A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

Alexandrov, Sergei; Manabe, Katsushi

doi:10.1007/s00419-011-0529-9

Cited by 24 publications

(25 citation statements)

References 19 publications

(24 reference statements)

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“…The present paper extends the solution given in [ 17 ] to finite plane strain bending under tension of isotropic and kinematic hardening sheets. Prager’s law [ 20 ] is used to describe kinematic hardening.…”

Section: Introductionsupporting

confidence: 62%

“…The compatibility of the strain distribution found with the stress equations should be verified a posteriori . This approach for pure plane strain bending has been proposed in [ 15 ] and extended to plane strain bending under tension in [ 17 ]. These papers have not dealt with kinematic hardening.…”

Section: Strain Analysismentioning

confidence: 99%

“…The authors of [ 15 ] adopted an inverse method that assumed transformation equations that connect Eulerian and Lagrangian coordinates, and showed that these equations described the geometry of plane strain bending at large strains. These equations can be used in conjunction with many constitutive equations [ 16 , 17 ]. The basic geometric assumptions used in [ 15 ] were similar to or even less restrictive than those accepted in papers published in journals devoted to metal forming [ 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

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Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

2021

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The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

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Section: Introductionsupporting

confidence: 62%

Section: Strain Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

2021

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“…(23)). Then, the distribution of the radial stress is given by Eqs, (19) and (21). This distribution depends on two variables, a and ] .…”

Section: Discussionmentioning

confidence: 99%

Plane strain bending under tension as an ideal flow process in pressure – dependent plasticity

Alexandrov

Date

2017

MATEC Web Conf.

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Abstract. Ideal plastic flows are those for which all material elements follow minimum work paths. Ideal flow solutions are widely used as the basis for inverse methods for the preliminary design of metalworking processes. The present paper provides the first ideal flow solution in pressure-dependent plasticity. In particular, the process of bending under tension is considered and it is shown that there are relations between the bending moment and tensile force that result in ideal flow paths.

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“…In addition to experimental measurement, analytical solution for prediction of residual stresses due to bending is considered by researchers. 28,29 In slitting method, uncertainty analysis has an important role for prediction of stress profile. 30–32 The proper order of polynomial basis function is obtained according to uncertainty analysis.…”

Section: Introductionmentioning

confidence: 99%

Residual stresses due to roll bending of bi-layer Al-Cu sheet: Experimental and analytical investigations

Sedighi

Joudaki

Kheder

2017

The Journal of Strain Analysis for Engineering Design

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Applications of bi-layer sheets are developing in different industries. In many cases, manufacturers need to form bi-layer sheets to a desired curve by roll bending process. This process can induce considerable residual stresses. In this article, the residual stress distribution due to bending to specified curvature radius is measured in an Al-Cu sample. The sample is bent by three roll bending process to curvature radius of 350 mm. The slitting method is extended to measure induced residual stresses in bi-layer sheets. Also, an analytical solution has been proposed for prediction of residual stresses in bi-layer sheet. The analytical solution has been derived for material with elastic-power law hardening plastic behavior as the actual behavior of aluminum and copper is. Also in the analytical solution, the neutral axis movement due to different elastic moduli of aluminum and copper layer is considered. A maximum and minimum of measured residual stresses equal to 35 and 228 MPa, respectively, showing a remarkable magnitude in comparison with 51 and 36 MPa yield strength of copper and aluminum layer, respectively. Comparing the results show good agreement between analytical solution and experimental results.

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A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

Cited by 24 publications

References 19 publications

Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets

Plane strain bending under tension as an ideal flow process in pressure – dependent plasticity

Residual stresses due to roll bending of bi-layer Al-Cu sheet: Experimental and analytical investigations

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