Localization in elasto-plastic materials: Influence of the plasticity yield surface in biaxial loading conditions

Abstract Fatigue data obtained under biaxial loading conditions for adhesively bonded joints are used to plot S-N type diagrams to assess the effects of biaxiality in loading. Independently Loaded Mixed-Mode Specimens (ILM MS) are used for data collection purposes. These specimens are basically two (steel) beams bonded to be fatigue loaded under cantilever (opening) mode while a simultaneous but physically separate in-plane (static) shear load is also induced with the aid of a small hydraulic piston embedded in the specimen. Application of such static shear loads results in different S-N behavior for the bonded joint. The model adhesives used are Metlbond 1113-2 and Metlbond 1113 solid film thermosetting adhesives similar to those commonly used in aircraft and aerospace industries. The former is an elastomer-modified epoxy adhesive and the latter is identical except that it containes a synthetic earner cloth. Thus, the effects of carrier cloth in adhesive’s S-N behavior is also assessed. Analytically, the classical linear log-log representation of the adhesive S-N data is explored and modifications necessary to reflect the effects of biaxiality in loading and also the presence of a carrier cloth are assessed. The fatigue failure results are also compared with results obtained under monotonic biaxial loading conditions.

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Transient Small-Scale Yield Behavior of Textured Copper Tubing Under Biaxial Loading

Journal of Engineering Materials and Technology ◽

10.1115/1.3225849 ◽

1986 ◽

Vol 108 (2) ◽

pp. 127-134 ◽

Cited By ~ 3

Author(s):

Hamid Garmestani ◽

Brent L. Adams

Keyword(s):

Yield Surface ◽

Bauschinger Effect ◽

Biaxial Loading ◽

Small Scale ◽

Isotropic Hardening ◽

Initial Surface ◽

Transient Time ◽

Dependent Behavior ◽

Copper Tubing ◽

Final Yield

Biaxial microplastic yielding (8 microstrain) of 101 copper tubing was studied at room temperature to assess the transient time-dependent behavior of subsequent yielding following small prestrains (2000 microstrain). The specimens investigated were thin-walled tubes loaded in variable combinations of uniaxial tension/compression and internal pressurization. Prestraining in three different directions introduced a Bauschinger effect as manifested by a translation of the yield surface in the direction of stressing. The yield surface also showed an expansion in size. Subsequent yield surfaces, measured at other time intervals, showed that the Bauschinger effect recovered up to 90 percent after 120 hours, and the final yield locus retained the same shape anisotropy as the initial surface. This implies a shift from kinematic to isotropic hardening. Hart’s phenomenological model was used to predict the experimental data. In this model, the Bauschinger effect and other shape changes of the yield surface are attributed to anelastic phenomena.

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Fracture capacity of girth welded pipelines with 3D surface cracks subjected to biaxial loading conditions

International Journal of Pressure Vessels and Piping ◽

10.1016/j.ijpvp.2011.10.019 ◽

2012 ◽

Vol 92 ◽

pp. 115-126 ◽

Cited By ~ 25

Author(s):

Yi Dake ◽

Idapalapati Sridhar ◽

Xiao Zhongmin ◽

Shashi Bhushan Kumar

Keyword(s):

Biaxial Loading ◽

Surface Cracks ◽

Loading Conditions ◽

3D Surface

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

Volume 6: Materials and Fabrication, Parts A and B ◽

10.1115/pvp2008-61800 ◽

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.

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