Ramberg-Osgood Parameters for 63–37 Sn-Pb Solder

1992 ◽  
Vol 114 (2) ◽  
pp. 234-238 ◽  
Author(s):  
A. J. Rafanelli
Keyword(s):  
Strain Hardening ◽  
Power Law ◽  
True Strain ◽  
Material Constant ◽  
Strain Hardening Exponent ◽  
J Integral ◽  
Engineering Strain ◽  
Fracture Properties ◽  
Preliminary Step ◽  
Stress Levels

As part of a fracture properties study, the Ramberg-Osgood parameters were evaluated for 63-37 Sn-Pb (tin-lead) solder. This work was a preliminary step in experimentally determining J-integral values via the Hutchinson-Rice-Rosengren (HRR) power law for hardening materials. Consideration was given to both engineering strain and true strain when plotting the curves. Results disclosed little effect of either engineering or true strain at linear stress levels. For a strain-hardening exponent of 1.0, a material constant of 0.9849 was determined.

Strain-Hardening Characteristics of Ti-6Al-2Sn-4Zr-2Mo Alloy

1975 ◽  
Vol 97 (4) ◽  
pp. 382-383 ◽  
Author(s):  
Amiya K. Chakrabarti ◽  
James A. Roberson ◽  
William R. Kerr
Keyword(s):  
Grain Size ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Power Law ◽  
True Strain ◽  
True Stress ◽  
Strain Hardening Exponent ◽  
Strain Relation

The strain-hardening exponent (n) is considered to be numerically equal to the uniform plastic strain for materials which exhibit a power low true stress true strain relation. In Ti-6Al-2Sn-4Zr-2Mo alloy a considerable deviation between the uniform plastic strain and the strain hardening exponent has been observed irrespective of the variations in microstructures and grain size. The present investigation indicates that a power law true stress true strain relation of the type σ = Kεn may not be valid for this material.

A Proposed Generalized Model for Forming Limit Diagram

2015 ◽  
Author(s):  
Aly El Domiaty ◽  
Abdel-Hamid I. Mourad ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Strain Hardening ◽  
Power Law ◽  
Yield Criterion ◽  
Rate Of Change ◽  
Forming Limit ◽  
Strain Hardening Exponent ◽  
Sensitivity Factor ◽  
Generalized Model

One of the most significant approaches for predicting formability is the use of forming limit diagrams (FLDs). The development of the generalized model integrates other models. The first model is based on Von-Misses yield criterion (traditionally used for isotropic material) and power law constitutive equation considering the strain hardening exponent. The second model is also based on Von-Misses yield criterion but uses a power law constitutive equation that considers the effect of strain rate sensitivity factor. The third model is based on the modified Hill’s yield criterion (for anisotropic materials) and a power law constitutive equation that considers the strain hardening exponent. The current developed model is a generalized model which is formulated on the basis of the modified Hill yield criterion and a power law constitutive equation considering the effect of strain rate. A new controlling parameter (γ) for the limit strains was exploited. This parameter presents the rate of change of strain rate with respect to strain. As γ increases the level of the FLD raises indicating a better formability of the material.

Shakedown Loads for Pressure Vessels of Strain Hardening Materials

1969 ◽  
Vol 11 (3) ◽  
pp. 340-342 ◽  
Author(s):  
T. E. Taylor
Keyword(s):  
Strain Hardening ◽  
Power Law ◽  
Pressure Vessels ◽  
Strain Hardening Exponent ◽  
Rigid Plastic ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Creep Analysis ◽  
Family Of Curves ◽  
The Relationship

A power law, well known in creep analysis, embodies a family of curves which express the stress-strain relations for a family of materials ranging from linear elastic to rigid perfectly plastic. A linearization of the relationship between stress concentration factor and the reciprocal of strain hardening exponent for geometrically similar pressure vessels made of materials within the family has enabled a view of shakedown in vessels of strain hardening materials to be formulated. The absence of discontinuities in the power law, except at the rigid plastic end point, results in shakedown loads dependent on strain hardening exponent and previous loading history.

THREE-DIMENSIONAL SIMULATION OF DEFORMATION FIELDS UNDERNEATH VICKERS INDENTER: EFFECTS OF POWER-LAW PLASTICITY

2010 ◽  
Vol 24 (01n02) ◽  
pp. 238-246 ◽  
Author(s):  
NUWONG CHOLLACOOP ◽  
UPADRASTA RAMAMURTY
Keyword(s):  
Yield Strength ◽  
Strain Hardening ◽  
Power Law ◽  
Strain Distribution ◽  
Three Dimensional ◽  
Strain Hardening Exponent ◽  
Al Alloy ◽  
Element Analysis ◽  
Vickers Indenter ◽  
Experimental Heat

The effects of power-law plasticity (yield strength and strain hardening exponent) on the plastic strain distribution underneath a Vickers indenter was systematically investigated by recourse to three-dimensional finite element analysis, motivated by the experimental macro- and micro-indentation on heat-treated Al - Zn - Mg alloy. For meaningful comparison between simulated and experimental results, the experimental heat treatment was carefully designed such that Al alloy achieve similar yield strength with different strain hardening exponent, and vice versa. On the other hand, full 3D simulation of Vickers indentation was conducted to capture subsurface strain distribution. Subtle differences and similarities were discussed based on the strain field shape, size and magnitude for the isolated effect of yield strength and strain hardening exponent.

The J-Integral for a Single-Edge Cracked Panel Subjected to Combined Remote Tension and Bending

2009 ◽  
Author(s):  
Masaaki Matsubara
Keyword(s):  
Crack Initiation ◽  
Ductile Fracture ◽  
Strain Hardening ◽  
Structural Integrity ◽  
Crack Size ◽  
Strain Hardening Exponent ◽  
J Integral ◽  
Single Edge ◽  
Energy Concept

On structural integrity evaluation, a single-edge cracked panel subjected to combined remote tension and bending is the typical one. The J-integral is a valid way for handling the ductile fracture problem immediately after stable crack initiation. The complimentary energy concept combined with fully plastic solutions to make it to estimate the J-integral of the panel. The proposed method is able to give us the J-integral as a function of the crack size/panel width and the strain hardening exponent.

scholarly journals Transition from engineering strain to the true strain in analytical description of metals hardening

2021 ◽  
pp. 66-70
Author(s):  
A.M. Dolzhanskyi ◽  
T.A. Ayupova ◽  
O.A. Nosko ◽  
O.P. Rybkin ◽  
O.A. Ayupov
Keyword(s):  
Strain Hardening ◽  
True Strain ◽  
Theoretical Data ◽  
Analytical Description ◽  
Metals And Alloys ◽  
Technical Literature ◽  
Engineering Strain ◽  
Cold Forming ◽  
Mathematical Expressions ◽  
Deformation Hardening

Purpose of the work is related with the impossibility of correctly estimating the strain hardening of metals (alloys) in the area of their large total deformations due to absence of additivity in the traditionally used value of engineering strain g, its nonlinear change in the area of large values, and absence of data in the technical literature Hall-Petch coefficient Ai for logarithmic true deformations, which led to the task of correct transition from the values of the engineering strain 0 < g < 50...60 % to the value of the true logarithmic strainn 0 < e < 1...3. Methodology. The theoretical analysis of the regularities of deformation hardening of metals (alloys) from the engineering strain is carried out, the transition from engineering to logarithmic ("true") strain of metals (alloys) by analytical representation of metal hardening graphs as a function of logarithmic (true) strain. in contrast to the degree of engineering strain is presented. Originality. Analytical expressions are presented that allow the use of known theoretical data on the strain hardening of metals (alloys) at small (50...60 %) total engineering strains g during cold pressure treatment to transition to logarithmic (true) strain e with large total deformations. Practical value. The obtained mathematical expressions allow to use the accumulated in the technical literature experimental data on the hardening of metals and alloys with small engineering strains in the processes of cold processing of metals (alloys) by pressure to determine the hardening with large total logarithmic (true) strains. These data can also be used to solve metallophysical problems of metal processing by pressure associated with large total compressions. Keywords: cold forming of metals and alloys; hardening; degree of deformation

Diagnostics of Strain Hardening Exponent and Material Constant of Steel Sheets

2014 ◽  
Vol 616 ◽  
pp. 252-259 ◽  
Author(s):  
Erika Fechová ◽  
Jozef Kmec
Keyword(s):  
Strain Hardening ◽  
Material Constant ◽  
Working Environment ◽  
Strain Hardening Exponent ◽  
Suitable Material ◽  
Nonparametric Models ◽  
Steel Sheets ◽  
Real Model ◽  
Standard Linear ◽  
Matlab Programming

This paper deals with evaluation of n strain hardening exponent and C material constant at various velocities of the strain rate according to EN 10002-1. Dependence of tensile stress on elongation is carried out at INSTRON shredder in digital form and it is directly introduced into MATLAB working environment. To determine these material parameters suitable material models (Krupkowsky model) and MATLAB programming pack, mainly its Curve Fitting toolbox, which provides the library of standard linear, nonlinear and nonparametric models (e.g. polynomial, rational, etc.), are used. At automobile crash tests kinetic energy conversion into energy of deformation (where it is necessary to know n, C) is theoretically calculated at certain velocities so that the solid parts of the car body would be protected from damage. It would be the best to compare correctness of those calculations to the test carried out at a real model or by simulation created on the computer with necessary software equipment.

Effect of Microalloying Elements (B, Nb, V and Ti) on the Strain Hardening Behavior of High-Manganese TWIP Steels.

2012 ◽  
Vol 1373 ◽  
Author(s):  
F. Reyes-Calderón ◽  
I. Mejía ◽  
J.M. Cabrera
Keyword(s):  
Strain Hardening ◽  
True Strain ◽  
Research Work ◽  
Strain Hardening Exponent ◽  
High Manganese ◽  
Hardening Behavior ◽  
Slope Change ◽  
Twip Steels ◽  
Microalloying Elements ◽  
Strain Hardening Behavior

ABSTRACTThe present research work analyses the influence of microalloying elements (B, Nb, V and Ti) on the tensile strength and the strain hardening behavior of a high-manganese TWIP steel. The analysis was carried out by means of true stress-true strain curves derived from uniaxial tension tests. The work hardening exponent was determined by using the Hollomon and differential Crussard-Jaoul models. Metallographic characterization was carried out to determine the metallurgical changes associated with n values. The results indicate that the Hollomon analysis results in strain hardening exponent values up to 0.46. On the other hand, the differential Crussard-Jaoul analysis establishes a clear distinction of n value for two stages of plastic deformation which are determined by a sharp slope change in the plot of ln(dσ/dε)-lnε.

The Effect of Precipitate Configuration on the Strain Hardening Behavior of Al-Mg-Si Alloy Sheet

2010 ◽  
Vol 146-147 ◽  
pp. 1163-1169
Author(s):  
Ni Tian ◽  
Gang Zhao ◽  
Bo Nie ◽  
Jian Jun Wang ◽  
Liang Zuo ◽  
...  
Keyword(s):  
Strain Hardening ◽  
True Strain ◽  
Strain Range ◽  
Alloy Sheet ◽  
Strain Hardening Exponent ◽  
Hardening Effect ◽  
Polycrystalline Alloy ◽  
The Matrix ◽  
Strain Hardening Behavior ◽  
Yielding Process

The microstructure especially the size, shape, number and distribution of precipitate, together with the strain hardening exponent n value at different strain range during plastic deformation of the Al-0.9Mg-1.0Si-0.7Cu-0.6Mn alloy sheet, subjected to different heat treatment were investigated. The results showed that the strain hardening exponent n values of Al-0.9Mg-1.0Si-0.7Cu-0.6Mn alloy sheet at any different strain range are different from each other, which is in agreement with the result that the relationship between true strain and true stress of polycrystalline alloy sheet during tensile test does not fully meet the Hollomon formula. The continuous strain hardening exponent nc defined in this paper essentially represents the approximate liner strain hardening effect during the total calculating strain range, while the stage strain hardening exponent ns defined in the paper can objectively indicate the counteraction of the micro strain hardening with the micro strain softening of alloy sheet during plastic deforming. When the precipitate in the matrix of alloy sheet can be cut by dislocation, the alloy sheet has the weakest strain hardening effect at the beginning of yielding process. Otherwise, the alloy sheet has the most prominent strain hardening effect at the beginning of yielding process when the precipitate in the matrix can be bowed bypass operation of dislocation. Gridded precipites is of no advantage to the glide and multiplication of dislocation of alloy sheet.

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