Forming Limit Strain Analysis for Sheet Metal Failure Prediction
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Solution Overview
Problem
Current methods for forming limit strain analysis in sheet metal forming, particularly in deep-drawing processes, face challenges in assessing material failure due to non-proportional strain paths, as existing forming limit strain curves are path-dependent, making it difficult to compare and visualize strain states accurately, and the sensitivity of stress changes near failure is low, leading to uncertainties in failure assessment.
Innovation Solution
A method that converts non-proportional strain states to equivalent strain states using a proportional strain trajectory in stress space, allowing for a single forming limit strain curve to assess all observed points, independent of the strain path, by iteratively adapting strain ratios and using stored mappings or approximation functions to determine equivalent strains, which correspond to proportional strain states for failure assessment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If forming limit strain curves are used for non-proportional strain paths, then material failure can be assessed, but the assessment accuracy deteriorates due to path-dependency
Solution Approach 1:
The patent transforms the strain path representation by introducing a decomposition approach where the non-proportional strain path is separated into a proportional component (for which FLC is valid) and a non-proportional component (which is quantified but not used for FLC assessment). This parameter transformation allows the use of existing FLC while accounting for path effects through the separation of strain components.
Solution Approach 2:
The patent introduces an intermediate representation system using proportional and non-proportional strain components as mediators. The proportional strain component serves as the intermediary that connects the actual non-proportional strain state to the forming limit strain curve, enabling accurate failure assessment by filtering out the path-dependent effects.
2Reliability
If multiple forming limit strain curves are created for different strain paths, then each path can be accurately assessed, but the analysis complexity increases
Solution Approach 1:
The patent makes the forming limit strain curve universal by demonstrating that it can be applied to all strain paths through the proportional strain component extraction. Instead of creating multiple path-specific curves, a single FLC is used in conjunction with the strain decomposition method, allowing one curve to serve multiple functions across different loading histories.
Solution Approach 2:
Instead of adapting the forming limit criterion to different strain paths (the conventional approach), the patent inverts the problem by adapting the strain path representation to match the criterion. By decomposing the strain path into proportional and non-proportional components, the method makes the strain data conform to the assumptions of the traditional FLC.
3Adaptability or versatility
If stress-based forming limit criteria are used, then path-independence is achieved, but the sensitivity to detect near-failure states decreases
Solution Approach 1:
The patent applies local quality by treating the proportional and non-proportional strain components differently in the assessment process. The proportional component is used for FLC assessment (where sensitivity is critical), while the non-proportional component is quantified separately. This differentiated treatment preserves the sensitivity advantages of strain-based criteria while achieving path-independence through selective usage.
Data Source
AI summary
In the computed-based analysis of forming processes, for example, manufacturing sheet metal parts for the automobile industry, the material loading is represented by major and minor strains εI, εII and is visualised with respect to a forming limit strain curve. In the method according to the invention, one proceeds from a target state (4n) of the material, as has been determined in the computed simulation of the forming process. A proportional trajectory of a loading and thus of the state variables of the material, in particular of the stresses (σ), is determined, which leads to the same target state. The associated proportional strain trajectory is evaluated for this proportional loading trajectory. The strain state (4p) which results from this strain trajectory, is called the equivalent strain state (4p) and may be used in the forming limit strain diagram for assessing the target state. Thereby, the equivalent strain state is set in relation to the forming limit strain curve (1) for the proportional trajectories.