• 한국생산제조학회지
• /
• 제22권3_1spc호
• /
• pp.504-508
• /
• 2013

This paper describes in detail the life prediction models and simulations of thermal fatigue under different mold compounds and chip sizes for wafer-level embedded SiP. Three-dimensional finite element models are built to simulate the viscoplastic behaviors for various mold compounds and chip sizes. In particular, the bonding parts between a mold and silicon nitride (Si3N4) are carefully modeled, and the strain distributions are studied. Three different chip sizes are used, and the effects of the mold compounds are observed. Through the numerical studies, it is found that type-C, which has a relatively lower Young's modulus and higher CTE, has a better fatigue life than the other mold compounds. In addition, the $4{\times}4$ chip has a shorter life than the $6{\times}6$ and $8{\times}8$ chips.

• 유변학
• /
• 제11권2호
• /
• pp.143-152
• /
• 1999

본 연구에서는 Rheometrics Fluids Spectrometer(RFS II)를 사용하여 세 종류의 상용 반고형 식품(마요네즈, 토마토 케찹, 와사비)의 정상유동특성 및 소진폭 전단변형하에서의 동적 점탄성을 광범위한 전단속도와 각주파수 영역에서 측정하였다. 이들 측정결과로부터 정상유동특성의 전단속도 의존성 및 동적 점탄성의 각주파수 의존성을 보고하였다. 그리고 항복응력의 항을 갖는 몇 가지 점소성 유동모델을 사용하여 정상유동특성을 정량적으로 평가하고 이들 모델의 적용성을 비교.검증하였다. 나아가서 수정된 형태의 지수법칙 관계식을 도입하여 정상유동특성(비선형 거동)과 동적 점탄성(선형 거동)간의 상관관계에 대해 검토하였다. 이상의 연구를 통해 얻어진 결과를 요약하면 다음과 같다. (1) 반고형 식품류는 상당한 크기의 항복응력을 갖는 점소성 물질로서 전단속도가 증가할수록 정상류점도가 급격히 감소하는 shear-thinning 거동을 나타낸다. (2) Herschel-Bulkley 모델, Mizrahi-Berk 모델 및 Heinz-Casson 모델은 반고형 식품류의 정상유동거동을 잘 기술할 수 있다. 이들 중에서도 Heinz-Casson 모델이 가장 우수한 적용성을 갖는다 (3) 반고형 식품류는 임계 전단속도를 경계로 shear-thinning 특성이 변화한다. 즉 낮은 전단속도에 비해 높은 전단속도 영역에서 분산입자 응집체의 구조파괴가 더욱 활발하게 진행되어 보다 현저한 shear-thinning 특성을 나타낸다. (4) 저장 탄성률 및 손실탄성률은 양자 모두 각주파수가 증가할수록 점차로 증가하나 각주파수 의존성은 그다지 크지 않다. 또한 광범위한 각주파수 영역에서 탄성적 성질이 점성적 성질에 비해 보다 우세하게 나타난다. (5) 정상류점도, 동적점도 및 복소점도는 모두 power-law 모델의 거동을 잘 만족한다. 또한 정상유동특성과 동적 점탄성간의 상관관계는 수정된 형태의 지수법칙 관계식에 의해 잘 기술될 수 있다.

• Journal of Mechanical Science and Technology
• /
• 제20권12호
• /
• pp.2178-2188
• /
• 2006

The stress collapse in the formation of shear bands in elasto-thermo-viscoplatic materials is systematically studied within the framework of one-dimensional formulation via analytical and numerical methods. The elastic energy released in a domain is found to play an important role in the collapse behavior of shear localization. A non-dimensional parameter named the stability indicator is introduced to characterize the collapse behavior, with approximate forms of the incremental governing equations. The stability indicator offers useful information regarding the degree of severity of an abrupt change of deformations during the stress collapse. Numerical experiments are carried out to verify the stability indicator by varying material properties.

• 수산해양기술연구
• /
• 제28권1호
• /
• pp.79-92
• /
• 1992

This is analyzed using the finite element method which is appling excellent isoparametric curve element in the aspect of large usages of dynamic responses in which is regarding geometric and material nonlinear of a large scale shell structure of an airplane, a submarine, a ship, and an ocean structure. The solution of dynamic equations is got by direct integration method using time-stepping procedure and regarding Central Difference Method of the both solutions. But because formal matrix factorization is not necessary in each time step and it does not take less time to compute relatively, this method must be regarded very few time steps on the condition. Axisymmatric shell problems are inspected using 8 node Isoparametric element in this paper. Partial axisymmatric spherical shell is used as a model to analyze axisymmatric nonlinear dynamic behavior regarding. Total Lagrangian formulation in geometric nonlinear behavior and elastio-viscoplastic in material nonlinear behavior.

• 소성∙가공
• /
• 제13권2호
• /
• pp.160-167
• /
• 2004

In order to theoretically analyze the creep behavior of high Cr steel at $600^{\circ}C$, a unified elasto-viscoplastic constitutive model based on the consideration of dislocation density is proposed. A combination of a kinetic equation describing the mechanical response of a material at a given microstructure in terms of dislocation glide and evolution equations for internal variables characterizing the microstructure provides the constitutive equations of the model. Microstructural features of the material such as the grain size and spacing between second phase particles are directly implemented in the constitutive equations. The internal variables are associated with the total dislocation density in a simple model. The model has a modular structure and can be adjusted to describe a creep behavior using the material parameters obtained from uniaxial tensile tests.

• 한국농공학회지
• /
• 제43권3호
• /
• pp.85-93
• /
• 2001

In this study, a computer program considering shape imperfections of arch under dynamic loading was developed. The shape imperfection of arch was assumed as higher degree polynomial expressed as $\omega$$_{i}$ = $\omega$$_{o}$ (1-(2$\chi$/L)$^{m}$ )$^n$and sinusoidal curve such as $\omega$$_{i}$ = $\omega$$_{o}$ sin(η$\pi$$\chi$/L). In finite element formulation, the material nonlinear behavior was assumed the elasto-viscoplastic model highly corresponding to the real behavior of the material and the geometrically nonlinear behavior was modeled using Lagrangian description of motion. Also, the behavior of steel was modeled by applying yield criteria of Von Mises. The developed program was applied to the analysis of the dynamic behavior for the clamped beam subjected to the concentrated load at midspan and the results were compared with those from other research to investigate accuracy of the presented finite element program. In numerical examples, the shape imperfections of L/500, L/1,000 and L/2,000 were considered and the modes of shape imperfections of the symmetric and antisymmetric were adopted. The effects of the shape imperfections on the dynamic behavior of arch were conspicuous and results of analysis indicate that the reasonable values of arch rise to arch span ratio ranged between 0.1 and 0.3.

• 대한기계학회논문집A
• /
• 제27권9호
• /
• pp.1562-1570
• /
• 2003

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. The radial return mapping is one of the most robust integration scheme currently used. Nonlinear kinematic hardening model of Armstrong-Fredrick type has recovery term and the direction of kinematic hardening increment is not parallel to that of plastic strain increment. In this case, The conventional radial return mapping method cannot be applied directly. In this investigation, we expanded the radial return mapping method to consider the nonlinear kinematic hardening model and implemented this integration scheme into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using Newton method and bisection method. Using dynamic yield condition derived from linearization of flow rule, the integration scheme for elastoplastic and viscoplastic constitutive model was unified. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• 소성∙가공
• /
• 제14권5호
• /
• pp.466-472
• /
• 2005

Inelastic deformation behavior of metals and alloys is considered rate dependent. Uniaxial ratcheting experiments performed by Ruggles and Krempl, and Hassan and Kyriakides exhibited that higher mean stress for a fixed stress amplitude resulted in higher ratchet strain within a rate independent framework and higher stress rate resulted in lower ratchet strain, respectively. These phenomena are qualitatively investigated by numerical experiments through unified viscoplasticity theory. The theory does not separate rate-independent plasticity and rate-dependent creep, and thus uses only one inelastic strain to describe inelastic deformation processes with the concept of the yield surface. The growth law for the kinematic stress, which is a tensor valued state variable of the constitutive equations, is modified to predict the linear evolution of long-term ratchet strain.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 1997년도 추계학술대회 논문집
• /
• pp.973-976
• /
• 1997

Process behavior in metal cutting results from the chip formation process which is not easily observable and measurable during machining. By means of the finite element method chip formation in orthogonal metal cutting is modeled. The reciprocal interaction between mechanical and thermal loads is taken into consideration by involving the thermo-viscoplastic flow behavior of workpiece material. Local and temporal distributions of stress and temperature in the cutting zone are calculated depending on the cutting parameters. The calculated cutting forces and temperatures are compared with the experimental results obtarned from orthogonal cutting of steel AISl 4140. The model can be applied in process design for selection of appropriate tool-workpiece combination and optimum cutting conditions in term of mechanical and thermal loads.

• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 1996년도 추계학술대회논문집
• /
• pp.38-47
• /
• 1996

Sectional analysis program for plane strain or axisymmetric geometry of aluminum alloy sheet metals was developed. For modeling the anomalous behavior of aluminum alloy, Barlat's strain rate potential and Hill's 1990 non-quadratic yield theory arranged under the plane stress assumption were employed. 2-D rigid-viscoplastic FEM formulation based on the bending-augmented membrane theory was derived, solving simultaneously force equilibrium as well as non-penetration condition. Isotropic hardening law was also assumed for yielding behavior. To verify the validity and availability of the developed program, 2-D stretch/draw forming process for plane strain geometry and cylindrical cup deep drawing process for axisymmetric geometry were simulated.