A general method of stress analysis for a generalized linear yield criterion under plane strain and plane stress

2018 ◽  
Vol 31 (3) ◽  
pp. 841-849 ◽  
Author(s):  
Sergei Alexandrov ◽  
Prashant Date
Keyword(s):  
Stress Analysis ◽  
Plane Strain ◽  
Plane Stress ◽  
Yield Criterion ◽  
General Method

scholarly journals A method of finding stress solutions for a general plastic material under plane strain and plane stress conditions

2020 ◽  
Vol 37 ◽  
pp. 100-107
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng
Keyword(s):  
Coordinate System ◽  
Plane Strain ◽  
Principal Stress ◽  
Plane Stress ◽  
Plastic Material ◽  
Yield Criterion ◽  
Boundary Value ◽  
Equilibrium Equations ◽  
Geometric Problem ◽  
Principal Lines

Abstract A general plastic material under plane strain and plane stress is classified by a yield criterion that depends on both the first and second invariants of the stress tensor. The yield criterion together with the stress equilibrium equations forms a statically determinate system. This system is investigated in the principal lines coordinate system (i.e. the coordinate curves of this coordinate system coincide with trajectories of the principal stress directions). It is shown that the scale factors of the principal lines coordinate system satisfy a simple equation. Using this equation, a method for constructing the principal stress trajectories is developed. Therefore, the boundary value problem of plasticity theory reduces to a purely geometric problem. It is believed that the method developed is useful for solving a wide class of boundary value problems in plasticity.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

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.

Effect of State-of-Stress and Yield Criterion on the Bauschinger Effect

1968 ◽  
Vol 90 (3) ◽  
pp. 403-408 ◽  
Author(s):  
S. T. Rolfe ◽  
R. P. Haak ◽  
J. H. Gross
Keyword(s):  
Yield Strength ◽  
Plane Strain ◽  
Plane Stress ◽  
Bauschinger Effect ◽  
Yield Criterion ◽  
Cold Deformation ◽  
Stress Relief ◽  
Cold Forming ◽  
State Of Stress ◽  
Direction Opposite

During fabrication, the cold forming of structural components may reduce the yield strength of a component if it is loaded in a direction opposite to that of the cold forming. This reduction in yield strength, referred to as the Bauschinger effect, is influenced by the state-of-stress under which the cold forming is performed, by the criterion used to determine the yield strength, and by the use of post-forming stress relief. To establish the importance and magnitude of these effects, specimens from 2 1/2-in-thick plates of HY-80 steel, cold-formed by plane strain bending, were tested along with specimens that were cold-formed by plane-stress axial straining. For material tested in a direction opposite to that of cold forming, the Bauschinger effect was observed both in tension and compression, whereas for material tested at 90 deg to the direction of cold forming in plane strain, both the tensile and compressive yield strengths increased and no Bauschinger effect was observed. Because of the difference in restraint, the Bauschinger effect was greater for plane-stress axial deformation than for plane-strain bending deformation. The Bauschinger effect was greater when the yield strength was determined at small offsets and was essentially eliminated at an offset greater than 0.5 percent. In addition, the Bauschinger effect was greatest for small amounts of cold deformation and was progressively decreased by strain hardening at large amounts of cold deformation. The reduction in secant modulus and in yield strength (Bauschinger effect) in cold-formed material was essentially eliminated by stress-relief treatment at 1025 deg. F. The results indicate the importance of knowing the cold-forming state-of-stress, the criterion used in determining yield strength, and the effects of stress relief when assessing the effects of cold deformation on mechanical properties.

Improved Compliance Solutions for C(T), SE(B) and Clamped SE(T) Specimens Including Side-Grooves, Varying Thicknesses and 3-D Effects

2014 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Felipe Cavalheiro Moreira
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Potential Drop ◽  
Crack Size ◽  
Growth Conditions ◽  
Size Estimation ◽  
Unloading Compliance ◽  
Integrity Assessments ◽  
Elastic Unloading

Fracture toughness and Fatigue Crack Growth (FCG) experimental data represent the basis for accurate designs and integrity assessments of components containing crack-like defects. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance since characterize, respectively, ductile fracture and cyclic crack growth conditions. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain - modulus vary between E (plane stress) and E/(1-ν2) (plane strain), revealing effects of thickness and 3-D configurations; ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Previous results from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging clamped SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D, thickness and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W=0.1 and a/W=0.7 and varying thicknesses (W/B = 4, W/B = 2 and W/B = 1). Side-grooves of 5%, 10% and 20% are also considered. The results include compliance solutions incorporating all aforementioned effects to provide accurate crack size estimation during laboratory fracture and FCG testing. All proposals revealed reduced deviations if compared to existing solutions.

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