A Damage Constitutive Relationship For Pearlitic Steel With Fine Laminar Microstructure

Investigations showed that one of the most important characteristics of pearlitic materials is the decrease of ratcheting rate,the plastic shakedown capability,and the memory and recovery of the accumulated plastic strain under asymmetrical stress cycles. It was found that the interaction between phases plays an important role in the mechanical behavior of pearlitic materials,such as wearability and contact fatigue life. It is known that a pearlitic material is composed of numerous pearlitic colonies with randomly distributed orientations,and in each colony there are many parallel ferrite and cementite laminas arranged alternatively. Most existing constitutive models do not take into account the interactions between different phases of pearlitic steel and cannot illustrate why such kind of materials has excerllent mechanical properties. It is,therefore,necessary to develop a new method,which can describe the macroscopic behavior,damage and failure of the materials and their micro structural dependence.In this paper,based on a non-classical theory of plasticity and the continuum damage mechanics,a damage evolution based on an ellipsoidal void model for mixed hardening materials is obtained. The change of void geometry is considered in this model. The damage evolution law obtained from the model is related to the void volume fraction,the void shape,as well as triaxiality stress. The damage evolution law is embedded in the adopted constitutive equation,and a damage constitutive equation is obtained for the ferrite phase. The overall constitutive description for a pearlitic colony is derived from the combination of constitutive models respectively for ferrite and cementite phases and the geometric characteristics with a mixture theory. And the constitutive model for the plasticity and damage description is further derived based on the Hill's self-consistent scheme. The elastoplastic response of the typical dual-phase pearlitic steel BS11 subjected to asymmetrically cyclic loading is analyzed,and the comparison between the computed and experimental results shows satisfactory agreement. The non-proportional cyclic plasticity of BS11 is also analyzed,in which stress develops along a semi-circle in a biaxial tension/compression and shear stress plane,as is typically experienced by the surface elements in rolling and sliding contact. The computed results is quite satisfactory compared with the results obtained by Bower and Hohnson. The comparison of the results for damaged and undamaged model also demonstrates the validity of the developed damaged constitutive description.