Cu-Cu direct bonding is an important technology in advanced semiconductor chip packaging for 3D integration. It offers benefits such as reduced vertical dimensions and increased interconnection density, which are crucial for data-driven scientific and engineering tasks. Despite extensive research into Cu-Cu bonding, there's a gap in understanding from both experimental and material mechanics perspectives. In experiments, Cu-Cu bonding was simply determined by changing the temperature and pressure conditions to ascertain whether bonding had been successfully achieved. But the deformation history of Cu film at bonding interface during the bonding process was not thoroughly studied. In this study, Cu-Cu bonding experiments were conducted on electroplated Cu film wafers that underwent chemical-mechanical polishing (CMP). The experiments varied pressure and temperature levels, and microscope measurements were used to evaluate bonding quality, revealing a correlation between temperature, pressure, and bonding quality. In addition, the surface roughness effect was considered to propose correlation between bonding quality and surface roughness. Surface roughness during bonding can induce local stress concentration, leading to plastic deformation and void formation. High thermal stresses from temperature and pressure during bonding can also cause plastic deformation and material flux of Cu, affecting bonding quality. To explain these findings, a thermomechanical, elastoplastic, and multiscale analysis using the finite element method (FEM) was performed. To summarize the key findings, in the Cu-Cu bonding process, an increase in temperature enhances the material flux at all boundary surfaces of a void, thereby influencing the overall void closure. However, an increase in pressure generates a pressure gradient at the contact surfaces, which in turn increases the material flux into the void from the contact boundary, determining the local void morphology. From the numerical simulation results, the void formation at the Cu-Cu bonding interface can be explained and validated with experimental void morphology results.