Residual Stress Distribution in Pure Bending Beam Subjected to Tensile Failure on One Side
The stress distribution on the midsection of a pure bending beam where tensile strain localization band initiates on the tensile side of the beam and propagates within the beam is analyzed. Using the static equilibrium condition on the section of the midspan of the beam and the assumption of plane section as well as the linear softening constitutive relation beyond the tensile strength, the expressions for the length of tensile strain localization band and the distance from the tip of the band to the neutral axis are derived. After superimposing a linear unloading stress distribution over the initial stress distribution, the residual stress distribution on the midsection of the beam is investigated. In the process of strain localization band’s propagation, strain-softening behavior of the band occurs and neutral axis will shift. When the unloading moment is lower, the length of tensile strain localization band remains a constant since the stress on the base side of the beam is tensile stress. While, for larger unloading moment, with an increase of unloading moment, the length of tensile strain localization band decreases and the distance from the initial neutral axis to the unloading neutral axis increases. The neutral axis of midsection of the beam will shift in the unloading process. The present analysis is applicable to some metal materials and many quasi-brittle geomaterials (rocks and concrete, etc) in which tensile strength is lower than compressive strength. The present investigation is limited to the case of no real crack. Moreover, the present investigation is limited to the case that the length of strain localization band before unloading is less than half of depth of the beam. Otherwise, the residual tensile stress above the elastic neutral axis will be greater than the tensile strength, leading to the further development of tensile strain localization band in the unloading process.
W. Reimers and S. Quander
X.B. Wang, "Residual Stress Distribution in Pure Bending Beam Subjected to Tensile Failure on One Side ", Materials Science Forum, Vols. 524-525, pp. 253-258, 2006