A process for cohesive bonding between a metal surface and a nonmetallic substrate is provided. The non-metallic substrate may comprise a plurality of microfilaments and/or nanofilaments dispersed into and below the surface of the substrate. The application of pressure and laterally-oriented high frequency and low amplitude vibration may allow for diffusion bonding between the metal surface and material of the nanofilaments. Another method includes discharging energy from a bank of capacitors to melt adjoining surfaces of the metal surface and nonmetallic substrate. Additionally, a cohesive bonding method may further comprise converting electrical oscillations of ultrasonic frequency into ultrasonic vibrations which are transmitted to the metal body and/or substrate for fusing the two materials together.