DRAFT Proceedings of the ASME 2010 Pressure Vessels & Piping Division / K-PVP Conference PVP2010 July 18-22, 2010, Bellevue, Washington, USA PVP2010-25018 PRIMARY CREEP MODELING BASED ON THE DEPENDENCE OF THE ACTIVATION ENERGY ON THE INTERNAL STRESS Luca Esposito and Nicola Bonora DiMSAT – Dept. of Mechanics, Structures and Environment, University of Cassino Via G. Di Biasio 43, 03043 Cassino (FR), Italy E-mail: l.esposito@unicas.it ABSTRACT In the high temperature component design the accumulation of creep strain during the primary stage cannot be ignored, since most the allowable design strain occurs in this stage, for which appropriate modelling is needed. In this work a mechanism based model for primary creep has been derived assuming that the creep rate in the transient regime can be given as a fraction of the steady state creep rate and as a function of the internal stress. Taking into account that the apparent activation energy varies with the internal stress and that the internal stress kinetic can be given as a function of strain, an exponential form of the creep rate vs creep strain has been obtained. The proposed model has been applied to high chromium steel P91 and the evolution of the decay constant and scaled activation volume with the applied stress has been determined. INTRODUCTION Traditionally, creep modeling is focused on the study of the secondary creep stage while the transitory processes, such as those occurring during primary creep stage, are usually neglected. However, for several pure metals and alloys the accumulation of creep strain during the primary stage cannot be ignored, since most of the allowable design strain occurs in this stage , therefore, an appropriate modeling is needed. In the past, several additive models in which primary and secondary creep contributions are treated separately, each one given by a specific strain hardening or time hardening law, have been proposed [1, 2]. Although mathematically simple, and consequently attractive from the engineering design point of view, these models showed a very poor performances especially when dealing with the projectability of the parameters with respect to stress and temperature. Today, it is well known that transient creep behavior of crystalline solids is directly related to microstructural changes which occurs with time, [3]. Several processes may take place: recrystallization and void formations cause an increase of the creep rate as for tertiary creep stage; dislocation multiplication, formations of dislocation tangles, cells and subgrains, as well as second phase precipitation, cause creep deceleration. Steady state creep is the special case where the microstructure remains constant with time and the creep rate is kept at the steady state value. Creep transients, such as primary creep and after stress changes, have been correlated with variations in dislocation density, dislocation arrangements and subgrain formations. In the early stage of primary creep, rapid dislocations multiplication occurs with consequent rapid increases of the dislocation density. As a result of this, the creep rate decreases as a consequent of the strain hardening. At later time, dislocations rearrangement takes place causing further change in the creep rate. If the temperature is high enough to produce a steady state, recovery processes (dislocations rearrangements and annihilation) balance strain hardening leading to a condition of microstructural dynamical equilibrium, [4]. According to this, primary, secondary, and tertiary creep should be described by the evolution of continuous variables where the effect of the structural changes is responsible for the different creep rate accumulation. A valuable variable for describing the overall effect of microstructure evolution on the creep response is the mean internal stress, i  . It is defined as the stress level at which the macroscopic strain rate is zero and it can be experimentally determined though well defined procedures [5]. In this work, a physically based model for primary creep has been derived assuming that the current creep rate in the transient regime can be expressed as a function of the creep