Multi-scale modeling in damage mechanics of composite materials

This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies––the hierarchical and the synergistic––are reviewed in the context of deformational response. Finally, the “big picture” as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed.     

Thermal, mechanical and vibration characteristics of epoxy-clay nanocomposites

Diglycidyl ether of bisphenol-A (DGEBA) epoxy resin system filled individually with organoclay (OC) and unmodified clay (UC) were synthesized by mechanical shear mixing with the addition of diamino-diphenylmethane (DDM) hardener. The unmodified clay used was Na⁺-Montmorillonite (MMT) and the organoclay was alkyl ammonium treated MMT clay. The reinforcement effect of OC and UC in the epoxy polymer on thermal, mechanical and vibration properties were studied. X-ray diffraction (XRD) and Transmission electron microscopy (TEM) were used to study the structure and morphology of nanocomposites. Curing study shows that the addition of OC in epoxy resin aids the polymerization by catalytic effect, and UC addition does not show any effect in the curing behavior of epoxy polymer. Thermogravimetry analysis (TGA) shows enhanced thermal stability for epoxy with OC fillers than that of epoxy with UC fillers. The epoxy with OC fillers shows considerable improvement on tensile and impact properties over pure epoxy polymer and epoxy with UC fillers. The improvement in tensile and impact properties of nanocomposites is supported with the fracture surface studies. Epoxy with OC fillers shows enhanced vibration characteristics than that of the pure epoxy polymer and epoxy with UC fillers.     

Multidroplet Impact Model for Prediction of Residual Stresses in Water Jet Peening of Materials

In this article, a multidroplet impact model, proposed for predicting residual stresses induced on materials subjected to water jet peening, is presented. This approach considers the impact pressure distribution due to high-velocity droplets impinging on the material surface instead of stationary pressure distribution for prediction of residual stresses on water jet-peened surfaces. It makes use of Reichardt's theory for predicting the velocity distribution of droplets and liquid impact theory for predicting the impact pressure and duration of impact of high-velocity droplets. For predicting residual stresses on the surface and subsurface of material subjected to water jet peening, finite element modeling approach was adopted by using transient elastoplastic finite element analysis by considering an impingement of a set of droplets in succession to one another over a certain time period after which this pressure is released. The effectiveness of the proposed approach was demonstrated bv comparing the predicted residual stresses with those predicted by using the single set of droplets approach proposed by Rajesh et al. [6]. Finally, the practical relevance of the proposed approach was shown by comparing the predicted results with the experimental results obtained by water peening of 6063-T6 aluminium alloy.     

Validation of models with multivariate output

This paper develops metrics for validating computational models with experimental data, considering uncertainties in both. A computational model may generate multiple response quantities and the validation experiment might yield corresponding measured values. Alternatively, a single response quantity may be predicted and observed at different spatial and temporal points. Model validation in such cases involves comparison of multiple correlated quantities. Multiple univariate comparisons may give conflicting inferences. Therefore, aggregate validation metrics are developed in this paper. Both classical and Bayesian hypothesis testing are investigated for this purpose, using multivariate analysis. Since, commonly used statistical significance tests are based on normality assumptions, appropriate transformations are investigated in the case of non-normal data. The methodology is implemented to validate an empirical model for energy dissipation in lap joints under dynamic loading.     

Numerical analysis on compliance and electrical behavior of multi-copper-column flip-chip interconnects for wafer-level packaging

This paper presents modeling and simulation results of a modified copper-column-based flip-chip interconnect with ultrafine pitch for wafer-level packaging, and the process and prototyping procedure are described as well. This interconnect consists of multiple copper columns which are electrically in parallel and supporting a solder bump. A simple analytical model has been developed for correlation between the interconnect geometry and the thermal fatigue life. In comparison to the conventional single-copper-column (SCC) interconnects, numerical analysis reveals that the multi-copper-column (MCC) interconnect features enhanced compliances and, hence, higher thermomechanical reliability, while the associated electrical parasitics (R, L, and C) at dc and moderate frequencies are still kept low. Parametric studies reveal the effects of geometric parameters of MCC interconnects on both compliances and electrical parasitics, which in turn facilitate design optimization for best performance. By using coplanar waveguides (CPWs) as feed lines on both chip and package substrate, a high-frequency (up to 40 GHz) S-parameter analysis is conducted to investigate the transmission characteristics of the MCC interconnects within various scenarios which combines various interconnect pitches and common chip and package substrates. An equivalent lumped circuit model is proposed and the circuit parameters (R, L, C, and G) are obtained throughout a broad frequency range. Good agreement is achieved for the transmission characteristics between the equivalent lumped circuit model and direct simulation results.     

Investigating Role of Growing Adsorbent Bed in a Dead-End PAC/UF Process

A two-stage mathematical model was developed to describe adsorbate removal in a dead-end powdered activated carbon/ultrafiltration (PAC/UF) membrane process. Para-nitrophenol (PNP) was used as the model organic compound. The first stage accounted for adsorbate removal during transport from the initial PAC contact with the PNP solution to the membrane system, and the second stage accounted for additional PNP removal due to the retention of the PAC in a growing bed on the membrane surface. The PAC adsorptive capacity was described using the Langmuir isotherm, whose parameters were estimated from isotherm experiments. Transport of the PNP through the PAC particle was described using the homogeneous surface diffusion model and the surface diffusivity was estimated from batch experiments. The two stage model predicted the effluent concentrations from the PAC/UF process during the early stages of the experiments, but model improvements are required to more accurately predict the latter stages. A batch model can be used to describe the effluent PNP concentration from the PAC/UF process if dispersion is neglected.     

Stimulating Biological Nitrification via Electrolytic Oxygenation

The feasibility of electric current prompted aerobic biodegradation of NH4+–N in an attached growth bioreactor system is demonstrated. Nitrification was induced at electric current densities of 1.25 and 2.5?mA/cm2 and with pure oxygen supplied at a rate equivalent to 1.25?mA/cm2 when the bioreactor was operated in batch mode at 6 days detention time. About 84% (27?mg/L)?NH4+–N loss was observed at the end of each detention period during all three experimental conditions, indicating that the electric current did not negatively impact the rate of nitrification. Nitrite accumulation was observed during the initial stages of nitrification experiments with 1.25?mA/cm2 current intensity, but nitrite did not accumulate during the other two sets of nitrification experiments. A mathematical model formulated to obtain the rates of biological reactions showed that rates of NH4+–N removal are similar for all aeration conditions. Abiotic experiments showed that NH4+–N was not removed electrolytically and via stripping, confirming that NH4+–N disappearance is due to biological activity.     

A simple method for the evaluation of fracture toughness of a multi-layered laminate based on the failure stress of sub-laminates

A simple analytical method is presented that can be used to predict the intralaminar fracture toughness of multilayered composite laminate based on the failure stresses of its sub laminates. MCCI approach is followed to verify the fracture toughness of a base laminate and the method is validated comparing the available test data on the toughness value of the base laminate with the prediction. It is observed that a better representation of carbon —epoxy base laminate by its sub laminate gives very good agreement in prediction within 3%.     

Redefining the Diamond Cutting Edge: A Technique that Complements Nano-Metric Surface Generation

Ongoing developments in broadband digital networks and optical devices require mechanical components having nano-metric surface finishes and ultra precision shapes. Such components are processed using the technology of diamond micro-machining in which diamond tools are extensively used. However, these tools are susceptible to chemical attack at high temperatures and induce severe wear, especially when cutting ferrous materials. As a result, these diamond tools need to be redefined (i.e., resharpened) on a regular basis in order to facilitate micro-cutting and to generate nano-metric surface finishes. This paper describes a new way of diamond tool edge re-sharpening and its conditions to achieve both increased accuracy and material removal rate.