# Experimental Study on the Modified P–V–T Model to Improve Shrinkage Prediction for Injection-Molded Semi-Crystalline Polymer

## TL;DR

This paper introduces a new method to improve shrinkage prediction in injection-molded semi-crystalline polymers by using a modified P–V–T model with a thermal enthalpy transformation approach.

## Contribution

The novelty lies in the Thermal Enthalpy Transformation Method (TETM) for determining process-relevant solidification time and crystallization-completion temperature from in-cavity temperature monitoring.

## Key findings

- The TETM method provides a more consistent and near-linear relationship between target specific volume and measured shrinkage rate.
- The modified P–V–T model with TETM improves the robustness of solidification-time identification in injection molding.
- A two-stage packing strategy was effective in achieving comparable shrinkage performance under varying conditions.

## Abstract

Shrinkage of injection-molded parts is a major challenge for dimensional accuracy, especially for semi-crystalline polymers where crystallization induces pronounced volume change and heat release during cooling. Because packing pressure is effective only before gate or local solidification, multi-stage packing is commonly used to regulate the overall shrinkage behavior. In practice, however, the solidification/transition temperature taken from standard material tests does not necessarily represent the actual in-cavity state behavior under specific cooling rate and pressure history, which compromises the consistency of P–V–T-based shrinkage prediction. In this study, a modified P–V–T-based framework (Tait equation) is developed for polypropylene (PP) by introducing a Thermal Enthalpy Transformation Method (TETM) to determine a process-relevant solidification time and crystallization-completion temperature (including the corresponding target specific volume) directly from in-cavity melt temperature monitoring using an infrared temperature sensor. The novelty TETM utilizes the crystallization-induced enthalpy release to identify the temperature–time plateau, from which one can identify the effective solidification point. Because the Tait equation adopts a two-domain formulation (molten and solidified states), accurate identification of the domain-switching temperature is critical for reliable shrinkage prediction in practical molding conditions. In the experiment execution, the optimum filling time was defined using the minimum pressure required for melt-filling. Four target specific volumes, three melt temperatures, and two mold temperatures were examined, and a two-stage packing strategy was implemented to achieve comparable shrinkage performance under different target specific volumes. A conventional benchmark based on the solidification temperature reported in the Moldex3D material database was used for comparison only. The results show that the target specific volume determined by the TETM exhibits a more consistent and near-linear relationship with the measured shrinkage rate, demonstrating that the TETM improves the robustness of solidification-time identification and the practical usability of P–V–T information for shrinkage control.