Crystal Elasticity

10Vibration Measurements and Macroscopic Internal Stresses

Let us start this chapter by an unexpected question: How is a guitar or a piano tuned? The answer is very simple: by applying a static force on the strings using a mobile mechanism for their rollup at one of their edges. If this problem is addressed in the context of a beam bending vibration test the question is: What is the resonance frequency if there is a macroscopic longitudinal stress in the material? The answer is that it must vary, irrespective of whether there is an applied or internal stress.

Reversing the question, is it possible, based on the resonance frequencies of the same material in a static stressed state and in an unstressed state, to quantitatively go back to the initial stress level? This chapter focuses on the development of a Lagrangian approach that can be used to propose an alternative to the determination of the level of internal or residual stresses at macroscopic scale. It can be used in addition to local methods such as X-ray diffraction analysis and to macroscopic approaches such as the beam deflection method.

10.1. Experimental evidence of the relaxation of the internal stresses of bulk materials

Before any calculation, it is important to illustrate the experimental evidence of the release of internal stresses in the case of two materials that had initially residual stresses due to their elaboration mode.

The first example concerns a MAX phase, which is an alloy sintered under a high isostatic ...