Originally Posted by
JAlberts
Since you have already stressed the tube(s) at those points beyond their yield stress by clamping then you must assume that their residual stress at those points remains at the material's min yield level even without any additional loadings. Ironically, the vibrations probably initially do some degree of stress relief to an indeterminate static stress below that yield stress point; but, without knowing that residual stress value it is impossible to calculate a potential fatigue life of the tube(s).
At the same time, I agree with the prior post that if the customer is having cracking and failure at those points' then it doesn't matter what your calculation result is, the clamp designs are insufficient for their intended service. Working in new product development for industrial valves for 20+ years has taught me one thing above all else: "Regardless of the amount of inhouse product testing or its results, the final true test of a product will be performed in service by the customers."
Anyone that is demanding any "proof" calculation(s) is both wasting your time, delaying an obviously required clamp redesign and insuring there will be more unnecessary customer problems.
Adding more clamps on a closer spacing may help the issue; but, in the long run using clamps with the appropriate internal elastomeric cushioning will be a better and more all around economic solution.