Elastic-plastic Stress Distribution Research Articles

Elastic–Plastic Stress Distribution in a Rotating Annular Disk

The plane state of stress in an elastic–plastic rotating annular disk was studied. The analysis was based on the Mises yield criterion and its associated flow rule. The radius of the elastic–plastic boundary was found as a function of angular velocity. In particular, it was shown that this radius is sensitive to the magnitude of the angular velocity. The method of stress analysis developed is illustrated by numerical results. A comparison with the solution obtained using the Tresca yield criterion is given.

Three-Dimensional Finite Element Analysis of Tensile-Shear Spot-Welded Joints in Tensile and Compressive Loading Conditions

Three-dimensional finite element analysis is applied to verify mechanical behavior of spot welds for one, three and five spot welds under tensile and compressive loading conditions. The elastic-plastic stress distribution at edge of hot spot weld is used for strength calculations. To obtain exact and reliable results for finite element analysis of spot welds, which are generally very small relative to other dimensions, sub-modeling technique is applied. The proposed numerical calculation scheme allows one to take into account the material parameters and geometrical non-linearity effects related to a gap between thin plates, buckling, etc. We provide the analysis of elastic and elastoplastic behavior of specimens with various configuration of spot welds subjected to tensile and compressive axial loads.

Fatigue life duration prediction for welded spots by volumetric method

The mechanical behavior of spot-welds under tensile-shear for one, three and five spot-welds is investigated in detail. Volumetric approach is applied to find fatigue life duration of welded spots. The three-dimensional finite element models for different geometries, including gap effects and non-linear features of materials are applied to obtain fatigue life. The elastic–plastic stress distribution at edge of hot spot-weld is considered and effective stress, effective distance and notch strength reduction factor are obtained. The comparison between experimental and volumetric approach reveals good agreement with real fatigue life.

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.

On the Elastic–Plastic Deformation of a Rotating Disk Subjected to a Radial Temperature Gradient

Elastic–plastic stress distribution in a nonisothermal rotating annular disk is analyzed by the use of Tresca and von Mises criteria. An energy equation that accounts for the convective heat transfer with a variable heat transfer coefficient is modeled. For a given angular velocity, the steady temperature distribution in the disk is obtained by the analytical solution of the energy equation. Tresca yield criterion and its associated flow rule are used to obtain the analytical stress distributions for a linearly hardening material. A computational model is developed to analyze elastic–plastic deformations of the disk using von Mises yield criterion and its flow rule. This model incorporates Swift's hardening law to simulate linear as well as nonlinear hardening material behavior. It is shown that the stress distribution in the disk is affected significantly by the presence of the temperature gradient.

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.

指数硬化異材界面端弾塑性特異応力場の有限要素解析

The singular stress distribution around an interface edge of bonded different power-law hardening materials has been investigated by elastoplastic finite element analysis. The theoretical results based on the displacement-matching method has shown that the stress singularity depends only on the material with larger hardening exponent. However, the numerical results has shown that both the size of the yield zone and the elastic-plastic stress distribution are dependent of the material combination. It is found that there is a region within which the theoretical elastic-plastic solution is valid, but the size of such a region is strongly effected by the material combination. If the difference of the hardening exponent is small, the elastic-plastic theoretical solution may lose its physical meaning because its domain region is too small, and the logarithmic stress distribution near the interface edge behaves no longer as linear.

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.

Elastic–plastic solid disk with nonuniform heat source subjected to external pressure

The elastic–plastic stress distribution of a solid disk due to nonuniform heat source under external pressure is investigated in this work. The nonuniform heat generation rate q ̇ (r) is taken to be a function of the radial position in the form q ̇ (r)=q 0[1−n(r/a)] s] , where a denotes radius of the solid disk; q 0, n and s are constants. 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 this analysis, the plastic core in the general case consists of three parts with different forms of the yield condition. The present solution is illustrated by numerical results and is compared with uniform heat generation case. This work provides the basis for a comprehensive investigation of the influence of nonuniform heat generation.

Application of a new model proposal for fatigue life prediction on notches and key-seats

The aim of this paper is to introduce a new macro-mechanical model for fatigue life prediction, taking into consideration an elastic–plastic stress distribution and the stress gradient evolution. Mainly based on the stress field intensity approach, this new model tries to better take into account the role of the most important factors influencing the fatigue failure process. A very brief review of some previous models facilitates the comparison between these approaches and fatigue test results obtained on notched specimens with two different radii. A description of the stress field intensity model is then given, followed by the new model in more detail. In order to better verify the fatigue life prediction given by this method on another kind of notch geometry, a comparison between the method and test results on the rotating bending of specimens with key-seats, is carried out. In all cases, the fatigue life predictions obtained by use of this method, are in very good agreement with the respective test results.

Induction heating of large steel disks: Coupled electromagnetic, thermal and mechanical simulation

The coupled electromagnetic, thermal and mechanical simulation is described for new technological processes of induction heating of large steel disks. Non-uniform temperature distribution of induction heated disks may cause plastic deformations and buckling. The goal of this investigation is to determine the mechanical behaviour of induction heated disks by means of coupled finite element computation in different formulations. The paper contains the detailed description of an applied numerical technique and of obtained results including elastic-plastic stress distribution, plastically deformed state and the most likely modes of the disk buckling.

Elastic-Plastic Stresses in Rotating Discs by von Mises and Tresca

The von Mises and Tresca yield criteria are combined with an equilibrium equation to provide the elastic-plastic stress distribution within the discs rotating at high speed. The Tresca criterion provides a closed solution that is traditionally associated with this problem. This paper examines and compares this with an alternative solution from the von Mises criterion. The latter requires that a suitable numerical solution to a govening differential equation is matched to the boundary conditions. For this a Runge-Kutta and a predictor-corrector method are combined to ensure a state of yield and continuity in stress at the interface between the inner core of perfectly plastic material and the outer elastic annulus. A comparison between the two solutions in a hollow disc shows that Tresca advances the elastic-plastic interface further than von Mises for a given speed. Thus, the Tresca prediction to the fully plastic speed is lower. The distributions of radial and hoop stress corresponding to the two criteria show only subtle differences within the elastic-plastic speed range for this disc. By contrast, in a solid disc there is a marked difference in the radial stress predictions. This alters the distribution of residual stress and the apparent benefit that can be gained from compressive residual stress when pre-stressed discs are raised to their operating elastic speeds.

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.

Modelling of rotational factor in notched bend specimen under general and local yield situation

The location of the plastic hinge axis in a three point SEN bend specimen is a highly controversial issue. An unambiguous and reliable estimation of rotational factor ( r p) is very essential for the accurate determination of CTOD data. In contrast to the numerous studies reported on the r p determination in a cracked situation, limited information is available for a blunt notch situation, although many engineering structures do contain notchlike defects with finite root radius. An attempt is made to determine r p for two situations, namely well below the general yield and around the general yield. The work is based on a theoretical estimation of the plastic zone size using the stress concentration factor and the elastic as well as the elastic-plastic stress distribution. A theoretical estimation of r p in both the pseudo-elastic and the elastic-plastic situation is estimated through analytical modelling involving factors like plastic zone size, bend angle and notch opening displacement. The values of the rotational factor are found to increase from a small value to around 0.29 in a well below general yield situation to 0.53 to 0.54 in a general yield situation with continued loading. A wide discrepancy in the P P GY ratio separating the two situations, i.e. well below general yield and around general yield, is observed. Consideration of the elastic and the elasto-plastic stress distribution indicates a much smaller value of P P GY as compared to the ratio obtained from experimental load-displacement plots.

Plastic node method considering strain-hardening effects

Extending the basic theory of the plastic node method (PNM), a general theory for the elasticplastic analysis of structures considering strain-hardening effects is proposed. In the plastic node method, plastic deformations of a finite element are concentrated at the nodes, while the inside of the element remains elastic. A strain-hardening rate for the plastic nodal displacement is proposed by equating the plastic work done at the plastic node with that evaluated in the actual elastic-plastic stress distribution within the element. For framed structures, this nodal-point strain-hardening rate gives a reasonable definition of strain-hardening rate at a plastic hinge subjected to combined loads. Two yield criteria for beam-column and shell elements are employed, one of which is based on a full plastic condition, while in the second criterion an intermediate plastic state between the initial yielding and the full yielding of sections is taken into account. Applying the extended theory of plastic node method, several examples including an elastic-plastic large deflection analysis of plates are shown, and the validity and usefulness of the proposed method are demonstrated.

Elastic-plastic stress distribution in the rotating annular disk with variable thickness

The plane state of stress in a rotating annular disk with variable thickness is studied. The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening.

Elastic-Plastic Analysis of Framed Structures under Cyclic Loads by Plastic Node Method

Extending the basic theory of Plastic Node Method (PNM), a new method of elastic-plastic analysis of framed structures considering combined strain-hardening effects is developed. The proposed method is applied to two and three-dimensional frames under cyclic loads. In the PNM, a generalized hinge mechanism (plastic node) based on the flow theory of plasticity is introduced at a node of beam-column elements. A strain-hardening rate for the plastic node is obtained by equating a plastic work done at the plastic node with that evaluated in the actual elastic-plastic stress distribution in the element. The resulting elastic-plastic stiffness matrix can be derived simply by matrix calculation. The numerical results are compared with those calculated by FEM program MARC. It was shown that the proposed. method provides very accurate results in a short computation time.

Influences of grain size and precracking load on the critical stress intensity factor of mild steel

The effects of grain size and precracking load on the critical stress intensity factor are studied. A plane stress model of elastic-plastic stress distribution which includes the strain hardening effects is used. The effects of residual stresses and strain hardening due to fatigue load are calculated by choosing plastic zone size as fracture criterion. Experimental results are obtained to demonstrate the reliability of theoretical calculations.

Elastic-plastic stress distribution in a rotating solid shaft

Based on Tresca's yield condition and the associated flow rule, the stress distribution in a rotating solid cylinder of elastic-perfectly plastic material under plane strain is discussed. It is shown that the plastic core consists of two parts with different regimes of the yield condition. With increasing angular velocity, a second plastic zone forms at the boundary and spreads inwards.

Elastic-plastic stress distribution around a circular drift under V. V. Sokolovskii plasticity conditions

Elastic-plastic stress distribution around a circular drift under V. V. Sokolovskii plasticity conditions