{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T15:57:00Z","timestamp":1792079820742,"version":"4.4.0"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:00:00Z","timestamp":1775692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"JSPS KAKENHI","doi-asserted-by":"publisher","award":["JP 25K15500"],"award-info":[{"award-number":["JP 25K15500"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>This study investigated mechanical properties of composite materials consisting of an isotactic polypropylene (iPP) matrix reinforced with whisker-like fillers: carbon nanofibers (CBNF) and wollastonite (WN). We strove to develop mechanical models specifically for predicting yield stress and fracture toughness. Experimentally obtained results validated findings obtained using the proposed models. Regarding the elastic modulus, data suggest that conventional rules of mixture, typically used for glass fiber-reinforced polymers, remain applicable, indicating that filler addition enhances stiffness in a predictable manner. However, yield stress and fracture toughness exhibited distinct behaviors. Results revealed that these properties are governed predominantly by shear yielding of the iPP matrix rather than reinforcement effect of the fillers. Despite the presence of whiskers, the overall yield and fracture mechanisms depend heavily on the matrix\u2019s plastic deformation and energy dissipation. The constructed models consistently explain these findings, supporting quantitative evaluation of the matrix\u2019s contribution. These results emphasize that developing high-performance iPP composites requires knowledge of the intrinsic ductile properties of the matrix alongside filler selection and dispersion.<\/jats:p>","DOI":"10.3390\/polym18080917","type":"journal-article","created":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T12:21:32Z","timestamp":1775737292000},"page":"917","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mechanical Modeling of Whisker-Filled Dispersed Isotactic Polypropylene: Matrix-Dominated Yielding and Fracture Mechanisms"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5170-8346","authenticated-orcid":false,"given":"Tetsuo","family":"Takayama","sequence":"first","affiliation":[{"name":"Graduate School of Organic Materials Science, Yamagata University, Yamagata 992-8510, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daisuke","family":"Shimizu","sequence":"additional","affiliation":[{"name":"Graduate School of Organic Materials Science, Yamagata University, Yamagata 992-8510, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1186\/s11671-023-03952-z","article-title":"Research and application of polypropylene: A review","volume":"19","author":"Hossain","year":"2024","journal-title":"Discov. Nano"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"117","DOI":"10.25130\/tjes.31.2.11","article-title":"The effect of chain tacticity on the thermal energy parameters of isotactic and syndiotactic polypropylene","volume":"31","author":"Nabhan","year":"2024","journal-title":"Tikrit J. Eng. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1177\/0892705711428659","article-title":"Mechanical properties of polypropylene composites","volume":"26","author":"Shubhra","year":"2013","journal-title":"J. Thermoplast. Compos. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"109706","DOI":"10.1016\/j.compositesb.2022.109706","article-title":"Mechanical properties and damage analysis of S-glass: A reactive molecular dynamics study","volume":"234","author":"Yeon","year":"2022","journal-title":"Compos. Part B Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3748","DOI":"10.1002\/pc.25672","article-title":"Mechanical properties of extruded glass fiber reinforced thermoplastic polyolefin composites","volume":"41","author":"Ghanbari","year":"2020","journal-title":"Polym. Compos."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1002\/pc.25966","article-title":"Improvement in mechanical properties of recycled polypropylene composite by controlling the length distribution of glass fibers","volume":"42","author":"Kang","year":"2021","journal-title":"Polym. Compos."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/j.jmrt.2021.05.076","article-title":"Characterization of interfacial properties between fibre and polymer matrix in composite materials\u2014A critical review","volume":"13","author":"Huang","year":"2021","journal-title":"J. Mater. Res. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7071","DOI":"10.2147\/IJN.S471546","article-title":"Recent advances in whiskers: Properties and clinical applications in dentistry","volume":"19","author":"Han","year":"2024","journal-title":"Int. J. Nanomed."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Umer, U., Abidi, M., Almutairi, Z., and Aboudaif, M. (2025). A multi-phase analytical model for effective electrical conductivity of polymer matrix composites containing micro-SiC whiskers and nano-carbon black hybrids. Polymers, 17.","DOI":"10.3390\/polym17020128"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2661","DOI":"10.1111\/j.1151-2916.1998.tb02674.x","article-title":"Elastic anisotropy of \u03b2-silicon nitride whiskers","volume":"81","author":"Hay","year":"1998","journal-title":"J. Am. Ceram. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3676","DOI":"10.1002\/pc.24396","article-title":"Surface modification of magnesium hydroxide sulfate hydrate whiskers and its toughness and reinforcement for polyvinyl chloride","volume":"39","author":"Gong","year":"2018","journal-title":"Polym. Compos."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.5714\/CL.2013.14.3.131","article-title":"Carbon nanotubes-properties and applications: A review","volume":"14","author":"Ibrahim","year":"2013","journal-title":"Carbon Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Takayama, T., Shimizu, D., and Kobayashi, S. (2025). Processing stability of carbon nanofiber-reinforced glass fiber\/polypropylene composites under repeated extrusion for mechanical recycling. Materials, 18.","DOI":"10.3390\/ma18204777"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1002\/pc.25403","article-title":"Mechanical properties of wollastonite reinforced thermoplastic composites: A review","volume":"41","author":"Chan","year":"2020","journal-title":"Polym. Compos."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Takayama, T., Kobayashi, S., Yuasa, Y., and Jiang, Q. (2024). Effect of carbon nanofiber distribution on mechanical properties of injection-molded aramid-fiber-reinforced polypropylene. Polymers, 16.","DOI":"10.3390\/polym16081110"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1002\/jbm.a.10140","article-title":"Hydroxyapatite whiskers provide improved mechanical properties in reinforced polymer composites","volume":"67A","author":"Roeder","year":"2003","journal-title":"J. Biomed. Mater. Res. Part A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1007\/s12633-019-00297-0","article-title":"Low velocity impact and mechanical behaviour of shot blasted SiC wire-mesh and silane-treated aloevera\/hemp\/flax-reinforced SiC whisker modified epoxy resin composites","volume":"12","author":"Murugan","year":"2019","journal-title":"Silicon"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mur\u010dinkov\u00e1, Z., Postawa, P., and Winczek, J. (2022). Parameters influence on the dynamic properties of polymer-matrix composites reinforced by fibres, particles, and hybrids. Polymers, 14.","DOI":"10.3390\/polym14153060"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rajak, D., Pagar, D., Menezes, P., and Linul, E. (2019). Fiber-reinforced polymer composites: Manufacturing, properties, and applications. Polymers, 11.","DOI":"10.3390\/polym11101667"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Setyanto, D., Jayatun, Y., Basoeki, P., and De Fretes, A. (2022). Physical properties of glass-fibre-reinforced polymer filled with alumina trihydrate and calcium carbonate. Polymers, 14.","DOI":"10.3390\/polym14122464"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"04024021","DOI":"10.1061\/JCCOF2.CCENG-4392","article-title":"Flexural behavior and design of ultrahigh-performance concrete beams reinforced with GFRP bars","volume":"28","author":"Peng","year":"2024","journal-title":"J. Compos. Constr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/0022-5096(65)90035-9","article-title":"Tensile properties of fibre-reinforced metals: Copper\/tungsten and copper\/molybdenum","volume":"13","author":"Kelly","year":"1965","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_23","first-page":"640","article-title":"The application of a representative volume element (RVE) model for the prediction of rice husk particulate-filled polymer composite properties","volume":"10","author":"Saigal","year":"2019","journal-title":"Mater. Sci. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108243","DOI":"10.1016\/j.compscitech.2020.108243","article-title":"Multiscale image-based modelling of damage and fracture in carbon fibre reinforced polymer composites","volume":"198","author":"Sencu","year":"2020","journal-title":"Compos. Sci. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jiang, Q., Takayama, T., and Nishioka, A. (2023). Impact energy dissipation and quantitative models of injection molded short fiber-reinforced thermoplastics. Polymers, 15.","DOI":"10.3390\/polym15214297"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"134205","DOI":"10.1103\/PhysRevB.76.134205","article-title":"Effective dynamic mass density of composites","volume":"76","author":"Mei","year":"2007","journal-title":"Phys. Rev. B"},{"key":"ref_27","unstructured":"(2022). Plastics\u2014Determination of the Melt Mass-Flow Rate (MFR) and Melt Volume\u2014Flow Rate (MVR) of Thermoplastics\u2014Part 1: Standard Method (Standard No. ISO 1133-1:2022)."},{"key":"ref_28","unstructured":"(2019). Plastics\u2014Determination of Flexural Properties (Standard No. ISO 178:2019)."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Takayama, T., and Oneda, S. (2026). Evaluation of mechanical properties and interface interactions in thermoplastic composites including discarded musical instrument reeds. Recycling, 11.","DOI":"10.3390\/recycling11030045"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Jiang, Q., Takayama, T., and Nishioka, A. (2024). Improving the accuracy of the evaluation method for the interfacial shear strength of fiber-reinforced thermoplastic polymers through the short beam shear test. Polymers, 16.","DOI":"10.3390\/polym16070883"},{"key":"ref_31","unstructured":"(2023). Plastics\u2014Determination of Charpy Impact Properties\u2014Part 1: Non-instrumented Impact Test (Standard No. ISO 179-1:2023)."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Da Silveira, P., Santos, M., Chaves, Y., Ribeiro, M., Marchi, B., Monteiro, S., Gomes, A., Tapanes, N., Pereira, P., and Bastos, D. (2023). Characterization of Thermo-Mechanical and Chemical Properties of Polypropylene\/Hemp Fiber Biocomposites: Impact of Maleic Anhydride Compatibilizer and Fiber Content. Polymers, 15.","DOI":"10.3390\/polym15153271"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/S0032-5910(02)00274-7","article-title":"Exponential formula for computing effective viscosity","volume":"129","author":"Cheng","year":"2003","journal-title":"Powder Technol."},{"key":"ref_34","first-page":"20","article-title":"Injection molding temperature dependence of elastic coefficients obtained using three-point bending tests to ascertain thermoplastic polymer coefficients","volume":"8","author":"Takayama","year":"2021","journal-title":"Mech. Eng. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"106353","DOI":"10.1016\/j.polymertesting.2020.106353","article-title":"Measurement of viscoelastic properties for polymers by nanoindentation","volume":"83","author":"Wang","year":"2020","journal-title":"Polym. Test."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103064","DOI":"10.1016\/j.mechmat.2019.103064","article-title":"Weld strength of injection molded short fiber reinforced polypropylene","volume":"136","author":"Takayama","year":"2019","journal-title":"Mech. Mater."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2","DOI":"10.6089\/jscm.48.2","article-title":"Interfacial Shear Strength Evaluation of Short-fiber-reinforced Polypropylene Using a Short Beam Method","volume":"48","author":"Quan","year":"2022","journal-title":"J. Jpn. Soc. Compos. Mater."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/0022-5096(60)90013-2","article-title":"Yielding of steel sheets containing slits","volume":"8","author":"Dugdale","year":"1960","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1002\/pen.760150611","article-title":"The determination of the fracture parameters for polymers in impact","volume":"15","author":"Plati","year":"1975","journal-title":"Polym. Eng. Sci."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/8\/917\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T12:33:43Z","timestamp":1775738023000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/8\/917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,9]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["polym18080917"],"URL":"https:\/\/doi.org\/10.3390\/polym18080917","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,9]]}}}