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.

scholarly journals A Limit Load Solution for Anisotropic Welded Cracked Plates in Pure Bending

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1764
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Alexander Pirumov ◽  
Dinh Kien Nguyen
Keyword(s):  
Numerical Method ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Bending Moment ◽  
Limit Load ◽  
Vertical Axis ◽  
Pure Bending ◽  
Cracked Plates ◽  
Base Materials ◽  
Assessment Procedures

The present paper’s main objective is to derive a simple upper bound solution for a welded plate in pure bending. The plate contains a crack located in the weld. Both the weld and base materials are orthotropic. Hill’s quadratic yield criterion is adopted. The solution is semi-analytic. A numerical method is only required for minimizing a function of two independent variables. Six independent dimensionless parameters classify the structure. Therefore, the complete parametric analysis of the solution is not feasible. However, for a given set of parameters, the numerical solution is straightforward, and the numerical method is fast. A numerical example emphasizes the effect of plastic anisotropy and the crack’s location on the bending moment at plastic collapse. In particular, the bending moment for the specimen having a vertical axis of symmetry is compared with that of the asymmetric specimen. It is shown that the latter is smaller for all considered cases. The solution found can be used in conjunction with flaw assessment procedures.

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.

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.

An Upper Bound Solution for Upsetting of Anisotropic Hollow Cylinders

2009 ◽  
Vol 623 ◽  
pp. 71-78 ◽  
Author(s):  
Elena Lyamina ◽  
Gow Yi Tzou ◽  
Shao Yi Hsia
Keyword(s):  
Velocity Field ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Friction Stress ◽  
Limit Load ◽  
Flow Rule ◽  
Friction Law ◽  
Maximum Friction ◽  
Hollow Cylinders ◽  
Associated Flow Rule

The paper concerns with an effect of plastic anisotropy on the load required to deform hollow cylinders between two parallel, rough dies. It is assumed that the material obeys Hill’s quadratic yield criterion and its associated flow rule. The friction stress is supposed to be proportional to the corresponding shear yield stress, including the maximum friction law as a special case. The kinematically admissible velocity field is chosen such that the stress field following from the associated flow rule satisfies the boundary condition at the plane of symmetry. Moreover, this velocity field is singular in the vicinity of the friction surface. Therefore, in the case of the maximum friction law the friction law is satisfied, again if the associated flow rule is combined with the velocity field. A significant effect of plastic anisotropy on the limit load is illustrated.

Modeling of Anisotropic Plastic Behavior of Advanced High Strength Steel Sheet TRIP 780

2011 ◽  
Vol 410 ◽  
pp. 232-235 ◽  
Author(s):  
Sansot Panich ◽  
Vitoon Uthaisangsuk ◽  
Surasak Suranuntchai ◽  
Suwat Jirathearanat
Keyword(s):  
High Strength Steel ◽  
Steel Sheet ◽  
Plastic Anisotropy ◽  
High Strength ◽  
Uniaxial Tensile ◽  
Plastic Behavior ◽  
Biaxial Test ◽  
Advanced High Strength Steel ◽  
Yield Criteria ◽  
Anisotropic Plastic

Anisotropic plastic behavior of advanced high strength steel sheet of grade TRIP780 (Transformation Induced Plasticity) was investigated using three different yield functions, namely, the von Mises’s isotropic, Hill’s anisotropic (Hill’48), and Barlat’s anisotropic (Yld2000-2d) criterion. Uniaxial tensile and balanced biaxial test were conducted for the examined steel in order to characterize flow behavior and plastic anisotropy for different stress states. Especially, disk compression test was performed for obtaining balanced r-value. All these data were used to determine the anisotropic coefficients. As a result, yield stresses and r-values for different directions were calculated according to these yield criteria. The results were compared with experimental data. To verify the modelling accuracy, tensile tests of various notched samples were carried out and stress-strain distributions in the critical area were characterized. By this manner, the effect of stress triaxiality due to different notched shapes on the strain localization calculated by the investigated yield criteria could be studied.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Evaluation of Weld Metal Strength Mismatch in X100 Pipeline Girth Welds

2004 ◽  
Author(s):  
Henryk G. Pisarski ◽  
Yuri Tkach ◽  
Marie Quintana
Keyword(s):  
Fracture Toughness ◽  
Adverse Effects ◽  
Weld Metal ◽  
Axial Stress ◽  
Limit Load ◽  
Allowable Stress ◽  
Simple Method ◽  
Weld Width ◽  
Girth Welds ◽  
Assessment Procedures

A relatively simple method based on standard fracture mechanics flaw assessment procedures, such as BS 7910, but modified using published mismatch limit load solutions is described. It is used to illustrate the effects of weld width and strength mismatch on CTOD requirements for girth welds in Grade X100 strength pipeline material subjected to axial stress. It is shown that fracture toughness requirements based on standard analyses not allowing for mismatch effects can be unnecessarily conservative when either undermatched or overmatched welds are present. Adverse effects of undermatching, in reducing the allowable stress, can be mitigated by reducing weld width. It is shown that even small amounts of overmatching (e.g. 10%) can be beneficial by allowing axial stress to exceed the SMYS of the parent pipe and reducing CTOD requirements.

scholarly journals A Dynamic Cavity Expansion Model for Rigid Projectile Penetration into Concrete considering the Compressibility and Nonlinear Constitutive Relations

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Fei Gao ◽  
Zhen Wang ◽  
Zhu Wen ◽  
Yuguo Ji
Keyword(s):  
Yield Criterion ◽  
Constitutive Relations ◽  
Cavity Expansion ◽  
Depth Of Penetration ◽  
Proposed Model ◽  
Rigid Projectile ◽  
Calculation Results ◽  
Expansion Model ◽  
Constitutive Parameters ◽  
Nonlinear Constitutive Relations

The P-α equation of state (EOS) and a nonlinear yield criterion are utilized to characterize the dynamic constitutive behavior of concrete targets subjected to projectile normal penetration. A dynamic cavity expansion model considering the compressibility and nonlinear constitutive relations for concrete material is developed. Then, a theoretical model to calculate the depth of penetration (DOP) for rigid projectile is established. Furthermore, the proposed model is validated based on the available test data as well as the calculation results by the linear compressible EOS and linear yield criterion. This study shows that the proposed model derived using the P-α EOS and nonlinear yield criterion can effectively reflect the plastic mechanical properties of concrete and is also suitable for predicting the DOP of concrete targets. In addition, the influence law of concrete constitutive parameters such as the cohesion strength, shear strength, internal friction coefficient, and elastic limit pressure on the DOP is revealed.

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.

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