Thermal degradation of ballistic steels under multiple impacts: a theoretical framework and the cumulative thermal degradation index (ctdi) for armox 500t

High-hardness armor (HHA) steels such as Armox 500T are qualified against singleshot threats, yet multi-hit studies show that repeated impacts within a limited footprint can degrade residual protective capacity in ways the single-shot paradigm does not capture. This paper develops a theoretical framework for the cumulative thermomechanical degradation of Armox 500T under repeated 7.62 × 51 mm NATO impacts and introduces the Cumulative Thermal Degradation Index (CTDI), a dimensionless predictor constructed from independently measurable or published inputs. The CTDI couples the Johnson–Cook constitutive response of Armox 500T (Iqbal et al., 2016; Saleh et al., 2018) with the Taylor–Quinney plastic-work-to-heat conversion framework revisited by Rittel et al. (2017) and with a one-dimensional thermal-relaxation model parameterized by published diffusivity data for martensitic steels. Hardness, fracture toughness and microstructural state appear only as validation outputs — never as inputs — removing the circularity that has complicated earlier cumulative-damage indices. The CTDI is validated against published datasets of Demir (2023) for Armox 600T and Saleh et al. (2018) for Armox 500T. Against Demir (2023) the CTDI shows Pearson r = 0.993 (p < 0.001, RMSE = 0.34 %); against Saleh et al. (2018) r = 0.997 (p = 0.003, RMSE = 0.11 %). Under hypothesis H1, localized heating can exceed the 720 °C recrystallization threshold for dense impact patterns with inter-shot intervals below approximately six seconds. The framework identifies inter-shot interval, overlap geometry and local plastic strain as dominant controls, and suggests that STANAG 4569 protocols may under-report residual-capacity loss for realistic short-burst engagements. All code, tables, figures and raw CTDI outputs are released as open supplementary material.