A Microstructure-Damage-Based Description for the Size Effect of the Constitutive Behavior of Pearlitic Steels

A microstructure-based description is proposed for the size effect of the elastoplastic behavior and damage of pearlitic steel. Pearlitic steel is composed of numerous randomly orientated colonies, and each colony is further composed of many fine lamellas of ferrite and cementite. Experiments showed that pearlitic steels with smaller interlamellar spacing possess better mechanical properties such as higher rupture strength, better ductility, longer fatigue life, and so on. The dependence of the mechanical properties of pearlitic steels on the interlamellar spacing during elastoplastic deformation is investigated with a microstructure-damage-based micro-macro approach. A unified evolution law is obtained for the damage corresponding to different patterns of microdefects in different phases by making use of the concepts of energy release rate and continuum damage mechanics. It is interesting that the damage evolution contains the interlamellar spacing as an explicit parameter. The constitutive and damage description for each phase is formulated by embedding the obtained damage and evolution in its elastoplastic model. The constitutive formulation for a single pearlitic colony is then derived based on its multiphase lamellar microstructure. Finally, the constitutive description for pearlitic steel is obtained with the Hill’s self-consistent scheme. The proposed model can easily account for the size effect of the multiphase materials with lamellar microstructure. The corresponding numerical algorithm is developed. The analytical results are in satisfactory agreement with the experimental ones, demonstrating the validity of the proposed approach.