功能梯度材料（Functionally Graded Materials, FGMs）因具備連續材料性質分布，可有效降低異質材料界面熱應力，廣泛應用於高溫結構。然而，現有FGM圓柱熱應力研究多以邊界熱源為主，本研究建立Al2O3-Ni功能梯度中空圓柱於感應加熱下之磁熱耦合模型，考慮陶瓷-金屬材料之導電率模型，建立符合導電相連通行為之空間導電率分布；同時參考文獻所採用之非均勻孔隙率分布，將孔隙率影響納入熱傳導率、楊氏模數與導電率模型中，以探討孔隙對感應熱源、溫度場與熱應力之影響。同時，比較不同梯度指數與內外側材料配置下之溫度場與熱應力安全比，以評估各案例隨加熱時間之安全程度。
結果顯示，感應加熱與邊界熱源所形成的溫度梯度與熱應力分布仍會因熱源空間分布不同而明顯不同，顯示感應加熱有必要作為獨立之熱源形式探討。不同內外側材料配置與梯度指數會改變金屬相及導電區域的分布，進而影響感應熱源、溫度場與熱應力。孔隙會降低材料之熱傳能力與剛性，使整體溫度升高，局部應力會重新分配，且以環向應力變化最為明顯;所造成之升溫與變形不均亦會縮短安全加熱時間。因此，功能梯度材料在感應加熱下的溫度與熱應力行為，需同時考慮材料梯度、配置方式及孔隙對材料性質的影響。

Functionally graded materials (FGMs) provide continuous spatial variations in material properties and can reduce interfacial thermal stresses in heterogeneous high-temperature structures. This study investigates an Al2O3-Ni radially functionally graded hollow cylinder under induction heating using a coupled electromagnetic and thermal finite element model. Material composition is described by a power-law distribution, with effective electrical conductivity and porosity-dependent properties included. The effects of material arrangement, gradient index, and porosity on heat generation, temperature, and thermal stress are examined.
The results show that induction and boundary heating produce different temperature and thermal-stress distributions. Material arrangement and gradient index alter the metallic-phase distribution and thus control the location of heat generation and the resulting thermomechanical response. Extreme gradient indices concentrate the material transition near one surface, reducing the ability of the FGM to distribute thermal-expansion mismatch. Porosity increases the temperature and shortens the allowable heating duration, although its influence on the overall stress distribution is limited. These results highlight the combined importance of material distribution, porosity, and mechanical constraints in the design of FGMs under induction heating.

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