圆弧形单向纤维增强树脂复合材料的I型层间断裂韧性测试及分析

层合板的I型层间断裂韧性的测量方法通常为单向纤维增强树脂复合材料的末端切口(End notched flexure, ENF)试样的双悬臂梁(Double cantilever beam, DCB)试验。为了得到带有弧度的层合复合材料结构的I型层间断裂韧性,对圆弧形末端切口(Arc-ENF)试样进行DCB试验。基于梁的弯曲理论和Irwin-Kies公式得到Arc-ENF试样的柔度公式与I型临界能量释放率G_IC公式,并且利用ABAQUS软件对DCB试验进行数值模拟。最终,通过对比分析理论公式计算结果、数值模拟结果和DCB试验结果来验证柔度公式和G_IC公式的合理性和有效性,对带有任意弧度的DCB试样的I型层间断裂韧性的测试与分析具有参考价值。      

Study on the compressive strength of laminated composite with through-the-width delamination

A nonlinear finite element code, DELAM3D, with a three-dimensional layered solid element based on the updated Lagragian formulation, is developed to simulate the compressive response of a laminated composite plate with multiple delaminations. An analytical model is established to characterize the mechanical behaviors such as postbuckling, contact of the delaminating interface, delamination growth and fiber-matrix failure. Double cantilever beam (DCB) and end notched flexure (ENF) tests, with T300/976 graphite/epoxy, are performed to verify the energy release rate of the material. Experiments with various crack numbers, sizes, locations and layer orientations have been conducted and compared with the numerical solution. Good agreement is expected.     

Panel stiffener debonding analysis using a shell/3D modeling technique

A shear loaded, stringer reinforced composite panel is analyzed to evaluate the fidelity of computational fracture mechanics analyses of complex structures. Shear loading causes the panel to buckle. The resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. The panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot, web and noodle as well as the panel skin near the delamination front were modeled with a local 3D solid model. Across the width of the stringer foot, the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with a mixed-mode failure criterion of the graphite/epoxy material. The objective was to study the effect of the fidelity of the local 3D finite element model on the computed mixed-mode strain energy release rates and the failure index.     

Integrated XFEM-CE analysis of delamination migration in multi-directional composite laminates

Progressive damage and failure in composites are generally complex and involve multiple interacting failure modes. Depending on factors such as lay-up sequence, loading and specimen configurations, failure may be dominated by extensive matrix crack-delamination interactions, which are very difficult to model accurately. The present study further develops an integrated extended finite element method (XFEM) and cohesive element (CE) method for three-dimensional (3D) delamination migration in multi-directional composite laminates, and validates the results with experiment performed on a double-cantilever beam (DCB). The plies are modeled by using XFEM brick elements, while the interfaces are modeled using CEs. The interaction between matrix crack and delamination is achieved by enriching the nodes of cohesive element. The mechanisms of matrix fracture and delamination migration are explained and discussed. Matrix crack initiation and propagation can be predicted and delamination migration is also observed in the results. The algorithm provides for the prediction of matrix crack angles through the ply thickness. The proposed method provides a platform for the realistic simulation of progressive failure of composite laminates.     

Experimental determination of validated, critical interfacial modes I and II energy release rates in a composite sandwich panel

A validated experimental approach to obtaining critical mode I and mode II energy release rates for interfacial failure in a sandwich composite panel is outlined in this paper. By modifying the geometry of the sandwich structure to align the face sheet-core interface to coincide with the neutral axis, it is possible to obtain critical mode I and mode II energy release rates by conducting Double Cantilever Beam (DCB) and End Notch Flexure (ENF) tests, respectively. The values so obtained were used to predict the crack growth histories of modified DCB and ENF tests, and a Single Leg Bend (SLB) test, using a discrete cohesive zone method (DCZM). In addition, the influence of material and geometry were also analyzed.     

Evaluation of initiation criteria used in interlaminar fracture tests

The objective of this work was to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria that are commonly used to define initiation in interlaminar fracture tests. This study is in the sequence of a previous paper where the mode I DCB and mode II ENF specimens were analysed. Finite element (FE) simulations of delamination growth were here performed for the mode II end-loaded split (ELS) and 4-point end-notched flexure (4ENF) tests. The results indicated that the formation of large process zones could affect significantly NL criteria. The maximum load point gave the most accurate toughness values, especially for the 4ENF specimen. Finally, present and previous results were compared to experimental data available in the literature.     

Effect of initial crack length on the measured bridging law of unidirectional E-glass/epoxy double cantilever beam specimens

In this paper, the effect of initial delamination length is experimentally investigated on obtaining the mode I bridging law of unidirectional E-glass/epoxy double cantilever beam (DCB) specimens manufactured by hand layup method. To this end, an experimental test set-up is established for accurate measurement of crack tip opening displacement (CTOD) using digital image processing method. DCB tests are performed for three different delamination lengths and the corresponding bridging laws are calculated using J-integral approach. Results showed that the maximum bridging stress, the shape of bridging law and energy dissipation in bridging zone are slightly affected by changing initial crack length. In other words, the measured bridging law acts independent of initial delamination length. Therefore, the obtained bridging law can be used with the cohesive elements available in the commercial finite element software to simulate the delamination propagation behavior in unidirectional DCB specimens.     

层合板层间断裂分析的组合界面单元及其特性

提出了一种由刚性元和零厚度的内聚力单元组合而成的新型界面单元,该界面单元嵌在板壳结构界面之间,可用来模拟界面损伤的起始和演化,能考虑板壳的平动和转动对分层损伤的作用。该界面单元具有有限厚度,八个结点,每个结点有五个自由度,通过刚性元将板壳单元结点的位移和结点力转换到内部零厚度的内聚力单元上,界面损伤通过内聚力单元的损伤演化体现出来。采用板壳单元和新型界面单元建立有限元模型,对混合弯曲(MMB)试验和双悬臂梁(DCB)弯曲试验进行了计算模拟,计算结果能很好地模拟结构的界面损伤过程。相比传统的用内聚力单元和三维实体单元组成的模型,建模方便,在精度相当的前提下,可以使单元尺寸增大一倍,减少裂尖内聚力区域(cohesive zone)内的单元数量,缩小计算规模,提高计算效率。     

含面芯界面缺陷的蜂窝夹芯板侧向压缩破坏模式

为了对含面芯层间脱胶缺陷的蜂窝夹芯板在侧向压缩载荷作用下的典型破坏模式进行数值预报, 建立了基于蔡-希尔破坏准则和粘结模型的计算模型。该计算模型是建立在对蜂窝夹芯板的双悬臂梁(DCB)和单臂梁(SLB) 试验中所发现的一种新的破坏模式的分析基础之上的。对蜂窝夹芯板的侧向压缩破坏行为的数值预报中, 发现一种新的破坏模式: 位于脱胶区域的面板首先发生局部屈曲失稳, 随后面板内部靠近芯子的45°/0°层间出现分层, 与此同时最靠近芯子的45°铺层发生断裂, 伴随着45°/0°层间分层的扩展, 面板发展成为对称性整体屈曲失稳。与侧向压缩试验测试结果对比发现, 计算模型模拟中所预报的破坏模式在实验测试中也得到了很好的验证。      

Assessment of initiation criteria used in interlaminar fracture tests of composites

Finite element (FE) simulations of delamination growth in mode I double cantilever beam (DCB) and mode II end-notched flexure (ENF) specimens were conducted in order to evaluate the non-linearity (NL) and 5% offset or maximum load (5%-Max) criteria. The results showed a good performance of the 5%-Max criterion, while the NL criterion was inadequate for the ENF test. However, it was also found that large process zones in common ENF specimens may lead to significant toughness underestimations. In order to obtain accurate results it was necessary to increase the starter crack length and the support span.     

Composite toughness enhancement with interlaminar reinforcement

An experimental investigation of a newly proposed through-thickness reinforcement approach aimed to increase interlaminar toughness of laminated composites is presented. The approach alters conventional methods of creating three-dimensional fiber-reinforced polymer composites in that the reinforcing element is embedded into the host laminate after it has been cured. The resulting composite is shown to possess the benefits of a uniform surface quality and consolidation of the original unreinforced laminate. This technique was found to be highly effective in suppressing the damage propagation in delamination double-cantilever beam (DCB) test samples under mode I loading conditions. Pullout testing of a single reinforcing element was carried out to understand the bridging mechanics responsible for the improved interlaminar strength of reinforced laminate and stabilization and/or arrest of delamination crack propagation. The mode I interlaminar fracture of reinforced DCB samples was modeled using two-dimensional cohesive finite-element scheme to support interpretation of the experiments.     

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.     

Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually.     

Bending effect of through-thickness reinforcement rods on mode II delamination toughness of ENF specimen: Elastic and rigid–perfectly plastic analyses

In this paper, a new simple metallic z-rod model is proposed to study the bending effect of the metallic z-rods on mode II delamination toughness of laminated composites. A new transverse shear force–deformation relationship for a metallic z-rod is obtained by using the classical beam theory and modeling its surrounding matrix as linearly elastic, rigid–perfectly plastic or linearly elastic–perfectly plastic springs. The bridging traction provided by a metallic z-rod to the mode II delamination toughness is assumed to be only the shear force carried by a z-rod created by the relative slippage between two substrate beams in an end-notched flexure (ENF) specimen, whereas the longitudinal sliding friction is assumed to make negligible contribution to the bridging traction. Mode II strain energy release rate (SERR) is employed to evaluate the influence of the metallic z-rods on the interlaminar fracture toughness of end-notched flexure (ENF) specimens. A parametric study of ENF specimens reinforced with the z-rods is conducted to demonstrate the effect of the new bridging mechanism by the metallic z-rods on the mode II delamination toughness.     

Acoustic Emission Characterization of Failure Modes in GFRP Laminates Under Mode I Delamination

In order to design structural components using composite materials a deep understanding of the material behaviour and its failure mechanisms is necessary. To create a better understanding of the initiation, growth and interaction of the different types of damage, damage monitoring during mechanical loading is very important. To this direction, AE is a powerful non destructive technique for real time monitoring of damage development in materials and structures which has been used successfully for the identification of damage mechanisms in composite structures under quasi static and dynamic-cycle loading. In this present work, pure resin plate and GFRP composite laminates with stacking sequence of [0⁰]₆, are fabricated using Hand lay-up method. During the layup a Teflon tape of width 45 mm is kept in the mid plane of the laminate which serves as an initiator for delamination during loading. As per ASTM STD D5528 01 DCB (Double Cantilever Beam) specimens are cut out from the laminates and are subjected to tensile test in the transverse direction along with acoustic emission monitoring. While loading, Markings are made on the sides of the specimen to track the crack front using a magnifying lens. Parametric analysis is performed on the AE data obtained during crack propagation to discriminate the failure modes. Fast Fourier Transform (FFT) enabled the calculation of frequency content of each damage mechanism. Further STFFT analysis is performed on a portion of the waveforms representing the dominant frequency content pertaining to each damage mechanism.     

Analysis of mode I delamination of z-pinned composites using a non-dimensional analytical model

We present a non-dimensional analytical model for crack propagation in a z-pinned double cantilever beam specimen (DCB) under mode I loading. Effect of various design parameters on the crack bridging length and apparent fracture toughness are investigated using this model. The efficacy of the analytical model is evaluated by comparing the results with 3D finite element (FE) simulations of the DCB. In the FE model the z-pins are modeled as discrete nonlinear elements. Bi-linear cohesive elements are used ahead of the crack tip to account for the interlaminar fracture toughness of the composite material. The results for load–deflection and crack length obtained from the analytical model and the FE model are compared and found to be in good agreement. The proposed non-dimensional analytical model will be useful in the design and analysis of translaminar reinforcements for composite structures.     

Three-dimensional finite element analysis of fracture modes for the pull-off test of a thin film from a stiff substrate

A three-dimensional geometrically nonlinear finite element analysis model is presented to study the interfacial delamination for the pull-off test of a thin film strip debonded from a stiff substrate. The strain energy release rates of all three modes (mode I, mode II, and mode III) along the debond front are considered and calculated to investigate the mixed fracture modes for the entire deformation regime from bending plate to stretching membrane. These results indicate that the individual strain energy release rates and the total energy release rate vary along the width of the debond front and strong three-dimensional edge effects exist near the free edges of the film. Interestingly, residual stress also plays an important role in controlling mixed fracture modes and the variation of the energy release rates. Finally, the three-dimensional finite element model is compared with an analytical solution developed earlier. The three-dimensional finite element model is found to provide additional insights for interfacial delamination for the pull-off test.     

Delamination of beams: an application to the DCB specimen

This paper deals with the problem of the delamination of laminated beams. A model based on adhesion theory is adopted. The laminate is modeled as two beams in adhesion, with an initial defect in part of the interface. Adhesion is governed by two state variables: the relative displacement of the points belonging to the two beams and lying at the interface, and a damage parameter. This model is governed by a nonsmooth functional. Then, a simple regularized model is derived for the interface. The corresponding differential equations are given and the closed form solution is provided. Both the perfect nonsmooth and the regularized proposed models are used to study the classical double cantilever beam (DCB) specimen. In particular, a simple theory is developed to predict the external loads leading to delamination for pure mode I or pure mode II. Numerical computations, developed for both the nonsmooth and the smooth proposed models, are compared with results available in the literature.     

Charakterisierung des Delaminationsverhaltens von Schichtverbunden unter Mode I- und Mode II-Belastungen

Characterization of the delamination behaviour of composites under mode I- and mode II-loading In order to determine fracture toughness properties of fibre-reinforced polymers the „Double Cantilever Beam”︁-test (DCB) has been used for mode I loading and the „End Notched Flexure”︁-test (ENF) for mode II loading. By these methods the energy release rate G and the corresponding R-curve (crack resistance curve) have been measured which characterise the crack resistance of the material against delamination. Especially the influence of fibre coatings, different structures of the laminate, and matrix modifiers on fracture toughness have been examined for epoxy as well as for thermoplastic composites (polyamide and polypropylene/glass fibres).