Local Approach of Ductile Rupture Under Cyclic Loading Conditions

Abstract

Experiments have shown that ductile failure occurs sooner under cyclic loading conditions than under monotone ones. This reduction of ductility probably arises from an effect called “ratcheting of the porosity” that consists of a continued increase of the mean porosity during each cycle with the number of cycles. Improved micromechanical simulations confirmed this interpretation. The same work also contained a proof that Gurson's classical model for porous ductile materials does not predict any ratcheting of the porosity. In a recent work (Morin et al., 2017, “A Gurson-Type Layer Model for Ductile Porous Solids With Isotropic and Kinematic Hardening,” Int. J. Solids Struct., 118–119, pp. 167–178), the authors proposed a Gurson-type “layer model” better fit than Gurson's original one for the description of the ductile behavior under cyclic loading conditions, using the theory of sequential limit analysis. A very good agreement was obtained between the model predictions and the results of the micromechanical simulations for a rigid-hardenable material. However, the ratcheting of the porosity is a consequence of both hardening and elasticity, and sequential limit analysis (Yang, 1993, “Large Deformation of Structures by Sequential Limit Analysis,” Int. J. Solids Struct., 30(7), pp. 1001–1013

Leu, 2007, “Analytical and Numerical Investigation of Strain-Hardening Viscoplastic Thick-Walled Cylinders Under Internal Pressure by Using Sequential Limit Analysis,” Comput. Methods Appl. Mech. Eng., 196(25–28), pp. 2713–2722

Leblond et al., 2018, “Classical and Sequential Limit Analysis Revisited,” C. R. Méc., 346(4), pp. 336–349.) is strictly applicable in the absence of elasticity. In this work, a proposal is made to take into account elasticity in the layer model through the definition of a new objective stress rate leading to an accurate expression of the porosity rate accounting for both elasticity and plasticity. This proposal is assessed through comparison of its predictions with the results of some new micromechanical simulations performed for matrices exhibiting both elasticity and all types of hardening. Finally, a comparison of the predictions regarding finite element modeling of pipes loaded cyclically is proposed.