Prediction of Equilibrium and Stability of Molten Solder Geometries by Finite Element Analysis

2005 ◽  
Author(s):  
Takahiro Nagata ◽  
Takaya Kobayashi
Keyword(s):  
Surface Tension ◽  
Liquid Drop ◽  
Dynamic Effect ◽  
Shell Element ◽  
Molten Solder ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Creep Model ◽  
Element Analysis ◽  
Liquid Drops

Improving the reliability on solder joints is one of the major tasks to achieve downsizing of electronics products. Taking the molten solder profile as an object of study, a new procedure to model solder liquid with a structural FEM has been developed, which enables us to solve an issue of predefining the geometrical profile of solder liquid drops in a state of static equilibrium taking the surface tension into account, and also a problem concerning dynamic stability of the liquid drops. Molten solder liquid is treated as viscous fluid. Deformation of the material due to its viscosity can be represented by the structural analysis using rheological approach. Two types of the constitutive laws, creep model or viscoelasticity model, can be applied. Such a simple case as the Newtonian fluid, either constitutive law may be employed. Using these types of the constitutive laws in the analysis with time incremental steps, it becomes possible not only to obtain the stabilized shape of liquid drops, but also to analyze problems involved with transient (including dynamic effect) stability. As the size of a liquid drop is microscopic in a range of 100 to 1000 μm, the effect of the surface tension must become so predominant in the loading conditions. In most of the conventional theoretical researches, it is found that the surface tension is treated as the pressure difference varying according to the surface curvature. However, this method is not only so complicated, but also may lead to numerical instability particularly in the transient analysis subjected to large deformations. In this study, an effective method has been developed in which the surface tension can be represented with good accuracy through simplified input data with allocating the shell element generating a constant membrane force over the surface of a liquid drop.

Plastic Deformation Theory Application in Finite Element Analysis

2012 ◽  
Vol 594-597 ◽  
pp. 2723-2726
Author(s):  
Wen Shan Lin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Element Analysis ◽  
Finite Element Program ◽  
Theory Of Plasticity ◽  
Element Program

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

Prediction of Equilibrium and Stability of Molten Solder Profiles by Finite Element Analysis

2002 ◽  
Author(s):  
Takahiro Nagata ◽  
Takaya Kobayashi ◽  
Hiroshi Sakuta
Keyword(s):  
Surface Tension ◽  
Solder Joint ◽  
Flip Chip ◽  
Deformation Analysis ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Liquid Drops ◽  
Practical Applications ◽  
Updating Procedure ◽  
2D And 3D

In development of surface mount technology for Ball Grid Array (BGA) or flip-chip assemblies, it is important to reduce stress concentration in solder joints as it is immediately effective in improving the fatigue life of the assembly. Thus, the ability to predict and control the joint geometries is critical to obtaining robust and reliable designs of interconnects. Other than the issue of the bump shape, there are many problems concerning soldering such as bridging or self-alignment in which surface tension is definitely involved. This paper attempts to apply the FEM approach in solving these problems. Rigid-plastic FEM which is based on iteration for the velocity field in an incompressible viscous fluid is an approach to large deformation analysis. The flow stress is described by the viscosity of the fluid and the strain rate. By introducing an automatic mesh updating procedure, transient problems with free boundary can be treated. We applied this concept to the prediction of solder joint shapes. In this kind of problem, effects of surface tension dominate. Since surface tension is a distributed load that depends on surface curvature, we employed 2D and 3D methods in which the load is updated based on instantaneous state of surface. To verify the accuracy of this method, we analyzed some shape and stability problems of liquid drops for which theoretical solutions were given. Practical applications of the method were also performed for the 2D and 3D solder joint problems, and the results showed a good agreement with experimental ones.

Remarks concerning a free boundary problem arising in the theory of liquid drops and in plasma physics

1989 ◽  
Vol 111 (1-2) ◽  
pp. 169-181 ◽  
Author(s):  
John W. Barrett ◽  
Charles M. Elliott
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Plasma Physics ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Liquid Drop ◽  
Liquid Drops ◽  
Plasma Problem ◽  
A Free Boundary Problem ◽  
Surface Tension Coefficients

SynopsisWe consider a generalisation of the liquid drop problem, introduced in [1, Part II], by allowing the upper and lower surfaces to have different surface tension coefficients γv and γu. We study the existence, uniqueness and regularity of this problem. In addition, we show that as γv/γu →0, the solution of this problem converges to the solution of the “plasma problem”.

Creep Modeling of Welded Joints Using the Theta Projection Concept and Finite Element Analysis

1999 ◽  
Vol 122 (1) ◽  
pp. 22-26 ◽  
Author(s):  
M. Law ◽  
W. Payten ◽  
K. Snowden
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
High Temperature ◽  
Welded Joints ◽  
Creep Model ◽  
Projection Data ◽  
Predictive Capability ◽  
Element Analysis ◽  
High Temperature And Pressure ◽  
Temperature And Pressure

Modeling of welded joints under creep conditions with finite element analysis was undertaken using the theta projection method. The results were compared to modeling based on a simple Norton law. Theta projection data extends the accuracy and predictive capability of finite element modeling of critical structures operating at high temperature and pressure. In some cases analyzed, it was found that the results diverged from those gained using a Norton law creep model. [S0094-9930(00)00601-6]

Analysis of Thick-Walled Pipeline Elements Operating in Creep Conditions

2015 ◽  
Vol 712 ◽  
pp. 63-68
Author(s):  
Przemysław Osocha ◽  
Bohdan Węglowski
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Creep Test ◽  
Power Plants ◽  
Steam Pressure ◽  
Creep Model ◽  
Creep Process ◽  
Fe Model ◽  
Element Analysis ◽  
Wide Range

In some coal-fired power plants, pipeline elements have worked for over 200 000 hours and increased number of failures is observed. The paper discuses thermal wear processes that take place in those elements and lead to rupture. Mathematical model based on creep test data, and describing creep processes for analyzed material, has been developed. Model has been verified for pipeline operating temperature, lower than tests temperature, basing on Larson-Miller relation. Prepared model has been used for thermal-strength calculations based on a finite element method. Processes taking place inside of element and leading to its failure has been described. Than, basing on prepared mathematical creep model and FE model introduced to Ansys program further researches are made. Analysis of dimensions and shape of pipe junction and its influence on operational element lifetime is presented. In the end multi variable dependence of temperature, steam pressure and element geometry is shown, allowing optimization of process parameters in function of required operational time or maximization of steam parameters. The article presents wide range of methods. The creep test data were recalculated for operational temperature using Larson-Miller parameter. The creep strain were modelled, used equations and their parameters are presented. Analysis of errors were conducted. Geometry of failing pipe junction was introduced to the Ansys program and the finite element analysis of creep process were conducted.

Verification of a Finite Element Analysis Procedure for Modeling the Nonlinear, Monotonic In-Plane Behavior of 4 Inch, Schedule 10, Stainless Steel, 90° Elbows

2003 ◽  
Author(s):  
James K. Wilkins
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stainless Steel ◽  
Nonlinear Behavior ◽  
Shell Element ◽  
Analysis Procedure ◽  
Hoop Strain ◽  
Element Analysis ◽  
Butt Welding ◽  
Strain Data

A project has been conducted to verify a finite element analysis procedure for studying the nonlinear behavior of 90°, stainless steel, 4 inch schedule 10, butt welding elbows. Two displacement controlled monotonic in-plane tests were conducted, one closing and one opening, and the loads, displacements, and strains at several locations were recorded. Stacked 90° tee rosette gages were used in both tests because of their ability to measure strain over a small area. ANSYS shell element 181 was used in the FEA reconciliations. The FEA models incorporated detailed geometric measurements of the specimens, including the welds, and material stress-strain data obtained from the attached straight piping. Initially, a mesh consisting of sixteen elements arrayed in 8 rings was used to analyze the elbow. The load-displacement correlation was quite good using this mesh, but the strain reconciliation was not. Analysis of the FEA results indicated that the axial and hoop strain gradients across the mid-section of the elbow were very high. In order to generate better strain correlations, the elbow mesh was refined in the mid-section of the elbow to include 48 elements per ring and an additional six rings, effectively increasing the element density by nine times. Using the refined mesh produced much better correlations with the strain data.

Analysis and Optimization of Bellows With General Shape

1998 ◽  
Vol 120 (4) ◽  
pp. 325-333 ◽  
Author(s):  
B. K. Koh ◽  
G. J. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Beam Theory ◽  
Inequality Constraints ◽  
Shell Element ◽  
Scalar Function ◽  
Programming Algorithm ◽  
Multiple Objective ◽  
Axially Symmetric ◽  
Element Analysis

A bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axially symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze the bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis program is developed to analyze various bellows. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. A shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function with weighting factors. The stiffness, strength, and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the natural frequencies, the fatigue limit, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is utilized to solve the problem.

The stability of pendent liquid drops. Part 2. Axial symmetry

1974 ◽  
Vol 63 (3) ◽  
pp. 487-508 ◽  
Author(s):  
E. Pitts
Keyword(s):  
Surface Tension ◽  
Energy Change ◽  
Maximum Volume ◽  
Experimental Conditions ◽  
Liquid Drops ◽  
Stable Equilibria ◽  
Equilibrium Shapes ◽  
The Stability ◽  
The Many ◽  
Horizontal Support

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

scholarly journals Granular impact cratering by liquid drops: Understanding raindrop imprints through an analogy to asteroid strikes

2014 ◽  
Vol 112 (2) ◽  
pp. 342-347 ◽  
Author(s):  
Runchen Zhao ◽  
Qianyun Zhang ◽  
Hendro Tjugito ◽  
Xiang Cheng
Keyword(s):  
High Speed ◽  
Granular Media ◽  
Liquid Drop ◽  
Impact Craters ◽  
High Speed Photography ◽  
Impact Cratering ◽  
Liquid Drops ◽  
Asteroid Impact ◽  
Liquid Marble ◽  
Crater Morphology

When a granular material is impacted by a sphere, its surface deforms like a liquid yet it preserves a circular crater like a solid. Although the mechanism of granular impact cratering by solid spheres is well explored, our knowledge on granular impact cratering by liquid drops is still very limited. Here, by combining high-speed photography with high-precision laser profilometry, we investigate liquid-drop impact dynamics on granular surface and monitor the morphology of resulting impact craters. Surprisingly, we find that despite the enormous energy and length difference, granular impact cratering by liquid drops follows the same energy scaling and reproduces the same crater morphology as that of asteroid impact craters. Inspired by this similarity, we integrate the physical insight from planetary sciences, the liquid marble model from fluid mechanics, and the concept of jamming transition from granular physics into a simple theoretical framework that quantitatively describes all of the main features of liquid-drop imprints in granular media. Our study sheds light on the mechanisms governing raindrop impacts on granular surfaces and reveals a remarkable analogy between familiar phenomena of raining and catastrophic asteroid strikes.

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