AE Felicity ratio

Most materials remember the highest load they have ever seen. Re-load them and they stay acoustically quiet until that previous maximum is approached — the Kaiser effect. The Felicity ratio quantifies the breakdown of that memory: it is the load at which significant emission resumes divided by the previous maximum load, FR = P_onset / P_previous. A ratio of 1.0 or more means the Kaiser effect held and the structure is behaving elastically. A ratio well below 1.0 means emission started early, which is the acoustic signature of damage that is still growing — matrix cracking, fibre breakage, delamination, or in metals crack extension and fretting at previously loaded sites.

The measurement is only as good as the definition of "significant emission". Codes define it explicitly, usually as a stated hit rate, count rate or amplitude crossing sustained over a defined load increment, and the same definition must be used on every vessel in a programme or the ratios cannot be compared. The onset load is read off the load-versus-cumulative-emission plot, not judged by ear.

Felicity ratio is the primary acceptance parameter for fibre-reinforced plastic vessels and tanks, where a value below about 0.95 is rejectable, and it is used alongside emission during hold, total counts and amplitude distribution rather than on its own. Applied to metallic equipment it is a supporting indicator, not a standalone accept/reject criterion. Always read the ratio together with the emission-during-hold result: continuing emission at constant load is a more damning indication than the ratio itself.

FR = P_onset / P_previous_max
Minimum acceptable onset load = FR_min × P_previous_max