A Damage-coupled Criterion of Localized Necking Based on Acoustic Tensor

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Abstract
The development of a localized necking criterion for strain-softening materials is presented. The criterion is applicable to materials with anisotropic damage and anisotropic plasticity. The critical condition of damage evolution leading to localized necking is of primary interest in this investigation. As a consequence of plastic instability, the singularity of acoustic tensor is taken as the critical condition for localized necking in strain-softening materials, which often occurs prior to fracture. Effective tangent modulus tensor for materials with anisotropic damage is established. The damage-coupled localized necking criterion, along with the inclination angle of localization band, for strain-softening materials is derived. The closed-form expression of the localized necking criterion has potential applications in the failure analysis of strain-softening materials such as hot metals, rocks, soil, solder, etc. Tensile testing at elevated temperature (450°C) has been performed for aluminum alloy Al6061 with multiple unloading paths to determine material damage. The test results displaying the strain-softening and material damage behaviors are employed to formulate the constitutive equations of the material. Forming limit strains for a particular loading path are computed and compared with the test result.

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