bluuebunny/crossref_metadata_2025 huggingface dataset:
Dispersion of Waves in Composite Laminates With Transverse Matrix Cracks, Finite Element and Plate Theory Computations
Authors: A˚berg M. , Gudmundson P.
Published: February 2008

Dispersion relations for laminated composite plates with transverse matrix cracks have been computed using two methods. In the first approach it is assumed that the matrix cracks appear periodically and hence it is possible to consider a periodic cell of the structure using Bloch-type boundary conditions. This problem was formulated in complex notation and solved in a standard finite element program (ABAQUS) using two identical finite element meshes, one for the real part and one for the imaginary part of the displacements. The two meshes were coupled by the boundary conditions on the cell. The code then computed the eigenfrequeneies of the system for a given wave vector. It was then possible to compute the phase velocities. The second approach used may be viewed as a two step homogenization. First the cracked layers are homogenized and replaced by weaker uncracked layers and then the standard first-order shear-deformation laminate theory is used to compute dispersion relations. Dispersion relations were computed using both methods for three glass-fiberepoxy laminates ([0/90]2,[0/90]sand[0/45/-45]s with cracks in the 90 and ±45 deg plies). For the lowestflexural mode the difference in phase velocity between the methods was less then five percent for wavelengths longer than two times the plate thickness. For the extensional mode a wavelength often plate thicknesses gave a five percent difference.
Analysis for Elastic Strips Under Concentrated Loads
Authors: Chiu Yu-Tsung , Wu Kuang-Chong
Published: February 2008

The problem of a general anisotropic elastic strip under concentrated loads is analyzed. By using the Stroh formalism for anisotropic elasticity in conjunction with the Fourier transform, the elastic fields for a concentrated load are expressed as integrals which can be evaluated by residue theory to give eigenfunction expansions. The eigenfunction expansions can be divided into two parts. The first part arises from the singularities at the origin of the integrands of the Fourier integrals and corresponds to classical beam bending and stretching solutions. The second part consists of the other terms in the eigenfunction expansions and corresponds to exponentially decaying self-equilibrium solutions. The solution for a concentrated load is used to investigate the problems of a pair of collinear compressive loads and three-point bending.
A Geometrically Nonlinear Model for Laminated Composite Strips With Extension-Twist Coupling in the Presence of Delamination
Authors: Makeev A. , Armanios E.
Published: February 2008

A geometrically nonlinear analysis for the extension-twist coupling in pretwisted laminated composite strips in the presence of delamination is developed. Closed-form solutions for strips with internal and edge delaminations are obtained. A parametric study is performed to investigate the influence of delamination length, material system, and stacking sequence on the extension-twist coupling in a class of hygrothermally stable laminates. The model predictions are in good agreement with test data. The results indicate that internal delamination has a negligible influence on the extension-twist coupling behavior while free-edge delamination could result in a significant drop in coupling.
Nonlinear Theory for Composite Laminated Shells With Interfacial Damage
Authors: Cheng Zhen-qiang , Kitipornchai S.
Published: February 2008

Interfacial damage is incorporated in the proposed nonlinear theory. for composite laminated shells. A spring-layer model is employed to characterize damaged interfaces spanning from perfect bonding to different degrees of imperfect bonding in shear. By enforcing compatibility conditions for transverse shear stresses both at interfaces and on two bounding surfaces of a laminated shell, only five unknowns are needed for modeling its behavior. The principle of virtual work is used to derive the governing equations, which are of 14th order in lines of curvature coordinates, variationally self-consistent with seven prescribed boundary conditions. This theory includes the conventional higher-order zigzag model for a perfectly bonded shell as a special case. Numerical results provide a physical understanding of the effect of interracial damage on bending and buckling responses of composite laminated shells.
Elastoplastic Micromechanical Modeling of Two-Dimensional Irregular Convex and Nonconvex (Re-entrant) Hexagonal Foams
Authors: Overaker D. W. , Cuitin˜o A. M. , Langrana N. A.
Published: February 2008

A nonlinear micromechanical model for two-dimensional irregular hexagonal foams has been developed that allows for anisotropy in morphology and/or material. Based upon the orientation, cross section, length, and material properties of each strut, the resulting microlevel beam behavior within the unit cell determines its structural properties. Nonlinearity is introduced as coupled elastoplastic beam behavior, where the elastoplastic behavior of each beam is considered. The analytical. formulation for the stiffness matrix of the general elastoplastic unit cell is. found by considering compatibility and equilibrium of the unit cell. The structural properties of the elastoplastic unit cell are embedded in a continuum finite element model as material properties, thus capturing the microstructure of the foam in an accurate and efficient model. Structural nonlinearity is therefore directly linked to localized plasticity and its evolution at the microlevel. Elastic analyses investigated the degree of anisotropy in structural properties that was induced by various morphological changes. The differences in stress and deformation behavior between a regular hexagonal foam and a re-entrant foam were also demonstrated. Plastic analyses showed how structural nonlinearity could be explained by localized microstructural behavior. The advantage of this micromechanical model is that it allows a study of the effects of morphology and/or material anisotropies on the overall foam behavior.
A Note on the Effective Lame´ Constants of Polycrystalline Aggregates of Cubic Crystals
Authors: Lubarda V. A.
Published: February 2008

It is well known that the Voigt and Reuss estimates of the effective shear modulus of a polycrystalline aggregate of cubic crystals are, respectively, the upper and lower bounds for this constant (μR ≤ μ ≤ μV). It is pointed out in this note that the opposite is true for the Lame´ constant λ (λV ≤ λ ≤ λR).
On the Extreme Values of Young’s Modulus, the Shear Modulus, and Poisson’s Ratio for Cubic Materials
Authors: Hayes M. , Shuvalov A.
Published: February 2008

For homogeneous cubic elastic materials with positive definite stored energy it is shown that the maximum and minimum values of Young’s modulus E are related to the maximum and minimum values of the shear modulus G through the simple connection 1/Gmin−1/Gmax=3(1/Emin−1/Emax). It is deduced that the ratio of compliances −s12/s44 is the maximum value of Poisson’s ratio v in the cubic materials with a positive parameter χ=2s11−2s12−s44, and the minimum value of ν in the cubic materials with negative χ.
A Stress Analysis Method for Bi-axially Loaded Fastener Hole in Composite Laminate of Finite Geometry
Authors: Xiong Y.
Published: February 2008

A stress analysis method has been developed for a biaxially loaded fastener hole in a laminated plate of finite geometry. The method is based on a variational formulation involving complex variables. In this method, the equilibrium and compatibility equations are satisfied in the domain of the plate due to the employment of the complex stress potentials and all the boundary conditions are satisfied through a variational statement. Therefore, the requirement for finite width corrections in relatively large fastener hole cases is avoided. The method has been verified through comparison with finite element results.
Local Similarity in Nonlinear Random Vibration
Authors: Krenk S. , Roberts J. B.
Published: February 2008

A response analysis procedure is developed for oscillators with highly nonlinear stiffness and light nonlinear damping excited by non-white wide-band random noise based on local similarity between the random response and the deterministic response at the same energy level of the corresponding undamped oscillator. The analysis consists of three parts: introduction of modified phase plane variables, derivation of an approximate general form of the probability density of the response energy. for non-white excitation, and derivation of the spectral density function of the response from the conditional covariance function for a given energy level. The use of modified phase plane variables leads to a completely symmetric formulation and reformulates the stiffness nonlinearity as a nonlinear variation of the instantaneous angular frequency, and thereby a local rescaling of time. The probability density is obtained by averaging the full Fokker-Plank-Kolmogorov equation using local similarity, thus avoiding some theoretical problems associated with the traditional averaging of the stochastic differential equations. The use of local similarity with the exact undamped solution in the derivation of the conditional spectral density leads to a spectral density estimate, that contains the higher harmonic components explicitly. Comparisons of theoretical predictions with digital simulation estimates of both the probability and spectral densities for the Duffing oscillator demonstrate the accuracy of the theory.
On Nanobuckling of Monomolecular Layers Adhering to a Substrate
Authors: Chiskis A. , Parnes R.
Published: February 2008

It is shown that the first buckling mode corresponding to the lowest buckling force of a plane monomolecular layer glued to a substrate may not be smooth. The resulting saw-like configuration of neighboring molecules leads to corrugation on a molecular level and we name such a phenomenon nanobuckling. A criterion governing this smooth—not smooth transition is derived. The model presented may also describe surface instability of a perfect crystal due to contraction.
Surface Bifurcation in Anisotropic Materials With Application to Aluminum Alloys
Authors: Nestorovic´ M. D. , Chu E. , Triantafyllidis N.
Published: February 2008

Surface bifurcation is an instability mechanism which appears in the form of surface waviness on traction-free surfaces in ductile solids subjected to large strains. In sheet metal forming, the practical interest in this phenomenon stems from the fact that it occurs past the onset of localization, i.e., the forming limit, but prior to the local fracture failure in a quasi-static, monotonic loading process. In this work, we apply the general theory for surface bifurcation in a homogeneously strained, anisotropic, rate-independent, elastoplastic half-space, to study the influence of material anisotropy on the onset of surface instabilities. In particular, we calculate the critical principal strains ε1cε2c and the corresponding eigenmode orientation angle Ωc when the principal strain axes are at a fixed angle a with respect to the rolling direction of the solid. The presented calculations are for a 2024-T3 aluminum alloy, whose constitutive properties have been determined experimentally. It is found that by varying the strain orientation angle α, the surface bifurcation strains can vary up to an order of 80 percent for in-plane principal strains of a different sign, but only up to an order of ten percent for principal strains of the same sign. The eigenmode orientation angle Ωc is calculated for a particular strain orientation (α=π/6), for which case it is found that Ωc is close to the forming limit angle ψc only for positive principal strains. The presentation is concluded by a discussion of the influence of the anisotropy and the yield surface parameters of the constitutive model on surface bifurcation.
Crack Propagation in a Brittle Elastic Material With Defects
Authors: Valentini M. , Serkov S. K. , Bigoni D. , Movchan A. B.
Published: February 2008

A two-dimensional asymptotic solution is presented for determination of the trajectory of a crack propagating in a brittle-elastic, isotropic medium containing small defects. Brittleness of the material is characterized by the assumption of the pure Mode I propagation criterion. The defects are described by Po´lya-Szego¨ matrices, and examples for small elliptical cavities and circular inclusions are given. The results of the asymptotic analysis, which agree well with existing numerical solutions, give qualitative description of crack trajectories observed in brittle materials with defects, such as porous ceramics.
A Higher-Order Theory for Plane Stress Conditions of Laminates Consisting of Isotropic Layers
Authors: Wu X. J. , Cheng S. M.
Published: February 2008

In this paper, a higher-order theory is derived for laminates consisting of isotropic layers, on the basis of three-dimensional elasticity with displacements as higher-order functions of z in the thickness direction. The theory employs three stress potentials, Ψ (an Airy function), p (a harmonic function), and its conjugate q, to satisfy all conditions of stress equilibrium and compatibility. Interlaminar shear stresses, i.e., antiplane stresses, are shown to be present at the interfaces, especially near material discontinuities where gradients of in-plane stresses are usually high. For illustrating its practical application, the problem of a plate containing a hole patched with an intact plate is solved.
Application of the Lie Group Transformations to Nonlinear Dynamical Systems
Authors: Pilipchuk V. N. , Ibrahim R. A.
Published: February 2008

This paper describes the theory of Lie group operators in a form suitable for the applied dynamics community. In particular, it is adapted to analyzing the dynamic behavior of nonlinear systems in the presence of different resonance conditions. A key ingredient of the theory is the Hausdorff formula, which is found to be implicitly reproduced in most averaging techniques during the transformation process of the equations of motion. The method is applied to examine the nonlinear modal interaction in a coupled oscillator representing a double pendulum. The system equations of motion are reduced to their simplest (normal) form using operations with the linear differential operators according to Hausdorff's formula. Based on the normal form equations, different types of resonance regimes are considered. It is shown that the energy of the parametrically excited first mode can be regularly (or nonregularly) shared with the other mode due to the internal resonance condition. If the second mode is parametrically excited, its energy is localized and is not transferred to the first mode, even in the presence of internal resonance.
Response of Finite Cracks in Orthotropic Materials due to Concentrated Impact Shear Loads
Authors: Rubio-Gonzalez C. , Mason J. J.
Published: February 2008

The elastodynamic response of an infinite orthotropic material with a finite crack under concentrated in-plane shear loads is examined. A solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for several example materials are obtained. The results differ from mode I in that there is heavy dependence upon the material constants. This solution can be used as a Green's function to solve dynamic problems involving finite cracks and in-plane shear loading.
The Full-Space Elastodynamic Green’s Functions for Time-Harmonic Radial and Axial Ring Sources in a Homogeneous Isotropic Medium
Authors: Lu Y.
Published: February 2008

The elastodynamic Green’s functions for time-harmonic radial and axial ring sources in a homogeneous, isotropic, linear elastic full-space medium are derived using the Fourier-Hankel transform. The Green’s functions are found to have the same logarithmic singularities as the Legendre functions of positive and negative half-degree of the second kind. As the frequency approaches zero, the Green’s functions approach the corresponding elastostatic Green’s functions. The far-field displacement and stress components are also derived.
Elastodynamic Green’s Function for Laminated Anisotropic Circular Cylinders
Authors: Zhuang W. , Shah A. H. , Dong S. B.
Published: February 2008

The construction of a steady-state Green’s function for a laminated anisotropic circular cylinder is presented herein. The cylinder’s profile through its depth consists of any number of perfectly bonded, uniform thickness concentric cylindrical layers, with each able of having its own distinct elastic cylindrically anisotropic properties. Green’s function is predicated on the superposition of numerically generated modal solutions from a system of equations based on a semi-analytical finite element formulation. Two methods are proposed for its construction, both relying on the same set of eigendata. One is by means of an integral transform. The other may be viewed as the forced vibration of a cylinder with cylindrically monotropic properties under symmetry/antisymmetry conditions on the cross section containing the source load. The second method, being more restrictive with respect to material properties, was intended primarily as a cross-check of the integral transform version of Green’s function. Numerical implementation details are discussed in terms of two example thickness profiles to show the essential keys for the convergence and accuracy of Green’s function.
Heteroclinic Bifurcations in Rigid Bodies Containing Internally Moving Parts and a Viscous Damper
Authors: Gray G. L. , Kammer D. C. , Dobson I. , Miller A. J.
Published: February 2008

Melnikov’s method is used to analytically study chaotic dynamics in an attitude transition maneuver of a torque-free rigid body in going from minor axis to major axis spin under the influence of viscous damping and nonautonomous perturbations. The equations of motion are presented, their phase space is discussed, and then they are transformed into a form suitable for the application of Melnikov’s method. Melnikov’s method yields an analytical criterion for homoclinic chaos in the form of an inequality that gives a necessary condition for chaotic dynamics in terms of the system parameters. The criterion is evaluated for its physical significance and for its application to the design of spacecraft. In addition, the Melnikov criterion is compared with numerical simulations of the system. The dependence of the onset of chaos on quantities such as body shape and magnitude of damping are investigated. In particular, it is found that for certain ranges of viscous damping values, the rate of kinetic energy dissipation goes down when damping is increased. This has a profound effect on the criterion for chaos.
Elastic-Plastic Stress Field in a Coated Continuous Fibrous Composite Subjected to Thermomechanical Loading
Authors: You L. , Long S. , Rohr L.
Published: February 2008

A micromechanics investigation was performed in the present work to analyze the stress field in a coated continuous fibrous composite subjected to thermal and mechanical loading based on a four-concentric-cylinders model. A temperature-independent stress-plastic strain relationship for the metallic matrix and coating layer with linear strain-hardening behaviour were introduced. Tresca’s yield criterion and the associated flow law were employed to derive the governing equation of the coating and matrix. The closed-form solution of the governing equation was obtained. Some numerical examples were given. The numerical results indicate that the plasticity of the coating greatly decreases the circumferential and axial stresses in the coating itself, but has very limited influence on the stresses in other constituents of the composite. The plasticity of the matrix imposes no significant influence on all the stresses in the composite.
The Elasto-Electric Field for a Rigid Conical Punch on a Transversely Isotropic Piezoelectric Half-Space
Authors: Chen W.-Q. , Shioya T. , Ding H.-J.
Published: February 2008

This paper exactly analyzes the problem of a rigid conical punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to include the piezoelectric effect. By using the previous results of pure elasticity, exact solution is derived. It is found that all the elastoelectric variables are expressed in terms of elementary functions. Numerical results are finally performed.
Experimental and Numerical Studies on Microscale Bending of Stainless Steel With Pulsed Laser
Authors: Chen G. , Xu X. , Poon C. C. , Tam A. C.
Published: February 2008

Laser forming or laser bending is a newly developed, flexible technique which modifies the curvature of sheet metal by thermal residual stresses instead of external forces. The process is influenced by many parameters such as laser parameters, material properties, and target dimensions. In this work, a pulsed Nd:YLF laser was used as the energy source. The laser beam was focused into a line shape irradiating on the stainless steel specimen to induce bending. The bending angle was measured at various processing conditions. A finite element analysis was performed with the use of a two-dimensional plane strain model to calculate the thermoelastoplastic deformation process. Experimental measurements and computational results were in good agreement. Numerical sensitivity studies were performed to evaluate the effects of the unavailable material property data at high temperature. It was found that both optical reflectivity and thermal expansion coefficient influenced the bending angle significantly, while other extrapolated material properties at high temperature yielded acceptable results.
Instability of Pipelines on Slopes
Authors: Palmer A. C. , Tebboth L. , Miles D. , Calladine C. R.
Published: February 2008

A serious incident occurred during construction of a 36-inch pipeline in Colombia. A 500 m length of pipe on a hillside slipped on its supports, buckled, and slid down the hill, causing deaths and serious material damage. On a steep slope friction is not large enough to carry the downslope component of the weight. The frictional force from the supports then acts upslope. If the temperature subsequently increases, the frictional force partially reverses. The longitudinal force becomes more compressive and the pipeline can lift off the supports in overbends. A graphical construction gives a simple method of assessing the stability of the pipe in an arbitrary profile. The incident has important lessons for the construction of pipelines in steep terrain.
Self-Excited Vibration in Flexible Rotating Disks Subjected to Various Transverse Interactive Forces: A General Approach
Authors: Tian J. , Hutton S. G.
Published: February 2008

A generalized approach to predict the physical instability mechanisms that are involved in the interaction between a rotating flexible disk and a stationary constraining system is developed. Based upon equations derived for an energy flux analysis, unified instability conditions for various lateral interactive forces are presented. These developments lead to a clear understanding of the physical mechanisms involved in the development of vibrational instabilities. New developments also involve the stability analysis of a rotating disk subjected to multiple moving concentrated regenerative and follower interactive forces that act over a space-fixed sector. The lateral regenerative interactive forces that are responsible for self-excited vibrations in saw-blade cutting are identified and modeled. The generalized Fourier series method is proposed to develop a characteristic equation for time-varying dynamic systems with or without time lag. The resulting equation can be solved efficiently by using Mu¨ller’s algorithm with deflation.
Application of the Cosserat Spectrum Theory to Stokes Flow
Authors: Liu W. , Plotkin A.
Published: February 2008

This paper presents an application of the Cosserat spectrum theory in elasticity to the solution of low Reynolds number (Stokes flow) problems. The velocity field is divided into two components: a solution to the vector Laplace equation and a solution associated with the discrete Cosserat eigenvectors. Analytical solutions are presented for the Stokes flow past a sphere with uniform, extensional, and linear shear freestream profiles.
A Numerical Study on the Free Vibration of Symmetric Cross-Ply Laminated Cylindrical Helical Springs
Authors: Yildirm V.
Published: February 2008

The free-vibration problem of (0°/90°/90°/0°) laminated composite cylindrical helical springs is modeled theoretically as a continuous system. The first-order shear deformation theory is employed in the mathematical model. The free-vibration equations are solved by the transfer matrix method. A nondimensional parametric study is performed to investigate the effects of the number of active coils, the ratio of the diameter of the cylinder to the thickness of section, the helix pitch angle, and material types on the first six natural frequencies of helical springs with square section and fixed-fixed ends.
Application of Finite-Part Integrals to Planar Interfacial Fracture Problems in Three-Dimensional Bimaterials
Authors: Chen M.-C. , Noda N.-A. , Tang R.-J.
Published: February 2008

This paper deals with linear elastic fracture problems for a planar crack on an interface between two dissimilar elastic half-space solids bonded together. The finite-part integral concept is used to derive hypersingular integro-differential equations for the interfacial crack from the point-force solutions for a bimaterial space. Investigations on the singularities and the singular stress fields in the vicinity of the crack are made by the dominant-part analysis of the two-dimensional hypersingular integrals. Thereafter the stress intensity factor K-fields and the energy release rate G are exactly obtained by using the definitions of stress intensity factors and the principle of virtual work, respectively. The results show that, unlike the homogenous case, the asymptotic fields always consist of all three modes of fracture. Finally, some numerical examples of various aspects of elliptical cracks subjected to constant pressures are given.
Effective Constitutive Properties of Linear Elastic Cellular Solids With Randomly Oriented Cells
Authors: Dimitrovova´ Z.
Published: February 2008

A new methodology to derive the linear effective constitutive law for a group of composites with random microstructure of a special kind is described as an extension of the methodology proposed in Warren and Kraynik (1988) and of the methodology used in polycrystal theory. The results are expressed in the form of specific bounds on effective elastic constants. Practical importance is in the specific bounds when the methodology is applied to cellular solids. Several examples are shown and compared with other published results. The new contribution of this paper lies in the presentation of the methodology, derivation of new specific bounds in two dimensions, and comments related to already published works on cellular solids.
Microstructural Stress Tensor of Granular Assemblies With Volume Forces
Authors: Bagi K.
Published: February 2008

This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed—assuming that the grains are in equilibrium—in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.
Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices
Authors: Saha S. K.
Published: February 2008

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.
Three-Dimensional Interface Cracks in Anisotropic Bimaterials: The Non-Oscillatory Case
Authors: Qu Jianmin , Xue Yibin
Published: February 2008

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available. In this paper, a penny-shaped crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two-dimensional elasticity in conjunction with the Fourier transform method. Fracture mechanics parameters such as the stress intensity factor, crack-opening displacement, and energy release rate are obtained in terms of the interfacial matrix M. To illustrate the solution procedure, a circular delaminations in a unidirectional and a cross-ply composite are considered. Numerical results for the stress intensity factors and energy release rate along the crack front are presented.
On Diverging Concertina Tearing
Authors: Wierzbicki T. , Trauth K. A. , Atkins A. G.
Published: February 2008

A simplified theory of the process of concertina tearing of thin plates with two diverging cracks is developed. The cracks initiate from a local cut and propagate away from the initiation site as the loading punch is pushed in the in-plane direction. At the same time the plate strip between the two cracks folds back and forth in much the same way as the “concertina” collapse pattern of circular tubes, studied extensively in the literature. Closed-form solutions are derived for the punch force and the length of the folding wave. Postulating a differential equation for the direction of the crack growth, a path of the tearing fracture is determined. It is shown that the crack trajectories depend on the plate thickness and the size of the initiation cut but, perhaps surprisingly, are independent of the material properties of the plate. This means that the process of concertina tearing would be similar for metal, plastic, paper, leather, etc. A series of experiments on 0.4-mm-thick mild steel plate was performed showing a very good agreement with the theoretical predictions.
Tangential Loading of General Three-Dimensional Contacts
Authors: Ciavarella M.
Published: February 2008

A general three-dimensional contact, between elastically similar half-spaces, is considered. With a fixed normal load, we consider a pure relative tangential translation between the two bodies. We show that, for the case of negligible Poisson’s ratio, an exact solution is given by a single component of shearing traction, in the direction of loading. It is well known that, for full sliding conditions, the tangential force must be applied through the center of the pressure distribution. Instead, for a full stick case the tangential force must be applied through the center of the pressure distribution under a rigid flat indenter whose planform is the contact area of the problem under consideration. Finally, for finite friction a partial slip regime has to be introduced. It is shown that this problem corresponds to a difference between the actual normal contact problem, and a corrective problem corresponding to a lower load, but with same rotation of the actual normal indentation. Therefore for a pure translation to occur in the partial slip regime, the point of application of the tangential load must follow the center of the “difference” pressure. The latter also provides a complete solution of the partial slip problem. In particular, the general solution in quadrature is given for the axisymmetric case, where it is also possible to take into account of the effect of Poisson’s ratio, as shown in the Appendix.
Fatigue of Microlithographically-Patterned Free-Standing Aluminum Thin Film Under Axial Stresses
Authors: Read David T. , Dally James W.
Published: February 2008

Fatigue life as a function of number of stress cycles has been determined for three-layer titanium-aluminum-titanium thin-film specimens. For nominal stresses ranging from 50 to 90 percent of the upper-bound ultimate strength, the fatigue lives ranged up to 76 cycles. In all specimens, active cracks were observed after only a few stress cycles. These cracks grew with repeated cycling. The fatigue life was reached when the specimen could no longer sustain the maximum cyclic stress.
Contact Analysis of Regular Patterned Rough Surfaces in Magnetic Recording
Authors: Bhushan Bharat , Tian Xuefeng
Published: February 2008

The contact of regular patterned rough surface in magnetic recording was analyzed to predict the contact area, meniscus force and permissible load under thin-film lubricated conditions. The contact area, the meniscus force, and the permissible load at the magnetic head-disk interface were studied as a function of the shape, size and the occupation of asperities. Optimum design criteria for both constant occupation and nonconstant occupation of identical asperities were developed to design future magnetic head and disk surfaces.
Forced Convective Cooling Enhancement Through a Double Layer Design
Authors: Chung B. T. F. , Li H. H.
Published: February 2008

Numerical simulation of fluid flow and heat transfer during the cooling of electronic modules mounted on printed circuit boards are performed to examine the feasibility of a proposed double layer design. Conjugate solution of the two-dimensional energy equation is obtained for the incompressible flow over a number of uniformly heated blocks and the double layer board. Enhancement in heat convected from the modules along with the drop in maximum temperature of each module, obtained without increase in pressure head loss, characterizes the cooling improvement by the proposed design. Systematic calculations also provide sufficient data of the flow and temperature distributions for analyzing the cooling mechanism.
Steady-State Investigation of Vapor Deposited Micro Heat Pipe Arrays
Authors: Mallik A. K. , Peterson G. P.
Published: February 2008

An experimental investigation of vapor deposited micro heat pipe arrays was conducted using arrays of 34 and 66 micro heat pipes occupying 0.75 and 1.45 percent of the cross-sectional area, respectively. The performance of wafers containing the arrays was compared with that of a plain silicon wafer. All of the wafers had 8 × 8 mm thermofoil heaters located on the bottom surface to simulate the active devices in an actual application. The temperature distributions across the wafers were obtained using a Hughes Probeye TVS Infrared Thermal Imaging System and a standard VHS video recorder. For wafers containing arrays of 34 vapor deposited micro heat pipes, the steady-state experimental data indicated a reduction in the maximum surface temperature and temperature gradients of 24.4 and 27.4 percent, respectively, coupled with an improvement in the effective thermal conductivity of 41.7 percent. For wafers containing arrays of 66 vapor deposited micro heat pipes, the corresponding reductions in the surface temperature and temperature gradients were 29.0 and 41.7 percent, respectively, and the effective thermal conductivity increased 47.1 percent, for input heat fluxes of 4.70 W/cm2. The experimental results were compared with the results of a previously developed numerical model, which was shown to predict the temperature distribution with a high degree of accuracy, for wafers both with and without the heat pipe arrays.
Modeling Solder Joint Fatigue Life for Gullwing Leaded Packages: Part I—Elastic Plastic Stress Model
Authors: Gupta V. K. , Barker D. B.
Published: February 2008

It is a challenge to assess solder joint fatigue life in the modern electronics industry because of complex geometries, complex non-linear viscoplastic material properties, and the frequently changing environmental conditions. The first step in the fatigue life assessment process is to find the stress distribution in the solder. Traditionally, this has been done using numerical tools like finite element methods. The finite element approach requires a highly trained and experienced analyst and huge computing resources, while the accuracy is always questioned. This study aims to develop a more accurate analytical-cum-empirical model to predict critical stresses in the solder joint so as to avoid the necessity of finite element simulation. This paper presents a generic elastic-plastic stress model that is obtained based on theoretical stress analysis solutions that is tweaked by using a design of experiments technique with FEA simulations.
Evaluation of Design Parameters for Leadless Chip Resistors Solder Joints
Authors: Jih Edward , Pao Yi-Hsin
Published: February 2008

Failures in electronic packaging under thermal fatigue often result from cracking in solder joints due to creep/fatigue crack growth. A nonlinear, time-dependent finite element analysis was performed to study the effect of critical design parameters on thermal reliability of leadless chip capacitor or resistor solder joints. The shear strain range based on thermal hysteresis response was used to study the sensitivity of various parameters, such as solder stand-off height, fillet geometry, Cu-pad length, and component length and thickness. The results were used as guidelines for designing reliable solder joints. In addition, an analytical model for the solder joint assembly was derived. It can be used .as an engineering approach for rapid assessment of large numbers of design parameters. The accuracy and effectiveness of the analytical model were evaluated by comparing with finite element results.
Cleaning and Reflow of Pb-Sn C4 Solder Bumps
Authors: Lee Caroline S. , Crafts Doug C. , Eagar T. W.
Published: February 2008

The Pb/Sn electroplating process for C4 technology requires the ability to etch Ball Limiting Metallurgy (BLM) in the presence of the Pb/Sn bumps. Upon etching, a surface corrosion layer is formed and an appropriate cleaning acid must be used to remove this layer prior to solder reflow of the bumps. It was found that the morphology of the surface layer formed upon etching on the Pb/Sn solder bumps is critically dependent on the concentration of the etchant. Using a gravimetric test, XPS and AES analysis, PbO containing small amounts of Sn and S, was identified to be the primary component of the surface. The thickness morphology, composition and the growth rate of the layer are critically dependent on the sulfur from the etchant. In H2O2-rich solutions, the surface appears to be loosely packed and the growth rate on the surface of the bump was found to be reaction-rate limited; whereas, in H2SO4-rich solutions, the diffusion rate is the controlling step informing the surface layer on the solder bumps, thus producing a thin and dense layer.
Natural Convection in Shallow, Horizontal Air Layers Encountered in Electronic Cooling
Authors: Papanicolaou Elias , Gopalakrishna Sridhar
Published: February 2008

A numerical study of natural convection induced in a horizontal, enclosed air layer due to a discrete, constant heat flux source at the bottom surface is carried out in this paper. The nature of the transition from conduction to a cellular convection regime for this discrete-heating case is characterized. Multiple sources are also considered and the results are compared to those for a single source. The governing equations of continuity, momentum, and energy conservation are formulated for a two-dimensional layer. The important parameters are the overall aspect ratio (length/height of the layer), the ratio of source length to total length, and the Rayleigh number. The effect of varying these parameters is investigated, and heat transfer correlations are derived, for both single and multiple sources, in the form Nus ∝ C (Ra)c>, where Nus is the Nusselt number averaged over each source. The value of C is found to depend strongly on the aspect ratio and the source size. Based on the heat transfer results, the tendency of each geometric configuration to fully attain transition to the convection regime is evaluated. This can provide guidelines for maintaining certain critical dimensions that best exploit natural convection effects, in systems where fan-driven cooling is not available.
An Experimental Technique for Studying Mixed-Mode Fatigue Crack Growth in Solder Joints
Authors: Yao Daping , Zhang Z. , Shang J. K.
Published: February 2008

Failures of solder joints often result from development of cracks under complex mixed-mode loading conditions. In this study, a flexural peel technique was developed to investigate the growth of cracks at the interface between solder and Cu substrate. The technique was based on a tri-layer solder/Cu joints, with the solder layer sand-wiched between two Cu layers of desired thicknesses. Finite element analysis was used to calculate the mixed-mode condition at the crack tip as a function of the thicknesses of Cu outerlayers and the solder interlayer. The application of this technique to studying interface crack growth under fatigue loading is demonstrated for eutectic solder joints.
Bus Bar Solder Joint Durability Evaluation
Authors: Wong T. Eric , Cohen Harold M.
Published: February 2008

Thermostructural analyses were conducted in support of an investigation into bus bar solder joint reliability for military aircraft. In electronics packaging applications, the most common cause of solder joint failure is repeated straining during temperature cycling as a result of mismatch of the coefficients of thermal expansion (CTE) of the solder joint assembly. To ensure that the bus bar solder joints for military aircraft have sufficient reliability to withstand the environmental exposures, a thermostructural evaluation becomes necessary. To analyze the durability of bus bar solder joints, nonlinear finite element analyses were conducted with the ABAQUS computer code. In the analysis, the solder constitutive relation was incorporated into the ABAQUS code to calculate the nonlinear strains of the solder joints during temperature cycling. These nonlinear strains, combined with modified Manson-Coffin fatigue life prediction theory and Miner’s cumulative damage law, were then used to predict the cumulative damage index (CDI) of the solder joints for two thermal cycling life times. The CDI was also estimated for the case where cracks have initiated and propagated through about half the length of the solder joint. All analysis results indicate that these solder joints have sufficient structural margins to survive two thermal cycling life times.
Determination of Parameters Affecting Solder Paste Tack Strength as Measured in the IPC Tack Test: A Classical Design of Experiments Approach
Authors: Anson Scott , Sahay C. , Head Linda , Constable James
Published: February 2008

Solder paste is used in the electronics industry to connect surface mount circuit components to printed wiring boards. A printed wire board (PWB) is populated with components by applying solder paste on the PWB, placing components and finally reflowing the solder paste in an oven. Between the time the component is placed on the PWB and the solder paste is reflowed, the components are to be held in position. This is helped by tackiness of the paste. The present paper describes an experimental investigation of the tack strength of three solder pastes with probe size, probe surface roughness, drying time, and surrounding pressure. The results indicate that the probe size has a significant and dominant effect on all the pastes examined. A Mechanistic view of the possible mechanism for this phenomenon is also presented. Measured tack strength is shown not to be simple adhesion, but to include a vacuum under the test probe that increases tack strength (force per unit area) as probe size increases.
Prediction of Solder Joint Geometries in Array-Type Interconnects
Authors: Heinrich S. M. , Schaefer M. , Schroeder S. A. , Lee P. S.
Published: February 2008

An approximate mathematical model is developed for predicting the shapes of solder joints in an array-type interconnect (e.g., a ball-grid array or flip-chip interconnect). The model is based on the assumption that the geometry of each joint may be represented by a surface of revolution whose generating meridian is a circular arc. This leads to simple, closed-form expressions relating stand-off height, solder volume, contact pad radii, molten joint reaction force (exerted on the component), meridian curvature, and solder surface tension. The qualitative joint shapes predicted by the model include concave (hourglass-shaped), convex (barrel-shaped, with a truncated sphere as a special case), and truncated-cone geometries. Theoretical results include formulas for determining the maximum and minimum solder volumes that can be supported by a particular pair of contact pads. The model is used to create dimensionless plots which summarize the general solution in the case of a uniform array (i.e., one comprising geometrically identical joints) for which the contact pads on the component and substrate are of the same size. These results relate the values of joint height and width (after reflow) to the solder joint volume and the molten-joint force for arbitrary values of the pad radius and solder surface tension. The graphs may be applied to both upright and inverted reflow, and can be used to control stand-off for higher reliability or to reduce bridging and necking problems causing low yields. A major advantage of the model is that it is numerically efficient (involving only simple, closed-form expressions), yet generates results that are in excellent agreement with experimental data and more complex models. Thus, the model is ideally suited to performing parametric studies, the results of which may be cast in a convenient form for use by practicing engineers. Although in the present paper the array is assumed to be doubly-symmetric, i.e., possess two orthogonal planes of symmetry, the model may be extended to analyze arrays of arbitrary layout. The motivation for predicting joint geometries in array-type interconnects is two-fold: (1) to achieve optimal joint geometries from the standpoint of improved yield and better reliability under thermal cycling and (2) to take full advantage of the flexibility of new methods of dispensing solder, such as solder-jet and solder-injection technologies, which enable the volume of each individual joint to be controlled in a precise manner. Use of dispensing methods of these types permits the solder volumes in the array to be distributed in a non-uniform manner. Results such as those presented here (in combination with appropriate fatigue studies) can be used to determine the optimal arrangement of solder volumes.