Munson-Dawson Model: Pure Shear Test (FLAC3D)

Note

The project file for this example may be viewed/run in FLAC3D.[1] The main data file used is shown at the end of this example.

This verification test for the Munson-Dawson model exemplifies a typical pure shear loading and response to temperature changes. At t = 0 days, an instantaneous isotropic strain results from pure thermal expansion, increasing from 300 to 330 K (27 to 55 °C). Simultaneously, a pure shear state of \(\sigma_{xx} =5\) MPa, \(\sigma_{yy} =0\) MPa, and \(\sigma_{zz} =-5\) MPa is applied. The temperature remains constant at 330 K until t = 50 days. At t = 50 days, at which point it rises to 385 K (112 °C) while the applied stresses maintain their initial pure shear state. This sudden increase in temperature leads to a step change in thermal strain, followed by accelerated creep observed over the subsequent 50 days.

The material properties are summarized in the table below.

shear

\(G\)

12.4 (GPa)

bulk

\(K\)

20.7 (GPa)

hosford

\(a\)

16

f-exponent

\(\chi\)

1

A-0

\(A_0\)

5.617e1 (\(s^{-1}\))

activation-ratio-0

\(Q_0/R\)

5123 (K)

n-0

\(n_0\)

1.595

A-1

\(A_1\)

8.386e22 (\(s^{-1}\))

activation-ratio-1

\(Q_1/R\)

12580.5 (K)

n-1

\(n_1\)

5.5

A-2

\(A_2\)

4.415e16 (\(s^{-1}\))

activation-ratio-2

\(Q_2/R\)

5123 (K)

n-2

\(n_2\)

6.279

B-1

\(B_1\)

6.086e6 (\(s^{-1}\))

B-2

\(B_2\)

3.034e-2 (\(s^{-1}\))

stress-limit

\(\sigma_0\)

20.57e6 (MPa)

stress-constant

\(q\)

5335

k-0

\(k_0\)

5.277e-2

c-0

\(c_0\)

8.882e-3 (\(K^{-1}\))

m-0

\(m_0\)

0.9201

k-1

\(k_1\)

3.052e12

c-1

\(c_1\)

8.882e-3 (\(K^{-1}\))

m-1

\(m_1\)

5.282

alpha-hardening

\(\alpha_h\)

3.367

beta-hardening

\(\beta_h\)

-0.6838

alpha-recovery

\(\alpha_h\)

0.58

beta-recovery

\(\beta_r\)

0.0

Figure 1 illustrates the strain response up to t = 100 days. The FLAC3D solution shows a good match with the reference analytical solution in Reedlunn (2018).

References

Reedlunn, B. Enhancements to the Munson-Dawson model for rock salt (No. SAND-2018-12601). Sandia National Laboratories, Albuquerque, NM, USA (2018).

../../../../../_images/md-pureshear-strain.png

Figure 1: Pure shear test on a Munson-Dawson material: numerical strain values versus time.

Data File

model new
model large-strain off
fish automatic-create off
model title "Pure shear test --- Munson-Dawson model"
model configure creep
model creep active off
;
zone create brick size 1 1 1
zone face skin
zone cmodel assign elastic
zone property density 2300 bulk 20.7e9 shear 12.4e9
;
zone initialize stress xx 0 yy 0 zz 0
zone gridpoint initialize displacement-x [30*45e-6] add range group "East"
zone gridpoint initialize displacement-y [30*45e-6] add range group "North"
zone gridpoint initialize displacement-z [30*45e-6] add range group "Top"
zone face apply velocity-z 0 range group 'Bottom'
zone face apply velocity-y 0 range group 'South'
zone face apply velocity-x 0 range group 'West'
model solve
;
model creep active on
zone cmodel assign munson-dawson
;; Cal-3B
zone property density 2300 temperature 330
zone property bulk 20.7e9 shear 12.4e9 f-exponent 1 hosford 16
zone property A-0 5.617e1  activation-ratio-0    5123 n-0 1.595
zone property A-1 8.386e22 activation-ratio-1 12580.5 n-1 5.5
zone property A-2 4.415e16 activation-ratio-2    5123 n-2 6.279
zone property B-1 6.086e6 B-2 3.034e-2 stress-limit 20.57e6 stress-constant 5335
zone property k-0 5.277e-2  c-0 8.882e-3 m-0 0.9201
zone property k-1 3.052e12  c-1 8.882e-3 m-1 5.282
zone property alpha-hardening 3.367 beta-hardening -0.6838
zone property alpha-recovery 0.58 beta-recovery 0.0
;
zone face apply stress-xx -5.0e6 range group 'East'
zone face apply stress-zz  5.0e6 range group 'Top'
;
[global zp = zone.head]
[global gp = gp.find(8)]
fish define sxx_
    global sxx_ = zone.stress.xx(zp)
    global syy_ = zone.stress.yy(zp)
    global szz_ = zone.stress.zz(zp)
    global exx_ = -gp.disp.x(gp)*100
    global eyy_ = -gp.disp.y(gp)*100
    global ezz_ = -gp.disp.z(gp)*100
end
history interval 100
model history name 'time' creep time-total
fish history name 'sxx' sxx_
fish history name 'syy' syy_
fish history name 'szz' szz_
fish history name 'exx' exx_
fish history name 'eyy' eyy_
fish history name 'ezz' ezz_
; --- creep test ---
model creep timestep starting 1e-12
model creep timestep automatic
model creep timestep minimum 1e-12 
model creep timestep maximum 1000
model creep timestep upper-multiplier 0.99
model creep timestep lower-multiplier 1.01
;
model solve creep time-total [3600*24*50]
model save 'shear1'

model creep active off
zone property temperature 385
zone gridpoint initialize displacement-x [55*45e-6] add range group "East"
zone gridpoint initialize displacement-y [55*45e-6] add range group "North"
zone gridpoint initialize displacement-z [55*45e-6] add range group "Top"
model cycle 10 

model creep active on
model creep timestep starting 1e-12
model creep timestep automatic
model creep timestep minimum 1e-12 
model creep timestep maximum 1000
model creep timestep upper-multiplier 0.99
model creep timestep lower-multiplier 1.01

history interval 10
model solve creep time-total [3600*24*100]

history export 'time' 'exx' 'eyy' 'ezz' file "pureshear-md.txt" truncate
model save 'pureshear-md'