Incremental Stress-Strain Law Applied to Work-Hardening Plastic Materials

1959 ◽  
Vol 26 (4) ◽  
pp. 594-598
Author(s):  
Chintsun Hwang
Keyword(s):  
Work Hardening ◽  
Yield Condition ◽  
Transverse Load ◽  
Rational Approach ◽  
Total Stress ◽  
Stress Strain ◽  
Hardening Material ◽  
Plastic Materials ◽  
Von Mises ◽  
Supported Work

Abstract For problems involving work-hardening plastic materials, the incremental stress-strain law is considered to be a more rational approach than the conventional total stress-strain law. Up to the present the incremental stress-strain law was not subject to widespread use because it is mathematically inconvenient to handle. In this paper a method is developed in which the incremental law is applied to a work-hardening material in plane stress corresponding to the yield condition of von Mises. The method is illustrated by an analysis of the plastic bending of a simply supported work-hardening circular plate under uniformly distributed transverse load. The resulting difference-differential equations are solved by the NCR 304 digital computer.

A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids

1956 ◽  
Vol 23 (4) ◽  
pp. 493-496
Author(s):  
William Prager
Keyword(s):  
Work Hardening ◽  
Yield Condition ◽  
Transverse Load ◽  
Flow Rule ◽  
Total Stress ◽  
Stress Strain ◽  
Hardening Material ◽  
Characteristic Features ◽  
Associated Flow Rule ◽  
Yield Conditions

Abstract For work-hardening plastic solids, segmentwise linear yield conditions and the associated flow rules constitute a reasonable compromise between the mathematically convenient but physically unsound total stress-strain laws and the physically sound but mathematically inconvenient incremental laws. They allow total stress-strain laws to be used in the small, but retain the characteristic features of incremental laws in the large. The use of a segmentwise linear yield condition and the associated flow rule is illustrated by the analysis of the bending moments and deflections of a simply supported circular plate that is made of a work-hardening material and subjected to a uniformly distributed transverse load.

An Application of Incremental Plasticity Theory to Fatigue Life Prediction of Steels

1991 ◽  
Vol 113 (4) ◽  
pp. 404-410 ◽  
Author(s):  
W. R. Chen ◽  
L. M. Keer
Keyword(s):  
Fatigue Life ◽  
Life Prediction ◽  
Kinematic Hardening ◽  
Yield Condition ◽  
Strain Curve ◽  
Fatigue Life Prediction ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Stress Strain ◽  
Von Mises

An incremental plasticity model is proposed based on the von-Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and the uniaxial fatigue test results on smooth specimens. Experimental data of 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional loadings are given by this model

Plastic Wave Speeds in Isotropically Work-Hardening Materials

1977 ◽  
Vol 44 (1) ◽  
pp. 68-72 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Work Hardening ◽  
Wave Speed ◽  
Three Dimensional ◽  
Yield Condition ◽  
Elastic Response ◽  
Plastic Wave ◽  
Wave Speeds ◽  
Shear Wave Speed ◽  
Perfectly Plastic ◽  
Von Mises

Plastic wave speeds in materials whose elastic response is linear and isotropic while the plastic flow is incompressible and isotropically work-hardening are obtained. One of the three plastic wave speeds is identical to the elastic shear wave speed regardless of the form of the yield condition. The other two plastic wave speeds, cf and cs, are determined for materials obeying the von Mises yield condition. The dependence of cf and cs on the stress state and the direction of propagation is investigated in detail. The largest and smallest cf and cs, and the directions along which they occur are also presented. For materials obeying the Tresca’s yield condition, it is shown that one can obtain the corresponding results by simply specializing the results for the von Mises materials. Unlike in one-dimensional analyses where the plastic wave speed becomes zero for perfectly plastic solids, the three-dimensional analyses show that the ratio of cf to c1, where c1 is the elastic dilatation wave speed, is always larger than 3/7 for the von Mises materials and 1/2 for the Tresca’s materials. For most materials under moderate loadings, this ratio is much higher.

Thermal Stresses in an Elastic, Work-Hardening Sphere

1960 ◽  
Vol 27 (4) ◽  
pp. 629-634 ◽  
Author(s):  
Chintsun Hwang
Keyword(s):  
Work Hardening ◽  
Thermal Stresses ◽  
Yield Condition ◽  
Numerical Data ◽  
Spherical Body ◽  
Thermal And Mechanical Properties ◽  
Plastic Range ◽  
Cooling Process ◽  
Von Mises ◽  
Transient Thermal

In this paper, a method is presented for obtaining the transient thermal-stress distribution and the residual stresses in a spherical body where the time-dependent temperature distribution is symmetrical with respect to the center of the sphere. The material is assumed to be elastoplastic, while in the plastic range it work-hardens isotropically. The von Mises yield condition is used. The thermal and mechanical properties of the material are assumed to be temperature independent. The problem is reduced to a single nonlinear differential equation which is solved numerically on the NCR 304 digital computer. Several sets of numerical data representing various degrees of work-hardening in the spherical bodies during a cooling process are presented.

Optimization of Stepped Elastic Plastic Plates

2013 ◽  
Vol 742 ◽  
pp. 209-214 ◽  
Author(s):  
Jaan Lellep ◽  
Boriss Vlassov
Keyword(s):  
Algebraic System ◽  
Yield Condition ◽  
Necessary Optimality Conditions ◽  
System Of Equations ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Differential Algebraic System ◽  
Theory Of Optimal Control ◽  
Von Mises ◽  
Elastic Plastic Materials

A method of analysis and optimization of stepped plates made of elastic plastic materials is developed. The stress-strain of the plate is defined for the initial elastic and subsequent elastic plastic stages of deformation. Necessary optimality conditions are derived with the aid of variational methods of the theory of optimal control. This results in a differential-algebraic system of equations. The latter is solved numerically. The effectivity of the design established is assessed in the cases of one-and multi-stepped plates assuming the material obeys the Tsai-Wu or von Mises yield condition.

On the Use of Singular Yield Conditions and Associated Flow Rules

1953 ◽  
Vol 20 (3) ◽  
pp. 317-320
Author(s):  
William Prager
Keyword(s):  
Plastic Deformation ◽  
Closed Form ◽  
Circular Hole ◽  
Work Hardening ◽  
Yield Condition ◽  
Flow Rule ◽  
System Of Equations ◽  
Hardening Material ◽  
Perfectly Plastic ◽  
Yield Conditions

Abstract It is well known that the use of Tresca’s yield condition frequently leads to a simpler system of equations for the stresses in a plastic solid than the use of the yield condition of Mises. However, in most cases where Tresca’s yield condition has been used, the flow rule associated with the Mises condition has been retained. Following Koiter, it is shown that further simplification results from the use of the flow rule associated with the Tresca condition. The reason for this is discussed in connection with two examples concerning the finite enlargement of a circular hole in an infinite sheet of perfectly plastic or work-hardening material. The second example is probably the first nontrivial case in which a problem of finite plastic deformation of a work-hardening material has been treated in closed form by the use of incremental stress-strain relations.

MODELING OF THE STRESS-STRAIN STATE OF A TRANSPORT TUNNEL UNDER LOAD AS A MEASURE TO REDUCE OPERATIONAL RISKS TO TRANSPORTATION FACILITIES

2020 ◽  
Vol 3 (8) ◽  
pp. 28-34
Author(s):  
N. V. IVANITSKAYA ◽  
◽  
A. K. BAYBULOV ◽  
M. V. SAFRONCHUK ◽  
◽  
...  
Keyword(s):  
Strain State ◽  
Moving Load ◽  
Element Model ◽  
Transport Infrastructure ◽  
Design Stage ◽  
Surface Load ◽  
Stress Strain ◽  
Stress Strain State ◽  
Operational Risks ◽  
Von Mises

In many countries economic policy has been paying increasing attention to the modernization and development of transport infrastructure as a measure of macroeconomic stimulation. Tunnels as an important component of transport infrastructure save a lot of logistical costs. It stimulates increasing freight and passenger traffic as well as the risks of the consequences of unforeseen overloads. The objective of the paper is to suggest the way to reduce operational risks of unforeseen moving load by modeling of the stress-strain state of a transport tunnel under growing load for different conditions and geophysical parameters. The article presents the results of a study of the stress-strain state (SSS) of a transport tunnel exposed to a mobile surface load. Numerical experiments carried out in the ANSYS software package made it possible to obtain diagrams showing the distribution of equivalent stresses (von Mises – stresses) according to the finite element model of the tunnel. The research results give grounds to assert that from external factors the stress state of the tunnel is mainly influenced by the distance to the moving load. The results obtained make it possible to predict in advance the parameters of the stress-strain state in the near-contour area of the tunnel and use the results in the subsequent design of underground facilities, as well as to increase their reliability and operational safety. This investigation gives an opportunity not only to reduce operational risks at the design stage, but to choose an optimal balance between investigation costs and benefits of safety usage period prolongation.

Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

Numerical Modeling and Analytical Investigation of Autofrettage Process on the Fluid End Module of Fracture Pumps

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Mahdi Kiani ◽  
Roger Walker ◽  
Saman Babaeidarabad
Keyword(s):  
Residual Stresses ◽  
Kinematic Hardening ◽  
Analytical Formula ◽  
Strain Analysis ◽  
Material Model ◽  
Analytical Investigation ◽  
Stress Strain ◽  
Element Analysis ◽  
Hardening Material ◽  
Strain Evolution

One of the most important components in the hydraulic fracturing is a type of positive-displacement-reciprocating-pumps known as a fracture pump. The fluid end module of the pump is prone to failure due to unconventional drilling impacts of the fracking. The basis of the fluid end module can be attributed to cross bores. Stress concentration locations appear at the bores intersections and as a result of cyclic pressures failures occur. Autofrettage is one of the common technologies to enhance the fatigue resistance of the fluid end module through imposing the compressive residual stresses. However, evaluating the stress–strain evolution during the autofrettage and approximating the residual stresses are vital factors. Fluid end module geometry is complex and there is no straightforward analytical solution for prediction of the residual stresses induced by autofrettage. Finite element analysis (FEA) can be applied to simulate the autofrettage and investigate the stress–strain evolution and residual stress fields. Therefore, a nonlinear kinematic hardening material model was developed and calibrated to simulate the autofrettage process on a typical commercial triplex fluid end module. Moreover, the results were compared to a linear kinematic hardening model and a 6–12% difference between two models was observed for compressive residual hoop stress at different cross bore corners. However, implementing nonlinear FEA for solving the complicated problems is computationally expensive and time-consuming. Thus, the comparison between nonlinear FEA and a proposed analytical formula based on the notch strain analysis for a cross bore was performed and the accuracy of the analytical model was evaluated.

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