hybrid thermal methods in experimental stress analysis

ATEM'03, JSME-MMD, Sep. 10-12, 2003

Corresponding author: Eann Patterson, [email protected]

Hybrid thermal methods in experimental stress analysis

Eann Patterson1, Richard Greene1, Manuel Heredia1

and Jon Lesniak2

1. Department of Mechanical Engineering, University of Sheffield, Sheffield, UK

2. Stress Photonics Inc., Madison, Wisconsin, USA

Abstract: Many traditional methods of full-field strain analysis provide convoluted or limited strain data. For instance, photoelasticity provides data related to the difference in principal strains and strain separation is problematic; whilst moiré can provide in-plane or out-of-plane displacements. It has long been recognized that integrating two techniques can enhance the information available, for example holophotoelasticity; this is particularly valid when one technique operates in the infrared spectrum. Combined thermo-photo-elasticity was first attempted about a decade ago and an instrument for simultaneous capture of thermoelastic and photoelastic data has been developed and used to acquire maps of separated principal strains in complex components. When thermography and moiré are combined, a new technique emerges which allows meas-urement of in-plane and out-of-plane strain. These novel techniques are described and examples given of their application to strain measurement in composites and complex engineering components. Key words: Hybrid experimental stress analysis, Photoelasticity, Thermoelasticity, Moiré.

1. INTRODUCTION Experimental stress analysis has suffered a steady de-

cline in popularity during the last quarter of a century and numerical methods of stress analysis have become the norm. Advances in computer technology have delivered sufficient power in the desktop or lap-top computer that many engineering problems can be solved in a matter of minutes by an engineer’s personal computer. The defini-tion of the problem and its boundary conditions remain a demanding exercise and a source of concern particular for complex problems. As consequence, there is still a re-quirement for experimental stress analysis to provide data for validation and verification of numerical models. The speed of computational analysis and the quantity of data generated has raised expectations for experimental me-chanics.

Improvements in electronics and, in particular, in sen-sors combined with cheap and portable computing power is transforming experimental mechanics laboratories. The quality and quantity of experimental data available is rapidly increasing as innovative methods and devices are developed to meet the raised expectations. Hybrid tech-niques have been used previously, for example moiré combined with photoelasticity [1] and photoelastic holo-graphy [2]. The integrated use of two techniques either provides more information than the individual techniques are capable of supplying, or allows convoluted data such as the difference in principal stresses to be separated or deconvoluted.

In this paper, the use of data collected in the infrared spectrum is shown to extend the potential of moiré so that both in-plane and out-of plane data can be derived from the same optical arrangement; and to allow photoelastic data to be separated in a field of view without reference to

neighbouring points. Although the two hybrid techniques share the same concepts, that is integrating a thermal method with a traditional technique of stress analysis, the methodologies developed and apparatus employed are significantly differently and so they are described sepa-rately below. 2. THERMAL MOIRE 2.1. Principles

The novel technique brings together the concepts of thermography and geometric moiré. Thermography is used as a tool in non-destructive testing for detecting and quantifying damage in structures. In passive thermo-graphy the heat generated at damage sites is monitored using an infrared camera, whilst in active thermography a heat source is employed to ‘illuminate’ the structure. A temperature gradient is induced in the component, by ei-ther heating or cooling using an external source, and the heat diffusion is witnessed using infrared thermal imaging. Propagation of heat depends on the density, heat capacity, and thermal conductivity of the material, which allows the detection of material inhomogeneities and defects that disturb the uniformity of heat propagation such as de-bonding, de-lamination, or cracks. A number of techniques have been developed, including pulse thermo-graphy [3], modulated or lock-in thermography [4], or pulse phase thermography [5], which combines these concepts. It has been recently proposed that inducing in-plane heat flow improves the detectability of certain types of flaws [6]. Forced diffusion thermography [7] makes use of patterned radiation to force heat flow in-plane for crack detection, and coating tolerant thermo-graphy [8] is a variation based on the same principle that

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allows the separation of the effects of structural defects from variations in surface emissivity. The variation in heat transmission or reflection by the structure reveals the site and extent of damage. Thermal moiré extends these concepts to imprinting a thermal motif on the structure and employs conventional geometric moiré principles to ob-tain displacement and deformation data. Previously, some attempts have been made at correcting for shape effects in pulse thermography, using the ‘shape-from-shading’ theory from machine vision in thermal images [9].

In essence, the new technique involves imprinting a thermal grating onto the surface of the object of interest, to form the object grating. This can be created by physical contact with a hot stencil, or by projection from an infrared lamp. Rigid body motion or deformation of the object can be monitored by observation of the thermal object grating using an infrared imaging system either with or without a thermal reference grating. When a thermal reference grating is not employed, the technique becomes a form of fringe processing rather than moiré. If the de-formation of the initially imprinted thermal motif is tracked then the technique allows in-plane displacements and thus strains to be evaluated; whereas the repeated imprinting of the motif, allows out-of-plane displacements to be followed. In the latter case, the method is directly analogous to the fringe projection method.

Fig. 1. Contact prototype, with components highlighted (top left), the corresponding temperature distri-bution (top right) and in operation (bottom).

2.2. Apparatus

Thermal imprinting of a motif can be achieved by two types of method, namely contact by a hot stamp or brand, or projection of an infrared image [10]. Examples of both methods are given below, and in each case an infrared camera is used to record the resulting image of the im-printed motif on the object of interest. The authors have used a cross or dot motif in both their contact and projec-tion versions of the technique, since this approach allows both u and v displacement fields to be determined from a

single image of the deforming object. Contact printing was performed using a specially de-

signed device shown in Fig 1, which consisted of three plates held together by bolts and with spacers between them at the corners. The lower two plates were drilled with a regular array of holes through which a set of steel pins were placed. The pins had heads at their top end which prevented the end from passing through the holes in the middle plate. The heads of the pins were in contact with a silicone rubber pad heater which together with a foam block was held in place by the upper plate. The heated pad contained electric heating elements, which were controlled by a simple dimmer switch. The pins were allowed to heat up to about 340K before being pressed into contact with the object as shown in fig. 1.

Projection of a thermal motif has been achieved using a simple projection incorporating a 2500W halogen source operating at 3200K. A standard configuration of optical elements for a projector in the visible spectrum was em-ployed but the individual elements were selected for use in the infrared spectrum. The grating was photo-etched onto a gold-plated steel substrate. The projection system is shown in fig 2.

2.3. Fringe processing

The temperature distribution in the imprinted motif can be described as an intensity field observed by the camera such that: I(x,y) = A + B (cos(φx x) + cos(φy y) + 2 cos(φx x) cos(φy y))

where A is a background term, B the amplitude modu-

lation, and φx, φy are the frequency of the dot pattern in the x and y directions respectively. The x and y terms were separated using a variation of the Fourier transform method [11] in which filters are applied in the frequency domain as illustrated schematically in fig. 3. This process yields two fringe patterns namely an image with vertical fringes corresponding to φx and one with horizontal fringes corresponding to φy. These images are combined with corresponding reference patterns to generate u and v dis-placement maps in same manner as for the visible spec-trum [10].

2.4. Examples

Figure 4 shows a thermal motif projected onto a human forearm using the system shown in fig 2. In the first image the motif has been projected onto the skin of the forearm held in a relaxed position, and in the second image, the subject has dragged his finger across the skin causing deformation which can be observed in the distortion of the thermal motif.

Figure 5 shows a second example consisting of a rubber sheet with a central hole that has been subject to a vertical tensile strain. Before applying the load, the sheet was imprinted with a dot motif using the device shown in fig.1. The thermal images were recorded using an Agema 900 system with an array of sensors operating in the 8-12µm bandwidth with a sensitivity of 0.08°C at 30°C. In fig. 5 the strains in the x and y directions obtained from the fringe processing together with those obtained by finite element analysis are shown. There is good correlation between the two sets of results.

Heater

Foam block

Steel pins

Guide plates

Heater

Foam block

Steel pins

Guide plates

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Fig. 2. Infrared projection arrangement shown dia-grammatically above and in the laboratory below with the image projected on a sample shown inset.

3. THERMO-PHOTO-ELASTICITY 3.1. Principles

The concepts of reflection photoelasticity are well known and documented [12]. Briefly, a coating of transparent polymer is bonded onto an engineering com-ponent using an adhesive containing reflective particles. Polarised light is employed to illuminate the coating and is reflected back through the coating by the reflective parti-cles and viewed using a polariscope. The coating acts as a witness to the surface strain in the component, so that when load is applied to the component, fringes are ob-served in the coating. The fringes result from the strain-induced birefringence of the coating and are con-tours of the difference in the principal strains.

Recently, it has been shown that the phase-stepping technique for fringe analysis [13] can be used in reflection [14]. This is technique requires the collection of a minimum of four phase-stepped images in order to allow the direction and difference in the principal strains to be established for the field of view. The use of beam-splitting optics allows the simultaneous collection of the four phase-stepped images [15,16] and provides the potential for real-time digital photoelasticity.

Thermoelastic stress analysis [17] is a less known tech-nique and has only become practical in last few decades [18]. When a solid body is subject to cyclic strain it ex-periences a temperature change that is 180° out-of-phase with the forcing signal, i.e. tensile strain produces a re-duction in temperature and compressive strain generates a rise in temperature. These temperature changes are of the order of 0.001°C and can be detected using infrared sen-sors. The amplitude of the cyclic temperature change is directly proportional to the amplitude of the cyclic varia-tion of first strain invariant (sum of the principal strains) experienced by the body.

It is usual in thermoelastic stress analysis to apply a layer of matt black paint to the component in which the strain is being measured in order to provide a surface with a uni-form emissivity and to maximize the photon emissions in the bandwidth of the sensor. Recently, it has been shown that photoelastic coatings are black at the infrared wave-lengths employed for thermoelastic stress analysis [19] and behave as strain witnesses when the component is

Object

Heat Source

Grating

LensesCollector

Object

Heat Source

Grating

LensesCollector

IR camera

Projector

Specimen

IR camera

Projector

Specimen

FFT Reference

FFT Object

v

u

FFT Reference

FFT Object

v

u

Fig. 3. The reference and object images are filtered in the fre-quency domain to yield vertical and horizontal fringe patterns with the information rela-tive to the x and ydirections respec-tively. These pat-terns can be ana-lysed in pairs using conventional methods to obtain respectively the uand v components of displacement.

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subjected to cyclic strain. As a consequence, it is possible to measure the cyclic strain in a photoelastic coating using thermoelastic stress analysis to obtain the sum of the principal strains and using reflection photoelasticity to obtain the difference in the principal strains [20-22]. The use of beam-splitting optics that separate the visible and infrared spectra allow these measurements to be made simultaneously [23]. The strains can be separated by addition and subtraction of the two sets of data in order to give maps of the maximum and minimum principal strains in which the values at each point have been determined independently of their neighbours.

Fig. 4. Infrared images showing a thermal pattern im-printed onto the forearm of a human subject using the projection prototype, in a relaxed position (top) and with the subject dragging his finger across his forearm from left to right, stretching the skin of his forearm (bottom).

3.2. Apparatus

A combined thermoelastic and photoelastic instrument has been built using two previously independent tech-nologies, namely a Deltatherm 1550 (StressPhotonics Inc, Madison, WI, USA) for the thermoelasticity and a solid state polariscope known as a poleidoscope [16]. The op-tical layout of the instrument is shown in Fig. 6 and in-cludes a beam-splitting element which allows the polei-doscope and Deltatherm to share a common view of the object by dividing the incoming light beam into infrared and visible components. The object is coated with a Photostress coating (Measurement Group Inc, Rayleigh,

NC, USA) and illuminated by a circularly polarised light source. The object is subjected to a cyclic load and the amplitude of the temperature variation and the relative retardation are evaluated independently by the operating systems of the Deltatherm and poleidoscope systems. Then, the resultant data maps are combined as a pair of matrices. A suite of software has been produced specially for this process and enables the thermoelastic (σ1+σ2) and photoelastic (σ1-σ2) data to be read in their generic and proprietary formats, calibrated using the properties of the coating employed, correlated spatially and then combined to yield individual data maps of individual principal stresses, σ1 and σ2. 3.3. Examples

The results of combined analysis of two components are shown in figs. 7 and 8. A composite panel subject to a high cyclic strain on the top-left to bottom-right diagonal whilst zero cyclic strain conditions were maintained on the top-right to bottom-left diagonal is shown in figure 7. The panel is about 80mm in diameter and has a 0.5mm PS1 coating bonded on the left hand half and a 1 mm think PS3 coating on the right-hand side. The panel is con-strained around its circumference by the loading mecha-nism.

Figure 8 shows the results for a gas turbine blade subject to an excitation at its first natural frequency. It was coated with a PS 1 coating 1mm thick and excited by mounting it on shaker. 4. DISCUSSION AND CONCLUSIONS

The hybrid use of well-known techniques of experi-mental stress analysis such as geometric moiré and pho-toelasticity with infrared or thermal technologies, signifi-cantly enhances their capabilities. In the case of ther-moelasticity and photoelasticity, the combined technique inherits the major disadvantages of both techniques, namely the requirement for cyclic loading and for a bonded coating. However, the combined technique gen-erates separated stress data that is a significantly better quality than any individual technique can provide. The combined technique has particular potential in the analysis of anisotropic and heterogeneous materials due to the ca-pability to separate surface strain at individual points without reference to neighbouring points.

Thermal moiré removes the principal disadvantage of geometric moiré which is the requirement to bond or print a grating to the component in order to measure in-plane strain. The principle can also be extended to moiré in-terferometry using an infrared laser to generate the grat-ings. The removal of the requirement for a grating to be affixed to the object and the capability to evaluate in-plane and out-of-plane displacements extends the potential of moiré techniques to three-dimensional objects.

Whilst, further work remains essential to fully define the capabilities and the limitations of these innovative tech-niques the overview provided above clearly illustrates the potential achieved by creating hybrid techniques in ex-perimental stress analysis.

5. ACKNOWLEDEMENTS The authors would like to acknowledge the financial support from the United Kingdom Engineering and

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Physical Sciences Research Council (EPSRC) in sup-porting the studies included in this paper. The authors would like to express their gratitude for the help of Qinetiq and Rolls-Royce plc in conducting the experiments de-scribed in section 3.3 and Figs. 7 and 8, although the views and data presented in the paper remain the responsibility of the authors. REFERENCES 1. A. J. Durelli, V. J. Parks, and C. J. del Rio, Exptl. Mech. 8

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Fig. 5. Experi-mental measure-ments of u (bottom left) and v (bottom right) components of displacement and the results of a nu-merical simulation (top) for a rubber plate with a hole.

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Fig. 6. Schematic diagram (left) and photograph (right) of combined thermoelastic and photoelastic instrument, showing

1. infrared mirror, 2. beamsplitter, 3. poleidoscope, 4. baseplate, and 5. Deltatherm instrument.

Fig. 7. Data from a composite panel subject to biaxial stress showing (a) calibrated thermoelastic data in MN/m2; (b)

calibrated photoelastic fringe order; (c) maximum principal stress and (d) minimum principal stress in MN/m2.

Fig. 8. Data from a gas turbine blade subject to high frequency excitation showing (a) calibrated thermoelastic data in

MN/m2; (b) calibrated photoelastic fringe order; (c) maximum principal stress and (d) minimum principal stress in MN/m2.

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hybrid thermal methods in experimental stress analysis

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