Experimental Solution of Elastic-Plastic Plane-Stress Problems

1962 ◽  
Vol 29 (4) ◽  
pp. 735-743 ◽  
Author(s):  
P. S. Theocaris
Keyword(s):  
Plane Stress ◽  
Yield Condition ◽  
Strain Curve ◽  
Loading Path ◽  
Flow Rule ◽  
Stress And Strain ◽  
Stress Strain ◽  
Plane State ◽  
Elastic Plastic ◽  
Principal Strains

The paper presents an experimental method for the solution of the plane state of stress of an elastic-plastic, isotropic solid that obeys the Mises yield condition and the associated flow rule. The stress-strain law is an incremental type law, determined by the Prandtl-Reuss stress-strain relations. The method consists in determining the difference of principal strains in the plane of stress by using birefringent coatings cemented on the surface of the tested solid. A determination of relative retardation using polarized light at normal incidence, complemented by a determination in two oblique incidences at 45 deg along with the tracing of isoclinics, procures enough data for obtaining the principal strains all over the field. The calculation of the elastic and plastic components of strains is obtained in a step-by-step process of loading. It is assumed that during each step the Cartesian components of stress and strain remain constant. The stress increments and the stresses can be found thereafter by using the Prandtl-Reuss stress-strain relations and used for the evaluation of the components of strains and their increments in the next step. The method can be used with any material having any arbitrary stress-strain curve, provided that convenient formulas are established relating the stress and strain components and their increments at each point of the loading path. The method is applied to an example of contained plastic flow in a notched tensile bar of an elastic, perfectly plastic material under conditions of plane stress.

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

On Thick-Walled Cylinder Under Internal Pressure

2003 ◽  
Vol 125 (3) ◽  
pp. 267-273 ◽  
Author(s):  
W. Zhao ◽  
R. Seshadri ◽  
R. N. Dubey
Keyword(s):  
Internal Pressure ◽  
Strain Curve ◽  
Stress Strain ◽  
Piecewise Linearization ◽  
Elastic Plastic ◽  
Plastic Cylinder ◽  
Parametric Functions ◽  
The Difference ◽  
New Formulation ◽  
Walled Cylinder

A technique for elastic-plastic analysis of a thick-walled elastic-plastic cylinder under internal pressure is proposed. It involves two parametric functions and piecewise linearization of the stress-strain curve. A deformation type of relationship is combined with Hooke’s law in such a way that stress-strain law has the same form in all linear segments, but each segment involves different material parameters. Elastic values are used to describe elastic part of deformation during loading and also during unloading. The technique involves the use of deformed geometry to satisfy the boundary and other relevant conditions. The value of strain energy required for deformation is found to depend on whether initial or final geometry is used to satisfy the boundary conditions. In the case of low work-hardening solid, the difference is significant and cannot be ignored. As well, it is shown that the new formulation is appropriate for elastic-plastic fracture calculations.

scholarly journals Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Longling Fan ◽  
Jing Yao ◽  
Chun Yang ◽  
Dalin Tang ◽  
Di Xu
Keyword(s):  
Wall Thickness ◽  
Material Properties ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain ◽  
Material Stiffness ◽  
The Mean ◽  
Lv Volume ◽  
Parameter Values

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress–strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress–strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole–diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Elastic-Plastic Stress Distribution in a Plastically Anisotropic Rotating Disk

2004 ◽  
Vol 71 (3) ◽  
pp. 427-429 ◽  
Author(s):  
N. Alexandrova ◽  
S. Alexandrov
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Rotating Disk ◽  
Flow Rule ◽  
Plane State ◽  
Annular Disk ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Associated Flow Rule

The plane state of stress in an elastic-plastic rotating anisotropic annular disk is studied. To incorporate the effect of anisotropy on the plastic flow, Hill’s quadratic orthotropic yield criterion and its associated flow rule are adopted. A semi-analytical solution is obtained. The solution is illustrated by numerical calculations showing various aspects of the influence of plastic anisotropy on the stress distribution in the rotating disk.

The Elastic-Plastic Analysis of Tubes—II: Variable Loading

1992 ◽  
Vol 114 (2) ◽  
pp. 222-228 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Closed Form Solution ◽  
Yield Condition ◽  
Complex Loading ◽  
Form Solution ◽  
Stress And Strain ◽  
Variable Loading ◽  
Elastic Plastic ◽  
Incremental Method ◽  
Plastic Analysis ◽  
General Program

This paper is concerned with the elastic-plastic analysis of tubes subjected to variable loads. The yield condition for a material having residual stress and strain is first derived. Then by incremental method, the stresses and strains of the tube at any loading stage can be found. A closed-form solution is achieved as an example of tubes incurring ratchetting, and a general program is developed to make the theory applicable to complex loading situations.

Further Investigation of the Hydrostatic Bulge Test in a Plasticity Laboratory

2009 ◽  
Vol 37 (2) ◽  
pp. 159-174
Author(s):  
O. Ifedi ◽  
Q. M. Li ◽  
Y. B. Lu
Keyword(s):  
Tensile Test ◽  
Effective Stress ◽  
Strain Curve ◽  
Plasticity Theory ◽  
Loading Path ◽  
Uniaxial Tensile ◽  
Bulge Test ◽  
Uniaxial Tensile Test ◽  
Stress Strain Curve ◽  
Stress Strain

In plasticity theory, the effective stress–strain curve of a metal is independent of the loading path. The simplest loading path to obtain the effective stress–strain curve is a uniaxial tensile test. In order to demonstrate in a plasticity laboratory that the stress–strain curve is independent of the loading path, the hydrostatic bulge test has been used to provide a balanced biaxial tensile stress state. In our plasticity laboratory we compared several different theories for the hydrostatic bulge test for the determination of the effective stress–strain curve for two representative metals, brass and aluminium alloy. Finite element analysis (FEA) was performed based on the uniaxial tension test data. It was shown that the effective stress–strain curve obtained from the biaxial tensile test (hydrostatic bulge test) had a good correlation with that obtained in the uniaxial tensile test and agreed well with the analytical and FEA results. This paper may be used to support an experimental and numerical laboratory in teaching the concepts of effective stress and strain in plasticity theory.

Significance of Lu¨der’s Plateau on Pipeline Fault Crossing Assessment

2010 ◽  
Author(s):  
Lanre Odina ◽  
Robert J. Conder
Keyword(s):  
Finite Element ◽  
Compressive Strain ◽  
Strain Curve ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Pipe Material ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Integrity Assessment ◽  
Analytical Approaches

When subjected to permanent ground deformations, buried pipelines may fail by local buckling (wrinkling under compression) or by tensile rupture. The initial assessment of the effects of predicted seismic fault movements on the buried pipeline is performed using analytical approaches by Newmark-Hall and Kennedy et al, which is restricted to cases when the pipeline is put into tension. Further analysis is then undertaken using finite element methods to assess the elasto-plastic response of the pipeline response to the fault movements, particularly the compressive strain limits. The finite element model is set up to account for the geometric and material non-linear parameters. The pipe material behaviour is generally assumed to have a smooth strain hardening (roundhouse) post-yield behaviour and defined using the Ramberg-Osgood stressstrain curve definition with the plasticity modelled using incremental theory with a von Mises yield surface, associated flow rule and isotropic hardening. However, material tests on seamless pipes (X-grade) show that the stress-strain curve typically displays a Lu¨der’s plateau behaviour (yield point elongation) in the post-yield state. The Lu¨der’s plateau curve is considered conservative for pipeline design and could have a significant impact on strain-based integrity assessment. This paper compares the pipeline response from a roundhouse stress-strain curve with that obtained from a pipe material exhibiting Lu¨der’s plateau behaviour and also examines the implications of a Lu¨der’s plateau for pipeline structural integrity assessments.

Existence and uniqueness of solutions to uni-axial elastic-plastic wave interactions

1969 ◽  
Vol 264 (1154) ◽  
pp. 497-556 ◽  
Keyword(s):  
Wave Speed ◽  
Initial Conditions ◽  
Strain Curve ◽  
Wave Functions ◽  
Local Analysis ◽  
Plastic Wave ◽  
Uniqueness Of Solutions ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Single Interface

This paper treats the propagation of stress waves through an elastic-plastic medium on the assumption of uni-axial displacement. With the further simplification to a piecewise linear stress-strain curve in terms of engineering stress and strain, wave equations are obtained for the longitudinal stress in both elastic and plastic regions, each with a distinct constant Lagrangian wave speed. The stress distribution in any region is then simply expressed in terms of two wave functions. In a general motion the medium will be divided into a sequence of alternating elastic and plastic regions separated by moving interfaces. A detailed analysis is presented for a single-interface wave interaction under general initial conditions, namely, continuous initial waves in the two directions in both elastic and plastic regions with a non-uniform yield stress in the elastic region. For different sets of initial conditions six distinct types of solution are shown to exist, and these are classified according to the direction and speed of the interface. In particular, two types involve interface speeds in excess of the elastic wave speed, not, to the authors’ knowledge, demonstrated in previous plastic wave treatments, noting the absence of possible shock formation for the present linearized stress-strain laws. Further, it is shown that stress discontinuities cannot form at the interface (or elsewhere) from initially continuous stress profiles. Associated with the different types of solution are four distinct sets of interface conditions so that there is no common form for the interaction solution. Each of the six types of solution is shown to be consistent with the elastic-plastic model only under a restricted set of initial conditions, and these sets are found to be mutually exclusive for the six types, thus deciding a unique choice for the type of single-interface solution. The six sets, however, are not inclusive of all possible initial conditions, indicating a need for multi-interface solutions in the exceptional situations. Multi-interface solutions may be possible even in the non-exceptional situations, but this possibility is felt to be unlikely. Finally, it can be noted that the analysis dealing with validity of solution is, for most cases, only local in that it applies in some small neighbourhood of the current point on the interface path, being based on expansions about this point. The results of such local analysis will therefore extend to the case of non-uniform wave speeds arising from non-linear stress-strain laws, provided that no shock is formed in the neighbourhood, but a global solution can no longer be expressed simply in terms of wave functions.

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