posted on May 14, 2023
PA 12 (also known as Nylon 12) is a good general-use plastic with broad additive applications and is known for its toughness, tensile strength, impact strength and ability to flex without fracture. PA 12 has long been used by injection molders due to these mechanical properties.
Several years ago a test lab shared some test data on PA12. The test data consists of :
- Three monotonic pull tests at rates of 5, 50, and 500 mm/min (crosshead velocities).
- One cyclic test to see hysteresis loops.
- Three stress relaxation tests performed below the yield stress.
All test data is from uniaxial deformations. Attempts at using the Abaqus PRF to model these tests were not successful because the available creep laws for the viscous networks could not mimic the saturation of stress that occurs in the monotonic pull tests near ultimate. In Abaqus, the TLVP (Two Layer Visco-Plastic) model is similar to the PRF model in that it is a network model. Like the PRF model it has an elastic-plastic network and a viscoelastic network. The Anand and Darveaux creep laws are available in the TLVP model. While we call them "creep laws" these are really visco-plastic in nature, and can represent the saturation of stress that one sees in the monotonic pull tests.
Using the calibration app in the 3DExperience platform (public cloud, R2023x HotFix 2.14), I revisited this nylon 12 material and have calibrated several variations of the TLVP model. In the images above, the dots are the test data and the solid lines are the TLVP model responses. The full TLVP material model is shown below. The aggregate R2 error norm for this calibration was 0.9897 and the individual R2 values for each dataset are shown in an image below.
Some notes on the Darveaux model parameters:
The parameter α enters the hyperbolic sine function, sinh. Negative values of α are not possible because it will cause a negative value of the sinh function. If α=0, then sinh = 0 and the creep strain rate will be zero (no creep). Therefore it makes sense that α should be positive.
This example is not intended to calibrate a temperature dependence. The parameter QR_Ratio is set arbitrarily to 1000.0 and is not a design variable. All test datasets are specified to be at 20 degrees C (293 deg K). The temperature term "exp(...)" contributes a constant scale factor of 0.0330 In hindsight, perhaps a better value for QR_Ratio would be a small one, like 1e-10, so that the temperature term "exp(...)" would be close to 1.0
The parameter ϵT controls the primary creep. We expect the creep rate to be greater during primary creep, so ϵT≥0 (note also that B>0 so that primary creep effects decay exponentially). When t=0 the creep strain rate is (1+ϵTB) times greater than at steady state. Setting ϵT=0 would simply mean that primary creep is ignored and not included in the simulation.
Here is the resulting TLVP material model:
**Units
** Length - Millimeter
** Mass - Tonne
** Time - Second
** Temperature - Kelvin degree
**
*MATERIAL, NAME = TLVP
*ELASTIC, TYPE = ISOTROPIC
2154.0765, 0.4
*PLASTIC, HARDENING = JOHNSON COOK
26.931895, 36.724585, 0.32377983, 0, 1773, 1273
*VISCOUS, LAW = DARVEAUX
** Css QR_Ratio alpha n eT B f
0.01, 1000, 0.092222, 4.5448, 0.00088295, 11999.701, 0.44018
The zip file attached here contains the calibration app's 3dxml file, a material model snippet and a .png image from the calibration app.
Back to: Sharing Material Test Data
Back to: Material Modeling and Calibration - An Overview and Curriculum
