Mechanisms of fatigue and relation to loading mode

The origin of fatigue is the initiation of cracks and their eventual propagation.^{Reference Meyers and Chawla12,Reference Ashby, Shercliff and Cebon13} Compared to crack initiation, crack propagation can take place for a long period of time before eventual failure.^{Reference Meyers and Chawla12} Slowing crack propagation is essential for maintaining the material’s integrity over many cycles. Figure 1a illustrates the crack propagation after a large number of repetitive tensile stress cycles. The already initiated crack has a stress concentration around the tip of the crack. The stresses at the exact tip of a crack exhibit extremely large values and in theory approach infinity.^{Reference Meyers and Chawla12} This is considerably higher than the yield strength of the material. A plastic zone arises in the vicinity of the crack tip with the ability to deform substantially, and the crack tip increases the radius of curvature in order to relax the stress concentration. Under tensile stress, new surfaces can be stretched out of the plastically deformed region with a blunt crack tip.^{Reference Ashby, Shercliff and Cebon13} Upon removing the tensile stress, the newly generated surfaces require additional space to fold in, and thus they advance along the direction perpendicular to the axis of tensile stress. The advancing process repeats in the subsequent loading–unloading cycles.

Figure 1.

Mechanisms of crack propagation. Schematic of crack advancing under (a) tensile and (b) compressive cycles with stress amplitude Δσ. Adapted with permission from Reference Ashby, Shercliff and CebonReference 13. © 2007 Elsevier.

On the other hand, compressive loading (Figure 1b) can delay the advancing of cracks by curtailing the driving force for generation of new surfaces. The extension of crack length can be slowed down in subsequent cycles. Furthermore, creating a thin, compressive layer on a material surface can improve fatigue strength up to 60%^{Reference Zhang and Lindemann14} and extend fatigue life nearly three times.^{Reference Luong and Hill15} Therefore, compressive stress is an effective route to prolong the fatigue life of materials.

Mechanism of tension–compression asymmetry

Stress-induced martensitic transformation can be achieved through compressive or tensile stress. Figure 2a^{Reference Gall and Sehitoglu16} shows the parameters in a single-crystal transformation from austenite (labeled “parent phase”) to martensite. On the habit plane (an unrotated and undistorted plane), the maximum shear stress resolved from the external load can align positively or negatively with respect to the prescribed transformation direction.^{Reference Gall, Sehitoglu, Chumlyakov and Kireeva17}

Figure 2.

Tension–compression asymmetry in shape-memory alloys. (a) Schematic showing transformation parameters of favorably oriented martensite in stress-induced martensitic transformation. Reproduced with permission from Reference Reference Gall and Sehitoglu16. © 1999 Elsevier. (b) Superelastic stress–strain curves obtained for polycrystalline Ni-Ti when applying tensile and compressive stress within the austenite state.^{Reference Cui, Wu, Muehlbauer, Hwang, Radermacher, Fackler, Wuttig and Takeuchi5}

The shear component of the transformation direction can dominate over the normal component when there is only a slight volume change in single-crystal Ni-Ti.^{Reference Buchheit and Wert18} The crystallographic constraints permit the martensitic transformation to initiate if the maximum resolved shear stress is positive toward the prescribed transformation shear direction.^{Reference Gall, Sehitoglu, Chumlyakov and Kireeva17,Reference Gall, Sehitoglu, Anderson, Karaman, Chumlyakov and Kireeva19} As a result, the martensitic transformation exhibits a unidirectional nature at a crystallographic orientation for a given stress state, and has strong tension–compression asymmetry for a single crystal.^{Reference Gall, Sehitoglu, Chumlyakov and Kireeva17}

When crystals are aggregated into textured polycrystals as commonly encountered in drawn wires or bars,^{Reference Gall and Sehitoglu16,Reference Liu, Xie, Van Humbeeck and Delaey20} the tension–compression asymmetry due to the strong texturing is expected to be similar to the asymmetry resulting from crystallographic orientation dependence in single crystals. The compressive superelasticity of polycrystalline Ni-Ti wires in Figure 2b shows higher critical transformation stresses, greater transformation stress–strain slopes, and smaller transformation strains than those in tension. The difference is attributed to the dependence of the maximum resolved shear stress on crystallographic orientation and the stress direction.^{Reference Gall and Sehitoglu16,Reference Gall, Sehitoglu, Chumlyakov and Kireeva17} For example, the [111] orientation in polycrystalline Ni-Ti has the maximum value of the orientation tensor (or Schmid factor^{Reference Gall, Sehitoglu, Anderson, Karaman, Chumlyakov and Kireeva19}) of 0.39 for tension versus 0.27 for compression, while the [100] direction has values of 0.21 for tension versus 0.4 for compression. The larger the maximum value of the orientation tensor, the higher the effective conversion and thus the smaller the required applied stress.^{Reference Gall and Sehitoglu16} Since the entire austenite domain is converted into martensite^{Reference Sehitoglu, Wu and Ertekin21} and the cooling potential dictated by the latent heat (on the order of 10 J g⁻¹ for Ni-Ti alloys^{Reference Cui, Wu, Muehlbauer, Hwang, Radermacher, Fackler, Wuttig and Takeuchi5,Reference Hou, Simsek, Stasak, Hasan, Qian, Ott, Cui and Takeuchi7} ) is fully unleashed, compression can deliver the same cooling capacity as tension and extend the fatigue life despite the necessary high transformation stress and the large transformation stress–strain slope.

Compression-based design of elastocaloric materials

The understanding of the benefits of compression motivates the utilization in designing cooling devices with SMAs as the solid refrigerant.^{Reference Qian, Alabdulkarem, Ling, Muehlbauer, Hwang, Radermacher and Takeuchi9,Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi22} SMA tubes have been chosen as refrigerant components to allow the cooling medium (typically water) to flow through. Figure 3a^{Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi22} shows one example configuration of the SMA tubes in a bundle. To prevent buckling (a common failure mode under compression), the tubes are grouped into a hexagonal cross-sectional shape preserving symmetrically distributed stress, and a rigid holder is employed for lateral mechanical support (Figure 3b^{Reference Qian23}). After cooling is generated in the bundle of SMA tubes, heat-transfer fluid carries the heat. Additional components to compress tubes with fluid flowing are illustrated in Figure 3c. Figure 3d shows the completed Ni-Ti tube bundles supported by linear bearings to ensure axially compressive loading. A cooling capacity of 100 W can be generated in one bundle with twenty 250-mm-long Ni-Ti tubes with outer diameter of 4.7 mm, inner diameter of 3.8 mm, and latent heat of 12 J g⁻¹ operated at 0.1 Hz.^{Reference Qian, Alabdulkarem, Ling, Muehlbauer, Hwang, Radermacher and Takeuchi9} The cooling power scales proportionally with the total material mass and with the operation frequency.^{Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi22}

Figure 3.

Compression-based design of Ni-Ti materials for elastocaloric systems. (a) Geometry of Ni-Ti tubes and a stack of multiple tubes and (b) assembly of a bundle of Ni-Ti tubes into a holder to prevent buckling.^{Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi22,Reference Qian23} (c) Schematic of Ni-Ti bundles and loading heads. The heat exchange fluid is made to flow through the tubes for heat transfer.^{Reference Qian, Alabdulkarem, Ling, Muehlbauer, Hwang, Radermacher and Takeuchi9} (d) Picture of final assembly of the loading heads and Ni-Ti bundles in a linearly aligned configuration for an elastocaloric system.^{Reference Qian, Geng, Wang, Muehlbauer, Ling, Hwang, Radermacher and Takeuchi22}

Designing compression-based elastocaloric systems

Full recovery of strain in SMAs upon unloading is shown in Figure 4a. A mechanical system can be devised so that unloading force in one material can be harnessed as a part of the driving stress for another material. The configuration in Figure 4b is realized by axially aligning two SMA tube bundles. Each bundle is initially in a compressed state with half of the maximum reversible strain. When bundle 1 is compressed by means of an input actuation mechanism applied via the movable frame, the unloading force from half strain to zero strain of bundle 2 assists in driving the movable frame so that the required input work for bundle 1 is reduced. This process is called work recovery. When bundle 1 is loaded to reject heat, bundle 2 is unloaded to absorb heat and deliver cooling, which repeats in a reciprocating manner. Figure 4c depicts experimental stress–strain curves for the two SMA bundles during one cycle of operation of the prototype. When strain is increased in bundle 1, strain is decreased in bundle 2 in a synchronized manner. A process of heat recovery can also be implemented to improve the heat-exchange efficiency of the entire system.^{Reference Qian, Ling, Muehlbauer, Hwang and Radermacher24} Optimization of the system configuration with work recovery and heat recovery enhanced the coefficient of performance by 30% to 4.1 compared to SMAs produced without work and heat recovery processes.^{Reference Qian, Alabdulkarem, Ling, Muehlbauer, Hwang, Radermacher and Takeuchi9}

Figure 4.

Concept of work recovery, and the implemented work-recovery design in an elastocaloric system. (a) Schematic of the typical superelastic behavior in shape-memory alloys (SMAs).^{Reference Hou, Simsek, Stasak, Hasan, Qian, Ott, Cui and Takeuchi7} (b) Concept of work recovery achieved by linearly stacking two SMA tube bundles.^{Reference Qian, Alabdulkarem, Ling, Muehlbauer, Hwang, Radermacher and Takeuchi9} The double arrows above the movable frame signify the axis of movement. (c) Compressive stress–strain curves of the two SMA tube bundles in a prototype system to incorporate work recovery. The bottom x-axis has increasing values and the top x-axis has decreasing values.

Compressive stability of elastocaloric cooling

Extending fatigue life of materials may also be achieved by implementing mechanically robust SMA materials and by applying smaller strains.^{Reference Ashby, Shercliff and Cebon13,Reference Pelton25} The endurance limit—a stress amplitude below which failure is avoided—has a positive correlation with the ultimate strength.^{Reference Ashby, Shercliff and Cebon13} Figure 5^{Reference Wu, Ertekin and Sehitoglu26–Reference Yang, Cong, Sun, Nie and Wang31} shows a summary of elastocaloric materials and their performance indicating that high-strength materials such as Ni-Ti with transformation stress of ≈650 MPa (versus ≈150 MPa in Cu-Zn-Al) can produce stable elastocaloric cooling over 10,000 cycles under compression without degradation. High-strength materials can thus have long fatigue life and the potential for stable elastocaloric cooling. If one envisions a 10-year operation of a commercial elastocaloric cooling device such as an elastocaloric air conditioner, this would require about a million cycles of SMAs under 0.05 Hz operation, assuming usage for half a day for six months in a year. The fatigue requirement of SMAs would further become less stringent if there is lower frequency of device. Decreasing applied strain can lead to extended fatigue life,^{Reference Pelton25,Reference Robertson, Pelton and Ritchie32} and from Figure 5, a small amplitude of strain such as 1.0% in Fe–Pd (versus 6.0% in Cu-Zn-Al) appears to help maintain elastocaloric cooling cycles despite concomitantly reduced cooling ΔT. As previously discussed, cyclic tension can lead to fracturing in a relatively smaller number of cycles, as marked by the X for Ni–Ti in Figure 5.

Figure 5.

Evolution of elastocaloric cooling performance of different materials over cycles of operation. Absolute value of cooling ∆T versus cycles in different classes of shape-memory alloys. Unfilled symbols are for tensile mode, and solid symbols are for compressive mode. A crossmark indicates the cycle where failure took place, while no crossmark means there was no failure at the end of cycling. The test temperature, T _test, and the strain amplitude, Δε, of each material are displayed in the legend.^{Reference Bechtold, Chluba, De Miranda and Quandt6,Reference Wu, Ertekin and Sehitoglu26–Reference Yang, Cong, Sun, Nie and Wang31}

Concluding remarks

Compression-based elastocaloric cooling enables extended operation due to prolonged fatigue lifetime in SMAs compared to tension-based cooling. This is due to the unidirectional nature of stress-induced martensitic transformation and the tension–compression asymmetry in superelasticity inherent to SMAs. Employing mechanically strong alloys and applying low strains are also good strategies to facilitate long-term operation of elastocaloric cooling materials. Compression-based elastocaloric cooling has been successfully implemented in the development of elastocaloric prototype systems. Based on compression-based designs, exploration of high-capacity elastocaloric materials for extended cooling and optimization of systems with improved heat transfer can competitively advance elastocaloric cooling into the arena of practical cooling technologies.