Plastic Bending of Work Hardening Materials

Abstract

The plane strain plastic bending of rigid-work hardening materials has been investigated and two models have been proposed. In Model I, a numerical solution based on a linear σ¯ – ε¯ approximation for fibers in reversed loading has been presented. Model II is an extension of Proksa's analysis to the case of materials described by Ludwik's equation. It has been demonstrated that the results of these models are generally in close agreement. Also, the bending moment and the decrease in plate thickness predicted by these models compare favorably with reported experimental data.

The bending moment and springback in pure bending of anisotropic sheets

“…The elastic-plastic solution at large strains given in Wang et al (1993) has the aforementioned drawback that the actual distribution of strain in the vicinity of the neutral line has been replaced with an approximate distribution. Even though such an approach significantly simplifies the solution, an effect of the simplification on the accuracy of the final result is unclear (Dadras and Majless, 1982). An influence of plastic anisotropy on springback has been studied by Chan and Wang (1999).…”

“…The first exact solution at large strains has been given Hill (1950) for rigid perfectly plastic material. Approximate formulations for pure bending of rigid plastic, hardening material and corresponding solutions have been proposed in Dadras and Majless (1982). A similar approach has been employed by Verguts and Sowerby (1975) to study the pure bending process of laminated sheets of rigid perfectly plastic and rigid plastic hardening materials.…”

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

“…5. In the ranges 0 ≤ f ≤ f 1 ≈ 0.275 and f 2 ≤ f ≤ f 3 ( f 2 ≈ 0.528 and f 3 ≈ 0.69), the inequality (75) places no additional restriction on the range of the validity of the entire solution, i.e., the solution is valid in the range 0 ≤ ε 1 ≤ ε(2) 1 .In the range f 1 < f < f 2 , the condition (75) is violated at ζ = ζ 1 . In the rangef 3 < f ≤ f 4 ≈ 0.81,the condition (75) is violated at ζ = ζ 2 .…”

Solid solution softening and enhanced ductility in concentrated FCC silver solid solution alloys

“…The true uniform strain is the true strain at the maximum load, i.e., strain upon UTS point, which is often useful in estimating the ductility and formability of metals. In the plastic deformation region, the true stress can be also expressed mathematically in terms of yield stress and true plastic strain, depicted by Ludwik's equation [23], as shown in Eq. (3).…”