scholarly journals Influence of the Replacement of the Actual Plastic Orthotropy with Various Approximations of Normal Anisotropy on Residual Stresses and Strains in a Thin Disk Subjected to External Pressure

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1834
Author(s):  
Yaroslav Erisov ◽  
Sergei Surudin ◽  
Sergei Alexandrov ◽  
Lihui Lang
Keyword(s):  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Practical Importance ◽  
External Pressure ◽  
Metallic Materials ◽  
Normal Anisotropy ◽  
Residual Strains ◽  
Axis Of Symmetry ◽  
Residual Stresses And Strains ◽  
Elastic Unloading

Plastic anisotropy is very common to metallic materials. This property may significantly affect the performance of structures. However, the actual orthotropic yield criterion is often replaced with a criterion based on the assumption of normal anisotropy. The present paper aims to reveal the influence of this replacement on the distribution of strains and residual strains in a thin hollow disk under plane stress conditions. The boundary-value problem is intentionally formulated such that it is possible to obtain an exact semi-analytical solution without relaxing the boundary conditions. It is assumed that the disk is loaded by external pressure, followed by elastic unloading. The comparative analysis of the distributions of residual strains shows a significant deviation of the distribution resulting from the solutions based on the assumption of normal anisotropy from the distribution found using the actual orthotropic yield criterion. This finding shows that replacing the actual orthotropic yield criterion with the assumption of normal anisotropy may result in very inaccurate predictions. The type of anisotropy accepted is of practical importance because it usually results from such processes as drawing end extrusion with an axis of symmetry.

Modeling of Plastic Behavior of Anisotropic Sheet Metals With Voids

2000 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Three Dimensional ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Normal Anisotropy ◽  
The Matrix

Abstract The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. (Mechanics of Materials, 1997, pp. 213-226). Three fitting parameters are suggested in the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations.

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Investigation of Residual Strains of the Second Kind in Plastically Deformed Metallic Materials

1994 ◽  
Vol 376 ◽  
Author(s):  
M. Vrána ◽  
P. Klimanek ◽  
T. Kschidock ◽  
P. Lukáš ◽  
P. Mikula
Keyword(s):  
High Resolution ◽  
Neutron Diffraction ◽  
Stacking Faults ◽  
Metallic Materials ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Neutron Diffractometer ◽  
Residual Strains ◽  
Good Agreement

ABSTRACTInvestigation of strongly distorted crystal structures caused by dislocations, stacking-faults etc. in both plastically deformed f.c.c. and b.c.c. metallic materials was performed by the analysis of the neutron diffraction line broadening. Measurements were realized by means of the high resolution triple-axis neutron diffractometer equipped by bent Si perfect crystals as monochromator and analyzer at the NPI Řež. The substructure parameters obtained in this manner are in good agreement with the results of X-ray diffraction analysis.

Effect of the Constitutive Law on the Accuracy of Prediction of the Forming Limit Curves

2012 ◽  
Vol 504-506 ◽  
pp. 77-82 ◽  
Author(s):  
Liana Paraianu ◽  
Dan Sorin Comsa ◽  
Ioan Pavel Nicodim ◽  
Ioan Ciobanu ◽  
Dorel Banabic
Keyword(s):  
Sheet Metal ◽  
Mechanical Response ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Equivalent Stress ◽  
Point Of View ◽  
Constitutive Law ◽  
Forming Limit ◽  
Accuracy Of Prediction ◽  
Forming Limit Curves

The accuracy of the forming limit curves predicted by the Marciniak-Kuczynski model depends on the type and flexibility of the constitutive equations used to describe the mechanical response of the sheet metal. From this point of view, the yield criterion has the most significant influence. The paper presents a comparative analysis referring to the quality of the forming limit curves predicted by the Marciniak-Kuczynski model for the case when the plastic anisotropy of a DC04 sheet metal is described by the BBC2005 yield criterion. The coefficients included in the expression of the BBC2005 equivalent stress are evaluated using different identification strategies (with 4, 6, 7, and 8 mechanical parameters). The forming limit curves predicted by the Marciniak-Kuczynski model in each of the cases previously mentioned are compared with experimental data.

scholarly journals Influence of Plastic Anisotropy on the Limit Load of an Overmatched Cracked Tension Specimen

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1079
Author(s):  
Elena Lyamina ◽  
Nataliya Kalenova ◽  
Dinh Kien Nguyen
Keyword(s):  
Common Property ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Limit Load ◽  
Anisotropic Materials ◽  
Isotropic Case ◽  
Yield Criteria ◽  
Analysis And Design ◽  
Assessment Procedures ◽  
Constitutive Parameters

Plastic anisotropy is a common property of many metallic materials. This property affects many aspects of structural analysis and design. In contrast to the isotropic case, there is a great variety of yield criteria proposed for anisotropic materials. Moreover, even if one specific yield criterion is selected, several constitutive parameters are involved in it. Therefore, parametric analysis of structures made of anisotropic materials is quite cumbersome. The present paper demonstrates the effect of the constitutive parameters involved in Hill’s quadratic yield criterion on the upper bound limit load for weld stretched overmatched tension specimens containing a crack of arbitrary shape, assuming that the crack is located inside the weld. Different sets of the constitutive parameters are involved in the yield criteria for weld and base materials. Since the limit load is an input parameter of many flaw assessment procedures, the final result of the present paper shows that it is necessary to take into account plastic anisotropy in these procedures. It is worthy of note that the limit load is involved in the flaw assessment procedures in combination with the stress and strain fields near the tip of a crack. In anisotropic materials, these fields may become non-symmetric even under symmetric loading. This behavior affects the propagation of cracks.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

scholarly journals An Extended Drucker Yield Criterion to Consider Tension–Compression Asymmetry and Anisotropy on Metallic Materials: Modeling and Verification

Metals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 20
Author(s):  
Bingtao Tang ◽  
Zhongmei Wang ◽  
Ning Guo ◽  
Qiaoling Wang ◽  
Peixing Liu
Keyword(s):  
Aluminum Alloys ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Function ◽  
Close Packing ◽  
Bending Test ◽  
Rolled Plate ◽  
Face Centered Cubic ◽  
Metallic Materials ◽  
Stress Invariant

Pressure sensitive asymmetric Drucker yield criterion is developed to deal with pressure dependent sheet metals for instance steels and aluminum alloys. The sensitivity to pressure is conserved by introducing three-dimensional anisotropic parameters in the first stress invariant; while the third deviatoric stress invariant is remained in odd function form to consider the strength differential effect (SDE). To describe the flow stress directionalities of metallic materials, the Drucker yield function is extended using two transformation matrix consisting of anisotropic parameters. The proposed Drucker yield criterion is utilized to predict the anisotropic yield and plastic deformation of aluminum alloys with weak SDE: AA 2090-T3 with face-centered cubic (FCC) crystal systems and AA 2008-T4 with body-centered cubic (BCC) crystal systems as well as metals with strong SDE: Zirconium clock-rolled plate with hexagonal close packing (HCP) crystal systems. The comparison between the predicted anisotropic behavior and experimental results reveals that the extended anisotropic Drucker yield criterion can precisely model the anisotropy for FCC, BCC and HCP metals. The proposed function is implemented into ABAQUS VUMAT subroutines to describe the four-point bending test which is used to consider the effect of various yield functions and material orientations on deformation behavior. The obtained contours of the cross-section, strain components distribution and also the shift of neutral layer indicate that the extended Drucker yield function can well predict the final geometric configuration of the deformed Zirconium beam.

Mechanical Anisotropy of Aluminium Laminates Produced by ARB

2011 ◽  
Vol 702-703 ◽  
pp. 151-156 ◽  
Author(s):  
P. Chekhonin ◽  
B. Beausir ◽  
J. Scharnweber ◽  
C.G. Oertel ◽  
J. Jaschinski ◽  
...  
Keyword(s):  
Experimental Data ◽  
Tensile Testing ◽  
Plastic Anisotropy ◽  
Mechanical Anisotropy ◽  
Recrystallization Behavior ◽  
Planar Anisotropy ◽  
Normal Anisotropy ◽  
Roll Bonding ◽  
Self Consistent ◽  
Aluminium Sheets

The plastic anisotropy was studied on aluminium sheets with layers of different purity (A: 5N and B: 2N+) produced by accumulative roll bonding (ARB). Both material layers show a contrasting recrystallization behavior where A and B are discontinuously and continuously recrystallized, respectively. Global textures were measured by neutron diffraction. The mechanical anisotropy was measured by tensile testing after different numbers of ARB cycles. The planar anisotropy decreases with the number of ARB cycles while the normal anisotropy reaches a plateau after 4 cycles. Simulations of the Lankford parameters were carried out with the help of the viscoplastic self-consistent scheme (based on the global texture) and compared with the experimental data. Deviations of the simulated values from those of experiment are discussed with regard to through-thickness texture and material heterogeneities.

Modified Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals

2000 ◽  
Vol 123 (4) ◽  
pp. 409-416 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Plastic Behavior ◽  
Computational Results ◽  
Sheet Metals ◽  
Element Analysis ◽  
The Matrix

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. 1997, “Approximate Yield Criteria for Anisotropic Porous Ductile Sheet Metals,” Mech. Mater., pp. 213–226. Three fitting parameters are suggested for the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the modified anisotropic Gurson’s yield criterion under uniaxial and equal biaxial tensile loading conditions.

Structural Reinforcement of Viewports in Spherical Pressure Hull for Manned Submersibles

2014 ◽  
Vol 48 (3) ◽  
pp. 17-24 ◽  
Author(s):  
Bhaskaran Pranesh ◽  
Dharmaraj Sathianarayanan ◽  
Sethuraman Ramesh ◽  
Gidugu Ananda Ramadass
Keyword(s):  
Atmospheric Pressure ◽  
Hoop Stress ◽  
Sea Water ◽  
External Pressure ◽  
Element Analysis ◽  
Structural Reinforcement ◽  
Replacement Method ◽  
Axis Of Symmetry ◽  
Spherical Pressure ◽  
Design Pressure

AbstractManned submersibles are underwater vehicles. These vehicles are equipped with an atmospheric pressure casing called a spherical pressure hull, which can accommodate up to three people. The spherical pressure hull facilitates safe passage to high-pressure environments. It has circular openings that serve as viewports to enable underwater viewing and intervention. The regions near the openings are the weakest in the pressure hull and must be reinforced. Reinforcement of the viewports is performed using the area replacement method. The amount of material removed from the viewport opening must be replaced along the axis of symmetry of the opening. This is the minimum amount of material that must be placed along the circumference of the viewports. Reinforced viewports in the pressure hull are analyzed using finite element analysis, and the stresses are classified into primary and secondary stresses. The reinforcements of the viewports are carried out in such a way that the calculated primary and secondary stresses are below the permissible limits.Abbreviations:P ‐ External pressure (design pressure)Dm ‐ Mean diameter of the pressure hullRm ‐ Mean radius of the pressure hullt ‐ Thickness of the pressure hullσ ‐ Hoop stressPy ‐ Pressure at yield strength of the materialPb ‐ Buckling pressureE ‐ Young’s modulus of the materialγ ‐ Poisson’s ratioMSW ‐ Meters of sea water

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