탄성 불균질 재료의 미시역학거동 (Part I :이론적 기초)

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

Korean Journal of Materials Research, Vol.11, No.5, 354-360, May, 2001

Export Citation

탄성 불균질 재료의 미시역학거동 (Part I :이론적 기초)

Micromechanical Properties in Elastically Inhomogeneous Materials (Part I : Theoretical Basis)

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

초록

본 연구에서는 탄성문제에 관한 Eshelby의 이론을 응용하여 다수의 개재물이 모상 중에 균일하게 분산하고 탄성적으로 불균질한 복합재료의 거시적 응력-변형관계를 정식화하였다. 정식화의 과정에서, 주위의 구속을 받지 않는 어떤 영역에 응력의 발생을 동반하지 않는 변형률 (transformation strain ε kl ), 즉 열팽창 제수를 갖는 물체가 온도변화 ΔT 를 갖는 경우의 열팽창 변형 α ΔT 나, 물체가 일정한 소성 변형을 받았을 때의 소성 변형 등을 예로들 수 있는 역학 장을 정의하였다. 본 연구에서 전개한 방법은 선형 탄성론에 기초를 두고 있으며 복합체의 탄성거동만이 아니라 탄성-소성 거동의 해석 또한 가능하게 하였다.

By applying Eshelby's theory on the'transformation' and' inhomogeneity'problems of an ellipsoidal inclusion, a microscopic stress-strain is formulated for a composite material consisting of a matrix and a large number of aligned ellipsoidal inclusions. Some of the composites of practical interest, such as unidirectionally fiber- reinforced, Particle dispersion strengthened and layered composites can be treated by changing the axial ratios of the ellipsoidal inclusion. The macroscopic stress-strain relation obtained is applicable to elastic and elasto-plastic deformation of the composite in uniform loading.

Keywords:elastically inhomogeneous materials . Eshelby′s theory . transformation strain;inhomogeneity problems;ellipsoidal inclusion;microscopic stress-strain;composites

[References]

Hanshin Z, Appl. Mech. Rev., 17, 1 (1964)
Hanshin Z : Appl. Mechanics of Composite Materials (Wendt FW, Liebowitz H & Perrone N, Eds.), Pergamon, Oxford, 201 (1967) (1967)
Sendeckyj GP : Composite Materials., (Broutman LJ & Krock RH, Eds.) Vol. 2, Mechanics of Composite Materials, Academic, New York, 45 (1973) (1973)
Hanshin Z, Shtrikman S, J. Mech. Phys. Solids, 11, 127 (1963)
Hanshin Z, J. Mech. Phys. Solids., 13, 119 (1965)
Hill R, J. Mech. Phys. Solids, 12, 199 (1964)
Adams DF, Doner DR, J. Compos. Mater., 1, 4 (1964)
Adams DF, Doner DR, J. Compos. Mater., 1, 152 (1967)
Chen CH, Cheng S, J. Compos. Mater., 1, 30 (1967)
Eshelby JD, Proc. Roy. Soc. London, A241, 376 (1957)
Eshelby JD, Proc. Roy. Soc. London, A252, 561 (1959)
Eshelby JD: Progress in Solid Mechanics II , Sneddon and Hill, Eds.) North - Holland, Amsterdam, 87 (1961) (1961)
Mori T, Tanaka K, Acta Met., 21, 573 (1973)
Mori T, Tanaka K, J. Compos. Mater., 8, 391 (1974)
Mura T : Micromechanics of Defects in Solids, 2nd ed., Matinus Nijhoff, Dordrecht, 74 (1987) (1987)
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)

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

[2] Hanshin Z : Appl. Mechanics of Composite Materials (Wendt FW, Liebowitz H & Perrone N, Eds.), Pergamon, Oxford, 201 (1967) (1967)

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

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

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

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

[7] Adams DF, Doner DR, J. Compos. Mater., 1, 4 (1964)

[8] Adams DF, Doner DR, J. Compos. Mater., 1, 152 (1967)

[9] Chen CH, Cheng S, J. Compos. Mater., 1, 30 (1967)

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

[11] Eshelby JD, Proc. Roy. Soc. London, A252, 561 (1959)

[12] Eshelby JD: Progress in Solid Mechanics II , Sneddon and Hill, Eds.) North - Holland, Amsterdam, 87 (1961) (1961)

[13] Mori T, Tanaka K, Acta Met., 21, 573 (1973)

[14] Mori T, Tanaka K, J. Compos. Mater., 8, 391 (1974)

[15] Mura T : Micromechanics of Defects in Solids, 2nd ed., Matinus Nijhoff, Dordrecht, 74 (1987) (1987)

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

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