This commercial alloy is subject to stress corrosion cracking (SCC) when used in .... er reactors and is subject to SCC ...... Sci. and Eng., AI13 (1989), 219-230.
CONSTITUTIVE DEFORMATION MODEL FOR ANALYSIS OF
STRESS CORROSION CRACK TIP STRAIN-RATES IN Ni·Cr-Fe ALLOY 600
M. M. Hall, Jr. and D. M. Symons Bettis Atomic Power Laboratory Bechtel Bettis, Inc.
Abstract A constitutive deformation model is being developed for application to Ni-Cr-Fe Alloy 600. This commercial alloy is subject to stress corrosion cracking (SCC) when used in some nuclear power-reactor applications. Our goal is to develop a constitutive equation for use with SCC models that relate crack growth rate to crack tip strain-rat~. We begin with an assumption that rate-dependent deformation oCcurs by the thernially activated glide of dislocations. '. This assumption is consistent with the relatively low temperatures ofreactor operation (T < 0.35 ToJ and the high stresses present at Ii crack tip (cr> cry); We have adapted the phenomenological model that was derived by Kocks, Argon and Ashby (KAA) in their 1975 treatise on the thermodynamic and kinetic fundamentals of slip. Using a dynamic strain aging (DSA) model that was developed by Louat, we have extended the KAA model to account for "plateaus" and "humps" that occur .in the DSA temperature range of the Alloy 600 flow-stress versus temperature data plots. The flow stress data that were used in this study were obtained at temperatures from 77 K to 1173 K"pre-strain levels from 0 to 0.26, for two strain rates and three carbon concentrations of 0.002%,0.020% and 0.063% by weight. The data were analyzed to obtain measures of the carbon, temperature and pre-strain sensitivities of the flow stress and the strain rate sensitivity of the flow stress. The potential influences of crack tip strain-rate and DSA on the stress and temperature sensitivities of Alloy 600 SCC crack growth-rate are discussed.
Hydrollen Effects on Material Behavior and Corrosion Deformation Interactions
Edited by N.R, Moody, A. w: Thompson, R,E. Ricker, G, w: Was and R.H. Jones
TMS (The Minerals, Metals & Materials Society), 2003
811
Introduction
The reference stress, ad, is propo ad serves as a state variable th Although attainable in practice on stress at 0 K as this stress is not a the current value of the accumulal such as the concentration of sub expre~sion for crd with Equations equation:
There are models of stress corrosion cracking (SCC) that assume stress corrosion crack growth rate'is fundamentally related to crack pp straincrate (1,2,3). To apply these models, one must determine crack tip strain-rate by analysis .. Unfortunately, the analysis currently must rely on empirical estimates of crack tip strain-rate. None of the available analytic solutions for static load crack tip strain-rate (4,5) describes the high stress (cr > cry), low temperature (T < 0.35 T nJ and rate-dependent deformation that occurs at an SCC crack tip. The purpose of this paper is to report progress in the development of the needed strain rate model and to apply the model to Ni Cr-Fe Alloy 600. This alloy is widely used in nuclear power reactors and is subject to SCC when used in some structural and heat-transfer applications
Development of the Constitutive Model Flow Stress due to Interactions between Dislocations~~mt~hort-Range U~tacles Deformation of nickel base engineering alloys at temperatures representative of nuclea:l; power ft reactor operation occurs by the thermal activation of dislocation glide • At these temperatures, dislocation climb provides no significant contribution to deformation. In 1975, Kocks, Argon and Ashby (KAA) published a treatise on the thermodynamics and kinetics of thermally activated/slip (6). They applied the thermodynamics of stressed solids and the theory of process b rates to the mechanical interactions of mobile dislocations with short-range obstacles to glide . -According to reaction rate theory, the strain rate equation is given by (1)
where ilH(cr) is the activation enthalpy, cr is stress, T is temperatUre, R is the molar gas constant and the pre-exponential factor, 80 , is a product of factors that include the density of mobile dislocations, the elementary strain accumulated per successful thermal fluctuation, the activation frequency and an entropy factor. Based on phenomenological considerations of the glide of short-range obstacles, KAA developed an expression for ilH(cr) that resistance includes a on stress and includes four parameters. Two of these are descriptive of the shape and spacing of the. obstacles to glide. A disadvantage of the KAA expression for our use is that determination of unique obstacle shape and spacing parameters is not possible due to the effects of dynamic strain aging that appear in the Alloy 600 data. For this reason, we adopted a phenomenological expression for LlH(cr) that has been used by others (7) and that requires two fewer parameters: (2)
In this equation, LlH~ is the stress-free activation enthalpy for dislocation glide and ad is a reference stress. The effective stress for dislocation glide, crd, which we introduced in Equation (2), is the applied stress, cr, minus the "internal resistance" stresses due to interactions between mobile dislocations and solute atoms, cr., and between mobile dislocations and athermal long range obstacles, cr.:
Note that we have changed notati corresponds to the reference stress i rather than the equivalent power-la' is a. function of the appliedeffecti intend to fit our model using· fl( temperature and strain rate, we invel
Internal Stresses due to Interactions t
Mobile solutes may dtffusivelysegre ener~needed fora dislocation to o~ requtred for the dislocation to move ( the solute to diffuse over this distan. solute drag stress, cr,. There are man drag, collectively called dynamic str' odeled in the literature. One effect ~ IS the appearance of a "plateau" i: ten;per~ture .r~ge. that is encompas5 which mst~bJ!lties m plastic flow OCCl ~~e Portevl~-Le'Chatelier (PLC) effe Jer)
