The influence of the relationship between yield strength and temperature on the stress state in a thin hollow disk

A thin hollow elastoplastic or perfectly plastic disk placed in a rigid cylindrical container and subjected to the action of a temperature field is considered. The conditions of plane stress state are assumed. The Mises yield condition is satisfied in the plastic zone. The main feature of the problem formulation is in the relationship between yield strength and temperature, taken in arbitrary form. A parametric analysis of the solution is carried out for the linear relationship. It was shown that the relationship between yield strength and temperature needs to be taken into account for some materials to define the stress-strain state in the disk and to estimate the conditions of the transition of the whole disk to the plastic state.     

Integrated adaptive element free Galerkin model for elastoplastic contact of engineering surfaces

Abstract

This paper presents an h-adaptive element free Galerkin (EFG) model and its formulation based on stain energy gradient for solving elastoplastic contact problems. In this model, the element free Galerkin finite element (EFG–FE) coupling method uses the initial stiffness method, and an error estimation approach based on strain energy gradient and a local adaptive refinement strategy are combined. Two-dimensional elastic contact problem between a rigid cylinder and an elastic plane is analysed to validate the adaptive elastoplastic EFG model. The results indicate that the adaptively refined solutions are accurate as compared to the Hertz theoretical solution or the uniformly refined solutions, while the cost of CPU time used by the adaptive model is less than that by the uniformly refined model under the same condition. Furthermore, the elastoplastic contacts involving a rough surface of elastic perfectly plastic and elastoplastic properties are investigated.     

Elastic–plastic deformations of rotating variable thickness annular disks with free, pressurized and radially constrained boundary conditions

Analytical solutions for the elastic–plastic stress distribution in rotating variable thickness annular disks are obtained under plane stress assumption. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. The thickness of the disk is assumed to vary in parabolic form in radial direction which leads to hypergeometric differential equations for the solution. It is shown that, depending on the boundary conditions used, the plastic core may contain one, two or three different plastic regions governed by different mathematical forms of the yield criterion. The expansion of these plastic regions with increasing angular velocity is obtained together with the distributions of stress, displacement and plastic strain. It is also shown mathematically that in the limiting case the variable thickness disk solution reduces to the solution of rotating uniform thickness disk.     

无缺陷弯管的塑性极限载荷的统一解

采用双剪统一强度理论,分析等厚度薄壁弯管在内压作用下的塑性极限载荷问题,推导出塑性极限载荷统一表达式。在该表达式中,当其系数取不同的值时,就可得到按Tresca屈服准则、双剪统一屈服准则所得的结果,并能较好逼近Mises屈服准则所得的结果。     

Mathematical modeling of individual asperity sliding on the elastic-plastic half space

There is a solution to the contact problem for sliding on the elastoplastic half space of an individual asperity. It has been shown that the solution adequately reflects the mechanics of individual asperity sliding on the surface of an elastoplastic solid that begins with their interactions under elastic contact conditions and ending the interaction with perfect plastic contact.     

The plastic collapse of sandwich beams with a metallic foam core

Plastic collapse modes of sandwich beams have been investigated experimentally and theoretically for the case of an aluminium alloy foam with cold-worked aluminium face sheets. Plastic collapse is by three competing mechanisms: face yield, indentation and core shear, with the active mechanism depending upon the choice of geometry and material properties. The collapse loads, as predicted by simple upper bound solutions for a rigid, ideally plastic beam, and by more refined finite element calculations are generally in good agreement with the measured strengths. However, a thickness effect of the foam core on the collapse strength is observed for collapse by core shear: the shear strength of the core increases with diminishing core thickness in relation to the cell size. Limit load solutions are used to construct collapse maps, with the beam geometrical parameters as axes. Upon displaying the collapse load for each collapse mechanism, the regimes of dominance of each mechanism and the associate mass of the beam are determined. The map is then used in optimal design by minimising the beam weight for a given structural load index.     

An elastoplastic analysis of flange wrinkling in deep drawing process

The onset of flange wrinkling of a deep drawing cup is analyzed as an elastoplastic bifurcation problem. The flange is modeled as an elastoplastic annular plate subject to axisymmetric radial tension along its inner edge. As observed in the laboratory as well as practical industrial applications, aluminum alloy sheets usually wrinkle in the plastic range. Therefore, the critical condition governing the onset of elastoplastic wrinkling is formulated within the context of the general bifurcation theory. A closed-form solution for the critical drawing stress is developed based on an assumed nonlinear plastic stress field and the deformation theory of plasticity. The theory properly accounts for the plastic anisotropy of the aluminum sheets and the critical drawing stress at the onset of wrinkling is also compared against the one employing the flow theory of plasticity. The predicted critical bifurcation stress and the wave numbers are compared to those obtained by Senior's one-dimensional theory. It is demonstrated that there is a strong dependency of the critical bifurcated stress at the onset of wrinkling on the shear stress induced on the flange. The effects of flange width, drawing ratios, material properties, strain hardening on the onset of wrinkling are investigated. The differences between the present theoretical approach and Senior's theory are emphasized.     

A simulation of cold-roll forming for elastoplastic materials

A kinematical approach was proposed in a previous paper for predicting the optimal shape and the deformed length of a rigid-plastic metal sheet during cold-roll forming. Because the elastic effects are important in this kind of process, the method has been extended here to elastoplastic materials. In the new formulation, the sheet is still considered as a thin shell and its middle surface is described as a Coons patch depending on one geometrical parameter. Moreover, the material now satisfies a constitutive rate equation in which the corotational rate of stress is used. The Prandtl-Reuss model, including the von Mises yield criterion and the normality flow rule, is used. In order to integrate the elastoplastic constitutive equations, a radial return scheme is adapted so that the plastic power rate is calculated, using a Gauss method. Its minimization gives the optimal shape for a strain hardening elastoplastic material, as well as the optimal velocity field. This approach has been implemented on a workstation and, as for rigid-plastic materials, it gives a very fast simulation of the cold-roll forming process.     

Inelastic nonlinear behavior of steel trusses cooled down from a heating stage

This paper is to study the inelastic nonlinear behavior of steel trusses cooled down from a heating stage, a problem that was rarely investigated before. Bilinear elastoplastic model is adopted for steel. Softening of elastic modulus and yield stress at elevated temperatures is considered by the reduction factors of Eurocode3. The plastic strain resulting from strain reversal is included in the stress-strain curves. Instantaneous modulus is proposed for simulating the unloading (loading) behavior caused by cooling (heating). Both the thermal and plastic strains are considered in the force-displacement relation for truss members. The temperature-deflection curves obtained for a simple truss serve as the benchmark problem for checking the validity of other approaches in treating the heating and cooling stages. For general applications, the elastoplastic finite element derived was adopted to solve the cooling responses of preheated steel trusses by the Newton-Raphson method. The permanent deformation and residue stress computed for each member are useful for evaluating the reusability and safety of steel trusses after a fire attack.     

Elastic-plastic stress distribution in a rotating hyperbolic disk with rigid inclusion

The elastic-plastic stress distribution of a rotating hyperbolic annular disk mounted on a circular rigid shaft is investigated in this work. The exact solution presented is based on the usual assumptions of plane stress, Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. According to the present analysis the plastic core consists of three parts with different forms of the yield condition. The theory presented is illustrated by numerical results. The results show that the plastic flow and maximum stresses are influenced by the thickness parameter.     

The effect of doubly tapered strut morphology on the plastic yield surface of cellular materials

Although the literature on the mechanics of cellular materials is vast, there is no theoretical model to account for the effects of axial yielding of struts aligned to the applied loading direction on the plastic yield surface under multiaxial loading conditions. An anisotropic hexagonal model having tapered strut morphology is developed to show these effects on the plastic yield surface under multiaxial tensile loading condition. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square cellular materials, and three-dimensional (3D) hexagonal and rhombic cellular materials of rod-like columnar structure. A tetrahedral element with tapered strut morphology is also used for a foam model to illustrate these effects on the yield surface under axisymmetric loading condition. Plastic collapse due to bending moment in the inclined struts is a dominant mode. However, under multiaxial tensile loading, the collapse due to axial yielding of struts parallel to the loading direction is found to be an important mode. The shape of plastic yield surface was found to depend not only on relative density but also on the strut morphology.     

Shakedown theory for elastic-perfectly plastic bodies revisited

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter shakedown theory. Classical shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-shakedown collapse modes of elastic plastic structures.     

On bounding the life of structures subjected to steady load and operating within the creep range

The paper offers a simplified life assessment for structures nominally subjected to constant load and operating within the creep range. It is shown that the life of any structure, subjected to conditions where creep occurs, may be bounded by two procedures.In the particular case where the plastic yield surface is similar to the isochronous creep failure surface, the upper bound on life is obtained from a knowledge of the plastic collapse load. The lower bound approach requires a knowledge of the stationary state stress distribution. The authors argue that the actual time of failure relative to these bounds is governed by a material property rather than the geometry of the structure.The bounds on life have been applied to some simple structures where a more complete analysis or experimental data are available. It is shown that the upper bound solution gives a close approximation to the life of these structures provided that there is adequate ductility.     

Plastic collapse analysis of thin-walled pipes based on unified yield criterion

Based on a unified yield criterion (UYC), the plastic collapse analysis of thin-walled pipes is conducted in the framework of finite strain. A unified analytical solution for the burst pressure of end-capped defect-free pipes is derived, which is fit for various kinds of non-SD (strength differential) materials. A series of solutions can be deduced from this unified solution, and those solutions of burst pressure on the basis of Tresca, von Mises, ASSY, and TS criteria are special cases of it. By comparing with existing test result, it is found that the present unified solution is very convenient and effective for the prediction of burst pressure.     

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.     

Plastic deformation modes of regular hexagonal honeycombs under in-plane biaxial compression

A limit analysis approach is employed to identify the plastic deformation modes of regular hexagonal honeycombs with relatively large wall-thickness-to-length ratios under in-plane biaxial compression. An infinite block of honeycomb material is considered and a representative block consisting of four hexagonal cells is defined when assuming the kinematic admissibility of the modes and a periodic repeatability of the representative block in both spatial directions. In general, three plastic collapse modes are found to be preferable depending on the direction of loading, and in some particular cases they are similar to the modes that occur elastically under stress or strain controlled in-plane biaxial compression. It is shown that the critical forces at the onset of the plastic collapse depend on the assumed constraints for the deformation of the representative block. The results obtained from the theoretical analysis and the numerical simulations are compared and discussed.     

Analysis on collapse strength of casing wear

Carrying capacity of the casing will reduce after the casing is worn, which seriously affects the subsequent well drilling, well completion, oil extraction and well repair. A lot of researches on calculation of casing wear collapse strength have been done, but few of them focus on collapsing failure mechanism, and influencing factors and law of collapse strength. So, significant difference between estimated value and actual value of collapse strength comes into being. By theoretical analysis, numerical simulation and actual test, the collapsing failure mechanism of casing wear as well as the influencing factors and laws of collapse strength are investigated, and the investigation results show that collapse of crescent casing wear belongs to "three hinged" instability. The severely-worn position on the casing is yielded into the plastic zone first then deformed greatly, which causes the plastic instability of the whole structure. The casing wear collapse strength presents changes of exponent, power function and linear trend with the residual casing wall thickness, wear radius and axial load, respectively. When the flexibility is less than 10°/30 m, the borehole bending has less impact on casing collapse strength. Thus, the computation model for the casing wear collapsing strength is established by introducing wear radius coefficient and casing equivalent yield strength, at the same time, the model is tested. The test results show that the relative error for the computation model is less than 5%. The research results provide a basis for design of the casing string strength and evaluation of down-hole safety.     

On the rotating elastic–plastic solid disks of variable thickness having concave profiles

In this paper, an analytical solution for the elastic–plastic stress distribution in rotating variable thickness solid disks is presented. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. It is shown that depending on the shape of the disk profile, the radial stress in the central region may exceed the circumferential stress. The plastic zone which develops away from the axis of the disk consists of three annular regions governed by different mathematical forms of the yield criterion. The propagation of these plastic regions with increasing angular velocity is obtained together with the distributions of stresses and deformations in nondimensional forms.     

Deflection analysis of strain hardening structures under repeated loading

An efficient method of historical analysis using an initial strain approach coupled with the matrix flexibility method is developed for elastoplastic structures. The spread of inelastic straining along members is taken into account using a trilinear moment-curvature relationship with linear elastic unloading. Stresses are computed using a computer aided iterative numerical procedure, which converges rapidly. Theoretical results compare very well with published tests. The extent of the yield plateau is found to be the most critical parameter in the estimation of deflections.     

低频振动塑性成形粘弹塑性模型的体积效应分析

采用Kirchner对应变时间历程的基本假设,针对振动拉伸建立一个一维粘弹塑性模型;利用MATLAB中的符号计算,推导粘弹塑性本构方程的显式表达式.通过确立粘弹塑性边界并对本构方程进行数值求解,可以确定金属在振动加工过程中,其应力应变在粘弹性与粘塑性之间的变化情况.通过计算瞬时应变的大小与屈服限建立粘弹性变形和粘塑性变形的判断准则.在考虑粘弹塑性本构关系中的后继屈服情况、应变历程、应变率历程及弹性应变等因素后,可以确定单轴振动拉伸时材料变形的动态应力和平均应力.根据所给定的振型参数和材料力学性能参数,结合特定的振动拉伸实例,分别得出金属在准静态拉伸和振动拉伸时的动态应力-时间、动态应力-应变和平均应力-应变率的变化趋势等,实现基于粘弹塑性本构关系的低频振动塑性成形的体积效应机理分析.