Joint design stress analysis

Procedures for the determination of important properties are essential for the selection of an appropriate product and for joint design and analysis. We have seen that adhesive polymers are sensitive to temperature and moisture, and to the rate at which stress is applied. Their bondline behaviour in joints depends greatly upon the system stiffness, and upon more subtle variations such as bondline thickness. It is therefore important that test methods are relevant to the real application, the fabrication conditions, the actual materials to be joined, and so on. Many standard test methods exist, for both strength and durability assessment, and these were discussed in Chapter 4. 

The thin-wall bellows element should be designed for membrane stresses to conform to code-allowable stresses. The sum of membrane and secondary bending stresses should not exceed 1.5 times the yield stress in order to prevent the collapse of the corrugations caused by pressure. Bellows subjected to external pressure can be analyzed in a manner similar to a cylinder, utilizing an equivalent moment of inertia. The fatigue life can be estimated based on the sum of deflections and pressure stresses as compared to S/N curves based on bellows test data or using the curves in B31.3 Appendix X, Metal Bellows Expansion Joints. Formulas for the stress analysis of bellows are available in the Expansion Joints Manufacturing Association (EJMA) Standards (37). 

Analysis of a bolted repair follows the analysis of a bolted joint. The behaviour of composites in bolted joints differs considerably from what occurs with metals. The brittle nature of composites necessitates more detailed analysis to quantify the level of various stress peaks as stress concentrations. Composite joint design is more sensitive to edge distances and hole spacing than metal joint designs and requires specialised fasteners. Interference fit fasteners or rivets must not be used but expanding sleeves can be installed as required. 

The rigorous procedure utilises analytical models to determine the stress state in the adhesive. In the immediate vicinity of the through-thickness stress peak in the adhesive, the adherends are expected to experience the same stress. In the analysis the joint design is satisfied when the following conditions are met ... 

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The finite element analysis technique has been used very successfully to confirm the regions of concentrated stress and strain. In this technique, the bonded assembly is subdivided into small elements and the forces relevant to each element are computed using basic mathematical equations. This is very useful, particularly in the understanding of complex joint designs. 

There is the static analysis method that determines reaction forces at the attachment positions of resting mechanisms when a constant load is applied. As long as zero velocity is assumed, static analysis can be performed on mechanisms at different points of their range of motion. Static analysis allows the designer to determine the reaction forces on whole mechanical systems as well as interconnection forces transmitted to their individual joints. The data extracted from static analysis can be useful in determining compatibility with the various criteria set out in the problem definition. These criteria may include reliability, fatigue, and performance considerations to be analyzed through stress analysis methods. 

Krieger R.B., Jr., Stress analysis concepts for adhesive bonding of aircraft primary structure. In Johnson, W.S. EA.),Adhesively Bonded Joints Testing. Analysis and Design, ASTM STP 981. American Society for Testing and Materials, Philadelphia, PA, 1988, pp. 264-275. 

Butt joints for testing adhesives in tension are also usually designed with a circular cross-section to facilitate manufacture and to maintain symmetry. In this case, it would appear to make little difference whether they are annular (Fig. 63(a)) or solid (Fig. 63(b)). In a butt joint subjected to a tensile load, the adhesive is restrained in the radial and circumferential directions by the adherends. In the absence of this restraint, the adhesive would tend to contract radially with respect to the adherends because of its much lower modulus. The presence of the adherends has the effect of inducing radial and circumferential stresses in the adhesive, so increasing the stiffness of the joint. The simplest analysis makes the assumption that the radial and circumferential strains in the adherend and the adhesive are zero, in which case the radial and circumferential stresses are given by ... 

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