Applied Mathematics and Mechanics >
Thermal fracture analysis of two collinear cracks in a functionally graded medium based on the three-phase-lag model
Received date: 2024-10-25
Revised date: 2024-12-24
Online published: 2025-03-03
Supported by
Project supported by the Natural Science Foundation of Shandong Province of China (No. ZR2024MA085), the Science and Technology Plan Project of Zhejiang Province of China (No. 2023C03143), and the Fundamental Research Funds for the Central Universities of China
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The three-phase-lag (TPL) heat conduction model is an accurate representation of the actual heat transfer process. It would be interesting to investigate how the TPL model affects the thermal fracture behavior when there are defects existing in the medium. This paper aims to analyze the thermoelastic responses of two collinear cracks within a functionally graded half-space under thermal loadings by means of the TPL model. The thermoelastic problem is transformed into a series of singular integral equations using the integral transformation methods. The transient temperature and stress intensity factors (SIFs) are obtained through the application of Chebyshev polynomials. The effects of crack spacing and non-homogeneous parameters on the transient thermoelastic responses are presented, and the results of the TPL model are compared with those of the Fourier model, Cattaneo and Vernotte (CV) model, and dual-phase-lag (DPL) model. It is shown that crack spacing and non-homogeneous parameters have important effects on the thermoelastic responses, and the fluctuation phenomenon under the TPL model is the most pronounced due to the existence of the thermal displacement lag term.
Zhangna XUE, Huameng WANG, Jianlin LIU, Minjie WEN, Z. T. CHEN . Thermal fracture analysis of two collinear cracks in a functionally graded medium based on the three-phase-lag model[J]. Applied Mathematics and Mechanics, 2025 , 46(3) : 501 -520 . DOI: 10.1007/s10483-025-3223-6
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