A Warren-Averbach1-4 X-ray line profile analysis was applied to broadened X-ray diffraction peaks from copper deformed in fatigue. The copper specimens were fatigued by four-point bending at peak-strain amplitudes between 0.00105 and 0.00442 in./in., and measurements were made at various fractions of the total fatigue life. The analysis results in an estimation of (a) an average coherently diffracting domain size normal to the diffracting planes and (b) an rms strain distribution function where the strain normal to the diffracting planes is averaged over a given distance at all points in the diffracting crystals and expressed as a function of averaging distance.
Prior to fatigue cycling, the annealed copper exhibited extinction, which reduced the integrated intensity from the low-angle reflections. After fatigue cycling, the integrated intensity increased with increasing strain amplitude of fatigue. The integrated intensities and the rms strains were established during the first few percent of the fatigue life and were found to increase with fatigue strain amplitude. The measured strains were larger in the <100> direction than in the <111> direction, but the absolute values were small. On the basis of transmission electron microscopy of thin foils, these results may be explained by assuming the strains are due to the presence of numerous dislocation dipoles.