{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T11:55:09Z","timestamp":1792842909058,"version":"4.5.0"},"reference-count":44,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T00:00:00Z","timestamp":1766275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fund of the Ministry of Education","award":["8091B012201"],"award-info":[{"award-number":["8091B012201"]}]},{"name":"Tsinghua University\u2014Mercedes Benz Institute for Sustainable Mobility","award":["20223910001"],"award-info":[{"award-number":["20223910001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>A multiscale model is developed to investigate the mechanical behavior and failure of in situ particle reinforced titanium matrix composites (PTMCs). Through the microstructural observation of the heterogeneous microscopic and mesoscopic structures in the in situ TiB\/Ti55531 composites, multiscale heterogeneous models coupled to the finite element method are employed to simulate the mechanical behaviors and failures. In the atomic scale, molecular dynamics (MD) simulations are applied to determine the traction-separation (T-S) responses of the cohesive zone model (CZM) describing the Ti\/TiB interface. Then, the mesoscale representative volume element (RVE) model with heterogeneous structure, including the Ti55531 matrix, the TiB particles, and their interfaces represented by the parameterized CZM, is established. The volume fraction and distribution morphology of TiB particles result from the microstructural analysis of titanium matrix composites. The simulation results show that the Young\u2019s modulus, tensile strength and elongation of multiscale are in excellent agreement with experimental results. The stress transfer, damage evolution and fracture behavior of the TiB particles in the composites are also analyzed using this multiscale approach.<\/jats:p>","DOI":"10.3390\/ma19010035","type":"journal-article","created":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T11:30:18Z","timestamp":1766489418000},"page":"35","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multiscale Modeling Analysis of the Mechanical Behaviors and Failures of In Situ Particle Reinforced Titanium Matrix Composites Based on Microstructural Characteristics"],"prefix":"10.3390","volume":"19","author":[{"given":"Xixi","family":"Geng","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kejian","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyang","family":"Liao","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhipeng","family":"Li","sequence":"additional","affiliation":[{"name":"Avic Shenyang Aircraft Design & Research Institute, Shenyang 110035, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhipeng","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qu","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112392","DOI":"10.1016\/j.compositesb.2025.112392","article-title":"Microstructure and mechanical properties of nano TiB whisker-reinforced titanium matrix composites using atomized Ti\u2013TiB composite powder as raw materials","volume":"298","author":"Liu","year":"2025","journal-title":"Compos. Part B Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2000688","DOI":"10.1002\/adma.202000688","article-title":"Multiscale Architecture and Superior High-Temperature Performance of Discontinuously Reinforced Titanium Matrix Composites","volume":"33","author":"Huang","year":"2021","journal-title":"Adv. Mater."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1002\/(SICI)1527-2648(200003)2:3<85::AID-ADEM85>3.0.CO;2-U","article-title":"Titanium Particulate Metal Matrix Composites\u2014Reinforcement, Production Methods, and Mechanical Properties","volume":"2","author":"Gofrey","year":"2000","journal-title":"Adv. Eng. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.wear.2014.05.013","article-title":"Microstructure and friction\/wear behavior of (TiB+TiC) particulate-reinforced titanium matrix composites","volume":"318","author":"Choi","year":"2014","journal-title":"Wear"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.compositesb.2019.01.080","article-title":"In-situ TiB\/Ti-6Al-4V composites with a tailored architecture produced by hot isostatic pressing: Microstructure evolution, enhanced tensile properties and strengthening mechanisms","volume":"164","author":"Cai","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"178215","DOI":"10.1016\/j.jallcom.2024.178215","article-title":"In-situ TiB reinforced titanium matrix composite coatings prepared by laser cladding: Effect of TiB2 content on microstructure, hardness and wear properties","volume":"1010","author":"Li","year":"2025","journal-title":"J. Alloys Compd."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.msea.2016.10.001","article-title":"Development of a molecular dynamic based cohesive zone model for prediction of an equivalent material behavior for Al\/Al2O3 composite","volume":"679","author":"Sazgar","year":"2017","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/j.matdes.2018.05.054","article-title":"Molecular dynamics-based cohesive zone representation of Ti6Al4V\/TiC composite interface","volume":"155","author":"Elkhateeb","year":"2018","journal-title":"Mater. Des."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"114397","DOI":"10.1016\/j.compstruct.2021.114397","article-title":"A molecular dynamics based cohesive zone model for interface failure under monotonic tension of 3D four direction SiCf\/SiC composites","volume":"274","author":"Wang","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"33185","DOI":"10.1016\/j.ceramint.2022.07.259","article-title":"Investigating the strength of Ti\/TiB interfaces at multiple scales using density functional theory, molecular dynamics, and cohesive zone modeling","volume":"48","author":"Attarian","year":"2022","journal-title":"Ceram. Int."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"180981","DOI":"10.1016\/j.jallcom.2025.180981","article-title":"Microscopic structural modeling and mechanical behavior of titanium boride reinforced titanium matrix composites with network configuration","volume":"1031","author":"Liu","year":"2025","journal-title":"J. Alloys Compd."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"141245","DOI":"10.1016\/j.msea.2021.141245","article-title":"Additive manufacturing of high strength near \u03b2 titanium alloy Ti-55511 by engineering nanoscale secondary \u03b1 laths via in-situ heat treatment","volume":"814","author":"Li","year":"2021","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.powtec.2018.09.088","article-title":"In-situ preparation and formation of TiB\/Ti-6Al-4V nanocomposite via laser additive manufacturing: Microstructure evolution and tribological behavior","volume":"342","author":"Cai","year":"2019","journal-title":"Powder Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1021\/cg050443k","article-title":"Growth Mechanism of In Situ TiB Whiskers in Spark Plasma Sintered TiB\/Ti Metal Matrix Composites","volume":"6","author":"Feng","year":"2006","journal-title":"Cryst. Growth Des."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1080\/14786435.2010.533134","article-title":"Nucleation and growth of \u03b1-Ti on TiB precipitates in Ti-15Mo-2.6Nb-3Al-0.2Si-0.12B","volume":"91","author":"Sasaki","year":"2011","journal-title":"Philos. Mag."},{"key":"ref_16","unstructured":"(2021). Metallic Materials\u2014Tensile Testing\u2014Part 1: Method of Test at Room Temperature (Standard No. GB\/T 228.1-2021)."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"128099","DOI":"10.1016\/j.molliq.2025.128099","article-title":"Molecular dynamics simulation of microstructure and surface tension in Fe-C-N-Ti quaternary molten steel system","volume":"435","author":"Luo","year":"2025","journal-title":"J. Mol. Liq."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"110875","DOI":"10.1016\/j.commatsci.2021.110875","article-title":"Development of a 2NN-MEAM potential for TiB system and studies of the temperature dependence of the nanohardness of TiB2","volume":"201","author":"Attarian","year":"2022","journal-title":"Comput. Mater. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108522","DOI":"10.1016\/j.compositesa.2024.108522","article-title":"Achieving ultra-high strength in TiB\/metastable-\u03b2 composites via short-process technology","volume":"188","author":"Zhang","year":"2025","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS\u2014A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales","volume":"271","author":"Thompson","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1088\/0965-0393\/18\/1\/015012","article-title":"Visualization and analysis of atomistic simulation data with OVITO\u2013the Open Visualization Tool","volume":"18","author":"Stukowski","year":"2010","journal-title":"Model. Simul. Mater. Sci. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1103\/PhysRevA.31.1695","article-title":"Canonical dynamics: Equilibrium phase-space distributions","volume":"31","author":"Hoover","year":"1985","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1063\/1.447334","article-title":"A unified formulation of the constant temperature molecular dynamics methods","volume":"81","year":"1984","journal-title":"J. Chem. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4671","DOI":"10.1016\/j.actamat.2009.06.023","article-title":"Molecular-dynamics-based cohesive zone law for brittle interfacial fracture under mixed loading conditions: Effects of elastic constant mismatch","volume":"57","author":"Zhou","year":"2009","journal-title":"Acta Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.compositesa.2010.12.005","article-title":"Molecular dynamics based cohesive zone law for describing Al\u2013SiC interface mechanics","volume":"42","author":"Dandekar","year":"2011","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112987","DOI":"10.1016\/j.mtcomm.2025.112987","article-title":"A randomized sequential dynamic adsorption algorithm for generating statistically equivalent composite material RVEs","volume":"47","author":"Zhang","year":"2025","journal-title":"Mater. Today Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.pmatsci.2018.02.003","article-title":"Generation of 3D representative volume elements for heterogeneous materials: A review","volume":"96","author":"Bargmann","year":"2018","journal-title":"Prog. Mater. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1007\/s12221-019-1178-9","article-title":"Study of the Effectiveness of the RVEs for Random Short Fiber Reinforced Elastomer Composites","volume":"20","author":"Chen","year":"2019","journal-title":"Fibers Polym."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.compstruct.2015.11.039","article-title":"On the generation of RVE-based models of composites reinforced with long fibres or spherical particles","volume":"138","author":"Catalanotti","year":"2016","journal-title":"Compos. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"112933","DOI":"10.1016\/j.ijsolstr.2024.112933","article-title":"FE modeling to generate composite RVEs with high volume fractions and various shapes of inclusions","volume":"300","author":"Tian","year":"2024","journal-title":"Int. J. Solids Struct."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Fu, W., Ma, J., Liao, Z., Xiong, H., Fu, Y., and Wang, B. (2023). New Numerical Method Based on Linear Damage Evolution Law for Predicting Mechanical Properties of TiB2 \/6061Al. Materials, 16.","DOI":"10.20944\/preprints202305.1750.v1"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/S0921-5093(01)00910-8","article-title":"Microstructure and tensile properties of in situ (TiB+TiC)\/Ti6242 (TiB:TiC=1:1) composites prepared by common casting technique","volume":"311","author":"Lu","year":"2001","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/S0167-577X(00)00395-5","article-title":"Mechanical properties of hybrid reinforced aluminum based composites","volume":"49","author":"Ge","year":"2001","journal-title":"Mater. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0010-4361(95)91381-E","article-title":"A combined microstructure strengthening analysis of SiCp\/Al metal matrix composites","volume":"26","author":"Sekine","year":"1995","journal-title":"Composites"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"107115","DOI":"10.1016\/j.compositesb.2019.107115","article-title":"3D micromechanical simulation of the mechanical behavior of an in-situ Al3Ti\/A356 composite","volume":"176","author":"Ma","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.jart.2016.11.001","article-title":"Ti-5Al-5Mo-5V-3Cr and similar Mo equivalent alloys: First principles calculations and experimental investigations","volume":"15","author":"Manda","year":"2017","journal-title":"J. Appl. Res. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"168616","DOI":"10.1016\/j.jallcom.2022.168616","article-title":"Effects of post heat treatment on microstructure and mechanical properties of Ti5553 parts made by laser powder bed fusion","volume":"938","author":"Ramachandiran","year":"2023","journal-title":"J. Alloys Compd."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3836","DOI":"10.1111\/j.1551-2916.2006.01280.x","article-title":"Elastic Properties of Titanium Monoboride Measured by Nanoindentation","volume":"89","author":"Guojian","year":"2006","journal-title":"J. Am. Ceram. Soc."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.scriptamat.2009.03.054","article-title":"Assessment of in situ TiB whisker tensile strength and optimization of TiB-reinforced titanium alloy design","volume":"61","author":"Boehlert","year":"2009","journal-title":"Scr. Mater."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.compscitech.2010.11.029","article-title":"Effect of porosity on the interface behavior of an Al2O3\u2013aluminum composite: A molecular dynamics study","volume":"71","author":"Dandekar","year":"2011","journal-title":"Compos. Sci. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"179365","DOI":"10.1016\/j.jallcom.2025.179365","article-title":"Actual microstructure-based modeling and failure evolution of SiC and SiC+B4C reinforced Al matrix composites","volume":"1020","author":"Baig","year":"2025","journal-title":"J. Alloys Compd."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"115425","DOI":"10.1016\/j.compstruct.2022.115425","article-title":"Multiscale 3D finite element analysis of aluminum matrix composites with nano&micro hybrid inclusions","volume":"288","author":"Peng","year":"2022","journal-title":"Compos. Struct."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jmst.2021.12.068","article-title":"Elastoplastic analysis of AA7075-O aluminum sheet by hybrid micro-scale representative volume element modeling with really-distributed particles and in-situ SEM experimental testing","volume":"123","author":"Sun","year":"2022","journal-title":"J. Mater. Sci. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compscitech.2015.11.014","article-title":"3D Microstructure-based finite element modeling of deformation and fracture of SiCp\/Al composites","volume":"123","author":"Zhang","year":"2016","journal-title":"Compos. Sci. Technol."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/1\/35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T11:36:57Z","timestamp":1766489817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/19\/1\/35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,21]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["ma19010035"],"URL":"https:\/\/doi.org\/10.3390\/ma19010035","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,21]]}}}