Week - 9 Material modeling from raw data

Aim:

Using the raw data provided in the image to create a material model and run the tensile test to validate the result.

Methods to Solve Engineering Problem:

Basically we have three methods to solve any engineering problem. They are:

Analytical:

It is classical approach and give 100% accurate result. It gives a closed for solution and applicable only for simple problems like centilever and simply supported beam etc.

Numerical :

It is a mathematical approach. Results are appropriate and assumption made to solve. Applicable even if a physical prototype is not available. It is real life problem and comples in nature. Results cannot be beleived blindly and it must be validated.

Experimental:

It is actual and time consuming method. Applicable if only physical prototype is available. Minimum 3 to 5 times prototype test done to confirm the result.

In this challenge they provide the experimental result as Engineering stress and engineering strain for the material which is done by tensile test. Using this data define the material and run the analysis to validate the result numerically by using the ls dyna.

The above figure shows the graph which is provided by them. In this graph we have the stress and strain value in ksi. Using the data digitizer extract the data into the excel sheet.

The extracted data have lot of points and which are very noisy. So we need to do the data clean up. Curve fitting method is used to clean the data which is shown in the above figure. Here I am using the logarthmic function to get the data points. For the simulation we are using only the positive region value. It is best to use the value only in plastic region, but here we are using the curve fit value which is non linear so we need to use the entire curve in the 1st quadrant.

The extracted data is in the unit of ksi. So convert the stress and youngs modulus unit from ksi to gpa.

1 KSi= 0.00689476 gpa.

In material model we need to define the data in the form effective plastic strain and true stress.

Engineering Stress and Strain:

Stress is defined as the internal force or internal resistance produced in a unit cross sectional area under the external load.

Strain define the shape changes. Ratio of change in length by original length.

In Stress strain Curve:

The above figure clearly shows the engineering stress - Strain curve and True stress - strain curve difference.

In engineering curve we only considered the final length or actual length. We know that stress and area are inversely proportional. But in engineering curve it shows even after the necking the stress is reduced

True curve we consider the instanatnaeous area which give accurate result .

Conversion of Engineering to True Stress:

True stress = Engineering stress *( 1 + Engineering Strain)

True Strain= ln(1+ Engineering Strain)

Effective plastic Strain = Total True Strain - True Stress/E.

Here ,given the data is true stress and strain only. Use the formula to get the effective plstic strain.

The above figure shows the curve which is defined in the material model to run the analysis. X axis represent the effective plastic strain and Y axis represent the stress. Here I am taking the value from 0.0012 strain to avoid the negative stress value to get the result.

Analysis Procedure:

Import the tensile test mesh file in ls dyna provided by them.

Create the Material card MAT 24 Piecewise linear plasticity and define the curve which is shown the above figure. Assign the value for dendity, youngs modulus and poison ratio.

Create the section card and specify the thickness value.

Specify the boundary condition to run the tensile test.

The above figure shows the node selected to define the Prescribed boundary motion set. The displacement curve is shown in the below figure with the scale factor 20.

SPC:

Here we are specifying the two SPC condition to capture the result accurately.

The above figure shows the SPC node which is contsrain only in Translation (x z) and rotational (x y z).

The above figure shows the Spc node which constrain the degree of freedom only in translation y direction.

Define the Control card and the database card to get the post process result (d3 plot)

Tensile test is a slow process and for this type if simulation implicit analysis is best suitable compare to the explicit analysis. Activate the implict analysis from the control implict general card.

Define the memory and run the k file in LS manager.

Result Analysis:

The above animation shows the deformation for the tensile test.

The boundary conditions are applied perfectly to get the tensile test behaviour of this material.

Von Mises Stress:

The above figure shows the effective value stress for this component .

The above Figure shows the result of the effective plastic strain.

Validation:

Since we get the result for this analysis by using the raw data of the material. But we need to validate whether the results are correct. In ls dyna the stress strain we get are true stress and true strain. To verify and vaildate, Compare the stress strain plot of this analysis with the stress strain plot given by them .

From the above figure, I get to know that Stress and strain figure not match in linear curve but non linear curve matches well with the given stress strain curve image.

The reason is since the data is very noisy. To clean the data we choose the logarthmic function, even we can use the polynomial function with higher order but the number of points will increase. In excel sheet already shows that the logarthmic curve and actual curve have some small error residuals. While modelling we only include the positive value of stress. Because of this data miscalculation we get that deviation. But this curve is match with the plastic region stress strain value perfectly.