Visualization of debonding of fully and partially embedded glass fibres in epoxy resins

Very short glass fibres have been embedded in bars of epoxy resin and the debonding process was observed under the microscope as the polymer was stressed. In addition, fibre pull-out specimens have been similarly watched while the fibre was pulled. The interfaces of the fully embedded fibres failed across the fibre ends at strains of 0·2–0·3%, and circumferential failure started at about 0·6% strain. The low values for the end failures are compatible with models involving stress concentrations at the fibre ends. The circumferential failure value is in agreement with the results of earlier pull-out studies. In the case of the pull-out specimen, the behaviour was complex. Fibres with short embedded lengths debonded first across the embedded end. Failure of the cylindrical surface was too fast for the direction of crack propagation to be determined. Longer fibres first debonded at the fibre entry point and then arrested while debonding occurred across the embedded end. Final failure was again very fast. Long fibres debonded continuously, starting at the entry point. A slow fracture process appeared to be involved at least initially, so that the average shear stress on the region still bonded increased continuously throughout the process. Fast fracture occurred only in the very last stages of the process. These observations are compatible with the traditional theory, but reverse bonding is not ruled out for the shortest embedded lengths.     

岩石-混凝土界面拉伸断裂性能的率相关性研究EI北大核心CSCD

该文弯曲断裂试验获得了不同应变率下界面的抗拉强度、荷载-加载点位移曲线、荷载-裂缝口张开位移曲线、起裂荷载和峰值荷载,通过夹式引伸计法和DIC法获得了临界裂缝扩展长度。并计算了界面断裂能及双K断裂参数,分析了不同应变率下界面断裂过程区演化规律及特征长度的变化。结果表明:随应变率的增大,断裂能和起裂韧度增大,临界裂缝长度和失稳韧度先增加后减小,断裂过程区长度及特征长度随应变率的提高而减小。该文从裂缝发展路径、自由水粘性、惯性效应三方面探讨了岩石-混凝土界面断裂参数的率效应。     

Statistical failure analysis of brittle coatings by spherical indentation: theory and experiment

The mode of failure and failure probability of a brittle coating on a compliant substrate subjected to a static load through a spherical indenter is investigated experimentally and theoretically. We extend our recent study (2003, J Mat Sci 38:1589) of surface crack initiation in a monolithic solid to the layered system, and account for the multi axial stress state of the indentation in the failure probability analysis. Two modes of failure, a Hertzian cone crack initiating from the contacting surface and a half-penny-shaped crack initiating from the interface, are investigated and the probability of failure initiation for both surfaces are theoretically predicted and compared with experimental data.The effect of interface debonding on failure phenomena is investigated. For a given load the failure probability for debonded specimens is significantly higher than that of well-bonded samples. For the debonded case the theoretical failure probability curve falls within the 90% confidence interval of the experimental data, while the experimental values for the completely bonded case show somewhat lower failure probabilities than that predicted. This may be attributed to the possible bridging effect by the adhesive on interfacial surface defects in the ceramic that is not accounted for in our model.     

Deformation micromechanics in model carbon fibre-reinforced composites

Raman spectroscopy has been used to study the deformation micromechanics of the single-fibre pull-out test for a carbon fibre/epoxy resin system using surface-treated and untreated versions of the same type of PAN-based fibre. It has been possible to determine the detailed strain distribution along embedded fibres and it has been found that it varies with the level of strain in the fibre outside the resin block. The variation of interfacial shear stress along the fibre/matrix interface has been determined using the balance of forces equilibrium and this has been compared with the single values of interfacial shear strength determined from conventional pull-out analyses. It has been demonstrated that it is possible to identify situations where the interface is well-bonded, partially debonded or fully debonded and also to follow the failure mechanisms in detail. It has been found that the level of interfacial adhesion is better for the surface-treated fibre and that, for the untreated fibre, interfacial failure takes place by the cohesive failure of a weakly-bonded surface skin that appears to be removed by the surface pretreatment process.     

A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour

This paper presents a detailed study of the influence of maximum interfacial stress on interface element analyses for composites delamination. The development of the non-linear cohesive zone ahead of a crack tip is analysed with respect to length, stress distribution and mode ratio. The energy absorbed by interface elements is compared with the crack tip strain energy release rate from fracture mechanics analyses. These studies are performed initially on standard fracture toughness specimens, where mode-ratio is fixed by the applied displacement constraints. Results show close agreement with linear elastic fracture mechanics solutions. A simple ply drop specimen is then modelled, where the mode ratio is not constrained by the boundary conditions, and results are compared with the Virtual Crack Closure Technique. In this case maximum interfacial stress has a far greater influence on the numerical results, due to its significant influence on cohesive zone length, mode ratio and energy absorbed.     

Analytical and numerical modeling of R curves for cracks with bridging zones

At the onset of fracture in materials with process zones, the fracture resistance, or R curve, rises as the process zone develops. After process zone development, crack propagation proceeds by steady state growth. By considering J integral contours inside and outside the process zone, the available energy can be partitioned into crack tip energy release rate and process zone energy. To model the rising R curve, however, required assumptions about damage mechanisms in the process zone and partitioning of its energy into released and recoverable energy. By considering process zones that are elastic fiber-bridging zones with softening regions caused by fiber breakage or damage, equations for rising R curves were derived as a function of crack tip toughness and bridging zone mechanics. The new methods were implemented into the Material Point Method for generalized numerical crack propagation simulations with bridging zones. The simulation method includes pure fracture mechanics and pure cohesive zone models as extreme special cases. The most realistic simulations for many materials will likely fall between these two extremes. The results guided comments on interpretation of experimental R curves.     

Mechanical properties and microstructure of Al/Al laminated structure produced via ultrasonic consolidation process

Mechanical properties of a 2024 aluminium alloy laminated structure produced by the ultrasonic consolidation were investigated. In comparison with the monolithic aluminium alloy, the existence of laminated structure gave different fatigue and fracture mechanisms that associated with the layer interfaces. The Al/Al laminated specimens had the lower tensile strength but much higher fracture toughness than the monolithic Al specimens due to the exit of interface delaminations around the crack tip. The fatigue life of the laminated specimens was comparable to that of the monolithic Al specimens, though the initiation and propagation of the crack in the laminated specimens depended strongly on the microstructure of each material. The interface between layers could arrest the fatigue crack and impede the further propagation.     

Shear-lag analysis of notched laminates with interlaminar debonding

This study considers a method of analysis for predicting the fracture behavior of a notched, unidirectional lamina in the presence of surface constraint layers with debonding between the unidirectional ply and the constraint layers. Two particular cases are presented, the first being a debonded zone of finite width with no longitudinal damage in the unidirectional ply. This solution is then extended to include longitudinal matrix yielding and splitting in the unidirectional ply at the crack tip. The analysis is based on a materials modeling approach using the classical shear-lag assumption to describe the shear transfer between fibers. The fracture behavior of the laminate is studied as a function of initial crack length, the relative physical and geometric properties of the constraint plies and the unidirectional lamina, and width of the debonded zone. The results indicate that debonding can reduce the maximum fiber stress at the crack tip on the order of ten percent. This effect is maximum for a debond width of two or three fiber spacings and is independent of the initial crack length. As the debond width grows beyond this point, the maximum stress increases. For widths of about ten fiber spacings or more, the maximum fiber stress is larger than for the fully bonded case. In the presence of longitudinal matrix damage the same general behavior is found; however, the location of the maximum fiber stress is quite complex. In some cases with large matrix damage and a high constraint ratio, the maximum fiber stress can occur at the end of the debonded zone away from the crack tip.     

The detailed structure of delamination fracture surfaces in graphite/epoxy laminates

Delamination fracture surfaces of angle-ply graphite/epoxy specimens failed in tension were studied in the SEM. The fracture surfaces contain resin-rich and resin-poor areas, with the former showing imprints from fibres while the latter show debonded fibres. A delamination crack propagates in the outer parts of the plies adjacent to the resin-rich interlaminar region and alternates from one ply to the adjacent ply and back as it propagates. The serrations formed in between fibres in the outermost parts of plies are tilted. The sense of the tilt is in agreement with the direction of the major tensile principal stress. The delamination is suggested to proceed in steps including debonding of fibres, crack opening by the major principal tensile stress and linking together of these fractures.     

The initiation of slow crack growth in linear polyethylene under single edge notch tension and plane strain

The kinetics and microstructural changes associated with the initiation of slow crack growth in PE were measured. The initiation process consists of an instantaneous deformation zone which grows at a constant velocity until the beginning of fracture. The velocity of the damaged zone accelerates when the fibril fracture begins at the root of the initial notch. It was found that the initial velocity of the deformation zone depended on stress to about the 4th power and had an activation energy of about 100 kJ mol^–1; these results are about the same as those found by Chan and Williams for the crack growth velocity. It is concluded that both crack initiation and crack growth are governed by the same fundamental process, notably fibril thinning.     

Numerical characterization of the nonlinear fracture process in concrete

The growth and development of the fracture process zone in plain concrete has been investigated. A fictitious crack model based noniterative numerical scheme is developed to study the fracture characteristics of specimens of different sizes and geometries. Results from numerical studies on four different geometrically similar specimen sizes and two different specimen geometries are reported and discussed. The finite element program developed accommodates linear as well as nonlinear softening laws for the fracture process zone in concrete. It is observed that the process zone reaches a steady state length which is specimen size as well as specimen geometry dependent. As long as the process zone is allowed to develop to its steady state length, the energy absorbed in the process zone appears to be size and geometry independent. Results from tests on three-point bending specimens and compact tension specimens reported in the literature have been compared with the numerical solutions obtained in this investigation. Specimen size and geometry dependence generally observed in these fracture experiments have been duplicated. The numerical model also successfully reproduces many of the other experimentally observed characteristics in the fracture of plain concrete.     

A model of brittle fracture propagation part I—continuum aspects

The micromechanism of crack propagation in steel is described and analyzed in continuum terms and related to the macroscopic fracture behavior. It is proposed that propagation of cleavage microcracks through favorably oriented grains ahead of the main crack tip is the principal weakening mode in brittle fracture. This easy cleavage process proceeds in the Griffith manner and follows a continuous, multiply connected, nearly planar path with a very irregular front which spreads both forward and laterally and leaves behind disconnected links which span the prospective fracture surface. A discrete crack zone which extends over many grains thus exists at the tip of a running brittle crack. Final separation of the links is preceeded by plastic straining within the crack zone and occurs gradually with the increasing crack opening displacement. It is suggested that in low stress fracture, straining of the links is the only deformation mode. However, it is recognized that under certain conditions plastic enclaves may adjoin the crack zone. This deformation mode is associated with high stress fracture, energy transition and eventually with crack arrest.

Energy dissipation resulting from the two deformation mechanisms is related to crack velocity, applied load and temperature and the crack velocity in a given material is expressed as a function of the external conditions. Fracture initiation and crack arrest are then discussed in terms of the conditions which are necessary to maintain the propagation process. Finally, the dimensions of a small scale crack tip zone for a steady state, plane strain crack are evaluated as functions of material properties and the elastic stress intensity factor.

The microstructural aspects of brittle fracture will be discussed in a separate Part 2 [1].     

Criterion of crack initiation and spreading

The area of the true stress/true strain diagram determined under tensile test conditions is equal to the energy absorbed per unit volume at the point of fracture. In the case of tensile as well as other loading tests like compression, low cycle fatigue, etc. a spreading crack will be initiated when the critical specific fracture energy ($\text{W}{}_{\mathrm{c}}$) characteristic of the material has been absorbed whereby the proportionality law of notched specimens can then be derived. The specific fracture energy of notched tensile test specimens as expressed in the function of temperature will describe the brittle fracture sensitivity of the material. From the specific fracture energy of notched specimens the fracture toughness and the critical energy release rate can be determined. The method described herein is also adaptable for the determination of the brittle fracture sensitivity of welded joints.     

Some aspects of crack growth and failure in fibre reinforced composites

A theoretical analysis, previously developed to deal with the machanics of matrix cracking in unidirectional composites and with transverse ply cracking in cross ply laminates, has been developed further to deal with the tensile failure of unidirectional fibrous composites in with the fibres have a known distribution of strengths. It is proposed that, under the application of a tensile load, stable transverse cracks are formed which originate from regions of initial damage and which become unstable at some critical strain value. The model takes account of various parameters including the interfacial fibre/matrix debonding energy, the residual frictional shear strength of the debonded interface and the elastic properties of fibres and matrix. Comparisons are made between the predictions of the model and the observed failing strains of the 0° plies in carbon fibre polymer matrix laminates. The relevance of the model to the study of delayed fracture in fibrous composites is discussed. The modification of this model, previously developed to describe crack growth in the transverse plies of 0°/90° laminates, is used to predict the initial cracking strains for a wide range of CFRP laminate geometries and initial crack sizes. Some aspects of the mechanics of crack extension across interply interfaces are discussed.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

An in situ technique for the assessment of adhesive properties of a joint under load

Slow crack propagation in adhesive bonded joints has been characterised using an asymmetric wedge test. Crack position was evaluated from strain gauge measurements, both in the debonded part of the joint and in the bonded zone. Test temperature was changed during loading, giving insight into bond evolution. The technique allows accurate, and virtually continuous, determination of crack position to be made, and therefore the evaluation of crack speed versus fracture energy curves, as well as elastic properties of the adhesive layer. This technique also enables the monitoring of crack propagation in controlled environmental conditions to be performed, without interruption of exposure for measurements. By using a Winkler elastic foundation model to analyse results, the method seems to be the first to describe a process zone, or region where the adhesive is significantly strained under load, and a finite length specimen effect, manifested by crack front acceleration during the final stage of the test. The method was found to offer great potential to study in situ fracture and bulk adhesive properties.     

Slow crack growth in cellulose fibre cements

Slow stable crack growth is a prominent feature of the fracture behaviour of cellulose fibre cements. It is shown that this characteristic can be described by crack growth resistance against crack extension curves based on linear elastic fracture mechanics. Double-cantilever-beam specimens with side grooves are used to obtain such crack resistance curves for a commercial cellulose cement containing approximately 8% mass fraction of bleached fibres. Both dry and wet samples are tested. Compliances measured during slow crack growth by the unloading/reloading technique at successive crack increments are less than those obtained for saw-cut notches with similar crack lengths. Residual displacements due to either mismatch fracture surfaces or a large inelastic process zone at the crack tip are also observed at zero load. A modified elastic potential energy release rate (G _R ^* ), and hence its equivalentK _R ^* [= (EG _R ^* )^1/2], must be used to include this residual displacement effect in order to yield the true crack growth resistance curves. This is found to be necessary for the wet samples due to their large residual displacements. The crack growth resistances of the wet samples are superior to those of the dry samples: this is explained in terms of the improved ductility and toughness of the wet cellulose fibres.     

Single groove double cantilever beam fracture specimens versus Dugdale specimens for estimating shear lip propagation energies: BPA polycarbonate

Cracks in double cantilever beam specimens with single side grooves (S-G DCB) exhibit crack tip plastic zones that mimic closely the plastic zones that produce shear lips in mixed mode crack propagation in thick specimens of polycarbonate. In both the S-G DCB plastic zone and the shear lip the plastic strain is 30%. The S-G DCB strain energy release rate is a linear function of thickness, as a result of the fact that the cross-sectional area of the plastic zone increases linearly with the square of the net section thickness while the plastic strain in the zone is independent of thickness. In Dugdale specimens the thickness dependence of G _C is different from and more complex than that in the S-G DCB specimens. For each geometry G _C starts at zero thickness, but for Dugdale specimens rises eight times faster with the thickness at first. This greater thickness dependence of G _C in the Dugdale specimens arises from a greater dependence of zone cross-sectional area on thickness and a greater zone plastic strain (50 to 60% mostly). Other advantages of S-G DCB specimens versus Dugdale specimens in assessing ductile fracture are discussed.     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。