Elasto-plastic material modelling from Raw data and validation using Ls Dyna

Objective:

• Using the diagram of the true stress-strain curve given for graphite iron casting, create a material model for the Dogbone specimen
• Validate the material model by performing a tensile test on a Dogbone specimen

Procedure for material modeling:

• Data Extraction from the Curve Image:

In general, The material test data is collected as

1. Force vs Displacement
2. Engineering stress vs strain
3. Raw data
4. The image representing the curve of the data points.

In this case, We got an Image representing a True Stress/ Strain curve with 3 different strain rate, From the graph, we can see The material shows elasto-plastic behavior with the elastic and plastic region Although many material models exist for elasto-plastic, one of the most robust models is *MAT_024 or *MAT_PIECEWISE_LINEAR_PLASTICITY. This material model is the standard workhorse and is the recommended starting point for elastic-plastic simulation of metals and general plastics since it can also handle viscoelastic behavior (i.e., strain-rate dependency).

From the above Plot, we will take The curve 2 data point for our material modeling purpose

Using the GRABIT Matlab GUI program, the data points are extracted from an image file.

• Data clean up – Curve fitting

The data point extracted from the image is always noisy and the data points are selected manually by picking each point so they will be some human error And Since, Ls dyna will accept only the monotonically increasing curves. We need to clean up the curve and fits the rough data, This method is called Curve fitting

Curve Fitting

Curve fitting is the process of constructing a curve, or mathematical functions, which possess the closest proximity to the real series of data. By curve fitting, we can mathematically construct the functional relationship between the observed dataset and parameter values, etc. It is highly effective in the mathematical modeling of some natural processes

We have performed a curve fitting process using MATLAB code our data points are fitted using SPLITWISE CUBIC PLOYNOMINAL METHOD. Splitwise method is an efficient way to obtain the perfect fit without increasing the degree of the polynomial

• Data/Unit conversion

For the Material card model we are using SI unit i.e Kg/mm/ms but if we noticed from the Stress and Strain graph units are give in ksi and percentage respectively so the unit of stress has to be changed from ksi to GPa and Strain has to change from percentage to actual value

0.2% offset Yield Strength

Well, the conversion from elasticity to plasticity can be very subtle for many materials so it might not be always very easy to figure out the yield point, that is the point on the stress-strain curve, where elasticity changes to plasticity. In other words, at the yield point, if you let go of the deforming force, the material will not come back to its original form there will be some amount of permanent deformation In this case, the offset yield strength is determined. A line is constructed parallel to the initial portion of the stress-strain curve but offset by 0.002 in/in (0.2%) from the origin. The 0.2% offset yield strength is the stress at which the constructed line intersects the stress-strain curve as shown:

0.2% offset yield strength : 0.2293570 GPa

Once the unit conversion is done we can see the extracted data are True stress and True strain But to define a Stress-Strain curve in *MAT_24 card, We have to defined it in Effective stress and Effective plastic strain

The true stress and strain values are converted into Effective stress and Effective plastic strain value using the following formula.

Effective stress = True stress

Effective plastic strain = True strain - True stress / E

Young’s Modulus is given for the material as 20E+6 psi i.e 144GPa

As the stress value increases, the recoverable strain (true stress/E) increases as well. For metals, E is very large compared to the yield stress so it's fairly common practice in the case of metals to just subtract off a constant value equal to the strain at initial yield from all subsequent strain values

True Stress / E = 0.000958

The hardening curve which is defined in the material card should start ideally with yield strength and effective plastic strain (at yield strength) as a first point. So, we can remove the elastic region data point from the curve.

• Defining Stress/Strain curve for material model

The stress/strain for the material is now in the form of Effective stress and Effective plastic strain which can be implemented on the MAT_24 material card

These data point for the Stress/Strain curve are inserted *DEFINE_CURVE Card with LCID

Material Model:

We will use graphite iron casting Properties for defining the material card

1. MID Material identification. A unique number or label not exceeding 8 Characters must be specified
2. RO Mass density= 7.100e-06
3. E Young’s modulus = 144.10001 GPa
4. PR Poisson’s ratio = 0.3
5. SIGY Yield stress = 0.2293570 from 0.2% offset yield strength
6. LCSS Load curve ID defining effective stress versus effective plastic strain.LCID from Define_curve

• Tensile Test – Pre Processing

Procedure :

• Mesh model of Dogbone specimen is imported
• The material model we created for graphite iron casting is used here
• Section shell card is used with 16: Fully integrated shell element formulation and thickness as 1mm

Boundary Condition

Since we performing a Tensile Test where one end of the specimen is fixed and the displacement is added to the other end so we will use two types of boundary condition on the Specimen

1. BOUNDARY_SPC_SET

• To fix one end of the specimen as test procedure we will constraint all the degree of freedom expect Y direction (because specimen will elongate in the X direction and simultaneously contract in Y) for edge node on one end of the specimen,

• We will select the mid-node on edge of both ends of the specimen and constrain only the Y direction

2. BOUNDARY_PRESCRIBED_MOTION_SET

• A set of a node is created on the edge specimen in which displacement is applied

• Displacement curve is created using Define_curve Card

• DOF in BOUNDARY_PRESCRIBED_MOTION_SET is set to be 1 which means displacement takes place in the X direction and VAD is set as 2 Displacement flag

Control card

1.*CONTROL_IMPLICIT_GENERAL

Activate implicit analysis and define associated control parameters. This keyword is required for all implicit analyses

• IMFLAG - Implicit/Explicit analysis type flag : 1- implicit analysis
• DT0 – Initial time step size for implicit analysis : 0.0050000
• IMFORM - Element formulation flag for seamless spring back: 2 retain original element formulation (default)

2.*CONTROL_IMPLICIT_SOLUTION

Use of these cards to specify whether a linear or nonlinear solution is desired

• NSOLVER – Solution method for implicit analysis: 12 For Non-linear problem
• ILIMIT-Iteration limit between automatic stiffness reformations: 11
• MAXREF- Stiffness reformation limit per time step: 15
• DCTOL- Displacement relative convergence tolerance: 001
• DNORM- Displacement norm for convergence test: 2 (Increment as a function of total displacement)

3.*CONTROL_IMPLICIT_SOLVER

The linear equation solver performs the CPU-intensive stiffness matrix inversion

• LSOLVR- Linear equation solver method: 4 (uses solve the simulation with single precision which consequently saves run time rather than going for a double-precision solver)

4.*CONTROL_IMPLICIT_AUTO card has been defined to adjusts the time step size

• IAUTOset to 1 which automatically adjusts the timestep size.
• ITEOPToptimizes the operation count step:11
• ITEWINis the iteration window: 5
• DTMIN Minimum allowable time step size: 000e-05
• DTMAXMaximum allowable time step size:5

Database Creation

• *BINARY_D3PLOT - It defines the frequency at which the animation file is to be created and is set to 5.000e-05 ms
• *DATABASE_HISTORY_NODE A nodes on Accel Block of head were defined to measure the acceleration and calculated HIC value
• *DATABASE_EXTEND_BINARY - this writes the strain tensor to d3plot when STRFLG is set to 1

ASCII_option keyword

The output request in ASCII format, The following keyword are Activated

1. GLSTAT- Global Data
2. MATSUM- Material Energies and
3. ELOUT- Element Output Data

Results:

Effective Stress

Max Stress: 0.2679GPa

Effective Stress is plotted for the element 108

Effective Plastic Strain

Max Effective Plastic Strain:8.031e-03

Effective Plastic Strain is plotted for element 125

Stress-strain Curve:

Material defined stress-strain data and simulated stress-strain data are compared . It can be seen that the elastic part is linear . The linear elastic part is calculated directly through the given young’s modulus andThe yielding starts after the first defined yeild point in the hardening curve .

Conuclsion :

• The stress-strain data extraced from image is validated with the MAT_024(Piecewise linear plasticity) material model.
• The stress-strain behaviour after yielding is considered by a hardening curve which is given as an input through MAT_024 card.
• The MAT_024 material model captures the actual stress-strain behaviour in a similar manner and almost matched the defined stress-strain curve in material model
• Also we seen the little variation in the simulation data, which can due to the lack of information like density and Poisson’s ratio for the raw data , Mesh Size of the model or defineing proper strain rate . These variation can be fine tuned by trying different values of these properties and by selecting more data points to better capture the curve feature