This question asks which technique can actually sense the stress trapped inside a material when there is no external load on it. Residual stress measurement methods fall into two broad groups: destructive methods like hole drilling or layer removal, and non-destructive methods like X-ray diffraction, neutron diffraction, ultrasonic and magnetic techniques. Let's go through the four choices given.
X-ray Diffraction (XRD): X-rays reflect off the lattice planes of a crystal according to $n\lambda = 2d\sin\theta$. A locked-in elastic strain changes the plane spacing $d$ by a tiny amount, so the diffraction angle shifts. Recording this shift at a few different sample tilts lets the strain, and then the stress, be worked out using the elastic modulus and Poisson's ratio of the material. This is a direct residual stress measurement method.
Tensile Testing: This pulls a specimen apart under a newly applied load to find its strength and ductility. It measures the response to that new load, not the stress that was already sitting in the specimen, and it breaks the specimen in the process.
Thermo-Gravimetric Analysis (TGA): This heats a sample and records how its weight changes, which is useful for studying oxidation or decomposition. Nothing in that process senses internal elastic strain.
Optical Microscopy: This shows grains, phases and surface defects under magnification. Very high residual stress can eventually crack a part, and a microscope can see that crack, but the microscope is reading the resulting damage, not the stress value that caused it.
Only X-ray diffraction directly reads the elastic lattice strain that residual stress produces inside the material, so it is the correct technique.
Let's summarize:
Residual stress cannot be read directly, so it must be inferred from an effect it produces, which is a change in interplanar spacing.
XRD picks up this change through Bragg's law and the $\sin^2\psi$ method, while tensile testing, TGA and optical microscopy do not measure stress this way.
The correct technique for determining residual stress in a material is X-ray diffraction (XRD).
