Material modeling from raw data using LS-DYNA
MATERIAL MODELING FROM RAW DATA:
INTRODUCTION:
Material modeling is a widely undertaken process in industries. This process involves testing of new material or alloy and modeling this material through the extracted test data and validating it with the test data and thus can be used in later stages in simulation.
Material modeling is carried out in most of the industries mainly in Research and development sectors because new materials are preferred by the industries to eliminate certain parameters and impart new one that could be beneficial for the application like improved fatigue, life cycle, thermal and wear-resistant, eliminating manufacturing costs, etc.
This newly modeled material can later be carried out in future engineering analysis using FEA tools thus preventing testing using a physical model and thus eliminating errors and increasing productivity.
OBJECTIVE:
To model a new material whose data either Force vs Displacement or Engineering Stress vs Strain data are collected through a different physical testing process. This data is represented in terms of a mathematical equation that replicates the behavior of the material can then be successfully used for future simulation tests.
This data is modeled in a MAT_024_PIECEWISE_LINEAR_PLASTICITY material card using the Load-Curve and hence its behavior replicates that of the newly modeled material and it is validated by performing a normal tensile test on a shell part.
The method of modeling a material using the provided data into a mathematical equation during simulation is explained in this report.
SETUP:
1. EXTRACTING TEST DATA:
The test data collected either as a Force vs displacement or as engineering stress vs strain is obtained either as a raw data or as an image representing the curve of the data points.
NOTE: In case the data is a Force vs displacement curve, then these data points must be converted into valid engineering stress vs strain and later on to effective plastic strain vs true stress data.
This conversion can be carried out through the basic formulas,
Stress = Force per unit Area
`sigma = F / A`
Strain = Change in length / Original length
`epsilon = (delL)/ L`
If in case this data is in form of a digital image, the data points can be extracted using "Graph Digitizer" where the X and Y ranges must be specified along with the image of the curve.
2. DATA CLEANUP:
It is more frequent than the data extracted from an image could always be noisy. In such cases, the data is filtered to bring about a smooth curve. This process of data filtering and cleanup is also called Curve fitting.
This process of curve fitting can either be performed using MATLAB, Excel, or using the SciPy library in python. Curve fitting clears up the noise in the data by generating a curve using a mathematical equation that closely follows the data points of the curve.
In our case, curve fitting is done using Excel where the mathematical function that needs to represent our curve, and simultaneously our data point is modeled using a logarithmic function. The other means of representing the curve can be linear, exponential, power, and polynomial. It is noted that among these, the logarithmic curve gives us a close representation of our data point with a success rate of about 96%.
NOTE: The curve can also more accurately modeled using the polynomial function of a higher-order i.e 2 or 3 which would give a more accurately fitted curve but the equation would involve a higher order.
If the stress data is in ksi, to be consistent it is preferable to convert it to Mpa.
1 ksi = 6.89475728 MPa
3. DATA CONVERSION:
The extracted and fitted curve data now comprises only of engineering stress and strain however to define the curve in a MAT_024 card the curve data must contain the effective stress and effective plastic strain data. Hence the engineering stress and strain data are converted into True Stress and strain and later into effective plastic strain using the following equations.
True strain = `ln (1+ epsilon)`
True stress = `sigma * (1 + epsilon)`
Effective plastic strain = True strain - True stress / E
where, E - Elastic modulus (GPa)
4. REFERENCE MODELED MATERIAL:
This material data now in the form of effective stress and plastic strain has to be referenced in the MAT_024 card. This can be achieved either by manually declaring each data point using LS-PrePost or using the .k/.dyn keyword file.
This is referenced under the DEFINE_CURVE card which is further referenced in the MAT_024 card along with the density, Elastic modulus, and other variable parameters.
5. KEYWORD SETUP:
To validate the behavior of the material a tensile test simulation needs to be carried out. Hence the keyword is modeled along with other cards like *SECTION, *CONTROL_TERMINATION, BOUNDARY_SPC, INITIAL_VELOCITY, DATABASE, etc.
POST-PROCESSING:
After the entire keyword file is modeled the file is submitted to the LS_DYNA solver and the following results have been obtained.
We can clearly visualize that the highest stress point occurs at the constrained end of the shell component with about 30.4 N/m.sq while the middle half portion of the shell has very little resistance since it experiences very little external force.
The d3plot also shows us that there occurs a large displacement at the loading end which latter finds resistance representing the behavior of the material. The nodal X-displacement at the loading end is shown below,
The Effective plastic strain of the material under loading is shown below,
CONCLUSION:
Hence we were able to model an un-defined material using its engineering stress and strain data extracted during testing of the material and we successfully modeled it using a curve which represents its stress and strain behavior during loading conditions.
This new material was compatible with the geometry model and had no issues with the solver during the process of defining it. The results obtained from the performed analysis tells us the behavior of the material which behaves as per the curve defined and the mathematical function that defines the curve.