Models for Phase Transition with Thermo-Mechanical Interaction

在这份提案中，我们要求资助一个涉及应用数学、计算机械工程和材料科学的基础研究项目。我们将在数学上和实验上开发和研究新的相场系统，模拟金属合金中的相变现象。作为一个参考问题，我们将研究含铅和无铅焊料中发生的相分离和粗化现象，这些焊料以微球的形式用作微电子元件中的电接头。这些过程，最终导致焊料的热机械性能的退化，并在其连接能力的降低，被加速的微观热机械应力的存在，加强材料内的微观形态的异质性演变。...

In this proposal we ask for funding of a fundamental research project involving applied mathematics, computational mechanical engineering, and materials science. We will develop and investigate both mathematically and experimentally new classes of phase-field systems modeling phase transition phenomena in metallic alloys. As a reference problem we will study the phase separation and coarsening phenomena occuring in lead-containing as well as in lead-free solders, which in form of tiny spheres are used as electric joints in microelectric components. These processes, which eventually result in the degradation of the thermo-mechanical properties of the solder and in a reduction of its joining capability, are accelerated by the presence of microscopic thermo-mechanical stresses which reinforce the heterogeneous evolution of the micro-morphology within the material. ...