Delamination failure of multilaminated adhesively bonded joints at low temperatures

A series of experimental investigations of multilaminated joints adhesively bonded by epoxy/polyurethane (PU) glue were conducted in order to examine the delamination failure characteristics under in-plane shear loading at low temperatures. In order to observe these phenomena, a series of lap-shear tests were carried out at various low temperatures (20 °C, −110 °C and −163 °C) and various adhesion areas (15 mm × 50 mm, 30 mm × 50 mm, 50 mm × 50 mm, 75 mm × 50 mm and 100 mm × 50 mm). The test results were used to investigate the delamination and material characteristics, as well as the material properties, e.g., ultimate shear stress and shear elongation. Furthermore, the dependencies of the characteristics of multilaminated adhesively bonded joints (MABJs) on temperature and adhesion area was analyzed using the stress–strain relationship, and closed form formulas that are functions of the dependent parameters are proposed.     

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.     

Uniqueness,loss of ellipticity and localization for the time‐discretized,rate‐dependent boundary value problem with softening

The discretization in time of the initial boundary value problem for rate‐dependent (elastic‐viscoplastic) solid materials in presence of softening is investigated in this paper. The emphasis is put on uniqueness, loss of ellipticity and localization. It is found that the time‐discretized problem resembles the incremental problem for rate‐independent materials and softening may lead to ill‐posedness (loss of ellipticity) if the time step is greater than a critical value. It is well established that the implication of loss of ellipticity for the numerical simulations after spatial discretization is the pathological mesh dependency of the computed results. We furnish a method to compute the critical time step and demonstrate its use for a simple example problem. Copyright © 2010 John Wiley & Sons, Ltd.     

Fracture analysis of composite co‐cured structural joints using decohesion elements

Delamination is one of the predominant forms of failure in laminated composite structures, especially when there is no reinforcement in the thickness direction. To develop composite structures that are more damage tolerant, it is necessary to understand how delamination develops, and how it can affect the residual performance. A number of factors such as residual thermal stresses, matrix‐curing shrinkage and manufacturing defects affect how damage will grow in a composite structure. It is important to develop computationally efficient analysis methods that can account for all such factors. The objective of the current work is to apply a newly developed decohesion element to investigate the debond strength of skin‐stiffener composite specimens. The process of initiation of delaminations and the propagation of delamination fronts is investigated. The numerical predictions are compared with published experimental results.     

Time‐dependent multiaxial fatigue and life prediction for nickel‐based GH4169 alloy

The fatigue behaviour of nickel‐based GH4169 alloy was studied under multiaxial loading at 650 °C. During the middle and late stages of the fatigue life at 650 °C, the axial and shear maximum stresses continue to decrease and plastic strains continue to increase, while at 360 °C different phenomena are observed. The intergranular cracks and certain quantities oxygen were observed in the fracture surfaces. The damage of creep and oxidation are related to temperature and strain range. The life prediction results with a time‐dependent fatigue damage model show the time‐related factors have a certain influence on the fatigue damage.     

Influence of the interface ply orientation on the fatigue behaviour of bonded joints in composite materials

The paper deals with the study of the fatigue behaviour of bonded joints in composite materials. The influence of the orientation of the composite layer at the adhesive–adherend interface is investigated on single lap joints prepared by carbon fabric/epoxy laminates bonded together with a two-part epoxy adhesive. Different laminate lay-ups ([45/0₂]_s and [45₂/0]_s), overlap lengths (20 and 40 mm) and corner geometry of bonded area (square edge and fillet, respectively) were investigated under tension–tension fatigue. Particular attention was devoted to the analysis of the fatigue damage evolution to identify initiation and subsequent growth of cracks. A previous model developed by the authors, for the prediction of the fatigue life of bonded joints as the sum of an initiation and propagation phase, was successfully applied to summarise the new data.     

Analysis of adhesive bonded composite lap joints with transverse stitching

The effect of transverse stitching on the stresses in the adhesive is investigated using an adhesive sandwich model with nonlinear adhesive properties and a transverse stitching model for adhesive bonded composite single-lap and double-lap joints. Numerical results indicate that, among all stitching parameters, thread pretension and stitch density have significant effect on the peel stresses in the adhesive; increase in the thread pretension and the stitch density leads to a decrease in peel stress in the adhesive, while an increase in other parameters generally results in a negligible reduction in peel stress. The effect of stitching was found to be negligible on the shear stresses in the adhesive. Thus it is concluded that stitching is effective for the joints where peel stresses are critical and ineffective for those where shear stresses are critical.     

Application of two‐state M‐integral for analysis of adhesive lap joints

With the aid of the two‐state M‐integral and finite element analysis, the asymptotic solution in terms of the complete eigenfunction expansion is obtained for adhesive lap joints. The notch stress intensity is introduced to characterize the singular stress field near the notch vertex of adhesive lap joints. The proposed scheme enables us to extract the intensity of each eigenfunction term from the far field data without resort to special singular elements at the vertex. It turns out that a weak stress singularity is not negligible around the vertex when it exists in addition to the major singularity. For a thin adhesive layer, there exist two asymptotic solutions: one is the inner solution approaching the eigenfunction solution for the vertex at which the adherend meets with the adhesive and the other is intermediate solution represented by the eigenfunction series that would be obtained in the absence of the adhesive layer. An appropriate guideline for choosing the geometric parameters in designing the adhesive lap joints, particularly the overlap length or the size of the adhesive zone, is suggested from the viewpoint of minimizing the notch stress intensity. Copyright © 2001 John Wiley & Sons, Ltd.     

On the implicit integration of rate‐dependent inelastic constitutive models

Although there are many different algorithms for the integration of inelastic constitutive models, the fully implicit backward Euler method has become the most popular one. In this study further investigations on the accuracy of the backward Euler method have been carried out. Also the performance of the discontinuous Galerkin family and some implicit Runge–Kutta time integrators is evaluated. By using a simple scalar model problem accuracy of some integrators is studied when a single finite time step is applied. Conclusions drawn from this scalar model problem has been verified to apply also to a full six‐dimensional strain space formulation by numerical means. Special emphasis is placed on rate‐dependent inelastic creep models. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of interface finite elements to three-dimensional progressive failure analysis of adhesive joints

ABSTRACT The paper presents a new model for three‐dimensional progressive failure analysis of adhesive joints. The method uses interface elements and includes a damage model to simulate progressive debonding. The interface finite elements are placed between the adherents and the adhesive. The damage model is based on the indirect use of fracture mechanics and allows the simulation of the initiation and growth of damage at the interfaces without considering the presence of initial flaws. The application of the model to single lap joints is presented. Experimental tests were performed in aluminium/epoxy adhesive joints. Linear elastic and elastoplastic analyses were performed and the predicted failure load for the elastoplastic case agrees with experimental results.     

Numerical evaluation for debonding failure phenomenon of adhesively bonded joints at cryogenic temperatures

In the present study, material characteristics, such as inelastic constitutive behaviour and debonding failure, of an adhesively bonded joint (ABJ) at cryogenic temperature have been evaluated using a computational approach. The modified Bodner-Partom model (BP model) has been introduced to describe the material nonlinearities of ABJ. The Gurson-Tvergaard model (GT model) has also been implemented into the constitutive model in order to analyse the phenomenon of debonding failure. An ABAQUS user-defined subroutine UMAT is developed using a damage-coupled constitutive model based on an implicit formulation. The numerical results are compared with a series of lap shear tests of ABJ at cryogenic temperature in order to verify the proposed method.     

Topology optimization by a time‐dependent diffusion equation

Most topology optimization problems are formulated as constrained optimization problems; thus, mathematical programming has been the mainstream. On the other hand, solving topology optimization problems using time evolution equations, seen in the level set‐based and the phase field‐based methods, is yet another approach. One issue is the treatment of multiple constraints, which is difficult to incorporate within time evolution equations. Another issue is the extra re‐initialization steps that interrupt the time integration from time to time. This paper proposes a way to describe, using a Heaviside projection‐based representation, a time‐dependent diffusion equation that addresses these two issues. The constraints are treated using a modified augmented Lagrangian approach in which the Lagrange multipliers are updated by simple ordinary differential equations. The proposed method is easy to implement using a high‐level finite element code. Also, it is very practical in the sense that one can fully utilize the existing framework of the code: GUI, parallelized solvers, animations, data imports/exports, and so on. The effectiveness of the proposed method is demonstrated through numerical examples in both the planar and spatial cases. Copyright © 2012 John Wiley & Sons, Ltd.     

Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods

Failure process, mode and strength of unidirectional composite single lap bonded joints were investigated experimentally with respect to bonding methods, that is, co-curing with or without adhesive and secondary bonding. The co-cured joint specimen without adhesive had the highest failure strength. Progressive failures along an adhesive layer occurred in the secondary bonded specimen. In the co-cured specimen with adhesive film, delamination failure occurred and the joint strength was lower than that of secondary bonded specimens. Delamination failure did not occur in the secondary bonded specimen because of early crack growth and progressive failure in the adhesive layer. Therefore, The failure strength of composite bonded joint is not always proportionate to adhesion strength of adhesive due to the weakness of delamination in composite materials. The influences of surface roughness, bondline thickness and fillets in the secondary bonded specimens were also studied.     

Crack growth analysis at adhesive–adherent interface in bonded joints under mixed mode I/II

The propagation of an interface crack subjected to mixed mode I/II was investigated for two 2024-T351 aluminum thin layers joined by means of DP760 epoxy adhesive produced by 3M^©. On the basis of beam theory, an analytical expression for computing the energy release rate is presented for the mixed-mode end loaded split (MMELS) test. The analytical strain energy release rate was compared by finite element (FE) analysis using the virtual crack closure technique (VCCT). Several fatigue crack growth tests were carried out in a plane bending machine to compare the experimental energy release rates to those of the analytical and FE solutions. Experimental results showed the relationship between the delamination modality and initial crack length rather than the applied load. The crack growth behavior showed stable crack growth followed by rapid propagation at the interface with the adhesive layer.     

Kinematical shakedown analysis with temperature‐dependent yield stress

This paper describes a direct shakedown analysis of structures subjected to variable thermal and mechanical loading. The classical kinematical shakedown theorem is modified to be implemented with any displacement‐based finite elements. The plastic incompressibility condition is imposed by the penalty function method. The shakedown limit is found via a non‐linear mathematical programming procedure. Two numerical shakedown methods are developed and implemented to provide alternative numerical means. The temperature‐dependent material model is included in theoretical and numerical calculation in a simple way. Its effect on shakedown limit is investigated. The numerical examination for some pressure vessel structures subjected to thermal and mechanical loading shows a satisfying precision and efficiency of the methods presented. Copyright © 2001 John Wiley & Sons, Ltd.     

Time‐domain soil–structure interaction analysis in two‐dimensional medium based on analytical frequency‐dependent infinite elements

A direct method for soil–structure interaction analysis in two‐dimensional medium is presented in time domain, which is based on the transformation of the analytical frequency‐dependent dynamic stiffness matrix. The present dynamic stiffness matrix for the far‐field region is constructed by assembling stiffness matrices of the analytical frequency‐dependent dynamic infinite elements, so that the equation of motion can be analytically transformed into the time‐domain equation. An efficient procedure is devised to evaluate the dynamic responses in time domain. Verification of the present formulation is carried out by comparing the compliances for a strip foundation on a homogeneous and layered half‐spaces with those obtained by other methods. Numerical analyses are also carried out for the transient responses of an elastic block and tunnel in a homogeneous and a layered half‐space. The comparisons with those by other approaches indicate that the proposed time‐domain method for soil–structure interaction analysis gives good solutions. Copyright © 2000 John Wiley & Sons, Ltd.     

A semi‐implicit integration scheme for a combined viscoelastic‐damage model of plastic bonded explosives

This paper presents a new implementation of a constitutive model commonly used to represent plastic bonded explosives in finite element simulations of thermomechanical response. The constitutive model, viscoSCRAM, combines linear viscoelasticity with isotropic damage evolution. The original implementation was focused on short duration transient events; thus, an explicit update scheme was used. For longer duration simulations that employ significantly larger time step sizes, the explicit update scheme is inadequate. This work presents a new semi‐implicit update scheme suitable for simulations using relatively large time steps. The algorithm solves a nonlinear system of equations to ensure that the stress, damaged state, and internal stresses are in agreement with implicit update equations at the end of each increment. The crack growth is advanced in time using a sub‐incremental explicit scheme; thus, the entire implementation is semi‐implicit. The theory is briefly discussed along with previous explicit integration schemes. The new integration algorithm and its implementation into the finite element code, Abaqus, are detailed. Finally, the new and old algorithms are compared via simulations of uniaxial compression and beam bending. The semi‐implicit scheme has been demonstrated to provide higher accuracy for a given allocated computational time for the quasistatic cases considered here. Published 2014. This article is a US Government work and is in the public domain in the USA.     

Rate‐dependent projection operators for frictional contact constraints

We develop rate‐dependent regularization approaches for three‐dimensional frictional contact constraints based on the Kelvin and Maxwell viscoelastic constitutive models. With the present regularization schemes, we aim to provide a basis to better model friction and to stabilize the contact analysis while keeping the contact model as simple as possible. The key feature of the regularization approaches, implemented using an implicit time integrator, is that one can recover in the limit the widely used rate‐independent elastoplastic regularization framework without encountering numerical difficulties. Intermediate contact tractions are defined in terms of the relative displacement, the relative velocity, and the regularization parameters. The projection operators operate on the intermediate tractions and yield contact tractions that satisfy all the discretized contact constraints. The use of projection operators allows a systematic implementation of the present regularization schemes. Through numerical simulations, we observed that the Maxwell‐type regularization effectively avoids convergence problems, even for relatively large time step sizes, while the Kelvin‐type regularization does not. Copyright © 2003 John Wiley & Sons, Ltd.     

A partition of unity FEM for time‐dependent diffusion problems using multiple enrichment functions

An enriched partition of unity FEM is developed to solve time‐dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximation space. The resulting enrichment is in the form of a local asymptotic expansion. Unlike previous works in this area where the enrichment must be updated at each time step, here, the temporal decay in the solution is embedded in the asymptotic expansion. Thus, the system matrix that is evaluated at the first time step may be decomposed and retained for every next time step by just updating the right‐hand side of the linear system of equations. The advantage is a significant saving in the computational effort where, previously, the linear system must be reevaluated and resolved at every time step. In comparison with the traditional finite element analysis with p‐version refinements, the present approach is much simpler, more efficient, and yields more accurate solutions for a prescribed number of DoFs. Numerical results are presented for a transient diffusion equation with known analytical solution. The performance of the method is analyzed on two applications: the transient heat equation with a single source and the transient heat equation with multiple sources. The aim of such a method compared with the classical FEM is to solve time‐dependent diffusion applications efficiently and with an appropriate level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd.