Strain viscoplasticity, creep

The creep and recovery behaviour of an UHMWPE was studied in the region of small xmiaxial deformations by Zapas and Crissman [152]. These results are used to illustrate the capability of the Schapery model to represent the viscoelastic/viscoplastic behaviour of UHMWPE. Creep and recovery experiments were carried out on specimens under creep stresses in the range 1-8 MPa. In Figure 7.9 are plotted the creep compliances obtained, showing to be stress dependent above 1 MPa. Using the appropriate values for the model parameters, the strain under creep and creep-recovery loading conditions were very well captured as shown in Figure 7.10. 

As the shear stress reaches some value, xSchW(, the region of slow viscoplastic flow, known as Schwedov s region (Fig. IX-24, region II ), is observed in the system with almost undestroyed structure. In this region the shear strain is caused by fluctuational process of fracture and subsequent restoration of coagulation contacts. Due to the action of external pressures this process becomes directed in a certain way. Such mechanism of creep may be described analogously to the mechanisms of fluid flow, the description of which was developed by Ya.B. Frenkel and G. Eiring. 

The time dependent response of high-density polyethylene was represented by a one-dimensional integral including recoverable viscoelastic strain and irrecoverable viscoplastic strain. The response was represented by an effective time concept. Creep, recovery, two-step creep, and constant stress loading and unloading rates. The concept can also model preconditioning of semicrystalline polymers. 

One of the challenges with both Pb/Sn and lead-free solders is that they nndergo viscoplastic deformation (creep) as a function of time, temperature, strain rate, and applied stress. A variety of creep deformation models have been used to model the viscoplastic behavior of lead-free solders. The Anand model has been successfully used to model the viscoplastic behavior of Pb/Sn solders. The model allows for the simultaneous incorporation of time-independent plastic deformation as well as time-dependent creep deformation. 

FIGURE 59.6 A typical creep strain versus time curve for viscoplastic materials. The curve shows that creep strain starts out as a non-linear curve, becomes steady for a significant period, and then increases significantly into tertiary creep. Most of the life of a solder joint is spent in the primary and secondary creep strain range of the curve. 

A relaxation or creep hold time induces faster softening depending on the nmnber of cycles. This effect is partly due to the increase in viscoplastic strain per cycle but also to a simple effect of time as shown by the variation of stress plotted as a function of the cumulated viscoplastic strain shown in Fig. 6.2(a). If held in tension, cycles become asymmetric towards negative stresses [40]. The inverse effect is observed if compression is maintained. Induced average stresses may be non-negligible. 

The viscoplastic strain accumulated imder creep loading conditions, after 1000 s, depends on the stress level as shown in Figure 7.11. For the highest creep stress level, 8 MPa, the viscoplastic strain corresponds to 14% of total strain after 1000 s. 

The critical task is the development of an appropriate constitutive equation for the Pb-Sn solder that is of interest. Current efforts in constitutive equation development have assumed the solder to be a continuum. Deformation is represented by a unified viscoplastic (or creep plasticity) constitutive equation [90,91]. The advantage of the unified viscoplastic approach is that both time-dependent deformation (creep) and time-independent deformation (plasticity from the stress-strain curve) are included in a single equation, thereby greatly facilitating the subsequent numerical computations. 

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