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constrain effect;elastic-plastic behaviour;finite element;size effect;solder joint;structural optimisation

ABSTRACT

The durability and reliability of lead-free solder joints depends on a large number of factors, like geometry, processing parameters, microstructure and thermomechanical loads. In this work, the nature and influence of the plastic constraints in the solder due to joining partners have been studied by parametric finite element simulation of solder joints with different dimensions. The apparent hardening due to plastic constraints has been shown to strongly depend on the solder gap to thickness ratio with an inversely proportional evolution.

Due to interaction of several parameters, the macroscopic stress–strain constitutive law of lead-free solder materials should be determined in the most realistic conditions. In order to identify the elasto-plastic constitutive law of Sn–Ag–Cu solders, a sub-micron resolution Digital Image Correlation technique has been developed to measure the evolution of strain in solder joints during a tensile test. Experimental results of the stress–strain response of Sn–Ag–Cu solder joints have been determined for several solder gaps. The measured load–displacement curves have been used in an inverse numerical identification procedure to determine the constitutive elasto-plastic behaviour of the solder material. The effects of geometrical constraints in a real solder joint with heterogeneous stress and strain fields are then studied by comparing the apparent (constrained) and constitutive (non-constrained) stress–strain relationships.

Once the size dependant constraining effects have been removed from the stress–strain relationship, the scale effects can be studied separately by comparing the constitutive elasto-plastic parameters of joints with a variable thickness. Experimental stress–strain curves (constrained and unconstrained) for Sn–4.0Ag–0.5Cu solder in joints of 0.25–2.4 mm gap are presented and the constraining and the size effects are discussed.