Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 7

Material fatigue damage is associated with heat production leading to material self-heating. In this context, measuring temperature fields on a specimen’s surface by infrared thermography is useful to analyze the fatigue response of the tested material. Calorific information can be also obtained by reconstructing the heat power density (heat sources) at the origin of the temperature changes. In particular, mechanical dissipation due to fatigue damage can be determined from the thermal response using specific temperature acquisition conditions. The processing is based the heat diffusion equation, whose different formulations have been proposed in the literature to perform heat source reconstruction. The present study compares two approaches for homogeneous fatigue tests, namely the zero-dimensional (0D) and one-dimensional (1D) approaches. The error generated by the 0D approach (compared to the 1D approach) was first determined from a model. For comparison purposes, experimental tests were performed on a copper specimen. Consequences of using the 0D processing for fatigue analysis are discussed.

Granular materials are defined as a collection of solid particles whose macroscopic mechanical behavior is governed by the interaction forces between the particles. Full-field experimental data on these materials remain few compared to numerical results, even though a wide literature deals with optical imaging (combined with digital image correlation) and photoelasticimetry (to measure shear stresses in particles made of birefringent materials). We applied infrared thermography to analyze two-dimensional granular media composed of cylinders and subjected to confined compression. We analyzed the calorific signature of the contact forces, especially by revealing mechanical dissipation in the interparticle friction zones. Moreover, two constitutive materials featuring entropic and isentropic elasticity were employed to compare distinct types of thermoelastic couplings. Couplings and mechanical dissipation were separately identified at two observation scales. The perspective of this work is the experimental analysis of soft granular media.

This study aims at identifying the loading applied by a tire on a landing gear wheel for an inflation case. A full scale test instrumented via stereo-DIC (Digital Image Correlation) and strain gages is performed. A 3D finite element model of the wheel is developed and a parameterization of the tire-rim loading is proposed based on model reduction techniques. This parameterization is further used for an inverse identification of the loading parameters. This approach leads to a simpler and more robust problem that can easily be extended to more complex service loadings.

Simple and fast procedures to measure the fatigue limit using infrared thermography were proposed in the literature in the last two decades ago. In general, they consider fatigue damage as an energy dissipation process that is accompanied by some temperature variation ΔT. Those procedures significantly reduce fatigue testing costs by decreasing the quantity of required specimens and by shortening the testing time. The aim of the present work is to evaluate the fatigue limit, the stress amplitude vs. number of cycles fatigue (S-N) curve, and the influence of mean stress on the fatigue strength. Pipeline steel API 5L Gr. B, very common in the pipeline industry, was the test material. Uniaxial tensile specimens were tested under quasi-static monotonic load or under cyclic loads for different minimum to maximum load ratios. During each test, the surface temperature of the specimens was recorded in real time by a microbolometer thermocamera.

A new inverse problem formulation for identification of constitutive parameters in orthotropic materials from load-induced thermal information is developed using Levenberg-Marquardt Algorithm and Airy stress function. Inverse methods were used to determine the constitutive properties as well as the thermoelastic calibration factors of a loaded perforated graphite/epoxy laminated composite by processing noisy simulated thermoelastic data with an Airy stress function in complex variables. Equilibrium, compatibility, and traction-free condition on the boundary of the circular hole are satisfied using complex-variable formulation, conformal mapping and analytic continuation. The primary advantage of this new formulation is the direct use of load-induced thermal data to determine the constitutive parameters, separate the stresses, i.e., evaluate the individual stress components, including on the edge of the hole, and smooth the measured data, all from a single test. The inverse method algorithm determined the constitutive properties with errors less than 10%.

Thermal fields are usually obtained by infrared camera (operating in 3–12 μm). However, the infrared cameras are expensive, fragile and low resolution, thus the infrared camera is more used for laboratory researches. Nowadays, silicon-based sensor camera has been widely used to perform real-time observation of the kinematic fields, mainly thanks to digital image correlation or interferometry. Silicon-based camera is also sensitive in the near infrared spectral ranges (operating in 0.7–1.1 μm). An automatic prediction of the camera exposure time is developed and presented in this paper to follow the surface emissivity of the sample and avoid saturation of the gray level.

This study attempts to experimentally validate the energy balance equation during a quasi-static loading of polymer composites with explicit consideration of the energy dissipated through acoustic emission (AE). The experimental protocol estimates the various terms of the energy balance equation, namely the external work done E_W, the elastic stored energy E_ε, the dissipated heat energy E_H, and the dissipated acoustic emission energy E_AE using in-situ measurements. The elastic stored energy E_ε is derived from strain gage data, the dissipated heat energy E_H is estimated from the temperature field obtained from quantitative infrared thermography (IT) and surface mounted thermocouples, and the acoustic emission energy E_AE is approximated using two surface mounted piezoelectric transducers. The total input energy E_w, i.e. the external work done by the loading system is calculated from the cross-head displacement. The energy balance equation, ignoring inertial forces, is written as E _W − E _ε − E _H − E _AE = Constant. The energy approach presented herein may be used to quantify the level of material degradation as well as remaining useful life in primary load carrying structures.

We present a model-based inversion approach to the interpretation of flash thermography data. Traditionally, flash thermography has been image sequences have been hard to interpret in the presence of lateral heat flows. This is a particularly significant problem for composite laminate materials where heat conducts readily in the fiber planes. We use a linear inversion approach to represent the observed surface temperature as a superposition of contributions from buried reflectors. We investigate the additional complexities of considering cases where the specimen is curved, changing the nature of the heat flow. By solving a large linear inversion problem we are able to determine the strengths of the buried reflectors and create a concrete representation of observed defects. Results from this approach are compared to more traditional analysis approaches for flash thermography.

The Experimentally Enhanced Computations project was motivated by the combined availability of advanced diagnostics such as digital image correlation (DIC) and non-quadratic, anisotropic yield functions for metals that have been implemented in computational mechanics codes. Here we propose to investigate the use of DIC combined with inverse methods as an alternative to traditional model calibration methods. The objective of this novel approach is to reduce the number of tests required for calibration, thus expediting the calibration process.

The present study investigates the thermomechanical behavior of closed-cell TPU foams. The effects of the density and the loading conditions on the softening, the residual strain and the hysteresis have first been characterized. The thermal responses exhibit numerous particularities. First, a threshold effect in terms of the density on the self-heating has been highlighted. Second, entropic effects are strongly weighted by energetic effects (internal energy variations) during the deformation. Typical changes in the thermal response highlight that SIC and crystallite melting occur during the deformation. The characteristic stretches of this phenomenon evolve with the maximum stretch applied. The lower the density, the lower the crystallinity. In the second part of this study, a complete energy balance is carried out during cyclic deformation of compact and foamed crystallizing TPUs. Results show that viscosity is not the only phenomenon involved in the hysteresis loop formation: a significant part of the mechanical energy brought is not dissipated into heat and is stored by the material when the material changes its microstructure, typically when it is crystallizing. Some of this energy is released during unloading, when melting occurs, but with a different rate, which contributes to the hysteresis loop. The part of the mechanical energy stored by the material has been quantified to investigate the effects of the loading rate and the void volume fraction on the energetic response of TPU. These effects cannot be predicted from the mechanical responses and the present study provides therefore information of importance to better understand and model the effects of the density and the loading conditions on the thermomechanical behavior of closed-cell TPU foams.

The crystallinity of stretched crystallizable rubbers is classically investigated using X-ray diffraction (XRD). In the present study, we propose a new method based on temperature measurement and quantitative calorimetry to determine rubber crystallinity during mechanical tests as those carried out with conventional mechanical testing machines. For that purpose, heat power density are first determined from temperature variation measurements and the heat diffusion equation. The increase in temperature due to strain-induced crystallization (SIC) is then deduced from the heat power density by subtracting the part due to elastic couplings. The heat capacity, the density and the enthalpy of fusion are finally used to calculate the crystallinity from the temperature variations due to SIC. The characterization of the stress-strain relationship is not required. Furthermore, nonentropic contributions to rubber elasticity are taken into account if any. This alternative crystallinity measurement method is a user-friendly measurement technique, which is well adapted to most of the mechanical tests. It opens numerous perspectives in terms of high speed and full crystallinity field measurements.

Leather materials are able to undergo various strain and stress states during their elaboration process and their use in numerous applications. Although the experimental mechanical response in tension of leathers has been studied in the literature for decades, scarce information is available on the nature of their elasticity and more generally on their thermo-mechanical behaviors. In the present study, two leathers were tested under uniaxial cyclic loading while temperature changes were measured at the specimens’ surface by infrared thermography. The heat power at the origin of the temperature changes was then determined by using an adequate version of heat diffusion equation which is applicable to homogeneous tests. Results enabled us to discuss on the physical nature of the thermoelastic coupling in leathers. Intrinsic dissipation caused by the mechanical irreversibility was also detected. Distinct behaviors are evidenced as a function of the type of leathers.

Here, we present our current progress towards Part~II of the Experimentally Enhanced Computations project: a~novel calibration approach. While the first part discussed the traditional calibration approach, the availability of advanced diagnostics combined with the development of a new finite element updating inverse method that utilizes full field displacement data and the virtual fields method enables a novel calibration approach.

For the use of thermal and environmental barrier coating (T/EBC) with ceramic matrix composite it is crucial to understand the behavior under extreme environments representative of the hot sections of turbine engines. An experimental setup to simulate such thermal loading has been developed with various instrumentation enabling for kinematic and temperature field measurements.

The purpose of this paper is to describe the methodology of measuring damage onset and growth in a composite structure during quasi-static loading using passive thermography and acoustic emission. The early detection and measurement of damage progression is important to understand failure modes. A single stringer panel was subjected to quasi-static loading to induce deformation which resulted in the formation of damage between the stiffener flange and skin. The loading was stopped when damage growth was detected. Passive thermography and acoustic emission were used to detect damage in real-time as a function of the applied load. Of particular interest are the small transient thermographic signals resulting from damage formation which can be challenging to detect, as compared to the persistent passive thermography indications of cyclic fatigue loading. We describe a custom developed thermal inspection system for detection of composite damage during quasi-static loading. The thermal results are compared to a two-dimensional multi-layered thermal simulation based on the quadrupole method. Acoustic emission is used to further characterize the damage by comparing the acoustic emission events with the thermal imagery. Results are compared to ultrasonic measurements to document the damage through-the-thickness.

The Fused Deposition Modelling (FDM) is nowadays one of the most widespread and employed processes to build complex 3D prototypes directly from a STL model. In this technique, the part is built as a layer-by-layer deposition of a feedstock wire. This typology of deposition has many advantages but it produces rapid heating and cooling cycles of the feedstock material that introduces residual stresses in the part during the building-up. Consequently, warping, de-layering and distortion of the part during the print process are common issues in FDM parts and are related to residual stresses. In the view to reduce this kind of issues, the high-level print systems use a heated chamber. The aim of the present work is to measure the residual stresses in several points of the printed parts, both on top and bottom, in order to verify if the use of the heated chamber during the printing produce substantial variation. The residual stresses have been measured in ABS parts employing the hole-drilling method. In order to avoid the local reinforcement of the strain gage, an optical technique, i.e. ESPI (electronic speckle pattern interferometry), is employed to measure the displacement of the surface due to the stress relaxation and, consequently, to calculate the residual stresses.

The topic of this paper is system identification of structures conducted with consideration of incomplete modal information. A continuum structure has infinite number of degrees of freedom and an infinite number of modes. Modal estimation method is therefore not employed to identify all modes of systems. In addition, incomplete modal information may be led from insufficient response data in practical vibration measurement. In this paper, by using channel-expansion technique, modal estimation from response data of insufficient channel can be performed through the Ibrahim time-domain method. Applicability and effectiveness of the proposed method is demonstrated by numerical simulation of a chain model. Identification of the mode shapes, however, is still a challenging problem to be resolve in the proposed method from incomplete modal information data.

Initial work on combining Thermoelastic Stress Analysis (TSA) and Digital Image Correlation (DIC) is presented with the purpose of exploring their used in assessing defects in composite materials. TSA is usually performed using photon detector cameras that are expensive, a further objective of the paper is to investigate the capabilities of low-cost bolometer IR cameras for TSA. A carbon fibre reinforced polymer (CFRP) sample with artificial ‘waviness’ was created, so that a crack was developed inside the material. Both TSA and lock-in DIC methods detected the damage inside the CFRP specimen. Using the bolometer for TSA has highlighted the need for longer data capture times and the deleterious effects of other features associated with image capture that are inherent in the bolometer system.

In many instances in life, materials are subject to deformation at high rates, for example: impact, crash, metal forming or pulsed welding. In this context, the transient and inhomogeneous nature of such loading as well as the strong multi-physic couplings induced by quasi-adiabatic conditions make: the experimental capture of the mechanical response very challenging. Additionally, assumptions regarding the constitutive relation of the deforming material are generally required. To overcome both issues, we demonstrate that experimental full-field measurements of acceleration fields can be directly used to invert the local equilibrium equation and reconstruct fields of the stress tensor with no assumption on the constitutive relation and its spatial and temporal variations. We also demonstrate that both experimental stress and strain fields can be recombined to eventually identify the local tangent stiffness tensor of the material. This study constitutes a first step in the field of “direct model identification”, as opposed to standard parametric model identification.

The presented activity consist in the measurement of the self-heating field during testing of a metallic material from quasi-static to intermediate strain rates (10⁻² s⁻¹–100 s⁻¹). It is expected that for these strain-rates the self-heating process will be between the isothermal and adiabatic domains. The investigated material is a dual-phase DP450 steel. The modelling of the self-heating is of great importance for the modelling of the intermediate strain-rates behaviour of metallic material, especially for complex and non-monotonic loading.

Short carbon fiber composite materials are receiving a lot of attentions because of their excellent moldability and productivity, however they show complicated behaviors in fatigue fracture due to the random fibers orientation. In this study, thermoelastic stress analysis (TSA) using an infrared thermography was applied to the evaluation of fatigue damage in short carbon fiber composites. Second harmonic component of thermoelastic temperature change that is obtained by lock-in processing based on double-frequency against loading frequency was conducted to identify the turbulence in thermoelastic waveform due to fatigue damage evolution. It was found that the portions showing high second harmonic component values coincided with the portions where delamination damages were detected.

Hybrid thermoelastic stress analysis (Hybrid-TSA) is an experimental thermographic method that has been successfully utilized for the stress analysis of numerous structures with various geometries, discontinuities and loading situations. Previous work has shown the capacity of such approach to separate stresses on diametrically loaded disks with known loading conditions. The objective of the present work is to investigate the capacity of such hybrid experimental-analytical approach in the stress analysis of two-dimensional granular materials. Previously, thermography has been successful at determining the hydrostatic stress network in cohesionless bidisperse granular systems (composed of cylinders placed in parallel) under confined compression. However, the analysis remained tricky because of the large number of cylinders considered, leading to a reduced number of thermal data per cylinder. The method which is proposed here relies heavily on analytical expressions of stress, which arise from mechanical compatibility and equilibrium conditions. It enables us to reconstruct a stress field on granular materials with low special resolution (few TSA points available per cylinder), and thus to analyze more precisely the mechanical state of tested granular systems.

The fatigue limit estimation method based on the dissipated energy measurement was applied to the single bead-on-plate weld. The stair-case-like stress level test was conducted to the bead-on-plate specimen. The local concentration of dissipated energy was observed in the weld toe. The change in dissipated energy at this local high dissipated energy point showed sharp increase from the certain stress amplitude, and this stress amplitude coincided with the fatigue limit for the bead-on-plate specimen obtained from S-N curves.

Until recently thermoelastic stress analysis (TSA) imaging required correlation between an electronic signal related to the stress in a target structure, and the thermal signal acquired in successive IR images. With the implementation of a new method dubbed “self-reference” the requirement for the electronic signal has been eliminated. In the self-reference modality, correlation is made between the temporal variation in the signal from a region-of-interest in the image, to each of the pixels in the image. This simple change of correlation parameters has had a dramatic effect on the applicability of TSA and the ease of use of TSA instruments. A review of a range of applications in the light of this change indicates a new level of applicability of the TSA technique for stress measurement.