## 1 Introduction  
Spot welding is a widely used method for assembling automobile structures, offering the advantages of high productivity and low cost. It is extensively applied in the automotive industry, particularly for assembling components such as auto-body panels and chassis. Its utility in mass production lines stems from its efficiency and cost-effectiveness, enabling rapid and streamlined vehicle assembly. Recent advancements in spot welding technology and quality assurance methods have enhanced the consistency of welding quality, even under varying material properties and assembly conditions. With the growing emphasis on lightweight automotive designs, spot welding has been increasingly employed for joining high-strength and lightweight materials. While high-strength materials are advantageous for weight reduction, they pose challenges in weldability. Numerous studies have investigated the applicability of spot welding under different welding conditions, such as current and electrode force [1; 2; 3; 4; 5]. The influence of welding current on nugget size was evaluated by observing the nugget growth rate under varying welding times and currents. It was found that the nugget growth rate decreased as both welding time and current increased, with the most rapid growth occurring during the initial welding cycle. This behavior suggests that the majority of nugget formation transpires early in the welding process, after which the growth rate diminishes. This observation aligns with the existing literature, which indicates that the nugget growth rate is most pronounced at the onset of welding and tapers off with prolonged welding time and increased current. For instance, a study on the effect of welding current on nugget geometry reported that at higher welding currents, the nugget size remains almost constant, indicating a reduced growth rate [6]. Understanding this relationship is crucial for optimizing welding parameters to achieve desired nugget sizes and ensuring the structural integrity of welded joints. Furthermore, research has demonstrated that the magnitude and distribution of welding residual stress within specimens expand with increasing welding time and current, with the welding current exerting a more significant influence on residual stress compared to welding time [7]. Investigations into the effect of electrode force on nugget diameter and residual stress in the spot welding of high-strength steel have shown that varying electrode force conditions significantly influence the residual stress distribution in weld joints [8; 9]. The nugget diameter was found to increase with higher electrode force, which also impacted the residual stress distribution. In addition, the potential for delayed fracture in spot weld joints has been explored by analyzing residual stress and hydrogen diffusion, focusing on the increased hydrogen concentration and its spread within the metal under high-temperature and high-residual-stress conditions [10]. Welding residual stress is a critical factor affecting the quality and strength of spot weld joints, motivating extensive research in this area [11; 12]. For spot welding in car body manufacturing, however, gaps between sheets often arise due to spring-back effects after applying electrode pressure, as illustrated in Figure 1[13]. These gaps can lead to deformation and misalignment during welding, thereby reducing weld integrity and productivity [14]. Spot welding in such high-strength steels results in the rapid formation of a martensitic structure due to the fast cooling rate, which increases the brittleness of the weld joint and makes it more prone to cracking [15]. It is well known from research findings that there is a close correlation between hardness and residual stress, as high hardness and residual stress are observed at the nugget center, while both hardness and residual stress decrease significantly in the heat-affected zone (HAZ) [16].