Nonlinear finite element analysis of stress and strain distributions across the adhesive thickness in composite single-lap joints

A geometrically nonlinear, two-dimensional (2D) finite element analysis has been performed to determine the stress and strain distributions across the adhesive bond thickness of composite single-lap joints. The results of simulations for 0.13 and 0.26 mm bond thickness are presented. Using 2-element and 6-element mesh schemes to analyze the thinner bond layer, good agreement is found with the experimental results of Tsai and Morton. Further mesh refinement using a 10-element analysis for the thicker bond has shown that both the tensile peel and shear stresses at the bond free edges change significantly across the adhesive thickness. Both stresses became increasingly higher with distance from the centerline and peak near but not along the adherend–adhesive interface. Moreover, the maximum shear and peel stresses occur near the overlap joint corner ends, suggesting that cohesive crack initiation is most likely to occur at the corners. The dependence of stress and corresponding strain distributions on bond thickness and adhesive elastic modulus are also presented. It is observed that the peak shear and peel stresses increase with the bond thickness and elastic modulus.     

Direct determination of cohesive stress transfer during debonding of FRP from concrete

Interface cohesive stress transfer between FRP and concrete during debonding is typically obtained using measured surface strains on the FRP, along the direction of the fibers. The cohesive material law is derived under a set of assumptions which include: (a) the bending stiffness of the FRP laminate is insignificant with respect to that of the concrete test block; (b) the strains in the bulk concrete produced by debonding are negligible, thus concrete substrate can be considered rigid; (c) there is stress transfer between FRP and concrete through the FRP–concrete interface which is of zero thickness; and (d) the axial strain in the FRP composite is uniform across its thickness. In this paper, a test procedure for directly obtaining the through-thickness strains in the FRP and the concrete substrate during cohesive stress transfer associated with debonding is presented. The displacement and strain fields are measured on the side of a direct-shear specimen with the FRP strip attached on the edge. Based on the experimental results, the influence of the assumptions which have been introduced to determine the cohesive law is discussed. Within the stress transfer zone there is a sharp gradient in the shear strain. The location of the interface crack within the stress transfer zone and the cohesive stress transfer during the propagation of the interface crack are determined.     

A maximum allowable flaw size for debond-resistant bimaterial layers

Free-edge debonding and subsequent interface crack extension are common modes of failure in a variety of engineering applications in which bonded layers of dissimilar materials are subject to differential expansion stresses. In this study, the susceptibility to debonding of short interface edge cracks is investigated for the global plane elasticity problem of a bimaterial strip with a uniform edge load applied to the top layer (a general model of differential expansion). The goal of this study is to determine the maximum crack length L for which interface crack extension is inhibited, or more specifically, for which the singular interface normal stresses are compressive. This is equivalent to a maximum allowable flaw size, which is of interest to both designers and inspectors of bimaterial systems. The critical crack length L has been extracted from parametric finite element analyses over a wide range of bimaterial configurations using the commercial software package ABAQUS. Results indicate that the critical crack length L increases with both the relative stiffness and thickness of the contracting layer, and may represent a significant inspectable flaw size for a variety of practical bimaterial configurations.     

Effect of damage levels and curing stresses on delamination growth behaviour emanating from circular holes in laminated FRP composites

This paper deals with the study of the effect of drilling induced delamination damage levels and residual thermal stresses (developed during manufacturing process of cooling the laminate form curing temperature to room temperature) on delamination growth behaviour emanating form circular holes in graphite/epoxy laminated FRP composites. Two sets of full three dimensional finite element analyses (one with the residual thermal stresses developed while curing the laminate and the other without residual thermal stresses i.e. with mechanical loading only) have been performed to calculate the displacements and interlaminar stresses along the delaminated interfaces responsible for the delamination onset and propagation. Modified crack closure integral (MCCI) techniques based on the concepts of linear elastic fracture mechanics (LEFM) have been used to calculate the distribution of individual modes of strain energy release rates (SERR) to investigate the interlaminar delamination initiation and propagation characteristics. Asymmetric variations of SERR obtained along the delamination front are caused by the overlapping stress fields due to the coupling effect of thermal and mechanical loadings. It is found that parameters such as ply orientation, drilling induced damage levels and material heterogeneity at the delaminated interface dictate the interlaminar fracture behaviour of laminated FRP composites.     

Crack front curvature: Influence and effects on the crack tip fields in bi-dimensional specimens

Crack front curvature is evidence in most experimental crack advance test. When classical linear elastic fracture mechanic theory deals with bi-dimensional crack configurations, it ignores the three-dimensional effects of crack propagation. Issues as the influence of the specimen thickness and the crack front curvature are not considered. Previous numerical studies have shed light on out-of-plane plastic zone development or stress state. Nevertheless, these numerical studies are based on the assumption that the crack front is ideally straight; despite it is well known that the crack front has some kind of curvature. In the present work, a CT aluminium specimen has been modelled three-dimensionally and several calculations have been made considering a huge combination of different single load levels, specimen thicknesses and crack front curvatures. Due to the abrupt transition from plane strain to plane stress, an ultrafine mesh along the thickness has been applied. The analysis of the evolution of the plastic zone and the stress state along the thickness provides information about the combined influence of these parameters on fracture mechanics.     

Impact of partial recrystallization on the performance of 6005A tube extrusions

Strain distribution in tube extrusion involves gradients not only across the thickness but also around the diameter in a cyclic fashion favouring recrystallization at the surfaces and weld seams where the peak strains occur. Recrystallized grains are coarse since only a small fraction of the potential nuclei are activated while the rest are pinned by the dispersoids. While coarse surface grain structure is typical in all 6005A tubes, only those with fully recrystallized weld seams have failed. Having been largely depleted of its defects during recrystallization, weld seams respond to a subsequent artificial ageing treatment favourably and enjoy a relatively higher hardness owing to the precipitation of the hardening precursor phases of the Mg₂Si. The interface between the harder weld seams and the relatively softer fibrous zones is believed to be a weak link, a very favourable site for crack initiation. Once initiated, cracks propagate along this interface until they reach the recrystallized surface layer. The recrystallized weld seams are judged to be a serious threat to the integrity of hollow extrusions.     

Fracture mechanics of piezoelectric materials

This paper presents an analysis of crack problems in homogeneous piezoelectrics or on the interfaces between two dissimilar piezoelectric materials based on the continuity of normal electric displacement and electric potential across the crack faces. The explicit analytic solutions are obtained for a single crack in an infinite piezoelectric or on the interface of piezoelectric bimaterials. For homogeneous materials it is found that the normal electric displacement D₂, induced by the crack, is constant along the crack faces which depends only on the remote applied stress fields. Within the crack slit, the perturbed electric fields induced by the crack are also constant and not affected by the applied electric displacement fields. For bimaterials, generally speaking, an interface crack exhibits oscillatory behavior and the normal electric displacement D₂ is a complex function along the crack faces. However, for bimaterials, having certain symmetry, in which an interface crack displays no oscillatory behavior, it is observed that the normal electric displacement D₂ is also constant along the crack faces and the electric field E₂ has the singularity ahead of the crack tip and has a jump across the interface. Energy release rates are established for homogeneous materials and bimaterials having certain symmetry. Both the crack front parallel to the poling axis and perpendicular to the poling axis are discussed. It is revealed that the energy release rates are always positive for stable materials and the applied electric displacements have no contribution to the energy release rates. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of crack nets development in thermal barrier coatings

After a relatively short time in service, components with thermal barrier coatings (TBCs) protection typically develop a system of cracks that propagate from the coated surface toward the interface. Usually these cracks propagate across the thickness of the protective coating and branch along the interface between the coating and the bank metal. The presence of these crack nets is a concern for the durability of the components with TBCs. In the study of thin TBCs by Rubinstein and Tang (Int J Solids Struct 42:5831–5847, 2005), it was found that in a number of cases, these components may still serve for a long time because of crack growth resistance development for cracks growing along the interface, which was found to be the most stable crack path under thermal loading conditions. One of the aims of this study is to determine whether similar fracture resistance is typical for thick TBC coatings as well. The emphases of the analysis presented here are on cases when the coating thickness is comparable to the thickness of the bank material, and on the effect of heat conduction changes due to branching of the developing cracks in a direction parallel to or along the interface. These items were not addressed in sufficient detail in the previous investigations.     

A mathematical framework of high-order surface stresses in three-dimensional configurations

The mathematical behavior of a curved interface between two different solid phases with surface or interface stress effects is often described by the generalized Young–Laplace (YL) equations. The generalized YL equations can be derived by considering force equilibrium of a thin interphase with membrane stresses along the interface. In this work, we present a refined mathematical framework by incorporating high-order surface or interface stresses between two neighboring media in three dimensions. The high-order interface stresses are resulting from the nonuniform surface stress across the layer thickness, and thereby effectively inducing a bending effect. In the formulation, the deformation of the thin interphase is approximated by the Kirchhoff–Love assumption of thin shell. The stress equilibrium conditions are fulfilled by consideration of balance for forces as well as stress couples. By simple geometric expositions, we derive in explicit form the stress jump conditions for high-order surface stresses. In illustrations, the bending deformation of nanoplates with high-order stresses is investigated and is compared with the results by the conventional YL equation.     

Delamination of Thin Films From Two-Dimensional Interface Flaws at Corners and Edges

This paper details the mechanics governing delamination of thin films driven by thermal expansion mismatch from two-dimensional interface flaws. Two scenarios are considered: (i) the edge of the film is concurrent with the edge of the substrate and (ii) the substrate extends past the edge of the film. Fully three-dimensional finite element models are used to analyze semi-circular interface flaws (along the edge) or quarter-circle interface flaws (at the corner of the film) for both scenarios. Results are presented for energy release rates and mode-mixity along two-dimensional crack fronts. For all cases considered, the crack driving force very close to the intersection of the crack front and the edge of the film is substantially larger than that for the interior portions of the crack front. For a given flaw size, the energy release rate along the entire front is higher when the substrate extends past the end of the film. The stress intensity factors are mixed-mode along the entire crack front; the predictions illustrate that the mode III component comprises a substantial contribution to the crack driving force over a significant part of the crack front. The implications of the results on film delamination is discussed in terms of critical flaw sizes, crack front profiles and the influence of the intersection singularity.     

K Variations and Anisotropy: Microstructure Effect and Numerical Predictions

Computer experiments were performed on simulated polycrystalline material samples that possess locally anisotropic microstructures to investigate stress intensity factor ( K ) variations and anisotropy along fronts of microcracks of different sizes. The anisotropic K , arising from inhomogeneous stresses in broken grains, was determined for planar microcracks by using a weight function-based numerical technique. It has been found that the grain-orientation-geometry-induced local anisotropy produces large variations in K along front of microcracks, when the crack size is of the order of few grain diameters. Synergetic effect of grain orientation and geometry of broken grains control K variations and evolution along the microcrack front. The K variations may diminish at large crack sizes, signifying a shift of K calculation to bulk stress dependence from local stress dependence. Local grain geometry and texture may lead to K anisotropy, producing unusually higher/lower K at a segment of the crack front. Either K variation or anisotropy cannot be ignored when assessing a microcrack.     

A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids

The stress fields near a crack front in a ductile solid are essentially three-dimensional (3D) in nature. The objective of this paper is to investigate the structure of these fields and to establish the validity of two-dimensional (2D) plane stress and plane strain approximations near the crack front under mixed mode (combined modes I and II) loading. To this end, detailed 3D and 2D small strain, elastic–plastic finite element simulations are carried out using a boundary layer (small scale yielding) formulation. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode II predominant loading. The implications of the 3D stress distribution on micro-void growth near the crack front are briefly discussed.     

Transverse fracture in multilayers from tension and line-wedge indentation

Crack propagation across laminated brittle solids from uniaxial tension or line-wedge loading is studied in real time using a model glass/epoxy architecture. The fracture progresses from one layer to the next via reinitiation from pre-existing flaws on the glass surfaces ahead of the primary crack in a process accompanied by some penetration through the interlayer but generally little or no delamination or deflection along the glass/epoxy interface. Depending on the system parameters, the material behind the crack front may be fully or intermittently severed. A 2D brittle fracture analysis is developed with the aid of the FEM technique taking into consideration stress gradients over flaws and flexure from contact loading. The analysis identified the flaw size and misfit in modulus, toughness and thickness between the layer and interlayer as the prime system variables. The results generally collaborate well with the experiments. Thick and compliant interlayers are generally advantageous except for contact loading, where they may promote crack reinitiation from the back surface of a layer. The explicit relations for crack penetration and reinitiation presented in this work facilitate convenient means for optimal design. Herzl Chai—on leave, School of Mechanical Engineering, Tel Aviv University, Israel.     

FRONT DEVELOPMENT OF A LONG FATIGUE CRACK DURING ITS GROWTH

Abstract— A 3-D elastic-plastic finite element analysis has been developed to simulate the deformation development along the front of a long mode I single edge crack in plates subjected to either monotonic or cyclic loading. Idealisations having both equal and unequal layers through the thickness of the plate were involved. Plane stress and plane strain 2-D finite element analyses were also performed and compared with the present 3-D solutions. The development of the monotonic and cyclic crack tip plastically deformed zones and opening displacements were traced and correlated to accommodate the effect of the plate thickness and the profile of the crack front. A previously developed crack tip deformation parameter was invoked to predict the effect of the specimen thickness on mode I fatigue crack growth and the associated change of crack front profile. Comparison of such a prediction and the experimental findings of the present work reflected the capability of that parameter in modelling fatigue crack growth through the plate thickness.     

Role of plasticity on interface crack initiation from a free edge and propagation in a nano-component

In order to elucidate the role of plasticity on interface crack initiation from a free edge and crack propagation in a nano-component, delamination experiments were conducted by a proposed nano-cantilever bend method using a specimen consisting of ductile Cu and brittle Si and by a modified four-point bend method. The stress fields along the Cu/Si interface at the critical loads of crack initiation and crack propagation were analyzed by the finite element method. The results reveal that intensified elastic stresses in the vicinity of the interface edge and the crack tip are very different, although the Cu/Si interface is identical in both experiments. The plasticity of Cu was then estimated on the basis of the nano-cantilever deflection measured by in situ transmission electron microscopy. The plasticity affects the stress fields; the normal stress near the interface edge is intensified while that near the crack tip is much reduced. Both the elasto-plastic stresses are close to each other in the region of about 10 nm. This suggests that the local interface fracture, namely, the crack initiation at the interface edge and the crack propagation along the interface, is governed by elasto-plastic normal stress on the order of 10 nm.     

Bonded elastic half-planes with an interface crack and a perpendicular intersecting crack that extends into the adjacent material—I

The solution is given for two bonded isotropic linearly elastic half-planes of different elastic properties having a crack along the interface as welt as a perpendicular crack in one of the half-planes which may intersect the interface crack. The appropriate integral equations are developed using displacement dislocations on the crack surfaces. Numerical results are presented for the stress intensity factors, strain energy release rate, stresses and displacements.     

Mixed-mode analysis of superimposed thermo-elastic effects in fiber-reinforced composites with embedded interface delaminations

This paper deals with the 3D finite element analysis of superimposed thermo-elastic effect on embedded interfacial delamination crack growth characteristics in fiber-reinforced laminated composites. Interlaminar fracture at the delamination front is found to be a mixed-mode phenomenon due to the anisotropy and heterogeneity of thermo-physical properties of composite materials. This leads to the requirement of finite element evaluation of energy release rates, based on the principles of linear elastic fracture mechanics. The strain energy release rate components along the delamination front due to a uniform temperature drop, during the manufacturing stages of composite laminates, to room temperature and subsequent mechanical loading is obtained by superimposing their respective effects based on the assumptions of linear elasticity. Numerical calculations are carried out for multi-layered cross-ply and angle-ply composite laminates and energy release rate plots demonstrate large asymmetries along the delamination front due to the interaction of residual stresses and superimposed transverse loading.     

In‐plane and out‐of‐plane constraint parameters along a three‐dimensional crack‐front stress field under creep loading

Full‐field three‐dimensional (3D) numerical analyses was performed to determine in‐plane and out‐of‐plane constraint effect on crack‐front stress fields under creep conditions of finite thickness boundary layer models and different specimen geometries. Several parameters are used to characterize constraint effects including the non‐singular T‐stresses, the local triaxiality parameter, the T_z ‐factor of the stress‐state in a 3D cracked body and the second‐order‐term amplitude factor. The constraint parameters are determined for centre‐cracked plate, three‐point bend specimen and compact tension specimen. Discrepancies in constraint parameter distribution on the line of crack extension and along crack front depending on the thickness of the specimens have been observed under different loading conditions of creeping power law hardening material for various configurations of specimens.     

The role of flaw geometry in thin film delamination from two-dimensional interface flaws along free edges

Delamination from planar interface edge flaws between a thin film and a semi-infinite substrate is examined to determine the roles of flaw width and depth relative to the film thickness. The flaws have curved and straight sections, and the crack front intersects the free edge at a right angle. Three-dimensional finite element models are used to extract local energy release rates and mode-mixity angles along the entire crack front. This paper focuses the crack dimensions required to reach steady state, wherein energy release rates are independent of flaw dimensions along the entire crack front. Results indicate that moderate elastic mismatch, although affecting mode mixity, plays a small role in determining the crack aspect ratios required to reach steady state. For wide cracks, the energy release rate for crack advance into the film interior approaches the plane-strain steady-state value when the half-width of the crack is approximately four times its depth (for cracks whose depths is several times the film thickness). For narrow cracks, the energy release rate near the free edge is significantly greater than the plane-strain steady-state result, and reaches a steady state when the depth approximately 10 times its width (for widths several time the film thickness). The results imply that delamination from wide cracks is reasonably accurately predicted via plane-strain analyses. Conversely, two-dimensional models are incapable of accurately predicting delamination from narrow cracks, which have a tendency to widen into flaws with more balanced aspect ratios (i.e. without growth in the depth direction).     

碳/铝复合材料界面反应对抗拉强度的影响

本文对Ti-B法制备的碳—铝合复材料经各种处理后产生的不同程度的界面反应与其纵向抗拉强度的关系进行了研究。碳—铝界面反应主要从三方面影响复合材料的抗拉强度:①界面结合强度;②界面脆性层;⑨纤维损伤。这三者的作用程度与界面反应程度有关。界面反应不严重时,主要是界面结合强度起作用;反应较严重时,界面脆性层的影响增大;反应很严重时,纤维发生严重损伤,对材料的抗拉强度产生很大的影响。