Adherends mismatch

Loading can be either load (or stress) controlled, displacement (or strain) controlled, or something in between. Examples include aerodynamic loads on an aircraft (see Aerospace applications), which tend to be load controlled, and the displacement of a sealant between relatively stiff adherends, which is displacement controlled. Because average adhesive strain, in its simplest form, is defined as displacement divided by bond thickness, strains and resulting stresses are higher in thin bondlines subjected to displacement-controlled loading scenarios. Joints loaded in such a manner often perform better with thicker bondlines. Displacement-controlled situations include thermal expansion/shrinkage of adherends, mismatched adherend expansion, and attachments bonded to pressure vessels or other adherends that are stressed. 

We must also mention the danger that can exist when adhesive and adherend mismatches produce unrecognized cracking in the interfacial area due to severe weathering conditions. These cracks in themselves may be insufficient to fail the bondline but, with continued entrance of... 

Stresses due to large mismatches in the CTEs of the adherends or residual stresses due to shrinkage during cure. 

Large mismatches between the expansion coefficients of the adhesive and the two adherends have been the primary cause of numerous failmes resulting in high... 

Where the adherends have closely matched CTEs as for silicon die (CTE = approx. 3 ppm/°C) attached to Kovar leadframes (CTE = approx. 5 ppm/°C), a high-modulus adhesive could be used. As Kovar leadframes were replaced by copper leadframes (CTE = 16-17 ppm/°C), low-modulus, stress-free adhesives were required to compensate for the large mismatches in CTEs. Large CTE mismatches also occur when silicon devices are directly attached to epoxy printed-circuit boards as for COBs or CSPs. 

The properties of the composite made when two adherends are united by adhesive are a function of the bonding, the materials involved and their interaction by stress patterns. Potential problems implied by the latter stem from the inherent mismatch between adhesives and the materials commonly employed in construction (Table 4.1). For instance, concrete adherends would benefit from being united with flexible and relatively low modulus products in... 

Adhesive failure is a rupture of an adhesive bond, such that the separation is at the adhesive—adherend interface. This failure is mainly due to a material mismatch or inadequate surface treatment. Adhesive failure should be avoided. 

Typically, the adhesive and/or the matrix in FRP retrofitting applications transfers three different stress categories. These are shear, peel and thermal residual stresses. The latter occur in FRP composite joints either upon fabrication due to mismatch in the hygrothermal and elastic properties of the fibres, matrices/adhesives and adherends or due to the difference between curing and operating temperatures of the FRP material. These three stress categories can be referred to as the good, the bad and the unavoidable, respectively. 

Adherend stiffness imbalance and thermal mismatch have a substantial effect on the lap-shear stress distribntion along the joint s bondlength. 

Fig. 18. Residual peel. stresses predicted within the adhesive layer due to mismatch in curvature of the tw o adherends.

The solutions covered in this introductory chapter all fall into a class of mechanics solutions known as mechanics of materials solutions because they involve assumptions that are typical of those made in the undergraduate level mechanics of materials courses. These closed form solutions are easy to apply, and can provide fundamental insights into the stress fields present within many idealized bonded joints. The shear lag concept is of fundamental importance to any bonded configuration where load is transferred from one adherend to another, primarily through shear. stresses within the adhesive layer. The beam on elastic foundation solution provides the basis for explaining the nature of bonded beams or plates subjected to lateral loads or applied moments. The material on residual stres.ses and curvature are important in understanding the significant stresses that can result from mismatches in properties such as the coefficients of thermal expansion. 

Corson, T, Lai, Y.-L. and Dillard, D.A., Peel stress distributions between adherends with varying curvature mismatch. J. Adhes., 33, 107-122 (1990). 

Adams et al. [18] investigated the influence of temperature on the single lap joint using finite element methods and it was shown that significant stress could result from cure shrinkage and the use of mismatched adherends which can lead to large residual stress within the adhesive layer. 

Due to the mismatch of the coefficients of thermal expansion, an equal biaxial residual stress ctq was induced throughout the adhesive layer after curing of the specimens. If the adherends are assumed to be relatively thick and rigid, as compared with the adhesive, the residual stress is accurately approximated by... 

Fig. 8 is a plot of the effect of adheiend stiffness imbalance on the strength of long-overlap double-lap joints (no out-of-plane bending), assuming that no other variables influence the behavior. It is seen that the effect, which is characterized mathematically by a simple formula in refs. [9,7], is quite significant. In the absence of thermal mismatch, as between composite and metallic adherends, this equation for the relative adhesive shear strengths of long-overlap joints is simply... 

Fig. 9. Reduction in joint strength resulting from adherend thermal mismatch.

The mechanism whereby adherend thermal mismatch causes a reduction in bonded joint strength is explained in Fig. 9, for a carbon-epoxy to titanium bonded joint typically cured at 250°F or 350°F and operated at as low a temperature as -67°F. 

The formula governing this bond strength limit P, per adhesive layer, for long-overlap joints, has four possible values whenever both adherend stiffness imbalance and thermal mismatch are present, with different tensile and compressive strengths. For tensile loads. 

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