluded that the interlaminar fracture toughness of multidirectional laminates is considerably higher than that of the unidirectional ones. The effect of initial interfacial stiffness and element size is studied and it is also shown that their value must not exceed a definite limit for the numerical simulations to converge. The model can also be further extended to simulate the mixed mode fracture in hybrid fiber metal laminates.     

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates

In previous papers the microscopic failure process of (0/90_n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs.

Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.     

Microscopic fatigue damage progress in CFRP cross-ply laminates

Damage progress in toughened-type carbon fibre-reinforced plastic (CFRP) cross-ply laminates under tensile fatigue loading was measured using the replica technique. The laminate configuration was [0/90_m/0], where m = 4, 8 and 12. The damage parameters, transverse crack density and delamination ratio, were determined. A power-law model was proposed, relating the cyclic strain range and the number of cycles at transverse crack initiation. Based on experimental data, a simple shear-lag analysis combined with the modified Paris law was conducted to model the transverse crack multiplication. An extension of the shearlag analysis for laminates containing delaminations initiating from the tips of the transverse cracks was used to conduct a modified Paris law analysis for delamination growth.     

Bridging effect on mode I fatigue delamination behavior in composite laminates

This paper discusses the bridging effect of fibres on mode I fatigue delamination growth in unidirectional and multidirectional polymer composite laminates based on a series of double cantilever beam (DCB) tests. From the results, there is sufficient evidence that fibre bridging can decrease the crack growth rate da/dN significantly, and using only one fatigue resistance curve to determine the delamination behavior in composite materials with large-scale fibre bridging may be inadequate. The bridging created in fatigue delamination is different from that of quasi-static delamination at the same crack length. So it is incorrect to use the resistance curve (R-curve) from quasi-static delamination tests to normalize fatigue delamination results.     

Fractographic observations on delamination growth and the subsequent migration through the laminate

This paper describes fractographic observations from the detailed examination of delamination fracture surfaces and offers an interpretation of the key growth mechanisms. Firstly, the relationship between toughness, delamination failure criteria and fracture morphology is presented and the influence of cusp formation and deformation on toughness is discussed. Observations regarding delaminations migrating through the lamina at multidirectional ply interfaces are then discussed. It is demonstrated how this migration process can be avoided in fracture toughness coupons and consequently the toughness of multidirectional ply interfaces can be characterised. The influence of migration on delamination growth from embedded defects in laminates under compression is presented, and these results are extended to demonstrate how migration influences damage growth in structures. The paper concludes by making recommendations for realistic modelling of migration, and suggests how it can be exploited in damage tolerant structural design.     

[±θ/902]碳/环氧层板横向裂缝与分层的测试及分析

本工作对[±θ/90₂]_S和[0_n/90₂]_S两系列碳/环氧层板在拉仲载荷下的横向裂缝与分层损伤,进行了实验研究和有限元分析.采用声发射技术跟踪配合显微观测多向层板损伤过程,分析了θ角变化与力学性能、初始损伤、累积等的关系.表明实测横向开裂与分层结果和采用能量判据有限元计算预测比较,符合良好.同时在扫描电镜内进行各类层板压缩试验,动态观测破坏形貌,讨论了不同θ铺层角的微观破坏机理.     

Interaction of Matrix Cracking and Delamination in Cross-ply Laminates: Simulations with Stochastic Cohesive Zone Elements

Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.     

Self-healing of delamination fatigue cracks in carbon fibre–epoxy laminate using mendable thermoplastic

This article examines the self-healing repair of delamination damage in mendable carbon fibre–epoxy laminates under static or fatigue interlaminar loading. The healing of delamination cracks in laminates containing particles or fibres of the mendable thermoplastic poly[ethylene-co-(methacrylic acid)] (EMAA) was investigated. The results showed that the formation of large-scale bridging zone of EMAA ligaments along the crack upon healing yielded a large increase (~300%) in the static mode I interlaminar fracture toughness, exceeding the requirement of full restoration. The mendable laminates retained high healing efficiency with multiple repair cycles because of the capability of EMAA to reform the bridging zone under static delamination crack growth conditions. Under fatigue loading, healing by the EMAA was found to restore the mode I fatigue crack growth resistance, with the rates of growth being slightly less than that pertinent to the unmodified laminate. The EMAA bridging zone, which generated high toughness under static loading conditions, does not develop under fatigue loading because of rapid fatigue failure of the crack bridging ligaments. Similar to the multiple healing capability of EMAA under static loading, multiple healing of delamination fatigue cracks is confirmed, with the fatigue crack growth rates remaining approximately unchanged. This study shows that EMAA was capable of full recovery of fatigue crack growth resistance and superior healing efficiency for static loading.     

Numerical investigation to prevent crack jumping in Double Cantilever Beam tests of multidirectional composite laminates

During the experimental characterization of the mode I interlaminar fracture toughness of multidirectional composite laminates, the crack tends to migrate from the propagation plane (crack jumping) or to grow asymmetrically, invalidating the tests.The aim of this study is to check the feasibility of defining the stacking sequence of Double Cantilever Beam (DCB) specimens so that these undesired effects do not occur, leading to meaningful onset and propagation data from the tests. Accordingly, a finite element model using cohesive elements for interlaminar delamination and an intralaminar ply failure criterion are exploited here to thoroughly investigate the effect of specimen stiffness and thermal residual stresses on crack jumping and asymmetric crack growth occurring in multidirectional DCB specimens.The results show that the higher the arm bending stiffness, the lower the tendency to crack jumping and the better the crack front symmetry. This analysis raises the prospect of defining a test campaign leading to meaningful fracture toughness results (onset and propagation data) in multidirectional laminates.     

Four-point bend interlaminar shear testing of uni- and multi-directional carbon/epoxy composite systems

Purpose of the paper is to investigate the possibility of extending the interlaminar shear strength (ILSS) results obtained by four-point bend testing of unidirectional laminates to multidirectional laminates, such as cross-ply and quasi-isotropic, the testing of which is a common practice in the industry but has not been previously validated in the literature. An experimental database is gathered through the known modified version of the ASTM D2344 short beam test and the results show a surprising proximity of results for the three different fiber architectures for the same composite system. Various finite element analyses were developed using ANSYS^® software, allowing for better insight on the mechanics of delamination in four-point bending, and showed extremely good agreement with the experimental values. The final and most accurate model partially confirmed observations made by other authors, and includes the ‘skewed’ profile of the shear stress through the thickness and its variation along the length, the distribution of the shear stress across the width, the location of delamination initiation and propagation and maximum ILSS and the shear stress contour.     

Matrix cracking and delamination in laminated composites. Part II: Evolution of crack density and delamination

This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress-strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained.     

复合材料层板层间应力的非线性有限元分析

本文针对pipes-Pagano模型建立了基于修正的Hahn-T sai非线性本构关系的准三维非线性有限元模型。分析了由一种具有明显材料非线性的碳/环氧复合材料构成的[45/-45]_s角交层板和正交对称层板的层间应力分布。结果表明:和弹性模型结果相比,当承受相同载荷时,材料非线性的存在在一定程度上会引起层间剪应力的降低,但对层间正应力的影响并不明显。      

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.     

Image analysis of delamination cracks in carbon-fibre composites by scanning acoustic microscopy

Fibre-reinforced composite laminates have been widely applied to many kinds of structures because of their superior properties. The delamination resistance of such composites is a weak point, however, and one of the most important problems is the non-destructive detection of delamination cracks. In this study, high-resolving-power observations with a recently developed scanning acoustic microscope (SAM) have been conducted for a study of the applicability of the technique for non-destructive inspection of delamination. The high-resolving-power observations were applied to carbon-fibre/epoxy and carbon-fibre/PEEK unidirectional, multidirectional reinforced and fabric composites. From the results obtained, the delamination micro-mechanisms are discussed and knowledge of non-destructive inspection with a SAM has been obtained.     

A criterion for modelling initiation and propagation of matrix cracking and delamination in cross-ply laminates

A variational approach is used to model the behaviour of composite cross-ply laminates damaged by transverse, longitudinal cracking and delamination. An energetic criterion is proposed. It is based on the strain energy release rate associated with each of the three damage modes. The first part of this paper is concerned with the modelling of the transverse and longitudinal cracking. In the second part, a model for studying delamination damage is presented. The numerical results show that these models provide a consistent level of accuracy for a variety of thin laminate material systems and configurations, with various combinations of delaminations and matrix cracks. In this paper several numerical simulations meant to describe initiation for each damage mode are proposed. The estimation of damage modes contributions is achieved for two thin laminates in order to predict the evolution of damage mode transition.     

Structural composites hybridized with epoxy compatible polymer/MWCNT nanofibrous interlayers

Surface reactive P(St-co-GMA) copolymer and P(St-co-GMA)/MWCNT fibrous mats are placed onto a conventional carbon fiber/epoxy prepreg as interlayer reinforcing material. Experimental observations are used to demonstrate excellent epoxy wetting and structural compatibility of the interlayers chemically tuned for the epoxy matrix. Comparisons of increase in mechanical performance by incorporating P(St-co-GMA) and P(St-co-GMA)/MWCNT interlayers also show the contribution of MWCNT presence in the copolymer nanofibers. Flexural strength and stiffness of (0/0/0) and (90/0/90) laminates increase up to 17% when the nanocomposite interlayers are integrated. Cross-sectional SEM analyses of the failure surfaces suggest reinforcing ability of interlayers both against transverse cracking and delamination. Further examination for the delamination resistance is presented by the End Notched Flexure (ENF) tests. An improvement up to 70% in mode II strain energy release rate (G_IIc) is recorded for the laminates with nanocomposite interlayers. The resistance against transverse matrix cracking in the presence of interlayers is also elaborated. Charpy-impact and transverse-tension tests result in up to 20% and 27% increase in the impact energy absorbance and transverse tensile strength, respectively. Overall, the test results suggest that mechanical behavior of the laminates is enhanced by the nanofibrous interlayers chemically-tuned for epoxy crosslinking, with no weight penalty.     

带脱层复合材料层板的低速冲击响应

研究了含脱层损伤的复合材料层板在低速冲击下的瞬态响应问题。首先,用基于Mindlin板理论的有限元法来描述层板的运动和变形,并同时考虑了层板大变形的影响。另外,用一种修正的Hertzian压痕法则来计算层板和刚球间的冲击力。同时为了有效地处理脱层间的动态接触问题,采用了由笔者以前提出的一种修正的Lagrange multiplier乘子法来提高计算精度和效率;为了研究脱层的扩展机理,提出了一种基于Mindlin板模型的应变能释放率的计算方法,用于计算脱层前沿的应变能释放率的分布。最后,算例研究了刚球的初始冲击速度、脱层面积和脱层位置对计算结果的影响,算例中提供的信息为人们更好地理解脱层损伤的扩展机理和它对复合材料层板的低速冲击响应的影响提供了依据。