Analysis of Stress Response to Various Strain-Paths in Axial-Torsional Deformation of Metals

1984 ◽  
Vol 106 (4) ◽  
pp. 361-366 ◽  
Author(s):  
Han C. Wu ◽  
Jen-Che Yao
Keyword(s):  
Stress Response ◽  
Plastic Strain ◽  
Strain Path ◽  
Sensitivity Study ◽  
Total Strain ◽  
Torsional Deformation ◽  
Torsional Strain ◽  
Straight Line ◽  
Phase Path ◽  
Strain Paths

The stress response to various axial-torsional strain paths is discussed. The modified endochronic plasticity theory, which is formulated based on plastic-strain is used for theoretical analysis. In a sensitivity study, it is shown that a substantial amount of change in the stress response is induced by a small perturbation on the plastic-strain path. Of this change a significant amount is due to perturbation in the direction of the plastic-strain path. Several stepwise strain paths, both total-strain and plastic-strain paths, are also included in the investigation. It has been found that, when the number of steps is increased to infinity such that the strain path converges to a straight line corresponding to an in-phase path, the stress response to such a path is wildly fluctuating in the stress space if the path is a plastic-strain path, and the stress response converges to that of the in-phase path if the path is a total-strain path.

Investigation of Endochronic Constitutive Equation Subject to Plastic Strain-Controlled Axial-Torsional Deformation

1986 ◽  
Vol 108 (3) ◽  
pp. 262-269 ◽  
Author(s):  
Han C. Wu ◽  
J. C. Yao ◽  
S. C. Chu
Keyword(s):  
Plastic Strain ◽  
Theoretical Study ◽  
Test System ◽  
Torsional Deformation ◽  
Endochronic Theory ◽  
Phase Path ◽  
Strain Paths ◽  
Theoretical Results ◽  
Material Test System ◽  
Good Agreement

Plastic-strain controlled test is investigated both experimentally and theoretically. The plastic-strain control is feasible by means of computer-aided material test system. Theoretical study is made by use of the modified endochronic theory in which plastic strain is employed to define intrinsic time. Three in-phase plastic-strain paths (a pure axial path, a pure torsional path and an axial-torsional in-phase path) and two out-of-phase plastic-strain paths (small and large perturbations from the axial-torsional in-phase path) are studied. It is shown that the theory and experiment have good agreement. Furthermore, both experimental and theoretical results show that strain-hardening is enhanced by out-of-phase loading.

The characteristics of coaxial and non-coaxial strain paths

1966 ◽  
Vol 1 (3) ◽  
pp. 216-222 ◽  
Author(s):  
T. C. Hsu
Keyword(s):  
Strain Path ◽  
Total Strain ◽  
Large Strains ◽  
Manufacturing Processes ◽  
Practical Applications ◽  
Principal Axes ◽  
Strain Paths

In manufacturing processes involving large strains, the properties of the material undergoing deformation depend not only on the current total strain but on the previous strain path as well. Strain paths are divided into two major types, those in which the principal axes of strain remain fixed with respect to the material (coaxial strain paths), and those in which they rotate (non-coaxial strain paths). The characteristics of the two types of strain path are explained. Particular types of non-coaxial strain path related to practical applications are discussed in further detail and examples based on actual measurements are given.

A review of stress-strain paths and constitutive relations in the plastic range

1981 ◽  
Vol 16 (4) ◽  
pp. 235-249 ◽  
Author(s):  
D W A Rees
Keyword(s):  
Plastic Strain ◽  
Radial Stress ◽  
Strain Path ◽  
Stress Path ◽  
Biaxial Stress ◽  
Strain History ◽  
Hardening Rule ◽  
Non Linear ◽  
Strain Paths ◽  
Good Agreement

Plastic strain paths produced by both radial and non-radial stress paths are reviewed for metals and alloys under uniaxial and biaxial stress. The present interpretation illustrates collective trends and offers theoretical solutions for each of several stress paths. In general the strain path is linear for a radial stress path for most materials at low to medium temperatures. The isotropic quadratic hardening rule of von Mises rarely describes the strain behaviour accurately. but a simple anisotropic quadratic form provides good agreement by the uniform hardening rule. Exceptions are found for magnesium and an associated alloy at room temperature and for the high temperature deformation in an aluminium alloy. Descriptive yield functions are presented and the anistropic constants determined for one particular function of the Bailey form. Strain paths produced by outward non radial zig-zag and stepped stress paths are approximately linear provided that they are confined to a narrow band in stress space. It is shown that an equivalent radial stress path analysis provides good agreement with experiment. The strain paths resulting from stress paths containing corners and from paths composed of partial or complete unloading followed by reloading in a different direction are non-linear. The behaviour is attributed to strain history; namely, a Bauschinger effect where unloading occurs and an interaction between direction dependent plastic strains for stress paths containing corners. For unloading-reloading paths a rotation in the strain path towards a linear direction is indicative of the transient nature of strain history. Good agreement is found with the prediction from each of three rules of anisotropic hardening. They are thus generalized to provide the plastic strain response to any stress path that is composed of linear segments. Modifications that account for the effects of non-linear work hardening and creep are discussed.

Forming Limit Curves for Complex Strain Paths

2013 ◽  
Vol 58 (2) ◽  
pp. 587-593 ◽  
Author(s):  
J. Rojek ◽  
D. Lumelskyy ◽  
R. Pęcherski ◽  
F. Grosman ◽  
M. Tkocz ◽  
...  
Keyword(s):  
Plastic Strain ◽  
Strain Path ◽  
Experimental Studies ◽  
Polar Coordinates ◽  
Forming Limit ◽  
Effective Plastic Strain ◽  
Steel Blank ◽  
Strain Paths ◽  
Complex Strain ◽  
Forming Limit Curves

This paper presents results of experimental studies of forming limit curves (FLC) for sheet forming under complex strain paths. The Nakazima-type formability tests have been performed for the as-received steel blank and for the blank pre-strained by13%. Prestraining leads to abrupt change of strain path in the blank deformation influencing the forming limit curve. The experimental FLC of the pre-strained blank has been compared with the FLC constructed by transformation of the as-received FLC. Quite a good agreement has been found out. The concept of strain-path independent FLCs in polar coordinates has been verified. Two types of the polar diagrams have been considered, the first one with the strain-path angle and effective plastic strain as the polar coordinates, and the second one originally proposed in this work in which the thickness strain has been used instead of the effective plastic strain as one of the polar coordinates. The second transformation based on our own concept has given a better agreement between the transformed FLCs, which allows us to propose this type of polar diagrams as a new strain-path in dependent criterion to predict sheet failure in forming processes.

scholarly journals Kinematic and tectonic significance of microstructures and crystallographic fabrics within quartz mylonites from the Assynt and Eriboll regions of the Moine thrust zone, NW Scotland

1986 ◽  
Vol 77 (2) ◽  
pp. 99-125 ◽  
Author(s):  
R. D. Law ◽  
M. Casey ◽  
R. J. Knipe
Keyword(s):  
Strain Path ◽  
Extensional Flow ◽  
Crystallographic Preferred Orientation ◽  
X Ray ◽  
Tectonic Significance ◽  
Thrust Zone ◽  
Thrust Sheets ◽  
Strain Paths ◽  
Tectonic Loading ◽  
Microstructural Studies

ABSTRACTUsing a combination of optical microscopy and X-ray texture goniometry, an integrated microstructural and crystallographic fabric study has been made of quartz mylonites from thrust sheets located beneath, but immediately adjacent to, the Moine thrust in the Assynt and Eriboll regions of NW Scotland. A correlation is established between shape fabric symmetry and pattern of crystallographic preferred orientation, a particularly clear relationship being observed between shape fabric variation and quartza-axis fabrics.Coaxial strain paths dominate the internal parts of the thrust sheets and are indicated by quartzc- anda-axis fabrics which are symmetrical with respect to foliation and lineation. Non-coaxial strain paths are indicated within the more intensely deformed quartzites located near the boundaries of the sheets by asymmetricalc- anda-axis fabrics. These kinematic interpretations are supported by microstructural studies. At the Stack of Glencoul in the northern part of the Assynt region, the transition zone between these kinematic (strain path) domains is located at approximately 20 cm beneath the Moine thrust and is marked by a progression from symmetrical cross-girdlec-axis fabrics (30cm beneath the thrust), through asymmetrical cross-girdlec-axis fabrics to asymmetrical single girdlec-axis fabrics (0·5 cm beneath the thrust).Tectonic models (incorporating processes such as extensional flow, gravity spreading and tectonic loading) which may account for the presence of strain path domains within the thrust sheets are considered, and their compatibility with local thrust sheet geometries assessed.

Local Mesh Refinement for Correlation of FEA Estimated Plastic Strain to Tests in Areas of High Plastic Strain

2018 ◽  
Author(s):  
Katharine Liu ◽  
Emma Xiao ◽  
Gregory Westwater ◽  
Christopher R. Johnson ◽  
J. Adin Mann
Keyword(s):  
Plastic Strain ◽  
Mesh Refinement ◽  
Sensitivity Study ◽  
Linear Elastic ◽  
Mesh Sensitivity ◽  
Local Mesh Refinement ◽  
Order Of Magnitude ◽  
High Plastic Strain ◽  
Stabilization Technique ◽  
The Impact

The total strain, elastic plus plastic, was measured with strain gages on valve bodies with internal pressure that caused surface yielding. The correlation of the simulated maximum principal strain was compared to strain gage data. A mesh sensitivity study shows that in regions of large plastic strain, mesh elements are required that are an order of magnitude smaller than what is used for linear elastic stress analysis for the same structure. A local mesh refinement was adequate to resolve the local high strain values. Both the location and magnitude of the maximum strain changed with a local mesh refinement. The local mesh refinement requirement was consistent over several structures that were tested. The test and simulation work will be presented along with the mesh sensitivity study. Some results on using an energy stabilization technique to aid convergence will be presented in terms of the impact on the predicted plastic strain.

Low Cycle Fatigue Life of Type 316 Stainless Steel Notched Specimen Under Proportional and Non-Proportional Multiaxial Loadings

2010 ◽  
Author(s):  
Takamoto Itoh
Keyword(s):  
Stainless Steel ◽  
Fatigue Life ◽  
Strain Path ◽  
Low Cycle Fatigue ◽  
Cycle Fatigue ◽  
Notched Specimen ◽  
Life Estimation ◽  
316 Stainless Steel ◽  
Strain Parameter ◽  
Strain Paths

This study discusses multiaxial low cycle fatigue life of notched specimen under proportional and non-proportional loadings at room temperature. Strain controlled multiaxial low cycle fatigue tests were carried out using smooth and circumferentially notched round-bar specimens of type 316 stainless steel. Four kinds of notched specimens were employed of which elastic stress concentration factors, Kt, are 1.5, 2.5, 4.2 and 6.0. The strain paths include proportional and non-proportional loadings. The former employed a push-pull straining or a reversed torsion straining. The latter was achieved by strain path where axial and shear strains has 90 degree phase difference but their amplitudes is the same based on von Mises’ criterion. The notch dependency of multiaxial low cycle fatigue life and the life estimation are discussed. The lives depend on both Kt and strain path. The strain parameter for the life estimation is also discussed with the non-proportional strain parameter proposed by the author with introducing Kt. The proposed parameter gives a satisfactory correlation with multiaxial low cycle fatigue life of notched specimen of type 316 stainless steel under proportional and non-proportional loadings.

Orientation and Path Dependence of Formability in the Stress- and the Extended Stress-Based Forming Limit Curves

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
Kaan Inal ◽  
Michael J. Worswick
Keyword(s):  
Strain Path ◽  
Path Dependence ◽  
Forming Limit ◽  
Stress Space ◽  
Forming Limit Diagrams ◽  
Metall Trans ◽  
Strain Paths ◽  
Strain Path Changes ◽  
Path Dependent ◽  
Forming Limit Curves

This article analyzes the formability data sets for aluminum killed steel (Laukonis, J. V., and Ghosh, A. K., 1978, “Effects of Strain Path Changes on the Formability of Sheet Metals,” Metall. Trans. A., 9, pp. 1849–1856), for Al 2008-T4 (Graf, A., and Hosford, W., 1993, “Effect of Changing Strain Paths on Forming Limit Diagrams of Al 2008-T4,” Metall. Trans. A, 24A, pp. 2503–2512) and for Al 6111-T4 (Graf, A., and Hosford, W., 1994, “The Influence of Strain-Path Changes on Forming Limit Diagrams of Al 6111 T4,” Int. J. Mech. Sci., 36, pp. 897–910). These articles present strain-based forming limit curves (ϵFLCs) for both as-received and prestrained sheets. Using phenomenological yield functions, and assuming isotropic hardening, the ϵFLCs are transformed into principal stress space to obtain stress-based forming limit curves (σFLCs) and the principal stresses are transformed into effective stress and mean stress space to obtain the extended stress-based forming limit curves (XSFLCs). A definition of path dependence for the σFLC and XSFLC is proposed and used to classify the obtained limit curves as path dependent or independent. The path dependence of forming limit stresses is observed for some of the prestrain paths. Based on the results, a novel criterion that, with a knowledge of the forming limit stresses of the as-received material, can be used to predict whether the limit stresses are path dependent or independent for a given prestrain path is proposed. The results also suggest that kinematic hardening and transient hardening effects may explain the path dependence observed in some of the prestrain paths.

Effect of Strain Paths on Formability Evaluation of TRIP Steels

2010 ◽  
Vol 89-91 ◽  
pp. 214-219 ◽  
Author(s):  
David Gutiérrez ◽  
A. Lara ◽  
Daniel Casellas ◽  
Jose Manuel Prado
Keyword(s):  
Strain Path ◽  
High Strength Steels ◽  
High Strength ◽  
Test Method ◽  
Forming Limit ◽  
Trip Steels ◽  
Advanced High Strength Steels ◽  
Strain Paths ◽  
Analysis System

The Forming Limit Diagrams (FLD) are widely used in the formability analysis of sheet metal to determine the maximum strain, which gives the Forming Limit Curve (FLC). It is well known that these curves depend on the strain path during forming and hence on the test method used to calculate them. In this paper, different stretching tests such as the Nakajima and the Marciniak tests were performed, with different sample geometries to obtain points in different areas of the FLD. An optical analysis system was used, which allows following the strain path during the test. The increasing use of advanced high-strength steels (AHSS) has created an interest in determining the mechanical properties of these materials. In this work, FLCs for a TRIP steel were determined using Nakajima and Marciniak tests, which revealed different strain paths depending on the type of test. Determination of the FLCs was carried out following the mathematical calculations indicated in the ISO 12004 standard and was also compared with an alternative mathematical method, which showed different FLCs. Finally, the tests were verified by comparing the strain paths of the Nakajima and Marciniak tests with a well-known mild steel.

Thermomechanical Fatigue Life Prediction of 63Sn/37Pb Solder

1992 ◽  
Vol 114 (2) ◽  
pp. 145-151 ◽  
Author(s):  
Q. Guo ◽  
E. C. Cutiongco ◽  
L. M. Keer ◽  
M. E. Fine
Keyword(s):  
Fatigue Life ◽  
Plastic Strain ◽  
Life Prediction ◽  
Strain Range ◽  
Thermomechanical Fatigue ◽  
Fatigue Tests ◽  
Experimental Results ◽  
Fatigue Life Prediction ◽  
Total Strain ◽  
Isothermal Fatigue

Isothermal and thermomechanical fatigue of 63Sn/37Pb solder is studied under total strain-controlled tests. A standard definition of failure is proposed to allow inter-laboratory comparison. Based on the suggested failure criterion, load drop per cycle, the Young’s modulus and the ratio of the maximum tensile to maximum compressive stresses remain constant, and the fatigue response of the solder is stable before failure, although cyclic softening was observed from the beginning. Experimental results of isothermal fatigue tests for a total strain range from 0.3 to 3 percent show that the log-log plot of the number of cycles to failure versus the plastic strain range has a kink at the point where the elastic strain is approximately equal to the plastic strain. In this paper, it is shown how the isothermal fatigue life of near-eutectic solder at lower strain ranges can be predicted by using the experimental data of fatigue tests at high strain ranges and early stage information of a fatigue test at the strain range in question. A thermomechanical fatigue life prediction is also given based on a dislocation pile-up model. Comparison with experimental results shows a good agreement.

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