TATB is an insensitive high explosive, attractive for use because of its safety aspects. TATB compactions, with or without binder, undergo irreversible volume expansion (or ratchet growth) upon thermal cycling. In the past, experimental elucidation of this phenomenon has focused on irreversible expansion as a function of the number of thermal excursions over a given temperature range, where growth is asymptotic with increasing cycle number. In this paper, we demonstrate that ratchet growth also occurs as a function of time at constant temperature, and that growth is substantial at elevated temperatures. We have measured strain response in PBX 9502, a TATB-based composite, by performing thermal-cycling tests with different durations at high temperature. Irreversible growth arises from the thermal ramps themselves (increasing and decreasing), as well as from the subsequent isotherms. PBX 9502 specimens with previously-identified TATB texture/orientation were used in order to eliminate and/or evaluate texture as a variable. Measurements were also performed on dry-pressed TATB (no binder) to confirm that expansion as a function of time (constant temperature) is not caused by the binder. A simple analysis of the time-response data demonstrates consistency in the results. We propose that the primary driving force for irreversible expansion is the proximity of the current strain value (due to thermal history) to the strain saturation point of the current cycle (i.e. strain at infinite high-temperature hold times or an infinite number of cycles). Such tests should aid in the understanding and modeling of ratchet growth response in these materials.