A Residual-Stress Screening Envelope from the Almen Record: A Moment-Equivalent Eigenstrain Interpretation and Its Limits

A designer who takes credit for shot peening needs a residual stress, not only a depth. This paper builds a candidate screening envelope for the as-peened stress profile from the qualified process-and-witness record (Almen intensity, shot size and media, and process conditions) and the tensile strength, and tests what published data can and cannot support. The strip is read through a moment-equivalent eigenstrain whose bending moment gives the arc height; its magnitude is 1.6–2.6 times a synchrotron measurement, so no physical eigenstrain transfer is claimed. With each laboratory withheld, the peak is predicted to 13.5% (7.6% with one profile of the material) but the complete profile only to 23.5% of peak, and the predicted shape is no better than a median shape. The principal result is therefore the screening construction; the eigenstrain profile model is a conditional interpretation and a hypothesis for experiment. The screening envelope multiplies a cavity-law depth factor, a peak factor and a lower shape envelope. In laboratory-withheld tests it was the only fixed-factor rule tried that stayed conservative; at matched conservatism, a strength-aware depth is essential, and the cavity law and an empirical four-constant power law perform equally. Within normal SAE practice it was empirically conservative on all 36 profiles tested from 12 laboratories (22 development, 13 locked in advance, one unblinded), but with measurement uncertainty it was non-conservative for a soft carbon steel and a stretched aluminium alloy, so its evidence domain is high-strength steels and IN718. It covers about a quarter of the measured compressive area and, used as a mean stress in illustrative fatigue checks, about a third of the amplitude benefit of a measured profile. Twelve measurement-chain conditions show that unstated layer-removal corrections, not reading precision, limit what published profiles support. A frozen-rule prospective test is specified. The P0 construction is a candidate screening envelope that was empirically conservative on the stated test profiles; it is not a statistical lower bound, design allowable or authority-approved structural credit.