Solder time-independent deformation

Time-independent or plastic deformation refers to a material performance that results from relatively fast loading rates. In the laboratory, time-independent deformation is typically generated by the stress-strain experiments. The tests are carried out under either strain-rate control or stress-rate control, but most often, the experiments are performed under strain-rate control. An approximate boundary between time-independent deformation and time-dependent deformation for solders are strain rates of s . The test sample dimensions are typically large, relative to the microstructural features of the material. However, there is a growing need to understand size or length-scale effects on these properties as solder interconnections become increasingly smaller, particularly solder joint dimensions less than 100 pm. 

The mechanical properties of bulk Pb-Sn solders are generally reproduced at the solder joint level. However, the actual strength values of Pb-Sn solder joints will differ from those of bulk solder. In particular, solder joint strength is affected by the gap size. An increase in joint strength with smaller gap sizes is most evident when joints are loaded in tension [66] this trend is mush less pronounced when joints are loaded in shear [67]. The shear strengths recorded for Pb-Sn solder joints made to Cu base metal are listed in Table 11 [62]. The typical deformation mode that accompanies time-independent deformation in the eutectic and near-eutectic Pb-Sn solders is grain boundary sliding [68], Fracture occurs in the solder, near to the intermetallic compound layer at the solder/base metal interface. 

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. 

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. 

The case of mechanical vibration is less well defined in terms of the predominance of creep versus time-independent (plastic) deformation. Although the applied stresses are often quite low, the strain rates can be sufficiently high, so that a mixture of creep and plastic deformation modes define the fatigue response of the material. This sensitivity of fatigue behavior to cyclic loading frequency has been widely studied for tin-lead (Sn-Pb) solders and is recognized as an important variable in the fatigue response of lead-free alloys (Ref 1-3). 

The time-independent (stress-strain or plastic) deformation properties of the Pb-free solders will be examined. The discussion will be limited primarily to the 96.5Sn-3.5Ag eutectic and Sn-Ag-Cu iloys. 

Time-Independent Plastic Deformation. The time-independent plastic deformation of a solder alloy can be represented as ... 

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