The full curve of the FPZ development in a mode I fracture of sandstone by acoustic emission(AE) cluster

A fracture process zone(FPZ) dominates the fracture initiation and propagation in rock and quasi-brittle materials. The complete development curve involves two FPZ characteristics：the fully-developed FPZ length and its corresponding loading stage. However，due to limitations in observation techniques and processing approaches，it is rare to have the full curve of the FPZ development in the literatures. In this study，a series of mode I sandstone beams under three-point bending are employed to induce the mode I fractures for laboratory testing，where acoustic emission(AE) is used to observe the fracture process. By employing an improved approach to analyze the AE cluster and determine the FPZ boundary，a full curve of the FPZ development in the mode I fracture is obtained. The main conclusions are as follows：(1) the derived curve of the FPZ development aligns well with the theoretical model，which not only provides accurate information of the FPZ(i.e.，the fully developed FPZ length and its corresponding loading stage) but also indicates that the FPZ is related to the material properties. (2) Based on the full curve，the FPZ can be divided into two parts：FPZ initiation and FPZ propagation，with the transition position occurring when the FPZ reaches its fully-developed stage. During the FPZ initiation，the FPZ length increases when the external load increases. Once the peak load is reached，the FPZ continues to grow until the fully-developed FPZ occurs. For the FPZ propagation，the length FPZ remains relatively constant，though fluctuations are observed in the curve，probably due to instability in FPZ propagation. However，these fluctuations are centered around the length of the fully developed FPZ，allowing it to be treated as a constant. Experimental results demonstrate that the FPZ in mode I fractures attains its fully developed stage when the external load exceeds the peak(at post-90%，indicating that the load is at 90% of the peak in the post-peak regime)，with its length nearly twice as the length observed at the peak(17 mm vs. 9 mm). This study confirms that the fully developed stage of the I-type fracture process zone is directly correlated with the cohesive force model through experimental measurements of local acoustic emission.