# Crack propagation under static and dynamic boundary conditions

## TL;DR

This paper explores the relationship between static and dynamic boundary conditions in crack propagation tests, aiming to establish a universal criterion for consistent results across both methods, thereby improving testing efficiency.

## Contribution

It introduces a simulation-based analysis of static and dynamic crack tests, revealing conditions for their equivalence and guiding better experimental design.

## Key findings

- Dynamic tests can detect velocity jumps with fewer samples.
- A universal condition links static and dynamic test results.
- Dynamic testing is more efficient and cost-effective.

## Abstract

Velocity jumps observed for crack propagation under a static boundary condition have been used as a controlling factor in developing tough rubbers. However, the static test requires many samples to detect the velocity jump. On the contrary, crack propagation performed under a dynamic boundary condition is timesaving and cost-effective in that it requires only a single sample to monitor the jump. In addition, recent experiments show that velocity jump occurs only in the dynamic test for certain materials, for which the velocity jump is hidden in the static test because of the effect of stress relaxation. Although the dynamic test is promising because of these advantages, the interrelation between the dynamic test and the more established static test has not been explored in the literature. Here, by using two simulation models, we elucidate this interrelation and clarify a universal condition for obtaining the same results from the two tests, which will be useful for designing the dynamic test.