Chapter 26
Full Bauschinger Effect
26.1 Secondary Yield Stress
For the considered materials, the initial section of the secondary loading diagram
(after preloading beyond the yield stress, unloading, and changing the loading
sign to the opposite) has a form of a smooth rounded curve, and defining the
position of the point (Q, Fig. 21.1) on it (and on the unloading curve), starting
with which plastic strain starts decreasing, causes serious complications. The stress
corresponding to this point and characterizing the Bauschinger effect is called [2]
the secondary yield stress. Most researchers define the value of the secondary yield
stress at some quantity of “tolerance” for plastic strain increment. As shown by
L.M. Kachanov [1], the secondary yield stress value substantially depends on the
tolerance since hardening in the beginning of the secondary loading diagram for
most materials is huge. In this manner, finding the secondary yield stress upon the
tolerance is significantly conditional due to arbitrariness in selecting the tolerance.
On the other hand, as noted above, for plastic materials, an increment of nonelastic strain of an opposite sign is observed experimentally irrespective of the
plastic strain quantity preceding unloading already in the case of full unloading.
Since this increment usually exceeds the size of the order of elastic hysteresis, it
may not be taken into account, and it can be believed that the opposite-sign plastic
strain starts after changing the loading sign to the opposite one. This assumption
eliminates arbitrariness in defining the tolerance when fixing the value of the
secondary yield stress.
If we measure the Bauschinger effect by the ratio between the secondary yield
stress and the yield stress of the material, according to the above assumption, this
ratio equals zero. This Bauschinger effect will be called full.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_26
345
Full Bauschinger Effect
26.1 Secondary Yield Stress
For the considered materials, the initial section of the secondary loading diagram
(after preloading beyond the yield stress, unloading, and changing the loading
sign to the opposite) has a form of a smooth rounded curve, and defining the
position of the point (Q, Fig. 21.1) on it (and on the unloading curve), starting
with which plastic strain starts decreasing, causes serious complications. The stress
corresponding to this point and characterizing the Bauschinger effect is called [2]
the secondary yield stress. Most researchers define the value of the secondary yield
stress at some quantity of “tolerance” for plastic strain increment. As shown by
L.M. Kachanov [1], the secondary yield stress value substantially depends on the
tolerance since hardening in the beginning of the secondary loading diagram for
most materials is huge. In this manner, finding the secondary yield stress upon the
tolerance is significantly conditional due to arbitrariness in selecting the tolerance.
On the other hand, as noted above, for plastic materials, an increment of nonelastic strain of an opposite sign is observed experimentally irrespective of the
plastic strain quantity preceding unloading already in the case of full unloading.
Since this increment usually exceeds the size of the order of elastic hysteresis, it
may not be taken into account, and it can be believed that the opposite-sign plastic
strain starts after changing the loading sign to the opposite one. This assumption
eliminates arbitrariness in defining the tolerance when fixing the value of the
secondary yield stress.
If we measure the Bauschinger effect by the ratio between the secondary yield
stress and the yield stress of the material, according to the above assumption, this
ratio equals zero. This Bauschinger effect will be called full.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_26
345