scholarly journals Lower Bound Yield Locus Calculations

1990 ◽  
Vol 12 (1-3) ◽  
pp. 89-101 ◽  
Author(s):  
William Hosford ◽  
Aitor Galdos
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Work Hardening ◽  
Stress Ratio ◽  
Yield Criterion ◽  
Yield Locus ◽  
Stress Strain ◽  
Strain Behavior ◽  
Yield Loci ◽  
The Hill

A lower-bound model for the deformation of work-hardening polycrystals is proposed. All grains are assumed to be loaded under the same stress and the stress–strain behavior is found by averaging the strains in all grains. The shapes of the yield loci have been calculated for textured metals which deform by {111} 〈110〉 slip (fcc) and by 〈111〉-pencil glide (bcc). As with the corresponding upper-bound models, the yield loci are best described by an anisotropic yield criterion with an exponent of 6 to 10 (instead of 2 as in the Hill theory). Also it is shown that a model of polycrystal deformation in which the grains are loaded to the same stress ratio (but not the same level of stresses) violates normality and is not a lower bound.

Applications of the Hill 1948 Yield Criterion Development, Performance Evaluation and Comparison for Describing the Behaviour of Different CRCA Grades

2021 ◽  
Vol 13 (2) ◽  
Author(s):  
S.P. Sundar Singh Sivam ◽  
Harshavardhana Natarajan ◽  
Durai Kumaran ◽  
P.R. Shobana Swarna Ratna
Keyword(s):  
Plastic Flow ◽  
Deep Drawing ◽  
Metal Forming ◽  
Yield Criterion ◽  
Principal Stresses ◽  
Yield Functions ◽  
Anisotropic Coefficient ◽  
Yield Loci ◽  
Criterion Development ◽  
The Hill

The sheet metal forming processes in several industries like automobile and aerospace suppose the yielding of the sheet metals once strained. Yielding is categorized by the plastic flow of the materials once strained. The yield purpose just in case of uniaxial tension may be simply determined from the stress strain graph, however just in case of multi axial stresses it gets complicated. A relationship among the principal stresses is required requiring the circumstances underneath that plastic flow happens. This complexity is addressed by the anisotropic yield functions. Also, the investigation to get yield loci could also be expensive and time taking. In such case these yield functions prove to be very effective. The yield criteria also facilitate in decisive planar distribution of yield stresses and anisotropic coefficients which gives a decent estimate of these mechanical parameters while not having to through the pain of experimental determination. This study aims at using Hill 1948 criterion to get the Yield Surface Diagrams for three different grades of CRCA Sheets such as ordinary (o), Deep Drawing (DD) and Extra Deep Drawing (EDD) to get the planar distribution of the uniaxial yield stress and anisotropic coefficient. Also, the performance analysis of different grades the distributions are done using accuracy index.

Technical Basis for the Extension of ASME Code Case N-494 for Assessment of Austenitic Piping

1996 ◽  
Vol 118 (4) ◽  
pp. 513-516 ◽  
Author(s):  
J. M. Bloom
Keyword(s):  
Lower Bound ◽  
Pressure Vessel ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Failure Assessment Diagram ◽  
Strain Behavior ◽  
Failure Assessment ◽  
Asme Code ◽  
Constraint Effects

In 1990, the ASME Boiler and Pressure Vessel Code for Nuclear Components approved Code Case N-494 as an alternative procedure for evaluating flaws in light water reactor (LWR) ferritic piping. The approach is an alternate to Appendix H of the ASME Code and allows the user to remove some unnecessary conservatism in the existing procedure by allowing the use of pipe specific material properties. The Code case is an implementation of the methodology of the deformation plasticity failure assessment diagram (DPFAD). The key ingredient in the application of DPFAD is that the material stress-strain curve must be in the format of a simple power law hardening stress-strain curve such as the Ramberg-Osgood (R-O) model. Ferritic materials can be accurately fit by the R-O model and, therefore, it was natural to use the DPFAD methodology for the assessment of LWR ferritic piping. An extension of Code Case N-494 to austenitic piping required a modification of the existing DPFAD methodology. Such an extension was made and presented at the ASME Pressure Vessel and Piping (PVP) Conference in Minneapolis (1994). The modified DPFAD approach, coined piecewise failure assessment diagram (PWFAD), extended an approximate engineering approach proposed by Ainsworth in order to consider materials whose stress-strain behavior cannot be fit to the R-O model. The Code Case N-494 approach was revised using the PWFAD procedure in the same manner as in the development of the original N-494 approach for ferritic materials. A lower-bound stress-strain curve (with yield stress comparable to ASME Code specified minimum) was used to generate a PWFAD curve for the geometry of a part-through wall circumferential flaw in a cylinder under tension and bending. Earlier work demonstrated that a cylinder under axial tension with a 50-percent flaw depth, 90 deg in circumference, and radius to thickness of 10, produced a lower-bound FAD curve. Validation of the new proposed Code case procedure for austenitic piping was performed using actual pipe test data. Using the lower-bound PWFAD curve, pipe test results were conservatively predicted (failure stresses were predicted to be 31.5 percent lower than actual on the average). The conservative predictions were attributed to constraint effects where the toughness values used in the predictions were obtained from highly constrained compact test specimens. The resultant development of the PWFAD curve for austenitic piping led to a revision of Code Case N-494 to include a procedure for assessment of flaws in austenitic piping.

Effect of tensile prestrain on the yield locus of 1100-f aluminium

1970 ◽  
Vol 5 (2) ◽  
pp. 128-139 ◽  
Author(s):  
J F Williams ◽  
N L Svensson
Keyword(s):  
Bauschinger Effect ◽  
Yield Criterion ◽  
Significant Degree ◽  
Yield Locus ◽  
Statistical Reasoning ◽  
Pure Aluminium ◽  
Stress Tests ◽  
Commercially Pure ◽  
Rounded Corner ◽  
Yield Loci

A series of combined stress tests in torsion-tension space is carried out on thin-walled tubes of 1100-F commercially pure aluminium. One initial and four subsequent yield loci are established to a maximum prestrain level of 14 per cent tensile plastic strain. The results are analysed in terms of a proposed, rationally based, yield criterion constructed according to statistical reasoning. It is shown that during prestrain a significant degree of geometrical distortion is undergone by the yield loci, accompanied by a strong Bauschinger effect and a flattening of part of the locus opposite to the loading point. It is found that the yield locus does not rotate during prestrain and, contrary to the case for torsion prestrain, exhibits evidence of a sharply rounded corner developing at the loading point. The proposed criterion is shown to fit the experimental results extremely well and the mechanism of distortion is explained in terms of a statistical model for work-hardening materials.

The Effect of the Rotation of the Stress Axes on the Yield Criterion of Prestrained Materials

1966 ◽  
Vol 88 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Tao-Ching Hsu
Keyword(s):  
Yield Stress ◽  
Stress Ratio ◽  
Biaxial Tension ◽  
Yield Criterion ◽  
Yield Locus ◽  
Characteristic Index ◽  
Axial Tension ◽  
Combined Stresses ◽  
Stress Direction ◽  
Tubular Specimens

The yield locus of a prestrained material can be based on different systems of combined stress, such as biaxial tension and combined tension and shear. No matter what the combined stresses may be, however, the deviatoric yield stress is a function of only two variables, the characteristic index, which represents the stress ratio, and the stress direction, or the inclination of the principal stress axes. It is shown that, when tubular specimens are tested under combined torsion and axial tension, the results show the mixed effects of the characteristic index and the stress direction on the yield stress. In such tests, the two effects can, however, be separated if the strain vectors as well as the yield stresses are known. The theory is applied to several groups of experimental results on the yield locus of prestrained materials, including Taylor and Quinney’s results.

A theory of the yield locus and flow rule of anisotropic materials

1966 ◽  
Vol 1 (3) ◽  
pp. 204-215 ◽  
Author(s):  
T. C. Hsu
Keyword(s):  
Experimental Data ◽  
Linear Relationship ◽  
Yield Stress ◽  
Plane Stress ◽  
Stress Ratio ◽  
Yield Criterion ◽  
Anisotropic Materials ◽  
Yield Locus ◽  
Flow Rule ◽  
Stress Components

A general yield criterion for anisotropic materials is derived from the linear relationship between strain and stress components. The particular forms of the yield criterion for plane stress and for certain types of symmetry are discussed and are compared with available experimental data. The separate effects of the stress ratio and the direction of the stress axes on the yield stress are also determined.

scholarly journals Characteristics of Stress-Strain Behavior for Lade's Single Work-Hardening Constitutive Model with Stress Path of Sands

2012 ◽  
Vol 11 (2) ◽  
pp. 1-9
Author(s):  
Chan-Kee Kim ◽  
Jong-Cheon Lee ◽  
Won-Beom Cho ◽  
Wook-Geun Park ◽  
Hwan-Wook Kim
Keyword(s):  
Constitutive Model ◽  
Work Hardening ◽  
Stress Path ◽  
Stress Strain ◽  
Strain Behavior

scholarly journals The Incorporation of Texture-Based Yield Loci Into Elasto-Plastic Finite Element Programs

1995 ◽  
Vol 24 (4) ◽  
pp. 255-272 ◽  
Author(s):  
P. Van Houtte ◽  
A. Van Bael ◽  
J. Winters
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Strain Rate ◽  
Crystallographic Texture ◽  
Metal Forming ◽  
Yield Criterion ◽  
Yield Locus ◽  
Stress Space ◽  
Plastic Modulus ◽  
Yield Loci

Elasto-plastic finite elements (FE) methods are nowadays widely used to simulate complex metal forming processes. It is then useful to generate an anisotropic yield criterion from the crystallographic texture and incorporate it into such model. The theory of dual plastic potentials (one in strain rate space and one in stress space) helps to achieve this. There is however a certain danger of losing the convexity of the yield locus during this procedure. Examples of this phenomenon are given and discussed. It is furthermore explained how the yield locus can be used to generate an elasto-plastic modulus for implementation in the FE code. Finally several examples of successful applications of the anisotropic FE code to metal forming problems are given.

Effect of torsional prestrain on the yield locus of 1100-F aluminium

1971 ◽  
Vol 6 (4) ◽  
pp. 263-272 ◽  
Author(s):  
J F Williams ◽  
N L Svenssoon
Keyword(s):  
Yield Criterion ◽  
Maximum Level ◽  
Significant Degree ◽  
Yield Locus ◽  
Statistical Reasoning ◽  
Pure Aluminium ◽  
Stress Tests ◽  
Combined Stress ◽  
Commercially Pure ◽  
Yield Loci

A series of combined stress tests in torsion-tension space is carried out on thin-walled tubes of 1100-F commercially pure aluminium, prestrained to a maximum level of 10 per cent torsional plastic strain. The results are analysed in terms of a proposed, rationally based, yield criterion constructed on statistical reasoning. It is shown that during prestrain, the yield loci undergo a significant degree of distortion, accompanied by a flattening of part of the locus opposite to the loading point. It is found that the yield locus does not rotate under prestrain and, contrary to the findings for tensile prestrain, little evidence of the development of corners at the loading point is observed. The proposed criterion is shown to provide a good fit to the experimental results.

Simulation of Deformation Texture Evolution Using an Intermediate Model

2005 ◽  
Vol 105 ◽  
pp. 251-258 ◽  
Author(s):  
Saïd Ahzi ◽  
S. M'Guil
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Upper Bound ◽  
Texture Evolution ◽  
Deformation Texture ◽  
Random Orientation ◽  
Intermediate Model ◽  
Strain Behavior ◽  
Tension And Compression ◽  
Texture Transition

The aim of this work is to propose the use of an intermediate model for large viscoplastic deformations that could predict the texture transition and stress-strain behavior in a range that spans from the upper bound (Taylor) to the lower bound (Sachs) estimates. In this model, we introduced a single parameter as a weight function to formulate the intermediate model which combines the Taylor and Sachs estimates. For the applications, we focus on the three main tests: plane strain compression, uniaxial tension and compression. An FCC polycristal represented by 100 crystals with an initially random orientation is used. The results for texture evolution show that a transition between the copper and brass type textures can be obtained by the proposed intermediate model.

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