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Using FEA to Model Shape Memory Alloys

FEA Modeling of Glasses Frame Superelastic Response | FEA Consulting
November 6, 2015 By: Peter Barrett

Have you ever wondered why some eyeglass frames can fully recover back to their original shape after being stepped on? (See Figure 1, above.)  Have you ever seen a magician heat a piece of wire that magically returns to its original shape?  These are not really magic, of course, but they demonstrate the unique material properties of the shape memory alloy Nitinol.

A shape memory alloy (SMA) is a metallic alloy that “remembers” its original shape. Upon loading and unloading cycles, a SMA can undergo large deformation without showing residual strains (pseudoelasticity effect, often called superelasticity), and can recover its original shape through thermal cycles (the shape memory effect). This material behavior is due to the material microstructure with two different crystallographic structures:

  • Austenite is the crystallographically more-ordered phase.
  • Martensite is the crystallographically less-ordered phase.

The austenite is stable at high temperatures and low stress.  The martensite is stable at low temperatures and high stress.  The key characteristic of a SMA is the occurrence of the reversible martensitic phase transformation which results in unique effects: the pseudoelasticity (PE) and the shape memory effect (SME).

The most common shape memory alloy is Nitinol, a nickel titanium (Ni-Ti) alloy discovered in the 1960s at the U.S. Naval Ordnance Laboratory (NOL). The acronym NiTi-NOL (or Nitinol) has since been commonly used when referring to Ni-Ti-based shape memory alloys where the mix of the nickel and titanium alters the material response.

For PE applications, the hybrid alloy Modulus of Elasticity is typically around 50 GPa with a transformation temperature less than 20 degrees C, so that at body temperature where medical devices such as stents are used, the transformation is purely stress induced.

For SME applications, the Modulus of Elasticity is typically around 35 GPa, with a transformation temperature somewhere between 50 and 100 degrees C, where a common application is a spring actuator with a temperature induced transformation.

Both PE and SME can be modeled using unique FEA material models which are best described in the  Journal of Biomechanical Engineering August 2005 article:

For the ANSYS PE material model, stress and strain inputs are used to define the hysteresis response which includes both the upper loading and lower unloading stress vs. strain response as illustrated in Figure 2.

Figure 2: Superelastic Stress vs. Strain & Corresponding ANSYS Material Input Coefficients (See Figure 4 for definitions)

The ANSYS Shape Memory Effect material model can be used either for temperature induced transformations or as a SE material model. The journal article referenced above provides details on the user input. Figure 3 illustrates how to convert the input coefficients defined in Figure 4 from the SME to the PE format when for example one needs to include a different modulus for Austenite vs. Martensite.

Figure 3: Shape Memory Stress vs. Strain Response & Corresponding ANSYS Material Input

Some tips when using these material models include:

  • Develop a one element model for testing where a displacement controlled solution can be used to cycle the element and duplicate the stress vs. strain response (An example is shown in Figure 4).
  • Use more substeps than usual to capture the material phase change response.
  • A large deflection analysis is required.
  • For the shape memory material model, I recommend the direct unsymmetric sparse solver for improved convergence, regardless of whether you are simulating PE or SMA response.

Has anyone else modeled Nitinol using FEA?  I am always eager to learn new tips and tricks from others!

Figure 4: ANSYS Superelastic & Shape Memory Coefficient Input That Produce the Same Stress vs. Strain Response