Weibull‐Based Probabilistic Analysis of Cracking Risk in Blast Furnace Hearth Carbon Bricks Under Thermomechanical Loading

Abstract

Unexpected cracking of carbon bricks in blast furnace hearths remains a critical challenge for campaign safety and long service life, while deterministic criteria based solely on stress magnitude are insufficient to describe the stochastic fracture behavior of porous brittle materials. In this study, a three‐dimensional thermomechanical finite element model with explicit brick‐joint geometry is established, and a Weibull‐based probabilistic criterion is introduced to relate stress state to crack initiation risk. Joint width, hot‐face temperature, and the thermal conductivity of the ramming mix are systematically analyzed. The results show that joint width governs a transition in stress mode and thereby changes the calculated cracking‐risk index: at 0.1 mm, strong constraint causes radial tensile‐stress concentration near the hot face, with a local cracking‐risk index of 19.1%, whereas at 0.5 mm, weakened constraint promotes the simultaneous increase of radial and circumferential tensile stresses, raising the index to 24.4%; by comparison, a joint width of about 0.3 mm gives the lowest cracking‐risk index of 17.8%. Hot‐face temperature is identified as the dominant variable. The local cracking‐risk index reaches 36.81% at 1450 °C and increases sharply thereafter. The proposed framework provides guidance for joint design and thermal management of blast furnace hearth carbon bricks.