Plastic Stress-Strain Relationships—Some Experiments to Derive a Subsequent Yield Surface

1964 ◽  
Vol 31 (4) ◽  
pp. 676-682 ◽  
Author(s):  
John Parker ◽  
M. B. Bassett
Keyword(s):  
Yield Surface ◽  
Yield Function ◽  
Loading Paths ◽  
Transverse Tension ◽  
Initial Loading ◽  
Degree Of Anisotropy ◽  
Subsequent Yield Surface ◽  
Definition Of ◽  
Radial Loading ◽  
Tubular Specimens

Experiments have been carried out on thin tubular specimens of alpha brass subjected to various combinations of torque and transverse tension, after initial overstrain in torsion. The loading paths were based upon a yield function expressing one degree of anisotropy which had been found previously to give good correlation of initial radial loading paths. The primary definition of yield used was the “Taylor-Quinney, Lode”; however, “Limit of Proportionality” and “Initial Loading Slope Tangent” definitions have also been investigated. The derived yield surface (Taylor-Quinney) shows strong positive cross effect, rotation, and a Bauschinger effect extending over the whole reversed quadrant to initial loading. No indication of the formation of a corner on the yield surface was found.

Plastic Stress-Strain Relationships—Further Experiments on the Effect of Loading History

1961 ◽  
Vol 28 (3) ◽  
pp. 439-446 ◽  
Author(s):  
J. Parker ◽  
J. Kettlewell
Keyword(s):  
Internal Pressure ◽  
Yield Surface ◽  
Yield Function ◽  
Loading History ◽  
Cross Effect ◽  
Stress Strain ◽  
Loading Paths ◽  
Degree Of Anisotropy ◽  
Alpha Brass ◽  
Plastic Stress

Further tests have been carried out on thin closed-ended tubes of alpha brass subjected to various combinations of torque and internal pressure. The effect of loading, unloading, and reloading along different paths has been investigated. The loading paths were based on a yield function which has previously been found to correlate initial radial loadings for this material, which possesses one degree of anisotropy. However, the results obtained from the second loadings suggest a cross effect which is greater than would be obtained from a nested set of yield surfaces of the foregoing form. There appears to be no evidence to support the presence of a corner in the yield surface.

Application of the Hybrid Constitutive Model for Cyclic Plasticity to Sinusoidal Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 172-179 ◽  
Author(s):  
H. Ishikawa ◽  
K. Sasaki
Keyword(s):  
Constitutive Model ◽  
Yield Surface ◽  
Strain Path ◽  
Good Description ◽  
Yield Function ◽  
Cyclic Plasticity ◽  
304 Stainless Steel ◽  
Subsequent Yield Surface ◽  
Type 304 ◽  
Type 304 Stainless Steel

In order to study the applicability of the proposed hybrid constitutive model for cyclic plasticity to nonproportional loading, type 304 stainless-steel specimens subjected to sinusoidal loading that could change the degree of nonproportionality of the strain path were examined in detail. The subsequent yield surface during the loading was discussed in advance because the plastic deformation induced anisotropy coefficient tensor in the yield function had to be determined from the yield surface obtained by the experiment. From the experimental results, the subsequent yield surfaces during the loading could be assumed to be of the quadratic form of stress. The simulations based on the model gave a good description of the sinusoidal loading, irrespective of the degree of nonproportionality of the strain path.

scholarly journals Investigation of Yield Surfaces Evolution for Polycrystalline Aluminum after Pre-Cyclic Loading by Experiment and Crystal Plasticity Simulation

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3069
Author(s):  
Damin Lu ◽  
Keshi Zhang ◽  
Guijuan Hu ◽  
Yongting Lan ◽  
Yanjun Chang
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Crystal Plasticity ◽  
Yield Surface ◽  
Plasticity Model ◽  
Anisotropic Hardening ◽  
Polycrystalline Aluminum ◽  
Crystal Plasticity Model ◽  
Subsequent Yield Surface ◽  
Definition Of

This study aims at introducing the back stress of anisotropic strain-hardening into the crystal plasticity theory and demonstrating the rationality of this crystal plasticity model to describe the evolution of the subsequent yield surface of polycrystalline aluminum at the mesoscopic scale under complex pre-cyclic loading paths. By using two different scale finite element models, namely a global finite element model (GFEM) as the same size of the thin-walled tube specimen used in the experiments and a 3D cubic polycrystalline aggregate representative volume element (RVE) model, the evolution of the subsequent yield surface for different unloading cases after 30 pre-cycles is further performed by experiments and numerical simulations within a crystal plasticity finite element (CPFE) frame. Results show that the size and shape of the subsequent yield surfaces are extremely sensitive to the chosen offset strain and the pre-cyclic loading direction, which present pronounced anisotropic hardening through a translation and a distortion of the yield surface characterized by the obvious “sharp corner” in the pre-deformation direction and “flat” in the reverse direction by the definition of small offset strain, while the subsequent yield surface exhibits isotropic hardening reflected by the von Mises circle to be distorted into an ellipse by the definition of large offset strain. In addition, the heterogeneous properties of equivalent plastic strain increment are further discussed under different offset strain conditions. Modeling results from this study show that the heterogeneity of plastic deformation decreases as a law of fraction exponential function with the increasing offset strain. The above analysis indicates that anisotropic hardening of the yield surface is correlated with heterogeneous deformation caused by crystal microstructure and crystal slip. The crystal plasticity model based on the above microscopic mechanism can accurately capture the directional hardening features of the yield surface.

Numerical Evaluation of Crashworthiness of Automotive Sheets

2007 ◽  
Vol 345-346 ◽  
pp. 1537-1540
Author(s):  
Han Sun Ryou ◽  
Myoung Gyu Lee ◽  
Chong Min Kim ◽  
Kwan Soo Chung
Keyword(s):  
Crystal Structures ◽  
Yield Surface ◽  
Numerical Evaluation ◽  
Kinematic Hardening ◽  
Sheet Thickness ◽  
Back Stress ◽  
Yield Function ◽  
Chaboche Model ◽  
Simulation Results ◽  
Function Shape

Crash simulations were performed for automotive sheets. To understand the influence of crystal structures in sheet materials on crashworthiness, the effect of the yield function shape was studied by adopting the recently developed non-quadratic anisotropic yield surface, Yld2004-18p. The effect of the back-stress was also investigated by comparing simulation results obtained for the isotropic, kinematic and combined isotropic-kinematic hardening laws based on the modified Chaboche model. In addition, the effects of anisotropy and sheet thickness on crashworthiness were evaluated.

A Yield Criterion for Porous Ductile Media at High Strain Rate

1997 ◽  
Vol 64 (3) ◽  
pp. 503-509 ◽  
Author(s):  
Ze-Ping Wang ◽  
Qing Jiang
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Yield Surface ◽  
High Strain ◽  
Yield Criterion ◽  
Matrix Material ◽  
Yield Function ◽  
Inertial Effects ◽  
The Matrix ◽  
Dynamic Yield

An approximate yield criterion for porous ductile media at high strain rate is developed adopting energy principles. A new concept that the macroscopic stresses are composed of two parts, representing dynamic and quasi-static components, is proposed. It is found that the dynamic part of the macroscopic stresses controls the movement of the dynamic yield surface in stress space, while the quasi-static part determines the shape of the dynamic yield surface. The matrix material is idealized as rigid-perfectly plastic and obeying the von Mises yield. An approximate velocity field for the matrix is employed to derive the dynamic yield function. Numerical results show that the dynamic yield function is dependent not only on the rate of deformation but also on the distribution of initial micro-damage, which are different from that of the quasi-static condition. It is indicated that inertial effects play a very important role in the dynamic behavior of the yield function. However, it is also shown that when the rate of deformation is low (≤103/sec), inertial effects become vanishingly small, and the dynamic yield function in this case reduces to the Gurson model.

A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

2008 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Yield Function ◽  
Surface Model ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Hardening Rule ◽  
Strain Data

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

A study on subsequent yield surface based on the distributed-element model

2002 ◽  
Vol 18 (1) ◽  
pp. 51-70 ◽  
Author(s):  
Dar-Yun Chiang ◽  
Kai-Hong Su ◽  
Ching-Hsing Liao
Keyword(s):  
Yield Surface ◽  
Element Model ◽  
Subsequent Yield Surface
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