Analysis and Design of Structures Made of Plastically Anisotropic Materials

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 December 2018) | Viewed by 24302

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Special Issue Editors

1. Laboratory of Technological Processes, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 119526 Moscow, Russia
2. School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Interests: plasticity theory; fracture mechanics; metal forming; structural mechanics
Special Issues, Collections and Topics in MDPI journals
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Interests: sheet metal forming; composite materials; ductile fracture
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Plastic anisotropy arises from different metal-forming processes, such as the production of rolled sheets, drawn sheets, extruded billets, and others. The most important cause of the anisotropic properties is the preferred orientation of grains. However, a quantitative treatment of plastic anisotropy is possible without regards to its crystallographic origin using this or that anisotropic yield criterion and a flow rule. The anisotropic yield criterion has a great effect on the analysis and design of structures and machine parts. The orthotropic form of anisotropy is most common. In this case, the anisotropic properties have two-fold symmetry. Another important form of anisotropy demands that a material has rotational symmetry about of the principal axes of anisotropy.

This Special Issue of Symmetry features articles about analytical and numerical methods of analysis and design of structures and machine parts assuming that the material is plastically anisotropic. We are soliciting contributions covering a broad range of topics including:  limit load, springback, stress intensity factor, defect assessment procedures, strain rate intensity factor, minimum weight and others. We are interested in contributions that show how this or that assumption concerning symmetry of anisotropic properties affects analysis and design of structures and machine parts. Articles devoted to the evolution of anisotropic properties of material in metal forming processes are also welcome with the understanding that the final result can be used for subsequent analysis and design of structures and machine parts.

Prof. Sergei Alexandrov
Prof. Lihui Lang
Guest Editors

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Keywords

  • plastic anisotropy
  • structures
  • machine parts
  • design

Published Papers (7 papers)

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Research

11 pages, 1060 KiB  
Article
Residual Stress Analysis of an Orthotropic Composite Cylinder under Thermal Loading and Unloading
by Somayeh Bagherinejad Zarandi, Hsiang-Wei Lai, Yun-Che Wang and Sergey Aizikovich
Symmetry 2019, 11(3), 320; https://doi.org/10.3390/sym11030320 - 04 Mar 2019
Cited by 2 | Viewed by 2172
Abstract
Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of [...] Read more.
Elastoplastic analysis of a composite cylinder, consisting of an isotropic elastic inclusion surrounded by orthotropic matrix, is conducted via numerical parametric studies for examining its residual stress under thermal cycles. The matrix is assumed to be elastically and plastically orthotropic, and all of its material properties are temperature-dependent (TD). The Hill’s anisotropic plasticity material model is adopted. The interface between the inclusion and matrix is perfectly bonded, and the outer boundary of the cylinder is fully constrained. A quasi-static, uniform temperature field is applied to the cylinder, which is analyzed under the plane-strain assumption. The mechanical responses of the composite cylinder are strongly affected by the material symmetry and temperature-dependent material properties. When the temperature-independent material properties are assumed, larger internal stresses at the loading phase are predicted. Furthermore, considering only yield stress being temperature dependent may be insufficient since other TD material parameters may also affect the stress distributions. In addition, plastic orthotropy inducing preferential yielding along certain directions leads to complex residual stress distributions when material properties are temperature-dependent. Full article
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18 pages, 2202 KiB  
Article
A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders
by Marina Rynkovskaya, Sergei Alexandrov and Lihui Lang
Symmetry 2019, 11(2), 280; https://doi.org/10.3390/sym11020280 - 22 Feb 2019
Cited by 7 | Viewed by 3132
Abstract
Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only [...] Read more.
Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke’s law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials. Full article
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10 pages, 411 KiB  
Article
Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution
by Sergei Alexandrov, Elena Lyamina, Pham Chinh and Lihui Lang
Symmetry 2019, 11(2), 270; https://doi.org/10.3390/sym11020270 - 20 Feb 2019
Viewed by 2290
Abstract
An infinite wedge of orthotropic material is confined between two rotating planar rough plates, which are inclined at an angle 2α. An instantaneous boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, [...] Read more.
An infinite wedge of orthotropic material is confined between two rotating planar rough plates, which are inclined at an angle 2α. An instantaneous boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, the solution being in closed form. The solution may exhibit the regimes of sliding or sticking at the plates. It is shown that the overall structure of the solution significantly depends on the friction stress at sliding. This stress is postulated by the friction law. Solutions, which exhibit sticking, may exist only if the postulated friction stress at sliding satisfies a certain condition. These solutions have a rigid rotating zone in the region adjacent to the plates, unless the angle α is equal to a certain critical value. Solutions which exhibit sliding may be singular. In particular, some space stress and velocity derivatives approach infinity in the vicinity of the friction surface. Full article
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15 pages, 12121 KiB  
Article
Generation of Numerical Models of Anisotropic Columnar Jointed Rock Mass Using Modified Centroidal Voronoi Diagrams
by Qingxiang Meng, Long Yan, Yulong Chen and Qiang Zhang
Symmetry 2018, 10(11), 618; https://doi.org/10.3390/sym10110618 - 09 Nov 2018
Cited by 31 | Viewed by 6775
Abstract
A columnar joint network is a natural fracture pattern with high symmetry, which leads to the anisotropy mechanical property of columnar basalt. For a better understanding the mechanical behavior, a novel modeling method for columnar jointed rock mass through field investigation is proposed [...] Read more.
A columnar joint network is a natural fracture pattern with high symmetry, which leads to the anisotropy mechanical property of columnar basalt. For a better understanding the mechanical behavior, a novel modeling method for columnar jointed rock mass through field investigation is proposed in this paper. Natural columnar jointed networks lies between random and centroidal Voronoi tessellations. This heterogeneity of columnar cells in shape and area can be represented using the coefficient of variation, which can be easily estimated. Using the bisection method, a modified Lloyd’s algorithm is proposed to generate a Voronoi diagram with a specified coefficient of variation. Modelling of the columnar jointed rock mass using six parameters is then presented. A case study of columnar basalt at Baihetan Dam is performed to demonstrate the feasibility of this method. The results show that this method is applicable in the modeling of columnar jointed rock mass as well as similar polycrystalline materials. Full article
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16 pages, 8161 KiB  
Article
Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks
by Woncheol Jeong, Sergei Alexandrov and Lihui Lang
Symmetry 2018, 10(9), 420; https://doi.org/10.3390/sym10090420 - 19 Sep 2018
Cited by 7 | Viewed by 2927
Abstract
Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses [...] Read more.
Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications. Full article
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10 pages, 23325 KiB  
Article
Investigation on the Effect of Type of Cooling on the Properties of Aluminum Alloy during Warm/Hot Hydromechanical Deep Drawing
by Gaoshen Cai, Chuanyu Wu and Dongxing Zhang
Symmetry 2018, 10(9), 362; https://doi.org/10.3390/sym10090362 - 26 Aug 2018
Cited by 5 | Viewed by 3114
Abstract
The warm sheet cylindrical deep drawing experiment of aluminum alloy was carried out and macro-mechanical properties and microstructure evolution of hydro-formed cups with different cooling medium were analyzed, which aimed to investigate the effects of different types of cooling on mechanical properties and [...] Read more.
The warm sheet cylindrical deep drawing experiment of aluminum alloy was carried out and macro-mechanical properties and microstructure evolution of hydro-formed cups with different cooling medium were analyzed, which aimed to investigate the effects of different types of cooling on mechanical properties and microstructure of cylindrical cups hydro-formed by warm Hydro-mechanical Deep Drawing (HDD). Results show that, under the condition of warm hydroforming, the mechanical properties such as yield stress and ultimate strength were influenced very little by air or water cooling. Grain coarsening of these hydro-formed cups can be inhibited to a certain extent with subsequent rapid water cooling. Moreover, it shows that the processing with warm sheet hydroforming and subsequent rapid cooling of 7075-O aluminum alloy has a positive significance in maintaining the stability of macro mechanical properties and inhibiting the degradation of the microstructure of materials. Full article
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17 pages, 726 KiB  
Article
Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model
by Michał Szymczyk, Marcin Nowak and Wojciech Sumelka
Symmetry 2018, 10(7), 282; https://doi.org/10.3390/sym10070282 - 13 Jul 2018
Cited by 9 | Viewed by 2892
Abstract
The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above [...] Read more.
The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme. Full article
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