The Fully Plastic, Plane-Strain Tension of a Notched Bar

1968 ◽  
Vol 35 (1) ◽  
pp. 111-116 ◽  
Author(s):  
J. E. Neimark
Keyword(s):  
Shear Strain ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plastic Material ◽  
Extremum Principle ◽  
Displacement Distribution ◽  
Plane Strain Tension

Hill’s extremum principle for a strain-hardening plastic material is applied to determine the displacement distribution and the strains at the center and at the roots of rounded V-grooves in a bar in tension. This analysis is used to present the shear strain at fracture as a function of triaxial tension for 7075-T6 aluminum, as compared to the more usual tension and torsion tests.

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.

Numerical Analysis of Plane-Strain Tension Test for Rate-Dependent Solids

1992 ◽  
Vol 59 (3) ◽  
pp. 485-490 ◽  
Author(s):  
P. Tugˇcu
Keyword(s):  
Numerical Analysis ◽  
Strain Rate ◽  
Plane Strain ◽  
Rate Sensitivity ◽  
Tension Test ◽  
Engineering Strain ◽  
Plane Strain Tension ◽  
Rate Dependent ◽  
Strain And Strain Rate ◽  
Strain Rate Hardening

The plane-strain tension test is analyzed numerically for a material with strain and strain-rate hardening characteristics. The effect of the prescribed rate of straining is investigated for an additive logarithmic description of the material strain-rate sensitivity. The dependency to the imposed strain rate so introduced is shown to have a significant effect on several features of the load-elongation curve such as the attainment of the load maximum, the onset of localization, and the overall engineering strain.

scholarly journals Rate-dependent ductile fracture under plane strain tension: experiments and simulations

2018 ◽  
Vol 183 ◽  
pp. 02022
Author(s):  
Vincent Grolleau ◽  
Vincent Lafilé ◽  
Christian C. Roth ◽  
Bertrand Galpin ◽  
Laurent Mahéo ◽  
...  
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Plane Strain ◽  
Static Loading ◽  
High Strain ◽  
Fracture Initiation ◽  
Surface Strain ◽  
Experimental Program ◽  
Loading Conditions ◽  
Plane Strain Tension

Among all other stress states achievable under plane stress conditions, the lowest ductility is consistently observed for plane strain tension. For static loading conditions, V-bending of small sheet coupons is the most reliable way of characterising the strain to fracture for plane strain tension. Different from conventional notched tension specimens, necking is suppressed during V-bending which results in a remarkably constant stress state all the way until fracture initiation. The present DYMAT talk is concerned with the extension of the V-bending technique from low to high strain rate experiments. A new technique is designed with the help of finite element simulations. It makes use of modified Nakazima specimens that are subjected to V-bending. Irrespective of the loading velocity, plane strain tension conditions are maintained throughout the entire loading history up to fracture initiation. Experiments are performed on specimens extracted from aluminum 2024-T3 and dual phase DP450 steel sheets. The experimental program includes quasi static loading conditions which are achieved on a universal testing machine. In addition, high strain rate experiments are performed using a specially-designed drop tower system. In all experiments, images are acquired with two cameras to determine the surface strain history through stereo Digital Image Correlation (DIC). The experimental observations are discussed in detail and also compared with the numerical simulations to validate the proposed experimental technique

scholarly journals Relationship Between Rockwell C Hardness and Inelastic Material Constants

2002 ◽  
Vol 124 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Akihiko Hirano ◽  
Masao Sakane ◽  
Naomi Hamada
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Strain Hardening ◽  
Yield Stress ◽  
Plastic Material ◽  
Stress And Strain ◽  
Material Constants ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Hardening Coefficient

This paper describes the relationship between Rockwell C hardness and elastic-plastic material constants by using finite element analyses. Finite element Rockwell C hardness analyses were carried out to study the effects of friction coefficient and elastic-plastic material constants on the hardness. The friction coefficient and Young’s modulus had no influence on the hardness but the inelastic materials constants, yield stress, and strain hardening coefficient and exponent, had a significant influence on the hardness. A new equation for predicting the hardness was proposed as a function of yield stress and strain hardening coefficient and exponent. The equation evaluated the hardness within a ±5% difference for all the finite element and experimental results. The critical thickness of specimen and critical distance from specimen edge in the hardness testing was also discussed in connection with JIS and ISO standards.

Sign in / Sign up

Export Citation Format

Share Document