Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9

Frontmatter

Chapter 1. Fatigue Behaviour of Stainless Steels: A Multi-parametric Approach

Abstract

In recent years different experimental methods have been experienced to enhance the fatigue characterisation of materials with the aim to overcome the Standard long-lasting tests, i.e. Wohler curve determination. Standard fatigue treatment requires at least 15 specimens being tested to get an estimation of material fatigue limit and it is worth noting that this kind of tests do not provide any information on damage phenomena occurring in the material. Thus, topic to be addressed in this research have to do with development of lock-in infrared measurement based thermal method for rapid evaluation of fatigue limit. By performing a single test , the adopted method leads to match different parameter information. The Assessed parameters are in number more than the ones provided by TSA, as well. Moreover, the adopted technique points to study damage by analysing the different phenomena involved in fatigue and in this regard, the aim of this paper is to show how a thermal technique can attain an early assessment of the failure processes during a cyclically loading test. The author is, also, focused on to illustrate the strong points of a method based on infrared measurements for assessing endurance limit for both austenitic and martensitic stainless steels while considering, as reference, the Standard Test methods.

R. De Finis, D. Palumbo, F. Ancona, U. Galietti

Chapter 2. Measurement of Mechanical Dissipation in SMAs by Infrared Thermography

Abstract

The reversibility of the phase transformation in shape-memory alloys (SMAs) directly governs the mechanical response of these materials. Infrared thermography is used in this study to measure the mechanical dissipation produced by copper-based SMAs under cyclic loading at ambient temperature. Several specimens with different chemical compositions are tested. Mechanical dissipation which is produced by the material is deduced from the temperature change using a 0D version of the heat equation. Results obtained show that the chemical composition as well as the nature of the phase involved (martensite or austenite) influence the mechanical dissipation produced by the specimens during cyclic mechanical loading.

Didier Delpueyo, Xavier Balandraud, Michel Grédiac, Sergiu Stanciu, Nicanor Cimpoesu

Chapter 3. The Effect of Microstructure on Energy Dissipation in 316L Stainless Steel

Abstract

The link between dissipated energy in a cyclically loaded AISI 316L stainless steel and its microstructural changes is investigated. After a brief introduction to energy dissipation in materials, the experiments devised to investigate if different microstructures, resulting from different heat treatments, has a measurable effect on the dissipated energy are detailed. The data processing procedure and some preliminary results are described. Future work aimed at characterising the dissipative heat source in welds is presented.

P. J. Seelan, J. M. Dulieu-Barton, F. Pierron

Chapter 4. Large Area Nondestructive Evaluation of a Fatigue Loaded Composite Structure

Abstract

Large area nondestructive evaluation (NDE) inspections are required for fatigue testing of composite structures to track damage initiation and growth. Of particular interest is the progression of damage leading to ultimate failure to validate damage progression models. In this work, passive thermography and acoustic emission NDE were used to track damage growth up to failure of a composite three-stringer panel. Fourteen acoustic emission sensors were placed on the composite panel. The signals from the array were acquired simultaneously and allowed for acoustic emission location. In addition, real time thermal data of the composite structure were acquired during loading. Details are presented on the mapping of the acoustic emission locations directly onto the thermal imagery to confirm areas of damage growth leading to ultimate failure. This required synchronizing the acoustic emission and thermal data with the applied loading. In addition, processing of the thermal imagery which included contrast enhancement, removal of optical barrel distortion and correction of angular rotation before mapping the acoustic event locations are discussed.

Joseph N. Zalameda, Eric R. Burke, Michael R. Horne, Eric I. Madaras

Chapter 5. Sensitivity Analysis of Hybrid Thermoelastic Techniques

Abstract

Stress functions have been used as a complementary tool to support experimental techniques, such as thermoelastic stress analysis (TSA) and digital image correlation (DIC), in an effort to evaluate the complete and separate full-field stresses of loaded structures. The need for such coupling between experimental data and stress functions is due to the fact that experimental techniques offer discrete information of stresses or displacements, e.g. isopachic stresses in the case of TSA, as well as unreliable data near edges. For TSA, additional information is needed to separate stresses, as it is often necessary for fatigue analysis and a general better understanding of structural integrity. This separation is often accomplished by using an Airy stress function, which stems from compatibility and equilibrium conditions, and is frequently represented in the form of an indefinite series of coefficients. To date, only ad hoc estimates for the number of coefficients necessary for accurate representation of a loaded structure are used, with the estimates being influenced by quality of experimental data, experimental noise, and complexity of loading and boundary conditions. Information presented here attempts to systematize the selection of the Airy stress function’s indefinite series coefficients relative to experimental thermographic data.

W. A. Samad, J. M. Considine

Chapter 6. Determining Stress Intensity Factors Using Hybrid Thermoelastic Analysis

Abstract

This paper presents and discusses a technique suited for the determination of mode I Stress Intensity Factors (SIF) of fatigue-initiated and propagated cracks at the keyhole of polycarbonate specimens. A hybrid approach combined Thermoelastic Stress Analysis (TSA) results with Linear Elastic Fracture Mechanics solutions using Westergaard’s stress function to describe the stress field near the crack tip. The TSA results used an experimental approach that does not require an infrared camera with lock-in capability. The experiments used a micro-bolometer camera A655sc from FLIR Inc. and a data processing software DeltaTherm2 from StressPhotonics Inc. Two distinct data fitting methods are presented. The first method measures the crack length, which makes the problem become linear, allowing for a simple Least Squares Method (LSM) approach. The second method, highlighting the true power of TSA as a fatigue analysis technique, uses the crack tip position as an adjustable parameter, making the problem non-linear and solvable by a complex numerical algorithm known as the Downhill Simplex Method (Nelder-Mead). The paper describes automated methodologies for making good initial estimates for the position of the crack, required by the non-linear approach, as well as for selecting data points to be fitted, both based on the loss of linearity of the TSA data due to non-adiabatic conditions.

R. B. Vieira, G. L. G. Gonzáles, J. L. F. Freire

Chapter 7. Stress Analysis of a Finite Orthotropic Plate Containing an Elliptical Hole from Recorded Temperature Data

Abstract

Individual stresses in an elliptically perforated graphite/epoxy laminated composite are determined from recorded load-induced thermal (TSA) information. Equilibrium and compatibility conditions are satisfied using complex-variable formulation, conformal mapping and analytic continuation. Processing the measured thermal data with a stress function simultaneous smooths the recorded information and evaluates the individual stress components, including on the edge of the hole. Experimental results agree with those from FEM and force equilibrium.

A. Alshaya, X. Shuai, R. Rowlands

Chapter 8. Using TSA to Identify Regions Having Developed Plastic Strain during Welding

Abstract

Residual stress can be related to plastic strain experienced by a component; therefore the measurement of plastic strain presents the potential for residual stress to be investigated. Previous work has shown that Thermoelastic Stress Analysis (TSA) can identify regions that have undergone plastic strain. To do this, it was necessary to manufacture a test specimen of identical geometry containing zero plastic strain known as a reference specimen. Identifying the regions that have undergone plastic strain is then a simple matter of subtracting two data sets. This approach assumes there is always a reference specimen available, which in an industrial context is not the case. To make the work applicable to in-service components it is necessary to create a simulated reference specimen. The paper presents a means of establishing the simulated TSA reference specimen using Finite Element (FE) modelling through building a linear, elastic model and then including effects of nonlinear plasticity. To validate the idea a welded mock-up is used that contains a known level of plastic strain alongside a strain free specimen of identical material and geometry to the mock-up that has been manufactured to shape using water jet cutting. The work in the paper describes the outcome of using both the experimental and simulated reference specimens and considers the effect of varying material properties.

Geoffrey P. Howell, Janice M. Dulieu-Barton, Mithila Achintha

Chapter 9. Finite Element Modelling of a Series of Austenitic Stainless Steel 316 L Weldments to Inform Thermoelastic Stress Analysis Residual Stress Assessment

Abstract

The RESIST (Residual Stress and Structural Integrity Studies using Thermography) project aims to develop a non-contact, non-destructive, full-field measurement and portable residual stress assessment technique based on thermoelastic stress analysis (TSA). The TSA residual stress assessment (RSA) technique relies upon a change in the thermal expansion coefficient when a material is subjected to plastic straining. TSA RSA has been successfully applied to non-welded materials, so the next stage is to assess the feasibility of application on weldments. The study focuses on establishing the validation of the technique on austenitic stainless steel AISI 316 L (EN 1.4404), which is commonly used in power generation industry. A series of increasingly complex ‘weld mock-ups’ made out of 316 L are designed to test the TSA RSA approach. Finite element (FE) simulations of the welded mock-ups were produced. The design, FE modelling and manufacture of two of the mock-ups are presented. The expected amount of plastic strain is compared with the TSA assessment in another part of the RESIST project, and thus, informs the validation of the technique on weldments.

E. C. Chevallier, S. Blackwell, J. M. Dulieu-Barton

Chapter 10. Residual Stress Measurement of Full-Scale Jet-Engine Bearing Elements Using the Contour Method

Abstract

Compressive residual stresses provide a well-known advantage to the fatigue life of bearing materials under rolling contact fatigue (RCF), but the stresses change under fatigue loading and may later contribute to failures. Previous measurements of the depth-wise distribution of residual stresses in post-fatigue bearings with X-rays involved the time consuming process of etching to determine subsurface stresses and only in limited locations. By contrast, the contour method determines the 2D residual stress map over a full cross section. The method involves the sectioning of the part using Electrical Discharge Machining, measuring the out of plane displacements of the exposed cross section, and using the afforded field as boundary conditions on a finite element model of the component to back calculate the causative residual stress. For this investigation, the residual hoop stresses in the split inner rings of the main shaft bearing assembly of an aircraft jet engine was mapped using the contour method. Prior to measurement, the full-scale bearing made of hardened AISI M50 was subjected to RCF during engine operation. In this talk, the unique challenges of the particular measurements are discussed. The tested bearings showed effectively no residual stresses induced by the RCF, probably because they were conservatively removed from service prior to sufficient cyclic loading. A more highly loaded bearing will be measured in future work.

Daulton D. Isaac, Michael B. Prime, Nagaraj Arakere

Chapter 11. ESPI Hole-Drilling of Rings and Holes Using Cylindrical Hole Analysis

Abstract

The simplest geometry for hole-drilling analysis is a perfectly cylindrical hole and that geometry is the first option when generating coefficients that correlate surface displacements with stress. The actual hole geometry usually isn’t quite perfect, though. Plunge drilling with square-end end mills, for instance, creates an inverted cone on the bottom of the hole. Also, core-drills may be the best option for drilling some materials, such as ceramics. This study was made to evaluate the error due to such geometry mismatch when coefficients for a cylindrical hole are used for the analysis. A shot-peened aluminum sample that is assumed to have a very homogeneous stress distribution was chosen for the study. Plunge drilling, orbital drilling and ring drilling with different sizes and diameter ratios was performed. All measurements were repeated twice to test measurement statistics.

T. J. Rickert, Wade Gubbels

Chapter 12. Preliminary Study on Residual Stress in FDM Parts

Abstract

The Fused Deposition Modelling (FDM) is nowadays one of the most widespread techniques for 3D object rapid prototyping. In recent years, the FDM evolved from rapid prototyping technique towards a rapid manufacturing method, changing the main purpose in producing finished components ready for use. However, as the parts are built as a layer-by-layer deposition of a feedstock wire, the FDM technique shows, during the building process, distortion and de-layering problems. This issue influences the shape and the final dimensions of the parts or it can prevent the finalization of the objects due to unsticking problems from the bed. Several techniques can be employed in order to obtain parts of correct shape and dimensions. Many of these, such as depositing glue on the bed, aim to constrain the object. As a consequence, the FDM parts could show residual strain and residual stress that could influence their mechanical behaviour. The aim of this work is to measure, by ESPI technique, the displacements around a hole drilled into the material. This can be considered as a preliminary indication of the level of residual stress inside the FDM parts.

C. Casavola, A. Cazzato, V. Moramarco, G. Pappalettera

Chapter 13. Predicting Residual Stress on X-ray Tomographed Complex Bi-Layer Geometries using 3D Finite Element Analysis

Abstract

Micro-Computed Tomography was performed on an artificial mandibular first molar crown. A complex bi-layer geometry finite element model representing a real dental crown shape was created by converting 3D reconstructed micro-tomographs into a meshed model. The distribution of thermal residual stresses, provided by finite elements, demonstrated how thickness of the veneer contributes to localized compressive residual stress at the external surface of the veneer layer. To inhibit fracture initiation, it is desirable to manufacture a crown with compressive residual stress on its external surface. In order to quantify the correlation between thicknesses of the veneer layer and compressive residual stress at the external surface of the veneer, the local thickness of each surface node is required. The method introduced here computes the minimum distance between two triangulated complex surfaces by finding the closest point on the facing surface for each surface vertex. Statistical correspondence between local thickness of the veneer layer and the calculated residual stress components from finite elements revealed a curvilinear relationship over the range of variables and suggests a preferred layer thickness for engineering future dental restorations.

Masoud Allahkarami, Leila Seyed Faraji, Jay C. Hanan

Chapter 14. Combining Hole-Drilling and Ring-Core Techniques

Abstract

The hole-drilling and ring-core techniques are two well-known approaches to residual stress measurement. They apparently are complementary: in the former, a small hole is drilled in the specimen and residual stresses are estimated from the displacement/strain field around the hole; in the latter a small ring is milled and residual stresses are computed from the displacement/strain field inside the ring. However, owing to the different stiffness of the constraining region, their sensitivity and depth range are somewhat different.

Although both techniques are implemented using strain gauges, the use of optical methods is nowadays largely accepted. As optical methods allow acquisition of data from both inside and outside the ring, in this work, we will try to exploit the different displacement release rates of the two regions to optimize residual stress measurement.

Antonio Baldi

Chapter 15. A Low-Cost Residual Stress Measuring Instrument

Abstract

The hole-drilling method is the approach most used for residual stress measurement and most of the commercially available instruments are based on this working principle. The idea is quite simple: drill a small hole on the surface of the components and measure the strain/displacement components resulting on the surface. The stress components can be estimated from these data with a reverse calibration process. The measurement of the displacement/strain field is usually performed using either strain gauges or interferometric optical methods, thus the cost of the instruments is significant.

Recently, it has been proposed to replace the interferometric method with an integrated Digital Image Correlation (i-DIC) approach: by using problem-specific displacement functions, all difficulties related to the low sensitivity of DIC are avoided and the measurement procedure simply requires acquisition of an image after each drilling step. This paper describes the development of a low-cost instrument based on this working principle: the imaging subsystem is based on a Raspberry-Pi camera module whereas step motors are controlled by an Arduino board. Finally, the frame is built using a 3D-printer.

Antonio Baldi, Filippo Bertolino

Chapter 16. Non-Destructive Internal Lattice Strain Measurement Using High Energy Synchrotron Radiation

Abstract

High energy synchrotron X-rays can penetrate large samples and real engineering components. Taking advantage of this capability, diffraction techniques using monochromatic X-rays have been widely used to measure the residual strains in engineering components. However, isolating a particular volume inside a large component and measuring the residual strain is a challenge when employing typical monochromatic X-ray techniques. In this work we describe a spiral slit system capable of isolating an interior volume in a polycrystalline sample and non-destructively measuring the lattice strains in the volume. An interference fit sample constructed from a Ni-based superalloy is used to demonstrate the capabilities of the system. We compare the strain results to those measured using a conical slit system, a more mature and established device. The results from several polycrystalline samples with non-cubic crystal symmetry are also presented.

Jun-Sang Park, John Okasinski

Chapter 17. Discussion on X-Ray and HDM Residual Stress Measurements

Abstract

The stress field remaining in some materials without application of external sources of stress is known as residual stress. These residual stresses are produced in almost all manufacturing processes or may occur during the life of structures. They have a fundamental role in welded joints because they affect the way to design structures (e.g. the safety coefficients), their fatigue life and their corrosion resistance. Quantify, as well as possible, the residual stress field is one of main issues for mechanical engineers. To this purpose, in the last decades, several techniques have been developed. Hole Drilling Method (HDM) and X-Ray Diffractometry (XRD) are two of the most diffused and the only standardized techniques to measure the stress field in depth on welded structures. Although both methods declare to make an accurate measurement of the stresses, few comparisons of these techniques applied on the same structure are described in scientific literature.

The aim of the present work is to compare the residual stress measurement between HDM and XRD on Ti-6Al-4 V (Grade 5) laser butt-welding joints to understand if a significant difference exists between the results obtained by the two methods or they may be considered comparable.

C. Barile, C. Casavola, V. Moramarco

Chapter 18. Reducing Full-Field Identification Cost by Using Quasi-Newton Methods

Abstract

The sensitivity fields required for identification methods such as Finite Element Method Updating (FEMU) or Integrated Digital Image Correlation (IDIC) are usually expensive to compute and require considerable amounts of memory storage. This research evaluates the application of Proper Orthogonal Decomposition (POD) to provide efficient means to reduce the weight to express these fields. It is shown that, as little as four orthogonal modes are required to adequately express the sensitivity fields needed to identify the parameters of a Voce isotropic hardening model.

J. Neggers, F. Mathieu, S. Roux, F. Hild

Chapter 19. Parameter Identification of Nonlinear Viscoelastic Material Model Using Finite Element-Based Inverse Analysis

Abstract

This study focuses on identifying the parameters of a nonlinear viscoelastic model from Berkovich nanoindentation experiment of an epoxy polymer using finite element-based inverse analysis approach. Instead of traditional approach of online optimization of model parameters, where finite element computation is placed inside of the optimization algorithm, this study utilizes a surrogate or meta-modeling approach. The surrogate model, which is based on Proper Orthogonal Decomposition (POD) and Radial Basis Function (RBF), is trained with finite element load–displacement data obtained by varying the different model parameters in a parameter space. Once trained POD–RBF based surrogate model is used to approximate the nanoindentation simulation data inside a multi-objective Genetic Algorithm. Current efforts are focused to validate identified parameter set of nonlinear viscoelastic model for different experimental conditions (e.g. maximum load, loading/unloading rate).

Salah U. Hamim, Raman P. Singh

Chapter 20. Stiffness Heterogeneity of Multiply Paperboard Examined with VFM

Abstract

Mechanical heterogeneity of a multiply paperboard was characterized in uniaxial tension using DIC and VFM. The specimen was divided into three subregions based on axial strain magnitude. VFM analysis showed that the subregions had stiffnesses and Poisson’s ratio’s that varied in a monotonically decreasing fashion, but with the stiffness differences between subregions increasing with applied tensile stress. An Equilibrium Gap analysis showed improved local equilibrium when comparing a homogeneous analysis with the subregion analysis. Although only a single specimen was examined, results suggest that high stiffness regions provide only marginal improvement of mechanical behavior. The analysis also showed that even though the subregions themselves were non-contiguous, their mechanical behavior was similar.

Anton Hagman, J. M. Considine, Mikael Nygårds

Chapter 21. Rigid-Body Motion Tolerance for Industrial Helical CT Measurements of Logs

Abstract

The major cost in sawmills is the log raw material. It is therefore important to maximize the value of the product yielded from each log. Computed Tomography (CT) has been explored as a sensing solution for determining log defects and making data-driven choices in product breakdown. However, the harsh conditions of the sawmill environment lead to limitations in data acquisition and log manipulation. This paper presents an iterative-solver CT reconstruction scheme that includes rigid-body motion compensation, greatly increasing reconstruction robustness for misalignments in the radiographic data. The motion compensation is carried out by using the known nominal distribution of density in softwood logs to approximate the geometric center of the log and its radius from the radiographs. This is then applied to an iterative reconstruction methodology based on a log-specific voxel geometry previously developed. The method is validated for synthetic phantoms, a physical phantom, as well as real log samples. Results indicate that the rigid body compensation effectively ameliorates motion blur for movement within in the detector field of view.

Edward Angus, Gary S. Schajer

Chapter 22. Development and Experimental Validation of Thermally Stable Unimorph SMP Actuators Incorporating Transverse Curvature

Abstract

Shape memory polymers (SMP) have the potential to be utilized as a lightweight, solid state actuator in modern reconfigurable structures including as deployment systems for satellite solar panels or morphing aircraft wings. This paper is predominantly focused on the use of Veriflex-S^®, a thermally activated SMP, and bi-directional carbon-fiber-reinforced polymer (CFRP) in a flexural unimorph actuator configuration. The disadvantage of a unimorph composite actuator (UCA) as opposed to an actuator with a SMP matrix or a SMP composite sandwich structure is that UCA behaves like a bimaterial strip when heated or cooled. This means that large temperature swings, like those seen in space environments, will result in large out-of-plane curvature. These deformations can greatly affect the effectiveness of reconfigurable structures. This paper explains the development and experimental validation of a closed-form solution for a thermally stable unimorph actuator which exhibits minimal out-of-plane deformation when subjected to a thermal stimulus. A closed-form solution of the SMP actuator was developed and a set of UCA actuators were experimentally evaluated utilizing digital image correlation (DIC) to validate the conceptual model created. The experimental results indicate that the closed-form solution appears to be accurate as the maximum out-of-plane deformations for several non-ideal thermally stable actuators were less than 0.6 mm for a 65 °C temperature change.

Jason T. Cantrell, Peter G. Ifju

Chapter 23. Identification of Constitutive Model Parameters in Hopkinson Bar Tests

Abstract

In this work, tension and compression tests have been carried out on aluminium samples at low and high strain rate, the latter performed by means of a direct tension Hopkinson bar equipment. The parameters of the Johnson-Cook constitutive model have been identified using different approaches; the first method consists in the classical Finite Element Model Updating, where numerical simulations are repeated with different material parameters until the mismatch between the experimental and numerical load–displacement curves falls below an acceptable threshold.

The second method is based on the analysis of the digital images acquired by a fast camera during the tests; this permitted to calibrate the JC model by an analytical minimization procedure, without any FE simulation. A third inverse technique was also implemented, consisting in applying the FE model updating but using an enriched cost function, where also the mismatch between the numerical and acquired specimen shape profiles is included and minimized.

The advantages and drawbacks of the different techniques are assessed and compared.

M. Fardmoshiri, M. Sasso, E. Mancini, G. Chiappini, M. Rossi