High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.
Here, a stable and nodally integrated meshfree formulation for modeling shock waves in fluids is developed. The reproducing kernel approximation is employed to discretize the conservation equations for compressible flow, and a flux vector splitting approach is applied to allow proper numerical treatments for the advection and pressure parts, respectively, based on the characteristics of each flux term. To capture the essential shock physics in fluids, including the Rankine–Hugoniot jump conditions and the entropy condition, local Riemann enrichment is introduced under the stabilized conforming nodal integration (SCNI) framework. Meanwhile, numerical instabilities associated with the advection flux are eliminated by adopting a modified upwind scheme. To further enhance accuracy, a MUSCL-type method is introduced in conjunction with an oscillation limiter to avoid Gibbs phenomenon and ensure monotonic piecewise linear reconstruction in the smooth region. The present meshfree formulation is free from tunable artificial parameters and is capable of capturing shock and rarefaction waves without over/undershoots. Finally, several numerical examples are analyzed to demonstrate the effectiveness of the proposed MUSCL-SCNI approach in meshfree modeling of complex shock phenomena, including shock diffraction, shock–vortex interaction, and high energy explosion processes.
A new model for determining band gaps for elastic wave propagation in a periodic composite beam structure is developed using a non-classical Bernoulli–Euler beam model that incorporates the microstructure, surface energy and rotational inertia effects. The Bloch theorem and transfer matrix method for periodic structures are employed in the formulation. The new model reduces to the classical elasticity-based model when both the microstructure and surface energy effects are not considered. The band gaps predicted by the new model depend on the microstructure and surface elasticity of each constituent material, the unit cell size, the rotational inertia, and the volume fraction. To quantitatively illustrate the effects of these factors, a parametric study is conducted. The numerical results reveal that the band gap predicted by the current non-classical model is always larger than that predicted by the classical model when the beam thickness is very small, but the difference is diminishing as the thickness becomes large. Also, it is found that the first frequency for producing the band gap and the band gap size decrease with the increase of the unit cell length according to both the current and classical models. In addition, it is observed that the effect of the rotational inertia is larger when the exciting frequency is higher and the unit cell length is smaller. Furthermore, it is seen that the volume fraction has a significant effect on the band gap size, and large band gaps can be obtained by tailoring the volume fraction and material parameters.
The Structural Reliability Partnership Workshop was held in Albuquerque, NM on August 29-30, 2017 and was hosted by Sandia National Laboratories. Attendees were present from academia, industry and several other national laboratories. The workshop kicked off with an introduction to the SRP to familiarize potential members with what the purpose, structure and benefits would be to their organization. Technical overviews were given on several topics by attendees from each sector – national labs, universities and industry – to provide a snapshot of the type of work that is currently being conducted on structural reliability. Attendees were then given the opportunity to suggest and discuss potential Challenge Scenario topics. Three were ultimately decided upon as being the most important: Additive Manufacturing, Hydrogen Pipeline Steels, and Bolted Joined Structures. These were then analyzed using Quad Charts to determine What, How, Who, and Why these areas would be further investigated. Rather than restricting future research to only one area, the option was left open to investigate both the top two, depending on interest and cost associated with hosting such an event. More informal collaboration may be undertaken for the third topic if members have time and interest. Other items discussed pertained to the organization, structure and policies of the Partnership. Topics including Data Management, IP, and mechanisms of partnering/information sharing were touched upon but final decisions were not made. Further action is needed before this can be done. Action items were outlined and assigned, where possible. The next workshop is to be held in early August 2018 in Boulder, CO and is to be hosted by NIST. In the interim, quarterly updates are to take place via WebEx to maintain a line of communication and to ensure progress on both the administrative and technical tasks.
Recent work at Sandia National Laboratories has focused on preparing strong predictive models for the simulation of ductile failure in metals. The focus of this talk is on the development of engineering-ready models that use a phenomenological approach to represent the ductile fracture processes. As such, an empirical tearing parameter that accounts for mean stress effects along the crack front is presented. A critical value of the tearing parameter is used in finite element calculations as the criterion for crack growth. Regularization is achieved with three different methods and the results are compared. In the first method, upon reaching the critical tearing, the stress within a solid element is decayed by uniformly shrinking the yield surface over a user specified amount of strain. This yields mesh-size dependent results. As a second method for regularization, cohesive surface elements are inserted using an automatic remeshing technique. In the third method, strain-localization elements are inserted with the automated remeshing.
We report our conclusions in support of the FY 2003 Science and Technology Milestone ST03-3.5. The goal of the milestone was to develop a research plan for expanding Sandia's capabilities in materials modeling and simulation. From inquiries and discussion with technical staff during FY 2003 we conclude that it is premature to formulate the envisioned coordinated research plan. The more appropriate goal is to develop a set of computational tools for making scale transitions and accumulate experience with applying these tools to real test cases so as to enable us to attack each new problem with higher confidence of success.
The purpose of microstructural control is to optimize materials properties. To that end, they have developed sophisticated and successful computational models of both microstructural evolution and mechanical response. However, coupling these models to quantitatively predict the properties of a given microstructure poses a challenge. This problem arises because most continuum response models, such as finite element, finite volume, or material point methods, do not incorporate a real length scale. Thus, two self-similar polycrystals have identical mechanical properties regardless of grain size, in conflict with theory and observations. In this project, they took a tiered risk approach to incorporate microstructure and its resultant length scales in mechanical response simulations. Techniques considered include low-risk, low-benefit methods, as well as higher-payoff, higher-risk methods. Methods studied include a constitutive response model with a local length-scale parameter, a power-law hardening rate gradient near grain boundaries, a local Voce hardening law, and strain-gradient polycrystal plasticity. These techniques were validated on a variety of systems for which theoretical analyses and/or experimental data exist. The results may be used to generate improved constitutive models that explicitly depend upon microstructure and to provide insight into microstructural deformation and failure processes. Furthermore, because mechanical state drives microstructural evolution, a strain-enhanced grain growth model was coupled with the mechanical response simulations. The coupled model predicts both properties as a function of microstructure and microstructural development as a function of processing conditions.
This report summarizes materials issues associated with advanced micromachines development at Sandia. The intent of this report is to provide a perspective on the scope of the issues and suggest future technical directions, with a focus on computational materials science. Materials issues in surface micromachining (SMM), Lithographic-Galvanoformung-Abformung (LIGA: lithography, electrodeposition, and molding), and meso-machining technologies were identified. Each individual issue was assessed in four categories: degree of basic understanding; amount of existing experimental data capability of existing models; and, based on the perspective of component developers, the importance of the issue to be resolved. Three broad requirements for micromachines emerged from this process. They are: (1) tribological behavior, including stiction, friction, wear, and the use of surface treatments to control these, (2) mechanical behavior at microscale, including elasticity, plasticity, and the effect of microstructural features on mechanical strength, and (3) degradation of tribological and mechanical properties in normal (including aging), abnormal and hostile environments. Resolving all the identified critical issues requires a significant cooperative and complementary effort between computational and experimental programs. The breadth of this work is greater than any single program is likely to support. This report should serve as a guide to plan micromachines development at Sandia.
A key issue of solder joint reliability is joint failure due to thermomechanical fatigue (TMF). TMF is caused by different coefficients of thermal expansion (CTEs) of the materials in an electronic package, combined with changes in the ambient temperature. Different CTEs result in cyclical strain in the assembly, and this strain is concentrated almost entirely in the solder because it is the most deformable portion of the package. Since solder alloy is at a significant fraction of its melting point even at room temperature, the cyclical strain enhances mass diffusion and causes dramatic changes in the alloy microstructure over time. As the microstructure changes and becomes coarser, the solder alloy weakens and eventually microcracks nucleate and grow in the joint, leading to component failure. the failure of solder joints is difficult to detect due to the inert nature of the electrical system. If the system is not on for extended periods then failures can not be observed. Therefore it is important to develop an advanced predictive capability which allows scientists and engineers to predict solder degradation and identify reliability problems in aging electronics early.
Computational materials simulations have traditionally focused on individual phenomena: grain growth, crack propagation, plastic flow, etc. However, real materials behavior results from a complex interplay between phenomena. In this project, the authors explored methods for coupling mesoscale simulations of microstructural evolution and micromechanical response. In one case, massively parallel (MP) simulations for grain evolution and microcracking in alumina stronglink materials were dynamically coupled. In the other, codes for domain coarsening and plastic deformation in CuSi braze alloys were iteratively linked. this program provided the first comparison of two promising ways to integrate mesoscale computer codes. Coupled microstructural/micromechanical codes were applied to experimentally observed microstructures for the first time. In addition to the coupled codes, this project developed a suite of new computational capabilities (PARGRAIN, GLAD, OOF, MPM, polycrystal plasticity, front tracking). The problem of plasticity length scale in continuum calculations was recognized and a solution strategy was developed. The simulations were experimentally validated on stockpile materials.
Severe plastic deformation in an eutectic tin-lead alloy is studied by imposing fast bending at room temperature, in an attempt to examine the microstructural response in the absence of thermally activated diffusion processes. A change in microstructure due to this purely mechanically imposed load is observed: the tin-rich matrix phase appears to be extruded out of the narrow region between neighboring layers of the lead-rich phase and alterations in the colony structure occur. A micromechanism is proposed to rationalize the experimental observations.
This study is devoted to providing a mechanistic rationale of coarsening induced failure in solder alloys during thermomechanical fatigue. Micromechanical modeling of cyclic deformation of eutectic tin-lead alloy was undertaken using the finite element method. The models consist of regularly arranged tin-rich and lead-rich phases, simulating the lamellar array and colony structure in a typical eutectic system. A fine structure and a coarse structure, bearing the same phase fraction but different in the aspect ratio of each lead-rich layer and in the number of lead-rich layers in each colony, are utilized for representing the microstructure before and after coarsening, respectively. Both phases are treated as elastic-plastic solids with their respective properties. For simplicity the creep effect is ignored without compromising the main objective of this study. Cyclic loading under pure shear and uniaxial conditions is modeled. It is found that both the fine and coarse structures exhibit essentially the same macroscopic stress-strain response. The coarse structure, however, shows a greater maximum effective plastic strain on a local scale throughout the deformation. The numerical result implies that, in a solder joint, a locally coarsened region may not be mechanically weaker than its surrounding, but it is subject to early damage initiation due to accumulated plasticity. Other implications regarding solder alloy failure and micromechanical modeling of two-phase materials are discussed.
This paper presents a viscoplasticity model taking into account the effects of change in grain or phase size and damage on the characterization of creep damage in 60Sn-40Pb solder. Based on the theory of damage mechanics, a two-scalar damage model is developed for isotropic materials by introducing the free energy equivalence principle. The damage evolution equations are derived in terms of the damage energy release rates. In addition, a failure criterion is developed based on the postulation that a material element is said to have ruptured when the total damage accumulated in the element reaches a critical value. The damage coupled viscoplasticity model is discretized and coded in a general-purpose finite element program known as ABAQUS through its user-defined material subroutine UMAT. To illustrate the application of the model, several example cases are introduced to analyze, both numerically and experimentally, the tensile creep behaviors of the material at three stress levels. The model is then applied to predict the deformation of a notched specimen under monotonic tension at room temperature (22 C). The results demonstrate that the proposed model can successfully predict the viscoplastic behavior of the solder material.
This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic damage considerations. A separate report will be made to present a comprehensive damage model describing life prediction of the solder material under thermomechanical fatigue loading. The method is based on a theory of damage mechanics which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behavior of a typical solder material. With the introduction of a damage effect tensor, the constitutive equations are derived to enable the formulation of a fatigue damage dissipative potential function and a fatigue damage criterion. The fatigue evolution is subsequently developed based on the hypothesis that the overall damage is induced by the accumulation of fatigue and plastic damage. This damage mechanics approach offers a systematic and versatile means that is effective in modeling the entire process of material failure ranging from damage initiation and propagation leading eventually to macro-crack initiation and growth. As the model takes into account the load history effect and the interaction between plasticity damage and fatigue damage, with the aid of a modified general purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.
