Continuum adhesive joints

Adhesive joints usually fail by the initiation and propagation of flaws and, since the basic tenet of continuum fracture mechanics is that the strength of most real solids is governed by the presence of flaws, the application of such theories to adhesive joint failure has received considerable attention. The reader is referred to reviews for detailed discussions of the general principles of fracture mechanics and to on the application of fracture mechanics to the failure of adhesive joints ". ... 

This chapter will discuss the testing, analysis, and design of structural adhesive joints. Adhesive bond test techniques to be considered include tensile, shear, peel, impact, creep, and fatigue. Some considerations will also be given to the effect of environment and test rate. A continuum approach to the analysis of adhesive joints will discuss tensile, shear, and peel stresses which arise in various joint geometries. Classical theories by Volkersen, Goland and Reissner, and others will be included. References to finite element analysis will be made where appropriate throughout the chapter. 

A review of the literature reveals that previous finite-element analyses of adhesive joints were either based on simplified theoretical models or the analyses themselves did not exploit the full potential of the finite-element method. Also, several investigations involving finite-element analyses of the same adhesive joint have reported apparent contradictory conclusions about the variations of stresses in the joint.(24,36) while the computer program VISTA looks promising (see Table 1), its nonlinear viscoelastic capability is limited to Knauss and Emri.(28) Recently, Reddy and Roy(E2) (see also References 37 and 38) developed a computer program, called NOVA, based on the updated Lagrangian formulation of the kinematics of deformation of a two-dimensional continuum and Schapery s(26) nonlinear viscoelastic model. The free-volume model of Knauss and Emri(28) can be obtained as a degenerate model from Schapery s model. 

Ediund [61] has applied continuum damage mechanics to adhesive joints, but... 

When a complex joint is to be introduced in a structure, the ideal situation is to test that specific joint. However, this approach is very expensive. Before real joints or prototypes are built, the designer should first come up with a good prediction of the failure load based, among other things, on the basic mechanical properties of the adhesive. The basic properties can mean the elastic properties, such as the Young s modulus and the Poisson s ratio in case the analysis is linear elastic. However, for the more realistic theoretical methods that take into account the nonlinear behavior of the adhesive, the yield stress, the ultimate stress, and the failure strain are necessary. The stress-strain curve of adhesives is necessary for designing adhesive joints in order to compute the stress distribution and apply a suitable failure criterion based on continuum mechanics principles. 

The adhesive shear and peel stresses peak at adhesive edges and the peak stresses increase to infinity with the adhesive thickness decreasing to zero. Therefore, the failure of the adhesive joint will be initiated from the adhesive edge generally. There are two types of failure criteria to assess adhesive joint strength, based on continuum mechanics and fracture mechanics, respectively. 

When the maximum stresses are determined and the allowable stresses are calibrated, failure criteria based on continuum mechanics can be used to predict adhesive joint failure. When the failure criteria in Eqs. 24.56a-c are used to predict joint failure, it is found (Adams 1989 Gleich et al. 2001 da Silva et al. 2006) that the failure trend for different adhesive thickness predicted by the adhesive-beam models proposed by Goland and Reissner (1944) is different from that of the experimental results. In theory, the maximum stresses increase with decreasing adhesive thickness. However, failure load decreases with increasing the adhesive thickness when it is relatively thick, such as fa > 0.1 mm. 

The fracture-based approach derives from continuum fracture mechanics theory, which claims the strength of most real solids is governed by flaws within the material [2]. To help predict this type of behavior, many test methods have been developed to determine fracture properties of adhesives. These tests are used to characterize the mode I, II, and III fracture properties of many types of material systems. In this study, the focus will be on the mode I and II characteristics of bonded joints for automotive applications. 

Now, by adopting a continuum fracture mechanics approach, the work of Andrews and Kinloch [14,15,113] and Gent and Kinloch [27] defined a geometry-independent measure of joint strength, the adhesive fracture energy. 

Thus it is possible, by using closed-form analyses of varying complexity, to predict the stresses in simple lap joints. (This approach is termed continuum mechanics.) In many instances, such solutions may be deemed acceptable. However, two problems still remain to be solved if it is required to predict the strength of real joints. These may be summarized as end effects and material non-linearity (adhesive and adherend plasticity). We will look first at end effects for linear elastic systems. 

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