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.

scholarly journals A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

2022 ◽  
Author(s):  
Abhishek Biswas ◽  
Surya R Kalidindi ◽  
Alexander Hartmaier
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crystal Plasticity ◽  
Hybrid Method ◽  
Hybrid Approach ◽  
Yield Function ◽  
Yield Locus ◽  
Stress Space ◽  
Crystal Plasticity Finite Element ◽  
Yield Loci

Abstract Direct experimental evaluation of the anisotropic yield locus of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the yield locus by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted yield locus estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal yield loci for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire yield locus and also experiments. In the second step, the point cloud data of stress tensors on the yield loci predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced yield locus from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.

scholarly journals Application of Yield Loci Calculated From Texture Data

1989 ◽  
Vol 11 (1) ◽  
pp. 23-39 ◽  
Author(s):  
P. van Houtte ◽  
K. Mols ◽  
A. van Bael ◽  
E. Aernoudt
Keyword(s):  
Finite Element ◽  
Plastic Anisotropy ◽  
Expansion Method ◽  
Yield Locus ◽  
Stress Space ◽  
Finite Element Calculations ◽  
Plastic Forming ◽  
Yield Loci ◽  
Analytical Expressions ◽  
Series Expansion Method

The concept of the yield locus as a means of representing the plastic anisotropy of a textured material is remembered. It is shown how such yield loci can be used in a very general way, i.e. in full six-dimensional stress space. As an example of how such yield loci can actually be obtained, the series expansion method based on Taylor factors is explained. It is finally shown that these six-dimensional yield loci can be approximated by analytical expressions and under such form brought into finite element calculations of elasto-plastic forming processes.

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.

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.

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.

Anisotropic Yield Locus Evolution During Cold Pilgering of Titanium Alloy Tubing

2002 ◽  
Vol 124 (2) ◽  
pp. 125-134 ◽  
Author(s):  
Richard W. Davies ◽  
Mohammad A. Khaleel ◽  
William C. Kinsel ◽  
Hussein M. Zbib
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Titanium Alloy ◽  
Yield Criterion ◽  
Yield Locus ◽  
Mechanical Anisotropy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cold Pilgering ◽  
Stress Relieving

The cold pilger metal forming technique is known to produce round titanium alloy tubing with mechanical properties that may be significantly anisotropic. These mechanical properties are of interest to both the manufacturers and consumers for defining initial manufacturing limitations and defining the final product design limitations. This study focuses on experimentally characterizing the yield locus development of Ti-3Al-2.5V seamless tubing during cold pilgering and a subsequent thermal stress relieving process. The materials are experimentally characterized using a biaxial testing apparatus, which subjects the specimen tubes to combined axial load and internal pressure. The Hill yield criterion is subsequently fit to the experimental results producing continuous yield loci. Each specimen is also experimentally characterized using X-ray diffraction to gain insight into the material textures that accompany the macroscopic properties. All work is focused on one particular pilger pass at two different production rates. A second experimental variable is introduced to the study by using two significantly different input materials, as characterized by X-ray diffraction. This study also investigates the nature of the plastic deformation of the tubing developed during cold pilgering via finite element analysis and discusses the relationship between the finite element predictions and the mechanical anisotropy.

Plane Strain Rigid Plastic Finite Element Formulation for Sheet Metal Forming Processes

1993 ◽  
Vol 207 (3) ◽  
pp. 167-171 ◽  
Author(s):  
P A F Martins ◽  
M J M Barata Marques
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Yield Criterion ◽  
Large Strain ◽  
Theoretical Development ◽  
Element Formulation ◽  
Rigid Plastic

A rigid plastic finite element model for analysing two-dimensional plane strain sheet metal forming processes is described. The model is based on the large strain formulation using membrane theory, and the material is assumed to be rigid plastic, work hardening and conforms to Hill's anisotropic yield criterion and associated flow rules. The theoretical development follows the work of Kobayashi and Kim on the axisymmetric modelling of sheet metal forming. An application of the model for plane strain cylindrical punch stretching is presented. The results obtained are compared with those provided through an analytical membrane solution described in this work. The agreement found between both solutions is excellent.

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.

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