感應硬化以高頻交變磁場在鋼材表層產生渦電流與焦耳熱，經快速淬火後形成高硬度麻田散鐵層，兼顧表面耐磨性與心部韌性。加熱、停留與冷卻過程同時涉及電磁、熱傳、相變及力學行為；溫度梯度與相變體積變化可能使硬化層與心部之間的過渡區出現瞬態拉應力，進而提高淬裂傾向。本研究以 CK45 碳鋼圓棒為對象，建立電磁場、熱傳場、相變場與固體力學的連續耦合有限元素模型，使各階段的溫度、相分率、應力與塑性應變歷程得以延續。模型考慮溫度與相分率相依的材料性質、相變動力學、相變體積應變、相變誘發塑性，以及由表面溫度、水衝擊密度與高斯型空間分布決定的非線性噴霧冷卻邊界。網格收斂後，模型預測加熱結束時表面下 2 mm 處溫度為 841.3 °C，與文獻基準值 840 °C 相近；各應變分量的演變趨勢與轉折時序亦與參考研究一致。

為評估過渡區在冷卻過程中的應力—強度關係，本研究追蹤麻田散鐵初生前緣（f_M = 0.1），並以最大主應力 σ1 與瞬態混相降伏強度 σy,mix 的比值定義相對指標 R(t)。基準模型的最終殘留應力呈現「表面壓縮—次表層拉伸—心部壓縮」分布，但 R(t) 的最高值出現在冷卻中期的移動前緣，而非最終拉應力最大處。參數分析顯示，3000–7000 A 使有效硬化層由 1.87 mm 增至 6.65 mm，R_max 對電流則呈非單調變化，於 6000 A 達 1.87；加熱時間由 2 s 延長至 6 s 時，R_max 由 1.31 降至 0.74；停留時間由 0.5 s 延長至 3 s 時，R_max 由 1.09 降至 0.95。水衝擊密度 V_s,max = 5–30 kg/(m²·s) 對約 1.86 mm 的硬化層及約 700 HV 的表面硬度影響很小，但使 R_max 由 0.95 增至約 1.1。上述指標中，加熱電流與加熱時間各組採逐時間步階峰值，停留時間與冷卻強度各組採三點移動平均，以濾除前緣快速推進時之單步尖峰。整體而言，硬化深度主要受加熱電流與加熱時間影響；延長停留時間及避免超過完成硬化所需的冷卻強度，可能有助於降低本模型計算的相對指標。由於本研究未直接模擬裂紋，上述數值僅供製程條件間的相對比較，仍需實驗驗證。

A continuously coupled electromagnetic-thermal-metallurgical-mechanical finite element model of the induction hardening of CK45 carbon steel was established, covering heating, dwell, and spray quenching without resetting the process history. The model reproduces the reference temperature of about 840 °C at 2 mm depth and the reported strain evolution. A relative index R(t), defined as the ratio of the maximum principal stress to the instantaneous mixed-phase yield strength at the moving fM = 0.1 transformation front, is used to compare process conditions. Heating current and heating time mainly govern the case depth, whereas dwell time and spray intensity mainly govern the transient stress-to-strength response. The peak of R(t) occurs during cooling rather than in the final residual stress state. Verification against published temperature and strain data confirms the implementation before the parametric study. Heating current, heating time, dwell time, and spray-water flux are then varied one at a time, and an equal-case-depth comparison identifies combinations that keep the effective hardened depth while lowering the transient risk index.

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