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Polymers
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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PubMed Central
Article . 2025
License: CC BY
Data sources: PubMed Central
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A Unified Equation for Predicting Crack Growth in Rubber Composites Across All Crack Growth Rates

Authors: Aaron M. Duncan; Keizo Akutagawa; Dimitrios G. Papageorgiou; Julien L. Ramier; James J. C. Busfield;

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

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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gold