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March 2014 • The PCB Magazine 27 SPHERICAL BEND TESTING continues out lined in previous work by the authors [8,9,10] . First, it represents the most conservative esti- mate of deflection limit. Second, it matches the conditions imposed by ICT equipment, which is a standard process step for many products and is a known source for board deflection. Third, it generates data at all four corners of the package because they are loaded equally. The spherical bend test fixture is based on a support plate with eight spherically ground pins evenly spaced on a circle with a diameter roughly 3x the diagonal dimension of the part. The sample under test is centered on the circle and the load is applied from the back side in the center of the package footprint by another spherically ground pin. The effect is to force the flat assembly into an area segment of a sphere whose radius is inversely related to the displacement of the loading pin. The attached package acts as a stiffener in the center of the slab and stress is imposed in a manner directly related to the diagonal distance from the center of the package. The effect is to load the corner solder joints to failure. In fracture mechanics engineering terms the loading is mixed mode I & II as depicted in Figure 3. • Mode I: A tensile component of the load as the stiffener (package) resists being deformed by flexure imposed on the board. This is a crack opening mode when describing a horizontal crack in the solder joint. • Mode II: An in-plane shear stress compo- nent as the package resists being stretched as curvature is imposed on the system. The principal strain on the board surface may not be coincident with the diagonal of the package but the maximum bending or minimum bend radius for the board is co- incident, therefore the strain gauges are located on the board at the corners of the package in the diagonal orientation. If the assembled test unit is relatively compliant, gauges attached to the package corner in the same orientation also provide information. However the heavy metal heat spreader and its attachment to the package substrate make that information indecipher- able for this sample set. Data collection is set up to simultaneously record resistance in the daisy chain, strain in the six gauges attached to the sample, displacement of the test head and the load induced by that displacement. Diagonal strain is recorded in the four aligned gauges and strain rate is calculated from the recorded data. The additional two gauges at a single corner allow calculation of the principal strain and principal strain rate. Experimental Design: DOE1 The initial experiment was designed to as- sess the mechanical strain limits for lead- free high- complexity assembly and characterize the effect of lead-free alloys and extended thermal requirements on safe working limits for board flexure in terms of peak strain and rising strain rate. Surface strain analysis in PCBAs is the meth- od by which we normalize a whole group of sub-parameters. Surface strain in uniform slabs is a function of deflection or curvature and board thickness (distance from the neutral axi s of the slab). In electronic assembly it is com- plicated by non-uniform reinforcement of the system by soldered components. Our interest is actually in the stress/strain concentrations that are inherent in the soldered connections. Specifically, the stresses that are imposed on the solder, the interfaces of the solder joint and the resin systems that are directly in con- tact with the solder pads. In this work we have introduced two factors which are "designed" to generate variation in the results. These are board thickness and strain rate. The other three factors: sphere alloy, laminate and pad plating are under study. The expectation i s that each Figure 3: crack stress modes [11] .