Analysis of Whisker-Toughened Ceramic Components -- A Design Engineer\u27s Viewpoint

The use of ceramics components in gas turbines, cutting tools, and heat exchangers has been limited by the relatively low flaw tolerance of monolithic ceramics. The development of whisker-toughened ceramic composites offers the potential for considerable improvement in fracture toughness as well as strength. However, the variability of strength is still too high for the application of deterministic design approaches. This report reviews several phenomenological reliability theories proposed for this material system, and reports on the development of a public domain computer algorithm. This algorithm, when coupled with a general-purpose finite element program, predicts the fast fracture reliability of a structural component under multiaxial loading conditions

Review: Inelastic Constitutive Modeling: Polycrystalline Materials

This article provides a literature review that details the development of inelastic constitutive modeling as it relates to polycrystalline materials. This review distinguishes between inelastic constitutive models that account for nonlinear behavior at the microstructural level, time-independent classic plasticity models, and time-dependent unified models. Particular emphasis is placed on understanding the underlying theoretical framework for unified viscoplasticity models where creep and classical plasticity behavior are considered the result of applied boundary conditions instead of separable rates representing distinct physical mechanisms. This article establishes a clear understanding of the advantages of the unified approach to improve material modeling. This review also discusses recent topics in constitutive modeling that offer new techniques that bridge the gap between the microstructure and the continuum

Music as Math Waves: Exploring Trigonometry Through Sound

Students studying transformations of trigonometric functions may learn formulas associated with period and frequency without developing an understanding of the concepts themselves. In this article, the authors present a task that uses arts integration in the form of sound waves to help students explore the relationship between period and frequency. Students are guided through a task of generating a ringtone for a smartphone that blends music, maths, and technology. Links to worksheets and a sample ringtone are provided to facilitate a teacher\u27s implementation of the task; suggestions and advice are included. Using the arts to teach traditional STEM topics, an initiative known as STEAM offers promising opportunities for students to apply creative elements to solve technical problems. Although the topic in this article is suitable for precalculus students, STEAM-based instruction is applicable across multiple grade levels