Experimental Techniques to Investigate Residual Stress in Joints

Residual stress arising from welding processes is matter of great concern in industrial practice since it can affect geometry, mechanical behavior and corrosion resistance of components. In order to evaluate residual stress in welded joints and optimize postwelding heat treatments, a lot of work has been devoted to the improvement of measurement methods with increasing sensitivity and accuracy. The chapter presents and discusses some of the experimental techniques commonly used today to determine residual stress in welds and describes recent results and advancements. Destructive (sectioning, contour, hole-drilling, instrumented indentation) and nondestructive (Barkhausen noise, ultrasonic, X-ray and neutron diffraction) methods are illustrated to highlight the specific characteristics, advantages and drawbacks.


Introduction
In order to satisfy scientific and industrial needs, a lot of work has been devoted to investigate the state of residual stress in metallic materials and its effects on mechanical properties.A number of comprehensive reviews on the topic can be found in the literature (e.g.see [1][2][3][4][5][6][7][8]).
It is well known that residual stress superimposes to external applied stress and plays a crucial role in the failure of components and structures; therefore, it is taken into account in advanced design in the aerospace, automotive and nuclear fields.All manufacturing processes modify the state of stress with either positive or negative consequences; for instance, compressive surface stress increases the fatigue limit, whereas tensile residual stress may decrease the corrosion resistance.
Welding may produce huge effects on the metals: when two pieces of plates or pipes are joined together, temperature ranges from the melting point of the material to room temperature and localized high residual stress coupled with shrinkage is generated near the weld seam.After cooling to room temperature, the locked-in stress is retained leading to distortion and/or buckling.The quantitative measurement of residual stress in welded joints is of the utmost importance for the safe operation of power plants, petrochemical plants, storage tanks and transmission pipelines.
To control such effects, it is necessary to predict the macroscopic transient fields of temperature, strain and stress.In principle, this can be done by solving the equations of continuum mechanics; however, a rigorous analysis of welds is a challenging task.At the macroscopic level, a weld represents a thermo-mechanical problem of computing transient temperature, stress and strain, whereas at the microscopic level, it is a problem of physical metallurgy involving phase transformations, defect recovery, recrystallization and grain growth.Welds may consist of tens of passes, each of which contributes to the mechanical and metallurgical effects.Interactions between thermal, mechanical, metallurgical and, in the molten pool, chemical and fluid processes are quite complex, and experimental measurements are required to validate theoretical and modeling predictions.
Generally, three types of residual stress can be identified on the basis of the range over, which they are observed: the first type (σ I ) is termed macro-stress and influences thousands of crystalline grains; the second one (σ II ), the micro-stress, occurs between different phases or grains and covers a distance of about one grain; the third one (σ III ) ranges over few atomic distances.To study the microstructural behavior of the material, σ II and σ III are very important because allow for a better understanding the way in which lattice defects, in particular, dislocation arrangements, evolve.The σ I stress is taken into consideration in designing engineering structures.
In many cases, the stress near the molten zone reaches the yield stress of the alloy and causes plastic deformation with microstructural changes, namely increase of point defect and dislocation density and decrease of grain size.The stresses σ II and σ III are strictly correlated to these microstructural features and are studied by X-ray and neutron diffraction.The techniques for analyzing σ II and σ III stresses involve the study of diffraction peak profiles and are not treated here because the topic goes beyond the scope of the chapter.
Several qualitative and quantitative techniques have been developed to measure residual stress.In fact, they measure strain rather than stress, and residual stress is then determined using the specific elastic constants of the material such as Young's modulus and Poisson's ratio.The wide range of available methods makes it impossible to include all of them in this chapter.In the following, some techniques, divided into two groups, namely destructive and nondestructive, will be reviewed.
The techniques of the first group are based on the destruction of the state of equilibrium of the residual stress in a mechanical component so residual stress is measured by its relaxing.The procedure used can be described as follows: (i) creation of a new stress state by machining or layer removal; (ii) detection of the local change in stress by measuring the strain and (iii) calculation of the residual stress as a function of the measured strain through either an analytical approach or finite element (FE) calculations.The methods described here are: (i) sectioning; (ii) contour; (iii) hole-drilling and (iv) instrumented indentation.
The second group of techniques consists of nondestructive methods based on the relationship between residual stress and physical or crystallographic parameters of the material.Here, the attention has been focused on: (i) Barkhausen noise; (ii) ultrasonic; (iii) X-ray and neutron diffraction.

Destructive techniques 2.1. Sectioning method
The sectioning method is a destructive technique used for decades from lots of researchers to measure residual stress in structural parts and welded components.The method was developed for the first time in 1888 by Kalakoutsky to determine longitudinal stresses in a bar by slitting longitudinal strips from the bar and measuring their change in length [9,10].The stress analysis is simplified by assuming that transverse stress is negligible and the cutting process alone does not produce appreciable strains [8].
The slitting process is delicate since it should not introduce plasticity or heat in the cut samples maintaining the original residual stress without the influence of external factors [6].The strains released during the cutting process are generally measured using electrical or mechanical strain gauges [6].To determine residual stress in a plate, some attentions about sample preparation have to be done; in particular, the number of the longitudinal strips to be cut depends on the residual stress gradient [10].
The use of mechanical strain gauges have been found to be particularly suitable for the sectioning method since the device is not attached to the specimen, is not damaged during the sectioning and can be used in repeated measurements.The stress distribution over a cross section can be determined by measuring the change in length of each strip and by applying the Hooke's law [10].
The main sources of error result from temperature changes and may be practically eliminated using a reference bar of the same material.
Sectioning method has been extensively used to analyze residual stresses in welded joints, for instance, in A36 steel with fillet welds [11], high strength steel Q460 box sections [12] and thin Al-5456 panels [13].Strips sliced at regions of high stress gradients can be considerably curved; thus, the change in length measured by the strain gauge is the change in the chord length rather than the change in arc length, which represents the actual strain [10].
In conclusion, the sectioning method is an adequate, accurate and economical technique for residual stress measurement in structural members thanks to its versatility and reliability [8,10].

Contour method
The contour method (CM) was first proposed by Prime in 2000 [14].CM is based on the superposition principle assuming that the material behaves elastically during the relaxation of residual stress and that the material removal introduces negligible stress [7,14].
As shown in Figure 1, the displacements due to the relaxation of the internal stress are compared to an assumed flat surface contour, and the longitudinal residual stress is recreated using a FE model.The forces required to ensure that the measured deformed surface is returned to its original position are directly correlated to the residual stress.The method provides a 2D map having a regular resolution of the residual stress normal to the cut surface [14,15].
The application of CM involves four steps: (i) cutting, (ii) measurement of surface contour, (iii) data handling and (iv) stress calculation [16].

i.
Cutting.The cut of the sample is a crucial step since it must be precise and straight without causing plastic deformation [16,17]; owing to its suitable characteristics, wire electric discharge machining (wire EDM) is commonly used for the purpose [18].Special attention is required for an adequate cutting process (single flat cut, proper constraint of the specimen to avoid its movement during cutting, a constant width of cut).Moreover, the type of cutting wire, the material, the geometry of the specimen and the EDM operating parameters are extremely important to realize an optimal cut.Finally, the cutting wire should be as thin as possible to remove the minimum material, particularly in the cases where there is a high stress gradient [19]. ii.
Measuring the surface contour.The contours of the cut surfaces can be measured using a coordinate measuring machine (CMM) [20]; typically, each surface contour is defined by about 10,000 points and the operation takes several hours.

Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments
In 2003, Prime et al. [21] developed a laser measuring system that works by moving one or more precision laser ranging probes over the entire surface with two orthogonal axes of motion, acquiring precision x, y and z spatial coordinates to submicron precision and resolution.A typical scan may take 30 min to an hour to complete with a resolution of 10 microns along the probe direction and 100 microns between scan lines.Noncontact laser surface contouring improves the capability of CM by allowing higher resolution measurement of a surface contour [21].
iii.Data handling.Data from the two measured surfaces are aligned.Such procedure generally requires flipping, translation and rotation of one data set to match the other.To smooth out noise in the measured surface data and to enable evaluation at arbitrary locations, the data are fitted to bivariate Fourier series.Finally, since the contour must be defined everywhere for calculating the stress, any missing area of the surface is filled in by extrapolating constant values from the defined region [16].
iv. Stress calculation.The residual stress is calculated from the measured surface contours using a FE model [22].
The multiaxial CM is a variation of the standard CM and its principles have been discussed by DeWald et al. [23].This method uses displacements to calculate the eigenstrain distribution within the body; then from eigenstrain, the residual stress is determined by means of FE.The motivation for using eigenstrain to determine residual stress in CM is that eigenstrain remains constant upon residual stress redistribution.Hence, multiple cuts can be made without changing the eigenstrain distribution [20,23].Implementation of the multi-axial CM involves making multiple cuts along different orientations of a continuously processed prismatic specimen.Initially, the specimen is cut into two halves as in the conventional CM.The new cut surfaces are measured, and the results are averaged.Then, the two halves are cut along their diagonal.
The displacements normal to the cut surfaces are contoured and averaged.After all the measurements are completed, the eigenstrain components are obtained from these three different measured and averaged surfaces [20].The multi-axial CM technique was successfully applied to measure residual stress in variable polarity plasma arc (VPPA)-welded plates of 2024-T35 aluminum alloy [20], thin sheets of Ti-6Al-4 V and thick laser peened plates of 316 L stainless steel [23].
The validity of CM measurements has been assessed by comparing its results with those from neutron diffraction, X-ray (lab and synchrotron) diffraction and hole drilling [15,18,[24][25][26].
Recently, Pagliaro et al. [27] suggested to use superposition to determine internal residual stresses by sectioning with CM and then measuring remaining stress with other methods.This approach allows measurements in parts where the internal stress were previously difficult to access and opens up possibilities to combine the advantages of different techniques [27].
While the sectioning technique is easier to determine residual stress over weld cross sections since almost no calculations are needed, CM provides a higher spatial resolution (1 mm spacing) [15].
CM can only be used to obtain high-resolution maps of the stress normal to the cut surface [6], but it is quite insensitive to inhomogeneities in the specimen as long as they do not significantly affect the elastic constants [29].CM is cheap and powerful and can be used to choose appropriate measurement lines in welded structures for more detailed study, for example using neutron diffraction [7].A further advantage of CM, compared to the few other methods that can measure a comparable stress map, is that it is relatively simple and inexpensive to perform and the equipment required is widely available [21].

Hole-drilling method
The hole-drilling method (HDM) is versatile, easy, cheap, quick and standardized [4][5][6]34] and is one of the techniques most used today for measuring residual stress.The principle, proposed more than 80 years ago [35], is based on the fact that relaxation occurs if some material is removed from a part with internal residual stress and it can be evaluated through the induced local deformation.In practical terms, an hole is drilled in the component at the center of a rosette strain gauge and a suitable model is used to determine the internal stress from strain data.
HDM equipment can be laboratory-based or portable, and the technique is applicable to a wide range of materials and components.
Drill speed and feed, centering of rosette and perpendicularity to the analysis surface are the main parameters affecting the measures of internal stress; operator skill and drilling equipment also play a significant role.Today, a modern integrate measure device consists of an automatic system including an high speed turbine (up to 400,000 rpm) with tungsten carbide tools and an electric stepping motor for the vertical cutter advancement with controlled drilling speed (0.1 mm/min); a microscope endowed of two orthogonal centesimal movements for drilling the hole at the center of rosette.
The other crucial aspect is the measure of the strain through rosette strain gauges.The ASTM E837-08 standard of reference for HDM residual stress evaluation [36] prescribes three kinds of rosette (Type A, B and C) as shown in Figure 2.
The ASTM E837-08 standard considers both uniform and nonuniform residual stress.
The evaluation of residual stress by HDM can be done in alternative ways.Since 1988, Schajer [37] introduced the incremental method for evaluating the nonuniform residual stress that allows to decide the number of step and the step depth.In the cases of coating or surface treatment processes, for example shot peening, where more interesting is the evaluation of the residual stress in the first layer of the surface, the method permits to increase the resolution by reducing the step depth near the surface.
The incremental deformation method, proposed by Schwarz and Kockelmann [38], is based on the measure of the incremental deformation during drilling.In addition to the standard hole obtained by high speed milling, Kockelmann proposed also a new hole shape to be obtained by electrochemical erosion.Improvements of the mentioned methods are available in literature in terms of evaluation of relaxation strain and models.One of them, proposed by Beghini et al. [39], takes in consideration the compensation of the principal parameters affecting the accuracy in the evaluation of residual stress.
In general, for the HDM, the following experimental factors play a crucial role: Rosette strain gauge installation: The installation needs to be performed by qualified person in compliance with the instructions of rosette and glue producer.Moreover, special attention should be paid to the cleaning of the surface where the strain gauge is bonded to avoid an alteration of the original state of residual stress.
Centering: The eccentricity between the center of the hole and the center of the rosette could introduce large error in the evaluation of residual stress.

Orthogonality and zeroing:
A not accurate orthogonality between hole axis and surface could induce difference in the right measure of the depth of the hole and difficulty in zeroing.
Hole bottom fillet radius: The error in evaluating residual stress increases with the fillet radius and decreases with the depth of the hole [40].
One of the most common fields of HDM application is the evaluation of residual stress induced by welding processes.In fact, residual stress could affect the operative strength of the part, fatigue life and stress corrosion strength.In as-welded conditions, often residual stress is close to yield stress and thermal or mechanical treatments are necessary to reduce it.So, a lot of research work was done for the evaluation of residual stress in different kinds of welding processes and materials [30,31,[40][41][42][43][44][45] with the final target to find the correct welding parameters and post processing conditions to minimize the residual stress.Some of these works use HDM as validation of nondestructive techniques such as ultrasonic [41][42][43][44][45][46], XRD [30] and neutron diffraction [31].Pappalettere et al. [47][48][49][50][51][52] applied an electronic speckle pattern interferometry (ESPI) method to avoid the use of conventional rosette strain gauges.The ESPI is based on the correlation between two speckle patterns, each one created by the interference between a reference beam and the image of an object illuminated by a laser.Typically, the two images are of an object before and after some deformation and the technique measures the 3D displacement by evaluating the phase difference of two recorded speckle interferograms.The apparatus consists of a diode-pumped solid state laser source that generates a radiation split into two beams and focused into two monomode optical fibers.One beam is collimated through a biconvex lens and illuminates the sample, whereas the second one passes through a phase shifting piezoelectric system and then it goes to the CCD camera where interferes with the light diffused by the optically rough surface of the specimen.The camera is equipped with an optical imaging system allowing fine focusing of the image.Initial phase and final phase are evaluated by the four-step phase shifting technique.Once the initial and the final phases are determined, it is possible to calculate the amount of displacement of each point into the analysis area. Figure 3 shows the experimental ESPI set-up [47].In fact, rosette strain gauges introduce a not negligible cost particularly in the case where a relevant number of measurements are required.Moreover, some sources of experimental errors, such as surface preparation, bonding and positioning, are irrelevant using the not contact ESPI.
These investigators were also able to evaluate how drilling speed affects error in HDM and HDM/ESPI and concluded that higher speed helps to increase accuracy and reduce data scattering.For instance, standard deviation in residual stress evaluation in titanium samples changes from less than 3% to about 19% if drilling speed is reduced from 50,000 to 5000 rpm.
HDM was used to validate the results of the ultrasonic technique in investigations on FSW joints of 5086 plates [42], AISI 304 pipes [43] and plates [44].The example in Figure 4 shows the good correspondence between ultrasonic and HDM residual stress evaluation.The contact stiffness S =dP/dh is obtained from the slope of initial part of the unloading curve (Figure 5b).
As the indenter, a rigid cone with α = 70.3, penetrates the materials, either plastic pile-up at the crater rim (when the ratio between yield stress σyand Young's modulus E, σy/E, is small) or elastic sink-in (when σy/E is large) is observed.The amount of pile-up/sink-in is denoted as h p (Figure 5a).For conical indenters, the projected contact area A is given by: where the contact depth, h c = h + h p , contains the contributions of both plastic pile-up around the indenter and elastic sink-in, which is counted negative.The pile-up and contact area can be measured experimentally or determined from numerical analysis (e.g.FE method).Once the contact area A is known, hardness H and Young's modulus E are usually obtained from the indentation curve.
Hardness H is the ratio between applied load P and contact area A (H = P/A).
The indentation modulus M is determined from indentation curve through the equation: where β is a shape factor (β = 1 for axisymmetric indenters and β = 1.03-1.05for indenters with square or rectangular cross-sections) and γ is a correction factor depending on indenter geometry.In the case of the conical indenter, γ can be written as: where ν is the Poisson's ratio.
For isotropic materials, the indentation modulus M corresponds to the plane-strain modulus E* where E I and ν I are the Young's modulus and Poisson's ratio of the indenter, respectively.
Therefore, E can be easily calculated from M through Eq. ( 4).
How to correctly determine residual stresses from instrumented indentation test has been debated for some years.Initially, indentation hardness was used as a parameter of the residual stress; however, successive studies [53,54] reported that the intrinsic hardness is invariant, regardless of the residual stress.Therefore, the change in contact morphologies with residual stress was modeled for constant maximum indentation depth assuming the independence of intrinsic hardness and residual stress [54].

Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments
The presence of residual stresses modify the indentation curve: with respect the stress-free state the same penetration depth h t is reached at smaller load P in the case of tensile stress while compressive stress induces the opposite effect [53][54][55].As shown in Figure 6, at the common penetration depth h t ,itisobservedthatP A (with tensile stress) < P B (stress free) < P C (with compressive stress).
The direct comparison of the indentation curve recorded in the investigated zone with that obtained in a zone of the same material without any residual stress allows to understand the nature of the stress (tensile or compressive).
To determine the value of residual stress, we will examine in the following the case of a material with residual tensile stress; a similar analysis can be made for compressive stress.
Since the average contact pressure due to indentation, P ave (equivalently, the hardness), is unaffected by any pre-existing tensile or compressive elastic stress [53], the relationship relates the indentation loads P and P 0 directly to the real contact areas A and A 0 of the material with and without residual stress, respectively.An equibiaxial tensile residual stress at the material surface can be considered equivalent to a tensile hydrostatic stress plus a uniaxial compressive stress component, Àσ H (see Figure 6).This compressive stress component induces a differential indentation force σ H A acting in the same direction as the indentation load P.On these grounds, a tensile residual stress aids indentation by lowering the indentation load needed to penetrate the material to a given depth, as compared to the virgin material.
From the initial part of the unloading curve, the real contact area A at maximum load P max for the material with the residual stress is where c is a constant depending on the indenter geometry (c = 1.167 for Berkovich indenter, c = 1.142 for the Vickers indenter).An analogous relationship is found for the unstressed material; thus, it can be easily demonstrated that where P ave is the average pressure.
The ratio A/A 0 is determined from the initial slopes of the unloading parts of the P-h curves.The value of A is calculated through Eq. ( 6), and at P = P max , the average pressure P ave = P max /A.The residual stress magnitude σ H is found by introducing the calculated values of A/A 0 and P ave into Eq.( 7).
The stress determined in this way is that of a layer of depth h max corresponding to P max and represents an average value over the layer.With the availability of macro-, micro-and nanoindenters, instrumented indentation can be used to probe local properties at different size scales.
The technique has been successfully used for determining residual stresses in different metallic alloys and recently also in tissues and other soft biological materials (e.g.see [56]).
Owing to its specific characteristics, indentation is quite useful for investigating welded mechanical parts because it allows to determine the residual stress on local scale, namely in the melted and heat affected zones of the joints.Instrumented indentation was applied by Jang et al. [57] for evaluating residual stress in A335 P12 steel welds in electric power plant facilities before and after stress-relaxation annealing.Comparison with the results of conventional saw-cutting tests showed the efficiency of indentation tests.The method was employed by Ullner et al. [58] to determine the local stresses in resistance-spot welded joints of advanced high strength steels.

Nondestructive techniques 3.1. Barkhausen noise method
Magnetic methods rely on the interaction between magnetization and elastic strain in ferromagnetic materials; they are sensitive to all three types of residual stress, but cannot distinguish between them.Here, only the Barkhausen noise (BN) method, based on the analysis of magnetic domain wall motion, will be presented and discussed.
Ferromagnetic materials consist of magnetically ordered regions called domains; each domain is magnetized along a certain direction and is separated from the others by walls where the direction of magnetization abruptly turns.The net magnetization of a material is the average of the magnetizations within all domains.
Under the action of an external magnetic field, the domain walls move and the resulting change in magnetization is detected as electrical pulses in a coil placed near the material surface.The process is not continuous but consists of small steps generated by domains jumping from one position to another.Pulses are random in amplitude, duration and temporal separation and give rise to a noise-like signal called Barkhausen noise.
BN is exponentially damped as a function of the traveled distance inside the material and the extent of damping determines the depth from which information can be obtained.Such depth mainly depends on the signal frequency together with conductivity and magnetic permeability of the tested material.Measurement depths in steels range from 0.01 to 3.0 mm; since this value is much higher than that of X-ray diffraction (some tens of microns), the BN method allows to quantify subsurface stress without need of removing the surface layer.
The intensity of BN depends on both stress and microstructure of the material; thus, a suitable calibration is of the utmost importance to properly determine uniaxial and biaxial surface stresses.Grain size, texture and dislocation structures play an important role in BN response; therefore, it is necessary to separate the contribution of stress from that of microstructure through a suitable calibration procedure.Calibration involves measurement of the BN signal on a representative section of the sample material using a known applied stress.A typical uniaxial calibration curve, taken from Kesavan et al. [9], is shown in Figure 7.The handbook [3] reports more details of uniaxial and biaxial stress calibration procedures and related results for isotropic and anisotropic materials.
As a result of magnetoelastic interaction, in materials with positive magnetic anisotropy (most steels and cobalt alloys), compressive stresses decrease the BN intensity, whereas tensile stresses increase it.Therefore, the measurement of BN intensity allows to determine the amount of residual stress and also defines the direction of principal stresses.The advantages of the BN method for stress measurements in welds are that it is fast, reliable and requires no specific surface preparation.Moreover, it can be used for continuous monitoring of stress in industrial processes.A significant example is reported in Figure 8 showing the effect of furnace stress relieving on a welded "T" section [3]; it is noteworthy that the stress profiles of the two seams before stress relieving are asymmetric because the left seam was welded first, being then subjected to a strong heating during the realization of the right seam.
Vourna et al. [59][60][61] examined through the BN method joints of an electrical steel (Si 2.18 wt%) welded by means of three different techniques, namely Tungsten Inert Gas (TIG), Plasma and Electron Beam, determining maps of residual stress across melted zone, heat affected zone and base material.The comparison of results with those from X-ray diffraction showed a good agreement.Similar good results were achieved by measurements performed on other types of steels such as API X65 [62], API 5 L X70 [63], AS1548-7-460R [64], structural steel [65] and Cr-Mo steel [66].As pointed out by many investigators who examined welds of different steels, BN technique requires a precise calibration procedure in all zones, which have a noticeably different microstructure, namely each zone should be separately considered for calibration [59,60,61,63].

Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments
The potential of BN technique for directly assessing fatigue processes and progressive residual stress relaxation in cyclically loaded welds has been shown by Lachmann et al. [67].
Beside the aforesaid advantages of the BN technique, some drawbacks place a severe restriction on its general applicability: (i) the material must be ferromagnetic; (ii) the total range of stress sensitivity (~6 MPa) is low; (iii) the measurement depth is limited to the surface layers and (iv) BN signal saturation may occur when tests are carried out on martensitic steels with very fine and complex microstructural features.

Ultrasonic method
The ultrasonic techniques are based on variations in the velocity of ultrasonic waves, which can be related to the residual stress state through the elastic constants of the material [34,44].
Like the magnetic methods, the ultrasonic techniques are sensitive to all three kinds of residual stress, but are not able to distinguish between them.
Ultrasonic stress measurement is founded on the linear relation between velocity of the ultrasonic wave and the material stress.This correlation, known as the acoustoelastic effect, establishes the following relationship between the velocity V and the stress σ: where K is the acoustoelastic constant (AEC) depending on the material and V 0 and V are the velocities in stress-free and stressed material, respectively [3].
In 1967, Crecraft showed that the acoustoelastic law can be employed for stress measurement of engineering materials [35,42,45].Changes in ultrasonic speed can be observed when a material is subjected to a stress, the changes providing a measure of the stress averaged along the wave path.The acoustoelastic coefficients necessary for the analysis are usually calculated using calibration tests.Different types of wave can be employed but the commonly used technique is the longitudinal critically refracted (Lcr) wave method [4].The Lcr wave is an acoustical wave that is excited when the angle of incidence is slightly smaller than the first critical angle, which is calculated from the Snell's law [44,68,69].It is a bulk longitudinal wave, traveling just below the surface of the specimen.This wave is more sensitive to stress and less sensitive to localized material texture changes [69].Different ultrasonic configurations can be employed for residual stresses measurements by Lcr technique.As a common experimental setup, longitudinal waves are propagated at the first critical angle by a transmitter transducer and then travel parallel the tested material surface and finally are detected by a receiver transducer.The residual stress in a subsurface layer is measurable while the depth of layer is related to the ultrasonic wavelength, often exceeding a few millimeters [43].The relation between measured travel-time change of Lcr wave and the corresponding uniaxial stress was derived by Egle and Bray [70]; with knowledge of the weld induced change in travel time and the measured acoustoelastic constant, the stress produced by the weld may be calculated [43].The principal steps to be followed in the measurement of residual stress by ultrasonic methods are: (i) selection of weld joint or component; (ii) determination of the acoustoelastic constant (AEC) of the material using standard tensile specimen by applying varying loads; (iii) ultrasonic velocity measurements in the weld joint or component of interest and (iv) determination of residual stress using AEC [68].
Javadi et al. [41][42][43] carried out a series of interesting studies on the ultrasonic method.They compared contact and immersion ultrasonic measurements of welding residual stress in dissimilar joints.A combination of FE welding simulation and Lcr ultrasonic waves was employed to reach the goal, and on the basis of experimental results, they concluded that both of the methods can measure the residual stress with an acceptable accuracy and the selection between them depends on geometry and dimensions of tested structure and also on the available experimental devices [41].
The same investigators developed a method (TLcr) that is the combination of Taguchi method (a technique to optimize welding parameters) and the Lcr ultrasonic method in order to study which process parameter has the highest effect on the longitudinal residual stresses in aluminum plates joined by the FSW process [42].Finally, Javadi et al. [43] studied the combination of FE and Lcr method (known as FELCR) confirming its ability to evaluate the pipe residual stresses through the thickness.
The ultrasonic technique was also successfully used in the study of residual stress in dissimilar joints [41]; residual stress through the thickness of stainless steel plates with 10 mm thickness [44]; longitudinal residual stress through the thickness of aluminum plates with 8 mm thickness [45]; for assessment of surface/subsurface longitudinal residual stresses in AISI type 316LN stainless steel weld joints made by ATIG and TIG welding processes [68]; welding residual stress through the thickness of stainless steel pipe [43] and prediction of total residual stress and fusion boundary in three pass welded stainless steel plates [71].
In conclusion, the ultrasonic technique is nondestructive, sensitive to microstructures and defects, has sufficiently good spatial resolution (5 mm) for longitudinal residual stresses across welded joints and is easy and simple to use and cost effective [8,69,72].Additionally, the instrumentation is portable and quick to implement [34] and it is well suited for routine inspection procedures and industrial studies of large components, such as steam turbine discs [4].On the other hand, this method has some difficulties in separating the effects of multiaxial stresses and in measuring the stress in an exact depth; since the penetration depths of the ultrasonic transducers are limited to a few millimeters, measurement of thick materials on both sides is recommended.

X-ray and neutron diffraction method
X-ray and neutron diffraction methods are based on the measurement of lattice strains by studying the variations of lattice spacings of the polycrystalline material.In other words, these techniques allow to determine the variations of lattice spacings induced by compressive or tensile stresses and to calculate the stresses from the strains, known the elastic constants of the material under investigation.Neutron and X-ray wavelengths used in diffraction experiments are about of the same magnitude; however, neutron diffraction differs from X-ray diffraction in several ways.Two aspects are of particular relevance to the present discussion: 1.The penetration depth in a material of a neutron beam is of the order of some centimeters and that of X-rays is of tens of microns.Therefore, X-ray diffraction measures the residual strain on the surface of the material, whereas neutron diffraction measures the residual strain within a volume of the sample.Owing to its unique deep penetration, neutron diffraction has been used to measure stresses in welds of 50-mm thick steel plates [73].
High energy X-rays from synchrotron sources have the penetration depth in between and are used to investigate subsurface stresses.
2. The intensities of X-ray diffraction lines depend on the atomic scattering factor f, which is directly proportional to the atomic number Z; thus, in a polyphasic material, the phases rich of light elements will exhibit diffraction patterns of lower intensity with respect to those rich of heavy elements.For instance, in a steel with perlitic structure (ferrite plus cementite), only the diffraction lines of ferrite are revealed, whereas those of cementite have a negligible intensity, comparable with background.
In the case of neutrons, scattering intensity varies quite irregularly with the atomic number Z; therefore, elements with quite different values of Z may scatter neutrons equally well.Furthermore, some light elements, such as carbon, scatter neutrons more intensely than some heavy elements.It follows that structure analyses can be carried out with neutron diffraction that are impossible, or possible only with great difficulty, with X-ray.
Both neutron and X-ray diffraction techniques can be used to study all three kinds of stresses.
The peak shift method is sensitive to σ I , whereas line broadening is sensitive to σ II and σ III .
Residual stresses in polycrystalline materials change the lattice spacings, which vary according to the orientation of planes relatively to the stress direction.In fact, the crystal lattice is used as a strain gauge.The elastic strain can be calculated from the variation of lattice spacing d: d 0 , determined by the position of the Bragg peak of stressed (θ) and stress-free (θ 0 ) material: The strain measured from shift of peak position is the elastic strain along the normal direction to diffracting planes, i.e. those parallel to the surface of the examined sample.
The sin 2 ψ method allows to determine the stress along any direction Φ in the plane XY (Figure 9).
The direction Φ is the projection on the plane XY of the direction OO' forming an angle ψ with the axis Z.The stress σ Φ is given by: and is determined by measuring d ψ and d z , known E and ν.Through X-ray and neutron diffraction, it is possible to measure uniaxial, biaxial and triaxial stress states, an exhaustive treatment of the topic can be found in Ref. [3].Since the Warren Averbach method [74] appeared in the 1950s, diffraction line broadening analysis is used to study the microstructural evolution of crystalline materials.Two factors contribute to line broadening: (i) the size of coherently diffracting domains (grains, sub-grains or cells) and (ii) micro-strains related to the density of dislocations, stacking faults and twins.Of course, line broadening is related to σ II and σ III and a lot of specific literature does exist on the matter; thus, we will not treat here the details of analysis.
Woo et al. [86] were able to determine the evolution of temperature and thermal stresses during friction stir welding of Al6061-T6 through in situ, time-resolved neutron diffraction technique.The method allows to deconvolute the temperature and stress from the lattice spacing changes measured by neutron diffraction.
Two case studies taken from the research activity of the authors are now presented to illustrate the application of the technique.

Case study 1
Electron beam (EB) welding has been used to realize seams on 2-mm thick plates of directionally solidified IN792 superalloy [91][92][93].The experiments evidenced the importance of preheating the workpieces to avoid the formation of long cracks in the seam and X-ray diffraction (XRD) was used to identify the better pre-heating temperature (PHT).The samples were mounted on a micrometric translating table that allowed to move the samples and irradiate the desired zone.indicating the presence of tensile stresses.On the basis of these results, the pre-heating of the plates at 300 C was identified as the optimal condition to realize EB joints of IN792 DS superalloy.

Case study 2
Case study 2 presents a study on a joint with a very complex structure.Because of its high melting point and good thermal conductivity, W is a promising armor material for protecting the components of International Thermonuclear Experimental Reactor (ITER) from plasma damage.However, the joining of W to other metals is challenging for the lower thermal expansion of W, its high elastic modulus and brittleness.An experimental campaign has been carried out by authors for realizing thick W-coatings on different metals, and Plasma Spraying was used as deposition technique for its simplicity, the possibility to cover complex and extended surfaces and the relatively low cost.The reported example regards 5-mm thick W coatings deposited on CuCrZr alloy.An appropriate interlayer was optimized to increase the adhesion of W on the metallic substrate and to provide a soft interface with intermediate thermal expansion coefficient for better thermo-mechanical compatibility.The bonding interface with thickness of ~800 μm was realized through successive deposition steps.It consists of a layer of pure Ni (thickness ~200 μm) directly on the CuCrZr substrate followed by a stratification of thinner layers (thickness ~30 μm) obtained by spraying grading mixtures of Al-12% Si, Ni-20% Al, Ni-20% Al and W powders.A detailed description is given in [94,95].
To verify the quality of joints, high temperature X-ray diffraction (HT-XRD) has been employed at increasing temperatures up to 425 C and XRD spectra are shown in Figure 11.
The vertical lines indicate the peak positions of the strain-free metals at room temperature.
The positions of Cu and W peaks at 25 C correspond to those of the stress-free condition, whereas Al and Ni peaks exhibit significant shifts.This means that residual strains are present in the interlayer but not in coating and substrate.At 425 C, all the peaks move towards lower angles, in part due to thermal expansion.Table 1 shows the strains, corrected from the effect of thermal expansion, which are quite different in the metals of the system W-CuCrZr.Among them, W exhibits the lowest strain level (~5 Â 10 À4 ) both at 25 and 425 C; thus, strain substantially does not change as temperature increases.At room temperature, also the strain of Cu is low (~1 Â 10 À3 ) but it increases at 425 C. In the interlayer, a different behavior between Ni and Al is observed: the strain level in Al is about one order of magnitude higher than that of Ni.
Such results are very interesting if one considers that cracks form in W near the interlayer and then propagate by a brittle and transgranular fracture mechanism towards the substrate.In fact, they demonstrate that interlayer properly works by accumulating stress and protecting the coating.On this basis, HT-XRD permits to evaluate the quality of the deposition and can be used to orientate the work for optimizing structure and composition of the interlayer and to find the right parameters of deposition process.

Figure 5 .
Figure 5. (a) Sketch of a sharp indentation on a homogeneous and isotropic material and (b) typical force-penetration depth curve obtained from an indentation experiment.

Figure 6 .
Figure 6.Effect of stress states on the indentation loading curve.
XRD spectra were collected by focusing the beam on melted zone and Figure10compares the {220} peak profiles of samples welded with PHT of 200 and 300 C at the same pass speed (1.5 m/min).The vertical line indicates the peak position of stress-free base material.The peak position of the sample welded with PHT = 300 C almost corresponds to that of stress-free material (vertical line), whereas the peak position of sample welded with PHT = 200 C is shifted to lower angles

Figure 9 .
Figure 9.The direction Φ is the projection on the plane XY of the direction forming an angle ψ with the axis Z.

Figure 10 .
Figure 10.{220} peak profiles collected from melted zone of samples welded at the same pass speed of 1.5 m/min with PHT of 200 and 300 C. The vertical line indicates the peak position of base material free from the stresses arising from welding [93].

Figure 11 .
Figure 11.XRD spectra collected from W-CuCrZr system.The markers indicate the peak positions of stress-free metals (JCPDS-ICDD database).
Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments Experimental Techniques to Investigate Residual Stress in Joints http://dx.doi.org/10.5772/intechopen.71564 Experimental Techniques to Investigate Residual Stress in Joints http://dx.doi.org/10.5772/intechopen.71564

Table 1 .
Strains at 25 and 425 C. Residual Stress Analysis on Welded Joints by Means of Numerical Simulation and Experiments