# Calibrated Pulse-Thermography Procedure for  Inspecting HDPE

Authors: Mohammed A. Omar; Yi Zhou; Rohit Parvataneni; Eric Planting
Journal: Research Letters in Materials Science
 (2008)

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## Abstract

This manuscript discusses the application of a pulse-thermography modality to evaluate the integrity of a high-density polyethylene HDPE joint for delamination, in nonintrusive manner. The inspected HDPE structure is a twin-cup shape, molded through extrusion, and the inspection system comprises a high-intensity, short-duration radiation pulse to excite thermal emission; the text calibrates the experiment settings (pulse duration, and detector sampling rate) to accommodate HDPE bulks thermal response. The acquired thermal scans are processed through new contrast computation named _self-referencing_, to investigate the joint tensile strength and further map its adhesion interface in real-time. The proposed system (hardware, software combination) performance is assessed through an ultrasound C-scan validation and further benchmarked using a standard pulse phase thermography (PPT) routine.


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## Body

## 1. Introduction

Pulse
or flash thermography is used in nonintrusively test and to evaluate bulks’
subsurface based on the thermal contrast between its different interfaces (i.e.,
different conduction rates). Due to its reliance on thermal conduction, this
modality has been applied for different classes of materials (isotropic,
anisotropic ferrous, nonferrous, etc.) to detect variety of defectives; cracks
and delaminations in CFRP/GFRP composites in [1], and for concrete structures in
[2]. This manuscript demonstrates the application of pulse thermography to
quantitatively evaluate the bond strength of HDPE molded joints, and map its
adhesion interface. The quantitative evaluation is done through correlating the
thermographic results with the pull force needed to break the joint using a
tensile machine, which is the current standard testing method. Additionally,
the synthesized adhesion interface is further validated with ultrasonic C-scan.
A cross section of the inspected joint is displayed in
Figure 1, which shows
the joint dimension, shape, and inspected area. The main deviations encountered
in such joints can be summarized into: structural and adhesive related. The
structural aspect comprises any misalignment in the joint structure and
diameter of contact at the neck region; while, the adhesion defects include adhesion
layer thickness, uniformity, and delaminations. Both classes of variations
affect the structure performance through its impact on joints’ breakage modes,
and its ultimate joint strength.Figure 1
HDPE joint under inspection, showing joint structure, cross-section, and
material layered structure.


## 2. Experimental Approach

Due to
the production constraints in terms of production rate and automation level in
addition to the warranty costs and its safety implications, a noncontact,
real-time inspection system is pursued, to evaluate 100% of the products. Even
through ultrasound scanning is effective in evaluating both defective classes
quantitatively, the need to an automated, full-geometry inspection scheme under
one minute, motivated a two-dimensional vision-based approach. Thermal imaging
or thermography has been used successfully in several two-dimensional,
real-time industrial implementations; as in quantifying the thickness of wet
paint when applied over fuel containers in [3], and over complicated car shell geometries
in [4]. In current application, a pulse thermographic procedure guarantees the
two-dimensional coverage of inspected joint in real-time, with fully automated
data correlation and processing. The developed system comprises a high-intensity, short 6400 joules of radiation perturbation (product of BALCAR,
France), to excite thermal emission. While an uncooled microbolometric, vanadium
oxide (VOx) coated 320×240  focal plane array (Product of FLIR, MA) is used
to acquire the thermal response (emission counts), at up to 30 Hz sampling. The
stimulation source and the thermal detector can be configured in either a
reflection mode, where both are set in the same side, or in transmission mode,
where they are set in opposite sides of the inspected joint, current
configuration applies a reflection mode, to accommodate the short inspection
time. To set the system parameters in terms of pulse, duration, intensity, and
the camera acquisition rate, a thermal calibration for the HDPE is warranted.
To do this we start with the facial thermal response of the inspected material,
when considered as one-dimensional heat propagation in an opaque bulk, which
can be mathematically described in (1) from [5]: (1)Ts(0,t)=2I0kαtπ[1+2π∑n=1∞{ε1−ε2ε1+ε2}nierfc(ndαt)], where, I0   is the absorbed energy density of the
pulse, α  is the thermal diffusivity of the HDPE, k   is its thermal conductivity, d   is the HDPE layer thickness, and ε  is the effuisivity (or thermal inertia ε=k×ρ×Cp)  for the HDPE
(subscript 1), and the delaminated layer (subscript 2), which is simulated as
an air interface. Then to decide on an optimized duration tp  for a rectangular pulse,
the response from (1) is manipulated into (2). (2)Tp(0,t)=Ts(0,t)-Ts(0,t-tp)fort>tp.
Equation
(2) graphical representation in Figure 2(a) provides the time of maximum contrast
between the defective and its surroundings by monitoring the corresponding time
for maximum contrast. The plot in Figure 2(a) indicates that for the thermal
reflection coefficient Γ={(ε1−ε2)/(ε1+ε2)}  between an air interface and HDPE bulk of
0.94, the best observation time tobs is found  to be within Fo=0.65, which means that the
pulse duration should be  tobs=Fo(d2/α)=4.22 seconds, for HDPE with  k=0.5W/m⋅K,ρ=950kg/m3, and Cp=1900J/K⋅kg, while the delamination
is embedded at 0.5 cm (i.e.,  at the adhesion interface). Thus, the camera
acquisition rate and duration should accommodate such time window; such that the experiment duration prevents missing
the maximum contrast signal while the acquisition rate allows for good sampling
because some time-averaging might be needed; the pulse is set at 20 milliseconds
duration with a detector acquisition rate of 20 Hz for one minute. To adjust
the calibration procedure for defectives located at different depths, we
propose (∂Tp/∂d)(0,t)    to describe the depth contrast in
(3), which
is graphically  displayed in Figure 2(b):
(3)∂Tp∂d(0,t)={∂Ts∂d,t≤tp∂Ts∂d(t)−∂Ts∂d(t−tp),t>tpwhile,∂Ts∂d(0,t)=−4×I0k∑n=1∞n(Γn)erfc(nFo).(a) Response to rectangular pulse, showing the departure time from defect
free cooling, (b) thermal contrast variation with delamination depth.
(a)(b)


## 3. Data Processing and Correlation

Several
calculation options exist for processing pulse-thermography sequences to
translate the temperature-time history into subsurface maps, which retrieve any
embedded delaminated locations and their shape. However, some of these routines
as thermal signal reconstruction (TSR) [6] requires a priori knowledge of the
defectives depth and their lateral dimensions, in other words their aspect
ratio (depth/lateral dimension), to provide accurate depth predictions.
Additionally, other routines such as pulse phase thermography PPT [7] provide
inconsistent predictions when varying the sampling rate and/or the experiment
duration [8, 9]. So, in this application we utilize a novel processing routine
named “self-referencing” presented in [10], due to its insensitivity to implants
aspect ratio and experiment variations. The self-referencing calculations
extract the temperature-time history of each pixel location Tpix and compare its values
to that of its neighbors’ statistics mainly Tavg mean  and standard deviation  σsurr. Then following the
criteria in (4), a contrast matrix is initiated to describe the deviation from
the defect-free behavior, additionally a time matrix is established to track
the time of maximum contrast. Finally, to produce the depth map, the contrast Cmax and time tmax   matrices are used in (5) from [11], for each
pixel location (i,j) to yield the defective
depth D   at that location:(4)|Tpix−Tavg|≥η⋅σsurr(i,j).(5)D=a[tmax(i,j)Cmax(i,j)b].
The
resulted contrast and time matrices are displayed in Figure 3, in addition to
the synthesized depth map using the proposed approach.Sequence of self-referencing code showing the
(a)  raw-thermogram, (b) time-gram, (c) contrast-gram,
(d) synthetic adhesion map.
(a)(b)(c)(d)To
benchmark the proposed routine, an ultrasound C-scan is acquired utilizing an
Ultrascan 5 transducer (Product of US Ultratek, CA), at a frequency of 5 MHz,
and a sampling of 100 MHz and a spatialX-Y increment of ~3 mm. The C-scan is
displayed in Figure 4(a),  which shows a clear agreement between the
pulse-thermography results and those of the C-scan, further computing the
%error in the depth-thermogram results in 15%. Additionally, using a well
publicized routine in thermography literature PPT, results in Figure 4(b). Finally,
the joint tensile strength is investigated by correlating it with the thermal
conduction heating profile across the joint, which is achieved through a
transmission mode of thermography. Figure 5 from [12] plots the conduction propagation
rates for different pulled samples while the legend indicates the tensile force
used to break the corresponding joint.(a) C-scan result, (b) PPT phase image.
(a)(b)Figure 5
Temperature evolution curves for transmission mode thermography, legends
corresponding tensile force.


## 4. Conclusion

The
manuscript presented a flash-thermography, nonintrusive procedure to inspect
HDPE molded joints. The text presented a new method to calibrate the
thermographic procedure to accommodate the inspected bulk in two domains, the
hardware by calibrating the pulse duration, detector sampling rate, and using
the material thermal response for a square pulse with finite duration.
Additionally, the software domain presented a robust, self-calibrated
calculation  to produce the adhesion layer thickness. C-scan results validated
the performance of the proposed scheme, while the temperature evolution curves
was in agreement with tensile force predictions.



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*Source: 186427-2009-01-20.xml*