A new analytical formulation is presented to study the steady-state creep in short fiber composites using complex variable method. In this new approach, both the fiber and matrix creep at low stresses and temperatures. To analyze the crept fiber, a plane stress model was used. Important novelties of the present analytical method are determination of displacement rates with proper boundary conditions in the crept fibers and also using the complex variable method in creep analyzing. It is noteworthy that the method can be useful to study the creep behavior in polymeric matrix composites due to their high capability of creep. Moreover, another significant application of the present method is to study on the creep or elastic behavior of carbon nanotube polymer composites. Finally, the results obtained from the present analytical method (complex variable method) show a good agreement with the existing experimental results.
KolosovGV. On the application of complex function theory to a plane problem of the mathematical theory of elasticity, 1st ed. Moscow: Yuriev University Press, 1909.
2.
MuskhelishviliNI. Some basic problems of the mathematical theory of elasticity, 4th ed. Moscow: Noordhoff, 1954.
ChurchillRV. Complex variables and applications, 2nd ed. New York: McGraw-Hill, 1960.
9.
KreyszigE. Advanced engineering mathematics, 8th ed. New York: John Wiley, 1999.
10.
TrjitzinskyWJ. Some general developments in the theory of functions of a complex variable. Acta Math1939; 70(1): 63–163.
11.
GaoXL. Alternative derivation of Marguerre’s displacement solution in plane isotropic elasticity. ASME J Appl Mech2000; 67: 419–421.
12.
HamadaHKohrG. On some classes of bounded univalent mappings in several complex variables. Manuscripta Math2010; 131(3-4): 487–502.
13.
HamadaH. Polynomially bounded solutions to the Loewner differential equation in several complex variables. J Math Anal Appl2011; 381(1): 179–186.
14.
ChouSIShamas-AhmadiM. Complex variable boundary element method for torsion of hollow shafts. Nucl Eng Des1992; 136: 255–263.
15.
MogilevskayaSG. The universal algorithm based on complex hypersingular integral equation to solve plane elasticity problems. Comput Mech1996; 18: 127–138.
16.
HuiCYMukherjeeS. Evaluation of hypersingular integrals in the boundary element method by complex variable techniques. Int J Solids Struct1997; 34(2): 203–221.
17.
MogilevskayaSGLinkovAM. Complex fundamental solutions and complex variables boundary element method in elasticity. Comput Mech1998; 22: 88–92.
18.
MogilevskayaSGCrouchSL. A Galerkin boundary integral method for multiple circular elastic inclusions. Int J Numer Methods Eng2001; 52: 1069–1106.
19.
WangJCrouchSLMogilevskayaSG. A complex boundary integral method for multiple circular holes in an infinite plane. Eng Anal Bound Elem2003; 27: 789–802.
20.
MogilevskayaSGCrouchSL. A Galerkin boundary integral method for multiple circular elastic inclusions with uniform interphase layers. Int J Solids Struct2004; 41: 1285–1311.
21.
LiewKMFengCChengY. Complex variable moving least - squares method: a meshless approximation technique. Int J Numer Meth Eng2007; 70: 46–70.
22.
VoorheesAMillwaterHRBagleyRL. Complex variable methods for shape sensitivity of finite element models. Finite Elem Anal Des2011; 47: 1146–1156.
23.
KellyATysonWR. Tensile properties of fibre reinforced metals—II. Creep of silver-tungsten. J Mech Phys Solids1966; 14(4): 177–184.
24.
MileikoST. Steady state creep of a composite with short fibres. J Mater Sci1970; 5: 254–261.
25.
DuttaaPKHuiD. Creep rupture of a GFRP composite at elevated temperatures. Comput Struct2000; 76: 153–161.
26.
OliveiraLCGomideHARadeRSL. Primary creep behavior of polyester resins from multiple relaxation curves. Proc IMechE, Part C: J Mechanical Engineering Science2003; 217(12): 1301–1313.
27.
XiaoLLuWJQinJN. Steady state creep of in situ TiB plus La2O3 reinforced high temperature titanium matrix composite. Mater Sci Eng A2009; 499(1–2): 500–506.
28.
KhanFYeakleC. Experimental investigation and modeling of non-monotonic creep behavior in polymers. Int J Plast2011; 27: 512–521.
29.
DragonTLNixWD. Geometric factors affecting the internal stress distribution and high temperature creep rate of discontinuous fiber reinforced metals. Acta Metall Mater1990; 38(10): 1941–1953.
30.
LimHJJungJWHanDB. A finite element model for asymmetric creep behavior of ceramics. Mater Sci Eng A1997; 224(1–2): 125–130.
31.
YueZFLuZZ. A numerical determination of the fiber/matrix interlayer creep properties from the indentation creep testing in fiber reinforced composites. Mater Sci Eng A2003; 352(1–2): 266–272.
32.
MondaliMAbedianAAdibnazariS. FEM study of the second stage creep behavior of Al6061/SiC metal matrix composite. Comput Mater Sci2005; 34: 140–150.
33.
GhavamiAAbedianAMondaliM. Finite difference solution of steady state creep deformations in a short fiber composite in presence of fiber/matrix debonding. Mater Design2010; 31: 2616–2624.
34.
LeeWJSonJHParkIM. Direct numerical predictions for the steady-state creep deformation of extruded SiCw/Al6061 composites using a representative volume element with random arrangement of whiskers. Comput Mater Sci2010; 48(4): 802–812.
35.
CoxHL. The elasticity and strength of paper and other fibrous materials. Br J Appl Phys1952; 3: 72–79.
36.
BermanIPaiDH. A theory of anisotropic steady-state creep. Int J Mech Sci1966; 8(5): 341–352.
37.
De silvaART. A theoretical analysis of creep in fibre reinforced composites. J Mech Phys Solids1968; 16(3): 169–186.
38.
HsuehCH. A modified analysis for stress transfer in fiber-reinforced composites with bonded fiber ends. J Mater Sci1995; 30: 219–224.
39.
AltenbachH. Topical problems and applications of creep theory. Int Appl Mech2003; 39(6): 631–655.
40.
JiangZLiuXLiG. A new analytical model for three-dimensional elastic stress field distribution in short fibre composite. Mater Sci Eng A2004; 366: 381–396.
41.
GaoXLLiK. A shear-lag for carbon nanotube-reinforced polymer composites. Int J Solids Struct2005; 42: 1649–1667.
42.
MondaliMAbedianAGhavamiA. A new analytical shear-lag based model for prediction of the steady state creep deformations of some short fiber composites. Mater Design2009; 30: 1075–1084.
43.
CannonWRLangdonTG. Creep of ceramics, Part 1: mechanical characteristics. J Mater Sci1983; 18: 1–50.
44.
CannonWRLangdonTG. Creep of ceramics, Part 2: an examination of flow mechanisms. J Mater Sci1988; 23: 1–20.
45.
SchulzM. Elastic creep in serpentine belt drives and adopting a suitable strain measure. Proc IMechE, Part C: J Mechanical Engineering Science2004; 218(12): 1421–1433.
46.
KnotheKGross-ThebingA. High-frequency contact mechanics: the derivation of frequency-dependent creep coefficient. Proc IMechE, Part C: J Mechanical Engineering Science1984; 198(3): 167–173.
47.
KachanovLM. Fundamentals of the theory of plasticity, Dover Ed edition. Moscow: Dover Publications, 2004.
48.
ChakrabartyJ. Theory of plasticity, 3rd ed. Oxford: Butterworth-Heinemann Publishing, 2006.
49.
LublinerJ. Plasticity theory, New York: Dover Publications, 2008.
50.
MonfaredVMondaliMAbedianA. Steady state creep behavior of short fiber composites by mapping, logarithmic functions (MF) and dimensionless parameter (DP) techniques. Arch Civ Mech Eng2012; 12(4): 455–463.
