# A Unified Equation for Predicting Crack Growth in Rubber Composites Across All Crack Growth Rates

## TL;DR

This paper introduces a new equation that simplifies predicting how cracks grow in rubber materials across all speeds, using fewer variables than previous models.

## Contribution

The novel contribution is a unified equation combining two energy dissipation mechanisms into a single model with only four variables.

## Key findings

- The model accurately predicts crack growth in various rubber types under different conditions.
- It enables predicting fast crack growth behavior using only slow crack growth data.
- The model reduces the number of required parameters from six to four.

## Abstract

The relationship between tearing energy and crack growth rates in elastomers is typically divided into three regions—slow crack growth, fast crack growth, and a transitional region—each described by separate power law relationships, requiring six variables to fully characterize the behavior. This study introduces a novel, unified equation that simplifies this relationship by combining two coexisting energy dissipation mechanisms into a single model with only four variables. The model consists of two terms, one for each energy dissipation mechanism: one term is dominant at slow crack growth rates and limited by a threshold energy, and the other is dominant at fast speeds. The transition region emerges naturally as the dominant mechanism shifts. The model’s simplicity enables new advances, such as predicting fast crack growth tearing and transition energies using only slow crack growth data. This capability is demonstrated across a wide range of non-strain crystallizing rubbers, including filled and unfilled compounds, tested at room temperature and elevated temperatures and in both swollen and unswollen states. This model offers a practical tool for material design, failure prediction, and reducing experimental effort in characterizing elastomer performance. Notably, this is the first model to unify slow, transition, and fast crack growth regimes into a single continuous equation requiring only four variables, enabling the prediction of high-speed behavior using only low-speed experimental data—a major advantage over existing six-parameter models.