IJE TRANSACTIONS C: Aspects Vol. 28, No. 3 (March 2015) 433-439   

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H. Moshrefzadeh-Sani, B. Saboori and M. Alizadeh
( Received: November 17, 2013 – Accepted: January 30, 2015 )

Abstract    In this paper, a continuum model is proposed so that a Stone-Wales (SW) defected carbon nanotube (CNT) is replaced by an initial circumferential crack in a continuum cylindrical shell. For this purpose, the critical energy release rate and then the fracture toughness of a defected CNT are calculated using the results of an existing atomistic-based continuum finite element simulation. Finally, the equivalent crack length is obtained from the fracture toughness. The proposed model can be applicable tovarious kinds of continuum-based simulations of nano-structures like nano-composites and nano-probes where the fracture resistance studies become important. It is concluded for a case study that the armchair (12, 12) CNT containing a SW defect could be replaced with a continuum cylindrical shell with a circumferential crack length of 0.83 nm. Furthermore, the damage variable is discussed to achieve a method for estimating the effective Young's modulus of defected nanotubes with numerous defects subjected to the progressive damage. This estimation method is evaluated by the atomistic based FE simulation of a double defected CNT.


Keywords    nanotube, continuum model, fracture toughness, energy release rate, damage


چکیده    در این مقاله یک مدل محیط پیوسته برای شبیه سازی نانولوله­ی حاوی خرابی از نوع استونوالس ارائه می­شود. بدین منظور نانولوله­ی تک جداره با یک استوانه­یجدارنازک حاوی یک ترک با طول مشخص جایگزین می­شود. از همین رو نرخ انرژی رهایی بحرانی و چقرمگی شکست یک نانولوله­ی حاوی خرابی استون­والس بر اساس یکی از مطالعات قبلی با استفاده از روش مکانیک ساختارمولکولی محاسبه شده و براساس آن طول ترکی محاسبه می­شود که می­تواند جایگزین این خرابی در یک استوانه­ی معادل توخالی شود. این مدل می­تواند در بسیاری از شبیه­سازی­های نانولوله که از روش محیط پیوسته استفاده می­کنند و در آنها در نظر گرفتن خرابی استون­والس دارای اهمیت است (مانند شبیه سازی نانوکامپوزیت­ها و نانوحس­گرها) مورد استفاده قرار گیرد. این مطالعه به طور موردی برای یک نانولوله­ی (12و12) انجام پذیرفت و مشخص شد طول ترکی که می­تواند جایگزین خرابی استون­والس شود باید دارای طول 83/0 نانومتر باشد. علاوه بر این، در این مقاله پارامتر خرابی مورد بررسی قرار گرفت و روشی برای تخمین مدولیانگنانولوله­ی حاوی چندین خرابی به دست آمد. ارزیابی این روش با نتایج حاصل از مطالعات مکانیک ساختار مولکولی حکایت از دقت مناسب این روش دارد.


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