内聚力模型的形状对胶接结构断裂过程的影响

内聚力模型被广泛应用于粘接结构的断裂数值模拟过程中,为深入分析不同形状内聚力模型与胶黏剂性质和粘接结构断裂之间的关系,本文分别采用脆性和延展性两种类型胶黏剂,对其粘接的对接试件进行了单轴拉伸、剪切实验,以及其粘接的双臂梁试件进行了断裂实验.3种类型的内聚力模型(抛物线型、双线型和三线型)分别模拟了以上粘接结构的断裂过程,并与实验结果进行对比.结果发现:双线型的内聚力模型适用计算脆性胶黏剂的拉伸与剪切的断裂过程;指数型内聚力模型较适合计算延展性胶黏剂的拉伸和剪切的断裂过程,临界应力、断裂能和模型的形状参数是分析拉伸和剪切的重要参数;双臂梁试件的断裂过程模拟结果发现,断裂曲线与胶黏剂性质有关,内聚力模型形状参数也有影响.通过实验与计算结果分析,双线型内聚力模型更适合脆性胶黏剂粘接的双臂梁断裂计算,而三线型更适合计算延展性胶黏剂粘接的双臂梁断裂过程,此研究结果对胶黏剂的使用和粘接结构的断裂分析有很重要意义.     

Modelling the R-curve effect and its specimen-dependence

This paper explores the specimen-dependence of the resistance (R-) curve for fracture of materials showing a pronounced R-curve effect. Using a cohesive zone framework, this paper demonstrates how to effectively predict the R-curve for a specimen type whose deformation is shear-dominated (compact tension, CT) from the R-curve of a specimen type whose deformation is bending-dominated (double cantilever beam, DCB). The mathematical relationships between crack extension and crack opening displacements for both CT and DCB specimens are first derived and related to a tri-linear cohesive law. Experimental tests for intralaminar fracture of CFRP are carried out and analysed. Using, as input, the experimental results from the DCB specimen, the cohesive law is shown analytically and using Finite Element (FE) to reproduce accurately the R-curve for the DCB and also to predict accurately the R-curve for the CT specimens.     

Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints

The interfacial fracture of adhesively bonded structures is a critical issue for the extensive applications to a variety of modern industries. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions for fracture problems of adhesively bonded joints. Numerous global tests have been conducted to measure the interfacial toughness of adhesive joints. Limited local tests have also been conducted to determine the interface traction-separation laws in adhesive joints. However, very few studies focused on the local test of effects of adhesive thickness on the interfacial traction-separation laws. Interfacial toughness and interfacial strength, as two critical parameters in an interfacial traction-separation law, have important effect on the fracture behaviors of bonded joints. In this work, the global and local tests are employed to investigate the effect of adhesive thickness on interfacial energy release rate, interfacial strength, and shapes of the interfacial traction-separation laws. Basically, the measured laws in this work reflect the equivalent and lumped interfacial fracture behaviors which include the cohesive fracture, damage and plasticity. The experimentally determined interfacial traction-separation laws may provide valuable baseline data for the parameter calibrations in numerical models. The current experimental results may also facilitate the understanding of adhesive thickness-dependent interface fracture of bonded joints.     

Nonlinear interface shear fracture of end notched flexure specimens

The nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G_IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.     

The role of the adhesive layer in a double cantilever joint

The problem of a double cantilever beam adhesive joint is reconsidered under the assumption of cohesive fracture within the adhesive bond layer. After properly accounting for the adhesive layer, the problem is reduced to a Fredholm integral equation of the second kind for the bond line traction. Numerical results for the bond line stress distribution and the crack tip stress intensity factor are presented for several combinations of the governing material and geometrical parameters.     

The influence of adhesive constitutive parameters in cohesive zone finite element models of adhesively bonded joints

The influence of adhesive parameters on the outcome of cohesive zone finite element simulations is reported. The simulations are of adhesively bonded joint configurations that are used to characterize joint performance (including the double cantilever beam, the end notch flexure, and the single lap joint). The coupon level experiments are often used individually to determine a single parameter in an adhesive constitutive model (such as a cohesive strength or toughness). In this study, the influence of strength, toughness, and other parameters are considered simultaneously in examining their effect on the finite element (FE) output for each test. In specifying input parameters, the assumed shape of the cohesive traction law is also considered. It is shown that the double cantilever beam model output is dependent primarily on one parameter, whereas the end notch flexure and single lap joint models are dependent on multiple adhesive parameters. By extension, these dependencies require consideration when mapping the results of physical experiments into a set of adhesive model inputs. It is also shown that the shape of the traction law appears insignificant to the outcome of the models. Sensitivities to input parameters are illuminated through kriging analysis of the finite element results; the parameter values are chosen via Latin hypercube sampling. Surrogate models are created and are used to quantify the sensitivities. A mapping technique is described for evaluating the output of physical tests.     

MIXED MODES INTERLAMINAR FRACTURE TOUGHNESS OF CFRP LAMINATES TOUGHENED WITH CNF INTERLAYER

In the present paper, the influence of carbon nanofiber on interlaminar fracture toughness of CFRP investigated using MMB(Mixed Mode Bending) tests. Vapor grown carbon fiber VGCF and VGCF-S, and multi-walled carbon nanotube MWNT-7 has been employed for the toughener of the interlayer on the CFRP laminates. In order to evaluate the fracture toughness and mixed mode ratio of it, double cantilever beam (DCB) tests, end notched fracture (ENF) tests and mixed mode bending (MMB) tests have been carried out. Boundary element analysis was applied to the CFRP model to compute the interlaminar fracture toughness, where extrapolation method was used to determine the fracture toughness and mixed mode ratio. The interlaminar fracture toughness and mixed mode ratio can be extrapolated by stress distribution in the vicinity of the crack tip of the CFRP laminate. It was found that the interlaminar fracture toughness of the CFRP laminates was improved inserting the interlayer made by carbon nanofiber especially in the region where shear mode deformation is dominant.     

Constraint effects in adhesive joint fracture

Constraint effects in adhesive joint fracture are investigated by modelling the adherents as well as a finite thickness adhesive layer in which a single row of cohesive zone elements representing the fracture process is embedded. Both the adhesive and the adherents are elastic-plastic with strain hardening. The bond toughness Γ (work per unit area) is equal to Γ₀+Γ_p, where Γ₀ is the intrinsic work of fracture associated with the embedded cohesive zone response and Γ_p is the extra contribution to the bond toughness arising from plastic dissipation and stored elastic energy within the adhesive layer. The parameters of the model are identified from experiments on two different adhesives exhibiting very different fracture properties. Most of the tests were performed using the wedge-peel test method for a variety of adhesives, adherents and wedge thicknesses. The model captures the constraint effects resulting from the change in Γ_p: (i) the plastic dissipation increases with increasing bond line thickness in the fully plastic regime and then decreases to reach a constant value for very thick adhesive layers; (ii) the plastic dissipation in the fully plastic regime increases drastically as the thickness of the adherent decreases. Finally, this model is used to assess a simpler approach which consists of simulating the full adhesive layer as a single row of cohesive elements.     

蜂窝夹芯试件破坏行为分析

通过平面拉伸试验和双悬臂梁试验研究了蜂窝夹芯试件的破坏行为. 在平面拉伸试验中, 发现的破坏模式不是预期的面芯界面脱胶破坏而是面板层间分层破坏;在双悬臂梁试验中, 发现了一种与以往文献报导中不同的破坏模式(面板层间分层,预制裂纹偏转和面板分层扩 展依次出现). 针对试验中所发现的新的破坏模式,结合粘结模型,建立了基于 蔡-希尔破坏准则和能量准则的计算模型. 模拟结果与试验结果对比发现,所建立 的计算模型能够很好地模拟所发现的破坏行为.     

A simple cohesive zone model that generates a mode-mixity dependent toughness

A simple, mode-mixity dependent toughness cohesive zone model (MDG_c CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction–separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDG_c CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. This dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.     

动载下韧性撕裂在三种管线钢材中传播阻力的研究

阐述了用实验确定在常温及静载和动载条件下韧性撕裂在三种管线钢材中传播时的断裂比能值。实验中采用了销钉加载双面开槽的双悬脊梁(DCB)试件。应用能量平衡法对实验结果进行了分析。考察了加载速率和试件厚度对撕裂韧性的影响。结果表明,管线钢材对韧性撕裂传播的阻力在动载条件下增大,对较薄的试件及应变率敏感性较高的材料其增大更为明显。对于纯剪切断裂的传播来说,撕裂韧性一般随试件厚度的增大而增加。     

复合材料Ⅰ型层间断裂韧性GIC和初始裂纹长度

从经典梁理论和弹性基础上的正交各向异性梁理论出发，分析了梁的弯曲剪切效应和弹性基础对用双悬臂梁试件测得的复合材料层合板Ⅰ型层间断裂韧性Ｇ＿（ＩＣ）的影响，发现当试件的初始裂纹长度较短时，剪切效应和弹性基础对Ｇ＿（ＩＣ）的影响是显著的，建议将初始裂纹长度取５０毫米。实验结果表明，初始裂纹长度由２０毫米增加到５０毫米时，测得的Ｇ＿（ＩＣ）值的离散系数降低２０％～４０％，数据趋于稳定，分散性减小。     

Numerical analysis of the dual actuator load test applied to fracture characterization of bonded joints

The dual actuator load test was numerically analyzed in order to assess its adequacy for fracture characterization of bonded joints under different mixed-mode loading conditions. This test enables asymmetric loading of double cantilever beam specimens, thus providing a large range of mixed-mode combinations. A new data reduction scheme based on specimen compliance, beam theory and crack equivalent concept was proposed to overcome several difficulties inherent to the test. The method assumes that the dual actuator test can be viewed as a combination of the double cantilever beam and end loaded split tests, which are used for pure modes I and II fracture characterization, respectively. A numerical analysis including a cohesive mixed-mode damage model was performed considering different mixed-mode loading conditions to evaluate the test performance. Some conclusions were drawn about the advantages and drawbacks of the test.     

Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.     

Experimental and Numerical Study of Paperboard Interface Properties

Laminated paperboard is widely used in packaging products. Interface delamination plays a crucial role in converting paperboard to a carton through the creasing and folding process. Thus, the aim of this study is to experimentally and numerically investigate the interface fracture behavior in pure crack opening mode (mode I) and sliding mode (mode II). Four experimental tests have been evaluated and compared to numerical simulation, namely, the z-directional tensile test (ZDT), double-notch shear test (DNS), double-cantilever beam test (DCB) and end-notched flexure test (ENF). It was shown that, for the paperboard specimens tested, the ZDT test was sufficient to fully characterize the mode I crack growth response. However, the DNS and ENF tests were required to determine the maximum shear stress and the fracture toughness of pure mode II, respectively. Further mixed-mode investigation would enable the analysis of paperboard delamination behavior during the creasing and folding process.     

Adhesive fracture of a lap shear joint

In many respects, adhesive and cohesive fractures are similar. It has been demonstrated in both cases that a Griffith-type energy balance can often be used to predict failure, e.g., crack growth. The only essential difference involves the interpretation of the energy required to create new (adhesive or cohesive) surface area. In the cohesive case, the specific fracture energy γ _c is that required to create a new surface in the same material, while in the adhesive case, the specific fracture energy γ _a is the energy per unit area required to separate different materials. The mechanical analysis, including a stress analysis to determine the strain energy and energy balance in principle remains unchanged. Generally speaking adhesive-bonded joints involve sharp corners or other “singularities” between adjacent materials which act as stress concentrators, particularly if a crack or other sharp imperfection is present or arises at such a location. The Griffith energy approach circumvents the problem of just how large this mathematically infinite stress must be to initiate failure. Recently, this method had been successfully applied to a number of different adhesive geometries; this paper discusses the case of a single-lap shear joint. This geometry is important because the lap-joint test is a common method for comparing adhesive strengths; in addition, the configuration itself is often used in engineering practice. Adhesive fracture is, therefore, compared on the basis of both energy and maximum stress criteria. Experimental data suggest the former to yield more accurate predictions.     

The effects of geometry and material properties on the fracture of single lap-shear joints

A review of the mechanics of lap-shear joints is followed by a detailed analysis of the problem using a cohesive-zone approach. The cohesive-zone model allows not only the influence of geometry to be considered, but also allows the cohesive properties of the interface and plastic deformation of the adherends to be included in the analysis. The first part of the paper examines the strength of elastic joints, with an emphasis on the effects of geometry, the cohesive strength of the adhesive, and mode-mixedness. The cohesive-zone models show a transition to the predictions of linear-elastic fracture mechanics under conditions where these are expected to apply. The second part of the paper examines the effect of plasticity in the adherends, and looks at the transition between the elastic and plastic regimes. The final part of the paper makes comparisons between the predictions of the numerical calculations and experimental observations for a model system consisting of a commercial adhesive used to bond an aluminum alloy. Using cohesive-zone parameters previously determined for this particular combination of materials, the numerical predictions show excellent agreement with the experimental observations.     

Ductile–brittle transitions in the fracture of plastically deforming,adhesively bonded structures. Part II: Numerical studies

To enable the effective and reliable use of structural adhesive bonding in automotive applications, the cohesive properties of a joint need to be determined over a wide range of loading rates. In this paper, a strategy for determining these properties has been described and used to analyze a set of experimental results presented in a companion paper. In the particular system studied, a crack growing in a toughened quasi-static mode could make a catastrophic transition to a brittle mode of fracture. The cohesive parameters for both the toughened and brittle modes of crack growth were determined by comparing numerical predictions from cohesive-zone simulations to the results of experimental tests performed using double-cantilever beam specimens and tensile tests. The cohesive parameters were found to be essentially rate-independent for the toughened mode, but the toughness dropped by a factor of four upon a transition to the brittle mode. The results of wedge tests were used as an independent verification of the cohesive parameters, and to verify that the quasi-static properties remained rate-independent to very high crack velocities corresponding to conditions of low-velocity impact. The effects of friction, and the use of the wedge test to determine cohesive parameters, were also explored.     

Local Interface Shear Fracture of Bonded Steel Joints with Various Bondline Thicknesses

Interfacial fracture is a critical issue for extensive applications of adhesively bonded structures to a variety of modern industries. Extensive global experimental tests have been conducted to measure the global behavior of adhesively bonded joint, such as ultimate load capacity and toughness. Recently, several studies have also been employed to characterize the local interfacial traction–separation laws. However, very few tests have investigated the dependency of the local interfacial constitutive laws on the adhesive thickness, particularly, under Mode-II loading conditions. In this work, six typical adhesive thicknesses (from 0.1 mm to 1.0 mm) are prepared for the bonded joints with a configuration of end notched flexure (ENF) specimen to realize the Mode-II fracture loading (shear fracture). With a recently developed analytical model, the global energy release rates of the ENF specimens are experimentally measured. Meanwhile, with the image analysis technique, the local slips between the two adherends are obtained. Finally, based on the J-integral theory, the local interfacial constitutive laws at different bondline thicknesses are obtained. Several experimental findings are reported in this work. This work may provide valuable baseline experimental data for the input in cohesive zone model (CZM) based analytical and numerical simulations.     

Determination of the complex shear modulus of structural adhesives using a doubly clamped sandwich beam

A method is described for calculating the complex shear modulus of structural adhesives from dynamic test data on a doubly clamped sandwich beam in which the adhesive is contained as a thin layer. The accuracy of the technique is validated by finite-element analysis. Values of modulus obtained using the doubly clamped beam technique are found to be in excellent agreement with values obtained from dynamic tests on bulk specimens of an epoxy adhesive.