Instability Prediction for Sheet Metal Using 3D Strain Space
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Solution Overview
Problem
Current methods for determining instability points in sheet metal forming, particularly for high-strength and ultra-high-strength materials, are inadequate as they rely on proportional expansion paths and inaccurate instability point determination, limiting their effectiveness in predicting material failure and crack formation.
Innovation Solution
A computer-implemented method that calculates the equivalent plastic deformation based on triaxiality and change in thickness, allowing for the prediction of instability points regardless of the loading path, using a three-dimensional space with parameters triaxiality, relative thickness, and equivalent plastic strain to define a localization area that indicates material instability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If classic FLD (Forming Limit Diagram) methods are used based on proportional expansion paths, then the prediction of instability points can be simplified, but the accuracy deteriorates for high-strength and ultra-high-strength materials where non-proportional expansion paths occur
Solution Approach 1:
The patent extends the traditional two-dimensional FLD (plotting major strain vs. minor strain) into a three-dimensional instability criterion by introducing the Lode angle parameter. This creates a 3D criterion space where the instability condition is defined by combining equivalent plastic strain, Lode angle, and hydrostatic pressure. This dimensional extension allows the method to capture non-proportional expansion path effects while maintaining a systematic prediction framework.
Solution Approach 2:
The patent fundamentally changes the parameter set used for instability prediction. Instead of relying solely on strain parameters (major and minor strain), it introduces stress state parameters (Lode angle and hydrostatic pressure) combined with equivalent plastic strain. This parameter transformation enables accurate prediction for both proportional and non-proportional loading paths, particularly for high-strength materials where the stress state significantly influences instability behavior.
2Device complexity
If traditional FLD methods are used, then the analysis can be performed with basic strain data, but the reliability deteriorates due to inability to account for non-proportional loading paths and complex stress states
Solution Approach 1:
The patent replaces the purely mechanical/kinematic approach of traditional FLD (based on geometric strain measurements) with a mechanics-based approach that incorporates stress state analysis. By using Lode angle and hydrostatic pressure derived from stress tensors, the method substitutes simple strain comparison with a more rigorous mechanical analysis that accounts for the actual physical state of the material during forming.
Solution Approach 2:
The patent introduces equivalent plastic strain as an intermediary parameter that bridges the kinematic description (strain) and the mechanical description (stress state). This intermediary allows the integration of deformation history with current stress state, enabling the instability criterion to reflect both the accumulated damage and the instantaneous loading conditions, thereby improving predictive reliability.
3Measurement precision
If more comprehensive simulation methods are used to calculate actual expansion paths, then the prediction accuracy improves, but the computational complexity and time requirements increase
Solution Approach 1:
The patent extracts the essential features needed for instability prediction from complex simulations. Instead of requiring complete detailed simulations of the entire forming process, it focuses on extracting the equivalent plastic strain, Lode angle, and hydrostatic pressure at critical points. This extraction approach maintains accuracy by capturing the key parameters that govern instability while reducing computational burden.
Solution Approach 2:
The patent establishes a pre-defined instability criterion in the 3D criterion space that can be used for direct comparison with simulation results. By preparing the instability surface beforehand (defining the failure envelope in terms of equivalent plastic strain, Lode angle, and hydrostatic pressure), the actual forming simulation only needs to compute these three parameters at each step and check against the pre-established criterion, rather than performing complex real-time instability analysis.
Data Source
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AI summary
The method involves providing the characteristic features of flat semi-finished material to determine deformation parameter, in a computer database. The equivalent plastic strain on preset load path is determined using content in database or determined deformation parameter, based on the triaxiality or similar to the voltage characterizing suitable size. A three-dimensional space is formed with the coordinate axes based on the change in thickness of the flat semi-finished material. The surface of semi-finished material is generated in the three dimensional space. Independent claims are included for the following: (1) computer system; and (2) machine readable medium storing program for determining instability conditions of flat semi-finished material.