Elastic-Plastic Constitutive Model for Springback Prediction
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Solution Overview
Problem
The existing methods for simulating the stress-strain relation of elastic-plastic materials during press forming, particularly when stress is reversed, are inaccurate due to the small magnitude of plastic strain in the unloading process, leading to difficulties in predicting the springback amount and accurately reproducing the Bauschinger effect.
Innovation Solution
A new elastic-plastic constitutive model is developed, modifying the Yoshida-Uemori model by adjusting the yield surface radius and using a kinematic hardening incremental vector to accurately simulate the stress-strain relation during unloading and re-tension, with the coefficient C determined by the stress-change amount after stress reversal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Yoshida-Uemori model is used to simulate stress-strain relation during unloading, then the Bauschinger effect can be reproduced, but the simulation accuracy deteriorates due to small plastic strain magnitude making coefficient determination difficult
Solution Approach 1:
The patent changes the parameter basis for determining the kinematic hardening coefficient from strain-based to stress-based. Specifically, the coefficient C is determined using stress-change amount (Δσ) after stress reversal instead of plastic strain, which overcomes the measurement precision problem caused by small plastic strain magnitude during unloading while maintaining reliable Bauschinger effect reproduction
Solution Approach 2:
The patent uses readily available stress-strain data from standard tensile tests to determine the kinematic hardening coefficient, eliminating the need for complex and difficult unloading tests. This approach uses 'cheap' (easy to obtain) data to achieve the same simulation reliability that would otherwise require difficult 'expensive' (complex testing) procedures
2Device complexity
If conventional isotropic-hardening model is used, then the model simplicity is maintained, but the springback prediction accuracy deteriorates due to inability to capture non-linear stress-strain relation after stress reversal
Solution Approach 1:
The patent introduces a dynamic kinematic hardening mechanism that allows the yield surface to translate in stress space based on stress reversal history. This dynamic adjustment of the yield surface position enables accurate capture of non-linear stress-strain behavior after unloading and re-tension, significantly improving springback prediction accuracy while adding manageable complexity through the stress-based coefficient determination
3Ease of manufacture
If linear approximation of stress-strain relation is used after yield point, then the calculation simplicity is improved, but the simulation accuracy deteriorates due to early yield phenomenon deviation from elastic deformation region
Solution Approach 1:
The patent segments the stress-strain behavior into distinct regions: elastic region, plastic deformation region with kinematic hardening, and unloading/re-tension region. By applying different constitutive relationships to each segment and using stress-change amount to control the transition and hardening behavior, the model accurately captures the non-linear early yield phenomenon while maintaining computational efficiency through the piecewise approach
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for accurate simulation of the stress-strain relation and prediction of springback amounts, improving the accuracy of springback analysis in press forming by matching calculated values with experimental results.
Implementation Method 1
a model of large-strain cyclic plasticity describing the Bauschinger effect and workhardening stagnation
Implementation Method 2
after the material undergoes the elastic deformation region, plastic deformation occurs
Implementation Method 3
plastic deformation occurs starting at the yield point A, and the plastic deformation continues to the point B
Data Source
Figure 1A~1B
Figure 2~3
Figure 4~5
AI summary
Displacement or a load is applied to an elastic-plastic material to deform the elastic-plastic material plastically to acquire experimental values of a stress-strain relation. With a kinematic-hardening incremental vector dαij of a yield surface in an elastic-plastic constitutive model as a predetermined first equation, the elastic-plastic constitutive model being defined as a function of stress and back stress, a computer identifies material constants contained in the elastic-plastic constitutive model with the acquired experimental values. The computer identifies material constants contained in a predetermined second equation on the basis of the acquired experimental values and the predetermined first equation into which the identified material constants are substituted. The computer simulates the stress-strain relation of the elastic-plastic material with the predetermined first equation, the predetermined second equation, and the elastic-plastic constitutive model into which the identified material constants are substituted.