Strain Energy Values Research Articles

Finite element analysis of the effect of silver content for Sn–Ag–Cu alloy compositions on thermal cycling reliability of solder die attach

Thermal performance of a chip-scale packaged power device can be improved by attaching a heat spreader to the backside of the heat generating silicon die via solder thermal interface materials [STIMs]/solder die-attach. Driven by government legislation, electronics industry has advanced to lead (Pb)-free solders due to environmental and health concerns emanating from the use of Pb-based solders. Though solder compositions in the form of Sn–Ag–Cu (SAC) ternary system have been widely accepted and preferred by the electronic industry as replacements for the traditional Pb-based solder alloys, debate continues over the optimal silver content in the Sn–Ag–Cu (SAC) solder alloys. Apparently, the effect of silver (Ag) content on thermo-mechanical reliability of SAC alloy compositions as small area solder joints (flip chip solder bump or ball grid array (BGA)) has been extensively studied but not enough information exist on the effect of Ag percentage in SAC solder alloys when employed as large area solder joint (die-attach application). In this study, non-linear finite element method (FEM) is used for a comparative analysis of the effect of Ag content on the thermal fatigue performance of Sn–3Ag–0.5Cu (SAC305) and Sn–4Ag–0.5Cu (SAC405) when used in die-attach applications under three different thermal cyclic loading cases. The results show that Von-Mises stresses and strain energy in each of the two different SAC solder joints were strong function of the thermal cycle profiles, increasing in the order −55–80°C<−55–125°C<−65–150°C. In addition, this study suggests that the range of stress was relatively greater for the SAC alloy with higher Ag content (SAC405) while the lower Ag content SAC solder (SAC305) experiences a comparatively larger accumulated plastic work under the same thermal cycling condition. Further failure analysis via visual inspection reveals that for all cases of thermal cyclic loading employed in this study, maximum values of strain energy were all located in the corner regions (critical regions) of the solder joints at the side next to the silicon die independent of the Ag content of the solder joints. This paper also highlights the concerns as regards the implementation of conventional thermal fatigue models for accurate life time prediction of large area solder joint.

Development of fibroblast-seeded collagen gels under planar biaxial mechanical constraints: a biomechanical study

Prior studies indicated that mechanical loading influences cell turnover and matrix remodeling in tissues, suggesting that mechanical stimuli can play an active role in engineering artificial tissues. While most tissue culture studies focus on influence of uniaxial loading or constraints, effects of multi-axial loading or constraints on tissue development are far from clear. In this study, we examined the biaxial mechanical properties of fibroblast-seeded collagen gels cultured under four different mechanical constraints for 6 days: free-floating, equibiaxial stretching (with three different stretch ratios), strip-biaxial stretching, and uniaxial stretching. Passive mechanical behavior of the cell-seeded gels was also examined after decellularization. A continuum-based two-dimensional Fung model was used to quantify the mechanical behavior of the gel. Based on the model, the value of stored strain energy and the ratio of stiffness in the stretching directions were calculated at prescribed strains for each gel, and statistical comparisons were made among the gels cultured under the various mechanical constraints. Results showed that gels cultured under the free-floating and equibiaxial stretching conditions exhibited a nearly isotropic mechanical behavior, while gels cultured under the strip-biaxial and uniaxial stretching conditions developed a significant degree of mechanical anisotropy. In particular, gels cultured under the equibiaxial stretching condition with a greater stretch ratio appeared to be stiffer than those with a smaller stretch ratio. Also, a decellularized gel was stiffer than its non-decellularized counterpart. Finally, the retained mechanical anisotropy in gels cultured under the strip-biaxial stretching and uniaxial stretching conditions after cell removal reflected an irreversible matrix remodeling.

Strain energy numerical technique for structural damage detection

In this paper, a computationally attractive damage index method is proposed for structural damage detection of cylindrical shell. It provides an insight to the extent of structural damage. Strain energy values computed for undamaged and damaged states are used in the corresponding damage index algorithms. It is derived from two parameters as moment response power spectral density and curvature response power spectral density. For all measured mode shapes, the damage index is defined by using the statistical parameter of relative root mean-square error of case before and after damage. The algorithm is applied to two numerical examples and its efficiency is demonstrated through damage simulations.

An efficient adaptive analysis procedure using the edge-based smoothed point interpolation method (ES-PIM) for 2D and 3D problems

Abstract In this paper, an efficient adaptive analysis procedure is proposed using the newly developed edge-based smoothed point interpolation method (ES-PIM) for both two dimensional (2D) and three dimensional (3D) elasticity problems. The ES-PIM works well with three-node triangular and four-node tetrahedral meshes, is easy to be implemented for complicated geometry, and can obtain numerical results of much better accuracy and higher convergence rate than the standard finite element method (FEM) with the same set of meshes. All these important features make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a novel error indicator is devised for ES-PIM settings, which evaluates the maximum difference of strain energy values among the vertexes of each background cell. A simple h -type local refinement scheme is adopted together with a mesh generator based on Delaunay technology. Intensive numerical studies of 2D and 3D examples indicate that the proposed adaptive procedure can effectively capture the stress concentration and solution singularities, carry out local refinement automatically, and hence achieve much higher convergence for the solutions in strain energy norm compared to the general uniform refinement.

Evaluation of Low Temperature Performance for Diatomite Modified Asphalt Mixture

According to the low temperature disease on asphalt pavement in the areas of cold and large temperature difference between day and night, conventional index test and low temperature bending creep test were used to analyze the influence of diatomite dosage on the low temperature performance of diatomite modified asphalt, and the mixture’s low temperature bending test was applied for verification. Test results show that after diatomite’s addition into asphalt, equivalent brittle point reduces significantly, ductility test cannot estimate low temperature performance very well, stiffness modulus increases and relaxation ability decreases; meanwhile, peak value of stiffness modulus and strain energy of asphalt mixture can be found, the low temperature crack resistance is enhanced; optimum dosage of diatomite is 13%. So, the low temperature performance evaluation method of diatomite modified asphalt mixture through BBR’s low temperature performance evaluation on diatomite modified asphalt remains to be discussed.

Fatigue Life of GX12CrMoVNbN9 -1 Cast Steel in the Energy-Based Approach

The paper presents the research on the controlled strain and temperature on the stress strength of martensitic GX12CrMoVNbN9 – 1 in the energy-based approach. The fatigue tests were carried out for five levels of total strain amplitude ac and two temperatures (the room one and 600oC). Performed research has shown that in terms of energy the investigated cast steel is characterized by changes in cyclic properties. Moreover, it has been proved that the temperature of study significantly influences the per-unit value of strain energy. The influence is slight in the area of large strains and gets stronger as the level of cyclic strains decreases.

A Method of Estimating Wind Turbine Blade Fatigue Life and Damage using Continuum Damage Mechanics

In this article, an energy-based model for predicting fatigue life and evaluation of progressive damage in a full composite wind turbine blade is proposed. Itis based on the assumption that the damage growth rate in a composite material depends on the maximum value of elastic strain energy per cycle. Design, finite element modeling, and dynamic analysis of the blade have been performed using ANSYS software. The first five natural frequencies and mode shapes of the blade were calculated and dangerous nodes in the critical location were determined using the modal and harmonic analysis techniques. Obtaining critical stresses from ANSYS analysis, fatigue life of the blade at the first natural resonance frequency was estimated by the model. Results showed that the calculated life of the analyzed blade could meet the design requirement.

Free Vibration Analysis of an Adhesively Bonded Functionally Graded Tubular Single Lap Joint

In this study, the three-dimensional free vibration analysis of an adhesively bonded functionally graded tubular single lap joint was carried out using the finite element method. The functionally graded tubes of the adhesive joint are composed of ceramic (Al2O3) and metal (Ni) phases varying through the tube thickness. The adhesive material properties, such as modulus of elasticity, Poisson's ratio, and density were found to have negligible effect on the first ten natural frequencies and mode shapes of the adhesive joint. The optimal design parameters of the adhesive joint, such as overlap length, inner radius of the inner tube, outer and inner tube thicknesses, and the through-the-thickness material composition variation were searched using both the artificial neural networks (ANNs) and the genetic algorithms (GAs). For this purpose, the natural frequencies and modal strain energy values were calculated for an adhesive joint with random geometrical properties and material compositions through the tube thicknesses, and were used for training the proposed artificial neural network models. The outer tube thickness, the inner tube-inner radius, and the compositional gradient exponent had considerable effect on the natural frequencies, mode shapes, and modal strain energies of the functionally graded tubular single lap joint, whereas the overlap length and the inner tube thickness had a minor effect. The GAs integrated with ANNs was employed to determine optimal design parameters satisfying both maximum natural frequency and minimum modal strain energy conditions for each natural mode of the tubular adhesive joint.

The Peak Stress Method for Fatigue Strength Assessment of welded joints with weld toe or weld root failures

The Peak Stress Method (PSM) has been presented in some previous papers, where it was shown that, in plane problems, the singular elastic maximum principal stress, evaluated at the weld toe of fillet-welded joints by means of a finite element analysis, is proportional to the Mode I Notch Stress Intensity Factor (NSIF), In parallel, a model based on the mean value of the strain energy (SED) averaged in a properly defined structural volume surrounding the point of fatigue crack initiation (either the weld toe or the weld root) has been proposed for fatigue strength assessments. The local strain energy values were given as a function of the Mode I and Mode II NSIFs neglecting the influence of the higher order (non-singular) stress terms. In the present work an expression linking the peak stress and the local strain energy value is presented, which can be used in plane problems when Mode II stress fields are non singular (at the weld toe) or of low intensity (at the weld root), By so doing, a single design scatter band valid for either weld root failures or weld toe failures can be calibrated in terms of elastic peak stress evaluated at the critical point.

A three-dimensional adaptive analysis using the meshfree node-based smoothed point interpolation method (NS-PIM)

In this paper, a three-dimensional (3-D) adaptive analysis procedure is proposed using the meshfree node-based smoothed point interpolation method (NS-PIM). Previous study has shown that the NS-PIM works well with the simplest four-node tetrahedral mesh, which is easy to be implemented for complicated geometry. In contrast to the displacement-based FEM providing lower bound solutions, the NS-PIM possesses the attractive property of providing upper bound solutions in strain energy norm. In the present adaptive procedure, a novel error indicator is devised for NS-PIM settings, which evaluates the maximum difference of strain energy values among four nodes in each of the tetrahedral cells. A simple h-type local refinement scheme is adopted and coupled with 3-D mesh automatic generator based on Delaunay technology. Numerical results indicate that the adaptive refinement procedure can effectively capture the stress concentration and solution singularities, and carry out local refinement automatically. The present adaptive procedure achieves much higher convergence in strain energy solution compared to the uniform refinement, and obtains upper bound solution in strain energy efficiently for force driven problems.

Model Sensitivity and Use of the Comparative Finite Element Method in Mammalian Jaw Mechanics: Mandible Performance in the Gray Wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.

Development and characterization of a gelatin‐based coating with unique sealing properties

AbstractThe experimental results on the development of thin (∼ 1.5 μm) gelatin‐based coatings and the investigation on their sealing attribute when applied onto oriented polypropylene (OPP) are reported. The sealing performance, expressed as the strain energy required to separate the sealed joints, was studied as a function of three different influencing factors. pH of the hydrogel solution was varied between 5 and 11. The highest seal strength values were obtained for pH values beyond the isoelectric point (IEP) of the gelatin molecule. The effect of the plasticizer (glycerol) was studied by changing its concentration from 2.5 wt % to 7.5 wt % to the total weight of the hydrogel solution. Glycerol concentration = 7.5 wt % was found to be the best for achieving adequate strain energy values. The influence of a hydrophobic component on the capability of the coating to act as a sealant has also been assessed. The hydrophobic component had a positive effect only up to a certain level (1 wt %, weight percent), whereas beyond this value, it affected the seal strength attribute. According to the best setting conditions, seal strength values for the OPP biocoated films of ∼ 61 N × mm were attained, with a corresponding maximum force required to break the joints of 2.4 N. These results are discussed by taking into consideration the modality of seals opening. Interestingly, the heat‐seal (temperature: 90°C; dwell time: 1 s; pressure: 4 bar) failed in both peeling and tearing mode failure, as confirmed by microscopy, spectrophotometric, and particle size analyzes. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

The Experimental Research of Delamination Damage Location Based on FBG Sensors Network in Solid Rocket Motor Shell

The fiber reinforced composite materials were widely used for aerospace aircrafts and missile weapons, and the delamination was a major problem which reduced the structural integrity and reliability of the solid rocket motor (SRM) composite shell seriously. In order to locate the delamination damage, the fiber Bragg grating (FBG) strain sensors network was embedded in SRM shell, and a multi-step approach of delamination damage location based on strain energy was performed: the strain field was measured in a scatter grid by the FBG strain sensors network in hydraulic testing; then the continuous displacement and strain field was reconstructed with relative sensors data using a moving least square (MLS) mesh-free fitting method; the strain energy of each subregions was calculated from the reconstructed data; finally the damaged subregions was identified successfully by singularity value of strain energy. The results of simulation and experiment indicated that the damage identification and location only required the measure of strain field of the SRM shell, and the presented approach achieved higher accuracy.

Nanoclay and Microballoons Wall Thickness Effect on Dynamic Properties of Syntactic Foam

The effect of nanoclay on the high strain rate mechanical properties of syntactic foams is studied. Two types of microballoons with different wall thicknesses are used in fabrication of plain and nanoclay syntactic foams. Plain syntactic foams are fabricated with 60% volume fraction of glass microballoons. 1%, 2%, and 5% volume fractions of Nanomer I.30E nanoclay are incorporated to produce nanoclay syntactic foams. High strain rate test using split Hopkinson pressure bar (SHPB) apparatus is performed on all types of plain and nanoclay syntactic foams. Dynamic modulus, strength, and corresponding strain are calculated using the SHPB data. Quasistatic test is also performed and results are compared with the dynamic SHPB results. The results demonstrate the importance of nanoclay and microballoon wall thickness in determination of syntactic foam dynamic properties. It is found that at a high strain rate, the strength and modulus of composite foams having K46 microballoons increase due to addition of 1% volume fraction of nanoclay. However, in composite foams having S22 microballoons, the increase in strength is not significant at a high strain rate. Further increase in nanoclay volume fraction to 2% and 5% reduces the strength and modulus of composite foams having S22 microballoons. Difference in wall thickness of microballoons is found to affect the strength, modulus, strain energy, and deformation of composite foams. Composite foams fabricated with thicker walled microballoons (K46) show comparatively higher values of strength, modulus, and strain energy compared with thin walled (S22) microballoons. Scanning electron microscopy shows that crack propagation behavior is distinct at different strain rates.

The HSAB principle as a means to interpret the reactivity of carbon nanotubes

Polycyclic curved aromatic fragments (C 24H 12) have been employed as models of the single-walled carbon nanotubes ( n,0), where n varies from 4 up to 30. Those structures were chosen on the basis of the analysis of the strain energy values calculated for the models possessing various sizes. The flat coronene structure has been chosen as a molecular fragment topologically resembling the honeycomb lattice in order to investigate the relation between the curvature and reactivity of the sidewalls of SWNTs. In the current study we took into account the interaction of CO and NH 2 (treated as probe molecules) with the exterior surface of nanotubes. Obtained results illustrate that both total as well as local hardness and/or molecular electrostatic potential (MEP) can be a good measure for the reactivity if the influence of geometrical changes is considered. The systematic theoretical studies also show that the calculated interaction energies of sorbed CO on those models are related to the both types of hardness. On the other hand, in the case of amidogen sorbed on the nanotube surface the correlation between the binding energy and MEP is visible. Those differences can be explained by various kinds of the adsorption mechanism, i.e. physical or chemical adsorption, respectively.

Frontal sinuses and head-butting in goats: a finite element analysis

Frontal sinuses in goats and other mammals have been hypothesized to function as shock absorbers, protecting the brain from blows during intraspecific combat. Furthermore, sinuses are thought to form through removal of ;structurally unnecessary' bone. These hypotheses were tested using finite element modeling. Three-dimensional models of domesticated goat (Capra hircus) skulls were constructed, with variable frontal bone and frontal sinus morphology, and loaded to simulate various head-butting behaviors. In general, models with sinuses experienced higher strain energy values (a proxy for shock absorption) than did models with unvaulted frontal bones, and the latter often had higher magnitudes than models with solid vaulted frontal bones. Furthermore, vaulted frontal bones did not reduce magnitudes of principal strain on the surface of the endocranial cavity relative to models with unvaulted frontal bones under most loading conditions. Thus, these results were only partially consistent with sinuses, or the bone that walls the sinuses, acting as shock absorbers. It is hypothesized that the keratinous horn sheaths and cranial sutures are probably more important for absorbing blows to the head. Models with sinuses did exhibit a more ;efficient' distribution of stresses, as visualized by histograms in which models with solid frontal bones had numerous unloaded elements. This is consistent with the hypothesis that sinuses result at least in part from the removal of mechanically unnecessary bone.

Effects of nuclear island connected buildings on seismic behaviour of reactor internals in a pool type fast breeder reactor

The seismic analysis of reactor assembly housing the primary circuit of a typical 500 MWe capacity pool type fast breeder reactor (PFBR) is reported. The reactor assembly is supported on the reactor vault within the nuclear island connected buildings (NICB). The seismic responses, viz. critical displacements, sloshing heights, stresses and strain energy values in the vessels are determined for the reactor assembly by detailed finite element analysis including the fluid–structure interaction and sloshing effects. Analysis is carried out to quantify the effects of inter-connection of the reactor vault with the adjacent buildings under the assumptions that the reactor vault along with reactor assembly is: (1) an isolated structural system from the adjacent buildings within reactor containment building (RCB) and (2) connected with the adjacent civil structures through floor slabs. Analysis indicates that, by inter-connecting the vault with the NICB, there are overall increases of all the governing parameters which decide the seismic design criteria. The significant effects are increases of: (1) radial and axial displacements of core top and absorber rods and vertical accelerations of core subassemblies which are of concern to reactor safety, (2) primary membrane stress intensities for the inner vessel and (3) strain energies developed at the critical portions which can enhance the buckling risks of main vessel, inner vessel and thermal baffles. Hence, it is preferable to isolate the reactor vault, directly constructing from the base raft without inter-connecting it with the NICB, from the seismic loading considerations.

Effect of structural arrest on Poisson’s ratio in nanoreinforced elastomers

We evaluate the strain amplitude (gamma) dependence of the dynamic storage and loss moduli for polybutadiene elastomers containing carbon black particles of varied size at a constant volume fraction of 0.18. Measurements of the low-strain hysteretic softening (Payne effect or unjamming transition) in both shear and uniaxial extension modes allow the gamma dependence of Poisson's ratio (nu) to be determined. For elastomers with a fully agglomerated filler network, the breakup of the jammed state with increasing strain induces a transition from nu approximately 0.35 to the limiting value for an incompressible material, nu=0.5 . This transition is more marked for samples containing smaller filler particles. The effect is similar to the change caused by temperature in the glass transition zone of amorphous polymers, reflecting the parallel between deformation in jammed systems and temperature (and the volume changes associated with it) in glasses; thus, the Payne effect resembles the glass transition in polymers and molecular liquids. We also show herein that the alleviation of structural arrest in filled rubber occurs at a constant value of strain energy, independent of the size of the reinforcing particles or the nature of the strain (shear vs tension). Contrary to the results for shear or tensile deformation, under hydrostatic pressure (volumetric strain) a value of nu=0.5 is maintained for all magnitudes of strain. Along with the absence of hysteresis in cyclic pressure-volume measurements, this demonstrates the distinct behavior of the filler network for hydrostatic compression, in which there is no relative displacement of polymer and filler.

Energy release and heat generation during the 1999 Ms7.6 Chi‐Chi, Taiwan, earthquake

On 20 September 1999, the Ms7.6 Chi‐Chi earthquake ruptured the Chelungpu fault in central Taiwan. Integrating observed and inversed results of source parameters, the fracture energy, Eg, and frictional energy, Ef, on the fault and its northern and southern segments are estimated. Together with given values of strain energy, ΔE, and seismic radiation energy, Es, the seismic efficiency, i.e., η = Es/ΔE, and the radiation efficiency, i.e., ηR = Es/(Es + Eg), are evaluated. The average fracture energy per unit area, G, is also calculated from Eg. The frictional heat caused by dynamic frictional stress is calculated from Ef. Results show a marked difference in source properties between the two segments. The average frictional and ambient stress levels on the two segments are estimated. The total energy budget of and heat generated by the earthquake are elucidated based on a two‐dimensional faulting model with frictional heat. Both observed and calculated results suggest the possible existence of fluids, which produced suprahydrostatic gradients, on the fault during faulting. Lubrication and thermal fluid pressurization might play a significant role on rupture.

DFT studies of copper complexes with biphenyldiimino dithioether II. Mechanical strain

The geometries of tetrahedral and square-planar Cu(bite) q complexes, q = +1 or +2, as well as of the macrocyclic bite ligand, bite = tetrabenz[a,e,g,k]-15,18-dithia-9,24-diaza-cyclohexadeca-9,23-diene, have been optimized using the DFT method. The reorganization and strain energy values of Cu(bite) +/2+ complexes are comparable with analogous DFT/MM data for tetracoordinate copper complexes with monodentate imidazole and thiolate ligands that are used as model systems for blue copper proteins.