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Experimental Mechanics

, Volume 13, Issue 1, pp 14–23 | Cite as

Evaluation of multiaxial theories for room-temperature plasticity and elevated-temperature creep and relaxation of several metals

Investigation is undertaken to evaluate the isotropic-hardening model for several ductile metals at both room temperature, where the inelastic deformation could be considered to be time independent, and at elevated temperatures, where the inelastic deformation was primarily time dependent
  • Omar M. Sidebottom
Article

Abstract

Based on the assumption that the material satisfies the condition of isotropic hardening for either a von Mises or a Tresca material, finite-strain theories are derived for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent. In the latter case, both creep and relaxation theories are derived. At room temperature the theories are evaluated for each of eight metals using finite-strain data from tension, compression and torsion members. Of the six metals that are found to satisfy the condition required for the isotropic-hardening model, two are von Mises, one is Tresca, and the other three are between von Mises and Tresca. At elevated temperatures, the theories are evaluated for each of five of the latter six metals, using data from tension and torsion members. Material properties obtained from the tension specimens are used to predict creep and relaxation curves for the torsion members. Contrary to the results at room temperature, creep curves for the torsion members do not all fall within the region bounded by von Mises and Tresca theories. In the case of relaxation, either excellent agreement is obtained between the von Mises strain-hardening theory and experimental data or the theory is conservative.

Keywords

Mechanical Engineer Material Property Elevated Temperature Fluid Dynamics Excellent Agreement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

r, θ,z

cylindrical coordinates

Δr, Δθ, Δz trθ, tθz, tzr εrc εθc, εzc

true-stress components

γrθc, γθzc, γzrc

true-creep-strain components (superscriptp denotes plastic components)

δ1, δ2, δ3

principal true-stress components

ε1c, ε2c, ε3c

principal true-creep-strain components (superscriptp denotes plastic components)

εe

effective true stress

εc, εp

effective true creep strain and effective true plastic strain

% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacciGaf8hcI4% Sbaiaaaaa!377F!\[\dot \in \]

effective creep rate

ε, ε1

normal true strain in tension specimen

εeng

engineering strain in tension specimen

τ

shearing stress in torsion member

γ

shearing strain in torsion member

γc, γp

creep and plastic components of shearing strain in torsion member

% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4SdCMbai% aaaaa!379D!\[\dot \gamma \]

shearing-strain creep rate in torsion member

Δγc

increment of shearing creep strain in torsion member

t, Δt

time and increment in time

Do

initial diameter of tension specimen

D

deformed diameter of tension specimen

R

outer radius of torsion member

r

variable radius of torsion member

θ

unit angle of twist

M

torque

γmaxe

MR/GJ

γmax

maximum shearing strain

E

Young's modulus

G

shearing modulus

ν

Poisson's ratio

J

polar moment of inertia

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References

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Copyright information

© Society for Experimental Mechanics, Inc. 1973

Authors and Affiliations

  • Omar M. Sidebottom
    • 1
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbana

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