Constitutive Equations for Large Plastic Deformation of Metals

1983 ◽  
Vol 105 (3) ◽  
pp. 162-167 ◽  
Author(s):  
C. S. Hartley ◽  
R. Srinivasan
Keyword(s):  
Stainless Steel ◽  
Constitutive Equations ◽  
True Strain ◽  
Type Equation ◽  
Power Laws ◽  
Maximum Load ◽  
Least Square ◽  
304 Stainless Steel ◽  
True Strain Rate ◽  
Increasing Temperature

Calculations of deformation behavior in metal forming operations require constitutive equations valid at large plastic strain. This work examines the quality of fit provided by two types of equations, an exponential form which generalizes power laws and a saturation-type relation, to data produced by isothermal, uniaxial testing of annealed 304 stainless steel and Zircaloy-4 at a constant total true strain rate and various temperatures. The use of annealed material reduces the number of independent parameters to three in the exponential equation and to four in the saturation-type equation. Physical reasoning places limits on the values of some parameters and identifies two with the true stress, σm, and true strain, εm, at the maximum load sustained by the specimen. Least-square fits of the data reveal that the Voce form of the saturation-type equation exhibits the lowest standard deviation of all equations studied. Material parameters representing σm, εm, and σs, the saturation stress, generally followed expected trends for the temperature dependence of measures of strength and ductility, except that εm, of 304 stainless steel tended to decrease with increasing temperature.

scholarly journals Study on the Hot Deformation Characterization of Borated Stainless Steel by Hot Isostatic Pressing

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7110
Author(s):  
Yanbin Pei ◽  
Xuanhui Qu ◽  
Qilu Ge ◽  
Tiejun Wang
Keyword(s):  
Stainless Steel ◽  
Hot Deformation ◽  
True Strain ◽  
Hot Isostatic Pressing ◽  
Microstructural Analysis ◽  
Critical Conditions ◽  
True Strain Rate ◽  
Isostatic Pressing ◽  
Different Temperatures ◽  
Borated Stainless Steel

Borated stainless steel (BSS) specimens have a boron content of 1.86 wt%, and are prepared by hot isostatic pressing (HIP) conducted at different temperatures, ranging from 1000 to 1100 °C and a constant true strain rate (0.01, 0.1, 1 and 10 s−1). These tests, with observations and microstructural analysis, have achieved the hot deformation characteristics and mechanisms of BSS. In this research, the activation energy (Q) and Zener–Hollomon parameter (Z) were contrasted against the flow curves: Q = 442.35 kJ/mol. The critical conditions associated with the initiation of dynamic recrystallization (DRX) for BSS were precisely calculated based on the function between the strain hardening rate with the flow stress: at different temperatures from 1000 to 1100 °C: the critical stresses were 146.69–254.77 MPa and the critical strains were 0.022–0.044. The facts show that the boron-containing phase of BSS prevented the onset of DRX, despite the saturated boron in the austenite initiated DRX. The microstructural analysis showed that hot deformation promoted the generation of borides, which differed from the initial microstructure of HIP. The inhomogeneous distribution of elements in the boron-containing phase was caused by hot compression.

Creep and Plastic Strains of 304 Stainless Steel at 593°C Under Step Stress Changes, Considering Aging

1982 ◽  
Vol 49 (2) ◽  
pp. 297-304 ◽  
Author(s):  
U. W. Cho ◽  
W. N. Findley
Keyword(s):  
Stainless Steel ◽  
Constitutive Equations ◽  
Time Dependent ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Strain Component ◽  
Plastic Strains ◽  
Aging Effects ◽  
Stress Changes ◽  
Step Down

Nonlinear constitutive equations for varying stress histories are developed and used to predict the creep behavior of 304 stainless steel at 593°C (1100°F) under variable tension or torsion stresses including reloading, complete unloading, step-up, and step-down stress changes. The strain in the constitutive equations (a viscous-viscoelastic model) consists of: linear elastic, time-independent plastic, time-dependent-recoverable viscoelastic, and time-dependent-nonrecoverable viscous components. For variable stressing, the modified superposition principle, derived from the multiple integral representation, and the strain hardening theory were used to represent the recoverable and nonrecoverable components, respectively, of the time-dependent strain. Time-independent plastic strains were described by a flow rule of similar form to that for nonrecoverable, time-dependent strains. The material constants of the theory were determined from constant stress creep and creep recovery data. Considerable aging effects were found and the effects on the strain components were incorporated in each strain predicted by the theory. Some modifications of the theory for the viscoelastic strain component under step-down stress changes were made to improve the predictions. The final predictions combining the foregoing features made satisfactory agreements with the experimental creep data under step stress changes.

Effects of Constant Engineering and True Strain Rates on the Mechanical Behavior of 304 Stainless Steel

2017 ◽  
Vol 3 (1) ◽  
pp. 76-82 ◽  
Author(s):  
Boon Him Lim ◽  
Hangjie Liao ◽  
Weinong W. Chen ◽  
Michael J. Forrestal
Keyword(s):  
Stainless Steel ◽  
Mechanical Behavior ◽  
True Strain ◽  
304 Stainless Steel ◽  
Strain Rates

Constitutive Equation Development for Large Strain Rate Deformation Processing of 2205 Duplex Stainless Steels

2011 ◽  
Vol 695 ◽  
pp. 381-384
Author(s):  
Zhi Yu Chen ◽  
De Ning Zou ◽  
Huan Liu ◽  
Hong Bo Wang
Keyword(s):  
Stainless Steel ◽  
Flow Stress ◽  
Strain Rate ◽  
Duplex Stainless Steel ◽  
Constitutive Equations ◽  
Large Strain ◽  
True Strain ◽  
Temperature Deformation ◽  
Compression Tests ◽  
2205 Duplex Stainless Steel

Elevated compression tests were conducted on 2205 duplex stainless steel using a Gleeble 3800 thermal simulator under constant strain rates ranging from 0.1 s−1 to 50 s−1 and at deformation temperatures ranging from 900°C to 1200°C for the sample. All tests were performed at a total true strain of 0.9. The elevated temperature deformation behavior of the 2205 duplex stainless steel was characterized based on an analysis of the stress–strain curves. A set of constitutive equations for 2205 duplex stainless steel was proposed by employing hyperbolic sine function. The equations revealed the dependence of flow stress on strain, strain rate and temperature. In order to evaluate the accuracy of the constitutive equations, the mean errors of flow stress between the experimental data and predicted results were calculated. The results showed that there was a good agreement between the prediction and experimental values.

A Plastic Fracture Mechanics Prediction of Fracture Instability in a Circumferentially Cracked Pipe in Bending—Part II: Experimental Verification on a Type 304 Stainless Steel Pipe

1981 ◽  
Vol 103 (4) ◽  
pp. 359-365 ◽  
Author(s):  
G. M. Wilkowski ◽  
A. Zahoor ◽  
M. F. Kanninen
Keyword(s):  
Stainless Steel ◽  
Crack Growth ◽  
Maximum Load ◽  
Stable Crack Growth ◽  
304 Stainless Steel ◽  
Fracture Instability ◽  
Stable Growth ◽  
Girth Welds ◽  
Type 304 ◽  
Type 304 Stainless Steel

The possibility of a pipe fracture emanating from a stress corrosion crack in the heat-affected zones of girth-welds in Type 304 stainless steel pipes was investigated. The J-resistance curve—tearing modulus parameter for the prediction of crack initiation, stable growth and fracture instability—was employed. To evaluate the analysis, a pipe fracture experiment was performed using a spring-loaded four-point bending system that simulated an 8.8-m (29-ft) long section of unsupported 102-mm- (4-in-) dia pipe. An initial through-wall crack of length equal to 104 mm (4.1 in.) was used. Fracture instability was predicted to occur between 15.2 and 22.1 mm (0.60 and 0.87 in.) of stable crack growth at each tip. In the actual experiment, the onset of fracture instability occurred beyond maximum load at an average stable crack growth of 11.7 to 19 mm (0.463 to 0.750 in.) at each tip.

Comparison of Recovery and Recrystallization in Stainless Steel Following Plane-Wave Shock Loading and Explosive Forming

1970 ◽  
Vol 28 ◽  
pp. 428-429 ◽  
Author(s):  
J. A. Korbonski ◽  
L. E. Murr
Keyword(s):  
Stainless Steel ◽  
Shock Loading ◽  
Pressure Pulse ◽  
Shock Pressure ◽  
304 Stainless Steel ◽  
Strain Rates ◽  
Two Dimensional ◽  
Aisi 304 Stainless Steel ◽  
Aisi 304 ◽  
Explosive Forming

Comparison of recovery rates in materials deformed by a unidimensional and two dimensional strains at strain rates in excess of 104 sec.−1 was performed on AISI 304 Stainless Steel. A number of unidirectionally strained foil samples were deformed by shock waves at graduated pressure levels as described by Murr and Grace. The two dimensionally strained foil samples were obtained from radially expanded cylinders by a constant shock pressure pulse and graduated strain as described by Foitz, et al.

Pyrolytic carbon filaments and associated catalytic particles formed in steel tubes

1984 ◽  
Vol 42 ◽  
pp. 662-663
Author(s):  
Y. L. Chen ◽  
J. R. Bradley
Keyword(s):  
Stainless Steel ◽  
Carbon Steel ◽  
Catalyst Particle ◽  
Pyrolytic Carbon ◽  
Plain Carbon Steel ◽  
304 Stainless Steel ◽  
Hydrocarbon Gases ◽  
Steel Tubes ◽  
Filamentous Carbon ◽  
Carbon Filaments

Considerable effort has been directed toward an improved understanding of the production of the strong and stiff ∼ 1-20 μm diameter pyrolytic carbon fibers of the type reported by Koyama and, more recently, by Tibbetts. These macroscopic fibers are produced when pyrolytic carbon filaments (∼ 0.1 μm or less in diameter) are thickened by deposition of carbon during thermal decomposition of hydrocarbon gases. Each such precursor filament normally lengthens in association with an attached catalyst particle. The subject of filamentous carbon formation and much of the work on characterization of the catalyst particles have been reviewed thoroughly by Baker and Harris. However, identification of the catalyst particles remains a problem of continuing interest. The purpose of this work was to characterize the microstructure of the pyrolytic carbon filaments and the catalyst particles formed inside stainless steel and plain carbon steel tubes. For the present study, natural gas (∼; 97 % methane) was passed through type 304 stainless steel and SAE 1020 plain carbon steel tubes at 1240°K.

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