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.

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.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

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.

Limit Analyisis of Frame Structure Based on the Elastic Modulus Reduction Method

2014 ◽  
Vol 578-579 ◽  
pp. 950-953
Author(s):  
Qiu Hua Duan ◽  
Yan Qing Guo ◽  
Dan Dan Zeng ◽  
Yue Jing Luo
Keyword(s):  
Elastic Modulus ◽  
Reduction Method ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Frame Structure ◽  
Structure Damage ◽  
Linear Elastic ◽  
Element Bearing ◽  
Modulus Reduction

An efficient linear elastic iterative finite element method, namely, the elastic modulus reduction method is introduced to calculate limit load of frame structure. The elastic modulus reduction method defines the element bearing ratio on the basis of the generalized yield criterion and the strain energy equilibrium principle. Because the bending moment is the main factor inducing the frame structure damage, the element bearing ratio only considering the bending moment yield is proposed. Numerical examples demonstrate the applicability and precision of the elastic modulus reduction method for limit analysis of frame structures.

Limit Load Solutions for Surface Cracks in Plates Under Different Loading Types

2002 ◽  
Author(s):  
Peter Dillstro¨m ◽  
Iradj Sattari-Far
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Crack Length ◽  
Crack Depth ◽  
Limit Load ◽  
Surface Cracks ◽  
Pure Bending ◽  
Element Analysis ◽  
Linear Finite Element ◽  
Cracked Plates

Limit load solutions of plates containing surface cracks are determined using non-linear finite element analysis. The study covers both shallow and deep cracks with different crack length/crack depth ratios under different loading types. The crack configurations consist of semi-elliptical surface cracks with a/t = 0.20, 0.40, 0.60, 0.80 and l/a = 2, 5, 10. Also studied are plates containing infinite surface cracks with a/t = 0.00, 0.20, 0.40, 0.60, 0.80. The cracked plates are subjected to pure tension, pure bending and combined tension and bending. The finite element results obtained from this study are compared with some published limit load solutions in the literature. It is shown that the exiting solutions are in general overly conservative.

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.

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