6. D modeling#

6.1. Characteristics of modeling#

We use a AXIS model.

Two calculations are performed that differ only in the integration algorithm: “NEWTON” and “RUNGE_KUTTA”.

In this case, the coefficient \({K}_{D}\) is chosen only depending on the temperature.

T (°C)

900

1000

1025

\({K}_{D}\)

15

15

15

Table 6.1-1 : K_D from the D modeling

The discretization in time is quite fine:

(JUSQU_A = 2, NOMBRE = 10),

(JUSQU_A = 2., NOMBRE = 10),

(JUSQU_A = 20., NOMBRE = 10),

(JUSQU_A = 200., NOMBRE = 10),

(JUSQU_A = 2000., NOMBRE = 10),

(JUSQU_A = 20000., NOMBRE = 10),

(JUSQU_A = 200,000., NOMBRE = 10),

(JUSQU_A = 1000000., NOMBRE = 30),

(JUSQU_A = 1600000., NOMBRE = 30),

(JUSQU_A = 1700000., NOMBRE = 40),

(JUSQU_A = 1800000., NOMBRE = 40),

(JUSQU_A = 1900000., NOMBRE = 40),

(JUSQU_A = 2000000., NOMBRE = 40),

(JUSQU_A = 2100000., NOMBRE = 40),

(JUSQU_A = 2200000., NOMBRE = 40),

(JUSQU_A = 2300000., NOMBRE = 40),

(JUSQU_A = 2400000., NOMBRE = 40),

(JUSQU_A = 2500000., NOMBRE = 40),

6.2. Characteristics of the mesh#

It is chosen to represent the cylindrical test piece by a quadrangle with 8 knots in axisymmetry.

Number of knots: 8

Number of stitches: 1 (QUAD8)

_images/10000201000001BD0000022CAEC440B46B4E3C28.png

Image 6.2-1: D modeling mesh

6.3. Tested sizes and results#

6.3.1. Case RUNGE_KUTTA + Matrix ELASTIQUE#

Evolution of the constraint, \({\sigma }_{0}\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

79.92289999999999998

0.5

1600000

“ANALYTIQUE”

70.90219999999999993

1.0

Table 6.3.1-1 : D modeling results

Evolution of the damage variable, \(D\) as a function of time. This value is tested at various times depending on the modeling:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

0.066266580000000005

1.0

1600000

“ANALYTIQUE”

0.090278800000000006

1.0

Table 6.3.1-2 : D modeling results

Evolution of the viscoplastic isotropic work hardening variable, \(r\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

2.747799999999999999E-3

0.5

1600000

“ANALYTIQUE”

2.7993599999999999E-3

0.5

Table 6.3.1-3 : D modeling results

Evolution of the viscoplastic isotropic work hardening variable, \(p\), as a function of time. This value is tested at various times:

Instant

Reference Type

Reference

Tolerance (%)

1000000

“ANALYTIQUE”

2.7522900000000001E-3

0.5

1600000

“ANALYTIQUE”

2.8137437999999999E-3

0.5

Table 6.3.1-4 : D modeling results

6.3.2. Case NEWTON + Matrix TANGENTE#

The quantities tested are the same as in the previous case. On the other hand, the tolerance is 4% (for all values tested).