2016
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Effect of Material Gradient on Stresses of FGM Rotating ThickWalled Cylindrical Pressure Vessel with Longitudinal Variation of Properties under Nonuniform Internal and External Pressure
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The present paper provides a semianalytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under nonuniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the existence of shear stress in the thick cylindrical shell due to material and pressure changes along the axial direction, the governing equations are obtained based on firstorder shear deformation theory (FSDT). These equations are in the form of a set of general differential equations with variable coefficients. Given that the FG cylinder is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The problem was also solved, using the finite element method (FEM), the results of which were compared with those of the multilayered method (MLM). Finally, some numerical results are presented to study the effects of applied pressure, nonhomogeneity index, and power law index of FGM on the mechanical behavior of the cylindrical shell.
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Mehdi
Jabbari
Mechanical Engineering Department, Yasouj University, Yasouj, Iran
Mechanical Engineering Department, Yasouj
Iran
smehdi.jabbari@gmail.com


Mohammad
Zamani Nejad
Mechanical Engineering Department, Yasouj University, Yasouj, Iran.
Mechanical Engineering Department, Yasouj
Iran
m_zamani@yu.ac.ir


Mehdi
Ghannad
Mechanical Engineering Faculty, Shahrood University, Shahrood, Iran
Mechanical Engineering Faculty, Shahrood
Iran
ghannad.mehdi@gmail.com
Thick cylindrical shell
Functionally graded material (FGM)
Multilayered method (MLM)
Longitudinal variation of properties
Nonuniform pressure
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Ghannad, “Thermoelastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading”, Int. J. Eng. Sci., Vol. 96, 2015, pp. 1–18. ##[6] G. Lamé, B. Clapeyron, “Mémoire sur l'équilibre intérieur des corps solides homogènes”, Journal für die reine und angewandte Mathematik, 1831, pp. 145169. ##[7] P. M. Naghdi, R. M. Cooper, “Propagation of elastic waves in cylindrical shells, including the effects of transverse shear and rotatory inertia”, J. Acous. Soc. America, Vol. 28, no. 1, 1956, pp. 5663. ##[8] I. Mirsky, G. Hermann, “Axially motions of thick cylindrical shells”, J. Appl. Mech., Vol. 25, 1958, pp. 97102. ##[9] F. Erdogan, G. Gupta, “The stress analysis of multilayered composites with a flaw”,, Int. J. Solids Struct., Vol. 7, no. 1, 1971, pp. 3961 ##[10] K. Shirakawa, “Displacements and stresses in cylindrical shells based on an improved theory”, Int. J. Mech. Sci., Vol. 26, no. 2, 1984, pp. 93103. ##[11] J. 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Commun., Vol. 33, no. 5, 2006, pp. 681691. ##[17] J. H. Kang, “Field equations, equations of motion, and energy functionals for thick shells of reVolution with arbitrary curvature and variable thickness from a threedimensional theory”, Acta Mech., Vol. 188, no. 12, 2007, pp. 2137. ##[18] M. Z. Nejad, G. H. Rahimi, M. Ghannad, “Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system”, Mechanika, Vol. 77, no. 3, 2009, pp. 1826. ##[19] H. Santos, C. M. M. Soares, C. A. M. Soares, J. N. Reddy, “A semianalytical finite element model for the analysis of cylindrical shells made of functionally graded materials”, Compos. Struct., Vol. 91, no. 4, 2009, pp. 427432. ##[20] N. Tutuncu, B. Temel, “A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres”, Compos. Struct., Vol. 91, no. 3, 2009, pp. 385390. ##[21] M. Z. Nejad, G. H. Rahimi, “Elastic analysis of FGM rotating cylindrical pressure vessels”, J. Chin. Ins. Eng., Vol. 33, no. 4, 2010, pp. 525530. ##[22] A. G. Arani, Z. K., M. R. M. Maraghi, A. R. Shajari, “Thermopiezomagnetomechanical stresses analysis of FGPM hollow rotating thin disk”, Int. J. Mech. Mater. Des., Vol. 6, 2011, pp. 341349, ##[23] M. Ghannad, M. Z. Nejad, “Complete elastic solution of pressurized thick cylindrical shells made of heterogeneous functionally graded materials”, Mechanika, Vol. 18, no. 6, 2012, pp. 640649. ##[24] V. V. Zozulya, “A highorder theory for functionally graded axially symmetric cylindrical shells”, Arc. App. Mech., Vol. 83, no. 3, 2013, pp. 331343. ##[25] M. Ghannad, M. Z. Nejad, “Elastic analysis of pressurized thick hollow cylindrical shells with clampedclamped ends”, Mechanika, Vol. 5, no. 85, 2010, pp. 1118. ##[26] M. Ghannad, M. Z. Nejad, “Elastic solution of pressurized clampedclamped thick cylindrical shells made of functionally graded materials”, J. Theor. App. Mech., Vol. 51, no. 4, 2013, pp. 10671079. ##[27] M. Ghannad, H. Gharooni, “Displacements and stresses in pressurized thick FGM cylinders with varying properties of power function based on HSDT”, J. Sol. Mech., Vol. 4, no. 3, 2012, pp. 237251. ##[28] M. J. Khoshgoftar, G. H. Rahimi, M. Arefi, “Exact solution of functionally graded thick cylinder with finite length under longitudinally nonuniform pressure”, Mech. Res. Commun., Vol. 51, 2013, pp. 6166. ##[29] M. Ghannad, G. H. Rahimi, M. Z. Nejad, “Determination of displacements and stresses in pressurized thick cylindrical shells with variable thickness using perturbation technique”, Mechanika, Vol. 18, no. 1, 2012, pp. 1421. ##[30] M. Ghannad, G. H. Rahimi, M. Z. Nejad, “Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials”, Comp. Part B Eng., Vol. 45, no. 1, 2013, pp. 388396. ##[31] K. Asemi, M. Salehi, M. Akhlaghi, “Elastic solution of a twodimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads”, Acta Mech., Vol. 217, no. 12, 2011, pp. 119134. ##[32] M. Z. Nejad, M. Jabbari, M. Ghannad, “A semianalytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using disk form multilayers”, Sci. Wor. J., 2014, Article ID, 932743, pp. 110. ##[33] A. G. Arani, E. Haghparast, Z. K. Maraghi, S. Amir, “Static stress analysis of carbon nanotube reinforced composite (CNTRC) cylinder under nonaxisymmetric thermomechanical loads and uniform electromagnetic fields”, Comp. Part B Eng., Vol. 68, 2014,136145. ##[34] R. C. Batra, “Material tailoring in finite torsional deformations of axially graded Mooney–Rivlin circular cylinder”, Math. Mech. Sol., Vol. 20, no. 2, 2015, pp. 183189. ##[35] M. Z. Nejad, M. Jabbari, M. Ghannad, “Elastic analysis of rotating thick cylindrical pressure vessels under nonuniform pressure: linear and nonlinear thickness”, Periodica Poly. Mech.Eng., Vol. 59, no. 2, 2015, pp. 573. ##[36] M. Shariati, H. Sadeghi, M. Ghannad, H. Gharooni, “Semi analytical analysis of FGM thickwalled cylindrical pressure vessel with longitudinal variation of elastic modulus under internal pressure”, J. Sol. Mech., Vol. 7, no. 2, 2015, pp. 131145. ##[37] S. Vlachoutsis, “Shear correction factors for plates and shells”, Int. J. Numer. Methods Eng., Vol. 33, 1992, pp. 1537–1552. ##G. R. Buchanan, C. B. Y. Yii, “Effect of symmetrical boundary conditions on the vibration of thick hollow cylinders”, App. Acou., Vol. 63, no. 5, 2002, pp. 547566.##]
Punch plastic deformation pipe cladding (PPDPC) as a novel tube cladding method
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This study presents a new mechanical tube cladding process named punch plastic deformation pipe cladding (PPDPC) based on local deformation by pressing a punch into the inner layer of the bimetal tube. To investigate the capability of the process, stainless steel tube (as the inner layer) is bonded to a carbon steel pipe (as the outer layer) to fabricate a bimetal pipe. Shear punch tests were used to evaluate the bond strength between layers. Also, optical microscopy (OM) was employed to investigate the bonding interface. Experimental results showed an excellent bonding at the interface of two layers. Shear punch test results showed that the bonding achieved from this new method is stronger than the conventional thermohydraulic cladding method. This process is influenced by several parameters including punch diameters, punch nose radius and the friction coefficient between the punch and cladding tube. The effects of these parameters were evaluated by finite element (FE) analysis. Good bonding, simplicity, lower cost and no change in the microstructure of the main pipe (outer layer) are the major advantages of this process.
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M.R.
Baghaei
University of Tehran
University of Tehran
Iran
mr.baghaei@alumni.ut.ac.ir


Ghader
Faraji
Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Department of Mechanical Engineering, College
Iran
ghfaraji@ut.ac.ir
Pipe cladding
Bimetal pipe
FEM
Experiment
[[1] F. Liu, J. Zheng, P. Xu, M. Xu, and G. Zhu, “Forming mechanism of doublelayered tubes by internal hydraulic expansion”, Int. J. Press. Vessel. Pip., vol. 81, no. 7, 2004, pp. 625–633. ##[2] N. R. Chitkara and A. Aleem, “Extrusion of axisymmetric bimetallic tubes: Some experiments using hollow billets and the application of a generalised slab method of analysis”, Int. J. Mech. Sci., vol. 43, no. 12, 2001, pp. 2857–2882. ##[3] J. S. Lee, H. T. Son, I. H. Oh, C. S. Kang, C. H. Yun, S. C. Lim, and H. C. Kwon, “Fabrication and characterization of TiCu clad materials by indirect extrusion”, J. Mater. Process. Technol., vol. 187–188, 2007, pp. 653–656. ##[4] Z. Chen, K. Ikeda, T. Murakami, T. Takeda, and J. X. Xie, “Fabrication of composite pipes by multibillet extrusion technique”, J. Mater. Process. Technol., vol. 137, 2003, pp. 10–16. ##[5] X. Sun, J. Tao, And X. Guo, “Bonding properties of interface in Fe/Al clad tube prepared by explosive welding”, Trans. Nonferrous Met. Soc. China, vol. 21, 2011, pp. 2175–2180. ##[6] N. Kahraman, B. Gülenç, and F. Findik, “Joining of titanium/stainless steel by explosive welding and effect on interface”, J. Mater. Process. Technol., vol. 169, 2005, pp. 127–133. ##[7] K. Bhanumurthy, “Development of tubular transition joints of aluminium/stainless steel by deformation diffusion bonding“, Mater. Sci. Technol., Vol. 22, 2006, pp. 321330. ##[8] Bhanumurthy K, Fotedar R K, Joyson D, Kale G B, Pappachan A L, Grover A K, Krishnan J. “Development of tubular transition joints of aluminium/stainless steel by deformation diffusion bonding“, Mater. Sci. Technol., Vol. 22, 2006, pp. 321330. ## [9] D. L. Sponseller, G. a. Timmons, and W. T. Bakker, “Development of Clad Boiler Tubes Extruded from Bimetallic Centrifugal Castings”, J. Mater. Eng. Perform., vol. 7, 1998, pp. 227–238. ##[10] S.H. Kim, H.W. Kim, K. Euh, J.H. Kang, and J.H. Cho, “Effect of wire brushing on warm roll bonding of 6XXX/5XXX/6XXX aluminum alloy clad sheets” , Mater. Des., vol. 35, 2012, pp. 290–295. ##[11] X. Li, G. Zu, Q. Deng, An Investigation of Deformation Behavior of Bimetal Clad Sheets by Asymmetrical Rolling at Room Temperature, Light Metals, 1rd ed., John Wiley & Sons, Inc., 2011, pp. 611. ##[12] V. Ocelík and J. T. M. De Hosson, Advances in Laser Materials Processing. 1rd ed., Elsevier, 2010, pp. 157. ##[13] X. Wang, P. Li, and R. Wang, “Study on hydroforming technology of manufacturing bimetallic CRAlined pipe”, Int. J. Mach. Tools Manuf., vol. 45, 2005, pp. 373–378. ##[14] M.A. Spence, C.V. Roscoe, “Bimetal CRAlined pipe employed for North Sea field development", Oil Gas J., vol. 97, 1999, pp. 80–88. ##[15] Z. L. Zhan, Y. D. He, D. Wang, and W. Gao, “Cladding inner surface of steel tubes with Al foils by ball attrition and heat treatment”, Surf. Coat. Technol., vol. 201, 2006, pp. 2684–2689. ##[16] R. Lapovok, H. P. Ng, D. Tomus, and Y. Estrin, “Bimetallic copperaluminium tube by severe plastic deformation", Scr. Mater., vol. 66, 2012, pp. 1081–1084. ##[17] M. S. Mohebbi and A. Akbarzadeh, “A novel spinbonding process for manufacturing multilayered clad tubes”, J. Mater. Process. Technol., vol. 210, 2010, pp. 510–517. ##[18] M. M. Samandari, K. Abrinia, and A. Akbarzadeh, “Production of Bilayer Al / St Tubes by Cold Spin Bonding and Investigation”, vol. 14, 2015, pp. 111–118. ##[19] T. Yoshida, S. Matsuda, and S. Matsui, “The development of corrosionresistant Tubing.” Offshore Technol., vol. 2, 1981, pp. 365–378,. ##[20] W.C. Chen, C.W. Petersen, “Corrosion performance of welded CRAlined pipes for flowlines", SPE Prod. Eng., vol. 7, 1992, pp. 375–378. ##[21] D. K. Russell and S. M. Wilhelm, “Analysis of bimetallic pipe for sour Service.” SPE Prod. Eng., vol. 7, 1991, pp. 291–296. ##[22] Internal tube cladding using plastic deformation, Patent no 84006, in persian. ##[23] G. Faraji, H.S. Kim, M. M. Mashhadi, “Microstructure inhomogeneity in ultrafine grained bulk AZ91 produced by accumulative back extrusion (ABE),” Mater. Sci. Eng. A, vol. 528, 2011, pp. 4312–4317. ##[24] G. Faraji, P. Yavari, S. Aghdamifar, M.M. Mashhadi, "Mechanical and microstructural properties of ultrafine grained AZ91 magnesium alloy tubes processed via multi pass tubular channel angular pressing (TCAP)", J. Mater. Sci. & Technol., vol. 30, no. 2, 2014, pp. 134–138. ##[25] G. Faraji, M.M. Mashhadi, A.R. Bushroa, A. Babaei, "TEM analysis and determination of dislocation densities in nanostructured copper tube produced via parallel tubular channel angular pressing process", Mater. Sci. Eng. A, vol. 563, 2013, pp. 193–198.##]
Evaluation of tribological properties of (Ti,Al)CN/DLC composite coatings deposited by cathodic arc method.
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In this study, Ti, Al and N doped DLC – referred to here after as “(Ti,Al)CN/DLC composite” coating and pure diamondlike coating (DLC) were produced by cathodic arc deposition technique and the effects of the coating thickness on their tribological properties were evaluated. The coatings were characterized, using scanning electron microscopy (SEM), atomic force microscopy (AFM), Xray diffraction (XRD) and Raman spectroscopy methods. The Raman and XRD patterns indicated that cathodic arc deposition method can potentially generate a composite coating consisting of TiC, Ti3AlN, Ti2N and Al2Ti crystalline phases dispersed in the amorphous carbon matrix. Moreover, friction and wear of the coatings were investigated, using pinondisc wear test method in ambient air. The results of wear test showed a desired tribological behavior of the (Ti,Al)CN/DLC composite coatings with low amounts of the mean coefficients of friction (0.2) and wear rate (9×108 mm3/N.m). In contrast with DLC coatings, it was also found that friction coefficient of the composite coated samples did not change significantly, when the thickness of the coating was increased from 1.5 to 3 μm.
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Laleh
Zahiri
Dep. of Mater. Eng.,
Fac. of Eng., Shahrekord Uni.,
Shahrekord, Iran
Dep. of Mater. Eng.,
Fac. of Eng., Shahrekord
Iran
laleh.zahiri@yahoo.com


Moahammad
saeri
Department Of Materials Eng., Faculty Of Eng., Shahrekord Uni., Shahrekord, Iran. Email: Saeri_Mohammad@Yahoo.com
Department Of Materials Eng., Faculty Of
Iran
saeri_mohammad@yahoo.com


Shahram
Alirezaee
NaghshE Jahan University, Baharestan, Isfahan, Iran. Email:
NaghshE Jahan University, Baharestan, Isfahan,
Iran
shahram79ir@yahoo.com


Alireza
Afkhami
M.Sc. in Materials Engineering, Researcher, Marine Industry,Department of Subsurface Vessels, Shahin Shahr, Isfahan, Iran.
M.Sc. in Materials Engineering, Researcher,
Iran
a.r.afkhami.aqda@iran.ir
DLC
composite coating
Friction
Wear
cathodic arc
[[1] T. Fu, Z.F. Zhou, Y.M. Zhou, X.D. Zhu, Q.F. Zeng, C.P. Wang, K.Y. Li and J. Lu, “Mechanical properties of DLC coating sputter deposited on surface nanocrystallized 304 stainless steel”, J Surf. Coat. Tech., Vol.207, 2012, pp. 555564. ##[2] A.M. Ladwig, R.D. Koch, E.G. Wenski and R.F. Hicks, “Atmospheric plasma deposition of diamondlike carbon coatings”, J. Diamond Related Mater., Vol. 18, 2009, pp.11291133. ##[3] C. Donnetand and A. Erdemir, “Tribology of DlC film Fundamentals and applications”, 2008, Springer, pp. 243316. ##[4] M. Moseler, P. Gumbsch, C. Casiraghi, A.C. Ferrari, J. Robertson, “The Ultrasmoothness of Diamondlike Carbon Surfaces” Surf. Sci., Vol. 309, 2005, pp. 15451548. ##[5] J. Choi, K. Soejima, T. Kato, M. Kawaguchi and W. Lee. “Nitriding of high speed steel by bipolar PBII for improvement in adhesion strength of DLC films” Nuclear Instrum. Methods. Phy. Res. Sec. B, Vol.272, 2012, pp. 357360. ##[6] S. Zhang, Y. Fu, H. Du, X.T. Zeng and Y.C. Liu, “Magnetron sputtering of nanocomposite (Ti,Cr)CN/DLC coatings”, J Surf. Coat. Tech., Vol. 162, 2002, pp. 4248. ##[7] C.F. Borges, E. Pfender and J. Heberlein, “Influence of nitrided and carbonitrided interlayers on enhanced nucleation of diamond on stainless steel 304”, J Diamond Relat Mater., Vol. 10, 2001, pp.19831990. ##Erdemir, C. Donnet, Topical review; Tribology of diamondlike carbon films: recent progress and future prospects, J. Phys. D: Appl. Phys., Vol. 39, 2006, p. R311. ##[8] S. Kukiełka, W. Gulbiñski, Y. Pauleau, S.N. Dub, J.J. Grob, “Composition, mechanical properties and friction behavior of nickel/hydrogenated amorphous carbon composite films”, Surf. Coat. Technol., Vol. 200, 2006, pp. 62586262. ##[9] D.Y. Wang, K.W. Weng, Ch.L. Chang, X.J. Guo, “Tribological performance of metal doped diamondlike carbon films deposited by cathodic arc evaporation.”, Diam. Relat. Mater., Vol. 9, 2000, pp. 831837. ##[10] X.M. He, M. Hakovirta, M. Nastasi, “Hardness, hydrophobic and optical properties of fluorine and boron coalloyed diamondlike carbon films.” Mat. Lett., Vol. 59, 2005, pp. 14171421. ##[11] K. Kato, “Wear In Relation To Friction — A Review”, J Wear, Vol. 241, 2000, pp. 151157. ##[12] W.P. Hsieh, “Characterization of the Tidoped diamondlike carbon coatings on a type 304 stainless steel”, J vacuum sci. tech., Vol. 17, 1999, pp. 10531058. ##[13] L. Wang, J.F. Su and X. Nie, “Corrosion and tribological properties and impact fatigue behaviors of TiN and DLCcoated stainless steels in a simulated body fluid environment”, J Sur. Coat. Tech., Vol. 205, 2010, pp. 15991605. ##[14] G. Cheng, D. Han, C. Liang, X. Wu and R. Zheng, “Influence of residual stress on mechanical properties of TiAlN thin films” J Surf. Coat. Tech., Vol. 228, 2013, pp. 328330. ##[15] J. Lapin, “TiAlbased alloys: Present status and future perspectives”, J Metal., Vol.5, 2009, pp. 1930. ##[16] C. Ruseta, E. Grigorea, G.A. Collinsb, K.T. Shortb, F. Rossic, N. Gibsonc, H. Dongd and T. Belld, “Characteristics of the Ti2N layer produced by an ion assisted deposition Method” J Surf. Coat. Tech., Vol. 174, 2003, pp. 698703. ##Tibrewala, “Piezoresistive Effect in Diamondlike Carbon Films”, 2006, Cuvillier Verlag, pp. 3336. ##[17] J. C. SánchezLópez, M. Belin, C. Donnet, C. Quiros and E. Elizalde, “Friction mechanisms of amorphous carbon nitride films under variable environments: a triboscopic study”, Surf. coat tech., Vol. 16, 2002, pp.138144. ##[18] R.A. Singh and E.S. Yoon, “Friction behaviour of diamondlike carbon films with varying mechanical properties”, J Surf. Coat. Tech., Vol. 201, 2006, pp, 43484351. ##[19] M. Sedlacek, B. Podornik, J. Vižintin, “Tribological properties of DLC coatings and comparison with test results: Development of a database”, Mater. Charact., vol. 59, 2008, pp. 151161. ##[20] K. Adachi, N. Sodeyama and K. Kato, “Effect of humidity on friction of carbonnitride coatings under N2 gas lubrication”, Proc. WTC II, WTC200564275, Sep.1216, 2005, Washington, D.C., USA. ##[21] R. Hauert, L. KnoblauchMeyer, G. Francz, A. Schroeder, E. Wintermantel, “Tailored aC: H coatings by nanostructuring and alloying”, Surf. Coat. Technol., Vol. 120121, 1999, pp. 291296. ##[22] J. Robertson, “Diamondlike amorphous carbon”, Mater. Sci. Eng. Report, Vol. 37, 2002, pp. 129281. ##[23] J. Neidhardt, Z. Czigany, I.F. Brunell, L. Hultman, “Growth of fullerenelike carbon nitride thin solid films by reactive magnetron sputtering; role of lowenergy ion irradiation in determining microstructure and mechanical properties.”, J Appl. Phys., Vol. 93, 2003, pp. 30023015. ##[24] I.A. Garcia, E. Berasategui, S.J. Bull, T.F. Page, J. Neidhardt, L. Hultman, N. Hellgren, “How hard is fullerenelike CNx Some observations from the nanoindentation response of a magnetronsputtered coating.”, Philos. Mag. A , Vol. 82, 2002, pp., 21332147. ##[25] R. Gilmore, R. Hauert, “Control of the tribological moisture sensitivity of diamondlike carbon films by alloying with F, Ti or Si.” Thin Solid Films, Vol. 398, 2001, pp. 199204. ##K.P. Shaha, Y.T. Pei, C.Q. Chen, J.Th.M. De Hosson, “Synthesis of ultrasmooth and ultralow friction DLC based nanocomposite films on rough substrates, Thin Solid Films”, Vol. 519, 2010, pp. 16181622.##]
Numerical Analysis of Severe Plastic Deformation by High Pressure Torsion
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Highpressure torsion (HPT) is a metal processing method in which the sample is subjected to a very high plastic shear deformation. This process can produce exceptional levels of grain refinement, and provides a corresponding improvement in mechanical properties. To investigate the stress and strain distribution due to HPT process finite element simulation were conducted to investigate effective parameters. The simulation results demonstrate that the lowest effective strain obtained in the centers of the disk and the highest at the edges. Also, the mean stress varies linearly from the center of the disk to the edge region. The compressive stresses are higher in the disk centers and lower at the edges. By increasing the friction coefficient and the die angle, mean stress decrease and stress variation along the disc diameters become more homogeneous. Increasing of the pressure load leads to increase the mean stress and its heterogeneity along the disc radius.
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mohammadreza
kaji
Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
Department of Mechanical Engineering, College
Iran
m.kaji@ut.ac.ir


Ghader
Faraji
Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
Department of Mechanical Engineering, College
Iran
ghfaraji@ut.ac.ir
Finite element modeling
High pressure torsion (HPT)
Stress and strain distribution
[References ##[1] G. Faraji, M. M. Mashhadi, S. H. Joo, H. S. Kim, "The role of friction in tubular channel angular pressing," Rev. Adv. Mater. Sci., Vol. 31, 2012, pp. 1218. ##[2] M. A. Meyers, A. Mishra, D.J. Benson, "Mechanical properties of nanocrystalline materials", Prog. Mater. Sci., Vol. 51, 2006, pp. 427556. ##[3] D. G. R. Willian D. Callister "Fundamental of materials science and engineering," 2010. ##[4] T.G.longdon, "the processing of ultra finegrained metal throught the application of several plastic deformation," J. Mater. Sci., Vol. 47, 2007, pp. 211216. ##[5] U. C. Patil Basavaraj V, T.S. Prasanna Kumarb, "Effect of geometric parameters on strain, strain inhomogeneity and peak pressure in equal channel angular pressing – A study based on 3D finite element analysis," J. Manuf. Processes., Vol. 261, 2014, pp. 1020. ##[6] T. G. L. Alexander P. Zhilyaev "Using highpressure torsion for metal processing: Fundamentals and applications," Prog. Mater. Sci., Vol. 53, 2008, pp. 893979. ##[7] M. L. Jung, G. Kim, N. Pardis, Yan E. Beygelzimer, Hyoung Seop Kim, "Finite element analysis of the plastic deformation in tandem process of simple shear extrusion and twist extrusion," Mater. Des., Vol. 83, 2015, pp. 858865. ##[8] M. N. M. Reihanian, "An analytical approach for necking and fracture of hard layer during accumulative roll bonding (ARB) of metallic multilayer," Mater. Des., Vol. 89, 2016, pp. 12131222. ##[9] G. Faraji, M. Ebrahimi, and A. R. Bushroa, "Ultrasonic assisted tubular channel angular pressing process," Mater. Sci. Eng., A, Vol. 599, 2014, pp. 1015. ##[10] A. Babaei, G. Faraji, M. Mashhadi, and M. Hamdi, "Repetitive forging (RF) using inclined punches as a new bulk severe plastic deformation method," Mater. Sci. Eng., A, Vol. 558, 2012, pp. 150157. ##[11] P. W. Bridgman, "Effects of High Shearing Stress Combined with High Hydrostatic Pressure," Phys. Rev, Vol. 48, 1935, pp. 825850. ##[12] P. H. R. P. Roberto, B. Figueiredo, M. Teresa, P. Aguilar, "Using finite element modeling to examine the temperature distribution in quasiconstrained highpressure torsion," Acta Mater., Vol. 60, 2012, pp. 13903198. ##[13] C. G. John, J. Jonas, "The equivalent strain in high pressure torsion," Mater. Sci. Eng., A, Vol. 607, 2014, pp. 530535. ##[14] G. Faraji, M. Mashhadi, A. Dizadji, and M. Hamdi, "A numerical and experimental study on tubular channel angular pressing (TCAP) process," J. Mech. Sci. Technol., Vol. 26, 2012, pp. 34633468. ##[15] D. Systèmes, Abaqus Documentation, ed, 2009. ##[16] P. R. C. Roberto, B. Figueiredoa, T. G. Langdonc,, "Using finite element modeling to examine the flow processes in quasiconstrained highpressure torsion," Mater. Sci. Eng., A, Vol. 528, 2011, pp. 81988204. ##[17] H. S. L. Kim H.S , Lee.YS, "deformation behavior of copper during High Pressure Torsion Processing," J. Mater. Process. Technol., Vol. 142, 2003, pp. 334337. ##[18] E. Y. Y. Dong Jun Lee, S. H. Lee, S. Y. Kang , Hyoung Seop Kim, "FINITE ELEMENT ANALYSIS FOR COMPRESSION BEHAVIOR OF HIGH PRESSURE TORSION PROCESSING," Rev.Adv. Mater, Vol. 31, 2012, pp. 2530. ##[19] E. Y. Y. Dong Jun Lee , D. H. Ahn , B. H. Park , H. W. Park , L. J. Park, "Dislocation densitybased finite element analysis of large strain deformation behavior of copper under highpressure torsion," Acta Mater., Vol. 76, 2014, pp. 281293.##]
Numerical Simulation of Fluid Flow over a Ceramic Nanoparticle in Drug Delivery System
2
2
In this work, for better understanding of drug delivery systems, blood flow over a ceramic nanoparticle is investigated through microvessels. Drug is considered as a nanoparticle coated with the rigid ceramic. Due to the low characteristic size in the microvessel, the fluid flow is not continuum and the noslip boundary condition cannot be applied. To solve this problem lattice Boltzmann method is used with the slip boundary condition on the particle surface. Furthermore, the effects of Reynolds number, Knudsen number and stiffness (which depends on the kind of material) on drag coefficient are investigated in this paper. The present results show that lattice Boltzmann method can be used accurately to simulate the effect of different parameters on drug delivery. Moreover, the results show that the accuracy of lattice Boltzmann method is the same as second slip boundary condition. Also, the effect of nanoparticle stiffness as the important parameter on the period of time to deliver drugs in system is demonstrated.
1

48
55


Mina
Alafzadeh
Academic center for education, culture and research (ACECR), Yazd branch
Academic center for education, culture and
Iran
m.alafzadeh@me.iut.ac.ir


Shahram
Talebi
Department of Mechanical Engineering, Yazd university Yazd, Iran
Department of Mechanical Engineering, Yazd
Iran
talebi_s@yazd.ac.ir


Mojdeh
Azizi
Academic center for education, culture and research (ACECR), Yazd branch
Academic center for education, culture and
Iran
mo.azizi@stu.yazd.ac.ir
Nanoparticle
slip boundary condition
Lattice Boltzmann method
Drug delivery
stiffness
[[1] Z. Wilczewska, K. Niemirowics, K. H. Markiewicz, H. Car, “ Nanoparticles as drug delivery systems”, Pharmacol. Rep., Vol. 64, 2012, pp. 10201037. ##[2] S. R. Mudshinge, A. B. Deore, S. Patil, Ch. M. Bhalgat, “Nanoparticles: Emerging carriers for drug delivery”, Sau. Pharm., Vol. 19, 2011, pp. 129141. ##[3] S. A. Kulkarni, S. S. Feng, “Effects of particle size and surface modification on cellular uptake and biodistribution of polymeric nanoparticles for drug delivery”, Pharm. Res., Vol. 30, 2013, pp. 25122522. ##Kumar, M. D. Graham, “ Segregation by membrane rigidity in flowing binary suspensions of elastic capsules”, Phys. Rev. E. Stat. Nonlin. Soft. Matter. Phys. , Vol. 84, 2011. ##[4] S. Shukla, F. J. Eber, A. S. Nagarajan, N. A. Difranco, N. Schmidt, A. M. Wen, S. Eiben, R. M. Twyman, C. Wege, N. F. Steinmetz, “ The impact of aspect ratio on the biodistribution and tumor homing of rigid softmatter nanorods”, Adv. Healthc. Mater, Vol. 4, 2015, pp. 874882. ##[5] Huang, P. J. Butler, S. Tong, H. S. Muddana, G. Bao, S. Zhang, “ Substrate stiffness regulates cellular uptake of nanoparticles”, Nano Lett., Vol. 4, 2013, pp. 16111615. ##[6] X. He, L. S. Luo, “Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation”, Phys. Rev. E, Vol.56, 1997, pp.68116817. ##[7] S. Succi, The lattice Boltzmann equation for fluid dynamics and beyond, Oxford University press, 2001. ##[8] T. S. Lee, H. Huang, Ch. Shu, “An axisymmetric incompressible lattice BGK model for simulation of the pulsatile flow in a circular pipe”, Int. J. Numer. Methods Fluids, Vol.49, 2005, pp.99116. ##[9] X. He, Q. Zou, “Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components”, J. Stat. Phys., Vol.87, 1995, pp.115136. ##[10] M. Bouzidi, M. Firdaouss., P. Lallemand, “Momentum transfer of Boltzmannlattice fluid with boundaries”, Phys. Fluids, vol.13, 2001, pp.34523459. ##[11] G. Karniadakis, A. Beskok, N. Aulru, Microflows and nanoflows fundamentals and simulation, Springer, 2005. ##[12] E. Cunningham, On the velocity of steady fall of spherical particles through fluid medium, Proc. R. Soc. Lond. A83, 1910, pp. 357365. ##[13] N. Davies, “Definite equation for the fluid resistance of spheres”, Proc. Phys. Soc., Vol. 57, 1945. ##[14] KoohyarVahidkhah, Nasser Fatouraee, “Numerical simulation of red blood cell ##[15] behavior in astenosed arteriole using the immersed boundary Lattice Boltzmann method”,Int. J. Numer. Meth.Biomed.Eng.., Vol. 28, 2011, pp.239256. ##[16] O. Filippova, D. Hanel, “Grid refinement for lattice BGK models”, J. Comput. Phys, vol. 147, 1998, pp. 219228. ##[17] F. W. White, Viscous fluid flow, McGrawHill, New York, 2006. ##[18] S. K. Stefanov, R. W. Barber, M. Ota, D. R. Emerson, “Comparison beween NavierStokes and DSMC calculations for low Reynolds number slip flow past a confined micro sphere”, 24th Symposium of Rarefied Gas Dynamics, American institute of physics,2005. ##[19] C.Guyton, J. E. Hall, Textbook of medical physiology, Elsevier Saunders, 2006. ##[20] Moshfegh, M. Shams, G. Ahmadi, R. Ebrahimi, “A novel surfaceslip correction for microparticles motion”, Collids and Surfaces A, Vol. 345, 2009, pp.321329. ##[21] Y. Geng, P. Dalhaimer, S. Cai, R. Tsai, M. Tewari, T. Minko, D.E. Discher, “ Shape effects of filaments versus spherical particles in flow and drug delivery”, Nat Nanotechnol, Vol. 2, 2007, pp. 249255.##]
Synthesis of nanostructured sphene and mechanical properties optimization of its scaffold via response surface methodology
2
2
Nanostructured sphene (CaTiSiO5) powder was synthesized via mechanical activation and heat treatment method. The synthesized powder was characterized by Xray diffraction (XRD), transmission electron microscopy (TEM), and simultaneous thermal analysis (STA). The sphene scaffolds were then fabricated via porogen method (using citric acid). Response surface methodology was successfully used to determine the effects of d (particle size) and %V porogen (volume percent of porogen) on the mechanical behavior of the prepared sphene scaffolds. Moreover, a suitable mathematical model for describing the relationship between the factors (d and %V porogen) and the response (compressive strength) was statistically developed. The use of porogen in the synthesis procedure can change the porosity value of the final scaffold; thus, the compressive strength of the sphene scaffolds varied widely. Statistical analysis results predicted that the maximum value of the compressive strength can be obtained at the following conditions: %V = 25% and d = 250 µm. At these conditions, the prepared scaffolds possess a compressive strength value as high as 7 MPa.
1

56
62


Amirmostafa
Amirjani
Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran
Department of Mining and Metallurgical Engineering
Iran
amirjani@aut.ac.ir;amirm.amirjani@gmail.com


Masoud
Hafezi
Nanotechnology and Advanced Materials Division, Materials and Energy Research Center, Iran
Nanotechnology and Advanced Materials Division,
Iran
mhafezi@merc.ac.ir


Ali
Zamanian
Nanotechnology and Advanced Materials Department, Materials and Energy Research Center, Alborz, Iran.
Nanotechnology and Advanced Materials Department,
Iran
ali.zamanian@merc.ac.ir


Mana
Yasaee
Department of Life Science Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran.
Department of Life Science Engineering, Faculty
Iran
mana.yasaee@gmail.com


Noor Azuan
Abu Osman
Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia.
Department of Biomedical Engineering, Faculty
Iran
azuan@um.edu.my
Bioceramics
Mechanochemical synthesis
Mechanical properties
Response surface methodology
[[1] J. Pantić, A. Kremenović, A. Došen, M. Prekajski, N. Stanković, Z. Baščarević, B. Matović, "Influence of mechanical activation on sphene based ceramic material synthesis", Ceram. Int., Vol. 39, No. 1, 2013, pp. 483488. ##[2] D. Clarke, "Ceramic materials for the immobilization of nuclear waste", Annu. Rev. Mater. Sci., Vol. 13, No. 1, 1983, pp. 191218. ##[3] Y. Teng, L. Wu, X. Ren, Y. Li, S. Wang, "Synthesis and chemical durability of Udoped sphene ceramics", J. Nucl. Mater., Vol. 444, No. 1, 2014, pp. 270273. ##[4] T. S. Lyubenova, F. Matteucci, A. Costa, M. Dondi, J. Carda, "Ceramic pigments with sphene structure obtained by both sprayand freezedrying techniques", Powder. Technol., Vol. 193, No. 1, 2009, pp. 15. ##[5] C. T. Wu, Y. Ramaswamy, D. Gale, W.R. Yang, K.Q. Xiao, L.C. Zhang, Y.B. Yin, H. Zreiqat, "Novel sphene coatings on Ti6Al4V for orthopedic implants using solgel method", Acta. Biomater. , Vol. 4, No. 3, 2008, pp. 569576. ##[6] C. Wu, Y. Ramaswamy, A. Soeparto, H. Zreiqat, "Incorporation of titanium into calcium silicate improved their chemical stability and biological properties", J. Biomed. Mater. Res. Part A., Vol. 86, No. 2, 2008, pp. 402410. ##[7] Y. Ramaswamy, C. Wu, C. R. Dunstan, B. Hewson, T. Eindorf, G. I. Anderson, H. Zreiqat, "Sphene ceramics for orthopedic coating applications: An in vitro and in vivo study", Acta. Biomater., Vol. 5, No. 8, 2009, pp. 31923204. ##[8] C. Wu, Y. Ramaswamy, X. Liu, G. Wang, H. Zreiqat, "Plasmasprayed CaTiSiO5 ceramic coating on Ti6Al4V with excellent bonding strength, stability and cellular bioactivity", J. R. Soc. Interface., Vol. 6, No. 31, 2009, pp. 159168. ##[9] M. Fathi, E. M. Zahrani, "Mechanical alloying synthesis and bioactivity evaluation of nanocrystalline fluoridated hydroxyapatite", J. Cryst. Growth., Vol. 311, No. 5, 2009, pp. 13921403. ##[10] S. H. Park, H. J. Kim, J. I. Cho, Optimal central composite designs for fitting second order response surface linear regression models, in Response Surface Linear Regression Models, PhysicaVerlag HD, Heidelberg, 2008, pp. 323329. ##[11] A. Amirjani, M. Bagheri, M. Heydari, S. Hesaraki, "Labelfree surface plasmon resonance detection of hydrogen peroxide; a bioinspired approach", Sens. Actuators. B, Vol. 227, 2016, pp. 373–382. ## [12] A. Amirjani, P. Marashi, D. H. Fatmehsari, "Effect of AgNO3 addition rate on aspect ratio of CuCl2–mediated synthesized silver nanowires using response surface methodology", Colloids. Surf., A, Vol. 444, 2014, pp. 3339. ##[13] A. Amirjani, P. Marashi, D. H. Fatmehsari, "Interactive effect of agitation rate and oxidative etching on growth mechanisms of silver nanowires during polyol process ", J. Exp. Nanosci., Vol. 10, 2015, pp. 13871400. ##[14] E. S. Dana, Manual of Mineralogy, 17th ed., John Wiley &Sons,Inc., 1959, pp. 412–413. ##[15] M. J. Mondrinos, R. Dembzynski, L. Lu, V.K. Byrapogu, D.M. Wootton, P.I. Lelkes, J. Zhou, "Porogenbased solid freeform fabrication of polycaprolactone–calcium phosphate scaffolds for tissue engineering", Biomater., Vol. 27, No. 25, 2006, pp. 43994408. ##[16] I. Zein, D. W. Hutmacher, K. C. Tan, S. H. Teoh, "Fused deposition modeling of novel scaffold architectures for tissue engineering applications", Biomater., Vol. 23, No. 4, 2002, pp. 11691185. ##[17] J. M. Williams, A. Adewunmi, R. M. Schek, C.L. Flanagan, P. H. Krebsbach, S. E. Feinberg, S. J. Hollister, S. Das, "Bone tissue engineering using polycaprolactone scaffolds fabricated via selective laser sintering", Biomater., Vol. 26, No. 23, 2005, pp. 48174827.##]
Finite Element Modeling of Strain Rate and Grain Size Dependency in Nanocrystalline Materials
2
2
Nanocrystalline materials show a higher strainrate sensitivity in contrast to the conventional coarsegrained materials and a different grain size dependency. To explain these phenomenon, a finite element model is constructed that considers both grain interior and grain boundary deformation of nanocrystalline materials. The model consist of several crystalline cores with different orientations and grain boundary phase. The nonlinear behavior of the nanocrystalline core is implemented by a grain size dependent crystal plasticity. The boundary phase is assumed to have the mechanical properties of quasiamorphous material. The constitutive equations for both grains interior and boundary phase are implemented into the finiteelement software Abaqus. A calibration procedure was used to tune some parameters of the model with the previously published experimental data on the nanocrystalline copper. Then the model is used to predict the material behavior in various strain rates and grain sizes. The stresses obtained from these simulations match well with the experimental data for nanocrystalline copper at different strains and strain rates. Deviation from the HallPetch law and inverse HallPetch effect are also well illustrated by the model.
1

63
74


Minoo
Tabanfard
Department of Mechanical Engineering,Islamic Azad University of Najafabad, Isfahan, Iran
Department of Mechanical Engineering,Islamic
Iran
m.tabanfard@smc.iaun.ac.ir
Nano crystalline materials
Grain boundaries deformation
Finite element modeling
Grain size dependent crystal plasticity
[[1] R.J. Asaro, S. Suresh, "Mechanistic models for the activation volume and rate sensitivity in metals with nanocrystalline grains and nanoscale twins", Acta Mater., Vol. 53, 2005, pp. 33693382. ##[2] H. Van Swygenhoven, P.M. Derlet, A.G. Froseth, "Nucleation and propagation of dislocations in nanocrystalline fcc metals", Acta Mater., Vol. 54, 2006, pp. 19751983. ##[3] Z. Jiang, X. Liu, G. Li, Q. Jiang, J. Lian, "Strain rate sensitivity of a nanocrystalline Cu synthesized by electric brush plating", Appl. Phys. Lett., Vol. 88, 2006, p.143115. ##[4] Z. Jiang, H. Zhang, C. Gu, Q. Jiang, J. Lian, "Deformation mechanism transition caused by strain rate in a pulse electric brushplated nanocrystalline Cu", J. Appl. Phys., Vol. 104, 2008, p. 053505. ##[5] G. Wang, J. Lian, Z. Jiang, L. Qin, Q. Jiang, "Compressive creep behavior of an electric brushplated nanocrystalline Cu at room temperature", J. Appl. Phys., Vol. 106, 2009, p. 086105. ##[6] S. Cheng, E. Ma, Y.M. Wang, L.J. Kecskes, K.M. Youssef, C.C. Koch, U.P. Trociewitz, K. Han, "Tensile properties of in situ consolidated nanocrystalline Cu", Acta Mater., Vol. 53, 2005, pp. 15211533. ##[7] A. Giga, Y. Kimoto, Y. Takigawa, K. Higashi, "Demonstration of an inverse HallPetch relationship in electrodeposited nanocrystalline NiW alloys through tensile testing", Scr. Mater., Vol. 55, 2006, pp. 143146. ##[8] C.A. Schuh, T.G. Nieh, T. Yamasaki, "HallPetch breakdown manifested in abrasive wear resistance of nanocrystalline nickel", Scr. Mater., Vol. 46, 2002, pp. 735740. ##[9] V.Y. Gertsman, M. Hoffmann, H. Gleiter,R. Birringer, "The study of grain size dependence of yield stress of copper for a wide grain size range", Acta Metall. Mater., Vol. 42, 1994, pp. 35393544. ##[10] H. Gleiter," Nanocrystalline materials", Prog. Mater Sci., Vol. 33, 1989, pp. 223315. ##[11] Y.M. Wang,E. Ma, "Strain hardening, strain rate sensitivity, and ductility of nanostructured metals", Mater. Sci. Eng., A, Vol. 375377, 2004, pp. 4652. ##[12] X. Li, J. Zhou, R. Zhu, Y. Liu, H. Jiang., "Grain rotation dependent nonhomogeneous deformation behavior in nanocrystalline materials", Mater. Sci. Eng., A, Vol. 527, 2010, pp.5677–5685. ##[13] Y. Wei, A.F. Bower, H. Gao, "Enhanced strainrate sensitivity in fcc nanocrystals due to grainboundary diffusion and sliding", Acta Mater., Vol. 56, 2008, pp. 17411752. ##[14] T.G. Desai, P. Millett, D. Wolf, "Is diffusion creep the cause for the inverse HallPetch effect in nanocrystalline materials?", Mater. Sci. Eng., A, Vol. 493, 2008, pp. 4147. ##[15] K.A. Padmanabhan, G.P. Dinda, H. Hahn, H. Gleiter, "Inverse HallPetch effect and grain boundary sliding controlled flow in nanocrystalline materials", Mater. Sci. Eng., A, Vol. 452453, 2007, pp. 462468. ##[16] H.W. Song, S.R. Guo, Z.Q. Hu, "A coherent polycrystal model for the inverse HallPetch relation in nanocrystalline materials", Nanostruct. Mater., Vol. 11, 1999, pp. 203210. ##[17] G.J. Fan, H. Choo, P.K. Liaw, E.J. Lavernia, "A model for the inverse HallPetch relation of nanocrystalline materials", Mater. Sci. Eng., A, Vol. 409, 2005, pp. 243248. ##[18] X. Liu, F. Yuan, Y. We, “Grain size effect on the hardness of nanocrystal measured by the nanosize indente”, Appl. Surf. Sci., Vol. 279, 2013, pp.159–166. ##[19] Y. Liu, J. Zhou, X. Ling, "Impact of grain size distribution on the multiscale mechanical behavior of nanocrystalline material", Mater. Sci. Eng., A, Vol. 527, 2010, pp.1719–1729. ##[20] H.S. Kim, Y. Estrin, M.B. Bush, "Plastic deformation behaviour of finegrained materials", Acta Mater., Vol. 48, 2000, pp.493–504. ##[21] Y.J. Wei, L. Anand, "Grainboundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals", J. Mech. Phys. Sol., Vol. 52, 2004, pp. 25872616. ##[22] R. Jafari Nedoushan, M. Farzin, M. Mashayekhi, "Effects of strain rate and grain size on behavior of nano crystalline materials", J. Nano Res., Vol. 17, 2012, pp. 3551. ##[23] R. Jafari Nedoushan, M. Farzin, "Effect of Hydrostatic Pressure on Nano Crystalline Materials Behavior", J. Nano Res., Vol. 1819, 2012, pp. 2742. ##[24] P. Valentini, T. Dumitric."Microscopic theory for nanoparticlesurface collisions in crystalline silicon", Phys. Rev. B: Condens. Matter., Vol. 75, 2007, pp. 22410612241069. ##[25] P. Valentini, W.W. Gerberich, T. Dumitric, "PhaseTransition Plasticity Response in Uniaxially Compressed Silicon Nanospheres", Phys. Rev. Lett., Vol. 99, 2007, pp.17570111757014. ##[26] A. C. F. Cocks, "Interface reaction controlled creep", Mech. Mater., Vol. 13, 1992, pp.165174. ##[27] J. Pan, A. C. F. Cocks, "Computer simulation of superplastic deformation", Comput. Mater. Sci., Vol. 1, 1993, pp. 95109. ##[28] B. Zhu, R.J. Asaro, P. Krysl,R. Bailey, "Transition of deformation mechanisms and its connection to grain size distribution in nanocrystalline metals", Acta Mater., Vol. 53, 2005, pp. 48254838. ##[29] Y.J. Wei, L. Anand, "Grainboundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals", J. Mech. Phys. Solids, Vol. 52, 2004, pp. 25872616. ##[30] X. Qing, G. Xingming, "The scale effect on the yield strength of nanocrystalline materials", Int. J. Solids Struct., Vol. 43, 2006, pp. 7793–7799 ##[31] R.J. Asaro, A. Needleman, "Texture development and strain hardening in rate dependent polycrystals", Acta Metall., Vol. 33, 1985, pp. 923953. ##[32] D. Peirce, R.J. Asaro, A. Needleman, "An analysis of nonuniform and localized deformation in ductile single crystals", Acta Metall., Vol. 30, 1982, pp. 10871119. ##[33] R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, "Some critical experiments on the strainrate sensitivity of nanocrystalline nickel", Acta Mater., Vol. 51, 2003, pp. 5159–5172. ##[34] S. Li, J. Zhou, L. Ma, N. Xu, R. Zhu, X. He,"Continnum level simulation on the deformation behavior of nanocrystalline nikel", Comput. Mater. Sci., Vol. 45, 2009, pp.390397. ##[35] N. Ahmed, A. Hartmaier, “A twodimensional dislocation dynamics model of the plastic Deformation of polycrystalline metals”, J. Mech. Phys. Solids, Vol. 58, 2010, pp.2054–2064. ##[36] S. Gollapudi, K.V. Rajulapat, I. Charit, C.C. Kocha, R.O. Scattergood, K.L. Murty, "Creep in nanocrystalline materials: Role of stress assisted grain growth", Mater. Sci. Eng., A, Vol. 527, 2010, pp.5773–5781. ##[37] C.F.O. Dahlberg, J. Faleskog, "Strain gradient plasticity analysis of the influence of grain size and distribution on the yield strength in polycrystals", Eur. J. Mech. A/Solid., Vol. 44, 2014, pp.1–16. ##]