Calculate the residual stress on a beam after bending

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Discussion Overview

The discussion revolves around calculating the residual stress on a beam after it has undergone bending, specifically focusing on analytical approaches to model the stress and strain in the beam due to elasto-plastic behavior and springback effects. Participants explore various mathematical formulations and methods to derive the residual stress profile following unloading.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a linear hardening model for predicting stress and strain during bending, defining strain and stress equations based on the bending radius.
  • Another participant suggests calculating the yielded material and allowing the beam to relax to reach an equilibrium condition, indicating the complexity of the problem.
  • Some participants note that elasto-plastic bending with hardening is challenging to solve analytically, suggesting the use of Finite Element Analysis (FEA) for verification of results.
  • A participant expresses a desire for an analytical solution and discusses calculating the bending moment and stress profile, seeking clarification on how to derive residual stress after unloading.
  • One participant proposes that the bending moment calculated accounts for springback, leading to the conclusion that the residual stress can be derived from the difference between loading and unloading stress profiles.
  • Another participant shares an example of a stress-strain curve obtained from FEA, prompting questions about the validity of the loading diagram used in the simulation.
  • Concerns are raised regarding the accuracy of the stress-strain curve generated from FEA, with calls for clarification on the material behavior represented.
  • A participant describes their approach to deriving the springback equation and the challenges faced due to the beam's geometry, emphasizing the use of Mathematica for complex integrals.

Areas of Agreement / Disagreement

Participants express a mix of viewpoints, with some advocating for analytical methods while others suggest FEA as a more practical approach. There is no consensus on the best method to calculate residual stress, and disagreements arise regarding the interpretation of stress-strain curves and material behavior.

Contextual Notes

Participants acknowledge the limitations of their approaches, including the complexity of the beam's geometry and the potential for errors in mathematical formulations derived from online resources. The discussion highlights the need for careful consideration of assumptions in modeling material behavior.

  • #31
Pradip Kandel said:
Thanks, I was confused because of the equations I was unfamiliar with and those functions for Sigma(Stress). Do you have any other worked-out examples pdf that I could follow? Can you suggest any other references please? That would be such a huge help.
What are the dimensions and material properties of the pipe? Also, to which bending radius do you need?

What have you worked out up to now? In order to have a proper insight of the results it is better to understand well the theory and also its limitations instead of just “using the formulas”.
 
Last edited:
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