Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

The present contribution proposes a formulation based on the use of hybrid equilibrium elements (HEEs), for the analysis of inter-element delamination and fracture propagation problems. HEEs are defined in terms of quadratic stress fields, which strongly verify both the homogeneous and inter-element equilibrium equations and they are employed with interfaces, initially exhibiting rigid behavior, embedded at the elements’ sides. The interface model is formulated in terms of the same degrees of freedom of the HEE, without any additional burden. The cohesive zone model (CZM) of the extrinsic interface is rigorously developed in the damage mechanics framework, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. After a brief review, the formulation is computationally tested by simulating the behavior of a double-cantilever-beam with diagonal loads; the obtained numerical results confirm the accuracy and potential of the method.

Photocatalytic Decolorization of Methyl Red on Nanoporous Anodic ZrO2 of Different Crystal Structures

High surface area, self-organized nanoporous ZrO2 arrays with perfect adhesion to the Zr substrate were synthesized by anodization in an aqueous electrolyte containing (NH4)2SO4 and NH4F. The obtained semiconductor materials were tested as photocatalysts for decolorization of the methyl red (MR) as a model azo dye pollutant. It was demonstrated that as-synthesized anodic ZrO2 anodic layers are already crystalline and, therefore, do not require further thermal treatment to provide a high photocatalytic performance. However, photocatalytic efficiency could be improved by annealing at a relatively low-temperature of 350 °C. Higher annealing temperatures caused a gradual drop of photocatalytic activity. The photocatalytic behavior was correlated with the crystal phase transformation in anodic ZrO2. It was found that higher photocatalytic activity was observed for the tetragonal phase over the monoclinic phase (predominant at elevated temperatures). It results from the optimal and complex electronic structure of annealed ZrO2 with three different energy states having absorption edges at 2.0, 4.01 and 5.28 eV.

The mechanism of reinforcement of nanocomposites polyurethane/graphene

The percolation model of reinforcement was used for the theoretical analysis of reinforcement mechanism for nanocomposites polyurethane/graphene. This model allows to elucidate influence of main factors (level of interfacial adhesion, nanofiller content, interfacial regions) on the degree of reinforcement or modulus of elasticity of the considered nanocomposites. It has been shown that for these nanocomposites actually nanofiller (graphene) serves as main reinforcing element. The sharp increasing of modulus of elasticity of nanocomposite occurs at achievement of critical content of nanofiller (∼9 % mas.). The same effect of increasing the level of interfacial adhesion is obtained by a polymer matrix-nanofiller, characterized by a transition from perfect adhesion to nanoadhesion. The structure type of nanofiller in polymer matrix (exfoliated or intercalated one) in one more factor. The proposed model is universal one for all nanocomposites polymer/2D-nanofiller.

Effect of Board-Level Reflow on Adhesion Between Lead-Free Solder and Underfill in Flip-Chip BGA Packages

The change in solder/underfill adhesion and its effect on fatigue life were investigated for Pb-free solder joints for which, during the reflow process, the solder has melted and resolidified inside the underfill cavities. The change in interfacial adhesion was simulated and its strength compared using button shear test. Surprisingly, the difference was found to be only about 11%. Suspecting the validity of the result, the study was extended to further investigate the adhesion effect on fatigue life under thermal cycles. The effect was assessed analytically using FEA model. Energy-based Darveaux’s fatigue life model [1] is used to calculate solder fatigue life under two extreme conditions: perfect adhesion (without delamination or void between underfill and solder) and non adhesion. The failure parameter, accumulated plastic work per cycle for non adhesion was significantly less than that for perfect adhesion case suggesting adverse effect of strong adhesion to the enhancement of structural integrity. In this simulation, the room temperature was taken as the stress free state.

Effective Properties of Nonlinear Laminated Composites With Perfect Adhesion

This paper is devoted to the homogenization of a nonlinear one-dimensional problem as a particular case of laminated composite and its solution by a Wavelet-Galerkin method. This approach is an extension of this method to nonlinear problems. Theoretical results are given and numerical examples are presented.

Modeling of Web Slip on a Roller and Its Effect on Web Tension Dynamics

This paper considers the effect of web slip over the rollers on the span tension dynamics. In classical development of the web span tension dynamics, it is assumed that there is strict adhesion between the web and the surface of the roller and thus, there is no slip-page between the web and the roller. As a result of this assumption, effect of tension disturbances in downstream spans on the upstream span tension is precluded. However, in practice, perfect adhesion between the web and roller surface is seldom achieved and tension disturbances propagate upstream also. Though web span tension dynamic models that include slippage between web and roller are proposed, these models rely to a great extent on numerical computation of slip arc angles and are prohibitively complex to be of practical use. This paper proposes an alternative, simple approach for developing web span tension dynamics to include the effect of web slip.

The Effect of Underfill and Underfill Delamination on the Thermal Stress in Flip-Chip Solder Joints

The stresses occurring in the solder joints during thermal loads have been studied by finite element analysis. Besides the cases of no underfill and perfect adhesion, underfill delaminations at the interfaces to the solder, to the chip, and to the substrate surfaces, respectively, have been considered. The simulation results indicate that rapid failing of the flip-chip modules due to delamination can be prevented effectively by using an underfill that has a high Young’s modulus at room temperature (even 20 GPa are not too high) and a CTE slightly lower than solder. Since the ultimate failure is always caused by growing of a major crack, the damage integral concept is valid for lifetime estimations even in the case of FC modules with underfill.

Some Consequences of Coulomb Friction in Modeling Longitudinal Traction

A three-component model for a belted radial tire, previously developed by the authors for free rolling without slip, is generalized to include longitudinal forces and deformations associated with driving and braking. Surface tractions at the tire-road interface are governed by a Coulomb friction law in which the coefficient of friction is assumed to be constant. After a brief review of the model, the mechanism of interfacial shear force generation is delineated and explored under traction with perfect adhesion. Addition of the friction law then leads to the inception of slide zones, which propagate through the footprint with increasing severity of maneuvers. Different behavior patterns under driving and braking are emphasized, with comparisons being given of sliding displacements, sliding velocities, and frictional work at the tire-road interface. As a further application of the model, the effect of friction coefficient and of test variables such as load, deflection, and inflation pressure on braking stiffness are computed and compared to analogous predictions on the braking spring rate.