scholarly journals An Accurate Limit Load Solution for an Anisotropic Highly Undermatched Tension Specimen with a Crack

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1941
Author(s):  
Sergei Alexandrov ◽  
Yun-Che Wang ◽  
Lihui Lang
Keyword(s):  
Upper Bound ◽  
Yield Criterion ◽  
Thickness Distribution ◽  
Plastic Anisotropy ◽  
Base Material ◽  
Limit Load ◽  
Orthotropic Materials ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Principal Axes

Plastic anisotropy significantly influences the behavior of structures subjected to various loading conditions. The extremum principles in the theory of rigid plastic solids are convenient and reliable tools for plastic design. The present paper combines the upper bound theorem and Hill’s quadratic yield criterion for orthotropic materials to evaluate the plastic collapse load of a highly undermatched welded tensile panel with a crack in the weld. The base material is supposed to be rigid. The shape of the crack is quite arbitrary. The orientation of the principal axes of anisotropy varies through the thickness of the weld. The upper bound solution is based on an exact solution for a layer of an anisotropic material. This feature of the upper bound solution is advantageous for increasing its accuracy. A numerical treatment is only necessary to find the solution for the uncracked specimen. This specimen has two axes of symmetry, which simplifies the solution. Simple analytic formulae transform this solution into a solution for the cracked specimens with one axis of symmetry and no symmetry. It is shown that the through-thickness distribution of anisotropic properties significantly affects the limit load.

Effect of Plastic Anisotropy on the Predictive Capacity of Flaw Assessment Procedures

2010 ◽  
Vol 638-642 ◽  
pp. 3821-3826 ◽  
Author(s):  
Sergei Alexandrov
Keyword(s):  
Yield Criterion ◽  
Input Parameter ◽  
Plastic Anisotropy ◽  
Three Dimensional ◽  
Base Material ◽  
Limit Load ◽  
Orthotropic Materials ◽  
Predictive Capacity ◽  
Essential Input ◽  
Assessment Procedures

The limit load is an essential input parameter of flaw assessment procedures. The present paper deals with an effect of plastic anisotropy on its value. An upper bound solution for three-dimensional deformation of a highly under-matched welded specimen subject to tension is proposed. The base material is assumed to be rigid, and the weld material obeys Hill’s quadratic yield criterion for orthotropic materials. It is demonstrated that it is crucial to account for both plastic anisotropy and three dimensionality of deformation in limit load calculations for flaw assessment procedures.

An Upper Bound Solution for Upsetting of Two-Layer Cylinder

2006 ◽  
Vol 505-507 ◽  
pp. 1303-1308 ◽  
Author(s):  
Gow Yi Tzou ◽  
Sergei Alexandrov
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Limit Load ◽  
Equivalent Strain ◽  
Industrial Applications ◽  
Upper Bound Theorem ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Perfectly Plastic ◽  
Plastic Materials

An upper bound solution for axisymmetric upsetting of two-layer cylinder made of rigid perfectly plastic materials is provided. An important feature of the solution is that the kinematically admissible velocity field, in addition to the necessary requirements of the upper bound theorem, satisfies the frictional boundary condition in stresses, the maximum friction law. The latter is archived by introducing a singular velocity field such that the equivalent strain rate approaches infinity at the friction surface. The dependence of the upper bound limit load on geometric parameters and the ratio of the yield stresses of the two materials is analyzed. The solution can be used in industrial applications for evaluating the load required to deform two-layer cylinders.

A Control Strategy and Upper Bound Solution for Non-Flat Tool Open Die Forging Automation

1999 ◽  
Author(s):  
T. J. Nye
Keyword(s):  
Control Strategy ◽  
Upper Bound ◽  
Sequence Generation ◽  
Bound Solution ◽  
Upper Bound Solution ◽  
Die Forging ◽  
Strategy Model ◽  
Model Predictions ◽  
Open Die Forging ◽  
Good Agreement

Abstract The open die forging process can provide a number of benefits if its costs can be made competitive through automation. This paper describes a control strategy for automated open die forging forming sequence generation. An upper bound solution for forging with radiused tools is developed, along with a method for using this solution to estimate forming results, a necessary component of the control strategy. Model predictions are compared to physical experimental data using plasticine, and show good agreement.

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.

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