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。      

Effect of Mode-Mixity on the Fracture Toughness of Ti-6Al-4V/FM-5 Adhesive Joints

Using several different fracture tests, the fracture toughness of a chromic acid anodized titanium (Ti-6A-4V)/polyimide (FM-5) adhesive system was evaluated. Mode I, mode II, and mixed mode (I and II) tests were conducted using double cantilever beam (DCB), end notch flexure (ENF), and mixed mode flexure (MMF) geometries. Interfacial type failures were observed in the ENF and MMF specimens as a result of the mode II loading inherent in these tests. Pure mode I loading, as is the case with symmetric DCB specimens, resulted in cohesive failures with a fracture energy around 2500 J/m² on as-received specimens. The asymmetric DCB specimens had fracture energy values around 2000 J/m², the MMF specimens close to 1970 J/m², and ENF specimens around 1300 J/m². All the above measurements were made on as-bonded (unaged) specimens. Titanium/FM-5 bonds supplied by the Boeing Company were then aged in one of three different environments for 2 and 6 months respectively. The environments included: 177^degC in air and 2 psia, and 204^degC in air. Following the aging, DCB, ENF, and MMF tests were conducted on the specimens. The results showed that aging in all three environments resulted in decreases in fracture energy for the above specimen testing configurations. The largest drop (20 percent) in fracture toughness was noted in specimens aged for 6 months in air at 204^degC. An unusual finding from this study, in contrast to what other researchers have seen on other systems, was that increasing mode II loading resulted in significant reductions in toughness. Crack path selection and interaction with the woven glass scrim within the bonded specimens may be responsible for the lower mode II fracture energies. From the tests conducted, failure envelopes were developed to predict failure energy and type for use in designing structural joints. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

Mode II fracture energy characterization of brittle adhesives using compliance calibration method

The end‐notched flexure (ENF) test is widely used for measuring the Mode II critical strain energy release rate of adhesively bonded joints (ABJs). Unstable crack growth in ENF joints with brittle adhesives is a common phenomenon. Classic data reduction methods like the direct beam theory (DBT) and the compliance‐based beam method (CBBM) usually result in unacceptable scatter when crack grows unstable. In this study, the application of a compliance calibration method (CCM) for ENF adhesive joints with a brittle adhesive is experimentally investigated. For this purpose, ENF specimens were manufactured and tested. Different data reduction methods were considered for treating the results. Afterwards, the obtained fracture energies were used as an input parameter in a finite element (FE) analysis with a cohesive zone model to evaluate the validity of the experimental data. It is shown that the fracture loads obtained by the CCM have the best agreement with the experimental ones comparing with the other data reduction approaches. To study the effect of geometry on the CCM results, ENF specimens with different adhesive thicknesses, substrate thicknesses and span lengths were also considered in this study, and some general conclusions are made about the geometrical parameters effect on the Mode II fracture energy.     

Crack path selection in adhesively bonded joints: the roles of external loads and speciment geometry

This paper investigates the roles of external loads and specimen geometry on crack path selection in adhesively bonded joints. First, the effect of mixed mode fracture on crack path selection is studied. Using epoxy as an adhesive and aluminum as the adherends, double cantilever beam (DCB) specimens with various T-stress levels are prepared and tested under mixed mode fracture loading. Post-failure analyses on the failure surfaces using X-ray photoelectron spectroscopy (XPS) suggest that the failure tends to be more interfacial as the mode II fracture component in the loading increases. This fracture mode dependence of the locus of failure demonstrates that the locus of failure is closely related to the direction of crack propagation in adhesive bonds. Through analyzing the crack trajectories in failed specimens, the effect of mixed mode fracture on the directional stability of cracks is also investigated. The results indicate that the direction of the crack propagation is mostly stabilized when more than 3% of mode II fracture component is present at the crack tip regardless of the T-stress levels in the specimens for the material system studied. Second, using a high-speed camera to monitor the fracture sequence in both quasi-static and low-speed impact tests, the effect of debond rate on the locus of failure and directional stability of cracks is investigated. Post-failure analyses including XPS, Auger electron spectroscopic depth profile, and scanning electron microscopy indicate that as the crack propagation rate increases, the failure tends to be more cohesive and the cracks tend to be directionally unstable. Last, as indicated by the finite element analyses results, the T-stresses, and therefore the directional stability of cracks in adhesive bonds, are closely related to the thickness of the adhesive layer and also the thickness of adherend. This specimen geometry dependence of crack path selection is studied analytically and is verified experimentally.     

Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

双悬臂梁试件裂纹动态扩展的准静态数值分析

本文采用双悬臂梁（DCB）试件研究了复合材料层合板层间插入韧性胶膜（Interleaf）层的Ⅰ型断裂行为。试验结果表明,含和不含Interleaf层试件分别呈现脆性非稳态和脆性稳态分层扩展特性。针对非稳定裂纹扩展问题,依据动态断裂力学中应变能释放率与动能变化率的关系,提出了以断裂韧性值G_IC变化来抵消动能变化对裂纹扩展过程影响的准静态分析方法,根据试验中裂纹扩展的韧性变化,推导出适用于准静态裂纹扩展模拟的等效韧性G_IC*,利用ABAQUS平台和虚裂纹闭合技术（VCCT）建立了三维有限元计算模型;实现了从起裂到止裂的整个裂纹动态扩展过程的数值模拟,揭示了非稳定裂纹扩展过程中一些复杂的力学现象。      

Experimental investigation on test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites

In this paper, experimental investigation on the test methods for mode II interlaminar fracture testing of carbon fiber reinforced composites are carried out. Mode II interlaminar fracture testing of unidirectional composite of carbon fiber reinforced epoxy (T800/#3631) are conducted using four kinds of test methods, namely end notched flexure (ENF) test, end loaded split (ELS) test, four-point bend end notched flexure (4ENF) test, and over notched flexure (ONF) test. An analytical model based on a point-friction assumption and classical beam theory is proposed to evaluate the effect of friction between crack faces on the mode II interlaminar fracture toughness in the 4ENF and ONF tests. The analytical model is validated by the comparison of analytical results with previous ones obtained from finite element analysis. Experimental results show that the ENF test gives reliable initiation value of fracture toughness with a small scatter and that the average value of fracture toughness obtained from 4ENF test is about 2% higher than that obtained from the ENF test. The effect of friction in the 4ENF test is much lower than that in the ONF test in which the effect of friction increases with the crack growing. It is concluded that the 4ENF test method is an effective test method for the experimental evaluation of mode II propagation interlaminar fracture toughness of carbon fiber reinforced composites.     

复合材料的Ⅰ型层间断裂韧性

本文采用铰链式双悬臂梁试件对碳/双马来酰亚胺复合材料的Ⅰ型层间断裂韧性进行了研究,分析比较了层间断裂韧性G_IC的表达方法,用三次多项式和幂函数拟合实验柔度的方法得到的结果比较满意,实验结果表明纤维桥连对单向层合板的G_IC的影响是显着的,用刀片切割桥连纤维后G_IC值下降百分之二十,分散性也有显着下降。另外发现G_IC值随试件厚度增加而增大。      

Predicting fracture of solder joints with different constraint factors

Double cantilever beam (DCB) specimens of 2.5‐mm‐long SAC305 solder joints were prepared with thickness of copper adherends varying from 8 to 21 mm each. The specimens were tested under mode I loading conditions (ie, pure opening mode with no shear component of loading) with a strain rate of 0.03 second^?1. The measured fracture load was used to calculate the critical strain energy release rate for crack initiation, J_ci, in each case. Fracture behaviour showed a significant dependence on the adherend thickness; the J_ci and plastic deformation of the solder at crack initiation decreased significantly with increase in adherend thickness. This behaviour was attributed to changes in stress distribution along the solder layer when the adherend thickness was varied. The capability of J_ci as a property was then assessed to predict the fracture load of solder joints in specimens with different constraint levels caused by variations in adherend thicknesses. In light of the results obtained, a cohesive zone model (CZM) was developed to predict the fracture load of solder joints as a function of adherend thickness. Finally, a CZM with a single set of parameters was established to predict the fracture loads for all the cases. It was concluded that CZM was a better methodology to account for changes in degree of joint constraint imposed by bonding adherends.     

A simplified beam analysis of the end notched flexure mode II delamination specimen

A modified classical beam theory solution is developed for the end notched flexure (ENF) specimen, one of the most widely used mode II delamination tests for fibre reinforced composite materials. The effect of crack tip deformation is analyzed by assuming that a region of certain length close to the crack tip rests on an elastic shear spring foundation. The mathematical procedure of the present analysis is simple and clear, and the resulting solutions for the compliance and the strain energy release rate of the ENF specimen are highly accurate. Excellent agreement is obtained over a wide range of material and geometrical properties of ENF specimens when the current results are compared with finite element results and other analytical analyses that include the effect of crack tip deformation in their solutions. The success of the present analysis indicates that the effect of crack tip deformation is the most important factor that must be considered when calculating the relationship between G_II and the load in the ENF specimen.     

Characterizing Mode II Delamination Cracks in Stitched Composites

This paper deals with characterizing the bridging mechanisms developed across delamination cracks by through-thickness reinforcement, using stitched carbon/epoxy laminates under mode II loading as a prime example. End Notched Flexure (ENF) tests are performed which show that stitching can provide stable crack growth. The bridging law, which characterizes the bridging action of the stitches, is deduced from both crack profile measurements and load vs. deflection curves. Consistent results are obtained from the two methods. The inferred laws imply that delamination cracks will commonly grow in conditions that are neither accurately nor properly described by linear elastic fracture mechanics. Large scale bridging calculations are required, in which the essential material property is the bridging traction law. The level of detail in which the law must be determined can be inferred from the sensitivity of predicted crack growth to variations in the law. It is recommended that the required parametric traction law be deduced in engineering practice from load vs. deflection data from the standard ENF (or similar) test, with due regard to selecting the notch size and other specimen dimensions to ensure that crack growth is stable in the test. This revised version was published online in August 2006 with corrections to the Cover Date.     

热塑性颗粒-无机粒子协同增韧碳纤维增强环氧树脂复合材料

针对碳纤维增强环氧树脂(CF/EP)复合材料层间断裂韧性进行研究,通过在CF/EP复合材料层间添加四种无机纳米粒子和三种热塑性颗粒对其进行II型层间断裂韧性(G_IIC)研究,选择工艺性和增韧性效果好的两种无机纳米粒子和热塑性颗粒进行协同增韧研究。结果表明,CF/EP复合材料的G_IIC在适当的无机纳米粒子含量下都得到提高,这主要是由于无机纳米粒子在层间形成了有效吸收断裂能的微结构,纳米羟基氧化铝(AlOOH)的工艺性及增韧性等综合性能最好,AlOOH质量分数为1wt%时,CF/EP复合材料的G_IIC达到931 J/m2,提高了29.3%;热塑性颗粒中,改性聚芳醚酮颗粒(PAEK)的综合性能最好,添加10wt% PAEK,CF/EP复合材料的G_IIC可以提高32%,这是由于预制在层间的热塑性颗粒随着基体流动而得到扩散,形成了独特的跨层间连续结构,从而使裂纹扩展的阻力增加,有效提高了CF/EP复合材料的G_IIC;10wt%PAEK和1wt%AlOOH共同增韧CF/EP复合材料的G_IIC达到1 368 J/m2,相对于未增韧的CF/EP复合材料提高了90%,增韧效果比PAEK和AlOOH对CF/EP复合材料的增韧效果之和大,这表明,PAEK和AlOOH同时加入CF/EP复合材料层间,对CF/EP复合材料具有协同增韧效应。      

Dynamic delamination fracture toughness in unidirectional polymeric composites

A modified end-notched flexure (ENF) specimen was used to determine Mode-II-dominated dynamic delamination fracture toughness of fiber composites at high crack propagation speeds. A strip of FM-73 adhesive film was placed at the tip of the interlaminar crack created during laminate lay-up. This adhesive film with its greater toughness delayed the onset of crack extension and produced crack propagation at high speeds. Dynamic delamination experiments were performed on these ENF specimens made of unidirectional S2/8553 glass/epoxy and AS4/3501-6 carbon/epoxy composites. Crack speed was measured by means of conductive aluminum lines created by the vapor deposition technique. A finite-element numerical simulation based on the measured crack speed history was performed and the dynamic energy release rate calculated. The results showed that the dynamic fracture toughness is basically equal to the static fracture toughness and is not significantly affected by crack speeds up to 1100 m/s.     

Fatigue crack growth analysis of different adhesive systems: Effects of mode mixity and load level

The aim of this paper is to investigate the fatigue fracture behavior of three different adhesive systems (epoxy‐based, acrylic, and a rubber‐like adhesive). To achieve this, double cantilever beam specimens were manufactured with different adhesives and tested under several mode mixities and different load levels. Fatigue crack growth rate was evaluated through a Paris law equation. For postprocessing, the compliance‐based beam method was used. Results showed that the variation of the threshold energy with load level is more pronounced for the epoxy‐based adhesive. The crack propagation life is higher for the acrylic adhesive. Although, for pure mode I conditions, the normalized threshold of the rubber‐like adhesive is lower, for pure mode II, it was higher than the epoxy‐based adhesive. Due to the normalization by the static fracture energy, the slope of the Paris law was approximately constant for all the adhesive systems.     

基于循环载荷的单搭胶接接头残余强度分析

为研究循环载荷下单搭胶接接头的残余强度及失效机理,以5052铝合金单搭胶接接头为研究对象,先后对其进行静强度测试、疲劳强度测试和残余强度测试,引入威布尔分布对试验数据进行分析,检验其有效性,并采用超声扫描显微镜和扫描电子显微镜对失效胶层进行失效机理分析。结果表明,在疲劳循环载荷作用下,接头刚度基本稳定,而残余强度随着疲劳循环载荷周次的增加,呈现出先增大后减小的变化趋势;疲劳裂纹从接头搭接端部的界面端点处开始萌生,并快速向中间扩展,当疲劳循环达到一定次数时,胶层瞬间断裂,裂纹萌生阶段几乎占据了其全部疲劳寿命,失效后的胶层会出现"凹台"状微观结构。     

Experimental Determination of Fracture Toughness of CFRP in Mode II by Raman Spectroscopy

Fracture toughness of Mode II of carbon fiber reinforced plastic (CFRP) was investigated using end notched flexure (ENF) specimens and a Raman coating method. Distribution of shear strain near the crack tip of CFRP was measured by Raman spectroscopy. A thin film of PbO on the measured surface of the ENF specimen was deposited by physical vapor deposition (PVD) as pretreatment to measure the strain by Raman spectroscopy. Fracture toughness of CFRP in Mode II was determined using the Raman results. The results coincided closely with those measured by the compliance method and FEM analyses (finite element method).     

缝合复合材料II型层间断裂特性研究

分别采用测量ENF试样加载点位移与测量其端部剪切位移CSD(Crack Shear Displacement)的试验方法,研究了缝合复合材料层合板的II型层间断裂韧性以及缝合密度,缝合线的直径等缝合参数对于缝合复合材料层合板II型层间断裂韧性和分层模式的影响。结果表明,缝合降低了层合板初始分层韧性G_IIi,但对于分层的扩展有良好的抑制作用。缝合参数对此有较大影响。      

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.