Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

Elasto-Plastic Asperity Contacts of Layered Media

2005 ◽  
Author(s):  
Qin Xie ◽  
Geng Liu ◽  
Tianxiang Liu ◽  
Ruiting Tong ◽  
Quanren Zeng
Keyword(s):  
Yield Criterion ◽  
Layered Media ◽  
Asperity Contact ◽  
Initial Stiffness ◽  
Programming Technique ◽  
Perfectly Plastic ◽  
Real Area Of Contact ◽  
Asperity Contacts ◽  
Elastic Perfectly Plastic ◽  
Von Mises

An elasto-plastic asperity contact model for layered media is developed in the work reported in this paper to analyze the influences of coating-substrate materials on contact when yielding and the strain-hardening properties of materials are taken into account. The finite element method, the initial stiffness method and the mathematical programming technique are employed to solve the model. The von Mises yield criterion is used to determine the inception of plastic deformation. The effects of different layer thickness and different coating-substrate materials on the contact pressure, real area of contact, average gap of rough surface, and stresses in layer and substrate under the elastic-perfectly-plastic and the elasto-plastic contact conditions are numerically investigated and discussed.

scholarly journals Influence of Material Compressibility on Displacement Solution for Structural Steel Plate Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Nelli Aleksandrova
Keyword(s):  
Structural Steel ◽  
Yield Criterion ◽  
Flow Rule ◽  
Perfectly Plastic ◽  
Open Hole ◽  
Practical Engineering ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Associated Flow Rule ◽  
Material Compressibility

Displacement field calculations are necessary for many structural steel engineering problems such as cold expansion of holes, embedment of bolts and rivets, and installation and maintenance of external devices. To this end, rigorous closed form analytical displacement solution is obtained for structural steel open-hole plates with in-plane loading. The material of the model is considered to be elastic perfectly plastic obeying the von Mises yield criterion with its associated flow rule. On the basis of this solution, two simplified engineering formulae are proposed and carefully discussed for practical engineering purposes. Graphical representations of results show validity of each formula as compared with rigorous solution and other studies.

scholarly journals The yield condition strongly influences the formation of Dugdale plastic strips ahead of crack tips under tensile plane stress loading conditions

2012 ◽  
Vol 21 (1-2) ◽  
pp. 37-39
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Yield Condition ◽  
Loading Conditions ◽  
Element Analysis ◽  
Plastic Strip ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractA finite element analysis indicates a good correlation between the Dugdale plastic strip model and a linear elastic/perfectly plastic material under plane stress loading conditions for a flow theory of plasticity based on the Tresca yield condition. A similar analysis under the von Mises yield condition reveals no plastic strip formation.

An Elastoplastic Finite Element Study of Displacement-Controlled Fretting in a Plane-Strain Cylindrical Contact

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Huaidong Yang ◽  
Itzhak Green
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Tangential Force ◽  
Ductile Material ◽  
Finite Element Study ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Element Study

This work presents a finite element study of a two-dimensional (2D) plane strain fretting model of a half cylinder in contact with a flat block under oscillatory tangential loading. The two bodies are deformable and are set to the same material properties (specifically steel), however, because the results are normalized, they can characterize a range of contact scales (micro to macro), and are applicable for ductile material pairs that behave in an elastic-perfectly plastic manner. Different coefficients of friction (COFs) are used in the interface. This work finds that the edges of the contacting areas experience large von Mises stresses along with significant residual plastic strains, while pileup could also appear there when the COFs are sufficiently large. In addition, junction growth is investigated, showing a magnitude that increases with the COF, while the rate of growth stabilization decreases with the COF. The fretting loop (caused by the tangential force during the fretting motion) for the initial few cycles of loading is generated, and it compares well with reported experimental results. The effects of boundary conditions are also discussed where a prestressed compressed block is found to improve (i.e., reduce) the magnitude of the plastic strain compared to an unstressed block.

scholarly journals Slope stability analysis: Barodesy vs linear elastic – perfectly plastic models

2019 ◽  
Vol 92 ◽  
pp. 16014
Author(s):  
Franz Tschuchnigg ◽  
Gertraud Medicus ◽  
Barbara Schneider-Muntau
Keyword(s):  
Stability Analysis ◽  
Slope Stability ◽  
Plane Strain ◽  
Constitutive Models ◽  
Failure Surface ◽  
Slope Stability Analysis ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Reduction Techniques ◽  
Elastic Perfectly Plastic

The results of slope stability analysis are not unique. Different factors of safety are obtained investigating the same slope. The differences result from different constitutive models including different failure surfaces. In this contribution, different strength reduction techniques for two different constitutive models (linear elastic - perfectly plastic model using a Mohr-Coulomb failure criterion and barodesy) have been investigated on slope stability calculations for two different slope inclinations. The parameters for Mohr – Coulomb are calibrated on peak states of element tests simulated with barodesy for different void ratios. For both slopes the predictions of the factors of safety are higher with barodesy than with Mohr-Coulomb. The difference is to some extend explained by the different shapes of failure surfaces and thus different values for peak strength under plane strain conditions. The plane strain predictions of Mohr-Coulomb are conservative compared to barodesy, where the failure surface coincides with Matsuoka-Nakai.

Analytical Solutions for Crack Tip Plastic Zone Shape Using the Von Mises and Tresca Yield Criteria: Effects of Crack Mode and Stress Condition

2004 ◽  
Vol 20 (3) ◽  
pp. 199-210 ◽  
Author(s):  
P. H. Jing ◽  
T. Khraishi
Keyword(s):  
Plastic Zone ◽  
Plane Stress ◽  
Stress Condition ◽  
Crack Tip ◽  
Mode Ii ◽  
Yield Criteria ◽  
Closed Form Solutions ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

AbstractAnalytical closed-form solutions for the crack tip plastic zone shape have been derived for a semi-infinite crack in an isotropic elastic-perfectly plastic solid under both plane stress and plane strain conditions. Two yield criteria have been applied: the Von Mises and Tresca yield criteria. The solutions have been developed for crack modes I and III (mode II has been published previously). The results, which favorably compare to a limited number of existing experimental and analytical findings, indicate that the Tresca zone is larger in size than the Von Mises zone. Moreover, an interesting observation is that both zones are generally much larger than the ones predicted by classical Irwin and Dugdale-Barenblatt solutions.

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