聚氯乙烯复合断裂性能研究

从弹塑性断裂力学理论出发,进行了硬质聚氯乙烯材料多角度下的Ⅰ/Ⅱ复合断裂试验,研究硬质聚氯乙烯材料复合断裂性能.利用数字图像相关技术,计算复合裂纹稳定扩展的临界裂纹尖端张开角值(ΨC1),尝试用该值作为一种断裂参数来描述硬质聚氯乙烯材料的断裂韧性.结果表明:(1)此材料与常见的金属材料不同,Ⅱ型加载模式下承载能力最大,纯Ⅰ型时承载能力最小;(2)当裂纹稳定扩展时,ΨC1值趋于稳定.故临界裂纹尖端张开角可作为硬质聚氯乙烯材料裂纹稳定扩展的断裂韧性.     

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.     

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.     

Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode deformations

An antisymmetric test fixture is employed to investigate interlaminar fracture behavior in graphite/epoxy composite material under mixed-mode deformations. Finite correction factors for the graphite/epoxy fracture specimen with various crack lengths are used to determine the interlaminar fracture toughness by finite-element stress analysis. Interlaminar fracture characteristics of graphite/epoxy composite material under mode-I, mode-II and mixed-mode deformations are evaluated experimentally. A mixed-mode fracture criterion is also investigated to obtain information on mixedmode interlaminar fracture behavior of graphite/epoxy composite material.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.     

A novel model of delamination bridging via Z-pins in composite laminates

A new micro-mechanical model is proposed for describing the bridging actions exerted by through-thickness reinforcement on delaminations in prepreg based composite materials, subjected to a mixed-mode (I–II) loading regime. The model applies to micro-fasteners in the form of brittle fibrous rods (Z-pins) inserted in the through-thickness direction of composite laminates. These are described as Euler–Bernoulli beams inserted in an elastic foundation that represents the embedding composite laminate. Equilibrium equations that relate the delamination opening/sliding displacements to the bridging forces exerted by the Z-pins on the interlaminar crack edges are derived. The Z-pin failure meso-mechanics is explained in terms of the laminate architecture and the delamination mode. The apparent fracture toughness of Z-pinned laminates is obtained from as energy dissipated by the pull out of the through-thickness reinforcement, normalised with respect to a reference area. The model is validated by means of experimental data obtained for single carbon/BMI Z-pins inserted in a quasi-isotropic laminate.     

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ_yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

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.     

Tensile-shear transition in mixed mode I/III fracture

The propensity of the transition of fracture type in either brittle or ductile cracked solid under mixed-mode I and III loading conditions is investigated. A fracture criterion based on the competition of the maximum normal stress and maximum shear stress is utilized. The prediction of the fracture type is determined by comparing τ_max/σ_max at a critical distance from the crack tip to the material strength ratio τ_C/σ_C, i.e., (τ_max/σ_max)<(τ_C/σ_C) for tensile fracture and (τ_max/σ_max)>(τ_C/σ_C) for shear fracture, where σ_C (τ_C) is the fracture strength of materials in tension (shear). Mixed mode I/III fracture tests were performed using circumferentially notched cylindrical bars made of PMMA and 7050 aluminum alloy. Fracture surface morphology of the specimens reveals that: (1) for the brittle material, PMMA, only tensile type of fracture occurs, and (2) for the ductile material, 7050 aluminum alloy, either tensile or shear type of fracture occurs depending on the mode mixity. The transition (in ductile material) or non-transition (in brittle material) of the fracture type and the fracture path observed in experiments were properly predicted by the theory. Additional test data from open literature are also included to validate the proposed theory.     

Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading

Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R _o ) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR _o = 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.     

Analytical investigation of nonlinear interlaminar fracture in trilayered polymer composite beam under mode II crack loading conditions using the J -integral approach

The present study is concerned with a nonlinear fracture analysis of trilayered beam built up by two unidirectional fiber-reinforced polymer composites. It is assumed that two interlaminar cracks exist between the layers. A tensile force applied to the middle layer generates pure mode II crack loading conditions. The J -integral approach is used to investigate the nonlinear fracture behavior of the beam. The elastic-linearly hardening model is applied to describe the mechanical behavior of the two composites. Sixth expressions for J -integral are derived using a beam theory model. These expressions correspond to the characteristic magnitudes of the external force. The validity of the formulae obtained is proved by comparison with the J -integral solution in the case of linear-elastic behavior of the composite materials. A numerical example is presented in order to demonstrate the ability of the expressions obtained for the analysis of nonlinear fracture in polymer composites.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

Experimental evaluation of mixed-mode fracture in adhesive bonds

Previous tests have shown that the mode II and mode III fracture energies of adhesive bonds coincide, with the nominal value dictated by post-yield shear deformation in the interlayer. This suggests that the complete mixed-mode fracture behavior may be dellineated by determining the interaction curve in either theG _I -G _II orG _I -G _III plane. A DCB-type specimen capable of delivering the entire opening versus shearing toughness spectrum in a single test was used. A brittle and a ductile epoxy resin were evaluated, with the adhesive thickness varying from a few micrometers up to 0.6 mm. Excluding very thin bonds, the mixed-mode fracture curve was approximately bilinear; when the applied energy release rate in shear,G _s , was relatively small, the total fracture energy equaledG _IC but otherwise, the fracture curve decreased essentially linearly with increasingG _S . In the case of the ductile adhesive, the transition in trends occurred whenG _S was approximately 55 percent of the shearing fracture energy. When the bond thickness was decreased to a few micrometers, the mixed-mode curve displayed a concave shape, with mode interaction occurring promptly. SEM analysis and analytical considerations suggest that this change in mixed-mode behavior was due to the development of a triaxial state of stress in the interlayer. Based on previous fracture studies of the individual fracture modes in adhesive bonds and laminated composites, the present results should be also applicable to mixed-mode interlaminar fracture of laminated composites.Herzl Chai, formerly associated with Polymers Division, Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899     

CTS试样I/II混合型断裂特性数值计算研究

采用CTS试样研究I/II混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用。文中采用有限元法研究紧凑拉伸剪切（CTS）试样在I/II平面混合型加载下的裂纹扩展行为。采用ANSYS建立CTS试样I/II混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析。通过与解析公式结果进行对比验证了该数值方法的可靠性。采用最大环向应力准则（MTS）,模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因。结合文中计算结果,在CTS试样I/II混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料I/II型混合型裂纹扩展速率曲线。     

Ductile–brittle transitions in the fracture of plastically-deforming,adhesively-bonded structures. Part I: Experimental studies

Rate effects for adhesively-bonded joints in steel sheets failing by mode-I fracture and plastic deformation were examined. Three types of test geometries were used to provide a range of crack velocities between 0.1 and 5000 mm/s: a DCB geometry under displacement control, a wedge geometry under displacement control, and a wedge geometry loaded under impact conditions. Two fracture modes were observed: quasi-static crack growth and dynamic crack growth. The quasi-static crack growth was associated with a toughened mode of failure; the dynamic crack growth was associated with a more brittle mode of failure. The experiments indicated that the fracture parameters for the quasi-static crack growth were rate independent, and that quasi-static crack growth could occur even at the highest crack velocities. Effects of rate appeared to be limited to the ease with which a transition to dynamic fracture could be triggered. This transition appeared to be stochastic in nature, it did not appear to be associated with the attainment of any critical value for crack velocity or loading rate. While the mode-I quasi-static fracture behavior appeared to be rate independent, an increase in the tendency for dynamic fracture to be triggered as the crack velocity increased did have the effect of decreasing the average energy dissipated during fracture at higher loading rates.     

Mixed-mode interface toughness of wafer-level Cu-Cu bonds using asymmetric chevron test

Characterization of interfacial adhesion is critical for the development of wafer bonding processes to manufacture microsystems with high yield and reliability. It is imperative that the test method used in such adhesion studies corresponds to the loading conditions present during processing and operation of the devices. In most applications in which wafers and die are bonded, the interface experiences a combination of shear and normal loading (i.e. mixed-mode loading) with the relative magnitude of the Mode I and II components varying in different scenarios. In the current work, the toughness of Cu-Cu thermocompression bonds, which are of interest for the fabrication of three-dimensional integrated circuits, is analyzed using a bonded chevron specimen with layers of different thickness that allows for the application of interfacial loading with variable mode mixity. The phase angle (a function of the degree of mode mixity at the interface) is varied from 0° to 24° by changing the layer thickness ratio from 1 to 0.48. The Cu-Cu bond toughness increases from 2.68 to 10.1 J/m², as the loading is changed from Mode I (pure tension) to a loading with a phase angle of 24°. The energy of plastic dissipation increases with increasing mode mixity, resulting in the enhanced interface toughness. The Mode I toughness of Cu-Cu bonds is minimally affected by plasticity, and therefore, provides the closest estimate of the interfacial work of fracture under the bonding conditions employed.