FCP Report No. 168

Cyclic Plasticity with an Emphasis on Ratchetting

by

Yanyao Jiang

Abstract

Two types of plasticity formulations, Armstrong-Frederick and Mroz multiple surface, were evaluated to determine their applicability to model ratchetting and other complex cyclic loading. A limited experimental base exists for loadings such as multiple step proportional and nonproportional loading. Ratchetting experiments have been conducted using a 1070 steel to broaden the experimental base with which the existing plasticity models were evaluated. All the Armstrong-Frederick type models are able to predict reasonable stress response for the balanced nonproportional loading. The Mroz multiple surface type models are inferior to Armstrong-Frederick type models for nonproportional loading.

Under single step loading, the experimental ratchetting rate decreases with increasing number of loading cycles for both proportional and nonproportional loadings, and can be fit using a power law relation. For multiple step loading, the material exhibits a memory of the previous loading history, and could ratchet in the direction opposite to the mean stress. The memory effect dissipates with increasing number of loading cycles. The Ohno-Wang model is the only existing model which can correlate with some of the experimental ratchetting observed for 1070 steel. A shortcoming of the Ohno-Wang model is its inability to predict a constant ratchetting rate for nonproportional loading, and adequately reflect the memory effect for multiple step loading.

Using a concept of the limiting surface for a backstress part, a new plasticity model is proposed to refine the Ohno-Wang model. The capability of the new model to improve predictions for long term and multiple step ratchetting is demonstrated. A convenient procedure to determine the material constants for the model, which is also applicable to othr Armstrong-Frederick type models, is described. The new plasticity model is applicable to a broad range of cyclic material behaviors including cyclic hardening/softening, non-Masing behavior, stress level effect, and a variety of ratchetting responses.

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