Anisotropic Behavior in Plasticity and Ductile Fracture of an Aluminum Alloy

Anisotropic mechanical behavior is investigated for an aluminum alloy of 6K21-IH T4 both in plastic deformation and ductile fracture. Anisotropic plastic deformation is characterized by uniaxial tensile tests of dog-bone specimens, while anisotropy in ductile fracture is illustrated with specimens with a central hole, notched specimens and shear specimens. All these specimens are cut off at every 15º from the rolling direction. The r-values and uniaxial tensile yield stresses are measured from the tensile tests of dog-bone specimens. Then the anisotropic plasticity is modeled by a newly proposed J2-J3 criterion under non-associate flow rule (non-AFR). The testing processes of specimens for ductile fracture analysis are simulated to extract the maximum plastic strain at fracture strokes as well as the evolution of the stress triaxiality and the Lode parameter in different testing directions. The measured fracture behavior is described by a shear-controlled ductile fracture criterion proposed by Lou et al. (2014. Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. Int. J. Plasticity 54, 56-80) for different loading directions. It is demonstrated that the anisotropic plastic deformation is described by the J2-J3 criterion with high accuracy in various loading conditions including shear, uniaxial tension and plane strain tension. Moreover, the anisotropy in ductile fracture is not negligible and cannot be modeled by isotropic ductile fracture criteria. Thus, an anisotropic model must be proposed to accurately illustrate the directionality in ductile fracture.

ANISOTROPIC DAMAGE MODELS FOR GEOMATERIALS: THEORETICAL AND NUMERICAL CHALLENGES

A new anisotropic damage model for rock is formulated and discussed. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. Drucker–Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Positivity of dissipation is ensured by using a nonassociate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Simulations show that the model meets thermodynamic requirements, follows a rigorous formulation, and predicts expected trends for damage, deformation and stiffness.

Theoretical and Numerical Predictions of Burst Pressure of Pipelines

It is known that the Tresca yield theory predicts a lower bound of burst pressure, whereas the von Mises yield theory provides an upper bound of burst pressure of pipelines. To accurately predict the burst pressure, the present authors [1] recently developed a new multiaxial yield theory for isotropic hardening materials, based on an average shear stress criterion (ASSC). Extensive classic experiments showed that the ASSC criterion can well correlate the stress-strain relations for both initial yield and subsequent yield states. Based on the ASSC yield theory, a new theoretical solution of the burst pressure of pipelines at plastic collapse is developed as a function of pipe geometry, material hardening exponent, and ultimate tensile strength. This solution is then validated by experimental data for various pipeline steels. The ASSC yield theory is further applied to accurately determine actual burst pressure using available finite element software like ABAQUS, which currently adopts the von Mises yield criterion and the associate flow rule for isotropic elastic-plastic analysis. Four burst failure criteria: the Mises equivalent stress criterion, the maximum principal stress criterion, the Mises equivalent strain criterion and the maximum tensile strain criterion are developed as functions of the ultimate tensile stress and the strain hardening exponent. Application demonstrates that the proposed failure criteria in conjunction with ABAQUS numerical analysis can accurately determine burst pressure of pipelines.