A comparison of two simple methods for measuring cyclic internal and effective stresses

Back stress strengthening and strain hardening in gradient structure

“…In other words, GNDs that produce the back stress do not change their density or configuration before the unloading yield, which keeps the back stress approximately constant. This assumption is important and was also adopted by Dickson et al [29] During the unloading, the back stress is the stress that drives the mobile dislocations to reverse their gliding direction to produce unloading yield. At the unloading yield point C (Figure 2(a)), the applied stress is low enough that the back stress starts to overcome the applied stress and the frictional stress to make dislocations glide backward, that is…”

“…As shown, the unloading starts at unloading strains (ε u ) at point A. The segment AB of the unloading curve is quasi-elastic and caused by stress relaxation [29] or viscous flow of the material. [30,31] The stress drop in this segment is called the thermal component of the flow stress.…”

“…We argue that Equation (3) is physically sounder than Equation (5) because we are defining unloading yield and reloading yield using the same criterion, that is, the same deviation of effective Young's modulus as discussed later. It has been recognized that Equation (5) overestimates the back stress, and was later modified by Dickson et al to include the thermal component of the flow stress: [24,29] …”

“…where σ * is the thermal component of the flow stress as defined in Figure 2(a), [24,29] which is also called the viscous stress. [31] Equation (3) is especially suitable for hysteresis loops with positive unloading yield stresses.…”

“…[30,31] The stress drop in this segment is called the thermal component of the flow stress. [24,29] or viscous stress. [30,31] The segment BC is the linear (elastic) part of the unloading stress with an effective unloading Young's modulus of E u .…”