A heuristic study of the Mullins effect in reinforced rubber by using the Weibull distribution

Abstract

Stress softening, known as the Mullins effect, has a significant effect on the durability and performance of filler-reinforced rubber, making it a critical issue in designing products for practical applications. While empirical equations are widely used, they fail to capture the intricate and nonlinear behaviors that are characteristic of filler-reinforced rubber. To address this limitation, this study developed a simplified equation to predict the Mullins effect. The model is based on the assumption that the Mullins effect originates from the destruction of particle aggregation structures, and the relationship between the degree of destruction and the stretch ratio is expressed using extreme value statistics. Validation against experimental data revealed that the equation accurately predicts the behavior of rubber reinforced with carbon black (CB) or silica. Additionally, in systems with CB-filled rubber, the equation demonstrated good agreement with the experimental results, even when the CB content was varied. These findings suggest that the proposed model is versatile and effective for predicting the Mullins effect under different conditions, providing a useful tool for understanding and optimizing the performance of filler-reinforced rubber in practical applications. Stress softening, or the Mullins effect, critically affects the performance of filler-reinforced rubber. This study proposes a simplified model based on the destruction of particle aggregates, using extreme value statistics to relate damage to stretch ratio. The model accurately predicts behaviors of rubber filled with carbon black or silica, showing good agreement with experiments across varying filler contents. It offers a practical tool for designing durable rubber materials.