General form of matching equation of elastic-plastic field near crack line for mode I crack under plane stress condition

2001 ◽  
Vol 22 (10) ◽  
pp. 1173-1182 ◽  
Author(s):  
Yi Zhi-jian ◽  
Yan Bo
Keyword(s):  
Plane Stress ◽  
Stress Condition ◽  
Mode I ◽  
Mode I Crack ◽  
Plane Stress Condition ◽  
Crack Line ◽  
Elastic Plastic ◽  
Matching Equation

scholarly journals Near Crack Line Elastic-Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Ya Li ◽  
Feng Huang ◽  
Min Wang ◽  
Chaohua Zhao ◽  
Zhijian Yi
Keyword(s):  
Stress Field ◽  
Elastic Stress ◽  
Small Scale ◽  
Mode I ◽  
Plane Stress Condition ◽  
Crack Line ◽  
Elastic Plastic ◽  
Rectangular Coordinates ◽  
Elastic Stress Field ◽  
Plastic Stress

By using the crack line analysis method, this paper carries out an elastic-plastic analysis for mode I cracks under plane stress condition in an elastic perfectly plastic solid and obtains the general form of matching equations of the elastic stress field and the plastic stress field near the crack line in rectangular coordinate form. The analysis in rectangular coordinates in this paper avoids the conversion from rectangular coordinates into polar coordinates in the existing analysis and greatly simplifies the power series forms of the elastic stress field and plastic stress field near the crack line during the solving process. Furthermore, by focusing on a new problem, i.e., the center-cracked plate with finite width under unidirectional uniform tension, this paper obtains the elastic stress field, plastic stress field, and the length of the elastic-plastic boundary near the crack line by using the general form of the solution. When the dimensions of the plate tend to be infinite, the results of this paper are consistent with those obtained for an infinite plate with a mode I crack. Furthermore, the variation curves of the length of the elastic-plastic boundary are also delineated in different sized center-cracked plates, and the results are compared with those obtained under the small-scale yielding conditions. The solving process and the results in this paper abandon the small-scale yielding conditions completely. The method used in this paper not only makes the solving process simpler during the elastic-plastic analysis near the crack line but also enriches the crack line analysis method.

scholarly journals Damaged behavior under plane stress

2011 ◽  
pp. 341-368
Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni
Keyword(s):  
Plane Stress ◽  
Constitutive Equations ◽  
Stress Condition ◽  
Time Integration ◽  
Reference Case ◽  
Plane Stress Condition ◽  
Integration Schemes ◽  
Hyperbolic Sine ◽  
Time Integration Schemes ◽  
Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

Study of the mechanical properties of a molybdenum alloy with a plane stress condition at low temperature

1980 ◽  
Vol 12 (1) ◽  
pp. 89-93
Author(s):  
A. A. Lebedev ◽  
F. F. Giginyak ◽  
V. V. Bashta ◽  
V. K. Kharchenko ◽  
V. N. Semirog-Orlik ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Low Temperature ◽  
Plane Stress ◽  
Stress Condition ◽  
Molybdenum Alloy ◽  
Plane Stress Condition

A Complete Perfectly Plastic Solution for the Mode I Crack Problem Under Plane Stress Loading Conditions

2006 ◽  
Vol 74 (3) ◽  
pp. 586-589 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Stress Field ◽  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Internal Crack ◽  
Mode I ◽  
Mode I Crack ◽  
Loading Conditions ◽  
Perfectly Plastic

A continuous stress field for the mode I crack problem for a perfectly plastic material under plane stress loading conditions has been obtained recently. Here, a kinematically admissible velocity field is introduced, which is compatible with the continuous stress field obtained earlier. By associating these two fields together, it is shown that they constitute a complete solution for the uncontained plastic flow problem around a finite length internal crack, having a positive rate of plastic work. The yield condition employed is an alternative criterion first proposed by Richard von Mises in order to approximate the plane stress Huber-Mises yield condition, which is elliptical in shape, to one that is composed of two intersecting parabolas in the principal stress plane.

A Plane Stress Perfectly Plastic Mode I Crack Solution With Continuous Stress Field

2005 ◽  
Vol 72 (1) ◽  
pp. 62-67 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Admissible Solution ◽  
Mode I ◽  
Mode I Crack ◽  
Perfectly Plastic ◽  
Compressive Stresses ◽  
Von Mises

A statically admissible solution for a perfectly plastic material in plane stress is presented for the mode I crack problem. The yield condition employed is an alternative type first proposed by von Mises in order to approximate his original yield condition for plane stress while eliminating most of the elliptic region as pertaining to partial differential equations. This yield condition is composed of two intersecting parabolas rather than a single ellipse in the principal stress space. The attributes of this particular solution of the mode I problem over that previously obtained are that it contains neither stress discontinuities nor compressive stresses anywhere in the field.

The exact solutions of elastic-plastic crack line field for mode II plane stress crack

1995 ◽  
Vol 16 (10) ◽  
pp. 977-984 ◽  
Author(s):  
Yi Zhijian ◽  
Wang Shijie ◽  
Wang Xiangjian ◽  
Wang Xiangjian
Keyword(s):  
Exact Solutions ◽  
Plane Stress ◽  
Mode Ii ◽  
Line Field ◽  
Crack Line ◽  
Elastic Plastic
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