• Tunnel and Underground Space
• /
• v.11 no.1
• /
• pp.59-63
• /
• 2001

The total number of elastic constants of an anisotropic body is 9 and thus it is very difficult to measure these constants experimentally. The number of elastic constants can be reduced if a rock or rock mass is regarded as isotropic or transversely isotropic material. Since only 4 stress-strain relationships can be obtained, it is theoretically impossible to determine all 5 constants from a single uniaxial compression teat. Lekhnitskii overcame this problem by suggesting the fifth equation based on laboratory tests. But his equation is theoretically wrong and does not agree with experimental results. This paper describes the stress-strain relationships and the independent/dependent elastic constants of an anisotropic mass and suggests a testing mothed to determine 5 independent elastic constants for a transversely isotropic rock.

• Tunnel and Underground Space
• /
• v.15 no.4 s.57
• /
• pp.288-295
• /
• 2005

Many mechanical defects originated from various geological causes make rock mass exhibit anisotropic characteristics. Understanding how the stress distribution occurs in anisotropic rock mass is, therefore, very important for the design of footings on rock and rock structures. In this study, the patterns of elastic stress distribution, developed by acting line load on the surface, in transversely isotropic was investigated. The influence of joint stiffness, joint spacing, and dip angle on the stress distribution was examined. By assuming the Mohr-Coulomb criterion as joint slip condition, the development of joint slip zone was also discussed.

• The Korean Journal of Rheology
• /
• v.7 no.2
• /
• pp.128-138
• /
• 1995

본 논문에서는 전단띠형성에 있어서 전단변형의 집중화 현상을 이방성 탄소성 재료 에 대해서 해석하였고 소성스핀과 비등방성이 전단띠 형성에 미치는 영향을 연구하였다. 평 면응력 상태에서 소성스핀을 갖고있는 이방성 탄-소성 재료에 대해서 재료 분랑ㄴ정 해서 을 수행하여 변형률 집중화의 시작에 미치는 소성스핀과 비등방성의 효과를 연구하였다. 해 석 결과 이방성 재료에서의 전단띠 형성은 압축 또는 인장의 하중 형태나 이방성 축의 초기 각도 그리고 소성스핀의크기에 따라 그 시작이 촉진되거나 지연되었고 전단띠 생성의 방향 도 달라졌다.

• Tunnel and Underground Space
• /
• v.11 no.1
• /
• pp.72-78
• /
• 2001

A method to determine elastic constants for transversely isotropic rock using a single uniaxial compression test was proposed by Kim(1995). However, some problems were found when this method was applied. We derived two different equations in determination of elastic constants using V$\sub$12/ and V$\sub$21/ and performed uniaxial compression tests for two specimens whose angles between transversely isotropic plane and horizontal plane are 30$^{\circ}C$ and 65$^{\circ}C$. The anisotropic elastic constants should be calculated with different equations depend on the angle. If the anisotropic angle is lower than 45$^{\circ}$, V$\sub$21/ may be used. However, if the anisotropic angle is higher than 45$^{\circ}$, V$\sub$12/ may be used.

• Proceedings of the KSEG Conference
• /
• 2001.03a
• /
• pp.83-90
• /
• 2001

• 기계와재료
• /
• v.23 no.3
• /
• pp.82-95
• /
• 2011

다결정압연판재는 열가공공정을 거쳐서 생산되므로 공정의 특성을 반영하는 미세조직/집합조직 특성을 가지게 된다. 결정립들은 특정방향으로 배향하고 결정립의 형상과 크기도 변화한다. 이러한 변화는 거시적으로 다결정판재의 이방성으로 귀결이 되는데, 근본적으로 판재를 구성하는 단결정들의 기계적 물성이 각각의 방향별로 이방성을 띄기 때문이다. 본 자료에서는 압연공정시 다결정판재의 수직/평면이방성의 발생원인을 집합조직과 결정소성학을 이용하여 제시하고자 하였다.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.8 no.5
• /
• pp.435-441
• /
• 1984

The matrix method, as an effective FEM formulation for the analysis of rigid-plastic deformation, was applied to the bore expanding of anisotropic sheet metal. The effect of planar anisotropy on sheet metal deformation was studied for bore expanding process under the uniform radial stretching condition, and the results were compared with isotropic and normal anisotropic solutions. Experiments were carried out using a flat punch for cold-rolled sheet metal. The experimental results were compared with computations from the matrix method with the boundary conditions corresponding to actual experiment. Both in theory and experiment, it is found that the maximum thinning which results in necking occurs in the direction of the minimum R-value. The results also suggest that the matrix method is efficient for analyzing planar anisotropic sheet metal. The comparison between theory and experiment suggests that Hill's theory of planar anisotropy is somewhat exaggerated. However, the theoretical predictions are in qualitative agreement with the experimental results.

• Tunnel and Underground Space
• /
• v.18 no.4
• /
• pp.252-262
• /
• 2008

In the uniaxial compressive test of a single specimen of transversely isotropic rock, its 5 independent elastic constants can not be defined since maximum 4 independent strain measurements are available theoretically. In order to solve this problem, one equation proposed by Saint Venant in 19C and confirmed by Lekhnitskii through the test experiences has been used for long time. Accordign to authors' experiences, however, this equation turned out to give erroneous elastic constants in some cases. Three new equations are suggested and their compatibilities are discussed in this paper. As the results of the analyses of the models, Lekhnitskii's suggested equation is effective for the specimen with the high dip angle whereas it results in the large erred output for that with dip angle less than $25{\sim}30$. It was found that the effectivenesses of three suggested equations and their compatibilities are subject to the dip angle and not to the amounts of elastic constants. Guide map to the selection of the compatible one of those suggested equations is presented as a result of the study.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.2
• /
• pp.248-258
• /
• 1992

Three-dimensional rigid-plastic finite element formulation based on the membrane theory was described and a computer program for large deformation analysis was developed. In the formulation, normal and planar anisotropy of sheet material and rotation of the principal axes of anisotropy was taken into consideration. Sheet metal was assumed to be rigid-plastic material obeying Hill's quadratic yield criterion and its associated flow rule. Deep drawing process, as a preliminary test, for normal anisotropic material was analyzed in order to examine the validity of developed finite element program. The results were consistent with the existing finite element solutions or experimental data. The present study was mainly concerned with the influence of planar anisotropy on deformation behaviour. Finite element analysis and experiment were carried out for the whole process of deep drawing of planar anisotropic material. The computational and experimental results on the shape of ear, strain distribution and punch load were in good agreement.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.6
• /
• pp.1792-1798
• /
• 1991

In this paper the path independent $J_{k}$(k=1, 2) integrals are evaluated in a rectilinear anisotropic body for two dimensional case. The relationship among elastic constants are examined. Using those relationship the expression of $J_{2}$ Integral in terms of $K_{I}$ is found to be very simple.e.e.