A shear thickening phenomenon in dipolar suspensions of magnetorheological (MR) fluid is reported. The stress of the MR fluid abruptly decreases when the applied magnetic field increases to above a critical value under a small constant shear rate. It abruptly increases when the shear rate is higher than a critical value under a constant magnetic field, accompanied by a change in normal stress during shear thickening or unshear thickening processes. A shear-thickened structure is important for an MR fluid to obtain a high yield stress, which is beyond the prediction of a traditional dipole or multipole interaction model.

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