Thermomechanical cycle

Microstructures near the TMAZ were also examined. A region near the shr zone/TMAZ interface, called the near-stir zone by the authors, exhibited a distinchve microstructural feature in welds made on both starhng microstructures. Small, equiaxed grains of a, approximately 1 pm in size, were reported. Again, their similar structure appeared to indicate that formation of the local microstructure was dependent on the thermomechanical cycle and not on the starhng microstructure. 

Microstructural Evolution in the Stir Zone. Important aspects of the microstructure of the stir zone include the grain size as well as the volume fraction and distribution of phases. Microstructural evolution in the stir zone is dictated by the thermomechanical cycle imposed during FSW. More specifically, the microstruc-ture develops in accord with the local strain/ strain-rate/temperature path. Little is known... 

For example, because of their close densities, polypropylene and high-density polyethylene can be recovered in the same fraction. However, these polymers often present antagonistic behaviors dtuing the thermomechanic cycles requited for their implementation. These cycles lead to breakages in polypropylene chains and... 

Extrusion with melt filtration can then be used as the ultimate way of purifying the material. Since each extrusion step exposes the material to thermomechanical cycles likely to further degrade the material, the number of extrusion steps should be kept to a minimum. For the final extrusion compounding, additives can be used to maintain or improve selected material properties, depending upon the composition and degree of degradation of the material. 

In the following sections, the thermomechanical cycles of the thermosetting polystyrene SMP and its syntactic foam wUl be discussed, which are programmed using the classical... 

Figure 3.15 Four-step thermomechanical cycles (step 1 high temperature loading—> step 2 cooling step 3 room temperature unloading step 4 free shape recovery) for the pure SMP and syntactic foam programmed under a stress-controlled condition with a pre-stress of 263 kPa at 79 °C followed by free recovery. Source [41] Reproduced with permission from Elsevier...

Since the programming is the same for the free recovery specimens and fully constrained specimens, the focus will be on step 4 of the thermomechanical cycles. The stress-temperature behavior under a fully constrained recovery condition is shown in Figure 3.19 for the two programming stresses (47 kPa and 263 kPa). The recovery stress-time behavior of the foam programmed at 47kPa pre-stress is also highlighted by the inset in Figure 3.19. The recovery stress comes from two parts thermal expansion stress and entropically stored stress or back stress. Since this is a 1-D fully constrained recovery, the thermal stress can be calculated as... 

In order to evaluate the effect of the pre-stress level on the thermomechanical behavior, four compressive pre-stress levels in the vertical direction were used. They were 168.3 kPa, 207.7 kPa, 247.6 kPa, and 300.7 kPa, respectively. Because of the symmetry of the truss fixture (the same length for each member) and the specimen, the tensile pre-stress in the horizontal direction was roughly the same as the corresponding vertical compressive pre-stress. In addition, some specimens with 300.7 kPa pre-stress experienced 10 thermomechanical cycles to evaluate the functional stability of the foam. 

Additionally, as shown in Figure 3.24 (c), the horizontal and vertical strains after 10 thermomechanical cycles are close to the strain evolution of the first thermomechanical cycle. The shape fixity ratio is 98.5% and the shape recovery ratio is 88.3%. It is noted that both the shape fixity ratio and shape recovery ratio are slightly lower than those in the first thermomechanical cycle (99.2% and 91.6%, respectively) under the same pre-stress level (300.7 kPa). This is because more unrecoverable damages have aeeumulated during eaeh... 

In order to understand the thermomechanical cycle of the syntactic foam under different test conditions better, the test results are presented in both 3-D and 2-D format. Typical 2-D axial stress-time and temperature-time curves for the foam confined by the nylon liner, programmed at 79 °C, and under 60% pre-strain level, and fully confined shape recovery are shown in Figure 3.29. Typical 3-D axial stress-axial strain-ternperamre thermomechanical cycles for the syntactic foam at a programming ternperamre of 71 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.30. Typical 3-D axial stress-axial strain-time behaviors at a programming temperature of 79 °C, pre-strain level of 30%, and fully confined shape recovery are shown in Figure 3.31. 

Figure 3.30 Axial stress temperature-axial strain thermomechanical cycle at a programming temperature of 71 °C and pre-strain level of 30%. The subplot shows the three-step thermal mechanical cycle of a specimen confined by a steel liner (step 1 (pre-stressing) and step 2 (cooUng and unloading) represent programming and step 3 represents stress recovery). Source [42] Reproduced with permission from Elsevier...

Figure 3.34 Strain-time response during the entire thermomechanical cycle for specimens programmed with (a) 30% and (b) 10% pre-strain (the four steps for the specimen with 120 min of stress relaxation time during programming are also shown). Source [51] Reproduced with permission from Elsevier...

The extremely nonlinear behaviors for the entire thermomechanical cycle, including a three-step glassy temperature programming process and one-step heating recovery in both the stress-strain-time view and stress-strain-temperature view, are shown in Figure 3.38 (a) and (b). 

Figure 3.38 Thermomechanical cycle in terms of (a) stress-strain-time and (b) stiess-strain-temperature responses for different stress relaxation times with a pre-strain level of 30% and 20%. Source [45] Reproduced with permission from ASME...

Figure 3.39 Schematic of the entire thermomechanical cycle (two-stage programming and one-step free shape recovery). Source [59] Reproduced with permission from the American Society of Civil Engineers...

Figure 3.43 Thermomechanical cycle in the tension direction for a specimen of T25C25 (step 1 —> pretension to 25% strain at temperatures above Tg, step 2 —> cooling down to room temperature while holding the pre-strain constant, step 3 —> unloading, which completes the first stage of programming. The Poisson effect is due to the second programming in the transverse direction by compression. Step 4 —> free shape recovery). Source [59] Reproduced with permission from the American Society of Civil Engineers...

Because Figure 3.44 is a stress-strain-temperature plot, step 2 (30 minutes of holding or relaxation) during cold-compression programming cannot be visualized. To have a better understanding of the stress-strain evolution with time, a typical thermomechanical cycle in terms of stress-strain-time for the four groups of specimens is shown in Figure 3.45 (a) to (d), respectively. In order to have both tension and compression direction in the same quadrant, the compression stress and compression strain are also treated as positive. 

It is noted that while the majority of constitutive modeling focuses on thermally induced dual-shape memory behavior, triple-shape and multishape SMPs have been developed recently and they call for constimtive modeling [1]. In addition, the effect of programming temperature and strain rate on the constimtive behavior also needs modeling [2]. Furthermore, some recent smdies have found that while the shape recovery ratio can be 100%, other mechanical properties such as recovery stress or modulus become smaller and smaller as the thermomechanical cycles increase, which has been explained by the shape memory effect in the microscopic scale [24]. Obviously, these new findings also call for constitutive modeling. 

The material is assumed to be without any damage during the thermomechanical cycle. This assumption is acceptable for small pre-strain and a low number of thermomechanical cycles. For large pre-strain or cyclic loading, damage will occur. 

As discussed in Chapter 3, pseudo-plastic deformation is the key for cold-programmed thermosetting SMP to display shape memory functionality. Therefore, the deformation includes both plastic/viscoplastic and elastic/viscoelastic deformation. The thermomechanical cycle also includes thermal deformation. Based on Figure 4.5, the deformation gradient F can be multiplicatively decomposed into thermal Fj and mechanical Fm, which are further decomposed into plastic F and elastic F, as follows ... 

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