Influence of the cohesive law parameters on the strength prediction of adhesively-bonded joints

Adhesive joints are largely employed nowadays as a fast and effective joining process. The respective techniques for strength prediction have also improved over the years. Cohesive Zone Models (CZM’s) coupled to Finite Element Method (FEM) analyses surpass the limitations of stress and fracture criteria and allow modelling damage. CZM’s require the energy release rates in tension (Gn) and shear (Gs) and respective fracture energies in tension (Gnc) and shear (Gsc). Additionally, the cohesive strengths (tn0 for tension and ts0 for shear) must also be defined. In this work, the influence of the CZM parameters of a triangular CZM used to model a thin adhesive layer is studied, to estimate their effect on the predictions. Some conclusions were drawn for the accuracy of the simulation results by variations of each one of these parameters.

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM). A finite element model considering solid elements of the ABAQUS® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.

Strength prediction of adhesively-bonded scarf repairs in composite structures under bending

This work reports on the experimental and numerical study of the bending behaviour of two-dimensional adhesively-bonded scarf repairs of carbon-epoxy laminates, bonded with the ductile adhesive Araldite 2015®. Scarf angles varying from 2 to 45º were tested. The experimental work performed was used to validate a numerical Finite Element analysis using ABAQUS® and a methodology developed by the authors to predict the strength of bonded assemblies. This methodology consists on replacing the adhesive layer by cohesive elements, including mixed-mode criteria to deal with the mixed-mode behaviour usually observed in structures. Trapezoidal laws in pure modes I and II were used to account for the ductility of the adhesive used. The cohesive laws in pure modes I and II were determined with Double Cantilever Beam and End-Notched Flexure tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures of the carbon-epoxy components also occurred in some regions, cohesive laws to simulate these failure modes were also obtained experimentally with a similar procedure. A good correlation with the experiments was found on the elastic stiffness, maximum load and failure mode of the repairs, showing that this methodology simulates accurately the mechanical behaviour of bonded assemblies.

Strength prediction and experimental validation of adhesive joints including polyethylene, carbon-epoxy and aluminium adherends

Polyolefins are especially difficult to bond due to their non-polar, non-porous and chemically inert surfaces. Acrylic adhesives used in industry are particularly suited to bond these materials, including many grades of polypropylene (PP) and polyethylene (PE), without special surface preparation. In this work, the tensile strength of single-lap PE and mixed joints bonded with an acrylic adhesive was investigated. The mixed joints included PE with aluminium (AL) or carbon fibre reinforced plastic (CFRP) substrates. The PE substrates were only cleaned with isopropanol, which assured cohesive failures. For the PE CFRP joints, three different surfaces preparations were employed for the CFRP substrates: cleaning with acetone, abrasion with 100 grit sand paper and peel-ply finishing. In the PE AL joints, the AL bonding surfaces were prepared by the following methods: cleaning with acetone, abrasion with 180 and 320 grit sand papers, grit blasting and chemical etching with chromic acid. After abrasion of the CFRP and AL substrates, the surfaces were always cleaned with acetone. The tensile strengths were compared with numerical results from ABAQUS® and a mixed mode (I+II) cohesive damage model. A good agreement was found between the experimental and numerical results, except for the PE AL joints, since the AL surface treatments were not found to be effective.

Information technology service management: an experimental approach towards IT service prediction

Dissertation presented to obtain a Masters degree in Computer Science

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single- and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.

Fractional discrete-time signal processing: scale conversion and linear prediction

Nonlinear Dynamics, Vol. 29

New results on fractional linear prediction

Proceedings of the European Control Conference, ECC’01, Porto, Portugal, September 2001

Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Limit Cycle Prediction of Systems with Fractional Controllers and Backlash

This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.