# Creep Compliance of Carbon Black-Filled Rubber Converted from Storage Modulus by Use of Collocation Method: Numerical and Experimental Validation

## TL;DR

This paper presents a method to predict the long-term creep behavior of carbon black-filled rubber using short-term storage modulus data and a collocation method, validated through experiments.

## Contribution

The novel use of the collocation method to avoid fitting curve waviness and predict creep compliance from storage modulus data.

## Key findings

- The master curve of storage modulus was successfully constructed using the time–temperature superposition principle.
- The collocation method provided reliable creep compliance predictions with an RMSE of 0.0055 compared to experimental results.

## Abstract

Carbon black (CB)-filled rubber has been widely used in engineering. However, its time-dependent behavior, such as creep, is undesirable during the service process. In addition, the long-term creep test is time- and cost-consuming. To this end, the objective of this paper aims to predict the creep behavior from the short-term storage modulus by use of the collocation method. First, the master curve of storage modulus was constructed based on the time–temperature superposition principle (TTSP), and the validation of shift factors was verified by use of the Williams–Landel–Ferry (WLF) equation. Second, the generalized Kelvin model was used to describe the master curve of storage modulus by use of the collocation method, and the corresponding parameters were obtained. Compared with the existing works, the collocation method had the advantages of avoiding the occurrence of waviness of the fitting curve. Lastly, the creep compliance of CB-filled rubber was calculated by substituting the fitting parameters into the creep compliance expression. In order to verify the reliability of the calculation result, the creep tests were carried out. It was obvious that the calculation result is in good agreement with the experimental one with a RMSE value of 0.0055, which means that the calculation result is reliable.