Determination of Residual-Stress-Free State and Mapping of Residual Stress Fields Using Speckle Interferometry and Thermal Relaxation

Abstract

We used an electronic speckle pattern interferometer (ESPI) for nondestructive measurement in-situ displacement fields in microsystems. A four-step phase-shift technique and magnifier with long working distance were adopted to increase displacement resolution to ∼10⁻² μm and spatial resolution to ∼2 μm. A thermal vacuum chamber was designed to induce thermal treatments, including annealing. From the identification of the residual-stress-free state, we quantitatively modeled thermal strains/stress fields, relaxation stresses during annealing, and residual stress fields. Thermoelasticity theory was applied to model the relationship between the relaxation stresses and the displacements measured by ESPI during the evolution of the residual-stress-free state. We assessed the surface residual stress fields of indented bulk Cu; a Fe-Ni lead frame of 100 μm width; and 0.5 μm Au film. In the indented Cu, the normal and shear residual stresses around the indented point range from –1.7 GPa to 700 MPa and –800 MPa to 600 MPa, respectively, and the residual stress in the bending area of the Fe-Ni lead frame was estimated at 148 MPa and verified using beam-bending theory. In the Au film, tensile residual stresses are uniformly distributed from 500 MPa to 800 MPa as verified by X-ray diffraction.