This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Unperturbed dimensions of stereoregular polymers.- Reinforcement of rubber by carbon black.- Transformations of phenolic antioxidants and the role of their products in the long-term properties of polyolefins.

Properties of polymers

Metallographic Methods for Revealing the Multiphase Microstructure of TRIP-Assisted Steels - some applications for steels

On strain hardening mechanism in gradient nanostructures

Dislocation mechanism based size-dependent crystal plasticity modeling and simulation of gradient nano-grained copper

Among generations of advanced high-strength steel alloys, dual-phase steels exhibit a unique combination of strength and formability making them excellent candidates for use in the automotive industry. In this study, we seek to establish a relation between mechanical properties and microstructure of DP980. Electron backscatter diffraction (EBSD)and nanoindentation are used to identify and characterize martensite and ferrite phases. Spatial distributions of martensite and ferrite phases of subjected to various annealing treatments are found using a 2-point correlation function. Micro- and macro-mechanical properties are measured with nanoindentation, Vickers hardness and tensile tests and the results are used to determine the relation between martensite and ferrite phases and the strength of the metal. During the annealing/recovery process, the strength of the martensite phase decreases, the dislocation structure relaxes in the phase boundary region of the ferrite, and the martensite alignment along the rolling direction decreases resulting in the observed metal strength reduction. It is also shown that the higher the annealing temperature, the more homogeneous and equiaxed the distribution of martensite.

Morphology and distribution of martensite in dual phase (DP980) steel and its relation to the multiscale mechanical behavior

Tempering treatment is conducted on a commercial dual phase (DP) 980 steel at 250 °C and 400 °C for 60 min each. Ferrite and martensite grains are distinguished using electron backscatter diffraction (EBSD) and scanning probe microscopy (SPM), and the martensite volume fractions (MVF) are determined based on the image quality (IQ) map. Indentation tests combined with a newly developed inverse method are used to obtain the individual phase flow properties in each sample. The results show that, i) tempering significantly reduces martensite yield strength, while it slightly reduces the ferrite yield strength; ii) tempering temperature has a more significant influence on the work hardening exponent of ferrite than that of martensite. As a validation, a simple rule-of-mixtures is used to verify the above-predicted individual phase flow stresses with the experimentally obtained overall true stress vs. true strain curves.

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Annie Ruimi

Papers

Morphology and distribution of martensite in dual phase (DP980) steel and its relation to the multiscale mechanical behavior

Quantifying the effects of tempering on individual phase properties of DP980 steel with nanoindentation

A dislocation-based model for deformation and size effect in multi-phase steels

Stress/strain gradient plasticity model for size effects in heterogeneous nano-microstructures

Nonlinear viscoelastic analysis of orthotropic beams using a general third-order theory