Isogeometric analysis-based phase-field modeling of brittle fracture in piezoelectric materials

• Main Author: Kiran Raj
• Other Authors: Zhou Kun
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Engineering::Mechanical engineering::Mechanics and dynamics
• Online Access: https://hdl.handle.net/10356/173387
• Institution: Nanyang Technological University

Piezoelectric materials find extensive applications as sensors, actuators, and transducers, however, most of the functional piezoelectric ceramics though possessing excellent electromechanical coupling characteristics are often limited by brittleness and low fracture toughness. On the other hand, piezoelectric composites offer improved characteristics but suffer from stress concentrations and interface cracks due to geometric imperfections, resulting in crack nucleation and propagation under complex loading conditions. Traditional analytical and experimental approaches fall short in unravelling the intricate fracture behaviour of piezoelectric materials, necessitating the development of accurate and robust numerical methods. Isogeometric analysis (IGA), with its precise geometry representation and high-order approximation capabilities, has emerged as a promising approach. Additionally, the phase-field method (PFM) approximates cracks as narrow damage bands, providing a computational tool for fracture analysis. Therefore, the primary objective of this Ph.D. research is to develop a comprehensive and robust isogeometric analysis-based framework to investigate the fracture behavior of piezoelectric materials using the phase-field modeling approach. In Chapter 3, a phase-field model based on an adaptive IGA is developed for the investigation of electromechanical brittle fracture in piezoelectric materials. The approach relies on constructing polynomial splines over hierarchical T-meshes (PHT-splines) based on isogeometric formulation. A second-order phase-field model is employed to approximate the cracked region and the energy functional coupling the mechanical, electrical and phase-field is considered. The evolution of the crack phase-field is defined using coupled electromechanical constitutive relationships. Additionally, an adaptive h-refinement strategy utilising PHT-splines is implemented to address the limitations associated with nonuniform rational B-splines-based isogeometric formulations. In such a refinement scheme, the phase-field parameter itself is employed to ascertain the need for refinement. This facilitates the dynamic tracking of propagating cracks without any need for a priori information on the crack paths. The propagation of cracks in piezoelectric ceramics subjected to different electric fields is simulated using this approach. A comprehensive set of numerical simulations on cracked piezoceramics capturing intricate crack propagation patterns including deflection and twisting is presented and benchmarked with experiments and other numerical studies. In Chapter 4, the developed adaptive phase-field model is extended to investigate interfacial fracture in piezoelectric composites under different electromechanical loadings. The model introduces interface and crack phase-field parameters to regularize the sharp interface and crack topologies, and regularized energy terms are incorporated in the energy functional corresponding to the crack and interface. The model also modifies the energy functional to scrutinize the interplay between interfacial damage and crack propagation in piezocomposites and thus, it can capture the resulting fracture patterns including interfacial debonding, matrix cracking and their interactions. The proposed model is convincingly validated through a series of numerical examples, showcasing its effectiveness and robustness in capturing complex electromechanical fracture behavior of piezoelectric composites. These simulations accurately capture various fracture mechanisms, including crack nucleation, interfacial debonding, matrix cracking, crack propagation, and coalescence. In Chapter 5, the isogeometric-based phase-field model is employed to probe the fracture behaviour of homogeneous piezoceramics under thermo-electromechanical loading conditions. The model considers thermo-electromechanical coupling to quantify the effects of temperature, electric field, and mechanical deformation on the critical fracture load in different modes of fracture. The evolution of the crack phase-field is accounted for solely by the tensile part of the mechanical energy. Numerical simulations reveal that temperature has an insignificant influence on the fracture load but may promote or delay fracture initiation while a negative electric field impedes crack propagation. A series of numerical examples demonstrate that the developed phase-field model can effectively capture the complex crack propagation paths and can provide insights into the fracture behaviour of piezoceramics in thermal environments. This thesis presents a comprehensive workflow and implementation of the adaptive phase-field model employing IGA to examine the brittle fracture in piezoelectric materials subjected to multiphysics loading conditions. Through the development of multiple phase-field models, this thesis focuses on addressing crucial aspects in terms of understanding and analysing the fracture characteristics of piezoceramics in real-world engineering applications. This research contributes to advancing the treatment of fracture behaviour in piezoelectric materials and provides key guidance for enhancing their reliability and performance in practical applications.