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Keywords
(6)
Composite Material
Energy Function
Fiber Reinforcement
Thermal Expansion
Thermal Expansion Coefficient
Upper and Lower Bounds
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Thermal Expansion Coefficients of Composite Materials Based on Energy Principles
Thermal Expansion Coefficients of Composite Materials Based on Energy Principles,10.1177/002199836800200308,Journal of Composite Materials,R. A. Schap
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Thermal Expansion Coefficients of Composite Materials Based on Energy Principles
(
Citations: 192
)
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R. A. Schapery
Bounds on effective
thermal expansion
coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity. Inequalities between certain approximate and exact forms of the potential and complementary energy functionals are first estab lished. These inequalities are then used in conjunction with a new method for minimizing the difference between
upper and lower bounds
in order to derive volumetric and linear
thermal expansion
coefficients. Application is made to two and threephase isotropic composites and a fiberreinforced material. It is found for some important cases that the solutions are exact, and take a very simple form. We also show conditions under which the ruleofmixtures and Turner's equation can be used for
thermal expansion
coeffi cients. Finally, simple methods for extending all results to viscoelastic composites are indicated.
Journal:
Journal of Composite Materials  J COMPOS MATER
, vol. 2, no. 3, pp. 380404, 1968
DOI:
10.1177/002199836800200308
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jcm.sagepub.com
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Citation Context
(25)
...According to Schapery [
24
], the averaged thermal expansion coefficient for dualphase materials with arbitrary phase geometry is expressed by: in which 1/
K
_{ L }
=
V
_{ m }
/
K
_{ m }
−
V
_{ c }
/
K
_{ c }
, and
Abdolhossein Fereidoon
,
et al.
Functionally Graded Materials Optimization Using Particle SwarmBased ...
...The thermal forces, moments and higher order moments caused by temperature change Δ
T
are defined by and where in which α
_{11}
and α
_{22}
are the thermal expansion coefficients measured in the fiber and transverse directions, respectively, and defined by Shapery
[12]
where α
_{ f1}
, α
_{ f2}
and α
_{ m }
are thermal expansion coefficients of the fiber and matrix respectively...
ZhiMin Li
,
et al.
Nonlinear buckling and postbuckling behavior of 3D braided cylindrica...
...The thermomechanical behavior of FGMs is strongly dependent on the accurate estimation of their modulus of elasticity and the coefficient of thermal expansion[
10
,
11
,
3742
]...
M. Didem Bagci
,
et al.
Thermal Residual Stresses in OneDirectional Functionally Graded Plate...
...At the same time disagreements can be observed in the predicted transverse CTE’s determined using the Schapery Equation [
21
] and the Eshelby/MoriTanaki [1516] approach...
B. Burks
,
et al.
Failure prediction analysis of an ACCC conductor subjected to thermal ...
...For an arbitrary phase geometry and composites with spherical inclusions, Turner [52], Kerner [22], Levin [25], Schapery [
41
], Fahmy and Ragai [13 ]a nd Rosen and Hashin [39] have derived equations for effective CTEs...
...For the isotropic two phase composites, the calculated CTE reduced to the bounds of Schapery [
41
], which was formulated using thermoelasticity equations...
Kamran A. Khan
,
et al.
Effective thermal properties of viscoelastic composites having fieldd...
References
(8)
Stress Analysis of Viscoelastic Composite Materials
(
Citations: 55
)
R. Schapery
Published in 1968.
Note on Thermal Expansion and Microstresses in TwoPhase Compositions
(
Citations: 12
)
W. D. KINGERY
Journal:
Journal of The American Ceramic Society  J AMER CERAM SOC
, vol. 40, no. 10, pp. 351352, 1957
A variational approach to the theory of the elastic behavior of multiphase materials
(
Citations: 381
)
Z. Hashin
,
S. Shtrikman
Published in 1963.
The Elastic and Thermoelastic Properties of Composite Media
(
Citations: 237
)
E. H. Kerner
Journal:
Proceedings of The Physical Society. Section B
, vol. 69, no. 8, pp. 808813, 1956
Elastic properties of reinforced solids: Some theoretical principles
(
Citations: 743
)
R. Hill
Journal:
Journal of The Mechanics and Physics of Solids  J MECH PHYS SOLIDS
, vol. 11, no. 5, pp. 357372, 1963
Sort by:
Citations
(192)
Functionally Graded Materials Optimization Using Particle SwarmBased Algorithms
Abdolhossein Fereidoon
,
Firouz Sadri
,
Hossein Hemmatian
Journal:
Journal of Thermal Stresses  J THERMAL STRESSES
, vol. 35, no. 4, pp. 377392, 2012
Stiff lattices with zero thermal expansion
Jeremy Lehman
,
Roderic Lakes
Journal:
Journal of Intelligent Material Systems and Structures  J INTEL MAT SYST STRUCT
, vol. 23, no. 11, pp. 12631268, 2012
Nonlinear buckling and postbuckling behavior of 3D braided cylindrical panels under axial compression in thermal environments
ZhiMin Li
,
YiXi Zhao
,
XiangDong Chen
Journal:
Mechanics of Advanced Materials and Structures  MECH ADV MATER STRUCT
, vol. justaccep, no. justaccep, 2012
Thermal Residual Stresses in OneDirectional Functionally Graded Plates Subjected to InPlane Heat Flux
(
Citations: 1
)
M. Didem Bagci
,
M. Kemal Apalak
Journal:
Numerical Heat Transfer Part Aapplications  NUMER HEAT TRANSFER PT AAPPL
, vol. 60, no. 1, pp. 5083, 2011
In vitro and in vivo induction of chromosome aberrations by alpha and betazearalenols: Comparison with zearalenone
Yosra Ayed
,
Imen AyedBoussema
,
Zouhour Ouanes
,
Hassen Bacha
Journal:
Mutation Researchgenetic Toxicology and Environmental Mutagenesis  MUTAT RESGENET TOXICOL E M
, vol. 726, no. 1, pp. 4246, 2011