{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:49:09Z","timestamp":1788364149405,"version":"build-2803163510"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T00:00:00Z","timestamp":1615248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100007637","name":"Departamento Administrativo de Ciencia, Tecnolog\u00eda e Innovaci\u00f3n (COLCIENCIAS)","doi-asserted-by":"publisher","award":["Ph.D. National Scholarship program 647"],"award-info":[{"award-number":["Ph.D. National Scholarship program 647"]}],"id":[{"id":"10.13039\/100007637","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004245","name":"Universidad del Norte","doi-asserted-by":"publisher","award":["UN-OJ-2015-29312"],"award-info":[{"award-number":["UN-OJ-2015-29312"]}],"id":[{"id":"10.13039\/501100004245","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nanomaterials"],"abstract":"<jats:p>In this publication, molecular dynamics simulations are used to investigate the fracture behavior of single-crystal aluminum. The stress intensity factor is estimated by means of four different methods, the accuracy is assessed for each approach and the fracture toughness is estimated. The proposed methodology is also applied to estimate the fracture toughness for graphene and diamond using published data from other scientific articles. The obtained fracture toughness for the single-crystal aluminum is compared with other nanomaterials that have similar microstructures. Dislocation emission during the fracture simulation of the cracked nano-crystal of aluminum is analyzed to study the fracture behavior. Brittle fracture behavior is the predominant failure mode for the nanomaterials studied in this research.<\/jats:p>","DOI":"10.3390\/nano11030680","type":"journal-article","created":{"date-parts":[[2021,3,9]],"date-time":"2021-03-09T12:08:01Z","timestamp":1615291681000},"page":"680","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Fracture Toughness Estimation of Single-Crystal Aluminum at Nanoscale"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3649-0657","authenticated-orcid":false,"given":"Wilmer","family":"Velilla-D\u00edaz","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad Aut\u00f3noma del Caribe, Barranquilla 080020, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luis","family":"Ricardo","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad Aut\u00f3noma del Caribe, Barranquilla 080020, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4947-5659","authenticated-orcid":false,"given":"Argemiro","family":"Palencia","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad Aut\u00f3noma del Caribe, Barranquilla 080020, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Habib","family":"R. Zambrano","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, Universidad del Norte, Barranquilla 081007, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.commatsci.2018.05.006","article-title":"Effect of sample size, temperature and strain velocity on mechanical properties of plumbene by tensile loading along longitudinal direction: A molecular dynamics study","volume":"151","author":"Das","year":"2018","journal-title":"Comput. Mater. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109931","DOI":"10.1016\/j.commatsci.2020.109931","article-title":"On the elastic modulus, and ultimate strength of Ge, Ge-Si nanowires","volume":"185","author":"Peyada","year":"2020","journal-title":"Comput. Mater. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.msea.2017.05.057","article-title":"Tensile properties of AlCrCoFeCuNi glassy alloys: A molecular dynamics simulation study","volume":"698","author":"Afkham","year":"2017","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.commatsci.2016.03.018","article-title":"Influence of Cu precipitation on tensile properties of Fe-Cu-Ni ternary alloy at different temperatures by molecular dynamics simulation","volume":"118","author":"You","year":"2016","journal-title":"Comput. Mater. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.commatsci.2016.01.001","article-title":"Molecular dynamics simulation of temperature effect on tensile mechanical properties of single crystal tungsten nanowire","volume":"117","author":"Ma","year":"2016","journal-title":"Comput. Mater. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.commatsci.2017.07.003","article-title":"Molecular dynamics simulations of single crystal copper nanocubes under triaxial tensile loading","volume":"138","author":"Yang","year":"2017","journal-title":"Comput. Mater. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102691","DOI":"10.1016\/j.tafmec.2020.102691","article-title":"A computational study of the mixed\u2013mode crack behavior by molecular dynamics method and the multi\u2014Parameter crack field description of classical fracture mechanics","volume":"109","author":"Stepanova","year":"2020","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"102735","DOI":"10.1016\/j.tafmec.2020.102735","article-title":"Multi-scale numerical simulation of fracture behavior of nickel-aluminum alloy by coupled molecular dynamics and cohesive finite element method (CFEM)","volume":"109","author":"Ding","year":"2020","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.tafmec.2018.12.007","article-title":"A semi-empirical fracture model for silicon cleavage fracture and its molecular dynamics study","volume":"100","author":"Liu","year":"2019","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"113075","DOI":"10.1016\/j.cma.2020.113075","article-title":"A concurrent multiscale study of dynamic fracture","volume":"366","author":"Tong","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.cma.2016.04.005","article-title":"A comparative molecular dynamics-phase-field modeling approach to brittle fracture","volume":"312","author":"Patil","year":"2016","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engfracmech.2018.09.006","article-title":"Fracture properties of nanoscale single-crystal silicon plates: Molecular dynamics simulations and finite element method","volume":"202","author":"Wei","year":"2018","journal-title":"Eng. Fract. Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.engfracmech.2014.09.011","article-title":"Molecular dynamics study on the mode I fracture of calcium silicate hydrate under tensile loading","volume":"131","author":"Hou","year":"2014","journal-title":"Eng. Fract. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0966-9795(97)00048-4","article-title":"Atomistic simulation of fracture in CoAl and FeAl","volume":"6","author":"Shastry","year":"1998","journal-title":"Intermetallics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8596","DOI":"10.1038\/srep08596","article-title":"Breakdown of Continuum Fracture Mechanics at the Nanoscale","volume":"5","author":"Shimada","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.engfracmech.2015.08.043","article-title":"Application of CTOD in atomistic modeling of fracture","volume":"150","author":"Skogsrud","year":"2015","journal-title":"Eng. Fract. Mech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/j.jmps.2016.05.005","article-title":"From yield to fracture, failure initiation captured by molecular simulation","volume":"95","author":"Brochard","year":"2016","journal-title":"J. Mech. Phys. Solids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/(ASCE)NM.2153-5477.0000130","article-title":"Mode-I Fracture Toughness Prediction of Diamond at the Nanoscale","volume":"7","author":"Ferdous","year":"2017","journal-title":"J. Nanomech. Micromech."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.commatsci.2016.12.023","article-title":"Molecular dynamics study of fracture toughness and trans-intergranular transition in bi-crystalline graphene","volume":"129","author":"Han","year":"2017","journal-title":"Comput. Mater. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1007\/s11837-014-0978-z","article-title":"Bulk nanocrystalline metals: Review of the current state of the art and future opportunities for copper and copper alloys","volume":"66","author":"Tschopp","year":"2014","journal-title":"Miner. Met. Mater. Soc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1473","DOI":"10.1016\/j.ijfatigue.2010.01.006","article-title":"Nanostructurally small cracks (NSC): A review on atomistic modeling of fatigue","volume":"32","author":"Horstemeyer","year":"2010","journal-title":"Int. J. Fatigue"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.eml.2015.01.007","article-title":"Molecular mechanics of polycrystalline graphene with enhanced fracture toughness","volume":"2","author":"Jung","year":"2015","journal-title":"Extrem. Mech. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1166\/jnn.2005.414","article-title":"Atomistic simulations of J-integral in 2D graphene nanosystems","volume":"5","author":"Jin","year":"2005","journal-title":"J. Nanosci. Nanotechnol."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhuo, X.R., Kim, J.H., and Beom, H.G. (2018). R-curve Evaluation of Copper and Nickel Single Crystals Using Atomistic Simulations. Crystals, 8.","DOI":"10.3390\/cryst8120441"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Anderson, T.L. (2005). Fracture Mechanics, Taylor & Francis. [3rd ed.].","DOI":"10.1201\/9781420058215"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1007\/s10853-006-0968-9","article-title":"Review on the fracture processes in nanocrystalline materials","volume":"42","year":"2007","journal-title":"J. Mater. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.tafmec.2018.03.014","article-title":"Atomic-scale mode separation for mixed-mode intergranular fracture in polycrystalline metals","volume":"96","author":"Mai","year":"2018","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Lee, G.H., Kim, J.H., and Beom, H.G. (2020). Cohesive Zone Modeling of Crack Propagation in FCC Single Crystals via Atomistic Simulations. Metals Mater. Int.","DOI":"10.1007\/s12540-020-00693-x"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1115\/1.3601206","article-title":"A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks","volume":"35","author":"Rice","year":"1968","journal-title":"J. Appl. Mech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.commatsci.2019.05.031","article-title":"The role of the grain boundary in the fracture toughness of aluminum bicrystal","volume":"167","author":"Zambrano","year":"2019","journal-title":"Comput. Mater. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1088\/0953-8984\/25\/15\/155402","article-title":"The application of an atomistic J -integral to a ductile crack","volume":"25","author":"Zimmerman","year":"2013","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2621","DOI":"10.1016\/j.commatsci.2011.04.004","article-title":"Crack Tip Opening Displacement in atomistic modeling of fracture of silicon","volume":"50","author":"Thaulow","year":"2011","journal-title":"Comput. Mater. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.msea.2016.12.060","article-title":"Effect of crystallographic orientation on nanomechanical modelling of an iron single crystal cracked cantilever beam","volume":"685","author":"Skogsrud","year":"2017","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcph.1995.1039","article-title":"Fast Parallel Algorithms for Short\u2013Range Molecular Dynamics","volume":"117","author":"Plimpton","year":"1995","journal-title":"J. Comput. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1080\/14786430802206482","article-title":"Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu","volume":"88","author":"Mendelev","year":"2008","journal-title":"Philos. Mag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1016\/j.commatsci.2016.02.032","article-title":"Molecular dynamics simulations of crack growth behavior in Al in the presence of vacancies","volume":"117","author":"Chandra","year":"2016","journal-title":"Comput. Mater. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.msea.2016.04.077","article-title":"Molecular dynamics simulation of grain boundary geometry on crack propagation of bi-crystal aluminum","volume":"666","author":"Fang","year":"2016","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.commatsci.2017.01.023","article-title":"An atomistic insight into the fracture behavior of bicrystal aluminum containing twist grain boundaries","volume":"130","author":"Chandra","year":"2017","journal-title":"Comput. Mater. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"6443","DOI":"10.1103\/PhysRevB.29.6443","article-title":"Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals","volume":"29","author":"Daw","year":"1984","journal-title":"Phys. Rev. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1557\/PROC-409-75","article-title":"Molecular statics simulation of crack propagation in a-fe using eam potentials","volume":"409","author":"Shastry","year":"1996","journal-title":"Mat. Res. Soc. Symp. Proc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S1359-6462(98)00193-6","article-title":"Fracture toughness from atomistic simulations: Brittleness induced by emission of sessile dislocations","volume":"39","author":"Farkas","year":"1998","journal-title":"Scr. Mater."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"106848","DOI":"10.1016\/j.engfracmech.2019.106848","article-title":"Micro-structural aspects of fatigue crack propagation in atomistic-scale via the molecular dynamics analysis","volume":"226","author":"Yasbolaghi","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1063\/1.3245303","article-title":"General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions","volume":"131","author":"Thompson","year":"2009","journal-title":"J. Chem. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"041111","DOI":"10.1063\/1.3215722","article-title":"VORO ++: A three-dimensional Voronoi cell library in C ++","volume":"19","author":"Rycroft","year":"2009","journal-title":"Chaos"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Stukowski, A. (2010). Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng., 18.","DOI":"10.1088\/0965-0393\/18\/1\/015012"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"085007","DOI":"10.1088\/0965-0393\/20\/8\/085007","article-title":"Automated identification and indexing of dislocations in crystal interfaces","volume":"20","author":"Stukowski","year":"2012","journal-title":"Model. Simul. Mater. Sci. Eng."},{"key":"ref_47","unstructured":"Dowling, N. (2012). Mechanical Behavior of Materials, Pearson. [4th ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevB.83.214113","article-title":"Roles of grain boundaries in improving fracture toughness of ultrafine-grained metals","volume":"83","author":"Shimokawa","year":"2011","journal-title":"Phys. Rev. B Condens. Matter Mater. Phys."},{"key":"ref_49","first-page":"1","article-title":"Molecular Dynamics Study of Uniaxial Deformation in Perfect and Defective Aluminum","volume":"53","author":"Tang","year":"2015","journal-title":"Chin. J. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Alabd Alhafez, I., Ruestes, C.J., and Urbassek, H.M. (2018). Size of the Plastic Zone Produced by Nanoscratching. Tribol. Lett., 66.","DOI":"10.1007\/s11249-017-0967-9"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"15697","DOI":"10.1016\/j.ijhydene.2020.04.062","article-title":"Atomistic simulation of hydrogen-induced plastic zone compression during cyclic loading","volume":"45","author":"Xing","year":"2020","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_52","first-page":"1","article-title":"Fracture toughness of graphene","volume":"5","author":"Zhang","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1126\/science.1157996","article-title":"Measurement of the elastic properties and intrinsic strength of monolayer graphene","volume":"321","author":"Lee","year":"2008","journal-title":"Science"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"6444","DOI":"10.1016\/j.tsf.2008.03.005","article-title":"Plane stress fracture toughness of freestanding nanoscale thin films","volume":"516","author":"Hosokawa","year":"2008","journal-title":"Thin Solid Film."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1021\/nl4040362","article-title":"Shape- and Symmetry-Dependent Mechanical Properties of Metallic Gold and Silver on the Nanoscale","volume":"14","author":"Mahmoud","year":"2014","journal-title":"Nano Lett."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1016\/j.commatsci.2017.05.011","article-title":"Mixed-mode fracture toughness evaluation of a copper single crystal using atomistic simulations","volume":"136","author":"Cui","year":"2017","journal-title":"Comput. Mater. Sci."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Xu, G.Q., and Demkowicz, M.J. (2020). Computing critical energy release rates for fracture in atomistic simulations. Comput. Mater. Sci., 181.","DOI":"10.1016\/j.commatsci.2020.109738"}],"container-title":["Nanomaterials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-4991\/11\/3\/680\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:35:34Z","timestamp":1760160934000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-4991\/11\/3\/680"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,9]]},"references-count":57,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["nano11030680"],"URL":"https:\/\/doi.org\/10.3390\/nano11030680","relation":{},"ISSN":["2079-4991"],"issn-type":[{"value":"2079-4991","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,9]]}}}