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.

図 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.
- I_shell=24
- I_shell=12
A material modeled with shell elements /SH3N.
- I_sh3n =0
A material with hexahedron elements /BRICK.
- I_solid =24
- I_solid =15
- I_solid =18
A material modeled with tetrahedron elements /BRICK.
- I_tetra4=0
- I_tetra4=3
- I_tetra10=0
- I_tetra10=2

Options and Keywords Used

The following keywords are used in the models:

/MAT/LAW36 (PLAS_TAB)
/PROP/TYPE14（SOLID）, //PROP/TYPE1（SHELL）, /PROP/TYPE20 (TSHELL)
/BRICK, /SHELL
/BCS and /IMPVEL
/FUNCT
/RBODY
/SKEW and /FRAME
/GRNOD/NODE

Input Files

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

RD-V-0240.zip

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).

図 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 図 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.

図 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 I_shell=24, 5 integration points through thickness.
図 4 shows the results of the plastic strain contour. Here, the beginning of striction can be observed.
図 4. Plastic strain contour plot for shell QEPH shell formulation

In 図 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 $ε e = Δ 1 / l 0$ . The elongation $Δ 1$ is measured from two instrumented nodes. The original distance l0 is 80 mm.
図 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 I_shell=12, 5 integration points through thickness
図 6 shows the results of the plastic strain contour. The beginning of striction can be observed.
図 6. Plastic strain contour plot for shell QBAT shell formulation

図 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:

I_sh3n = 0
図 8 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
図 8. Plastic strain contour plot for sh3n element

図 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), I_solid =24
図 10 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
図 10. Plastic strain contour plot for solid element

図 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), I_solid =18
図 12 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
図 12. Plastic strain contour plot for solid element

図 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), I_solid =15
図 14 shows the results of the plastic strain contour plot visualization. The beginning of striction can be observed.
図 14. Plastic strain contour plot for TShell element

図 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), I_tetra4=0
図 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.
図 16. Plastic strain contour plot

図 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), I_tetra4=3
図 18 shows the results of the plastic strain contour plot visualization. Using I_tetra4=3, the striction can be observed in contrast to the formulation above (with I_tetra4=0).
図 18. Plastic strain contour plot

図 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), I_tetra10=0
図 20 shows the results of the plastic strain contour plot visualization. You can spot the beginning of striction.
図 20. Plastic strain contour plot

図 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), I_tetra10=2
図 22 shows the results of the plastic strain contour plot visualization.
図 22. Plastic strain contour plot

図 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.

表 1. Shell and Sh3n elements
Model	Parameter	Relative Cost
Shell	`I`_shell=24	1
Shell	`I`_shell=12	1.64
Sh3n*	`I`_sh3n=0	2.17

* two times more SH3N elements than Shell elements in the model

表 2. Hexahedron elements
Model	Parameter	Relative Cost
Hexahedron	`I`_solid=24	1
	`I`_solid=18	1.17
	`I`_solid=15	1.07

表 3. Tetrahedron elements
Model	Parameter	Relative Cost
Tetrahedron	`I`_tetra4=0	1
	`I`_tetra4=3	1.3
	`I`_tetra10=0	14.07
	`I`_tetra10=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