The influence of the history of the shear rate on generation of shear hardening phenomenon of wormlike micelles aqueous solutions was investigated. An accelerated shear flow was applied to change the shear rate history and the influence of an acceleration rate on the time evolution behavior of the shear stress was observed. The relationship between the strain and the shear stress is given by one curve that is independent of a history of shear rate if the shear rate or the accelerated shear coefficient is higher than a certain critical value. A very high shear rate flow can be caused without the shear hardening by using the slowly accelerated shear flow but the SIS is generated if the shear rate in the moment exceeds the critical shear rate of the SIS formation.

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