Minimal failure probability for ceramic design via shape control

We consider the probability of failure for components made of brittle mate- rials under one time application of a load as introduced by Weibull and Batdorf - Crosse and more recently studied by NASA and the STAU cooperation as an objective functional in shape optimization and prove the existence of optimal shapes in the class of shapes with a uniform cone property. The corresponding integrand of the objective functional has convexity properties that allow to derive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). These properties require less restrictive regularity assumptions for the boundaries and state functions compared to [arXiv:1210.4954]. Thereby, the weak formulation of linear elasticity can be kept for the abstract setting for shape optimization as presented in the book by Haslinger and Maekinen

An Investigation into the Bonding Properties of New Generation Ceramic Brackets As Compared to a Stainless Steel Bracket

Introduction: More patients are seeking esthetic alternatives for their orthodontic treatment options, which has led to increased use of ceramic brackets in recent years. These brackets were marketed before independent scientific research was completed. Many of the early ceramic brackets used a silane coupling agent to allow for a chemical bond between the bracket and the adhesive resin. Early reports from clinicians of increased bond strengths and iatrogenic tooth damage after bracket removal were common. Manufacturers have made changes to their base designs, relying more on mechanical retention for bond strength. The goal of this study was to test the shear bond strength of two newer generations of mechanically retained ceramic brackets and compare them to a traditional stainless steel bracket. Materials and Methods: Two types of ceramic brackets, Clarity Advanced (3M Unitek, Monrovia, CA), and Avex CX (Opal Orthodontics, South Jordan, UT) and one type of metal bracket, Victory Series MBT (3M, Unitek, Monrovia, CA) were used in this study. Exemption from IRB Application was granted by the Marquette University Institutional Review Board (IRB) on 7-12-13. The shear bond strength of the three groups of brackets were examined after bonding to extracted premolars. Brackets were debonded with a universal testing machine (Instron Corporation, Canton, MA) in a motion parallel to the bracket/tooth interface. Each tooth and bracket was viewed under an optical stereomicroscope at 10x magnification and given an adhesive remnant index (ARI) score. The one way ANOVA and Tukey\u27s post hoc tests were used to determine significant differences in bond strengths, and the Kruskal-Wallis and Mann-Whitney post hoc tests were used to analyze the difference in ARI scores. Results: Statistically significant (p\u3c0.01) differences were found between the shear bond strengths of the Victory Series and Clarity Advanced groups, with the Victory Series having a mean strength of 199.4 N and the Clarity Advanced having an average of 136.0 N. Significant (p\u3c0.0001) differences in ARI scores were found between the Victory Series and both ceramic groups, with an average score of 1 for the Victory Series and an average score of 2 for both ceramic groups. The two ceramic brackets were not statistically different from each other in bond strength or ARI score. Conclusions: The shear bond strengths of the new generations of ceramic brackets are lower than those of the metal bracket tested, which suggests a safer bond to enamel. Further research on clinical debonding characteristics and behavior intra-orally are needed to support the in vitro results found in this study

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

Low-density materials with tailorable properties have attracted attention for decades, yet stiff materials that can resiliently tolerate extreme forces and deformation while being manufactured at large scales have remained a rare find. Designs inspired by nature, such as hierarchical composites and atomic lattice-mimicking architectures, have achieved optimal combinations of mechanical properties but suffer from limited mechanical tunability, limited long-term stability, and low-throughput volumes that stem from limitations in additive manufacturing techniques. Based on natural self-assembly of polymeric emulsions via spinodal decomposition, here we demonstrate a concept for the scalable fabrication of nonperiodic, shell-based ceramic materials with ultralow densities, possessing features on the order of tens of nanometers and sample volumes on the order of cubic centimeters. Guided by simulations of separation processes, we numerically show that the curvature of self-assembled shells can produce close to optimal stiffness scaling with density, and we experimentally demonstrate that a carefully chosen combination of topology, geometry, and base material results in superior mechanical resilience in the architected product. Our approach provides a pathway to harnessing self-assembly methods in the design and scalable fabrication of beyond-periodic and nonbeam-based nano-architected materials with simultaneous directional tunability, high stiffness, and unsurpassed recoverability with marginal deterioration

Evaluation of cellular glasses for solar mirror panel applications

An analytic technique was developed to compare the structural and environmental performance of various materials considered for backing of second surface glass solar mirrors. Cellular glass was determined to be a prime candidate due to its low cost, high stiffness-to-weight ratio, thermal expansion match to mirror glass, evident minimal environmental impact and chemical and dimensional stability under conditions of use. The current state of the art and anticipated developments in cellular glass technology are discussed; material properties are correlated to design requirements. A mathematical model is presented which suggests a design approach which allows minimization of life cost; and, a mechanical and environmental testing program is outlined, designed to provide a material property basis for development of cellular glass hardware, together with methodology for collecting lifetime predictive data. Preliminary material property data from measurements are given. Microstructure of several cellular materials is shown, and sensitivity of cellular glass to freeze-thaw degradation and to slow crack growth is discussed. The effect of surface coating is addressed

The mechanical response of cellular materials with spinodal topologies

The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies are investigated: "solid models," where one of the two phases is modeled as a solid material and the remaining volume is void space; and "shell models," where the interface between the two phases is assumed to be a solid shell, with the rest of the volume modeled as void space. In both cases, a wide range of relative densities and spinodal characteristic feature sizes are investigated. The topology and morphology of all the numerically generated models are carefully characterized to extract key geometrical features and ensure that the distribution of curvatures and the aging law are consistent with the physics of spinodal decomposition. Finite element meshes are generated for each model, and the uniaxial compressive stiffness and strength are extracted. We show that while solid spinodal models in the density range of 30-70% are relatively inefficient (i.e., their strength and stiffness exhibit a high-power scaling with relative density), shell spinodal models in the density range of 0.01-1% are exceptionally stiff and strong. Spinodal shell materials are also shown to be remarkably imperfection insensitive. These findings are verified experimentally by in-situ uniaxial compression of polymeric samples printed at the microscale by Direct Laser Writing (DLW). At low relative densities, the strength and stiffness of shell spinodal models outperform those of most lattice materials and approach theoretical bounds for isotropic cellular materials. Most importantly, these materials can be produced by self-assembly techniques over a range of length scales, providing unique scalability

Stochastic Simulation of Mudcrack Damage Formation in an Environmental Barrier Coating

The FEAMAC/CARES program, which integrates finite element analysis (FEA) with the MAC/GMC (Micromechanics Analysis Code with Generalized Method of Cells) and the CARES/Life (Ceramics Analysis and Reliability Evaluation of Structures / Life Prediction) programs, was used to simulate the formation of mudcracks during the cooling of a multilayered environmental barrier coating (EBC) deposited on a silicon carbide substrate. FEAMAC/CARES combines the MAC/GMC multiscale micromechanics analysis capability (primarily developed for composite materials) with the CARES/Life probabilistic multiaxial failure criteria (developed for brittle ceramic materials) and Abaqus (Dassault Systmes) FEA. In this report, elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio elements enabled the formation of crack boundaries, leading to development of mudcrack-patterned damage. Finite element models of a disk-shaped three-dimensional specimen and a twodimensional model of a through-the-thickness cross section subjected to progressive cooling from 1,300 C to an ambient temperature of 23 C were made. Mudcrack damage in the coating resulted from the buildup of residual tensile stresses between the individual material constituents because of thermal expansion mismatches between coating layers and the substrate. A two-parameter Weibull distribution characterized the coating layer stochastic strength response and allowed the effect of the Weibull modulus on the formation of damage and crack segmentation lengths to be studied. The spontaneous initiation of cracking and crack coalescence resulted in progressively smaller mudcrack cells as cooling progressed, consistent with a fractal-behaved fracture pattern. Other failure modes such as delamination, and possibly spallation, could also be reproduced. The physical basis assumed and the heuristic approach employed, which involves a simple stochastic cellular automaton methodology to approximate the crack growth process, are described. The results ultimately show that a selforganizing mudcrack formation can derive from a Weibull distribution that is used to describe the stochastic strength response of the bulk brittle ceramic material layers of an EBC

National Educators' Workshop: Update 1991. Standard Experiments in Engineering Materials Science and Technology

Given here is a collection of experiments presented and demonstrated at the National Educators' Workshop: Update 91, held at the Oak Ridge National Laboratory on November 12-14, 1991. The experiments related to the nature and properties of engineering materials and provided information to assist in teaching about materials in the education community

Optimal Reliability for Components under Thermomechanical Cyclic Loading

We consider the existence of optimal shapes in the context of the thermomechanical system of partial differential equations (PDE) using the recent approach based on elliptic regularity theory. We give an extended and improved definition of the set of admissible shapes based on a class of sufficiently differentiable deformation maps applied to a baseline shape. The obtained set of admissible shapes again allows one to prove a uniform Schauder estimate for the elasticity PDE. In order to deal with thermal stress, a related uniform Schauder estimate is also given for the heat equation. Special emphasis is put on Robin boundary conditions, which are motivated from convective heat transfer. It is shown that these thermal Schauder estimates can serve as an input to the Schauder estimates for the elasticity equation. This is needed to prove the compactness of the (suitably extended) solutions of the entire PDE system in some state space that carries a c2-H\"older topology for the temperature field and a C3-H\"older topology for the displacement. From this one obtains he property of graph compactness, which is the essential tool in an proof of the existence of optimal shapes. Due to the topologies employed, the method works for objective functionals that depend on the displacement and its derivatives up to third order and on the temperature field and its derivatives up to second order. This general result in shape optimization is then applied to the problem of optimal reliability, i.e. the problem of finding shapes that have minimal failure probability under cyclic thermomechanical loading.Comment: 32 pages 1 figur

Ceramic applications in turbine engines

The design and testing of gas turbine engines employing ceramic components is discussed. Thermal shock and vibration test results as well as spin tests of various engine components are discussed

GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks

This paper describes the project GivEn that develops a novel multicriteria optimization process for gas turbine blades and vanes using modern "adjoint" shape optimization algorithms. Given the many start and shut-down processes of gas power plants in volatile energy grids, besides optimizing gas turbine geometries for efficiency, the durability understood as minimization of the probability of failure is a design objective of increasing importance. We also describe the underlying coupling structure of the multiphysical simulations and use modern, gradient based multicriteria optimization procedures to enhance the exploration of Pareto-optimal solutions