Unsupervised Deep Learning for Advanced Forming Limit Analysis in Sheet Metal: A Tensile Test-Based Approach

An accurate description of the formability and failure behavior of sheet metal materials is essential for an optimal forming process design. In this respect, the forming limit curve (FLC) based on the Nakajima test, which is determined in accordance with DIN EN ISO 12004-2, is a wide-spread procedure for evaluating the formability of sheet metal materials. Thereby the FLC is affected by influences originating from intrinsic factors of the Nakajima test-setup, such as friction, which leads to deviations from the linear strain path, biaxial prestress and bending superposition. These disadvantages can be circumvented by an alternative test combination of uniaxial tensile test and hydraulic bulge test. In addition, the forming limit capacity of many lightweight materials is underestimated using the cross-section method according to DIN EN ISO 12004-2, due to the material-dependent occurrence of multiple strain maxima during forming or sudden cracking without prior necking. In this regard, machine learning approaches have a high potential for a more accurate determination of the forming limit curve due to the inclusion of other parameters influencing formability. This work presents a machine learning approach focused on uniaxial tensile tests to define the forming limit of lightweight materials and high-strength steels. The transferability of an existing weakly supervised convolutional neural network (CNN) approach was examined, originally designed for Nakajima tests, to uniaxial tensile tests. Additionally, a stereo camera-based method for this purpose was developed. In our evaluation, we train and test materials, including AA6016, DX54D, and DP800, through iterative data composition, using cross-validation. In the context of our stereo camera-based approach, strains for different materials and thicknesses were predicted. In this cases, our method successfully predicted the major strains with close agreement to ISO standards. For DX54D, with a thickness of 0.8 mm, the prediction was 0.659 (compared to ISO's 0.664). Similarly, for DX54D, 2.0 mm thickness, the predicted major strain was 0.780 (compared to ISO 0.705), and for AA6016, at 1.0 mm thickness, a major strain of 0.314 (in line with ISO 0.309) was estimated. However, for DP800 with a thickness of 1.0 mm, the prediction yielded a major strain of 0.478 (as compared to ISO 0.289), indicating a divergence from the ISO standard in this particular case. These results in general, generated with the CNN stereo camera-based approach, underline the quantitative alignment of the approach with the cross-section method.

Automated summary

An accurate description of the formability and failure behavior of sheet metal materials is essential for optimizing forming process design. The forming limit curve (FLC) based on the Nakajima test is a widely used method for evaluating the formability of sheet metal materials. However, this method has limitations that can be overcome by using a combination of uniaxial tensile test and hydraulic bulge test. Machine learning approaches have the potential to improve the determination of the forming limit curve by incorporating other parameters. This work focuses on using a machine learning approach based on uniaxial tensile tests to define the forming limit of lightweight materials and high-strength steels.