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.

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.

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.

Effect of three-dimensional deformation on the limit load of highly weld strength undermatched specimens under tension

2008 ◽  
Vol 222 (2) ◽  
pp. 107-115 ◽  
Author(s):  
S Alexandrov ◽  
M Kocak
Keyword(s):  
Upper Bound ◽  
Metal Forming ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Limit Load ◽  
Weld Strength ◽  
Structural Applications ◽  
Analytical Formulae ◽  
Current Article ◽  
Assessment Procedures

In the case of welded structures with cracks, a number of parameters, such as those with units of length, makes it difficult to present the results of numerical solutions in a form convenient for direct engineering applications, such as flaw assessment procedures. For centre-cracked components under tension, it is shown in the current article that an effect of crack length on the limit load can be taken into account by means of an upper bound limit load for the corresponding structure with no crack without any additional numerical treatment. Using this result, it is sufficient to find an upper bound limit load for the structure with no crack and then to apply the analytical formulae for finding the corresponding limit load for the structure of interest. Welding of some aluminium alloys for structural applications usually leads to a significantly lower strength (undermatched) weld joint. The approach proposed is used to demonstrate an effect of three-dimensional deformation on an upper bound limit load for such highly strength undermatched centre-cracked welded specimens under tension. This result can also be used in metal-forming applications where upper bound solutions are more useful than lower bound solutions.

Elastoplastic Solution and Limit Load Analysis of Orthotropic Cylindrical Shell Subjected to Internal Pressure

2019 ◽  
Author(s):  
Yujie Zhao ◽  
Min Xu ◽  
Chunxiao Li ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Shell Structure ◽  
Elastic Limit ◽  
Yield Criterion ◽  
Orthotropic Cylindrical Shell ◽  
Three Dimensional ◽  
Limit Load ◽  
Pressure Vessels ◽  
Plastic Limit ◽  
Plastic Limit Load

Abstract Cylindrical shell structure is widely used in pressure vessels. In this paper, the orthotropic cylindrical shell structure is analyzed based on the theory of elastoplastic mechanics and the Hill48 yield criterion, the elastoplastic limit load expression of the orthotropic cylindrical shell and the corresponding three-dimensional stress formulas at different stages are obtained. The effect of the radius ratio and the yield strength ratio on the elastic limit load and plastic limit load of the cylindrical shell are also discussed. Finally, the orthotropic cylindrical shell structure is simulated by finite element method, the numerical results verify the correctness of the analytical solutions.

Modelling of Shockwave Propagation in Orthotropic Materials

2013 ◽  
Vol 315 ◽  
pp. 557-561 ◽  
Author(s):  
Mohd Khir Mohd Nor ◽  
Rade Vignjevic ◽  
James Campbell
Keyword(s):  
Stress Tensor ◽  
Elastic Anisotropy ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Deformation Gradient ◽  
Tensor Decomposition ◽  
Material Model ◽  
Yield Function ◽  
Orthotropic Materials ◽  
Free Energy Function

Modelling of shockwave propagation in orthotropic materials requires an appropriate description of material behaviour within elastic and plastic regimes. To deal with this issues, a finite strain constitutive model for orthotropic materials was developed within a consistent thermodynamic framework of irreversible process in this paper. The important features of this material model are the multiplicative decomposition of the deformation gradient and a Mandel stress tensor combined with the new stress tensor decomposition generalised for orthotropic materials. The elastic free energy function and the yield function are defined within an invariant theory by means of the introduction of the structural tensors. The plastic behaviour is characterised within the associative plasticity framework using the Hills yield criterion. The complexity was further extended by coupling the formulation with the equation of state (EOS) to control the response of the material to shock loading. This material model which was developed and integrated in the isoclinic configuration provides a unique treatment for elastic and plastic anisotropy. The effects of elastic anisotropy are taken into account through the stress tensor decomposition and plastic anisotropy through yield surface defined in the generalized deviatoric plane perpendicular to the generalised pressure. To test its ability to describe shockwave propagation, the new material model was implemented into the LLNL-DYNA3D code. The results generated by the proposed material model were compared against the experimental Plate Impact test data of Aluminium Alloy 7010. A good agreement between experimental and simulation was obtained for two principal directions of material orthotropy.

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 Thermoplastic Materials for the Process-Simulation of Press-Fit Interconnections on Moulded Interconnected Devices

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Thomas Fellner ◽  
Elena Zukowski ◽  
Jürgen Wilde ◽  
H. Kück ◽  
H. Richter ◽  
...  
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Base Material ◽  
Creep Model ◽  
Assembly Process ◽  
Temperature Dependent ◽  
Reliability Modeling ◽  
Finite Element Software ◽  
Press Fit ◽  
Temperature Loads

This investigation is aimed at the modeling of both the fabrication process and the reliability of press-fit interconnections on moulded interconnect devices (MID). These are multifunctional three-dimensional substrates, produced by thermoplastic injection moulding for large-series applications. The assembly process and subsequently the durability of press-fit interconnections has been modeled and proved with a finite element software. Especially, a simulation tool for process optimizations was created and applied. In order to obtain realistic results, a creep model for the investigated base material, a liquid-crystal polymer (LCP), was generated and verified by experiments. Required friction coefficients between metal pin and base material were determined by adapting simulations and experiments. Retention forces of pins pressed into substrate holes during as well after the assembly process, and after temperature loads were predicted by simulations. Additionally, the decreasing extraction forces over time due to creep in the thermoplastic base material have been predicted for different storage temperatures as well with finite element analyses. Following, the numerical results of the process and reliability modeling were verified by experiments. It is concluded that the behavior of the mechanical contact of the pin-substrate system, can be suitably described time- and temperature-dependent.

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

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