We used samples of the ВТ41 two-phase titanium alloy to estimate the relationship between testing temperature, KCV fracture toughness values, width of the plastic strain zone and its formation specifics. We developed an efficient method of estimating the plastic strain zone width, based on a special X-ray imaging geometry enabling a high degree of locality for measuring variations in the X-ray line broadening when moving away from the fracture surface. We studied material texture close to the fracture zone and at a distance from it, which allowed us to detect the specifics of grain reorientation, in particular, texture diffusion and an increase in the concentration of basal and prismatic planes parallel to the fracture surface as a result of plastic strain and dislocation saturation. We hypothesise that pole density in the [0001] region grows due to the [1012]-oriented grain slip, while in the region around [1010] pole density grows due to slip of the grains whose orientation is close to [1120]. We verified our X-ray texture analysis data by texture analysis via electron backscatter diffraction (EBSD).