Interfacial debonding of pipe joints under torsion loads: a model for arbitrary nonlinear cohesive laws

Adhesively bonded pipe joints are extensively used in pipelines. In the present work, Cohesive Zone Model (CZM) based analytical solutions are obtained for the bonded pipe joints under torsion. An integral form based general expression is derived which is suitable for arbitrary type of nonlinear cohesive laws. The concept of the minimum interfacial cohesive shear slip δ _m is introduced and used in the fundamental expression of the external torsion load. It is found that, when the bond length of the pipe joint is large enough, the torsion load capacity is indeed independent of the shape of cohesive laws and the bond length. It is interesting to note that the maximum torsion load capacity is achieved when the torsion stiffness of the pipe and coupler are identical. A good agreement with finite element analysis (FEA) result indicates that the current model works well. The formulation to develop a simple test method for determining the τ–δ constitutive relationship in pipe joints under torsional loads is suggested. Parametric studies of various cohesive laws are conducted. This model deepens the understanding of the interfacial debonding problem of bonded joints. The fracture energy based formulas of the torsion load capacity derived in the present work can be directly used in the design of adhesively bonded pipe joints.     

An analytical investigation of debonding problems in beams strengthened using composite plates

This work deals with an enhanced analytical model for the analysis of typical edge debonding problems in concrete or steel beams strengthened/repaired with externally bonded composite laminated plates induced by beam/adhesive interface fracture phenomena. The strengthened system is viewed as composed by three physical different layers: the strengthened beam, the adhesive layer and the bonded plate. On the other hand, the structural model consists of two shear deformable mathematical layers, the upper one representing the beam and the lower one incorporating the adhesive layer and the bonded plate. Bonding conditions between layers are simulated by using the Lagrangian multipliers method and governing equations are obtained by a variational approach. In the context of a fracture mechanics approach, analytical solutions for both total and mode components of energy release rate are obtained by using stress resultant and strain discontinuities across at the crack tip. Closed form solutions are obtained for specific loading conditions and geometric configurations. Comparisons with predictions from very careful FE investigations point out the effectiveness of the proposed results which may form the basis for a design process taking into account properly of debonding failure modes triggered by interface fracture at the edge of the repairing composite plate. Finally, the significance of the paper relies in the analytical approach to the problem, which avoids the complexities commonly shared by FE-based methodologies, related to stress singularities and differences in length scales and in mechanical properties of the single components of the system.     

Fracture instability and limit strength condition in structures with re-entrant corners

When considering a structural element with a re-entrant corner, the experimental analysis shows how the fracture strength increases with the angle of the corner. Thus, the strength increases with a decrease of the mass of the structure, in contrast to what we are used to observe in different kind of collapses, e.g., plasticity. To predict this behaviour, a non-local theory, basically based on the Novozhilov’s hypothesis of existence of a fracture quantum, is herein presented. Theoretical predictions for the strength of finite structures (e.g., finite plates under tension or beams under bending) by varying both angle and relative depth of the corner are presented: accordingly, simple formulas, useful in the design of such structures, are provided. The theory is then compared with experimental and numerical results, showing a relevant agreement.     

Transversely compressed bonded joints

The load capacity of bonded joints can be increased if transverse pressure is applied at the interface. The transverse pressure is assumed to introduce a Coulomb-friction contribution to the cohesive law for the interface. Response and load capacity for a bonded single-lap joint was derived using non-linear fracture mechanics. The results indicated a good correlation between theory and tests. Furthermore, the model is suggested as theoretical base for determining load capacity of bonded anchorages with transverse pressure, in externally reinforced concrete structures.     

焊点间距对胶焊接头应力应变分布和强度的影响

采用数值分析和试验研究方法考察了焊点间距对两种胶焊中应力应变分布和接头强度的影响。结果表明,高弹性模量胶粘剂胶焊接头中,增大焊点间距,焊点就三小耐的妆区边缘胶层中的应力应变略有增大,低弹性模量释粘剂胶焊接头中,焊点应力集中程度和搭接区边缘胶层中的剪应变值都随焊点间距的增加而增大,增加焊点间距,两种接头的胶层中度都将降低。试验所得接头断裂时的名义应力随焊点间距的增加而略有减小,与计算结果吻合良好。     

Comparison of shear strength tests on AV119 epoxy-joined carbon/carbon composites

The results of an experimental investigation on carbon/carbon composites (C/C) bonded joints tested in shear at room temperature, under seven different configurations, are presented. The samples have been joined by an epoxy adhesive (AV119): this adhesive is not to be considered as a suitable joining material for C/C for high temperature applications, but just as a model joining material chosen to obtain several bonded samples in a short time. Advantages and disadvantages of each configuration are discussed from an experimental point of view. A finite element analysis is also performed to compare the stress distribution obtained within the joint for the different testing geometries. It is shown that the measured values of the apparent shear strength decrease with the maximum opening stress estimated within the middle of the joint.     

Analysis of deformations and stresses in balanced and unbalanced adhesively bonded single-strap joints

Adhesively bonded joints are increasingly being used in joining various structural components. Adequate understanding of the behaviour of adhesively bonded joints is necessary to ensure efficiency, safety and reliability of such joints. While several joint configurations, such as the single- and double-lap joints have received considerable consideration, the single-strap joint configuration has received little attention, partly because earlier studies have shown it to be the least efficient.

One of the objectives of this paper is to demonstrate that strap joints can be as efficient as lap joints, as long as they are properly designed. This will be done through a detailed analytical investigation into influence of the parameters that govern peak stresses in the adhesive. The next objective is to produce simple equations by which the design of strap joint could be facilitated in an effective manner. For this, the developed analytical expressions are simplified and shown to provide accurate results. The derived solutions provide better insight into understanding the parameters that most influence the edge forces.     

Joints in strips for electrodynamic magnetic levitation systems

The force disturbances experienced by the superconducting magnets of an electrodynamically levitated vehicle due to guideway strip thermal expansion joints are studied. The experimental investigation covers the low, intermediate, and high speed ranges, and it is shown that the change in eddy current distribution at a guideway strip discontinuity, i.e., at a simple butt joint, can cause severe transients in the electrodynamic forces. A number of possible joint configurations are examined, and it is shown that the use of an overlap joint or a backing/covering strip can reduce transients to an acceptable level.     

Fracture characterization of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending

A combined analytical and experimental approach is presented to characterize both mode-II and mixed mode fracture of Carbon fiber-reinforced polymer-concrete bonded interfaces under four-point bending load, and closed-form solutions of compliance and energy release rate of the mode-II (four-point symmetric end-notched flexure) and mixed (four-point asymmetric end-notched flexure) mode fracture specimens are provided. The transverse shear deformation in each sub-layer of bi-material bonded beams is included by modeling each sub-layer as an individual first order shear deformable beam, and the effect of interface crack tip deformation on the compliance and energy release rate are taken into account by applying the interface deformable bi-layer beam theory (i.e., the flexible joint model). The improved accuracy of the present analytical solutions for both the compliance and energy release rate is illustrated by comparing with the solutions predicted by the conventional rigid joint model and finite element analysis. The fracture of Carbon fiber-reinforced polymer-concrete bonded interface is experimentally evaluated using both the four-point symmetric and asymmetric end-notched flexure specimens, and the corresponding values of critical energy release rates are obtained. Comparisons of the compliance rate-changes and resulting critical energy release rates based on the rigid joint model, the present theoretical model, and numerical finite element analysis demonstrate that the crack tip deformation plays an important role in accurately characterizing the mixed mode fracture toughness of hybrid material bonded interfaces under four-point bending load. The improved solution of energy release rates for the four-point symmetric and asymmetric end-notched flexure specimens by the flexible joint model can be used to effectively characterize hybrid material interface, and the fracture toughness values obtained for the Carbon fiber-reinforced polymer-concrete interface under mode-II and mixed mode loading can be employed to predict the interface fracture load of concrete structures strengthened with composites.     

Experimental and numerical evaluations on the effects of adhesive fillet,overlap length and unbonded area in adhesive‐bonded joints

To realize robust structural design, the effects of the adhesive fillet, overlap length and unbonded area in adhesive‐bonded joints need to be fully understood and incorporated into a fatigue life estimation method. In the present work, both static and fatigue experiments are performed on six types of adhesive‐bonded joints to illuminate these effects systematically. A straightforward total fatigue life evaluation method is proposed to address these effects. A statistical crack initiation model is established based on the fatigue data of bulk adhesive specimens. Growth life is calculated using the interfacial crack model and mixed mode crack growth method. Good correlation is observed between the calculated and experimental fatigue lives. Furthermore, the effects of the adhesive fillet, overlap length and unbonded area are analysed based on both calculated and experimental results. Results indicate that adhesive fillet postpones crack initiation by reducing local strain level, both overlap length and unbonded area change the growth life by length. Besides, overlap length promotes the fraction of mode II strain energy release rate in total, reducing crack growth rates and extending growth life.     

Brittle fracture evaluation of a fine grain cement mortar in combined tensile-shear deformation

Different laboratory experiments are usually conducted to characterize the fracture behaviour and integrity properties of newly developed structural materials. However, the reported fracture tests data for an improved high strength cement mortar (HSCM) under combined tension-shear loading are not in agreement with theoretical predictions obtained from well-known fracture criteria. It is shown in this paper that the significant difference existing between the experimental and theoretical results is due to ignoring the effect of  T -stress on the processes of crack growth in the HSCM test specimens. A modified fracture model is then used to show that the theoretical predictions can be corroborated by the experimental results when the effect of  T -stress is taken into account.     

Elastic analysis of hybrid bonded joints and bonded composite repairs

The authors extend the closed-form bonded joint linear elastic analysis method of Delale et al. [Delale F, Erdogan F, Aydinoglu MN. Stresses in adhesively bonded joints: a closed-form solution. J Compos Mater 1981;15:249–71] and Bigwood and Crocrombie [Bigwood DA, Crocombe AD. Elastic analysis and engineering design formulae for bonded joints. Int J Adhes Adhes 1989;9(4):229–42] to include the composite deformation mechanisms and the thermal residual strains that arise in hybrid metal-composite joints such as those presented by bonded composite repairs applied to metallic aircraft structures. The analytical predictions for the adhesive stresses and the compliance are compared to the results of a linear elastic finite element model that has itself been validated by comparison with experimental results. The results are applied to the problem of coupled linear extension and bending of a bonded composite repair applied to a cracked aluminum substrate. The resulting stress intensity factor and crack-opening displacement in the repaired plate are compared to the results of a three-dimensional finite element analysis, and also exhibit excellent results. Throughout the text, observations are made regarding the practical application of the results to failure prediction in hybrid joints, whereby the authors demonstrate the need for consistency in the analytical methods used to determine the fatigue and failure of composites from the coupon level to the analysis of the final structural details.     

A study on the strength of adhesively bonded joints with different adherends

In this study, mechanical properties of adhesively bonded single-lap joint (SLJ) geometry with different configurations of lower and upper adherends under tensile loading were investigated experimentally and numerically. The adherends were AA2024-T3 aluminum and carbon/epoxy composite with 16 laminates while, the adhesive was a two-part liquid, structural adhesive DP 460. In experimental studies, four different types of single-lap joints were produced and used namely; composite–composite (Type-I) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-II) with lower and upper adherends of the same thicknesses and four different stacking sequences, composite–aluminum (Type-III) with lower adherend (composite) of the same thickness but upper adherend of three different thicknesses, aluminum–aluminum (Type-IV) with lower adherend of the same thickness but upper adherend of three different thicknesses, composite–composite (Type-V) with [0]₁₆ stacking sequences and three different overlap length, aluminum–aluminum (Type-VI) with three different overlap length. In the numerical analysis, the composite adherends were assumed to behave as linearly elastic materials while the adhesive layer and aluminum adherend were assumed to be nonlinear. The results obtained from experimental and numerical analyses showed that composite adherends with different fiber orientation sequence, different adherend thicknesses and overlap length affected the failure load of the joint and stress distributions in the SLJ.     

Mixed mode failure analysis of bonded joints with rate‐dependent interface models

The recent developments in joining technologies and the increasing use of composites materials in structural design justify the wide interest of structural mechanics researchers in bonded joints. Joints often represent the weakness zone of the structure and appropriate and rigorous mechanical models are required in order to describe deformation, durability and failure. The present work is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the time‐dependent behaviour of bonded joints. The interface laws are formulated in the framework of viscoplasticity for generalized standard materials and describe the softening response of the joint along its decohesion process in presence of shear and tensile normal tractions. These laws are derived in a thermodynamic consistent manner and take into account the rate dependency modifications of the fracture process zone making use of a sort of non‐local instantaneous dissipation. The interface constitutive laws are expressed both in rate and discrete incremental form for the purpose of numerical implementation. The consistent tangent matrix is derived. Finally, the problem of model parameters identification is approached making use of the finite element method for the experiments simulation and of an evolution strategy to solve the constrained optimization problem which mathematically represents the parameter identification inverse problem. Copyright © 2006 John Wiley & Sons, Ltd.     

A finite element algorithm to study creep cracks based on the creep hardening surface

This work addresses finite element (FE) modelling of creep cracks under reversed and cyclic loads in steels. A constitutive model based on the creep hardening surface developed by Murakami and Ohno has been selected for this purpose. This model is particularly accurate for describing creep under reversed and cyclic loads and requires no additional material constants. An FE algorithm for this model has been derived and implemented into a research code FVP. The algorithm is verified by comparing the numerical predictions with closed form solutions for simple geometries and loading configurations. FE predictions are compared with experimental data for a stationary crack in a compact tension specimen. The stress and strain fields in the vicinity of a crack under a sustained load are compared with those for the intermediate unloading case. Several integral fracture parameters are investigated as to their appropriateness for describing creep cracks under reversed and cyclic loads.     

Method for widening the reject-band in low-pass/band-pass filters by employing coupled C-shaped defected ground structure

Two new compact defected ground structure low-pass filters with broad stop-band and low insertion loss in the pass band are presented. The structures of these new microstrip low-pass filters are simple as they are composed of a pair of DGS-slots and an openstub. One filter is realised through the multi-layer method, and the second filter by cascading. With these configurations, two LPF with compact size, wide reject band and sharp transition from pass to stop-band are realised. The design formulas are derived by using an equivalent circuit model of coupled DGS resonators. Demonstration filters are designed, fabricated and tested. The experimental results show good agreement with theoretical results and demonstrate that the required characteristics of LPF could be simply obtained through the proposed methods. Finally a simple gap-method will be used in order to transform the LPF to BPF.     

A statistical micromechanical model of multiple cracking for ultra high toughness cementitious composites

A new statistical micromechanical model of multiple cracking is proposed in which a general expression of the fiber bridging stress laws in the crack plane is established. In this model, the random distribution properties of fibers are considered. And the Weibull function is adopted to represent the flaw size distribution. The relationships of stress versus strain and crack width versus strain are proposed. The formulas of the crack width, crack space, strain capacity and fracture energy density at the end of multiple cracking processes are also deduced. The validity of the proposed model was demonstrated by experimental results.     

Prediction of the fracture of metals in processes of cold plastic deformation. Part 2. Effect of anisotropic hardening and experimental verification of the model of plastic deformation and fracture

On the basis of the experimental investigation of the Bauschinger effect, in steels with developed prestrains, we generalize the model of plastic deformation to the case of anisotropic hardening. Within the framework of the model, we show that for high strains, the Bauschinger effect is caused by dislocations. We present the results of the experimental verification of the developed semiphenomenological model of the joint process of plastic deformation and fracture of metals under the conditions of cold deformation. It is shown that this model gives adequate predictions (in good agreement with the experimental data) of the probability of fracture of the metal caused by exhaustion of the plasticity margin in the processes of plastic deformation realized under the conditions of both simple and complex loading. Ufa State Aviation Technical University, Ufa, Russia. Translated from Problemy, Prochnosti, No. 2, pp. 74–84, March–April, 1999.     

Design equations for reinforced concrete members strengthened in shear with external FRP reinforcement formulated in an evolutionary multi-objective framework

Methods for predicting the shear capacity of FRP shear strengthened RC beams assume the traditional approach of superimposing the contribution of the FRP reinforcing to the contributions from the reinforcing steel and the concrete. These methods become the basis for most guides for the design of externally bonded FRP systems for strengthening concrete structures. The variations among them come from the way they account for the effect of basic shear design parameters on shear capacity. This paper presents a simple method for defining improved equations to calculate the shear capacity of reinforced concrete beams externally shear strengthened with FRP. For the first time, the equations are obtained in a multiobjective optimization framework solved by using genetic algorithms, resulting from considering simultaneously the experimental results of beams with and without FRP external reinforcement. The performance of the new proposed equations is compared to the predictions with some of the current shear design guidelines for strengthening concrete structures using FRPs. The proposed procedure is also reformulated as a constrained optimization problem to provide more conservative shear predictions.