8/3/2019 Analisis Tegangan Thermoelastik Untuk Pemeriksaan
Kerusakan Kapal_Transportasi Maritim_Hebb_Richard
1/1
Thermoelastic Stress Analysis for Damage AssessmentRichard Hebb
[email protected] - School of Engineering Sciences
Supervisors Prof. J. M. Barton, P. Tatum (AWE)
Aims and Objectives To develop understanding of stresses around
a crack tip using
Thermoelastic Stress Analysis (TSA).
Locate and identify both internal and external damage on small
scale
pipes.
Develop a non-contact method of excitation for TSA.
Thermoelastic Stress Analysis The relationship between the
change in stresses around a crack tip and
the temperature change in the material (under adiabatic
conditions) is
given by the Williams expansion:
[1]rOB
Btan
2
cosrBB2T
K
Ktan
2
cos
2
KK22
3
I
II12
II
2
Is
I
II1
2
II
2
I --
rAS
A = Constant for given loading a nd boundary conditions
BI,II = Constants
S = Signal produced by the detector for given r
KI and KII = SIFs
O = Higher order terms
Ts = T-stress constant term
= Coefficient of linear thermal expansion
Cp = Specific heat at constant pressure
= Mass density
It can then be shown the Williams expansion can be related to
the
temperature change induced by:
[2]ASC
TT
p
Therefore measuring the temperature change allows the Stress
Intensity
Factors (SIFs) to be calculated.
Ignoring the higher terms and re-arranging shows that a curve of
constant
signal takes the form of a cardioid:
[3]2cos1SA
KKr
22
2
II
2
I
Experimental Technique A crack is grown in a Dural plate (with a
centrally located spark eroded
starter slot) by fatiguing the plate below its fracture
toughness. For Dural
this is 19.0 MPa m0.5 which can be used to calculate the applied
stress
required by:
Fluid Structure Interactions
Research Group
Plot showing contours of first order (black) and higher
order (red) Williams expansion with the crack line (blue).
Simulated Data and Higher Order GA As opposed to fitting a
cardioid to isopachics, more accurate SIF
calculation is possible by fitting the full Williams expansion
to the ent ire
field.
Simulated fields are being created both as a control mechanism
for the
modified GA and to gain knowledge of the influence of the higher
orderterms by varying individual values.
Analysis Technique Isopachics extracted from the data are fed
into a genetic algorithm which
fits a cardioid curve to the raw data.
The fitness of the fit is determined by the inverse of the mean
squareerror for the curve fit:
[5]N
1i
2
iei2
r
rrN
100M
[6]
2
p02
II
2
IT
CT
2
rKK [7]
I
II
K
Ktan
Fitness = M-1as
SIFs then calculated by simultaneously solving:
Actual data set A simulated set of data
Work is currently ongoing to determine the physical meaning and
values
of the higher order terms.
Cardioid
Number
x (pixels
(mm))
y (pixels
(mm)
r0 (pixels
(mm)
2
(radians)Fitness
1 45.75 (13.7) 89.30 (26.8) 89.02 (26.7) 0.289 0.35978
2 41.99 (12.6) 80.79 (24.2) 53.86 (16.2) 0.393 0.49101
3 40.23 (12.1) 76.82 (23.0) 37.98 (11.4) 0.338 0.61657
4 39.41 (11.8) 77.39 (23.2) 29.48 (8.8) 0.442 0.58084
5 39.30 (11.8) 77.11 (23.1) 23.82 (7.1) 0.497 0.55064
Further Work Completion of the genetic algorithm.
Alternate excitation methods of the plate (ultrasound, shaker at
natural
frequency, transient load).
FEA analysis of pipe work to find natural frequencies, expected
response
from TSA.
Experimental work on pipe work, including alternate
non-contact
excitation methods.
Analysis of Data The genetic algorithm is used to fit a
cardioids to extracted isopachics
from the data.
The cardioids can be seen to rotate anti-clockwise with
increasing
distance from the crack-tip which the first order Westergaard
equation [3]
is unable to account for.
It has been shown that the previously omitted higher order terms
are the
cause of the extra rotation.
Results for fitting a cardioid to the extracted isopachics
[4]aC
k C1 k1C = 19.0 MPa m0.5
a = semi-crack length = 20mm
C = Geometry dependant constant = 1.004
This relates to an applied stress of 75.5 MPa for the plates, or
an applied
load of 49.15 kN.
The crack is grown to approximately 30mm, with TSA being
performed at
regular intervals.
Once the crack has grown, a smaller plate is cut from the
specimen with
the grown crack at the centre at an angle of 15, 30, 45 and 60
degrees, thus
giving specimens containing mixed-mode, centrally located
cracks.
TSA is then performed on the mixed-mode specimens.
Schematic of the specimens and mounts. Only the top mount has
been shown for clarity.
