bluuebunny/crossref_metadata_2025 huggingface dataset:
Consistent Hashin-Shtrikman Bounds on the Effective Properties of Periodic Composite Materials
Authors: Bisegna P. , Luciano R.
Published: February 2008

In this paper the four classical Hashin-Shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.
Singular Solutions in Second-Order Elasticity
Authors: Carroll M. M. , Rooney F. J.
Published: February 2008

The problems of a concentrated point force in an infinite medium (Kelvin's problem), or applied normal to the boundary of a half-space (Boussinesq's problem), as well as the corresponding problems for a concentrated couple, are solved to second order for incompressible isotropic elastic solids. The solutions are based on a simplified form of the second-order equations, obtained previously, and use of the Love's function representation for axisymmetric problems in the linear theory.
On the Dynamic Growth of a Spherical Inclusion With Dilatational Transformation Strain in Infinite Elastic Domain
Authors: Wang B. , Sun Q. , Xiao Z.
Published: February 2008

In this paper, the dynamic effect was incorporated into the initiation and propagation process of a transformation inclusion. Based on the time-varying propagation equation of a spherical transformation inclusion with pure dilatational eigenstrain, the dynamic elastic fields both inside and outside the inclusion were derived explicitly, and it is found that when the transformation region expands at a constant speed, the strain field inside the inclusion is time-independent and uniform for uniform eigenstrain. Following the basic ideas of crack propagation problems in dynamic fracture mechanics, the reduction rate of the mechanical part of the free energy accompanying the growth of the transformation inclusion was derived as the driving force for the move of the interface. Then the equation to determine the propagation speed was established. It is found that there exists a steady speed for the growth of the transformation inclusion when time is approaching infinity. Finally the relation between the steady speed and the applied hydrostatic stress was derived explicitly.
Lateral Thermal Buckling of Pipelines on the Sea Bed
Authors: Miles D. J. , Calladine C. R.
Published: February 2008

Lateral buckling can occur in a submarine pipeline laid (without trenching) on the seabed, when the oil temperature rises. Motion of the (elastic) pipe relative to the sea bed is resisted by friction. The initial buckling is a localization phenomenon, and the first buckle lobes to form grow in amplitude most rapidly as the temperature increases. But as the temperature continues to rise, these early buckles cease growing, and growth is transferred to adjacent, newly formed lobes. The lobes first formed thus eventually become “extinct.” We investigate these phenomena by means of a small-scale physical model and by computer simulation. The results of many computer runs can be condensed into a few universal curves by the use of suitable dimensionless groups. Simple formulas emerge for the amplitude and wavelength of the “extinct” lobes, and for the maximum bending strain experienced by the pipeline, as a function of temperature.
A Strip Element Method for Analyzing Wave Scattering by a Crack in an Immersed Composite Laminate
Authors: Liu G. R. , Xi Z. C. , Lam K. Y. , Shang H. M.
Published: February 2008

A strip element method is presented for analyzing wave scattering by a crack in a composite laminate submerged in a fluid. In this method, the fluid and laminated plate are modeled using two-nodal-line and three-nodal-line strip elements, respectively. A system of governing equations of the fluid and solid strip elements in frequency domain are derived using a variational method and the Hamilton principle, which are converted as a set of characteristic equations in wave number domain by applying Fourier transform techniques. A particular solution to the equations is obtained using a modal analysis method in conjunction with inverse Fourier transform techniques. A complementary solution to the equations is found employing horizontal boundary conditions on cross sections at the crack tips. The addition of the particular and complementary solutions yields a general solution. Numerical examples are presented for immersed steel and composite plates with either a horizontal or a vertical crack. Computed results indicate that the fluid has considerable influence on the wave fields scattered by a crack in a composite laminate.
The Onset of Tear Propagation at Slits in Stressed Uncoated Plain Weave Fabrics
Authors: Godfrey T. A. , Rossettos J. N.
Published: February 2008

A simple micromechanical model is developed to predict the onset of tear propagation at slit-like damage sites (i.e., a series of consecutive aligned yarn breaks) in biaxially stressed plain weave fabrics under increasing loading. A crucial aspect of the model is the treatment of the frictional slip of yarns near the damage site. Although the actual configuration of slipping regions is complex, the onset of tear propagation in large slits (i.e., more than, say, 35 breaks) is dominated by slip occurring on the first few intact yarns adjacent to the breaks. The assumptions in the mathematical model were motivated by both experimental observations and calculations for key configurations. Analytical results obtained for this simple model exhibit good agreement with experimental results, which are presented for a variety of fabrics with initial slits of 35 and 45 breaks.
The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables
Authors: Ghanem R.
Published: February 2008

A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The polynomial chaos expansion results in a representation of a stochastic process in terms of multidimensional polynomials orthogonal with respect to the gaussian measure with the dimension defined through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic finite element method, as well as for the analytical investigation of the mathematical properties of lognormal processes.
An Exact Periodic Solution of a Hydromagnetic Flow of an Oldroyd Fluid in a Channel
Authors: Ray R. N. , Samad A. , Chaudhury T. K.
Published: February 2008

The unsteady flow of a conducting Oldroyd fluid between two parallel plates, one of which is at rest and the other oscillating in its own plane with a constant mean velocity, has been investigated. Using separation of variables an exact periodic solution for the problem is obtained. Effects of viscoelastic parameters on velocity gradient, skin friction amplitude, and phase angle of the flow are discussed with graphs.
Response Bounds for Linear Damped Systems
Authors: Hu B. , Eberhard P.
Published: February 2008

In this paper response bounds of linear damped systems are reviewed and new response bounds are presented for free vibrations and forced vibrations under impulsive, step, and harmonic excitation. In comparison to the response bounds available in the literature, the ones presented here are not only closer to the exact responses, but are also simpler to compute. Previous bounds are given only on the Euclidean norm of the state vector or the displacement vector. Here, the response bounds are also given on individual coordinates, information which is more meaningful in engineering.
Identification of a Dynamic System Using Ambient Vibration Measurements
Authors: Feng M. Q. , Kim J.-M. , Xue H.
Published: February 2008

This paper demonstrates how ambient vibration measurements at a limited number of locations can be effectively utilized to estimate parameters of a finite element model of a large-scale structural system involving a large number of elements. System identification using ambient vibration measurements presents a challenge requiring the use of special identification techniques, which can deal with very small magnitudes of ambient vibration contaminated by noise without the knowledge of input forces. In the present study, the modal parameters such as natural frequencies, damping ratios, and mode shapes of the structural system were estimated by means of appropriate system identification techniques including the random decrement method. Moreover, estimation of parameters such as the stiffness matrix of the finite element model from the system response measured by a limited number of sensors is another challenge. In this study, the system stiffness matrix was estimated by using the quadratic optimization involving the computed and measured modal strain energy of the system, with the aid of a sensitivity relationship between each element stiffness and the modal parameters established by the second-order inverse modal perturbation theory. The finite element models thus identified represent the actual structural system very well, as their calculated dynamic characteristics satisfactorily matched the observed ones from the ambient vibration test performed on a large-scale structural system subjected primarily to ambient wind excitations. It is noted that newly developed optical fiber accelerometers were used for this ambient vibration test. The dynamic models identified by this study will be used for design of an active mass damper system to be installed on this structure for suppressing its wind vibration.
An Infrared Interferometer for Elastoplastic Crack-Tip Field Investigation of Homogeneous and Bimaterial Beams: A Study of Three-Dimensional Effects and J-Dominance
Authors: Sinha J. K. , Tippur H. V.
Published: February 2008

An infrared interferometer capable of performing real-time full-field noncontacting deformation field measurements on optically rough surfaces is proposed as a tool for elastoplastic fracture mechanics investigations. The choice of the infrared wavelength allows interferometric measurements on fracture samples with little or no surface preparation and is more tolerant of the damage accumulation near the crack. The interferometer also bridges a sensitivity gap among existing techniques for out-of-plane deformation measurement. First, a rigorous Fourier optics analysis is provided for the interferometer and the range of surface roughness that can be studied using this interferometer is examined. The interferometer is then used for mapping deformations near elastoplastically deformed cracks in aluminum beams and solder-copper bimaterials. The regions of dominant three-dimensional effects and J-dominance are examined on the sample surface by evaluating measurements along with companion finite element analyses and the HRR fields.
Mohr-Coulomb Failure Criterion Expressed in Terms of Stress Invariants
Authors: Schajer G. S.
Published: February 2008

A polynomial expression for the Mohr-Coulomb criterion for failure of brittle or frictional materials in terms of stress invariants is derived. The form of the polynomial expression corresponds to the pyramidal shape of the failure surface in principal stress space. The pressure-sensitive character of the failure of a Mohr-Coulomb material is indicated by a linear influence of the first stress invariant I1 in the polynomial expression.
Layer-Wise Mixed Models for Accurate Vibrations Analysis of Multilayered Plates
Authors: Carrera E.
Published: February 2008

This paper presents the dynamic analysis of multilayered plates using layer-wise mixed theories. With respect to existing two-dimensional theories at the displacement formulated, the proposed models a priori fulfill the continuity of transverse shear and normal stress components at each interface between two adjacent layers. A Reissner’s mixed variational equation is employed to derive the differential equations, in terms of the introduced stress and displacement variables, that govern the dynamic equilibrium and compatibility of each layer. The continuity conditions at the interfaces are used to write corresponding equations at multilayered level. Related standard displacement formulations, based on the principle of virtual displacements, are given for comparison purposes. Numerical results are presented for the free-vibration response (fundamental and higher order frequencies are calculated) of symmetrically and unsymmetrically laminated cross-ply plates. Several comparisons to three-dimensional elasticity analysis and to some available results, related to both layer-wise and equivalent single-layer theories, have shown that the presented mixed models: (1) match the exact three-dimensional results very well and (2) lead to a better description in comparison to results related to other available analysis.
Study of Residual Stress Distribution by a Combined Method of Moire´ Interferometry and Incremental Hole Drilling, Part I: Theory
Authors: Wu Zhu , Lu Jian , Han Bongtae
Published: February 2008

A new method combining Moire´ interferometry and the incremental hole-drilling method is developed to determine both uniform and nonuniform residual stress distribution in depth. The study is reported in two parts. In this first part, the theoretical development of the moire´ interferometry hole-drilling method is presented. The relationship between the in-plane surface displacements produced by introducing a blind hole and the corresponding residual stresses is established by employing the existing theoretical solution containing a set of undetermined coefficients. The coefficients are calibrated by the three-dimensional finite element method and they are processed nondimensionally for general use. The whole field in-plane surface displacements data Ux and Uy produced by the relaxation of residual stresses are obtained from moire´ interferometry after each increment of hole drilling. The high signal-to-noise ratio provided by moire´ interferometry allows accurate determination of fringe orders near the hole boundary which is essential for enhancing fidelity of residual stress determination. The experimental procedure to determine the signs of residual stresses is described and the accuracy of the method is also discussed.
On the Stress Field in Sliding Ellipsoidal Inclusions With Shear Eigenstrain
Authors: Lubarda V. A. , Markenscoff X.
Published: February 2008

A stress distribution in elliptical inclusions with sliding interface and uniform shear eigenstrain is analyzed. The existence of a nonvanishing stress in nearly circular inclusions is demonstrated, and an approximate method for its determination is suggested. An inherent nonlinear dependence of the stress on applied eigenstrain is indicated and discussed.
Inclusions of Uniform Eigenstrains and Constant or Other Stress Dependence
Authors: Markenscoff X.
Published: February 2008

It is shown that the Eshelby inclusions, that is inclusions of uniform eigenstrains and constant eigenstress, form in three dimensions a connected nine-dimensional manifold, and, as a consequence, the only perturbations of an ellipsoid that preserve the Eshelby property are into another ellipsoid. The method is illustrated in both two and three dimensions, and can be also used to treat similar questions of other than constant dependence of the stress.
A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems
Authors: Sun J. Q.
Published: February 2008

This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly from being linear to being strongly nonlinear. The nonuniform cell partition is shown to lead to more accurate steady-state solutions and enhance the computational efficiency of the GCM method.
Invariants of Chaotic Attractor in a Nonlinearly Damped System
Authors: Ravindra B. , Hagedorn P.
Published: February 2008

The characterization of a chaotic attractor in a driven, Duffing-Holmes oscillator with power-law damping is considered. State space reconstruction of the time series of the attractor is carried out to investigate its structure. The invariants associated with the attractor such as correlation dimension and entropy are computed. Also the maximum-likelihood (ML) estimation of dimension and entropy are carried out. The use of obtained invariants in building models for prediction and control using power-law dampers is discussed.
Solution of the Displacement Boundary Value Problem of an Interface Between Two Dissimilar Half-Planes and a Rigid Elliptic Inclusion at the Interface
Authors: Boniface V. , Hasebe N.
Published: February 2008

The displacement boundary value problem of a bimaterial interface is solved using the complex stress function technique. A rational mapping function is used to map the two half-planes into unit circles and analysis is carried out in the mapped plane. The symmetric bimaterial problem is considered and the particular case of a rigid elliptic inclusion at the interface is solved. Uniform remote tensions both along and normal to the interface are considered. Stress distributions on the inclusion boundary are shown. Stress concentration factors at the inclusion tips are obtained and are expressed in terms of the radius of curvature using an approximate form of a general expression. These results are used to predict the likelihood of debonding/cracking at the tips. Also, stress concentration factors at the tips of an elliptic inclusion and elliptic void are compared. Stress intensity factors at the tips of a thin rigid elliptic inclusion are also determined.
Effect of Material Properties in Certain Thermoelastic Contact Problems
Authors: Joachim-Ajao D. , Barber J. R.
Published: February 2008

When two conforming bodies slide against each other, frictional heating and thermoelastic distortion generally causes the contacting surfaces to become convex and hence leads to a reduction in the size of the contact area. It is shown that, under such circumstances, the contact area is independent of the applied contact loads and the thermal and mechanical fields are linearly proportional to these loads. For two-dimensional problems involving a plane boundary, it is shown that there is a reduced dependence on material properties and in the case of a single material, the solution depends only on a single parameter which can be interpreted as a dimensionless sliding speed. These results extend to both steady-state and transient problems and therefore also characterize the critical sliding speed above which the system is unstable.
Two Interpretations of Rigidity in Rigid-Body Collisions
Authors: Chatterjee A. , Ruina A.
Published: February 2008

We distinguish between, and discuss the applicability of, two levels of rigidity in rigid-body collision modeling. For rigidity in the strong force-response sense, collisional contact deformations must be highly localized. The bodies then move according to second-order rigid-body mechanics during the collision. Incremental collision laws and most collision models using continuum mechanics for the contact region depend on force-response rigidity. For rigidity in the weaker impulse-response sense, the deformations need not be localized but displacements during the collision need to be small everywhere. Only the time-integrated rigid-body equations, involving before-collision and after-collision velocities, then need apply. Although a force-response rigid body is also impulse-response rigid the converse is not true. Algebraic collision laws depend only on impulse-response rigidity. Elastic vibration models of collisions are also generally consistent with impulse-response rigidity.
Application of Homotopy Analysis Method in Nonlinear Oscillations
Authors: Liao Shi-Jun , Chwang A. T.
Published: February 2008

In this paper, we apply a new analytical technique for nonlinear problems, namely the Homotopy Analysis Method (Liao 1992a), to give two-period formulas for oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. These two formulas are uniformly valid for any possible amplitudes of oscillation. Four examples are given to illustrate the validity of the two formulas. This paper also demonstrates the general validity and the great potential of the Homotopy Analysis Method.
An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces
Authors: Hurmuzlu Y.
Published: February 2008

A new method to solve the collision problems of slender bars with massive external surfaces is developed. The proposed solution accounts for the effect of impact induced vibrations and multiple collisions on the post-collision velocities of the impacting members. The approach is based on representing the vibrational energy of the bars during the collision process in terms of a nondimensional parameter, termed the elastic energy percentile. The elastic energy percentile is expressed as a simple scalar function of the drop angle and a nondimensional parameter, which encapsulates the bar geometry, material, and the stiffness of the contact surface. The elastic energy percentile is then used to develop a new momentum-based solution method. The method relies on a revised energetic coefficient of restitution that resolves the effect of impact induced vibrations on the post-collision velocities of the impacting bars. The assumptions used in the theoretical development and the outcomes predicted by the proposed method were verified by conducting a set of experiments using several bars with varying geometric and material properties.
Anisotropic Constraint Effects on Interactive Damage Progression of General Lay-up Composites
Authors: Fan J. , Zhang J.
Published: February 2008

In this paper, a five-layer model is proposed to analyze the anisotropic constraint effects on interactive damage progression. Incorporating this model with the general theory of overall moduli of a cracked body, the effective damage factors proposed by Fan and Zhang in 1993 have been extended as quantitative measures for characterizing the anisotropic constraint effects on damage-induced stiffness reduction of general lay-up composites. By applying the first-order shear deformation plate theory to each sublayer these factors are determined and applied for investigating progressive matrix cracking-delamination interaction. Results show that by this rather unique approach, the intractable problem of anisotropic constraint effects of general lay-up composites on interactive damage progression can be handled in a systematic manner.
On the Existence of Normal Modes of Damped Discrete-Continuous Systems
Authors: Banks H. T. , Luo Zheng-Hua , Bergman L. A. , Inman D. J.
Published: February 2008

In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.
Wirebond Deformation During Molding of IC Packages
Authors: Tay A. A. O. , Yeo K. S. , Wu J. H. , Lim T. B.
Published: February 2008

During the transfer molding of IC packages, wirebonds are deformed by the action of flow-induced viscous forces acting along them. Excessive deformation of wirebonds could give rise to short circuits and bond pull-outs. In this paper, the deformation of gold wirebonds during transfer molding of IC packages is studied using the finite element method. Hitherto, only elastic deformation of wirebonds has been considered. In this paper, a more realistic elasto-plastic large-deflection model is employed. The gold wire is assumed to be made of a bilinear strain hardening material. It is shown that plastic deformation in the wirebond can occur even if the melt flowrate is not very high. However, wirebond deflection may still be within acceptable limits even though certain portions of the wirebond have yielded plastically. The deformation of parabolic wirebonds under the action of melt flow, both normal and parallel to the plane of the wirebond, is also studied. The melt flow within the cavity is simulated assuming creeping flow. Parametric studies of the effects of wirebond dimensions, namely bond height, span and wire diameter, on wirebond deformation are also carried out.
Three-Dimensional Creep Analysis of Solder Joints in Surface Mount Devices
Authors: Bhatti Pardeep K. , Gschwend Klaus , Kwang Abel Y. , Syed Ahmer R.
Published: February 2008

Three-dimensional finite element analysis has been applied for determining time-dependent solder joint response of leaded surface mount components under thermal cycling. Two main challenges are the geometric complexity in mesh development and computationally intensive analysis because of the highly nonlinear material properties. Advanced techniques have been applied, including multi-point constraints for mesh transition, which reduces the number of degrees of freedom in the model, and substructuring, which effectively reduces computational time in the iterative analysis. The result is a generic approach for nonlinear creep analysis using commercial FEA software on a high performance workstation. Illustrations are provided for J and gullwing leaded packages.
Numerical Study of Forced Convection in a Partially Porous Channel With Discrete Heat Sources
Authors: Hadim H. A. , Bethancourt A.
Published: February 2008

A numerical study was performed to analyze steady laminar forced convection in a channel partially filled with a fluid-saturated porous medium and containing discrete heat sources on the bottom wall. Hydrodynamic and heat transfer results are reported for the configuration in which the porous layers are located above the heat sources while the rest of the channel is nonporous. The flow in the porous medium was modeled using the Brinkman-Forchheimer extended Darcy model. Parametric studies were conducted to evaluate the effects of variable heat source spacing and heat source width on heat transfer enhancement and pressure drop in the channel. The results indicate that when the heat source spacing was increased within the range considered, there was a negligible change in heat transfer enhancement while the pressure drop decreased significantly. When the heat source width was decreased, there was a moderate increase in heat transfer enhancement and a significant decrease in pressure drop.
Laminar Heat Transfer Between a Series of Parallel Plates With Surface-Mounted Discrete Heat Sources
Authors: Kim S. H. , Anand N. K.
Published: February 2008

Two-dimensional laminar heat transfer between a series of parallel plates with surface mounted block heat sources was numerically studied. These channels resemble cooling passages of electronic equipment. Consideration was given only to periodically fully developed flow (PDF) and heat transfer. The computational domain was subjected to periodic condition in the streamwise direction and repeated condition in the cross-stream direction (double cyclic). The governing equations were solved by a finite volume technique. Calculations were made for a wide range of independent parameters (Re, ks/kf, s/w, d/w, H/w, and t/H). Consideration was given only to airflow (Pr=0.7). The friction factor was found to be a strong function of channel height and a weak function of block spacing. The thermal performance was studied in terms of the average Nusselt number and overall thermal resistance. For the most part, the thermal performance was independent of the Reynolds number, however, it deteriorated drastically for Re ≤ 500. The thermal resistance was found to decrease with an increase in substrate conductivity up to a particular value of ks/kf, and beyond this value thermal resistance did not decrease further. This value of ks/kf is a function of geometric parameters and occurs between 1 and 10. Correlations in terms of independent parameters were developed for friction factor, average Nusselt number, and thermal resistance.
An Approximate Method for Predicting Laminar Heat Transfer Between Parallel Plates Having Embedded Heat Sources
Authors: Figliola R. S. , Thomas P. G.
Published: February 2008

An approximate method for predicting the forced convection heat transfer for flow between parallel plates having embedded, discrete heat sources on one or both sides is presented. The spacing between sources is considered as adiabatic and the two-dimensional flow is laminar. The characteristics of such a flow can be described as flow in the isolated plate, developing flow, and fully developed flow regimes. The analysis uses appropriate forms for the surface temperature and Nusselt number solutions for the flow regimes encountered. Superposition is then applied to develop the discrete array solution for temperature and Nusselt number regardless of the arbitrary and step nature of the boundary conditions. Comparisons to existing numerical solutions show good agreement to within five percent of the predicted temperatures. A direct simulation of an existing experimental result shows reasonable agreement in the Nusselt number solution. These results validate the methodology for practical use including electronic cooling applications.
A Global Sensitivity Approach for the Dynamic Response of Printed Wiring Boards
Authors: Jensen H. , Cifuentes A. O.
Published: February 2008

This paper is concerned with the sensitivity of the dynamic response of printed wiring boards (PWB). A general method to study the sensitivity of the response of the board as a function of the variability of the design variables is presented. The method, which is based on a probabilistic approach, assumes that the design variables belong to a given interval and follow a known probabilistic distribution.
Transient Response Characteristics of Vapor Deposited Micro Heat Pipe Arrays
Authors: Peterson G. P. , Mallik A. K.
Published: February 2008

The transient thermal response of vapor deposited micro heat pipe arrays fabricated as an integral part of silicon wafers was measured to determine if these arrays could be used to reduce the local temperature gradients and improve the reliability of semiconductor devices. Wafers with arrays of 34 and 66 micro heat pipes were evaluated using an IR thermal imaging system in conjunction with a VHS video recorder. These arrays occupied 0.75 and 1.45 percent, of the wafer cross-sectional area, respectively. The wafers with micro heat pipe arrays demonstrated a 30 to 45 percent reduction in the thermal time constant when compared to that obtained for plain silicon wafers. This reduction in response time was shown to lead to a significant reduction in the maximum wafer temperature, due to the increased effective thermal conductivity caused by the vaporization and condensation occurring in the individual micro heat pipes. The experimental results were then used to validate a transient numerical model, capable of accurately predicting the transient temperature profile and thermal time constant of the wafer/heat pipe combinations.
Undercooling of 63SN-37PB Solder Pastes
Authors: Mei Zequn
Published: February 2008

Large-scale undercoolings and long incubation periods for solidification of 63Sn-37Pb solder pastes were observed through a differential scanning calorimeter, as functions of cooling rate and contact surface (aluminium versus copper). The undercooling reduced significantly with decreased cooling rate, but even at a rate of 2°C/minute, the undercooling was as large as 35°C for a no-clean solder paste in an aluminium sample pan. Poor wetting conditions (weak flux, nonwetting surfaces) led to large undercoolings and long incubation periods. The undercooling during a typical reflow process in electronic assembly was determined, by a simulated DSC test, to be about 50°C for a no-clean solder paste on bare copper surface. The large undercooling is probably caused by the reduced degree of the heterogeneous nucleation for solidification due to the small size of a solder joint and poor wetting with its contact surface.
Comparison of LCC Solder Joint Life Predictions With Experimental Data
Authors: Wen Liang-chi , Ross Ronald G.
Published: February 2008

The ability of solder joint life-prediction algorithms to predict the failure of solder joints due to temperature-cycling induced creep-fatigue has been investigated using representative leadless chip carriers (LCCs) as the test vehicle. Four different algorithms are assessed: the classic Coffin-Manson algorithm, a modified Coffin-Manson algorithm with dependency on peak stress, and two strain-energy based algorithms. JPL’s special purpose nonlinear finite element computer program was used to dynamically simulate the solder joint response to the standard NASA temperature cycling environment, which ranges from −55°C to +100°C with a 4-hour period. The computed stress-strain history provided the inputs needed by each of the failure algorithms. To test the accuracy of the analytical predictions, three different sizes of LCCs (68 pins, 28 pins, and 20 pins) were subjected to an experimental test program using the same 4-hour temperature cycle as used in the analytical predictions. The three different sized ceramic packages, each with a 50-mil pitch, provided a range of cyclic strain ranges and solder fillet geometries so as to test the algorithms against realistic electronic packaging variables. The study highlights limitations in the historical Coffin-Manson relationship, and points up possible improvements associated with incorporating a stress modifier into the Coffin-Manson equation. This modification is also somewhat simpler and more accurate than the energy-density based algorithms, which also performed quite well.
Simulation of the Influence of Manufacturing Quality on Reliability of Vias
Authors: Dasgupta A. , Ramappan V.
Published: February 2008

Techniques based on physics-of-failure principles are fairly well established for mechanical design of electronic packages. This paper provides an example where such techniques can also be exploited to develop guidelines for assessment of manufacturing quality and its impact on reliability. As a case study, this study examines the influence of plating waviness in vias and Plated Through Holes (PTH), on reliability during solder reflow cycles and during subsequent operational thermal cycling. The stress analysis is performed with elastic-plastic finite element models which are seeded with various levels of plating waviness defects. Sensitivity analysis is done with factorial parametric simulation studies based on Design of Experiment (DOE) methods. Buckling and fatigue failure models are used to establish inspection criteria for acceptable thresholds of plating waviness.
Reliability Issues in Plated-Through-Holes Due to Insertion-Mount Compliant-Pin Connectors
Authors: Ganguly G. , Dasgupta A.
Published: February 2008

Stresses arising in plated through holes (PTHs) and surrounding printed wiring board (PWB) substrates due to pin forces of insertion-mount compliant-pin connectors are modeled analytically. The analytical model is based on separation of variable techniques using Fourier series representation of the pin loads, and will be calibrated in the future using both experimental measurements as well as numerical finite element results. Linear and nonlinear results are presented in this paper, to predict deformation and stresses in the assembly. Incremental load-stepping methods are used, to handle nonlinear material properties such as elastic-plastic behavior of copper and post-damage behavior of the PWB substrate. The nonlinearity of the materials is modeled with a simplified bilinear stress-strain curve. The goal is to develop mechanistic predictive models for PTH behavior under insertion forces of compliant pins, to reduce the need for highly repetitive and costly failure analysis for damage evaluation, resulting in significant cost savings to the industry as a whole.
Interfacial Thermal Stresses in Layered Structures: The Stepped Edge Problem
Authors: Yin Wan-Lee
Published: February 2008

The intense, localized stress field produced by a temperature load in a multilayered structure may be significantly affected by the local geometry of the free edge. We examine here the stepped edge problem associated with bonding an elastic layer (silicon chip) to a single or multilayer substrate with a slightly larger length. Stress functions are introduced in various rectangular regions and the continuity of tractions are enforced across all inter-region boundaries. Furthermore, continuity of displacements is enforced across the junction of the two segments of the base laminate. The analysis results indicate that even a minute protrusion of the edge of the base laminate relative to the attached chip may cause significant changes in the peeling and shearing stresses in the end region of the interface.
Non-Fourier Heat Conduction in IC Chip
Authors: Guo Zeng-Yuan , Xu Yun-Sheng
Published: February 2008

Instead of the classic Fourier equation based on diffusion, a hyperbolic equation based on a wave model has been used to predict the rapid transient heat conduction in IC chips. The peak temperature, spatial difference, and time variation of temperature, which are critical to thermal reliability of the chip, are given and compared with that obtained from the Fourier equation. Analytical and numerical results show that non-Fourier effects, including the higher peak temperature and thermal stress, greater temperature difference between components, and stronger thermal noise, are significant to IC chip reliability.
A Study on Wire Sweep in Encapsulation of Semiconductor Chips Using Simulated Experiments
Authors: Han Sejin , Wang K. K.
Published: February 2008

An effort has been made in this study to develop a model which can predict wire sweep during semiconductor chip encapsulation with transfer molding. The calculation of wire sweep during encapsulation depends on many factors. In this study, a step-by-step approach has been used considering one factor at a time. As the first step, the wire deformation has been measured and calculated under a known dead-weight loading. The next step has been to measure and calculate the deformation of a single straight wire attached to the mid-plane of a rectangular cavity due to the flow of a clear and homogeneous fluid. Finally, the wire deformation due to the flow has been measured and calculated when a wire of general shape is attached to a leadframe. The effect of bubble on the wire-sweep has been analyzed qualitatively. Through this series of experiments, a first step in the development of model for the prediction of wire sweep during chip encapsulation has been made.
Finite Element Viscoelastic Analysis of Temperature and Moisture Effects in Electronic Packaging
Authors: Krishna Arvind , Harper B. D. , Lee J. K.
Published: February 2008

Several workers have demonstrated the presence of singular stress fields near the edge of a bimaterial interface subject to thermal gradients. Many of the analyses in the literature are limited to linear elastic materials and are useful as first estimates of stresses in such assemblies. However, a time-dependent stress analysis is necessary when viscoelastic materials such as polymer films are bonded to elastic substrates. This paper shows the relevance of viscoelastic modeling in demonstrating the effects of combined temperature and moisture loading on bimaterial interfaces and viscoelastic films sandwiched between elastic substrates. A 2-D finite element method for linear hygrothermoviscoelasticity based on an incremental creep strain rate form is developed. The correspondence principle of linear viscoelasticity is invoked and comparisons between FEA and analytical solutions are demonstrated. Moisture is modeled using Fick’s law and the thermorheologically simple material (TSM) postulate is extended to incorporate a moisture shift function in analogy with temperature. The analysis of a polyimide film sandwiched between elastic substrates subject to a thermal cycle with diffusion from the free edge shows stress reversals for the peel stresses that may explain failure modes not anticipated by an elastic analysis.
Investigation of a Heat Pipe Array for Convective Cooling
Authors: Howard A. H. , Peterson G. P.
Published: February 2008

A combined experimental and analytical investigation was conducted to evaluate a heat pipe convective cooling device consisting of sixteen small copper/water heat pipes mounted vertically in a 4 × 4 array which was 25.4 mm square. The analytical portion of the investigation focused on determination of the maximum heat transport capacity and the resistance of the individual heat pipes. The resistance of each heat pipe was found to be 2.51 K/Watt, or more than 3 times smaller than the resistance produced by a solid copper rod with the same dimensions. The maximum predicted heat rejection for the module was over 50 Watts, or a power density in excess of 7.75 Watts/cm2. In the experimental portion of the investigation, two different modules were tested. The first module utilized ten circular aluminum fins mounted on the condenser end of each heat pipe to enhance heat rejection, while the second contained only the sixteen copper/water heat pipes. The effects of flow velocity, input power, and base plate temperature on the overall thermal resistance and the heat rejection capacity were determined, as well as the pressure drop resulting from each module. The finned heat pipe array was found to have a lower overall thermal resistance and thus, a higher heat rejection capacity, but also resulted in a significantly larger pressure drop than the array without fins. The results of the heat pipe array experiments were also compared with experimental and empirical results obtained from flow over a flat plate 25.4 mm square.
Jet-Flow Scavenging of a Curing Oven—Part I: Flow Visualization
Authors: Zwick K. J. , Cohen I. M. , Ayyaswamy P. S.
Published: February 2008

A curing oven that is commonly used in microelectronic manufacturing has been analyzed to determine the causes of contamination of parts passing through the oven, and to eliminate this contamination. During the curing of microelectronic chip packages, a volatile component contained in the bonding epoxy is released as a vapor. This vapor is usually removed (scavenged) by blowing a process gas through jets. However, some condensation of this vapor may (and often does) occur on the chips, contaminating them and rendering them functionally useless. It is desirable to completely eliminate this condensation. This paper presents a flow visualization study of the complicated flow patterns within the oven created by the jet-flows. Vortices are produced due to jet interactions. These vortices inhibit scavenging (entrainment and removal) of the contaminant vapor and are undesirable. A new design that eliminates the vortices and enhances the scavenging is described. In Part II of this study, a numerical simulation of the process is described.
Study of Print Release Process in Solder Paste Printing
Authors: Sahay C. , Head L. M. , Shereen R. , Dujari P. , Constable J. H. , Westby G.
Published: February 2008

Solder paste printing is central to the mass reflow soldering process for surface mount technology. The miniaturization of components has put an increased demand on the printing process and requires it to successfully print 75 μm-100 μm(3 to 4 mil) wide apertures. The amount of solder paste deposited is a matter of concern. This study presents results from experiments on printing with apertures having circular, rectangular, square and triangular geometries. The ratio of the printed volume to the aperture volume has been used as a definition of print quality. It was observed that acceptable prints were obtained when the ratio of aperture area to the aperture wall area was more than 0.8. A simple analytical model is also presented for the release of solder paste as the stencil separates from the substrate board assuming that the apertures were filled. The solder is currently treated as a single phase material with Newtonian behavior. The motion of solder paste in the stencil aperture is modelled as the developing viscous flow with velocity boundary layers developing along the walls. The shear strength of the paste is used to determine the area sticking to the wall, thus making it possible to get an estimate of the print quality. The model incorporates the effect of paste properties like viscosity, density, tack and shear strength, and other process variables like aperture dimensions and separation (lift off) velocities between the stencil and the board in predicting the print quality. The model predicts the effect of shear to tack strength of the paste, stencil thickness, and the ratio of aperture to wall area ratio on print quality.
Analysis and Optimization of the Input/Output Fiber Configuration in a Laser Package Design
Authors: Suhir E.
Published: February 2008

The mechanical and thermally induced stresses in the input/output (I/O) fiber in a laser package design are evaluated for different fiber configurations. It is shown that, if the fiber experiences bending deformations, the mechanical stresses can be minimized by applying a proper end off-set. It is found also that, if the optical device can be rotated around the transverse axis by a small angle, this rotation can be effectively used for minimizing the stresses. The smallest fiber span can be achieved, if necessary, by making the fiber straight. In this case the fiber should be short enough to avoid buckling under the action of the compressive stress. We suggest that such a configuration be employed when the appropriate rotation of the device is possible, fiber ends can be easily aligned, and the support structures are strong enough to withstand the elevated thermal force from the compressed fiber. Although the results of the performed analysis can provide guidance for optimizing the I/O fiber configuration, the final selection of such a configuration can be made only after the allowable stress and the achievable end alignment (in the case of straight fiber) are established experimentally.