탄성 불균질 재료의 미시역학거동 (Part II : 탄성계수 및 열팽창계수)

강창석; 홍성길; Kenji Wakashima; Chang-Seog Kang; Sung-Kil Hong; Kenji Wakashima

Korean Journal of Materials Research, Vol.11, No.5, 372-377, May, 2001

Micromechanical Properties in Elastically Inhomogeneous Materials (Part II : Elastic Moduli and Thermal Expansion Coefficients)

강창석, 홍성길, Kenji Wakashima¹

전남대학교 금속공학과
¹동경공업대학

Chang-Seog Kang, Sung-Kil Hong, and Kenji Wakashima¹

Department of Metallurgical Engineering, Chonnam National University, Kwangju, 500-757, Korea
¹Precision and Intelligence Laboratory, Tokyo institute of technology, Yokohama 226, Japan, Korea

초록

Part I에서 도출된 기초 식을 적용하여 입자 분산 강화형, 섬유 강화형 및 적층형 복합재료의 유효탄성제수 및 열팽창계수를 산정 하였다. 일방향 섬유 강화 복합재료의 경우 섬유의 유효 축비 (aspect ratio)가 고려되었으며, 유효 탄성계수는 다른 연구 결과들과 비교하였다. 입자 분산 강화형 복합재료의 유효 체적탄성률 및 전단 탄성률은 Korner의 표식 및 Hanshin과 Shtrikman의 하한치 (lower bounds)와 일치하고 있다. 일방향 섬유 강화 복합재료에서는 6개, Hanshin과 Rosen의 모델에 나타낸 4개의 독립 탄성계수와 일치하고 있다.

A theory developed in Part I has been applied to calculate effective elastic and thermoelastic moduli of particle-strengthened, unidirectionally fiber-reinforced, and layered composites. For the unidirectional fiber composites the effect of fiber aspect ratio is taken into account. The analytical solutions obtained to the effective elastic moduli are compared with some of existing expressions and the following results are found. The effective bulk and shear moduli of the particle strengthened composites coincide with Korner's expressions, which correspond with the lower bounds of Hanshin and Shtrikman. The same expressions as the lower bounds of Hill and Hanshin are obtained for five independent moduli of the aligned continuous fiber composites, four of which coincide with Hanshin and Rosen's exact solutions for 'composite cylinder assemblage'.

Keywords:elastically inhomogeneous meterials . effective elastic moduli;thermal expansion coefficients;ellipsoidal inclusion;microscopic stress-strain;composites

[References]

Hanshin Z, Appl. Mech. Rev., 17, 1 (1964)
Sendeckyj GP: Composite Materials., (Broutman LJ, Krock RH, Eds.) Vol. 2, Mechanics of Composite Materials, Academic, New York, 45 (1973) (1973)
Hanshin Z : Appl. Mechanics of Composite Materials (Wendt FW, Liebowitz H & (1967) (1967)
Kang CS, Maeda K, Wang KJ, Wakashima K, Acta Mater., 46, 1209 (1998)
Kang CS, Ahn BK, Wakashima K, J. of the Korean Inst. of Met. & Mater., 38, 84 (2000)
Eshelby JD, Proc. Roy. Soc. London, A241, 376 (1957)
Cox HL, Brit. J. Appl. Phys., 3, 72 (1952)
Kerner EH, Proc. Phys, Soc., 69B, 808 (1956)
Hanshin Z, Shtrikman S, J. Mech. Phys. Solids, 11, 127 (1963)
Budiansky B, J. Mech. Phys., 13, 223 (1965)
Hill R, J. Mech. Phys. Solids, 13, 189 (1965)
Hanshin Z, J. Appl. Mech., 29E, 143 (1962)
Hill R, J. Mech. Phys. Solids, 12, 199 (1964)
Hanshin Z, J. Mech. Phys. Solids, 13, 119 (1965)
Hanshin Z, Rosen BW, J. Appl, Mech., 31, 223 (1964)

[1] Hanshin Z, Appl. Mech. Rev., 17, 1 (1964)

[2] Sendeckyj GP: Composite Materials., (Broutman LJ, Krock RH, Eds.) Vol. 2, Mechanics of Composite Materials, Academic, New York, 45 (1973) (1973)

[3] Hanshin Z : Appl. Mechanics of Composite Materials (Wendt FW, Liebowitz H & (1967) (1967)

[4] Kang CS, Maeda K, Wang KJ, Wakashima K, Acta Mater., 46, 1209 (1998)

[5] Kang CS, Ahn BK, Wakashima K, J. of the Korean Inst. of Met. & Mater., 38, 84 (2000)

[6] Eshelby JD, Proc. Roy. Soc. London, A241, 376 (1957)

[7] Cox HL, Brit. J. Appl. Phys., 3, 72 (1952)

[8] Kerner EH, Proc. Phys, Soc., 69B, 808 (1956)

[9] Hanshin Z, Shtrikman S, J. Mech. Phys. Solids, 11, 127 (1963)

[10] Budiansky B, J. Mech. Phys., 13, 223 (1965)

[11] Hill R, J. Mech. Phys. Solids, 13, 189 (1965)

[12] Hanshin Z, J. Appl. Mech., 29E, 143 (1962)

[13] Hill R, J. Mech. Phys. Solids, 12, 199 (1964)

[14] Hanshin Z, J. Mech. Phys. Solids, 13, 119 (1965)

[15] Hanshin Z, Rosen BW, J. Appl, Mech., 31, 223 (1964)