Constitutive Modeling of Asphalt Bound Granular Materials: Theoretical Background

Different kinds of hot mix asphalt mixtures are used in highway and runway constructions. Each of these mixtures cater to specific needs and differ from each other in the type and percentage of aggregates and asphalt used, and their response can be markedly different. Constitutive models used in the literature do not differentiate between these different kinds of mixtures and use models which treat them as if they are one and the same. In this study, we propose constitutive models for two different kinds of hot mix asphalt, viz., asphalt concrete and sand asphalt. We use a framework for materials that possess multiple natural configurations for deriving the constitutive equations. While asphalt concrete is modeled as a two constituent mixture, sand asphalt is modeled as a single constituent mixture due to the peculiarity in its makeup. In this study, we present a unified approach for deriving models for these different kind of mixtures. In a companion paper, we compare the predictions of the model for a compressive creep test with available experimental results.

Constitutive Modeling of Asphalt Bound Granular Materials: Applications to Sand Asphalt

In the earlier paper, we developed constitutive relations for two kinds of hot mix asphalt, viz., asphalt concrete and sand asphalt using the framework of materials with multiple natural configurations. In the present paper, we apply the framework that we developed for sand asphalt to study compressive creep experiments. Experimental studies of Wood and Goetz (1959) are used to compare with the predictions of the model.

Effects of Grain Boundary Sliding on Microstructural Evolution and Damage Accumulation in Tin-Lead Alloy

Experiments on the eutectic tin-lead alloy were conducted to study the effects of grain boundary sliding on the deformation and damage processes at the microscopic level. The primary objective is to gain mechanistic understandings of solder joint reliability in microelectronic packaging. Bulk specimens were subject to relatively fast deformations of tension, compression and bending, for the purposes of examining the pure mechanical effect without the influence of diffusion related phenomena. Grain realignment and phase redistribution were characterized by microscopy and microhardness indentation. A micromechanical model is proposed to elucidate the observed microstructural changes and progressive damage. This study illustrates the significance of damage in the form of microscopic heterogeneity caused by grain boundary sliding. It also illustrates the possibility of mechanically induced phase coarsening in actual solder joints. High-frequency cyclic shear tests on tin-lead solder joints showed damage along the coarsened band after only a short time, in accord with the proposed effects. Boundary sliding without the influence of atomic diffusion plays an essential role in fatigue damage in solder.

Multiphase Flows Through Poro-Elastic Media: A Continuum Model

Based on the basic balance laws and the second law of thermodynamics, a model for multiphase fluid flows through poro-elastic media is presented. The basic conservation laws. Including the balance of phasic equilibrated forces are are described. Based on the thermodynamics of the multiphase mixture, appropriate constitutive equations are formulated. It is shown that the present theory leads to the extension of Darcy’s law and contains, as its special case, Biot’s (1957) theory of saturated poro-elastic media. The special case of gas-liquid flows in porous media is discussed.

A Generalized Mixed Kinematic-Isotropic Hardening Plastic Model Coupled With Anisotropic Damage for Sheet Metal Forming

The paper presents a generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. A nonlinear anisotropic kinematic hardening is developed. For the predication of limit strains at localized necking in stamping under complex strain history, the model and its associated damage criterion for localized necking are established and implemented into LS-DYNA3D by compiling it as a user subroutine. The finite element simulation of LS-DYNA3D based on the present model is carried out. The location of localized necking for sheet metal forming has been successfully identified.

Die Life Prediction in Rapid Prototype Dies

To meet the growing demand for rapid, low-cost die fabrication technology in the sheet metal forming industry, easy-to-machine, polyurethane-based, composite board stock is used widely as a rapid tooling material. In practice, it is desirable to terminate die life by wear rather than by catastrophic fatigue. However, the failure mechanisms of the rapid prototyped tools are not clearly understood, thus making the prediction of tool life difficult. This paper presents a method to estimate the fatigue life of a sheet metal forming die fabricated from ATH (aluminum trihydrate)-filled polyurethane. A finite element model of 90° V-die bending process was developed, and the effects of process parameters on stress distribution in the punch and die were investigated through simulation. Mechanical testing was performed to characterize the fatigue properties of the tooling material. The computer-simulated results were verified through experiments using instrumented, laboratory-scale punch and die sets.

Discrete Characterization of Cohesion in Gas-Solid Flows

Cohesive forces between grains can arise from a variety of sources – such as liquid bridge (capillary) forces, van der Waals forces, or electrostatic forces – and may play a significant role in the processing of fine and/or moist powders. While recent advances have been made in our understanding of liquid-induced cohesion at the macroscopic level, in general, it is still not possible to directly connect this macroscopic understanding of cohesion with a microscopic picture of the particle properties and interaction forces. In fact, conventional theories make no attempt to distinguish between these modes of cohesion, despite clear qualitative differences (lubrication forces in wet systems or electrostatic repulsion are two good examples). In this work, we discuss several discrete characterization tools for wet (cohesive) granular material with simple, physically relevant interpretations. We examine the utility of these tools, both computationally and experimentally, by exploring a range of cohesive strengths (from cohesionless to cohesive) in several prototypical applications of solid and gas-solid flows.

A Unified Viscoplastic Fatigue Damage Model for 63Sn-37Pb Solder Alloy Under Cyclic Stress Control

A damage coupling viscoplastic model is developed to predict fatigue life of solder alloy 63Sn-37Pb under stress control. The viscoplastic flow rule chosen employs a hyperbolic sine function. A damage evolution equation is formulated based on three distinct material deformation behaviors: (i) stress rate independent damage evolution; (ii) stress rate dependent cyclic damage evolution; and (iii) stress rate dependent ductile damage evolution. The cyclic stress testing with different stress waveforms was first conducted to investigate their progressive viscoplastic deformations of the solder alloy. The investigation reveals that the material constants used in the model can be adequately determined from the results of standard creep tests. The constitutive model is validated by comparing the predicted and measured ratchetting results of the solder alloy under different forms of stress cycling. The proposed model is found to be capable of satisfactorily describing the viscoplastic deformation and ratchetting failure behaviors of the solder alloy under the conditions of the cyclic stress loading.

CART Impact Recorder Data Analysis Using Mathematical Modeling

This paper presents acceleration data of seventy-eight open-wheel, Indy car type, racecar impacts. These data were collected by the “Impact Sensor Program” conducted jointly by the Ford Motor Company and the Championship Auto Racing Teams (CART), Inc. The seventy-eight impacts consisted of forty-two side impacts, thirty rear impacts, three frontal impacts, and three rollover/flipping of cars. Related crash data were used as input to a CAE model of a racecar driver in a typical CART car to perform computer simulations of the impacts. This model was developed using MADYMO software, and was an enhanced version of one previously published. Enhancements to the model included accurate geometrical representations of the cockpit interior, the seat, and the energy-absorbing collar; a more realistic geometry of the driver’s head and an improved representation of the neck; a highly detailed model of the driver’s helmet; and improved contact algorithms to define the head-helmet, helmet-collar, and head-chin strap interactions. Additionally, data collected from twenty-six drivers were used to improve the seating posture of the driver in the model. Results of simulations performed established the validity of the model in predicting the potential injury risk to the drivers in the head and neck areas. Model predictions of injuries based on the “Head Injury Criterion” (HIC), the Injury Assessment Reference Values (IARVs) of upper neck forces and moments, and a biomechanical neck injury predictor compared well with the actual injuries sustained by the drivers. The model predictions of reversible concussions also compared well with results of recent brain injury risk studies. The present study shows that CAE modeling can be effectively used to predict potential injuries to racecar drivers involved in high “G” impacts, and that the model can be used to evaluate countermeasures to improve safety of CART cars.

Implementation of a Thermodynamic Framework for Damage Mechanics of Solder Interconnects in Microelectronic Packaging

A thermo mechanical fatigue life prediction model based on the theory of damage mechanics is presented. The damage evolution, corresponding to the material degradation under cyclic thermo mechanical loading, is quantified thermodynamic framework. The damage, as an internal state variable, is coupled with unified viscoplastic constitutive model to characterize the response of solder alloys. The damage-coupled viscoplastic model with kinematic and isotropic hardening is implemented in ABAQUS finite element package to simulate the cyclic softening behavior of solder joints. Several computational simulations of uniaxial monotonic tensile and cyclic shear tests are conducted to validate the model with experimental results. The behavior of an actual Ball Grid Array (BGA) package under thermal fatigue loading is also simulated and compared with experimental results.