## 1 Introduction  
Fe-36 Ni invar alloy, a prototypical low-expansion alloy, was discovered by physicist [PERSON] in 1986 while searching for suitable materials for the production of geodetic [1]. The invar alloy exhibits an exceptionally low coefficient of thermal expansion below the Curie temperature, with a value at room temperature that is just one-tenth that of conventional alloys. Invar alloy is used in many applications because it has very low thermal expansion and good mechanical properties. It is commonly found in pendulum clocks, precise electric devices, cryogenic storage containers, aerospace, oil and gas transportation, and high-voltage transmission, among others [2, 3, 4, 5, 6, 7]. Nonetheless, conventional manufacturing techniques for component fabrication, including processes like casting and machining, are subject to specific constraints. These processes are characterized by extended production cycles, significant tool wear, and challenges in manufacturing components with intricate structures [8; 9]. Accordingly, it is of paramount importance to identify a process that can enhance production efficiency and fabricate intricate structural components [10; 11]. Wire arc additive manufacturing technology has been widely used by the manufacturing industry because of its high efficiency and high process adaptability; it has been widely used in the manufacturing of steel products [12]. The invar alloy is an extensively malleable metal with a face-centered cubic lattice structure, renowned for commendable weldability and compatibility with the WAAM process [13; 14]. However, on account of the substantial heat input coupled with the intricate thermal cycling process inherent in the additive molding technique, several issues are manifested in the microstructure of invar alloy post-additive molding [15]. These issues include the presence of pores, discrepancies in microstructural homogeneity, and grain growth, all of which stand to compromise the mechanical properties of the invar 36 specimens produced through additive manufacturing [16]. Recently, [PERSON] et al. [17] found that during the additive manufacturing process, judiciously diminishing the heat input can simultaneously mitigate the occurrence of thermal cracks and increase the grain boundary density, thereby enhancing the overall mechanical properties of the invar alloy specimens produced through additive manufacturing. [PERSON] et al. [18] deposited thin-walled invar samples using both gas metal arc welding (GMAW) technology and plasma arc welding (PAW) technology. The investigation found that when heat input was lowered, the shape of the dendrites in the samples made using the GMAW technique became more consistent, and the carbides were smaller and more evenly spread out. [PERSON] et al. [19] employed the wire arc additive manufacturing technique to successfully fabricate invar alloy thin-walled specimens, and subsequent heat treatment experiments were conducted on these specimens. The research findings indicate that the mechanical properties of the specimens were substantially enhanced following heat treatment. This enhancement is primarily ascribed to the development of a fine grain size and a more uniform distribution of precipitates during the heat treatment process, which substantially bolstered the material's mechanical properties. [PERSON] et al. [20] used ultrasound to assist the WAAM process of Inconel 65 alloy, and the results showed that ultrasound promoted the transformation of columnar grains into equiaxed grains and refined the grain size, thereby reducing the anisotropy of mechanical properties. In the studies mentioned above, the researchers improved the properties of the invar alloy-deposited specimens mainly by adjusting the welding process. Nevertheless, the utility of these interventions in bolstering the performance of invar alloy-deposited specimens is constrained, and their adaptation to actual manufacturing processes presents certain challenges.