scholarly journals Prediction of the Constitutive Equation for Uniaxial Creep of a Power-Law Material through Microindentation Testing and Modeling

2012 ◽  
Vol 76 (10) ◽  
pp. 597-606
Author(s):  
Hidenari Takagi ◽  
Ming Dao ◽  
Masami Fujiwara
Keyword(s):  
Constitutive Equation ◽  
Power Law ◽  
Uniaxial Creep ◽  
Microindentation Testing

A Proposed Generalized Model for Forming Limit Diagram

2015 ◽  
Author(s):  
Aly El Domiaty ◽  
Abdel-Hamid I. Mourad ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Strain Hardening ◽  
Power Law ◽  
Yield Criterion ◽  
Rate Of Change ◽  
Forming Limit ◽  
Strain Hardening Exponent ◽  
Sensitivity Factor ◽  
Generalized Model

One of the most significant approaches for predicting formability is the use of forming limit diagrams (FLDs). The development of the generalized model integrates other models. The first model is based on Von-Misses yield criterion (traditionally used for isotropic material) and power law constitutive equation considering the strain hardening exponent. The second model is also based on Von-Misses yield criterion but uses a power law constitutive equation that considers the effect of strain rate sensitivity factor. The third model is based on the modified Hill’s yield criterion (for anisotropic materials) and a power law constitutive equation that considers the strain hardening exponent. The current developed model is a generalized model which is formulated on the basis of the modified Hill yield criterion and a power law constitutive equation considering the effect of strain rate. A new controlling parameter (γ) for the limit strains was exploited. This parameter presents the rate of change of strain rate with respect to strain. As γ increases the level of the FLD raises indicating a better formability of the material.

Computational and Experimental Characterization of Indentation Creep

2003 ◽  
Vol 795 ◽  
Author(s):  
Ming Dao ◽  
Hidenari Takagi ◽  
Masami Fujiwara ◽  
Masahisa Otsuka
Keyword(s):  
Finite Element ◽  
Power Law ◽  
Constant Load ◽  
Dislocation Creep ◽  
Solid Solution Alloy ◽  
Indentation Creep ◽  
Creep Tests ◽  
Uniaxial Creep ◽  
Self Similar ◽  
Power Law Creep

ABSTRACT:Detailed finite-element computations and carefully designed indentation creep experiments were carried out in order to establish a robust and systematic method to accurately extract creep properties during indentation creep tests. Finite-element simulations confirmed that, for a power law creep material, the indentation creep strain field is indeed self-similar in a constant-load indentation creep test, except during short transient periods at the initial loading stage and when there is a deformation mechanism change. Self-similar indentation creep leads to a constitutive equation from which the power-law creep exponent, n, the activation energy for creep, Qc and so on can be evaluated robustly. Samples made from an Al-5.3mol%Mg solid solution alloy were tested at temperatures ranging from 573 K to 773 K. The results are in good agreement with those obtained from conventional uniaxial creep tests in the dislocation creep regime.

scholarly journals On the identification of power-law creep parameters from conical indentation

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210233
Author(s):  
Yupeng Zhang ◽  
Alan Needleman
Keyword(s):  
Stress Relaxation ◽  
Stress Exponent ◽  
Power Law ◽  
Exponential Factor ◽  
Creep Stress ◽  
Uniaxial Creep ◽  
Creep Stress Exponent ◽  
Power Law Creep ◽  
Good Agreement ◽  
Conical Indentation

Load and hold conical indentation responses calculated for materials having creep stress exponents of 1.15, 3.59 and 6.60 are regarded as input ‘experimental’ responses. A Bayesian-type statistical approach (Zhang et al. 2019 J. Appl. Mech. 86 , 011002 ( doi:10.1115/1.4041352 )) is used to infer power-law creep parameters, the creep exponent and the associated pre-exponential factor, from noise-free as well as noise-contaminated indentation data. A database for the Bayesian-type analysis is created using finite-element calculations for a coarse set of parameter values with interpolation used to create the refined database used for parameter identification. Uniaxial creep and stress relaxation responses using the identified creep parameters provide a very good approximation to those of the ‘experimental’ materials with stress exponents of 1.15 and 3.59. The sensitivity to noise increases with increasing stress exponent. The uniaxial creep response is more sensitive to the accuracy of the predictions than the uniaxial stress relaxation response. Good agreement with the indentation response does not guarantee good agreement with the uniaxial response. If the noise level is sufficiently small, the model of Bower et al. (1993 Proc. R. Soc. Lond. A 441 , 97–124 ()) provides a good fit to the ‘experimental’ data for all values of creep stress exponent considered, while the model of Ginder et al. (2018 J. Mech. Phys. Solids 112 , 552–562 ()) provides a good fit for a creep stress exponent of 1.15.

scholarly journals A perturbative solution of the power-law viscoelastic constitutive equation for lithospheric rocks

1996 ◽  
Vol 39 (6) ◽  
Author(s):  
M. Dragoni ◽  
T. Lenci ◽  
S. Santini ◽  
F. Vetrano
Keyword(s):  
Constitutive Equation ◽  
Power Law ◽  
Laboratory Experiments ◽  
Deviatoric Stress ◽  
Viscoelastic Layer ◽  
Rock Composition ◽  
Seismogenic Layer ◽  
Perturbative Method ◽  
Perturbative Solution ◽  
Compressional Strain

A power-law, viscoelastic constitutive equation for lithospheric rocks, is considered. The equation is a nonlinear generalization of the Maxwell constitutive equation, in which the viscous deformation depends on the n-th power of deviatoric stress, and describes a medium which is elastic with respect to normal stress, but relaxes deviatoric stress. Power-law exponents equal to 2 and 3, which are most often found in laboratory experiments, are considered. The equation is solved by a perturbative method for a viscoelastic layer subjected to a constant, extensional or compressional, strain rate and yields stress as a function of time, temperature and rock composition. The solution is applied to an ideal extensional boundary zone and shows that the base of the crustal seismogenic layer may be deeper than predicted by a linear rheology.

Study on the Creep Property by Small Beam Specimen With Fixed Constraint

2018 ◽  
Author(s):  
Zhou Guo-Yan ◽  
Qin Hong-Yu ◽  
Wang Jun-Qi ◽  
Tu Shan-Tung ◽  
Gong Jian-Guo
Keyword(s):  
Constitutive Equation ◽  
Creep Deformation ◽  
Creep Property ◽  
Von Mises Stress ◽  
Beam Specimen ◽  
Creep Tests ◽  
Efficient Operation ◽  
Uniaxial Creep ◽  
Material Creep ◽  
Von Mises

To guarantee the safe and highly efficient operation of the high temperature plants, evaluation of the material creep properties and deterioration are necessary. As for small-structure components, especially in service, the material is not sufficient to provide a standard specimen for creep tests. So, as one of the promising techniques, small specimen creep tests have been developed. Three-point bending specimen with fixed constraint (TPBSF) has been attracting scholars’ increasing interests due to its simple stress state and easily achievement of rupture data. However, the TPBSF is limited in many applications for its different constitutive equations and larger errors. In this study, on the basis of beam bending theory, the creep deformation formula of TPBSF was modified. Its feasibility and accuracy was verified by comparing with the creep test data of A7N01 aluminum alloy at 380 °C in literature. Further, based on this modified constitutive equation, finite element method was used to investigate the creep behavior of 0Cr18Ni9 at 600°C. The results show that the modified creep deformation constitutive equation correlates better with uniaxial creep. The corresponding creep parameters B and n of 0Cr18Ni9 at 600°C by TPBSF test are much closer to the experimental results by uniaxial specimen. Von Mises stress and normal stress distribute almost symmetrically along center line at the beginning. But they redistribute with increasing time and reach to a steady state with constant values.

scholarly journals Linear to Non-linear Rheology of Wheat Flour Dough

2006 ◽  
Vol 16 (5) ◽  
pp. 265-274 ◽  
Author(s):  
Trevor S.K. Ng ◽  
Gareth H. McKinley ◽  
Mahesh Padmanabhan
Keyword(s):  
Constitutive Equation ◽  
Wheat Flour ◽  
Power Law ◽  
Relaxation Modulus ◽  
Liquid Form ◽  
Finite Extensibility ◽  
Filament Stretching ◽  
Non Linear ◽  
Linear Viscoelastic ◽  
Initial Power

Abstract We provide an overview of transient extensional rheometry techniques for wheat flour doughs in which the deformation and material response is well defined. The behavior of a range of model doughs was explored with a Filament Stretching Extensional Rheometer (FISER). The measurements were also compared to data obtained with a new wind- up extensional rheometer; the SER universal testing platform. A simple empirical constitutive equation, which allows characterization of the experimental results with a small number of parameters, is presented to describe the resulting measurements. To characterize the relaxation modulus of the doughs, small amplitude shear tests were performed on samples that have been shear-mixed in a mixograph for varying lengths of time. The linear viscoelastic properties were found to exhibit a broad power-law dependence on the imposed oscillatory frequency that is very reminiscent of that exhibited by a critical gel. The critical gel model of Winter and Chambon [1, 2] was used as the basis for constructing a non-linear constitutive equation for the material stress by combining the relaxation modulus for the critical gel with a Lodge rubber-like liquid form for the kinematics. Transient uniaxial extensional data recorded from the FISER and SER instruments were then compared to the predictions of the constitutive equation. The model captures the initial power- law response and subsequent strain-hardening; however additional physics is required to describe the rheological phenomena at very large Hencky strains, including finite extensibility effects and filament rupture in extensional flows.

Effect of Pre-Strain on Small Punch Creep Test of 316L Stainless Steel at 373K

2019 ◽  
Vol 795 ◽  
pp. 152-158
Author(s):  
Kai Shang Li ◽  
Jian Peng
Keyword(s):  
Stainless Steel ◽  
Power Law ◽  
Creep Behavior ◽  
316L Stainless Steel ◽  
Fe Simulation ◽  
Creep Model ◽  
Small Punch ◽  
Uniaxial Creep ◽  
Experimental Creep ◽  
Power Law Creep

Creep does not only appear at high temperature, but also appears at low temperature for 316L stainless steel that threatens the safety of equipment. In this work, the creep behavior of as-received and pre-strained 316L stainless steel at 373K was investigated by uniaxial creep (UC) tests and small punch creep (SPC) tests. The parameters of power-law creep model were determined from stress dependence of UC tests. Then, the creep behavior of SPC test was analyzed by finite element (FE) simulation combined with power-law creep model. Comparing with experimental creep deflection, the results of FE simulation can reasonably reflect the creep behavior of as-received and pre-strained small punch specimens. Based on the comparison of as-received specimen and pre-strained specimen from UC test, SPC test and FE simulation, pre-strain significantly restrains creep behavior of 316L austenitic steel at 373K.

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