A dimensional analysis based multi-scale thermal damage framework of brittle materials at elevated temperatures

Research on macro-scale damage prediction and micro-scale damage mechanisms of brittle materials at elevated temperatures is extremely important to the design and application of practical engineering structures. In this study, a multi-scale thermal damage framework is proposed for both describing macro-scale damage evolution and collective micro-scale cracks behavior of brittle materials at elevated temperatures. In the framework, the evolution equation of ideal micro-crack system is deduced to establish the relationship between the macro-scale damage and the micro-scale crack nucleation and growth based on dimensional analysis method. To support the multi-scale thermal damage framework, the multi-scale damage of the benchmark fracture test of the Brazilian disk at elevated temperatures is predicted and compared with the experimental results. The results support the effectiveness and ability of the multi-scale thermal damage framework, which can achieve thermal damage prediction of brittle materials in macro-scale as well as physical mechanisms description in micro-scale.