Design of a Carburizing Treatment of Steel Base Gear in the Materials Science Course

Diffusion PDE Application to Carburizing Treatment of Steel Base Gear An introductory materials-science course is required in the mechanical engineering curriculum of many universities. This article describes an example effort to incorporate programming, diffusion transfer, heat treatment process and mechanical-property determination as an integral part of the materials-science course instruction. This effort was undertaken in order to give students additional experience in Fick’s 1st and 2nd laws and in-depth understanding of physics and mathematics involved in diffusion analysis. We chose to focus on Fick’s second law because its applications are not restricted to the materials-science field [1]. As a matter of fact, the same form of parabolic partial differential equation also finds applications in financial derivatives pressure, heat transfer, and soil mechanics consolidation [2,3]. For instance, the diffusion coefficients all share the units of m2/s [2]. From the perspective of materials science, diffusion refers to an observable net flux of atoms or other species [1,4,5]. It depends upon the concentration gradient and temperature. It is vital for the carburization process (Carbon diffusion into steel), determining the proper hardness values not only for surface hardness of gear teeth but also for carbon penetration into specified depths. Students will be required to write a MATLAB program with input parameters of diffusion couple to calculate the atomic flux on the basis of diffusivity and concentration gradient. They are able to predict heat furnace design temperature and time required to heat the metal using error function values and one-dimensional diffusion equation with the specified boundary conditions. This paper focuses on the application of diffusion to material science engineering and provides an example of how diffusion may be adopted in an integrated instruction of materials science instructions. Keywords: Materials Science, Diffusion, Carburizing, PDE Solutions, MATLAB Programmin

Application of Computational Tools to Spaghetti-Based Truss Bridge Design

Application of Computational Tools to Spaghetti-Based Truss Design Statics and Strength of Materials are two foundational courses for Mechanical/Civil Engineering. In order to assist students in better understanding and applying concepts to a meaningful design task, SolidWorks and theoretical calculation were used for a spaghetti-bridge design contest with the constraints of given maximum weight and allowable support-material weight. As the first step of this iterative designing process, both extrude feature and structural member were introduced to model planar bridge trusses. Then SolidWorks’ Statics module was used to run FEA analysis of the structural performance in efforts to optimize the load-carrying capacity of the structure. To make simulation possible, a universal material-response testing apparatus was used to measure the key mechanical properties of the bridge material, namely spaghetti bundles, and add it to SolidWorks’ material database. The building stage started upon completion of design refinement, and the project culminated with performance prediction (as to the weakest spots of the structure) and testing. The theoretical calculation went down two paths—A full truss analysis was performed based on the method of joints, along with more thorough FEA analysis through coding, before comparing the internal forces, displacements, etc., with the simulation results. Through the holistic design process, the course turned out more engaging and students gained experience of solving a typical real-life engineering problem involving trade-off between economy and quality

Modeling of Ductile Fracture at Engineering Scales: A Mechanism-Based Approach

This paper summarizes the work we conducted in recent years on modeling plastic response of metallic alloys and ductile fracture of engineering components, with the emphasis on the effect of the stress state. It is shown that the classical J2 plasticity theory cannot correctly describe the plasticity behavior of many materials. The experimental and numerical studies of a variety of structural alloys result in a general form of plasticity model for isotropic materials, where the yield function and the flow potential are expressed as functions of the first invariant of the stress tensor and the second and third invariants of the deviatoric stress tensor. Several mechanism-based models have been developed to capture the ductile fracture process of metallic alloys. Two of such models are described in this paper. The first one is a cumulative strain damage model where the damage parameter is dependent on the stress triaxiality and the Lode parameter. The second one is a modification to the Gurson-type porous plasticity models, where two damage parameters, representing void damage and shear damage respectively, are coupled into the yield function and flow potential. These models are shown to be able to predict fracture initiation and propagation in various specimens experiencing a wide range of stress states

Modeling the Tension-Compression Asymmetric Yield Behavior of -Treated Zircaloy-4

Zirconium alloys such as Zircaloy-4 are used in nuclear applications due to adequate strength, ductility and resistance to radiation damage. Recent modeling efforts have focused on improvements to the predicted elastic–plastic response, complicated by the strong strength-differential (S-D) effects in HCP materials. This study develops a pressure-insensitive, continuum plasticity model, dependent on the second and third invariants of the stress deviator (J2 and J3), with an internal variable related to the plastic strain to describe the tension–compression asymmetry of a β-treated Zircaloy-4. Plastic deformation drives isotropic and distortional hardening of the non-Mises yield surface. The proposed plasticity model has been calibrated and validated using measured results from an experimental test program. Results show that the proposed model captures the complex elastic–plastic response observed in measured load–displacement and torque–rotation curves over a range of triaxiality and Lode parameter values