Abstract Fatigue damage of materials is generally evaluated by the degree of degradation of mechanical properties under fatigue loading. Existing experiments show that fatigue damage of ferromagnetic materials can also be evaluated utilizing changes in magnetization, but the quantitative relationship between magnetization changes and fatigue damage is still unclear. In this paper, a nonlinear magneto-mechanical coupling constitutive relation for ferromagnetic materials under fatigue loading is established based on the local equilibrium state of magnetization and the stress-strain response relationship in classical fatigue theory. The magnetic induction intensity of the ferromagnetic materials predicted by the present model increases with the number of cyclic loadings, and then tends to stabilize and finally increase rapidly, which is consistent with the existing experimental results. The model can also predict the evolution of complex magneto-mechanical coupling behavior under different loading times. In addition, the relationship between the evolution of spontaneous magnetic field (SMF) and fatigue damage for ferromagnetic materials is discussed in details. These results are helpful to understand the magneto-mechanical coupling behavior of ferromagnetic materials during fatigue damage process and also have important significance for the fatigue damage monitoring in practical engineering.

中文翻译：

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疲劳载荷作用下铁磁材料的磁-机耦合模型及其在金属磁记忆法中的应用

摘要 材料的疲劳损伤一般通过疲劳载荷作用下力学性能的退化程度来评价。现有实验表明，铁磁材料的疲劳损伤也可以利用磁化强度的变化来评估，但磁化强度变化与疲劳损伤之间的定量关系尚不清楚。本文基于磁化的局部平衡状态和经典疲劳理论中的应力-应变响应关系，建立了铁磁材料在疲劳载荷下的非线性磁力耦合本构关系。本模型预测的铁磁材料的磁感应强度随着循环加载次数的增加而增加，然后趋于稳定并最终迅速增加，这与现有的实验结果一致。该模型还可以预测不同加载时间下复杂磁-机械耦合行为的演变。此外，还详细讨论了自发磁场（SMF）演化与铁磁材料疲劳损伤之间的关系。这些结果有助于了解铁磁材料在疲劳损伤过程中的磁-机耦合行为，对实际工程中的疲劳损伤监测也具有重要意义。详细讨论了自发磁场（SMF）演化与铁磁材料疲劳损伤之间的关系。这些结果有助于了解铁磁材料在疲劳损伤过程中的磁-机耦合行为，对实际工程中的疲劳损伤监测也具有重要意义。详细讨论了自发磁场（SMF）演化与铁磁材料疲劳损伤之间的关系。这些结果有助于了解铁磁材料在疲劳损伤过程中的磁-机耦合行为，对实际工程中的疲劳损伤监测也具有重要意义。