Creep and Stress Relaxation in Solder Joints of Surface-Mounted Chip Carriers

When a surface-mounted ceramic chip carrier is subjected to thermal cycling, complex stresses and strains are generated in the solder joints. Using strain gauges along with some simple assumptions, we can indirectly measure the shear strain and shear force during these cycles. The force, the strain, and the temperature are related by a Simple linear equation with calculable coefficients. At any temperature, the solder simultaneously undergoes creep and stress relaxation in a process We call "stress reduction.'' The rate of stress reduction is controlled by the conventional constitutive relation in which the rate of change of shear strain at a given temperature is proportional to the shear stress raised to a constant power. The constitutive relation is used to develop an equation for stress as a function of time during isothermal stress, reduction. Experiments confirm this equation over the ,range of -28 tO 97°C. The measured time to half-stress depends on the initial stress. For typical values it was measured as 10 min to 1 h at 97°C, one month at 33°c, and (by extrapolation) 30 Years at - 28°C. Almost all methods for interpreting metal fatigue involve the strain amplitude during cycling. In temperature cycling the shear strain amplitude can be expressed as (BS/ H)
\triang
\alpha
T, where S is the in-plane distance from the center of the carrier to the solder joint, H is the height of the solder joint,
\triang
\alpha
is the expansivity difference and AT is the temperature amplitude. The parameter B is a solder Compliance factor. For small temperature amplitudes, B approaches unity at high temperatures and is 0.8 at 100°C, · but it is only 0.08 at 0°C Thus the ratio between the strain amplitude and temperature amplitude depends on the temperature, and this must be factored into any theory Which is used to explain thermal cycle, fatigue in solder joints of surface-mounted leadless chip carriers.