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Mechanical Properties of Metals and Alloys
Published in Yip-Wah Chung, Monica Kapoor, Introduction to Materials Science and Engineering, 2022
There are several common mechanisms of creep. Figure 4.23a illustrates the mechanism of Coble creep. When stress is applied as shown, atoms at grain boundaries oriented approximately parallel to the stress axis are under compression due to the Poisson contraction, while atoms at grain boundaries oriented perpendicular to the stress axis are under tension. To reduce the elastic strain energy associated with compression and tension in various grain boundaries, atoms migrate from grain boundaries under compression to grain boundaries under tension. The Coble creep rate is inversely proportional to d3, where d is the grain size. Figure 4.23b illustrates the mechanism of Nabarro-Herring creep. The situation is analogous to Coble creep, except that atomic diffusion is through the bulk. The Nabarro-Herring creep rate is inversely proportional to d2. Since the activation energy for grain boundary diffusion is smaller than that for bulk diffusion, Coble creep is dominant at lower temperatures, while Nabarro-Herring creep is more important at higher temperatures.
Creep and Fatigue of Metals
Published in Yichun Zhou, Li Yang, Yongli Huang, Micro- and MacroMechanical Properties of Materials, 2013
Yichun Zhou, Li Yang, Yongli Huang
where Dgb is the diffusion coefficient at the grain boundaries. We should note that in Nabarro-Herring creep equation, the creep rate is proportional to Dsd/d2; but in the Coble creep equation, the creep rate is proportional to Dgb/d3. Grain boundary sliding mainly includes intergranular shear slip. Although grain boundary sliding has no great influence on the steady-state creep rate, it plays an important role in intergranular cracking. In creep mechanisms, grain boundary sliding plays a supporting role in maintaining the continuity of grains [19].
Temperature Dependence of Microelectronic Package Failure Mechanisms
Published in Pradeep Lall, Michael G. Pecht, Edward B. Hakim, Influence of Tempemture on Microelectronics and System Reliability, 2020
Pradeep Lall, Michael G. Pecht, Edward B. Hakim
where σmet is the stress in the metallization, E is the elastic modulus, Vat,vl is the atomic volume, Bgm,fct is the geometric factor (approximately equal to 10) for grain matrix diffusion, dave,met is the average grain size in the metallization, hmet is the metallization thickness, fdiff,fct is the correlation factor for diffusion, and Dl,met is the lattice diffusivity of the metallization. The stress relaxation rate by grain-boundary migration (Coble creep) is dσmetdt=−Bgm,fctVat,vlEDb,metδdave,meth2metKBTσmet
An investigation on creep deformation and mechanical properties of a polycrystalline Fe-based alloy: a molecular dynamics study
Published in Mechanics of Advanced Materials and Structures, 2023
Abeer Abdullah Al Anazi, Ghaidaa Raheem Lateef Al-Awsi, Suphatchakorn Limhengha, Andrés Alexis Ramírez-Coronel, Shafik- Shaker Shafik, Abbas F. Almulla
The microstructural evaluation of samples was carried out to justify the outcomes given in the creep strain plots. Figure 5a demonstrates the initial atomic coordination number distribution for the FeCr15Al4 sample with 8.7 nm grain size crept at 900 K and 1200 K with applied stress of 0.5 GPa. The results indicate that the atomic coordination number in the grain boundaries is averagely lower than the grain interiors, implying that the atomic activity becomes sharper in the grain boundaries under the same loading value. In other words, the boundaries are the potential sites for the atomic motion and the defect nucleation. The initial atomic shear strain at the same condition is given in Figure 5b. It can be seen that the grain boundaries undergo the maximum shear deformation under the creep deformation. Hence, it is concluded that the creep mechanism begins at the grain boundaries through the Coble creep mechanism, where the applied stress is low, i.e. 0.5 GPa. However, one should note that the increase of applied stress changes the Coble creep mechanism to other ones. Using mean square displacement (MSD), it is possible to evaluate the average movement of a group of atoms as a function of time [46]: