The industry faces regularly long-term goals regarding the reduction of greenhouse gas emission. A lot of effort is therefore put in finding new design solutions and material selections, which can reduce the lifecycle ecological footprint through energy efficient production and reduced weight of e.g. vehicles. At the same time, innovative design and new materials have to fulfil the demand regarding final product performance.
Modelling and simulation to predict final properties of parts, as well as their manufacturing processes, is a very powerful tool to reduce time and costs during the development of new products, including novel material solutions introduced to the market.
Especially in the automotive and aerospace sector, industries demand being able to simulate processes like e.g. sheet metal forming and to predict performance such as crashworthiness and structural stiffness. However, the quality of modelling outcome is highly dependent on accurate mechanical material data. In sheet metal forming, large deformations often occur and there might be a risk of failure.
FormPlanet offers a fast and reliable method to obtain the flow stress from initial yielding to final fracture.
Stepwise Modelling Method
The Stepwise Modelling Method (SMM) is a novel direct method to characterise the constitutive stress-strain relation from initial yielding to final fracture based on tensile tests and deformation field data obtained by digital speckle photography (DSP) and digital image correlation (DIC).
A cross-section of the tensile specimen perpendicular to the loading direction is chosen, which is further used as an integration path to calculate the tensile force. The evaluated cross-section must experience plastic loading through the entire deformation process.
The modelling process is performed in a stepwise manner, where each evaluated DIC image represents one-time increment. At each increment, a new hardening modulus for the current effective plastic strain is added to the resulting piecewise linear hardening relation. The incremental hardening modulus is adjusted until the calculated force on the evaluated cross-section agrees with the measured force. This procedure is repeated for each time increment until the failure strain is reached.
Figure 1: SMM combines the local strain field with the tensile force to calculate the hardening behaviour in a direct method
Material testing at high temperature and strain rates
One strength of SMM, besides its reliability, is that it characterises the constitutive stress-strain relation as a piecewise linear curve and, therefore, is independent of equations from hardening laws. SMM can thereby also be used to characterise the constitutive stress-strain relation at elevated temperatures, as well as high strain rates.
By using the Stepwise Modelling Method it is possible to characterise the constitutive stress-stain relation at high temperatures and strain rates
Luleå University of Technology is equipped with high-speed cameras and induction heating systems facilitating testing at strain rates up 1000 s-1 and temperatures up to 1200˚C.
The SMM can predict the post necking behaviour, which is not covered with traditional tensile testing. Compared with conventional methods, as inverse modelling this novel method is faster and can be adapted easily to different material models, while the results of inverse modelling must be redone for every new material model.
Smart material model calibration
Depending on the manufacturing process or part performance to investigate, different material models can be applied demanding different specifications on the material models. Based on the application, suitable tests must be considered; a hot-forming simulation might need the tensile tests at various temperatures; a crash simulation needs tensile tests at high strain rates. By considering the application, the tensile testing may be kept to a minimum of tests, while maintaining the high quality of material data.
Based on the SMM results, material models are calibrated in a smart and simple way. Since the stresses, as well as the strains, are known on each surface point, the SMM results can be used to determine following parameters, which are important in fracture modelling:
- Plastic strain, εp
- Effective von Mises stress, σ ̅
- Mean stress, σm
- Triaxiality coefficient,
η
Figure 2: Example of a failure surface obtained by SMM
Within the FormPlanet Test Bed, a variety of different advanced high strength steels and new aluminium alloys will be tested to calibrate material models for forming and part performance simulations. This reduces time and costs for our industrial partners during the development of new products and materials.
Stefan Marth
Master’s degree in aerospace engineering. He is a PhD student in Solid Mechanics at the Department of Engineering Sciences and Mathematics of the Luleå University of Technology. His research field is Material Characterization for Modelling of Sheet Metal Deformation and Failure. Stefan Marth studies high strength steels and aluminium alloys for automotive and aerospace applications.
