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The Importance of Including Strain-Rate Effects in Explicit Dynamics Material Models

May 2, 2014 By: Steven Hale

When working on an FEA consulting project, converting a finite element model from a static analysis to an explicit dynamic analysis is not as simple as you might think.  There are a number of details that are part of this type of finite element analysis that need to be addressed such as applying loads in the time domain and modifying the mesh to eliminate tiny elements.  One issue that’s often overlooked is the need to consider the strain-rate sensitivity of materials.  It’s typically not enough to use the same stress-strain curve as the one you used in your static analysis.  Materials can behave very differently at the higher strain rates typical of moderate to high speed dynamic events such as drop tests and impacts.

A common example of this is the behavior of steel at high strain rates.  Mild steel is highly strain-rate dependent, as shown in Figure 1 and Figure 2.  Figure 1 shows stress-strain curves for a mild steel at three different strain rates.  Notice that the yield and post-yield stresses are significantly higher at faster strain rates.  Figure 2 shows the strain rate sensitivity of five different steels by plotting the difference in stress at 5% strain between high strain rate (1000 s-1) and static rate (.001 s-1) tests.  For a mild steel with the lowest static stress (“IF” point), the difference in the static versus high-rate stress is a whopping 270 MPa!

Figure 1: Strain-Rate Sensitivity for a Mild Steel

 

Figure 2: Strain Rate Sensitivity of Steels

Strain-rate sensitivity can be included in a number of different explicit dynamics material models.  Viscoelastic and viscoplastic models are commonly used for polymers.  For metals, Cowper-Symonds and Johnson-Cook models are often used. The Johnson-Cook model even includes strain-rate sensitive failure criteria.  These models, and others like them, are readily available in commercial finite element analysis (FEA) software codes like LS-Dyna, AUTODYN, and ANSYS/Explicit.  The Cowper-Symonds model is the simplest of these. It scales the flow stress by the following term:

The mild steel behavior illustrated in Figure 1, for example, uses the following Cowper-Symonds parameters:  C = 80 and P = 4.  To demonstrate the influence of including strain-rate behavior, this same material model was applied to a 20 mm thick cantilevered plate impacted by a 20 Kg rigid block traveling at 14 m/s (see Figure 3).  Figure 4 shows the resulting tip-deflection versus time for the strain-rate sensitive Cowper-Symonds plasticity model and for the same plasticity model but without the strain-rate sensitivity.  It’s obvious that the deflections are significantly influenced by the strain-rate behavior.  Also, a check of the maximum plastic strains shows values that are 17% higher for the model without the strain-rate sensitivity.  This can be very important for deformation-based design criteria and for models in which damage and failure is based on strain.

Figure 3: Plate Impact Test Model

 

Figure 4: Plate Tip Deflection History for Models With & Without Strain-Rate Sensitivity