Modeling variability of the electrical conductivity tensor for the induction welding of composites

Induction welding utilizes electromagnetic induction to heat carbon fiber reinforced thermoplastic (CFRTP) materials, enabling their fusion without direct contact. This heating process directly impacts material viscosity and bonding strength, with optimal temperatures ensuring proper fusion and strong adhesion between composite layers. The process is strongly influenced by material quality, as poor-quality materials can lead to uneven heating, incomplete fusion, and compromised structural integrity. To investigate the influence of the variation of CFRTP material properties on the generated heat, in this paper, we propose a novel way of modeling and propagating the stochastic electrical conductivity tensor through the physics based model describing the fusion bonding. The electrical conductivity of CFRTP is an anisotropic and inherently variable material property. To model this variation, we propose a stochastic model belonging to a family of positive definite tensors. In particular, we suggest the stochastic model in which both the scaling/strength and orientation of the tensor are separately modeled as stochastic. In this manner, we are capable of assigning a specific class of spatial symmetries and invariances to individual realizations of the stochastic tensor, all the while insisting that the average of the entire population adheres to a potentially ‘higher’ spatial invariance class. Finally, the proposed model is incorporated to the physics based model based on which the variation in the temperature field characterizing the fusion bonding process is quantified with the help of the sparse grid integration.