Elastic-plastic fields near crack tip growing step-by-step in a perfectly plastic solid

In this paper, based on the three-dimensional flow theory of plasticity, the fundametal equations for plane strain problem of elastic-perfectly plastic solids are presented. By using these equations the elastic-plastic fields near the crack tip growing step-by-step in an elastic incompressible-perfectly plastic solid are analysed.The first order asymptotic solutions for the stress field and velocity fields near the crack tip are obtained. The solutions show the evolution process of elastic unloading domain and the development process of central fan domain and reveal the possibility of the presence of the secondary plastic domain. The second order asymptotic solution for stress field is also presented.     

Irreversible deformation and subsequent unloading of a spherical elastoviscoplastic layer

Analytical solutions of a number of one-dimensional quasi-static problems that describe the processes of elastic deformation of the material of a hollow sphere and of generation and development of the plastic flow in this material with increasing pressure on the external boundary are presented. The process of unloading during slow removal of the loading pressure is studied. Stress fields, fields of elastic and plastic strains in the material of the spherical layer, the law of motion of the elastoplastic boundary, and residual stresses are determined. It is demonstrated that (in contrast to the ideal plasticity case) the allowance for the viscous properties of the material during its plastic flow eliminates the possibility of plastic flow emergence during unloading.     

An experimental determination of the fields of strains and stresses in the elastoplastic range

In order to determine the fields of strains and stresses in the elastic and plastic ranges, for the plane-stress problem, a so-called chromorheological (CHR) model has been utilized. On one side of the model the development of plastic deformations, including the elastoplastic boundaries at any stage of loading, can be either visually observed or recorded on film. On the other side of the model, a birefringent coating is adhered from which regular experimental data can be obtained. These data, together with the yield condition, render the possibility of finding the state of stresses at all the points of the known elastoplastic boundaries. The problem of stress in the plastic range is statically determinate. The experiment provides all the data on the boundaries, and thereby the field of stresses in the plastic range can be calculated. The field of strains in the elastic and plastic zones can be obtained by the well-known method of photoelasticity. In this way, the relationship between stresses and strains in the plastic zones can be worked out. The effectiveness of the approach on a strip with a central hole has been proven by experimental research.     

On the measurement of elastoplastic stresses

In principle, one should be able to measure elastoplastic stresses in the same manner as one does elastic stresses; i.e., measure the strains and compute the stresses from the constitutive law. In practice, this is rarely done because of the more complicated material response and the anisotropy of the plastic behavior. Further, elastoplastic stresses should be computed incrementally in the general case. This paper presents procedures for computing stresses from elastoplastic strains measured incrementally in a test under microcomputer control. The approach is evaluated for four different materials—two obeying the assumptions of classical plasticity and two showing anisotropic behavior—by computing the stresses in a smooth specimen from measured principal strains. A useful application is presented by computing the stresses at a notch root from biaxial strains measured with laser-based interferometry. The general conclusion is that even in situations where the material is clearly anisotropic, this approach can give a reasonableestimate of the largest local principal stress. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

CLOSED-FORM SOLUTIONS FOR ELASTOPLASTIC PURE BENDING OF A CURVED BEAM WITH MATERIAL INHOMOGENEITY

The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.     

Unloading of an elastic–plastic loaded spherical contact

The process of unloading of an elastic–plastic loaded sphere in contact with a rigid flat is studied by finite element method. The sphere material is assumed isotropic with elastic-linear hardening. The numerical simulations cover a wide range of material properties and sphere radius. The contact load, stresses, and deformation in the sphere during both loading and unloading, are calculated for a wide range of interferences. Analytical dimensionless expressions are presented for the unloading load–deformation relation, the residual interference and the residual curvature of the sphere after complete unloading. A new measure termed elastic–plastic loading index is introduced to indicate the plasticity level of the loaded sphere. Some ideas regarding reversibility of the unloading process and elasticity of multiple loading unloading are also presented.     

Strengthening of materials by intensive hydrostatic compression pretreatment

A solution is given for a sequence of boundary value problems in the theory of large deformations of materials with elastic, plastic, and viscous properties. This sequence is related to viscoelastic deformation and determination of the time and location of the plastic flow origination, development of this flow, and the subsequent unloading of the medium with a single spherical continuity defect. The level and distribution of residual stresses near the defect and its final dimensions are calculated.     

A Procedure to Measure Biaxial Near Yield Residual Stresses Using the Deep Hole Drilling Technique

Deep Hole Drilling (DHD) is a mechanical strain relief technique used to measure residual stresses within engineering components. Such techniques measure strains or displacements when part of the component is machined away and typically assume elastic unloading. However, in components containing high levels of residual stress, elastic–plastic unloading can occur which may introduce substantial error. For the case of the DHD technique, a modification to the technique referred to here as the incremental or iDHD technique has been developed to allow such high levels of residual stress to be measured. Previous work has demonstrated the accuracy of the iDHD technique, although only for axisymmetric residual stress distributions. In the present investigation, the application of the iDHD technique has been extended to the general case of biaxial residual stress fields. Finite element simulations are first carried out to demonstrate the ability of the iDHD technique to measure biaxial residual stress. Experimental measurements were then made on shrink fit components and ring welded components containing biaxial residual stress to investigate the performance of the technique in practice. Good agreements between iDHD measurements, neutron diffraction measurements and FE predictions of the residual stresses were obtained, demonstrating the generally improved accuracy of the iDHD technique compared to the standard DHD approach.     

Stability of an elastoplastic sphere under external pressure

The stability of ideally plastic, elastoplastic, and reinforced elastoviscoplastic bodies subjected to large subcritical strains was investigated in [1–4], The problems solved in these papers were related to the stability of systems in which homogeneous stress and strain fields arise in the initial state. The stability of an elastic thick-walled spherical shell subjected to external pressure leading to large subcritical strains was investigated in [5]. The stability of an axisymmetric sphere of elastoplastic material subjected to large plastic strains is examined below.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 155–159, September–October, 1977.     

Technological thermal stresses in the shrink fitting of cylindrical bodies with consideration of plastic flows

This paper presents a solution of a sequence of one-dimensional boundary-value problems of thermal stresses defining the elastic–plastic deformation processes used in the shrink fitting of cylindrical bodies. The initiation and development of plastic flow in the materials of the assembly elements are studied taking into account the temperature dependence of the yield stress of these materials. During temperature equalization, the flow can slow down, followed by unloading and formation of a residual stress field providing tension. The conditions of formation and motion of the boundaries of the elastic and plastic states in plastic flow and during unloading are determined.     

Bending of a thin strip by a circular tool

We present a model of transverse bending of a wide thin elastic, elastoplastic, or rigid-plastic strip by a circular tool in the case of large displacements. The bending of the initial rectilinear strip is modeled by small increments in the load on the tool with analysis of the forces, moments, curvature, and the midline equation. The final form of the strip and the residual stresses are determined after elastic unloading. The model describes technological operations of sheet slab bending in dies and on roller-bending machines.     

可压缩理想塑性体中逐步扩展裂纹顶端的弹塑性场

本文利用理想塑性固体平面应变问题的基本方程,分析了可压缩理想塑性体中逐步扩展裂纹顶端的弹塑性场,得到了关于应力的渐近场,分析了弹性卸载区的演变过程和修正的中心扇形区的发展过程,预示了出现二次塑性区的可能性,弹性可压缩性的影响明显表现在经典的中心扇形区必需加以修正,垂直于板面方向的应力偏量不再为零,而且随着新裂纹面的形成,裂纹前方的均匀应力场和紧连着的修正的中心扇形区的应力偏量将发生变化,这种变化是由于垂直于板面方向的应力偏量发生变化造成的。     

各向同性材料中微裂纹的最大屏蔽效应

通过对微裂纹屏蔽不同来源的分析及计算,发现在各向同性脆性材料中,残余应力释放引起的微裂纹对主裂尖产生最大屏蔽效应时该微裂纹的倾角与最大张应力的方向没有明显的对应关系．在Hutchinson[1]所指出的屏蔽效应的第二个来源中,还应计及微裂纹形成引起的远场应力在微裂纹处产生的应力场的释放从而导致应力场的再分布．     

Hoek–Brown criterion applied to circular tunnel using elastoplasticity and in situ axial stress

Based on the nonlinear Hoek–Brown failure criterion, elastoplastic analytical solutions are developed for the elastoplastic stresses, strains and plastic zones around a circular tunnel subjected to different value of the axial in situ stress. Effects of the transverse in situ stress, the axial in situ stress and the strength parameters of rock masses on the elastoplastic stresses, strains and plastic zones in the surrounding rock masses are investigated. It is found from the numerical results that the stresses, strains, and plastic zones in the surrounding rock depend not only on the transverse in situ stress but also on the axial in situ stress as well as the mechanical parameters of rock masses.     

On the Residual Stresses in the Vicinity of a Cylindrical Discontinuity in a Viscoelastoplastic Material

The one-dimensional deformation of a material and subsequent unloading in the vicinity of a single cylindrical discontinuity is calculated using the theory of large viscoelastoplastic strains. Emphasis is on the formation of a residual stress field during the loading-unloading process and the effect of the viscous properties of the material on the level and distribution of these stresses. A comparison is performed with results of solution of the corresponding problem using the theory of large elastoplastic strains. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 110–119, March–April, 2006.     

The bending moment and springback in pure bending of anisotropic sheets

Finite deformation rigid plastic and elastic–plastic analyses of plane strain pure bending of a plastically anisotropic sheet is presented. An efficient method for finding the exact solution is proposed by extending the previously developed method to the stage of unloading. Using this method the solutions are obtained in closed form or reduced to a numerical treatment of ordinary integrals, or an ordinary differential equation, or transcendental equations. An effect of plastic anisotropy and elastic properties on the bending moment is analyzed. The distribution of residual stresses is illustrated and an effect of material and process parameters on springback is investigated.     

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadilypropagating in an elastic-perfectly plastic compressible material are considered under plane strain condi-tions. Within the framework of infinitesimal displacement gradient theory, the material is character-ized by the Von Mises yield criterion and the associated J_2 flow theory of plasticity. Through rigorousmathematical analysis, this paper eliminates the possibilities of elastic unloading and continuousasymptotic fields with singular deformation, and then constructs a fully continuous and boundedasymptotic stress and strain field. It is found that in this solution there exists a parameter (?)_0 whichcannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly thevariations of continuous stresses, velocities and strains around the crack tip are given numerically fordifferent values of (?)_0.     

Irreversible deformation with subsequent unloading of a spherical viscoelastoplastic layer

Analytic solutions are obtained for a sequence of one-dimensional quasistatic problems describing viscoelastic deformation processes in the material of a hollow ball and the plastic flow nucleation and evolution processes occurring in the ball as the pressure on the outer boundary increases. The unloading process under slow removal of the loading pressure is considered as well. The stress fields and the elastic and plastic strain fields in the spherical layer material, the law of motion of the elastoplastic boundary, and the residual stress level and distribution are computed. It is assumed that at the stage preceding the plastic flow the material obeys the viscoelastic Voigt model and the loading surface is determined by the von Mises plastic flow condition.     

Unloading of an elastic–plastic spherical contact under stick contact condition

The unloading process of an elastic–plastic spherical contact under stick contact condition is analyzed for various material properties. The evolution of normal and shear stress distribution at the contact area as well as the residual profile of the sphere and residual von Mises stresses inside the sphere are presented. Empirical expressions for the residual interference and for the evolution of the interference and contact area during the unloading are provided. Good agreement with experimental results is shown.     

Multiple loading–unloading of an elastic–plastic spherical contact

A model for multiple repeated loading and unloading of an elastic–plastic sphere and a rigid flat is presented to cover a wide range of loading conditions far beyond the elastic limit. The sphere material is modeled as elastic linear isotropic hardening and follows the von Mises yield criterion. It is shown that although most of the plastic deformation occurs during the first loading, secondary plastic flow may evolve during the first unloading. The occurrence of this secondary plastic flow depends on the level of first loading and is strongly affected by the Poisson’s ratio and material hardening. The region of secondary plastic flow may propagate during the very first loading–unloading cycles, reaching a steady state after which the following loading–unloading cycles become fully elastic.