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Research Papers

An Internal State Variable Constitutive Model for Deformation of Austenitic Stainless Steels

[+] Author and Article Information
Paul S. Follansbee

Boyer School of Natural Science, Saint Vincent College, Latrobe, PA 15650paul.follansbee@email.stvincent.edu

The strain rate for measurements reported in product bulletins is rarely specified. However, the capabilities of standard testing machines imply that these strain rates (usually constant cross head velocity rather than true strain rate) are in the range 10−4 s−1 to 10−2 s−1 .

Clauss reports in Ref. [1] that these data are from U.S. Steel.

The Norström measurements were at a single strain rate; thus, the choice of ɛ·o is moot. Selecting constant values of these coefficients is consistent with the commitment not to use these as fitting parameters.

The grain size was measured for each lot of material. Thus, the target grain size for the medium-grain size material was 70 μm but the actual measured grain size was used in Eq. 8.

J. Eng. Mater. Technol 134(4), 041007 (Aug 24, 2012) (10 pages) doi:10.1115/1.4006822 History: Received October 31, 2011; Revised May 10, 2012; Published August 24, 2012; Online August 24, 2012

Austenitic stainless steels—particularly the 304 and 316 families of alloys—exhibit similar trends in the dependence of yield stress on temperature. Analysis of temperature and strain-rate dependent yield stress literature data in alloys with varying nitrogen content and grain size has enabled the definition of two internal state variables characterizing defect populations. The analysis is based on an internal state variable constitutive law termed the mechanical threshold stress model. One of the state variables varies solely with nitrogen content and is characterized with a larger activation volume. The other state variable is characterized by a much smaller activation volume and may represent interaction of dislocations with solute and interstitial atoms. Analysis of the entire stress–strain curve requires addition of a third internal state variable characterizing the evolving stored dislocation density. Predictions of the model are compared to measurements in 304, 304L, 316, and 316L stainless steels deformed over a wide range of temperatures (up to one-half the melting temperature) and strain rates. Model predictions and experimental measurements deviate at temperatures above ∼600 K where dynamic strain aging has been observed. Application of the model is demonstrated in irradiated 316LN where the defect population induced by irradiation damage is analyzed. This defect population has similarities with the stored dislocation density. The proposed model offers a framework for modeling deformation in stable austenitic stainless steels (i.e., those not prone to a martensitic phase transformation).

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Yield stress versus test temperature for 304 and 304L (open symbols, left ordinate) and for 316 and 316L (closed symbols, right ordinate) stainless steels reported by several sources

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Figure 2

Yield stress versus temperature and strain rate (which for data shown in unchanging) plotted on coordinates suggested by Eq. 5

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Figure 3

Measurements of Steichen and Paxton [14] in 304 stainless steel. The dashed line is Eq. 5 with g0  = 0.4 and σ̂t = 529 MPa.

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Figure 6

Comparison of model predictions for parameters listed in Table 2 with measurements of Norström for 0.11% N and a 75 μm grain size

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Figure 13

Comparison of the predicted stress strain curves with those measured by Byun [24] in 316 stainless steel at the specified temperatures and strain rate

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Figure 14

Comparison of the predicted stress strain curves (dashed lines) with those measured (solid lines) by investigators at Los Alamos National Laboratory in 304L (right ordinate) and 316L (left ordinate) stainless steels at room temperature and the specified strain rates

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Figure 15

Comparison of the predicted and measured stress strain curves for various austenitic stainless steels (see Table 5) at the specified strain rates and temperatures

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Figure 16

Comparison of the predicted (dashed lines) stress strain curves at various temperatures with those measured (solid lines) by Dai, Egeland, and Long in unirradiated 316 LN stainless steel and material irradiated to 5.3 dpa

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Figure 17

Comparison of the predicted (long- and short-dashed lines) stress strain curves at RT with those measured (solid lines) by Dai, Egeland, and Long in 316 LN stainless steel irradiated to 3 and 7.6 dpa

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Figure 12

Comparisons of the predicted stress strain curves with that measured by Albertini and Montagnani [30] in 316L (left ordinate) and by Conway [31] (right ordinate) in 316 stainless steel at the specified temperature and strain rate

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Figure 11

Estimate of the yield stress (solid bars) for each of the lots of 316 stainless steel analyzed by Hammond and Sikka [26] according to the nitrogen content and grain size specified by these investigators. The estimates are compared to the measured yield stresses.

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Figure 10

Variation of the activation volume for the “i” obstacle population (solid line, left ordinate) and the “N” obstacle population (dashed line, right ordinate) versus stress calculated from Eqs. 16,17

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Figure 9

Comparison of measurements by Byun [24] in 316 LN and 304 stainless steels with model predictions

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Figure 8

Variation of the two mechanical threshold stresses with nitrogen content for both the Norström and Brynes measurements

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Figure 7

Comparison of model predictions with two of Norström’s data sets

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Figure 5

Literature data shown in Fig. 1 along with the Norström data shown in Fig. 4 plotted on coordinates suggested by Eq. 5

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Figure 4

Measurements of yield stress as a function of nitrogen content (in percentage) and test temperature reported by Norström [22] in 316L stainless steel for material heat treated to give an average grain size of ∼70 μm (solid symbols, right ordinate) and by Brynes [23] in a very stable, high chromium and nickel containing, stainless steel (open symbols, left ordinate)

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