Fracture Mechanics Applied to Adhesive Joints

The application of fracture mechanics to adhesive joints was originated by Ripling, Mostovoy, and Patrick. The double cantilever beam (DCB) specimen which they used was described in Chapter 1. The derivation of the equation for Gic was also presented. 

The general fracture mechanics equation (Eq. 20) derived in Chapter 1 is used to derive Gj for the TDCB. The change in compliance with crack length, dC/dA, can be found from simple beam theory  

For detailed descriptions of these test specimens, the test methods, and sample fabrication procedures, reference should be made to ASTM D3433-75. Another test specimen designed to test structural adhesives in mode I is the cleavage specimen for metal-to-metal bonds as described in ASTM D1062-78. 

Tests also have been developed for mode II fracture, because structural adhesives encounter various loading patterns in actual design applications. 

Besides using these tests as a method for comparing various adhesives, they are also applicable for determining the dependence of adhesive properties on different variables. These variables can be test temperature, test rate, bond thickness, or environmental conditions. 

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To suggest an alternative failure criterion, based on the assumption that all materials contain inherent flaws, linear elastic fracture mechanics applied to adhesive joints was introduced. Basic fracture mechanics approaches were discussed, as well as available test techniques and the influence of various test conditions. 

The function of a structural adhesive joint is to transmit an external load to the structural member. If the joint fails to function as it is intended, it will undergo damage or failure. The damage could be actual fracture of the structure, excessive elastic deformation, or excessive inelastic flow. The criteria for what constitutes structural failure depend on the performance requirements of the joint. The fundamental problem in the mechanics of adhesives and joints is to obtain some relationship between the loads applied to the joint and a parameter that will adequately describe the criteria for strucmral failure. The most common criterion for such failure of lap-type joints is actual fracmre of the joint. For a given combination of adherend and adhesive, the stress analyst must decide what the mode or theory of failure would be if the applied loads become large enough to cause failure. The decision as to which theory would realistically determine the mode of failure is usually based on past experience, or upon some form of experimental evidence. ... 

A. J. Kinloch and S.. Shaw, A Fracture Mechanics Approach to the Failure of Structural Joints in Developments in Adhesives-2 , ed. A. J. Kinloch, Applied Science Publishers, London, 1979. 

Trantina [55] applied fracture mechanics to adhesive joints with some success and applied the failure criteria to a finite element model to find adhesive fracture energies. The influence of the glueline thickness was not accounted for. Hu [56] used a shear lag analysis and applied failure criteria in terms of Jc and it was shown that this gave good predictions of failure and was also able to account for the adhesive thickness. It was noted that this is consequently a good method of predicting failure for adhesive materials loaded in shear. 

Another fundamental mechanics solution that has many applications in bonded joints is that of a beam on an elastic foundation. Emil Winkler first reported this analysis in 1867 [49]. The method has been widely applied to a variety of problems, perhaps most obviously that of trains passing over rails supported by the earth, and has been included in most texts on advanced mechanics of materials [16]. Since many bonded Joints have beam-like adherends supported by a more flexible adhesive layer, this model of a beam on an elastic foundation is also of great importance for a variety of joints ranging from the lap shear specimen to fracture specimens, from peel specimens to the loop tack test. 

Another basic major advantage is that the cyclic-fatigue fracture-mechanics data may be gathered in a relatively short time-period, but may be applied to other designs of bonded joints and components, whose lifetime may then be predicted over a far longer time-span. Obviously, the fracture-mechanics tests need to be conducted under similar test conditions and environments as the joints, or components, whose service-life is to be predicted. This is important since the fracture-mechanics test specimens do need to exhibit a similar mechanism and locus of failure (e.g. cohesively through the adhesive layer, or interfacially between the adhesive and substrate, or through the oxide layer on the metallic substrate, etc.) as observed in the joints, or components, whose lifetime is to be ranked and predicted. 

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