RD-V: 0240 Tabulated Material (LAW36)

The analysis shows the behavior of the tabulated material /MAT/LAW36 under tensile load-cases.

Tabulated material law under tensile load-cases.
Figure 1. a) Shell element; b) sh3n element; c) solid element hexahedron; d) solid element tetrahedron




The analysis for 4 cases is conducted with tensile load-case for:
  • A material with shell elements /SHELL.
    • Ishell=24
    • Ishell=12
  • A material modeled with shell elements /SH3N.
    • Ish3n =0
  • A material with hexahedron elements /BRICK.
    • Isolid =24
    • Isolid =15
    • Isolid =18
  • A material modeled with tetrahedron elements /BRICK.
    • Itetra4=0
    • Itetra4=3
    • Itetra10=0
    • Itetra10=2

Options and Keywords Used

The following keywords are used in the models:

Input Files

Before you begin, copy the file(s) used in this problem to your working directory.

Model Description

Units: Kg, mm, ms, GPa

The coupon is extended from one side in the X-direction, while the other side is fixed in all six degrees of freedom using boundary conditions (/BCS). The nodes on the right-hand side of the coupon are constrained within a rigid body definition (/RBODY). A prescribed velocity of 1m/s in the direction of extension is applied to the main node of the rigid body (/IMPVEL).
Figure 2. All boundary conditions applied to the test model


Material Law Characterization

The material to be characterized is Q460 steel. The model is meshed with different elements previously mentioned above. The average element size is about 1mm.
Material Property
Value
Young's modulus
221 GPa
Poisson ratio
0.3
Thickness
1.7mm
The material test data and the engineering stress-strain curves were extracted from 1. Since experimental stress-strain curves are available, the tabulated von Mises-based material law, /MAT/LAW36 was selected. The formula in Figure 3 can be used to determine the True stress versus True strain curve. The plastic part of the curve can then be isolated. This True Stress versus Plastic True Strain curve is used as an input of LAW36.
Figure 3. a) Tensile engineering stress versus engineering strain curve; b) True stress versus True strain


Results

Tensile Coupon with Shell Elements

The following element formulations are evaluated:
  • /PROP/TYPE1 (SHELL), QEPH shell formulation Ishell=24, 5 integration points through thickness.
    Figure 4 shows the results of the plastic strain contour. Here, the beginning of striction can be observed.
    Figure 4. Plastic strain contour plot for shell QEPH shell formulation


    In Figure 5, the true stress versus true strain curve is directly extracted from an instrumented element at the center of the coupon.

    The engineering stress versus engineering strain curve is calculated globally with the following steps:
    • The engineering stress can be calculated by using σe= F/A0. The force is derived from the rigid body force. The original cross-sectional area is 20.4 mm2.
    • The engineering strain is calculated with ε e = Δ 1 / l 0 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTduMaam yzaiabg2da9iabfs5aejaaigdacaGGVaGaamiBaiaaicdaaaa@3E0D@ . The elongation Δ 1 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaaG ymaaaa@3818@ is measured from two instrumented nodes. The original distance l0 is 80 mm.
    Figure 5. Comparison of results using LAW36 for shell QEPH shell formulation


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

  • /PROP/TYPE1 (SHELL) QBAT shell formulation Ishell=12, 5 integration points through thickness
    Figure 6 shows the results of the plastic strain contour. The beginning of striction can be observed.
    Figure 6. Plastic strain contour plot for shell QBAT shell formulation


    Figure 7. Comparison of results using LAW36 for shell QBAT formulation


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

Tensile Coupon with SH3N Elements

The following element formulations are evaluated:
  • Ish3n = 0
    Figure 8 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
    Figure 8. Plastic strain contour plot for sh3n element


    Figure 9. Comparison of results using LAW36 for SH3N element


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

Tensile Coupon with Solid Hexahedron Elements

The following element formulations are evaluated:
  • /PROP/TYPE14 (SOLID), Isolid =24
    Figure 10 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
    Figure 10. Plastic strain contour plot for solid element


    Figure 11. Comparison of results using LAW36 for solid element


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

  • /PROP/TYPE14 (SOLID), Isolid =18
    Figure 12 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
    Figure 12. Plastic strain contour plot for solid element


    Figure 13. Comparison of results using LAW36 for solid element


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

Tensile Coupon with Thick Shell Elements

The following element formulation is evaluated:
  • /PROP/TYPE20 (TSHELL), Isolid =15
    Figure 14 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
    Figure 14. Plastic strain contour plot for TShell element


    Figure 15. Comparison of results using LAW36 for TShell element


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

Tensile Coupon with Solid Tetrahedron Elements

The tetrahedron properties used:
  • /PROP/TYPE14 (SOLID), Itetra4=0
    Figure 16 shows the results of the plastic strain contour plot visualization. As can be seen at the end of simulation the striction is barely initiated. This is due to the very stiff element formulation.
    Figure 16. Plastic strain contour plot


    Figure 17. Comparison of results using LAW36


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. After this point, the stress continues to increase, in contrast to other results presented previously. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

  • /PROP/TYPE14 (SOLID), Itetra4=3
    Figure 18 shows the results of the plastic strain contour plot visualization. Using Itetra4=3, the striction can be observed in contrast to the formulation above (with Itetra4=0).
    Figure 18. Plastic strain contour plot


    Figure 19. Comparison of results using LAW36


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

  • /PROP/TYPE14 (SOLID), Itetra10=0
    Figure 20 shows the results of the plastic strain contour plot visualization. You can spot the beginning of striction.
    Figure 20. Plastic strain contour plot


    Figure 21. Comparison of results using LAW36


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

  • /PROP/TYPE14 (SOLID), Itetra10=2
    Figure 22 shows the results of the plastic strain contour plot visualization.
    Figure 22. Plastic strain contour plot


    Figure 23. Comparison of results using LAW36


    The simulated true stress versus true strain curve matches perfectly the corresponding experimental curve. The simulated engineering stress versus engineering strain curve matches perfectly the corresponding experimental curve until striction starts at which point effort starts to decrease.

Conclusion

The materiel LAW36 was used with experimental data for different element to compare with simulations data. The simulation results of stress-strain curves overlay perfectly with input experimental curves for all element formulations evaluated.

The following tables summarize the different parameters used and comparing Starter + Engine runtime.
Table 1. Shell and Sh3n elements
Model Parameter Relative Cost
Shell Ishell=24 1
Ishell=12 1.64
Sh3n* Ish3n=0 2.17
* two times more SH3N elements than Shell elements in the model
Table 2. Hexahedron elements
Model Parameter Relative Cost
Hexahedron Isolid=24 1
Isolid=18 1.17
Isolid=15 1.07
Table 3. Tetrahedron elements
Model Parameter Relative Cost
Tetrahedron Itetra4=0 1
Itetra4=3 1.3
Itetra10=0 14.07
Itetra10=2 7.71
1 1. Li, Wenchao & Liao, Fangfang & Zhou, Tianhua & Askes, Harm. (2016). Ductile fracture of Q460 steel: Effects of stress triaxiality and Lode angle. Journal of Constructional Steel Research. 123. 1-17. 10.1016/j.jcsr.2016.04.018