Low-cycle, lap-shear fatigue behavior of Sn-based, Pb-free solder alloys, Sn-3.5Ag, Sn-3.5Ag-Cu, Sn-3.5Ag-Bi, and Sn-0.7Cu, were studied at room temperature using specimens with printed circuit board (PCB)/solder/PCB structure under total displacement of ±10 µm, 12 µm, 15 µm, and 20 µm. The fatigue lives of various solder joint materials, defined as 50% load drop, were correlated with the fracture paths and analyzed using the Coffin-Manson relation, Morrow's plastic-energy dissipation model, and Solomon's load-drop parameter. The Sn-3.5Ag, Sn-0.7Cu eutectics, and Sn-3.5Ag-Cu ternary alloys showed the same level of fatigue resistance, while Bi-containing alloys showed substantially worse fatigue properties. Cross-sectional fractography revealed cracks initiated at the solder wedge near the solder mask and subsequently propagated into the solder matrix in the former group of alloys, in contrast with the crack propagation along the solder/under bump metallurgy (UBM) interfaces in the Sn-3.5Ag-Bi alloys. Inferior fatigue resistance of Bi-containing alloys was ascribed to high matrix hardness, high stiffness, possible Bi segregation to the interface, and high residual stress in the interfacial area.
The practical applications of studies related to constant amplitude mode I loading are somewhat limited, since mode I crack growth is often influenced by mode I1 (sliding mode) or mode I11 (tearing mode) in industrial situations. For these cases, criteria, rules, and laws have to be worked out and verified by experiments. However, it is very difficult to evaluate mixed-mode fatigue cracking due to crack surface interference, crack closure, crack branching, etc. This paper, which defines the length of a branched crack as an effective slant crack with a length equal to the distance between the two crack tips, explains the influences of crack surface interference by introducing concepts of adhesive wear and scrutinizes some related researches on mixed-mode crack growth behaviour. Additionally an effective stress intensity factor range is described which considers crack closure and crack surface interference and is verified with crack growth tests under mode I fatigue loading and cyclic mode I with a superimposed static mode I1 loading. NOMENCLATURE 2a,,, 2a, = effective crack length and precrack length AK,, K,, = mode I SIF range and static mode I1 SIF, respectively A,,, = contact area under cyclic mode I with superimposed static mode I1 loading AK,,, AKeff = equivalent and effective stress intensity factor ranges, respectively K,,,,, Kll,lock = crack opening and crack locking stress intensity factors, respectively U = mode I crack opening ratio oad = adhesion strength
We describe direct observation of a geometrical phase in a noncyclic case as the rotation of the plane of polarization of a linearly polarized beam of light. The beam travels down uniformly wound half-turn single-mode optical fibers with various pitch angles.
The interplay of charge, spin, orbital and lattice degrees of freedom has recently received great interest due to its potential to improve the magnetocaloric effect (MCE) for the purpose of magnetic cooling applications. Here we propose a new mechanism for a giant inverse MCE in rare-earth tetraborides, especially for Ho1-xDyxB4 (x = 0.0, 0.5, and 1.0). For x = 0.0, 0.5, and 1.0, the maximum entropy changes of the giant inverse MCE are found to be 22.7 J/kg⋅K, 19.6 J/kg⋅K, and 19.0 J/kg⋅K with critical fields of ≈ 25 kOe, 40 kOe, and 50 kOe, respectively. It is remarkable that such a giant MCE is realized, even when applying a low magnetic field, which enables a field-tuned entropy change and brings about a significant advantage for several applications. For all compounds, we have systematically studied how the entropy changes as a function of the field and temperature and investigated their correlation with consecutive double transitions, i.e., the magnetic dipolar order at T = TN and the quadrupolar order at T = TQ (TQ < TN). We found that the maximum entropy change occurs at T = TQ and the critical field associated with the meta-magnetic transition, which is in good agreement with the experimental data.Thus, we elucidate that this unique behaviour is attributed to the strong coupling between magnetic dipoles and quadrupoles in the presence of strong spin-orbit coupling and geometric frustration. Our work offers new insights into both the academic interest of multipolar degrees of freedom in magnetic materials and the discovery of giant MCE with various applications for magnetic cooling systems. I. INTRODUCTIONThe magnetocaloric effect (MCE) is a thermodynamic property, in which heating or cooling occurs in magnetic materials when applying a magnetic field. For the conventional MCE, the cooling mechanism is based on the adiabatic demagnetization process. In contrast, the inverse situation can also occur, where the system is cooled via adiabatic magnetization. This is often termed as the inverse MCE.Refrigeration based on the conventional or inverse MCE is a solid-state cooling application, which is energy efficient, noise-free, and environmentally friendly. Thus, a large MCE is attractive as an alternative to conventional vapor refrigeration [1]. In particular, a large MCE in a low-temperature region is being actively studied for the purpose of gas liquefaction (hydrogen and helium), space technology, and diverse scientific research technologies. Although various methods have been devised for the development of novel solid-state cooling, the design and discovery of new materials that exhibit a large MCE are still important.Intuitively, a large MCE is expected in materials with a first order magnetic phase transition accompanied with a spontaneous magnetization jump. However, this gives rise to heat loss during the refrigeration cycle due to the hysteresis, irreversibility and the narrow working temperature range. As another promising candidate, a system with geometrical frustration may contain an enormous groun...
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