Creep of 2618 Aluminum Under Step Stress Changes Predicted by a Viscous-Viscoelastic Model

1980 ◽  
Vol 47 (1) ◽  
pp. 21-26 ◽  
Author(s):  
J. S. Lai ◽  
W. N. Findley
Keyword(s):  
Constitutive Equations ◽  
Superposition Principle ◽  
Viscoelastic Model ◽  
Multiple Integral ◽  
Constant Stress ◽  
Time Dependent ◽  
Stress Tests ◽  
Linear Elastic ◽  
Stress Changes ◽  
Dependent Strain

Nonlinear constitutive equations are developed and used to predict from constant stress data the creep behavior of 2618 Aluminum at 200°C (392°F) for tension or torsion stresses under varying stress history including stepup, stepdown, and reloading stress changes. The strain in the constitutive equation employed includes the following components: linear elastic, time-independent plastic, nonlinear time-dependent recoverable (viscoelastic), nonlinear time-dependent nonrecoverable (viscous) positive, and nonlinear time-dependent nonrecoverable (viscous) negative. The modified superposition principle, derived from the multiple integral representation, and strain-hardening theory were used to represent the recoverable and nonrecoverable components, respectively, of the time-dependent strain in the constitutive equations. Excellent-to-fair agreement was obtained between the experimentally measured data and the predictions based on data from constant-stress tests using the constitutive equations as modified.

48 Hour Multiaxial Creep and Creep Recovery of 2618 Aluminum Alloy at 200°C

1984 ◽  
Vol 51 (1) ◽  
pp. 125-132 ◽  
Author(s):  
J.-L. Ding ◽  
W. N. Findley
Keyword(s):  
Homogeneous Function ◽  
Maximum Shear Stress ◽  
Full Range ◽  
Viscoelastic Model ◽  
Multiple Integral ◽  
Constant Stress ◽  
Time Dependent ◽  
Creep Recovery ◽  
Aging Effects ◽  
Data Set

Data are reported from 48 hour constant multiaxial stress creep followed by 48 hour creep recovery with the magnitudes of the effective stress ranging from 34.5 MPa (5.00 ksi) to 175.5 MPa (25.46 ksi). They differed from a previous data set in the much longer constant-stress durations and the inclusion of data from low stress creep, compression creep, and short term aging tests. Data were represented by a viscous-viscoelastic model in which the time-dependent strain was resolved into recoverable and nonrecoverable components. Previous stress-strain relations for constant stress creep and recovery were modified to include the current experimental observations of the nonexistence of creep limits, negligible aging effects, and symmetry in tension and compression. The time dependence was represented by a power of time with different exponents for the recoverable and nonrecoverable components. A homogeneous function of maximum shear stress was developed to represent the full range of stress dependence of the nonrecoverable time-dependent components; the third-order multiple integral representation was used for the recoverable component.

Creep and Creep Recovery of 304 Stainless Steel Under Combined Stress With a Representation by a Viscous-Viscoelastic Model

1980 ◽  
Vol 47 (4) ◽  
pp. 755-761 ◽  
Author(s):  
U. W. Cho ◽  
W. N. Findley
Keyword(s):  
Stainless Steel ◽  
Viscoelastic Model ◽  
Multiple Integral ◽  
Time Dependent ◽  
304 Stainless Steel ◽  
Creep Recovery ◽  
Strain Component ◽  
Stress Dependence ◽  
Nonlinear Stress ◽  
Stress States

Creep and creep-recovery data of 304 stainless steel are reported for experiments under constant combined tension and torsion at 593°C (1100°F). The data were represented by a viscous-viscoelastic model in which the strain was resolved into five components—elastic, plastic (time-independent), viscoelastic (time-dependent recoverable), and viscous (time-dependent nonrecoverable) which has separate positive and negative components. The data are well represented by a power function of time for each time-dependent strain. By applying superposition to the creep-recovery data, the recoverable creep strain was separated from the nonrecoverable. The form of stress-dependence associated with a third-order multiple integral representation was employed for each strain component. The time-dependent recoverable and nonrecoverable strains had different nonlinear stress dependence; but, the time-independent plastic strain and time-dependent nonrecoverable strain had similar stress-dependence. A limiting stress below which creep was very small or negligible was found for both recoverable and nonrecoverable components as well as a yield limit. The limit for recoverable creep was substantially less than the limits for nonrecoverable creep and yielding. The results showed that the model and equations used in the analysis described quite well the creep and creep-recovery under the stress states tested.

Time-dependent strain development under constant stress in TRIP steels

2006 ◽  
Vol 55 (4) ◽  
pp. 287-290 ◽  
Author(s):  
L. Zhao ◽  
B. Mainfroy ◽  
M. Janssen ◽  
A. Bakker ◽  
J. Sietsma
Keyword(s):  
Constant Stress ◽  
Time Dependent ◽  
Strain Development ◽  
Trip Steels ◽  
Dependent Strain

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.

Nonproportional Loading Steps in Multiaxial Creep of 2618 Aluminum

1985 ◽  
Vol 52 (3) ◽  
pp. 621-628 ◽  
Author(s):  
J. L. Ding ◽  
W. N. Findley
Keyword(s):  
Experimental Data ◽  
Strain Hardening ◽  
Kinematic Hardening ◽  
Superposition Principle ◽  
High Stress ◽  
Material Behavior ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Strain Component ◽  
Dependent Strain

Experimental data on the creep behavior of 2618-T61 aluminum alloy under nonproportional loadings are presented. Among the important findings are the anisotropy induced by creep strain, synergistic effects during creep recovery, and strongly nonlinear material behavior at high stress levels. Data were compared with two theoretical models, a viscous-viscoelastic (VV) model and a viscoplastic (VP) model. In the VV model the time-dependent strain was decomposed into recoverable (viscoelastic) and nonrecoverable components. The VP model differs from the VV model in that all the time-dependent strain is assumed nonrecoverable. In each model, three viscoplastic flow rules based on different hardening natures, namely, isotropic strain hardening, kinematic hardening, and independent strain hardening were derived to describe the time-dependent nonrecoverable strain component, and compared with experiments. The viscoelastic component in the VV model was represented by the third-order multiple integral representation combined with the modified superposition principle. Predictions for all theories used material constants obtained from creep and recovery data only. Possible causes for the discrepancies between theories and experimental data were discussed. Further experimental and theoretical work necessary for the study of the time-dependent material behavior at high temperature were also suggested.

Approximate Analysis of Creep Strains and Stresses at Notches

2003 ◽  
Author(s):  
J. E. Nun˜ez ◽  
G. Glinka
Keyword(s):  
Elastic Stress ◽  
Notch Root ◽  
Constitutive Law ◽  
Time Dependent ◽  
Creep Model ◽  
Linear Elastic ◽  
Material Creep ◽  
Dependent Strain ◽  
Neuber's Rule ◽  
Good Agreement

A method for the estimation of creep induced strains and stresses at notches has been developed. The purpose of the method is to generate a solution for the time-dependent strain and stress at the notch root based on the linear-elastic stress state, the constitutive law, and the material creep model. The proposed solution is an extension of Neuber’s rule used for the case of time-independent plasticity. The method was derived for both localized and non-localized creep in a notched body. Predictions were compared with finite element data and good agreement was obtained for various geometrical and material configurations in plane stress conditions.

Longitudinal vertical crack analysis in beam with relaxation stresses

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Viscoelastic Model ◽  
Strain Energy Release ◽  
Time Dependent ◽  
Content Type ◽  
Dependent Strain

Purpose This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time. Design/methodology/approach Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results. Findings The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived. Originality/value The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Creep and Recovery of 2618 Aluminum Alloy Under Combined Stress With a Representation by a Viscous-Viscoelastic Model

1978 ◽  
Vol 45 (3) ◽  
pp. 507-514 ◽  
Author(s):  
W. N. Findley ◽  
J. S. Lai
Keyword(s):  
Mathematical Model ◽  
Time Dependence ◽  
Viscoelastic Model ◽  
Multiple Integral ◽  
Time Dependent ◽  
Strain Component ◽  
Combined Stress ◽  
Recoverable Strain ◽  
Creep And Recovery ◽  
Mathematical Expressions

Creep and recovery data are presented for combined tension and torsion of 2618 Aluminum at 200°C (392°F). These data are represented by a mechanical-mathematical model in which the strain is resolved into five components: elastic, time-independent plastic, recoverable viscoelastic, time-dependent nonrecoverable viscous (positive) and time-dependent nonrecoverable viscous (negative). By using recovery data the recoverable component is separated from the nonrecoverable creep strain. Results show that the time-dependence may be represented by a power of time (independent of stress) and that the time-dependence of the recoverable and nonrecoverable strains are the same. It is also shown that the proportion of recoverable versus nonrecoverable strain may be taken to be independent of stress. The mathematical expressions developed describe quite well the creep and recovery under tension and/or torsion. Results are presented in a form which may prove suitable for predicting creep or relaxation under variable input using the modified superposition simplification of the multiple integral representation for the recoverable strain component and strain hardening for the nonrecoverable component. Comparison between predicted strain or stress and actual tests under different variable stress or strain histories will be presented in subsequent papers.

Multiaxial Creep of 2618 Aluminum Under Proportional Loading Steps

1984 ◽  
Vol 51 (1) ◽  
pp. 133-140 ◽  
Author(s):  
J.-L. Ding ◽  
W. N. Findley
Keyword(s):  
Strain Hardening ◽  
Kinematic Hardening ◽  
Superposition Principle ◽  
Viscoelastic Model ◽  
Creep Recovery ◽  
Strain Component ◽  
Proportional Loading ◽  
Dependent Strain ◽  
Stress States ◽  
Multiaxial Creep

Creep data of 2618-T61 aluminum alloy under multistep multiaxial proportional loadings at 200°C (392°F) are reported. Two viscoplastic flow rules were developed using constant stress creep and creep recovery data. One was based on the accumulated strain (isotropic strain hardening), and the other on a tensorial state varible (kinematic hardening). Data were represented by two models: a nonrecoverable viscoplastic model, and a viscous-viscoelastic model in which the time-dependent strain was resolved into recoverable (viscoelastic) and nonrecoverable components. The modified superposition principle was used to predict the viscoelastic strain component under variable stress states. The experiments showed that the viscous-viscoelastic model with either isotropic strain hardening or kinematic hardening gave very good predictions of the material responses. Isotropic strain hardening was best in some step-down stress states. The viscoelastic component accounted for not only the recovery strain but also the transient creep strain upon reloadings and step-up loadings.

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