Thermomechanical Stress Analysis of Multi-Layered Electronic Packaging

2003 ◽  
Vol 125 (1) ◽  
pp. 134-138 ◽  
Author(s):  
Yujun Wen ◽  
Cemal Basaran
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Orthotropic Material ◽  
Thermal Stresses ◽  
Order Approximation ◽  
Closed Form Solution ◽  
Accurate Estimate ◽  
Form Solution ◽  
Element Analysis ◽  
Thermomechanical Stress

An accurate estimate of thermal stresses in multilayered microelectronics structures along the bonded interfaces is crucial for design and prediction of delamination-related failures. Compared with a numerical method, analytical closed-form solution can offer a more rapid method to obtain the stresses at the interfaces. An analytical model for ply-level sub-laminate analysis is investigated in this paper. The theory presented treats each layer as a beam-type plate with orthotropic material properties. As an example, the results are shown for a three-layer beam problem with special orthotropic material properties. Analytical model results are compared with the finite element analysis results, as a first order approximation.

Thermal Induced Stresses in Bridge-Wire Initiator Glass-to-Metal Seals

2006 ◽  
Vol 129 (3) ◽  
pp. 300-306 ◽  
Author(s):  
Luke M. Thompson ◽  
Michael R. Maughan ◽  
Karl K. Rink ◽  
Donald M. Blackketter ◽  
Robert R. Stephens
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Manufacturing Processes ◽  
Material Degradation ◽  
Element Analysis ◽  
Parametric Plane ◽  
Lumped Models

Cracks have been observed in the insulating glass of bridge-wire initiators that may allow moisture to penetrate the assembly, potentially leading to the corrosion and degradation of the bridge wire and the pyrotechnic material. Degradation of the pyrotechnic or the bridge wire may result in initiator failure or diminished performance. The goal of this research is to determine if the manufacturing processes could produce thermal stresses great enough to crack the glass. A parametric plane stress closed-form solution was used to determine the effects of changing material properties and dimensions of the initiator, and to determine potential stresses within the initiator from two different manufacturing scenarios. To verify and expand the plane stress closed-form solution, a two-dimensional axisymmetric finite element analysis was performed. To reproduce the two manufacturing scenarios, lumped models and models that included the effects of cooling the initiator were used. Both models showed that if the manufacturing process involves pouring molten glass into the initiator, the potential for cracking exists. Furthermore, if the surface of the initiator cools faster than the center, cracking is more likely.

Thermal Stress Analysis of a Multi-Layered Structure

2011 ◽  
Vol 467-469 ◽  
pp. 275-278
Author(s):  
Shiuh Chuan Her ◽  
Chin Hsien Lin
Keyword(s):  
Analytical Model ◽  
Layered Structure ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
Bernoulli Beam ◽  
Compatibility Conditions ◽  
Strain Compatibility ◽  
Good Agreement

Analytical model based on the Bernoulli beam theory and strain compatibility conditions at the interfaces between the two layers have been developed to predict the distribution of thermal stresses within the multi-layered structure due to the mismatch of thermal expansion. The closed-form solution of thermal stresses related to the material properties and geometry were obtained. It is useful to provide a simple and efficient analytical model, so that the stress level in the layers can be accurately estimated. The analytical results are compared with finite element results. Good agreement demonstrates that the proposed approach is able to provide an efficient way for the calculation of the thermal stresses.

scholarly journals Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

2021 ◽  
Author(s):  
Alessandro Barbiero ◽  
Asmerilda Hitaj
Keyword(s):  
Order Approximation ◽  
Linear Optimization ◽  
Closed Form Solution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Computation Time ◽  
Form Solution ◽  
Engineering Problem ◽  
Approximation Technique ◽  
Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

scholarly journals Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

2002 ◽  
Author(s):  
P.-S. Lam ◽  
Y. J. Chao ◽  
X.-K. Zhu ◽  
Y. Kim ◽  
R. L. Sindelar
Keyword(s):  
Carbon Steel ◽  
Test Data ◽  
Storage Tank ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Fracture Parameter ◽  
Element Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A2, while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-R curves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Displacement Formulations for Deformation and Vibration of Elastic Circular Torus

2021 ◽  
Author(s):  
bohua sun
Keyword(s):  
Free Vibration ◽  
Gaussian Curvature ◽  
Turning Point ◽  
Closed Form Solution ◽  
Complex Form ◽  
Form Solution ◽  
Element Analysis ◽  
Displacement Boundary ◽  
Engineering Mechanics ◽  
Maple Code

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

Thermal Stress Measurement of Solder Joints in BGA Packages: Theoretical and Experimental

2008 ◽  
Author(s):  
H. X. Shang ◽  
J. X. Gao ◽  
P. I. Nicholson
Keyword(s):  
Thermal Stresses ◽  
Solder Joints ◽  
Stress Measurement ◽  
Closed Form Solution ◽  
Dissimilar Materials ◽  
Form Solution ◽  
Bga Packages ◽  
Reliability Characteristics ◽  
Bga Package ◽  
Graded Interlayer

In this study, an analytical model to obtain a closed-form solution for thermomechanical behaviours of BGA (Ball Grid Array) package was derived and experimentally validated. In the theoretical analysis, the BGA package was represented by a three-layer axisymmetrical model: two layers of dissimilar materials jointed by a graded interlayer. Based on the classical bending theory, the thermal stresses induced by temperature changes were calculated accurately. 2-D FE (Finite Element) meshes of BGA packages subjected to high temperature were used to verify the theoretical solutions. Furthermore, two types of BGA samples, each with eutectic (63wt%Sn/37wt%Pb) and Pb-free SAC387 (95.5wt%Sn/3.8wt%Ag/0.7wt%Cu) solder joints respectively, were experimentally investigated by high resolution Moire´ Interferometry (MI). Thermal cycling tests were performed on each package with temperature variation from 25°C to 125°C. It was found that the thermal deformation obtained from moire´ tests matched well with those from analytical solutions and FE analyses. Based on the shear strain values, the reliability characteristics of BGA assemblies were also assessed.

Strengthening of wide-flange columns under load

1990 ◽  
Vol 17 (5) ◽  
pp. 835-843 ◽  
Author(s):  
H. Marzouk ◽  
S. Mohan
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Critical Load ◽  
Closed Form Solution ◽  
Welding Process ◽  
Form Solution ◽  
Element Analysis ◽  
Welding Stress ◽  
Existing Structures ◽  
Welding Sequence

The present work deals with formulation of theoretical and analytical methods leading to the development of column strength curves. The formulations were developed for both elastic and inelastic behaviour. Two types of reinforcement have been developed for strengthening the W-shape columns under load. Since the column strength curves are based in part on the magnitude and distribution of residual stresses, it is extremely important to consider the new pattern of residual stresses due to welding process. Also, the welding sequence will affect the magnitude and distribution of residual stresses. Theoretical formulations leading to a closed-form solution for the prediction of critical load were developed for two types of strengthening using the superposition of original residual, new welding, and initial loading stresses. A nonlinear finite element analysis based on the large deformation theory of stability was used to predict the strengthened column critical load. It takes into consideration the effect of cooling residual stresses and new welding residual stresses. The formulations were incorporated with gradual penetration of yielding, the spreading of inelastic zones along the member length, the presence of residual stresses, and strain hardening of the material. Experiments were carried out to determine the actual capacity of strengthened columns. Seven specimens were tested using two and four strengthening plates. The welding stresses were measured through a series of experiments, and it was found that the parabolic distribution is a very close approximation to the actual new welding stress distribution. Key words: reinforcement of steel columns, welding stresses, welding sequence, strengthening of existing structures, buckling, steel plating, finite element.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

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