Glue bonding is a composite connection technology that combines resistance spot welding (or projection welding) with adhesive bonding [1]. It has been widely applied in industries such as aerospace, automotive, and aviation. For instance, components like the airframe, flaps, fuel tanks, and support structures of fighter jets have adopted this welding process [2], and China has also made significant progress in this field [3]. The mechanical behavior of welded structures has attracted considerable attention from researchers globally. Extensive experimental and numerical studies have been conducted on single-welded lap joints [4,5]. However, there remains limited research on how joint spacing affects the mechanical performance of multi-joint structures. Solder joint pitch is a critical geometric parameter in the design and manufacturing of bonded structures. Choosing an appropriate pitch can ensure economical production and reliable performance. This paper uses both finite element analysis and experimental methods to study single-row multi-spot welded joints. When two adhesives with different elastic moduli are used, the stress-strain fields and fracture behavior are analyzed based on the distance between solder joints. ### 1. Joint Shape, Size, and Finite Element Mesh #### 1.1 Joint Shape and Dimensions The dimensions of a single-row, multi-spot welded lap joint are illustrated in Figure 1. Uniform tensile shear loads were applied to both ends of the specimen. The base metal was 08Al deep-drawing steel, 40 mm wide and 1 mm thick. To investigate the influence of adhesive elasticity on stress and strain distribution, high-modulus epoxy resin and low-modulus acrylate adhesives were used, each with a thickness of 0.4 mm. The overlap length was 40 mm, and five solder joints with diameters of 5 mm were evenly spaced along the Y-direction. The selected solder joint pitches were 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm. #### 1.2 Finite Element Meshing of Joints For the multi-spot welded joint shown in Figure 1, when the test piece is long along the Y-axis, the force conditions of the solder joints are similar, and due to symmetry about the X-axis, only half of the structure needs to be considered. Figure 2 shows the finite element mesh for a solder joint pitch of 40 mm. The total width of the mesh was 20 mm. Three-dimensional eight-node elements were used, with the upper and lower plates and adhesive layer divided into two layers. Grids were refined at the edges of the solder joints and overlapping areas, with a minimum grid size of 0.15 mm. The weld nuggets were simplified, assuming no defects or electrode indentation effects. Mechanical properties of the materials, including base metal, nugget, and adhesives, are listed in Table 1. A bilinear stress-strain curve was used to model elasto-plastic behavior, and ALGOR software was used to simulate the stress and strain fields under a nominal stress of 135 MPa. ### 2. Stress and Strain Distribution in Soldered Joints #### 2.1 Epoxy Adhesive Joints The simulation results showed that stress and strain distributions were similar across all five solder joint pitches. For clarity, data for pitches of 10 mm, 30 mm, and 50 mm are presented. Figure 3 illustrates the stress and strain distribution in the adhesive layer near the interface between the steel plate and the high-modulus epoxy adhesive. The normal stress σ_x was highest at the center of the solder joints and decreased toward the edges. The shear stress τ_zx was concentrated at the edges of the weld, with peak values decreasing as the pitch increased. The positive strain ε_x was higher in the adhesive layer than in the solder joint area, and the maximum positive strain increased slightly with larger pitches. Shear strain ε_zx was primarily distributed in the adhesive layer, with minimal concentration at the solder joint edges. #### 2.2 Acrylic Adhesive Joints Figure 4 presents the stress and strain distribution in the adhesive layer for low-modulus acrylate adhesives. Similar to the epoxy case, the normal stress was highest at the solder joints, but the stress concentration at the edges increased with larger pitches. Shear stress was concentrated at the edges of the solder joints, and the shear strain in the adhesive layer increased with the pitch. The results indicated that increasing the solder joint pitch reduced the number of loaded joints, which affected the stiffness and strength of the joint, especially with low-modulus adhesives. ### 3. Experimental Validation To validate the numerical results, static tensile shear tests were conducted using a CSS-1110 universal testing machine. Test specimens with solder joint pitches of 20 mm, 30 mm, and 40 mm were tested at a rate of 5 mm/min. The first load peak, corresponding to glue layer failure, was recorded. The nominal stress at fracture was calculated using the formula: σ_n = P_f / (I * t), where P_f is the fracture load, I is the plate width, and t is the plate thickness. The results showed that the nominal stress decreased slightly with increasing pitch, consistent with previous findings and numerical predictions. ### 4. Conclusion (1) With high-modulus adhesives, increasing the solder joint pitch reduces the stress in the joint area and slightly increases the stress in the adhesive layer at the overlap edge, but the overall load capacity decreases only marginally. (2) For low-modulus acrylic adhesives, stress concentration at the solder joints increases with larger pitches, and shear strain in the overlap edge region also rises. This leads to a decrease in joint stiffness and strength, which is more pronounced than with high-modulus adhesives. (3) In epoxy-based joints, the adhesive layer fails first. Larger pitches lead to higher fracture loads due to wider specimens, but the nominal fracture stress decreases with increasing pitch. (4) The effect of solder joint spacing on joint strength aligns with numerical predictions, confirming the reliability of finite element analysis in studying the mechanical behavior of joints.

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