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.

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.

Determination of large strains in metalforming

1982 ◽  
Vol 17 (2) ◽  
pp. 95-101 ◽  
Author(s):  
R Sowerby ◽  
E Chu ◽  
J L Duncan
Keyword(s):  
Nodal Point ◽  
Grid Method ◽  
Deformation Mode ◽  
Surface Phenomenon ◽  
Large Strains ◽  
Grid Pattern ◽  
Principal Axes ◽  
Strain Paths ◽  
Straight Lines

Certain techniques for the experimental determination of large strains in metalforming are discussed. The methods employ a grid pattern marked on the surface of the workpiece before forming and subsequently measured after deformation. The grid method is a surface phenomenon and the strain determination is reduced to a two dimensional problem. Any measurements taken on the initial and final grid configurations only, without knowing the deformation path, are insufficient to determine the strains precisely. Nevertheless, in practice, strains are determined by such a technique, often by using grid circles and by further assuming they deform into ellipses. The deformation process which transforms circles to ellipses and straight lines to straight lines, still does not define the straining path. Under such a deformation mode strain paths can be divided into two main types, those where an initially orthogonal pair of line elements (the principal axes) remain orthogonal throughout the deformation and those where they do not. The same change in shape can be achieved by either type of straining path, but the distinction between each straining mode is discussed and analysed in simple terms. The analysis is performed with reference to a square or quadrilateral grid of lines since automatic image analysis can be most effectively exploited when using coordinate or nodal point measures.

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.

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.

A numerical solution of cavity expansion problem in sand based directly on experimental stress-strain curves

1998 ◽  
Vol 35 (4) ◽  
pp. 541-559 ◽  
Author(s):  
Branko Ladanyi ◽  
Adolfo Foriero
Keyword(s):  
Numerical Solution ◽  
Strain Path ◽  
Shear Resistance ◽  
Cavity Expansion ◽  
Large Strains ◽  
Volume Changes ◽  
Stress Strain ◽  
Stress Variation ◽  
Cylindrical Cavity Expansion ◽  
State Of Stress

A numerical solution of a spherical and cylindrical cavity expansion problem in sand is presented herein. The underlying theory is unbiased in that it is based directly on experimentally determined stress-strain curves. The solution makes it possible to follow the continuous variation of strains, stresses, and volume changes produced by cavity expansion. It essentially uses the "strain path" approach to determine the state of stress around the cavity, taking into account large strains and the effect of spherical stress variation on the mobilized shear resistance and the associated volume strains. A limited comparison with experimental data shows a reasonable agreement between theory and measurements.Key words: cavities, expansion, sand, stress-strain curves, numerical solution.

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.

Experimental assessment of the response of sands under shear–volume coupled deformation

2008 ◽  
Vol 45 (9) ◽  
pp. 1310-1323 ◽  
Author(s):  
S. Sivathayalan ◽  
P. Logeswaran
Keyword(s):  
Shear Strength ◽  
Boundary Conditions ◽  
Pore Pressure ◽  
Effective Stress ◽  
Strain Path ◽  
Stress Ratio ◽  
Volumetric Strain ◽  
Strain Paths ◽  
Pressure Boundary Conditions ◽  
Effective Stress Ratio

An experimental study of the behaviour of an alluvial sand under different strain increment paths representing shear–volume coupled deformation is presented. Both pore pressure and pore volume change simultaneously in these tests. Linear strain paths with different levels of limiting volumetric strain and nonlinear strain paths that simulate different pore pressure boundary conditions were applied to the soil specimen in the laboratory. The strain paths imposed included both expansive and contractive volumetric deformation. Nonuniform excess pore pressures generated during earthquakes (on account of the heterogeneity in natural soils) often lead to such deformation in situ following the end of strong shaking. The shear strength of the soil could decrease significantly when the pore pressure boundary conditions result in volume inflow that leads to a considerable reduction of the effective confining stress. The rate of volume inflow plays a significant role on the resulting stress–strain and pore pressure responses. Both the peak and the minimum shear strength mobilized during the test were significantly dependent on the strain path. The effective stress ratio at the instant of peak pore pressure is independent of the strain path followed, and it is equal to the effective stress ratio noted at the instant of phase transformation in undrained tests.

scholarly journals Numerical aspects of fluid infusion inside a compressible porous medium undergoing large strains

2008 ◽  
pp. 819-827
Author(s):  
Pierre Celle ◽  
Sylvain Drapier ◽  
Jean-Michel Bergheau
Keyword(s):  
Porous Medium ◽  
Large Strains ◽  
Manufacturing Processes ◽  
Reliable Prediction ◽  
Fluid Infusion ◽  
Finite Element Software ◽  
Cost Reductions ◽  
Reactive Fluid Flow ◽  
Part Thickness ◽  
Numerical Treatments

A new model for a thermo-reactive fluid flow across a highly compressible porous medium has been proposed and employed to predict infusion-based manufacturing processes for polymer composites (Celle, 2006). These techniques consist in mixing the reinforcements and the resin during the manufacturing cycle, transversely to the fabrics plane, by applying a pressure on the resin/preform stacking. This yields cost reductions and avoids filling problems. The introduction of a numerical model in a finite element software to study infusion-based processes will increase their diffusion by a reliable prediction of both part thickness and porosity (Celle et al., 2008). The present paper deals mainly with the numerical treatments related to the resin layer.

scholarly journals Characterization of Flow Induced Anisotropy in Sheet Metal at Large Strain

2021 ◽  
Author(s):  
F. Gutknecht ◽  
H. Traphöner ◽  
T. Clausmeyer ◽  
A. E. Tekkaya
Keyword(s):  
Strain Rate ◽  
Sheet Metal ◽  
Strain Path ◽  
Large Strain ◽  
High Strength ◽  
Bulge Test ◽  
Large Strains ◽  
Steel Grades ◽  
Strain Path Change ◽  
Cross Hardening

Abstract Background Many metals exhibit a stress overshoot, the so-called cross-hardening when subjected to a specific strain-path change. Existing tests for sheet metals are limited to an equivalent prestrain of 0.2 and show varying levels of cross-hardening for identical grades. Objective The aim is to determine cross-hardening at large strains, relevant for forming processes. Mild steel grades (DC04, DC06, DX56) and high strength steel grades (BS600, DP600, ZE800) are investigated to quantify the level of cross-hardening between different grades and reveal which grades exhibit cross-hardening at all. Method A novel test setup for large prestrain using hydraulic bulge test and torsion of curved sheets is developed to achieve an orthogonal strain-path change, i.e. the strain rate tensors for two subsequent loadings are orthogonal. The influence of strain rate differences between the tests and clamping of curved sheets on the determined cross-hardening are evaluated. The results are compared to experiments in literature. Results Cross-hardening for sheet metal at prestrains up to 0.6 true plastic strain are obtained for the first time. For DX56 grade the maximum cross-hardening for all prestrains have a constant level of approximately 6%, while the maximum cross-hardening for DC04 and DC06 grades increases, with levels between 7 and 11%. The high strength grades BS600 and ZE800 do not show cross-hardening behavior, while, differencing from previous publications, cross-hardening is observed for dual phase steel DP600. Conclusion Depending on the microstructure of the steel grade the cross-hardening increases with large prestrain or remains constant.

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