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.

The Significance of Tensile and Other Mechanical Test Properties of Metals

1944 ◽  
Vol 151 (1) ◽  
pp. 116-146 ◽  
Author(s):  
Hugh O'Neill
Keyword(s):  
Grain Size ◽  
Tensile Test ◽  
Strain Hardening ◽  
Work Hardening ◽  
Mechanical Test ◽  
True Strain ◽  
Cold Work ◽  
Tensile Elongation ◽  
True Stress ◽  
High Plasticity

Critical consideration of the conventional quantities obtained from the tensile test reveals their limitations for design purposes, especially where notch-fatigue effects predominate. Against such notch-fatigue the importance of high work-hardening capacity in a metal is emphasized, and its relation to tensile elongation behaviour outlined. It is suggested that even conventional tensile records may yield some rough measure of work-hardening capacity prior to cracking by means of quantities which have here been called “plasticity ratio” and “plasticity value”. Attention is drawn to certain refined methods of plotting tensile diagrams. A review of published results indicates a basic generalization for plastic deformation. If a graph of true stress P against one of the several forms of true strain ∈ be obtained, then the basic deformation diagram is in general the same for tension, compression, torsion, and indentation. It consists first of a curved portion extending up to the point of critical plasticity which corresponds with the onset of “necking” in tension. The curve afterwards flattens out and continues upwards almost as a straight line. The complete diagram may be considered very approximately as of the logarithmic form P = κεm, and its gradient (or the value of m) will be high in materials with very high strain-hardening capacity, and low in those which have been cold-worked. Since work-hardening capacity has hitherto been largely determined by ball indentation tests, a correlation has been made between these and tensile tests. This has revealed some shortcomings of the Meyer n value for indentation. Heat treatment and crystal grain size influence the plastic properties of a metal and the effects of both have been studied. For specimens of various crystal sizes there is similarity in form between certain tensile and indentation diagrams. From these an appropriate ultimate true stress value may be obtained which is practically independent of crystal grain size and therefore enables comparisons of materials to be made. Similarly there is a fundamental limiting “pressure of fluidity” for metals which is independent of their initial content of cold work. Values for this pressure have been determined. The pressure of fluidity obtained by linear extrapolation of a Stead true-stress tensile diagram is lower than that determined by heavy cold-rolling experiments. The deformation and strain-hardening which take place up to the point of “critical plasticity” (i.e. “necking” in the tensile test) appear to differ in internal crystallographic mechanism from that developing beyond this point. It is found that several physical properties reach limiting values at the “necking” stress. Investigation shows that heat-treated steels with sorbitic microstructures may have a relatively low capacity for strain-hardening. Their employment under conditions of notch-fatigue is therefore not attractive. On the other hand their resistance to wear may be relatively good. Wear remains a complex problem, but examples are given where relatively good wear resistance has corresponded with relatively high “plasticity values”.

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.

Computational Process Simulation and Energy Parameter Analysis From Mechanical Deformation of Aerospace Alunimum Alloys

2002 ◽  
Author(s):  
James M. Fragomeni ◽  
Giridhar Venugopal
Keyword(s):  
Yield Strength ◽  
Experimental Testing ◽  
True Strain ◽  
Energy Parameter ◽  
True Stress ◽  
Parameter Analysis ◽  
Dissipated Energy ◽  
Strain Hardening Exponent ◽  
Element Analysis ◽  
Buckling Strength

Many systems that work on the processing of energy can be modeled in terms of that energy. The energy that is given to the system may be stored or dissipated in the form of heat. It was proposed to extend this concept to attainment of critical level of stored energy and/or dissipated energy for occurrence of buckling of a metal column under compressive loading. The fact that Energy Factor Parameter (E.F.P.) computed from the experimental true stress-true strain values, suddenly decreased and approached value close to zero indicated either buckling and/or softening, but deviated with the E.F.P. computed from the theoretical true stress and true strain values. The 7050-T7451 (Al-Zn-Mg-Cu-Zr) and Al-Li-Cu aluminum alloys in longitudinal and transverse grain orientations were compression tested for mechanical properties of yield strength, buckling strength, strength coefficient, strain hardening exponent. Correlation between ratio of buckling strength and yield strength with aging time for preaged ASTM compression specimens was established. The compression deformation of aluminum alloy 7050 was modeled using finite element analysis, with the experimental testing parameters and the database in the software package.

The Mechanical and Deformation Behavior of TWIP Steel Prepared by Directional Solidification

2014 ◽  
Vol 783-786 ◽  
pp. 761-765 ◽  
Author(s):  
Dan Wang ◽  
Kun Wang ◽  
Zi Mu Shi ◽  
Fu Sheng Han
Keyword(s):  
Mechanical Properties ◽  
Strain Hardening ◽  
Twip Steel ◽  
True Strain ◽  
Longitudinal Direction ◽  
True Stress ◽  
Grain Structure ◽  
Directionally Solidified ◽  
Twip Steels ◽  
Columnar Grain

A directionally solidified TWIP steel (Fe-25Mn-2.5Al-2.5Si) was prepared by liquid metal cooling technology. The microstructure and mechanical behavior were examined and compared with usually solidified samples. The directionally solidified TWIP steel shows a typical columnar grain structure, and the maximum true stress and true strain along the longitudinal direction of the sample are 1060MPa and 71% respectively. As a comparison, the usually solidified samples shows an equiaxed grain microstructure with the maximum true stress and true strain of only 994MPa and 58%, respectively. Moreover, the two solidification modes also lead to very different strain hardening behavior, particularly in the changes of strain hardening rate with strain. This suggests that the grain boundary plays a key role in the mechanical properties of TWIP steels, and changing the grain boundaries can be effective to improve the comprehensive mechanical properties of TWIP steels.

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.

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