{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T16:42:51Z","timestamp":1787244171205,"version":"build-2736575974"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T00:00:00Z","timestamp":1769558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001868","name":"National Science Council, Taiwan","doi-asserted-by":"publisher","award":["NSTC 114-2224-E-033-001 -"],"award-info":[{"award-number":["NSTC 114-2224-E-033-001 -"]}],"id":[{"id":"10.13039\/501100001868","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>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\u2013V\u2013T-based shrinkage prediction. In this study, a modified P\u2013V\u2013T-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\u2013time 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\u2013V\u2013T information for shrinkage control.<\/jats:p>","DOI":"10.3390\/polym18030349","type":"journal-article","created":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T15:56:12Z","timestamp":1769615772000},"page":"349","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Experimental Study on the Modified P\u2013V\u2013T Model to Improve Shrinkage Prediction for Injection-Molded Semi-Crystalline Polymer"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9367-6031","authenticated-orcid":false,"given":"Shia-Chung","family":"Chen","sequence":"first","affiliation":[{"name":"R&D Center for Smart Manufacturing, Chung Yuan Christian University, Taoyuan 32023, Taiwan"},{"name":"R&D Center for Semiconductor Carrier, Chung Yuan Christian University, Taoyuan 32023, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan-Xiang","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Chung Yuan Christian University, Taoyuan 32023, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Je","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Chung Yuan Christian University, Taoyuan 32023, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5133-0494","authenticated-orcid":false,"given":"Yu-Hung","family":"Ting","sequence":"additional","affiliation":[{"name":"R&D Center for Smart Manufacturing, Chung Yuan Christian University, Taoyuan 32023, Taiwan"},{"name":"Department of Mechanical Engineering, Chung Yuan Christian University, Taoyuan 32023, Taiwan"},{"name":"Moldintel Co., Ltd., Taoyuan 32023, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1002\/pen.25163","article-title":"Estimates for material shrinkage in molded parts caused by time-varying cavity pressures","volume":"59","author":"Bushko","year":"2019","journal-title":"Polym. Eng. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.jmatprotec.2017.05.038","article-title":"Monitoring and dynamic control of quality stability for injection molding process","volume":"249","author":"Zhou","year":"2017","journal-title":"J. Mater. Process. Technol."},{"key":"ref_3","unstructured":"Chang, C.H. (2010). Cavity Dynamic Pressure on the Injection Molding Plactic Parts. [Master\u2019s Thesis, National Taipei University of Technology]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s00170-014-6776-5","article-title":"Correlation between runner pressure and cavity pressure within injection mold","volume":"79","author":"Tsai","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_5","unstructured":"Zoller, P., and Walsh, D.J. (1995). Standard Pressure\u2013Volume\u2013Temperature Data for Polymers, Technomic Publishing Company Inc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4081","DOI":"10.1016\/S0032-3861(97)10388-3","article-title":"P-V-T relations in a series of longitudinal polymer liquid crystals with varying mesogen concentration","volume":"39","author":"Berry","year":"1998","journal-title":"Polymer"},{"key":"ref_7","unstructured":"KEP (2025, December 15). Material Properties and Test Methods for Molding Analysis. Available online: https:\/\/www.gpac-kpac.com\/download.php?Lang=En&Code=Tech5_en&Seq=5."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.polymertesting.2015.10.009","article-title":"Analytical review of some relevant methods and devices for the determination of the specific volume on thermoplastic polymers under processing conditions","volume":"48","author":"Naranjo","year":"2015","journal-title":"Polym. Test."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1002\/polb.1994.090320610","article-title":"Crystallization of polypropylene, nylon-66 and poly (ethylene terephthalate) at pressures to 200 MPa: Kinetics and characterization of products","volume":"32","author":"He","year":"1994","journal-title":"J. Polym. Sci. Part B Polym. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4592","DOI":"10.1063\/1.1659828","article-title":"Pressure-volume-temperature properties and transitions of amorphous polymers; polystyrene and poly (orthomethylstyrenes)","volume":"42","author":"Quach","year":"1971","journal-title":"J. Appl. Phys."},{"key":"ref_11","unstructured":"Johannaber, F. (1994). Injection Molding Machines: A User\u2019s Guide, Hanser Gardner Publications. [4th ed.]."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, J. (2012). P-V-T Properties of Polymers for Injection Molding, Some Critical Issues for Injection Molding, InTech.","DOI":"10.5772\/35212"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"940","DOI":"10.1002\/pen.11483","article-title":"Control of part weight in injection molding of amorphous thermoplastics","volume":"39","author":"Kamal","year":"1999","journal-title":"Polym. Eng. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jmatprotec.2006.10.037","article-title":"Cavity pressure based grey prediction of the filling-to-packing switchover point for injection molding","volume":"183","author":"Huang","year":"2007","journal-title":"J. Mater. Proccessing Technol."},{"key":"ref_15","unstructured":"Wu, W.W. (2002). Study on the Influence of Injection Molding Conditions of Shear Effect and Finished Surface Quality of Plastic Parts. [Master\u2019s Thesis, National Kaoshiung University of Applied Science]."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1080\/03602559.2011.578292","article-title":"Filling-to-packing switchover mode base on cavity temperature for injection molding","volume":"50","author":"Wang","year":"2011","journal-title":"Polym.-Plast. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"156","DOI":"10.3139\/217.3058","article-title":"Influence on product quality by P-v-T-optimised processing in injection compression molding","volume":"31","author":"Hopmann","year":"2016","journal-title":"Int. Polym. Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"050005","DOI":"10.1063\/1.4977309","article-title":"Effect of process parameters on cavity pressure in injection molding","volume":"1820","author":"Wang","year":"2017","journal-title":"AIP Conf. Proc."},{"key":"ref_19","first-page":"22","article-title":"Injection Molding: Why & how to do gate-seal experiments","volume":"56","author":"Bozzeli","year":"2010","journal-title":"Plast. Technol."},{"key":"ref_20","unstructured":"Lu, H.M. (2021). Research on the Relationship Between Key Factors of Injection Molding and Shrinkage Quality. [Master\u2019s Thesis, Chung Yuan Christian University]."},{"key":"ref_21","unstructured":"Lou, Y.-F. (2016). Study on the Relation Between Molding Parameters and Shrinkage by Using P-v-T Diagram. [Master\u2019s Thesis, Chung Yuan Christian University]."},{"key":"ref_22","unstructured":"Chang, Y.C. (2017). Investigation on the Establishment of P-v-T control Method and Its Application to Injection Molded Part Quality. [Ph.D. Thesis, Chung Yuan Christian University]."},{"key":"ref_23","unstructured":"Huang, P.K. (2017). The Study of Semi-Crystalline Parameters Optimization of Injection Molded Part Quality by PVT Control Method. [Master\u2019s Thesis, Chung Yuan Christian University]."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chen, S.C., Tsai, B.L., Hsieh, C.C., Cheng, N.T., Shen, E.N., and Feng, C.T. (2023). Prediction of part shrinkage for injection molded crystalline polymer via cavity pressure and melt temperature monitoring. Appl. Sci., 13.","DOI":"10.3390\/app13179884"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1002\/pen.10574","article-title":"Modifying the Tait equation with cooling-rate effects to predict pressure-volume-temperature behaviors of amorphous polymers: Modeling and experiments","volume":"36","author":"Chang","year":"1996","journal-title":"Polym. Eng. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, M.L., Chang, R.Y., and Hsu, C.H. (2018). Molding Simulation Theory and Practice, Hanser Publisher. Chapter 2.3.","DOI":"10.3139\/9781569906200.fm"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wang, M.L., Chang, R.Y., and Hsu, C.H. (2018). Molding Simulation Theory and Practice, Hanser Publisher. Chapter 4.3&6.1.","DOI":"10.3139\/9781569906200.001"},{"key":"ref_28","unstructured":"(2025, December 15). Futaba Web. Available online: https:\/\/mms.mtb.futaba.co.jp\/en\/products\/resintemperature\/."},{"key":"ref_29","unstructured":"CoreTech (2020). Molded3D Software, Moldex3D 2020, System Co., Ltd."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wang, M.L., Chang, R.Y., and Hsu, C.H. (2018). Molding Simulation Theory and Practice, Hanser Publisher. Chapter 6.","DOI":"10.3139\/9781569906200.fm"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"109136","DOI":"10.1016\/j.matdes.2020.109136","article-title":"Measurement of specific volume of polymers under simulated injection molding processes","volume":"196","author":"Wang","year":"2020","journal-title":"Mater. Des."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/3\/349\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T05:10:25Z","timestamp":1770095425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/3\/349"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,28]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["polym18030349"],"URL":"https:\/\/doi.org\/10.3390\/polym18030349","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,28]]}}}