Exploration of issues in thermal shock

1
Exploration of issues in thermal shock

• Background ideas
• FEA model
• Results
• Further work

2
Background ideas

• Shock may be caused by the sudden acceleration as
  heating starts/stops
• Need to understand magnitude of stress wave in
  terms of shape of heating in time and space
• FEA analysis will require short time a space
  scales to capture these effects

3
Time and space scales

• Speed of sound in aluminium 5,000 m/s
• One pulse 1 picosec
• Pulse shape may require 0.1picosec to describe
• Analysis should use time steps 0.01 picosec
  (1E-14 sec).
• At 5000 m/s the distance associated with
  0.01picosec is 5E-11 m, so element size should be
  a small fraction of this.
• NB we are talking elements smaller than atoms, so
  continuum assumptions are not valid. However,
  broad principles should apply

4
Model sizes

• Consider a heated zone just 0.5E-8m long, heated
  through 500C.
• Use E 70E9 Pa,
• poisson 0.27,
• density 2700 kg/m3
• CTE 23E-6.
• Unconstrained expansion would be 50023E-60.5E-8
  5.8E-11
• Fully constrained in one direction, stress would
  be 805 MPa.
• Constrained in all three directions, stress would
  be higher (see below)
• On these timecales, ignore conduction and
  consider enforced temperature rise.

5
Acceleration

• If the material were to expand by 5.8E-11m in
  1E-12 secs, velocity would be 58 m/s.
• If that velocity were reached in 0.1picosec,
  acceleration would be 6E13 g!
• What happens is that the material is subjected to
  an internal stress rather than a sudden movement,
  and starts to accelerate under that stress.
• The acceleration changes rapidly but that does
  not cause any near-singularities in velocity or
  position.
• And with heating as rapid as this, the material
  is nearly perfectly inertially confined

6
FEA model
7
Temperature/time history
Typical curve
Ramp region
Picosec
Rise region
8
Results

• Displacement (microns) at node 2 (end of heated
  zone)

9
Results

• Stress in x direction at t lt1picosec
• Heated zone 0.5E-2 micron, heating during 1
  picosec

10

• 1lttlt2 picosec

11

• 0lttlt5 picosec

12
Longer trise

• 0lttlt5 picosec

13
Shorter heated zone

• Heated zone was 0.2E-2 microns
• Stress does not reach the maximum level when the
  length of the heated zone is shorter than the
  distance travelled by sound during the heating
  period

14
Longer heated zone

• Heated zone now 1e-2 microns
• Note max stress in heated zone

15
Sievers, 1974

• Elastic stress waves in matter due to rapid
  heating by an intense high-energy particle beam /
  Sievers, P CERN-Lab-2-BT-74-2.- Geneva CERN, 26
  Jun 1974 . - 31 p     Fulltext

16
Reflection from constrained end
17
Reflection from free end

• Stress wave changes sign
• NO STRESS at free surface

18
3D effects part 1

• When the material is stressed in x there will be
  a tendency to strain in y and z (Poisson
  effect)
• When a material is constrained in y and z this
  will lead to stresses in y and z (and hence
  additional stress in x)
• We also introduce a failure criterion due to Von
  Mises

• S1, S2 and S3 can be taken as SX, XY and SZ in
  our case.
• Theory is that in ductile materials (does this
  apply at these strain rates?) failure will occur
  when SEQV exceeds a threshold amount.
• The factor 2 ensures that for simple
  unidirectional stress SEQV is the same as SX, so
  the critical value is simply equal to the normal
  failure strength. SEQV also know as deviatoric
  stress, the extent to which the stress state
  differs from hydrostatic stress. NB same stress
  in all three directions ZERO Von Mises stress.
  Tensile one way and compressive another way
  HIGH Von Mises stress.

19
3D effects part 1

• Imagine our rod of material is buried in a larger
  lump. It will not be able to expand sideways, in
  y and z.
• Add this constraint to the model.
• Stress at node 1 varying with time, without
  (left) and with this constraint

20
3D effects stress at the free surface

• SEQV at various times
• Still no stress at the free surface

21
Future work on 3D effects

• 3D effects part 2 include the effect of
  expansivity in y and z
• Should give ZERO equivalent stress within the
  heated zone, at least at first
• What about the edge of the heated zone and the
  free surface?

22
Early 3D results
SX
SYSZ
SEQV
23
Conclusions so far

• Good confirmation of Sievers results (so we are
  both right, or both wrong)
• If heated zone longer than tc, stress will reach
  a maximum level the same as if the zone were
  constrained. Shape of heating pulse (in time) is
  not important. (So concept of fracture
  temperature looks good, but)
• But need to do more work on 3D effects with
  Poisson, Von Mises, etc. (results so far show no
  stress at a free boundary).
• Waiting for standard text on shock waves (out of
  print) Stress Waves in Solids Paperback by
  Kolsky, H.

24
Animations from George

• Sample length is 5e-2 microns (5e-8m)
• Free at unheated end
• Heated zone is 1e-2 microns (1e-8m)
• Heated for 1 picosec
• 1 frame every 0.1 picosec
• Runs for 15 picosec
• Expansivity in x only - no 3D effects
• Expected stress at end of heating 805 MPa
• Expected expansion 1.2E-4 microns