Determination of parameters for thermally activated glide from stress- strain curves at different temperatures and strai
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I.
INTRODUCTION
P R I M A R Y creep in metals can be described by theories of the so-called 'overstress' type, m i.e., the driving force for deformation is the difference in stress between the actual stress and a corresponding stress at the same strain on an 'equilibrium' stre.ss-strain curve. The strain rate can be related to the driving stress either empirically, e . g . , usin~ nonlinear representations of spring-dashpot type models I J or semi-empirically using thermally activated dislocation glide theories. [21 In terms of the latter, the shear strain rate 5' can be written as a function of the shear stress difference 8o- by: 3" = ~'0(8o-//*) 2 exp - 8 F / k T [ 1 - (8o-/8~)P] q
[1]
where 5'0 is a constant,/z the shear modulus of elasticity, k Boltzmann's constant, and T the absolute temperature. The material parameters 8F and 8~" are related, respectively, to the free energy of activation for dislocation glide (AF), which is the free energy required by a dislocation to overcome lattice obstacles by means of thermal activation alone, and to the height of such barriers to flow (§ which is usually referred to as the 0 K flow stress. The constants p and q describe the obstacle shape. This relationship is similar to that often used for describing steady s t a t e flOW,[3'4] with 8o- replacing the full value of the applied stress or and the material parameters 8F and &~- replacing AF and -~, respectively. Equation [ 1] can be written in terms of the steady state material parameters AF and ~ since 8§ is the difference between § and the flow stress point on the equilibrium curve, z/and 8F represent the free energy of activation above a stress of z/. For cylindrical shaped barriers to flow where p = q = 1, Eq. [1] can be written: tsl 5'=5'o
exp--~
1 -
1
:~ [21
This relationship has the same form as that often used c6'vJ to describe flow which is driven by an effective stress, H. D. CHANDLER is with the School of Mechanical Engineering, University of the Witwatersrand, Johannesburg, P.O. 2050 wits, South Africa. Manuscript submitted September 4, 1987.
METALLURGICAL TRANSACTIONS A
zeff = o- - Zo where z0 represents an 'internal' stress. The internal stress arises from the effects of long range barriers to flow and is an athermal stress. Unlike the internal stress term, the flow stress in Eq. [2] depends on the short range structure as represented by the degree of work hardening, etc. and on the temperature. Previous work using Eq. [2] as a description of primary creep has been confined to tests carried out at room temperature. t2'sl For Eq. [2] to represent an adequate description of primary creep, the material parameters AF and ~" found from experiments at different temperatures should be independent of temperature over ranges in which the structure is thermally stable. Additionally it might be expected that, for a given structure, the flow stress ry should be a linear function of temperature. Frequently, an index of structure is taken to be a flow stress I31 which is defined as the stress necessary to achie
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