Material modelling from raw data

Material Modelling from Raw data

Objective: The aim of this project is to extract (stress and strain) data from a curve and find the yield strength, curve fit the extracted data, convert the Engineering stress and strain to True stress, True strain and Effective plastic strain.

Finally apply the data to material (MAT_24) using the dogbone specimen and run a simulation. The unit system to be considered is (kg, mm, ms, GPa, KN-mm)

Procedure: The stress strain data has been extracted from the given picture using the Getdata Graph digitizer software.

The test data has been performed THREE times so as to pick the best data possible.

Here the strain values are given in percentage so the offset for the yield strength is taken at 0.002 and the yield strength is found to be 0.16 GPa.

With the Yield strength obtained, only the plastic region of the data has been taken as plastic deformation is the point of interest.

Most of the metals and plastics (few) undergo linear and plastic deformation. These materials can go back to their original shape without any change in the mechanical properties till the Elastic limit. So, there is no point in knowing the behaviour in the linear region. The curve fit for the plastic region data has been plotted. The Engineering stress and strain is now being converted to True stress, strain and Effective plastic strain with the help for the conversion formulae.

Finally, the Effective plastic strain and Effective stress have been obtained.

Both the methods explicit and implicit methods have been conducted, starting with explicit.

Explicit Method:

Define curve: Two curves are to be defined one for the displacement vs time and the second one being Effective plastic strain and effective stress, which are to be assigned to the Boundary and Material.

Material creation: The dogbone specimen has been opened in the LS-PrePost and material card MAT_24 PIECEWISE_LINEAR_PLASTICITY has been defined with the values as shown.

Section creation: A shell section with ELFORM 16 has been selected as it is a fully integrated shell element and a thickness of 4.5454mm has been given.

The material and section cards are to be further assigned to the Part card, with their respective Id’s.

Boundary conditions:

Two single point constraints, one at one of the free ends of the specimen and the other at the centre points of both the free ends. The Degrees of Freedom can be given understood from the pictures below

Prescribed boundary motion set: Only one DOF in X-direction has been created.

Control Termination of 1ms is defined and the D3PLOT AND ELOUT have also been defined with a DT of 5E-4.

Control ENERGY card has also been defined to contain any Hourglassing.

HISTORY_SHELL has been called to obtain the effective stress and effective plastic strain at shell element 311

Implicit Method: Only control Implicit cards have to be invoked as that is the only difference between the explicit and implicit method.

To shift from explicit to implicit analysis CONTROL_IMPLICIT_GENERAL card has to be used and the IMFLAG is set to 1 to activate implicit analysis.

CONTROL_IMPLICIT_AUTO card has been defined with IAUTO set to 1 which automatically adjusts the timestep size. ITEOPT optimizes the operation count step. ITEWIN is the iteration window. DTMIN is DT/1000 and DTMAX is DT*10.

CONTROL_IMPLICIT_SOLUTION: This card is used to choose between linear and nonlinear analysis in implicit method. NSOLVR is set to 12 by default and LSMTD which is a Line Search Convergence Method is by default set to 4.

CONTROL_IMPLICIT_SOLVER: The stiffness matrix inversion is being done through this keyword. LSOLVR is by default set to 4 which is a single precision solver, but it is advisable to use 5 which is a double precision solver for better results in case of a complex implicit analysis.

Both the models are run and the results can are viewed by opening the D3PLOT.

Results:

Explicit Method:

Effective stress and effective plastic strain:

The maximum effective stress is found at element 503 which is 0.6480 GPa.

Effective stress Graph for Explicit

This graph is obtained through the HISTORY_SHELL card where element 311 is selected to get the values of Effective plastic strain and effective stress.The maximum Effective stress recorded at element 311 is 0.60388 GPa

Effective plastic strain graph for Explicit

The maximum Effective plastic strain recorded at element 311 is 0.4982.

Effective stress vs Effective plastic strain graph.

The stress strain curve is similar to that of the input data.

Implicit method:

Effective stress and Effective plastic strain:

Effective stress Graph for Implicit

The maximum Effective stress recorded at element 311 is 0.60779 GPa.

Effective plastic strain graph for Implicit

The maximum Effective plastic strain recorded at element 311 is 0.49709.

Effective stress vs Effective plastic strain graph for Implicit

All the values of graphs are saved in the form .csv file

To validate the results with that of the input data a graph has been plotted.

From the graph it is evident that both results are matching with that of the Input data.

Conclusion:

• It is known that the tensile test is a static or quasi static analysis.
• From the Original picture of Graphite iron it is clear that the material undergoes plastic deformation it can also be seen from the Effective stress and effective plastic strain input data.
• Implicit analysis is adopted because of Material Nonlinearity. If for a shell element when Element Formulation-16 is used, then it clear that the model is a First Order Nonlinear Implicit Analysis.
• The Fringe Component of strain and stress (images) are a sign that the Implicit Analysis is the more acceptable procedure in solving this problem, because in Implicit Analysis, the stress distribution is from the middle and proceeds to the ends of the dog bone specimen, whereas in the Explicit Analysis the stress distribution is high at the Prescribed boundary condition End.
• The graphs of True stress vs time and Effective plastic strain vs time also are an indication of uniformity in Implicit Analysis.
• The explicit analysis has also shown similar nonlinearity as that of the input data, but the above points mentioned have an edge as to why implicit method has to be adopted between the two.
• Finally not undermining the actual problem of material modeling from raw data, The stress strain values have been
• Extracted, Curve fitted, Converted to Effective stress and effective plastic strain accoring the required unit system and Validated the results with that of the input data.