A framework for modeling creep in pure metals
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I. INTRODUCTION
IT is remarkable that despite distinct differences in detailed mechanisms, all pure metals follow similar patterns of strength, rate sensitivity, and strain hardening as a function of temperature, strain, and strain rate. This has been clear since the seminal review of Sherby and Burke,[1] and many articles since this time have shown that by normalizing the strain rate by diffusivity, data taken over a wide range of temperatures and strain rates can collapse into a single line.[2–5] The works of Sherby, Weertman, Dorn, and others[6–9] have been very compelling and collectively have taught us to see creep as being described as an equation of the form n
␥˙ ss ⫽ ADo
Q e⫺ RT
冢冣
[1]
where ␥˙ ss is the steady-state strain rate, is the applied stress, is the elastic shear modulus, n is the stress exponent, Q is the activation energy for creep, T is the temperature, R is the gas constant, and A can be regarded as a fitting constant. By varying A, mildly varying n from its “typical” value of about 5, and mildly varying Q from its typical value of that for self-diffusivity, most data sets for pure metals in creep (and many for alloys and more complex materials) can be fit and rationalized. Often, if a good fit is not obtained, many groups have invoked modifications to this form, such as subtracting a threshold stress from the driving stress, which may itself be a function of temperature. A key problem is that at its essence, Eq. [1] is a phenomenological fit to a large amount of data. It represents an approach that Oleg Sherby honestly refers to as “enlightened empericism.”[11] It does not, however represent any distinct
HOLGER BREHM, Visiting Scholar, and GLENN S. DAEHN, Professor, are with the Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27-29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy. METALLURGICAL AND MATERIALS TRANSACTIONS A
mechanisms, nor does it contain component parts that can be clearly removed, examined, and modified to possibly represent changes in varied materials, mechanisms, or conditions. Presently, we propose a simple model of the creep behavior of pure metals. The model is numerical in nature because it is difficult to concurrently consider the required equations in closed form. This model reproduces the major features of the power-law creep of pure metals and the observed scaling behavior, using reasonable and measurable parameters and mechanistic relations as inputs. Further, we show that the model, being consistent with creep phenomenology, does not sensitively depend on the “correct” selection of parameters. Instead, reasonable behavior is obtained over a wide range of parameters. II. BACKGROUND—THE PHENOMENOLOGY OF
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