MATERIAL MODELLING FROM RAW DATA USING LS-DYNA

Objective:

LS-DYNA contains a wealth of material models that allow for the simulation of transient phenomena required to determine material model parameters where material properties are converted into values required by constitutive equations.

The main aim of this report is to model a new material whose Stress vs Strain data are collected through a different physical testing process. The extracted data is represented in terms of a mathematical equation that replicates the behavior of the material that can then be successfully used for future simulation tests.

A material model of MAT_024_PIECEWISE_LINEAR_PLASTICITY card is used with a load-curve of extracted data that represents the behaviour of newly modeled material.

Also to validate the material model by performing a tensile test on a Dogbone specimen using LS-DYNA.

Material modelling:

Material modelling is widely used in CAE industries that involves testing of new material or alloy and modeling the material through the extracted test data.The created material model is validated with the test data (input) and thus can be used in later stages of simulation.

Material modelling 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.

The newly modelled material can be used in engineering analysis using FEA tools, thus preventing testing using a physical model, eliminating errors and increasing productivity.

Procedure for material modelling:

1. Data extraction

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.

In this work, the following image of graph, representing True stress VS True strain percentage of a graphite cast iron material, is used to extract the data points using a Data digitizer.

The curve 2 from the above plot is used for our material modelling purpose.

Using the data digitizer, many data points of the curve are collected which are used as the input data of the test.

2. Data cleanup:

It is more frequent that the data extracted from an image could be noisy. In order to convert the noisy curve into a smooth curve that fits the rough data, a method of data cleanup is used which is called 'Curve fitting'.

In our case, the process of curve fitting can be done using MS Excel.Curve fitting clears up the noise in the data by generating a smooth curve using a mathematical equation that closely follows the data points of the curve.

In this work, our data points are fitted using a logarithmic function. The other means of representing the curve can be linear, exponential, power, and polynomial.The data points can also be used for curve fit with polynomial regression algorithm that involves higher order of data points.

3. Data conversion:

In industries, the extracted data from the test normally represent Engineering stress and strain values.They have to be converted to True stress and strain values first, then followed by converting into effective stress and effective plastic strain respectively.

In our case, the data is given in terms of True stress and True strain, hence there is no requirement for engineering stress-strain data.The unit of true stress is given in ksi (kilo pound per square inch) that should be converted to standard SI units for consistency.

The extracted and fitted curve is in True stress ans True strain format. However, to define a Stress-Strain curve in *MAT_24 card, the true stress and strain values are converted into Effective stress and Effective plastic strain value using following formula.

Effective stress = True stress

Effective plastic strain = True strain - True stress / E

where, E is Young's modulus of material which is given as 20E+6 psi which should be converted to SI unit system.

After having the effective stress and effective plastic strain data in SI unit system, the data are again converted into kg-mm-ms unit system.This is done to maintain a reliable relation between stress-strain curve.

4. Defining Stress-Strain curve:

This material data is now in the form of effective stress and effective plastic strain that has to be referenced in the *MAT_024 card.

This can be achieved either by manually declaring each data point using LS-PrePost or editing the respective LS-DYNA 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 Poisson ratio of the material.

The value of Elastic modulus is taken from the slope of Effective stress- plastic strain curve.

5. Keyword setup:

A tensile test simulation is carried out for a Dogbone specimen to validate the behaviour of modelled material.

The left end of the specimen is constrained with *BOUNDARY_SPC and with DOFs arrested except in tensile loading direction.

The right end of the specimen is defined with *BOUNDARY_PRESCRIBED MOTION using a displacement curve.

Therefore, to setup the simulation, other keywords like *CONTROL, *SECTION, *BOUNDARY, *DATABASE are defined.

The simulation is set to run in LS-DYNA manager using explicit solver.

Validation of output data:

The tensile test of dog-bone specimen simulation results can be obtained through binary plot file of respective keyword file.

'Validation assessment' is the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.

The goal of validation is to quantify confidence in the predictive capability of the model by comparison with experimental data.

1. Von-Mises stress

2. Plots with respect to time

The above plot shows the variation of maximum effective stress and plastic strain developed with respect to time.

3. Effective stress VS Effective plastic strain

=>The above plot shows the variation of Effective stress Vs Effective plastic strain developed during the tensile test simulation of Dog-bone specimen.

=>It can be seen that the variation is quite linear because of the material card which is been used (i.e. *MAT_24 / PIECEWISE_LINEAR_PLASTICITY).

=>The plastic non-linear portion of stress-strain curve is made linear which obeys the stress-strain curve of the tested input data.

=> A slight mis-match in the above curve in comparison with the test fitted curve arises because of logarithmic regression used.On the other hand, if the goodness of curve fit against raw data is achieved with linear regression method, the behaviour of the material would perfectly match.

Conclusion:

Hence we were able to model a new material using its stress and strain data extracted during testing of the material and we successfully modelled 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 mathematical function that defines the curve.

The materials being modelled by the material model are often complex and multi-variant in nature, and some form of approximation is needed to correlate real life to the mathematics.These factors have an impact on the fidelity of the simulation.

Therefore a careful consideration must be given to quantify the errors, so that they match with the simulation results perfectly.