Optimizing maximum equivalent strain on solder balls in flip‐chip packages

Flip‐chip packaging provides a high‐performance low‐cost approach for development of electronic packages. A three‐dimensional (3D) viscoelastic‐plastic finite element analysis using the commercial software ANSYS has been performed to study the thermo‐mechanical behavior in flip‐chips assemblies, i.e., the four components: chip, solder ball, underfill, and substrate. The viscoelastic behavior of underfill is modeled by a Maxwell constitutive equation, while the viscoplastic behavior of solder balls is modeled by an Anand model. Both chip and substrate are assumed to elastic materials modeled by Hooke's law. As in standard industry practice, temperature cycling from 125 to −40°C is used. Thermo‐mechanical behavior of solder balls is presented, and the effects of underfill material properties are investigated. Further, Taguchi methods are used to optimize flip‐chip package performance. The design goal is to minimize the maximum equivalent strain on the solder balls. The eight flip‐chip assembly factors chip‐thickness/substrate‐thickness ratio, underfill modulus (G_i), underfill relaxation time (λ_i), solder height‐to‐diameter ratio, chip coefficient of thermal expansion (CTE), underfill CTE, solder CTE, and substrate CTE are chosen for optimization. POLYM. COMPOS., 2008. © 2007 Society of Plastics Engineers     

Viscoelastic constitutive model for uniaxial time‐dependent ratcheting of polyetherimide polymer

Based on the experimental observations, a cyclic nonlinear viscoelastic constitutive model was proposed to describe the uniaxial time‐dependent ratcheting of polyetherimide (PEI) polymer under tension–compression and tension–tension cyclic loading. The model was constructed by extending the nonlinear viscoelastic Schapery model (Schapery, Polym. Eng. Sci., 9, 295 (1969)). The extension emphasized the changes of parameter functions used in the original model, which enabled the model to describe the ratcheting of polymer material. Comparing the simulations with corresponding experimental results, the capability of the extended model to predict the uniaxial time‐dependent ratcheting of PEI was verified. It is shown that the extended model can reasonably describe the uniaxial time‐dependent ratcheting of the polymer under the tension–compression and tension–tension cyclic loading with different peak‐holdings, stress rates, and stress levels. POLYM. ENG. SCI., 52:1874–1881, 2012. © 2012 Society of Plastics Engineers     

Using viscoelastic modeling and molecular dynamics based simulations to characterize polymer natural fiber composites

The potential for polymer natural fiber composites for manufacturing storage units for products with high ethanol content is explored. The influence of ethanol diffusion into the microstructure of the storage unit on its long-term mechanical (specifically creep compliance) and viscoelastic properties are measured. Burger's model for polymer viscoelasticity is used to predict durability and other fundamental properties of the composite based on the creep compliance trends. Properties such as the Maxwell moduli and Maxwell viscosities are then modeled as a function of net ethanol uptake and the concentration of natural fiber dispersed phase. Later, a combination of classical molecular dynamics (MD) and semi empirical modeling is used to predict the trends in ethanol diffusion coefficient as a function of temperature and natural fiber concentration. The most efficacious models for this purpose and the ways and means of further improving the simulation accuracy are discussed.     

INFLUENCE OF DRYING CONDITIONS ON THE RHEOLOGICAL PROPERTIES OF PRUNES

ABSTRACT

Rheological properties of rehydrated prunes were obtained applying compression–relaxation tests by using a Texture Analyzer TAXT2i. A mathematical development was adopted to determine the stress and area, along the deformation. Experimental data of stress versus time was fitted by using three different rheological models: generalized Maxwell, Normand & Peleg and Maxwell. Results showed that generalized Maxwell model can be used to describe the viscoelastic behavior of the samples. The rheological parameters obtained indicated that prunes exhibited elastic behavior more pronounced at low moisture content and drying air temperature. At high moisture content and temperature the sample became a more viscous and less rigid.     

Determination of relaxation time spectra by analytical inversion using a linear viscoelastic model with fractional derivatives

Recently, Friedrich proposed an empirical model for linear viscoelastic fluids corresponding to a constitutive equation with fractional derivatives [Phil. Mag. Lett., 66 , 287 (1992)]. For this model, the relaxation modulus, the dynamic moduli, the relaxation time spectrum, and other material functions have been explicitly calculated as a function of the few parameters that characterize a viscoelastic fluid within this model. By fitting this model to experimental data, the model parameters can be determined and other material functions, in particular the relaxation time spectrum, can be calculated immediately. This paper reports to what extent this method, which may be called analytical inversion, is appropriate for the determination of relaxation time spectra. For that pupose, the spectra of a number of very different polymeric materials are determined with this method. The spectra calculated in this way are compared with the spectra obtained by nonlinear regularization. It turns out that the empirical model describes the linear viscoelastic properties of a variety of different materials with high accuracy. Keeping in mind that the determination of the relaxation time spectrum requires the solution of an ill-posed problem, the agreement between the relaxation time spectra obtained by analytical inversion and by regularization is satisfactory for these materials.     

Version of mathematical modeling of deformation processes in synthetic fibres

A mathematical model of the deformation properties of synthetic fibres in the region of nondestructive mechanical effects is proposed based on a normalized arctangent function of the logarithm of the reduced time, which significantly increases the time, load, and deformation intervals in which calculation prediction of the viscoelastic processes of synthetic fibres is performed. Methods of determining the viscoelastic characteristics as parameters of this model based on the results of brief tests in simple relaxation and creep regimes were developed based on the proposed mathematical model. The methods of considering the irreversible pseudoplastic component of deformation in mathematical modeling of the viscoelastic properties of synthetic fibres increase the reliability of predicting complex deformation modes. __________ Translated from Khimicheskie Volokna, No. 6, pp. 49–51, November–December, 2007.     

Viscoelastic properties of polypropylene/organo‐clay nano‐composites prepared using miniature lab mixing extruder from masterbatch

Polypropylene (PP) was melt blended with nano organo‐clay masterbatch at different ratios; namely 5, 10, and 15 wt % of nano‐clay. The effect of organo‐clay content on the viscoelastic properties of the nano‐composite was studied. A miniature laboratory mixing extruder, LME, was used to blend the nano organo‐clay masterbatch with PP at 260°C and 250 rpm. The blend was pelletized first, and then a thin ribbon was extruded. Two viscoelastic tests were performed; frequency sweep at constant temperature of 80°C, and temperature sweep at constant frequency of 1.0 rad/s. As the loading of nano‐clay increased, the storage modulus, G', and the thermal resistance increased as well. Different viscoelastic models were tried and 3‐elements Maxwell model was found to describe well the viscoelastic properties of the nano‐composites. The ratio of the complex modulus to the corresponding matrix modulus at different frequencies was found to vary proportional to the nanoclay loading. This dependency was described reasonably well by modified Guth model using particle aspect ratio of 12.1. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

INFLUENCE OF DRYING CONDITIONS ON THE RHEOLOGICAL PROPERTIES OF PRUNES

Rheological properties of rehydrated prunes were obtained applying compression-relaxation tests by using a Texture Analyzer TAXT2i. A mathematical development was adopted to determine the stress and area, along the deformation. Experimental data of stress versus time was fitted by using three different rheological models: generalized Maxwell, Normand & Peleg and Maxwell. Results showed that generalized Maxwell model can be used to describe the viscoelastic behavior of the samples. The rheological parameters obtained indicated that prunes exhibited elastic behavior more pronounced at low moisture content and drying air temperature. At high moisture content and temperature the sample became a more viscous and less rigid.     

Cross-linkers control the viscoelastic properties of soybean oil-based biomaterials

Because of environmental concerns, biodegradable materials have been of increasing research interest over the last several years. Previously, we reported on a biobased material developed from epoxidized soybean oil (ESO) that displayed viscoelastic behavior similar to synthetic rubbers or plastics. In this work, the viscoelastic properties of several biomaterials made from ESO cross-linked by different amounts of two different cross-linking agents were investigated. The composites exhibited different glass transition temperatures and viscoelastic behaviors depending on the type and amount of cross-linker used. Higher glass transition temperatures and stronger viscoelastic properties of the materials were found with a greater amount of cross-linker. Comparing agent triethylene glycol diamine (TGD) with agent triethylenetriamine (TETA), we found that the material cross-linked by TETA had a higher glass transition temperature and stronger viscoelastic solid properties than the material cross-linked by the agent TGD.     

Semi-analytical solution for electro-thermo-mechanical non-stationary creep behaviour of rotating disk made of nonlinear piezoelectric polymer

Electro-thermo-mechanical non-stationary creep response of a rotating disk made of nonlinear polymeric piezoelectric material has been investigated. The viscoelastic properties of the material are time, stress and temperature dependent which vary along radius. The long-term creep constitutive equation is the Burgers viscoelastic model. A non-homogeneous differential equation with variable coefficients is derived using stress-displacement relations, equilibrium equation, charge equation of electrostatics and the Maxwell equation. Time-dependent creep strains are involved in the non-homogeneous term of the differential equation. A semi-analytical solution has been developed to obtain displacement, stresses, strains and electric potential in terms of creep strains. Then, Prandtl–Reuss relations and the creep constitutive model are employed in a novel numerical procedure based on the Mendelson method to obtain history of displacement, stresses, electric potential and strains. It has been concluded that the displacement is increasing with time while effective stresses are decreasing. The results are validated by finite element methods modelling using ABAQUS software. A very good agreements between the results can be observed.     

The influence of viscoelastic property measurements on the predicted rolling resistance of belt conveyors

This article discusses how determining the viscoelastic properties of the cover material of a conveyor belt, using different rheological test modes, can result in significant differences in properties for the same material and testing conditions. The viscoelastic properties are applied to two mathematical models used to predict and compare the indentation rolling resistance performance of two rubber compounds. This article demonstrates how inaccuracies in the testing of the viscoelastic properties could result in a material with higher indentation rolling resistance properties being selected for a conveying system, making the power consumption of the system larger than necessary. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40755.     

2-D Hydro-Viscoelastic Model for Convective Drying of Highly Deformable Saturated Product

The aim of this work was to simulate in two-dimensions the spatio-temporal evolution of the moisture content, the temperature, and the mechanical stress within a highly deformable and water saturated product during convective drying. The material under study was an elongated potato sample with a square section placed in hot air flow. A comprehensive hydro-thermal model had been merged with a mechanical model, assuming a viscoelastic material, a plane deformation, and an isotropic linear hydric-shrinkage of the sample. This model was validated on the basis of the average water content and core temperature curves for drying trials under different operating conditions. The material viscoelastic properties were measured by means of stress relaxation tests at different water contents. The viscoelastic behavior was described by a generalized Maxwell model whose parameters were correlated to water content. The simulations of the spatio-temporal distributions of mechanical stress were performed and interpreted in terms of product potential damage. The sample shape was also predicted all aver the drying process with reasonable accuracy.     

Modeling of thermo-viscoelastic material behavior of glass over a wide temperature range in glass compression molding

In glass compression molding, most current modeling approaches of temperature-dependent viscoelastic behavior of glass materials are restricted to thermo-rheologically simple assumption. This research conducts a detailed study and demonstrates that this assumption, however, is not adequate for glass molding simulations over a wide range of molding temperatures. In this paper, we introduce a new method that eliminates the prerequisite of relaxation functions and shift factors for modeling of the thermo-viscoelastic material behavior. More specifically, the temperature effect is directly incorporated into each parameter of the mechanical model. The mechanical model parameters are derived from creep displacements using uniaxial compression experiments. Validations of the proposed method are conducted for three different glass categories, including borosilicate, aluminosilicate, and chalcogenide glasses. Excellent agreement between the creep experiments and simulation results is found in all glasses over long pressing time up to 900 seconds and a large temperature range that corresponds to the glass viscosity of log (η) = 9.5 – 6.8 Pas. The method eventually promises an enhancement of the glass molding simulation.     

Viscoelastic properties of a 60 mol% para-hydroxybenzoic acid/40 mol% poly(ethylene terephthalate) liquid crystalline copolyester. II: Effect of shear history

Temperature sweeps of dynamic viscoelastic properties have shown that phydroxybenzoic acid (PHB)-based liquid crystalline polyesters, specifically in this case those copolymerized with poly(ethylene terephthalate) (PET), can be subjected to considerable supercooling if initial heating curves are compared to subsequent cooling curves, indicating that this type of material can be in quite different states even at the same temperature, depending on thermal history. Utilizing this supercooling behavior, viscoelastic properties of a 60 mol% PHB/40 mol% PET material produced by Unitika were monitored before and, particularly, after large-scale shear deformation to determine how potential structure changes induced by the shear are reflected in viscoelastic properties immediately, and with time. According to dynamic viscoelastic temperature sweep data four quite different initial states were employed including conditions with, as well as largely free of, crystallites. However, in all cases, post-shear monitoring showed decreased G′ and G″ values with almost no evidence of return towards initial values within approximately 25 min. These results, in addition to furthering somewhat the fundamental understanding of the flow and relaxation properties of liquid crystalline polymers, may be useful in polymer processing, where large-scale shear deformations employed in forming processes appear to be capable of changing considerably the subsequent behavior of such materials.     

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

In this article, visco‐hyperelastic constitutive model is developed to describe the rate‐dependent behavior of transversely isotropic functionally graded rubber‐like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate‐dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo‐Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history‐integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye‐BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber‐like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342–347, 2016. © 2016 Society of Plastics Engineers     

Main‐chain benzoxazine oligomers: Effects of molecular weight on the thermal,mechanical, and viscoelastic properties

With the intent to study materials processing properties during the curing process, oligomeric benzoxazines of different molecular weight and distribution were obtained from 4‐tert‐butylphenol, bisphenol A, 4,4′‐diaminodiphenylmethane and paraformaldehyde by varying the amounts of phenolic compounds. Average molecular weight and distribution of prepared mixtures of polybenzoxazine precursors were determined by gel permeation chromatography analysis. By knowing the molecular weight distribution of prepared mixtures of polybenzoxazine precursors its effect on thermal, mechanical, and viscoelastic properties of the resin during processing and polymerization could be investigated. Mixtures of polybenzoxazine precursors of higher average molecular weight and broader molecular weight distribution displayed faster curing, lower curing conversions, and higher crosslinking densities of cured resins leading to polybenzoxazines with improved properties. This investigation was oriented towards the material processing aspects with the focus on the effect of molecular weights and viscoelastic properties of starting materials on the proceeding of the curing, including changes in material properties, and sample molding. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46659.     

Probing the viscoelastic moduli of thin,soft films with a quartz crystal resonator

Coating biomaterials with thin, soft films can alter properties, such as the biocompatibility of the materials, whereas it remains a great challenge to probe the properties of such films. In this article, we show a method that allows for the determination of the viscoelastic moduli of thin, soft films deposited on the surface of a quartz crystal through the measurement of resonance frequency shifts and the broadening of the acoustic resonance of the crystal as a resonator. The method is based on transcendental equations, which describe the mechanical response of the quartz resonator with the deposited films. It differs from the currently widely used ones, which use a thin film approximation numerically through the solution of transcendental equations to determine the viscoelasticity of the films. We estimated the glass‐transition temperature of a thin poly(vinyl butyral) film by measuring the change in the viscoelastic moduli of the film with increasing temperature, and the results agree well with the temperature obtained from other techniques. The method was not constrained to the range of the elastic moduli of the film, except where the acoustic film resonance occurred, and thus, could be applied to the study of a wide variety of thin, soft layers under different conditions. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44532.     

Measurement approaches to develop a fundamental understanding of scratch and mar resistance

Instrumented indentation and confocal microscopy were used to characterize the surface mechanical response of polymeric materials. Viscoelastic behavior was measured using instrumented indentation. A model based on the contact between a rigid probe and a viscoelastic material was used to calculate values for the creep compliance and stress relaxation modulus for two polymeric materials, epoxy and poly(methyl methacrylate) or PMMA. Scratch testing was performed on these materials with various probes under a variety of conditions, and confocal microscopy was used to characterize the resulting deformation. Relationships among viscoelastic behavior, scratch damage, and appearance are currently being explored using these methods along with finite element modeling. Presented at the 81st Annual Meeting of the Federation of Societies for Coatings Technology, November 13–14, 2004, in Philadelphia, PA.     

Noise generation and propagation control in disc brake systems using composite friction materials composed of thermoplastic elastomers as viscoelastic materials

Attempts have been made for the first time to produce a thermal sensitive friction material by the inclusion of thermoplastic elastomers (TPE) with combined plastic and rubbery properties as viscoelastic polymeric materials into the composition of the friction material for the purpose of increasing damping behavior. To evaluate the viscoelastic parameters such as loss factor (tan δ) and elastic modulus (E′) of the friction material on the molecular scale, dynamic mechanical thermal analysis was performed on the samples. Natural frequencies and mode shapes of the friction material and brake disc were determined by modal analysis. Styrene–butadiene–styrene (SBS), styrene–ethylene–butylene–styrene (SEBS) and nitrile rubber/polyvinyl chloride (NBR/PVC) blend systems have been used as TPE materials. However, NBR/PVC and SEBS were found to be more effective in preventing the noise generation and reducing the amplitude of the brake vibrations. All the friction materials containing TPEs exhibited more damping characteristics within a wide range of temperature compared with the damping characteristics of the reference sample. POLYM. COMPOS. 27:461–469, 2006. © 2006 Society of Plastics Engineers.