Modelling of Cyclic Plasticity With Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects

1980 ◽  
Vol 102 (2) ◽  
pp. 215-222 ◽  
Author(s):  
A. K. Miller
Keyword(s):  
Constitutive Equations ◽  
Work Hardening ◽  
Hysteresis Loops ◽  
Experimental Tests ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Cyclic Softening ◽  
Cyclic Plasticity ◽  
Dislocation Loops ◽  
Work Hardening Coefficient

In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

Mechanical Behaviour and Microstructure Evolution of Eurofer97 during Low-Cycle Fatigue at Room Temperature and 550°C

2011 ◽  
Vol 465 ◽  
pp. 358-361 ◽  
Author(s):  
M.F. Giordana ◽  
I. Alvarez-Armas ◽  
Maxime Sauzay ◽  
A.F. Armas
Keyword(s):  
Room Temperature ◽  
Low Cycle Fatigue ◽  
Hysteresis Loops ◽  
Friction Stress ◽  
Back Stress ◽  
Cyclic Softening ◽  
Tempered Martensite ◽  
Cyclic Behaviour ◽  
Power Law Function ◽  
Martensite Structure

The cyclic behaviour of the steel EUROFER 97 during isothermal plastic strain-controlled tests was investigated at room temperature and at 550°C. Under these test conditions, the steel shows, after the first few cycles, a cyclic softening following a power-law function that continues up to failure. The rate of softening increases with temperature, being very pronounced at temperatures above 500°C. The evolution of the flow stress during cycling was studied by analyzing the so-called “back” and “friction” stresses obtained from the hysteresis loops measured along the entire test. From the analysis of the hysteresis loops and corroborated by electron microscopy observations, it can be concluded that the strong cyclic softening observed on these samples with a "tempered martensite" structure is produced by the softening exhibited by both stresses. However, the importance of each of these stresses on the softening depends on the applied strain amplitude and temperature. It was observed that, at low temperatures and applied strains, the friction stress shows the strongest influence on the cyclic softening. On the contrary, at higher temperatures and applied strains the back stress reveals the most important changes occurring in the interior of the material.

An Exponential Stress-Strain Law for Cyclic Plasticity

1976 ◽  
Vol 98 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. C. M. Liu ◽  
E. Krempl ◽  
D. C. Nairn
Keyword(s):  
Hysteresis Loops ◽  
Cyclic Hardening ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Strain Diagram ◽  
Stress Strain ◽  
Independent Case ◽  
Transcendental Functions ◽  
Product Forms ◽  
Type 304

A previously proposed nonlinear differential constitutive equation for creep-plasticity interaction under a uniaxial state of stress is specialized for the time independent case. The characteristics of the second derivative of the stress-strain diagram are matched by an exponential function. The integration yields higher transcendental functions. For the matching of the stress-strain diagram, four easily obtainable constants are necessary at each cycle which are fed into a newly developed FORTRAN computer program. A plotting routine yields stress-strain diagrams and hysteresis loops. The procedure gives good matches for stress-strain diagrams of Type 304 stainless steel. Specifically, stress-strain diagrams for various product forms and the initial cyclic hardening of this material are reproduced quite accurately without the usual decomposition into elastic and plastic strains.

Experimental Study on Fatigue Behavior of 35CrMo Steel after Torsional Prestrain

2013 ◽  
Vol 690-693 ◽  
pp. 1718-1722 ◽  
Author(s):  
Shi Yue Wang ◽  
Zhi Yu Wu ◽  
Xi Jie Yang ◽  
Zhao Ying Ren
Keyword(s):  
High Cycle Fatigue ◽  
Fatigue Behavior ◽  
Hysteresis Loops ◽  
Cyclic Hardening ◽  
Cyclic Softening ◽  
Sem Analysis ◽  
Fatigue Tests ◽  
Cycle Fatigue ◽  
35Crmo Steel ◽  
Scanning Electron

Low cycle and high cycle fatigue tests of 35CrMo steel at different pretorsional angles were conducted and cyclic hardening and softening curves, hysteresis loops and S-N curves were obtained of 35CrMo steel after the torsional prestrain. Scanning electron microscopy (SEM) analysis was also made of the fatigue fracture. The results show that: 35CrMo steel features obvious cyclic softening with basically the same law and degree at different torsional prestrains. The area surrounded by the stress-strain hysteresis loop decreases with the increment of the pretorsional angle; the torsional prestain reduces the fatigue life of the materials.

Quantitative Evaluation of Dislocation Structure Induced by Cyclic Plasticity

2007 ◽  
Vol 345-346 ◽  
pp. 49-52 ◽  
Author(s):  
Tsuyoshi Mayama ◽  
Katsuhiko Sasaki ◽  
Yoshihiro Narita
Keyword(s):  
Cyclic Loading ◽  
Quantitative Evaluation ◽  
Strain Amplitude ◽  
Dislocation Structure ◽  
Evaluation Method ◽  
Cyclic Hardening ◽  
Cyclic Softening ◽  
Cyclic Plasticity ◽  
Loading Test ◽  
Loading Tests

In the present study, a new approach is conducted to evaluate dislocation structure induced by cyclic plasticity. First, cyclic plastic loading tests are carried out up to 100 cycles with three different small strain amplitudes on SUS316L stainless steel at room temperature. The test result presents the dependence of the strain amplitude on cyclic hardening and softening behaviors. Specifically, it is found that the cyclic loading test with strain amplitude of 0.25% shows both cyclic hardening and cyclic softening, while the cyclic loading tests with strain amplitudes of 0.75% and 1.0% show no cyclic softening. Secondly, the dislocation structures of the specimens after cyclic loading are observed by using a transmission electron microscope (TEM), and this observation reveals that the dislocation structure after cyclic loading test depends on the strain amplitude. Finally, a quantitative evaluation method of the dislocation structure is also proposed. The TEM images are converted into binary images and the resolution dependence of the generated binary image is used to visualize the characteristics of the dislocation structure. The relationship between strain amplitudes of cyclic plasticity and dislocation structure organization is clarified by the evaluation method. Finally, the heterogeneity of the dislocation structure is discussed.

Observation of Dislocations Configuration of TiAl Alloy during Fatigue Tests at Elevated Temperatures

2012 ◽  
Vol 468-471 ◽  
pp. 2193-2200
Author(s):  
Hong Fu Xiang ◽  
An Lun Dai ◽  
Hui Li ◽  
S.X. Li ◽  
Yu You Cui ◽  
...  
Keyword(s):  
Cyclic Deformation ◽  
Tial Alloy ◽  
Elevated Temperatures ◽  
Mechanical Strain ◽  
Hysteresis Loops ◽  
Cyclic Hardening ◽  
Cyclic Softening ◽  
Fatigue Tests ◽  
Dislocation Configuration ◽  
Deformation Curves

Isothermal fatigue (IF) tests were carried out on the gamma-TiAl alloy in the temperature of 500°C, 650°C and 800°C under mechanical strain control in order to evaluate its cyclic deformation behaviors at elevated temperature. Cyclic deformation curves, stress-strain hysteresis loops under different temperature-strain cycles were analyzed and dislocations configurations were also observed by TEM. The mechanism of cyclic hardening or softening during IF tests was also discussed. Results show that during the IF tests, The hysteresis loops were almost symmetrical above 600 °C, such as 650 °C and 800 °C; The hysteresis loops at the temperature of 500 °C generated two apparent asymmetry, one was zero asymmetry, the other was tensile and compressive asymmetry; Dislocation configuration and slip behaviors are contributed to cyclic hardening or cyclic softening.

scholarly journals Modelling the Strain Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

Metals ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 832 ◽  
Author(s):  
Radim Halama ◽  
Jaromír Fumfera ◽  
Petr Gál ◽  
Tadbhagya Kumar ◽  
Alexandros Markopoulos
Keyword(s):  
Experimental Data ◽  
Strain Range ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Internal Variable ◽  
Austenitic Steels ◽  
Cyclic Plasticity ◽  
Isotropic Hardening ◽  
Plasticity Model ◽  
Cyclic Plasticity Model

This paper deals with the development of a cyclic plasticity model suitable for predicting the strain range dependent behavior of austenitic steels. The proposed cyclic plasticity model uses the virtual back-stress variable corresponding to a cyclically stable material under strain control. This new internal variable is defined by means of a memory surface introduced in the stress space. The linear isotropic hardening rule is also superposed. First, the proposed model was validated on experimental data published for the SS304 material (Kang et al. Constitutive modeling of strain range dependent cyclic hardening. Int J Plast 19 (2003) 1801–1819). Subsequently, the proposed cyclic plasticity model was applied to own experimental data from uniaxial tests realized on 08Ch18N10T at room temperature. The new cyclic plasticity model can be calibrated by the relatively simple fitting procedure that is described in the paper. A comparison between the results of a numerical simulation and the results of real experiments demonstrates the robustness of the proposed approach.

Micromechanical Method to Predict Fatigue Life of Solder

1990 ◽  
Vol 112 (2) ◽  
pp. 179-182 ◽  
Author(s):  
A. Zubelewicz ◽  
Q. Guo ◽  
E. C. Cutiongco ◽  
M. E. Fine ◽  
L. M. Keer
Keyword(s):  
Fatigue Life ◽  
Constitutive Equations ◽  
Cyclic Hardening ◽  
Cyclic Softening ◽  
Stress And Strain ◽  
Fatigue Lifetime ◽  
Eutectic Solder ◽  
Tension Tests ◽  
Physical Phenomena ◽  
High Lead

Fatigue lifetimes of low-tin high-lead and tin-lead eutectic solders under total strain controlled tension-tension tests were studied in this paper. Based on the stress and strain micro-macro correlations, a modified Coffin-Manson law is obtained. The modified lifetime prediction formulas which had been used to predict the fatigue lifetime for low-tin high-lead solder, exhibiting cyclic hardening and then saturation, was found to apply to the eutectic solder, where substantial cyclic softening has been observed. This micromechanically based approach allows one to model the known physical phenomena in solders by modifying the appropriate parameters in the predictive micromechanically based constitutive equations.

Rate Dependent Constitutive Equations of Cyclic Softening

1985 ◽  
Vol 40 (7) ◽  
pp. 653-665
Author(s):  
J. S. Mshana ◽  
A. S. Krausz
Keyword(s):  
Stress Relaxation ◽  
Low Temperature ◽  
Constitutive Equations ◽  
Strain Softening ◽  
Structural Characteristics ◽  
High Stress ◽  
Cyclic Strain ◽  
Cyclic Stress ◽  
Cyclic Softening ◽  
Stress Softening

Constitutive equations of cyclic strain and stress softening for materials with low internal stress levels are derived from the rate theory. The study shows that over the high stress and low temperature range where the description of plastic flow in cyclic softening can be approximated with activation over a single energy barrier, cyclic strain softening is well related to stress relaxation process while cyclic stress softening is related to creep process. The material structural characteristics for cyclic strain softening, cyclic stress softening and stress relaxation are identical. Subsequently, it is shown that cyclic stress and strain softening within the high stress and low temperature range can be evaluated from the constitutive equations using the material structural characteristics measured from a simple stress relaxation test.

Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

Cyclic Plasticity for Nonproportional Paths: Part 1—Cyclic Hardening, Erasure of Memory, and Subsequent Strain Hardening Experiments

1978 ◽  
Vol 100 (1) ◽  
pp. 96-103 ◽  
Author(s):  
H. S. Lamba ◽  
O. M. Sidebottom
Keyword(s):  
Strain Hardening ◽  
Effective Strain ◽  
Strain Range ◽  
Cyclic Hardening ◽  
Cyclic Plasticity ◽  
Phase Cycling ◽  
Strain Behavior ◽  
Subsequent Yield Surface ◽  
Strain Hardening Behavior ◽  
Annealed Copper

Extensive experiments were conducted on annealed copper under cyclic nonproportional strain histories. After cyclically stabilizing the material by uniaxial cycling, out-of-phase axial-shear strain cycling for the same effective strain range caused additional increases in stress amplitudes to restabilized levels. Following cyclic stabilization of the material under out-of-phase cycling, a cycle whose effective strain amplitude was comparable to those of previous cycles resulted in stress-strain behavior unique to that cycle and independent of prior stable deformation. The experimental verification of this material property, which has been the subject of much conjecture, allowed the design of a fundamental class of experiments that determined the subsequent yield surface and strain hardening behavior from only one specimen.

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