*3.1.2.3 Ultrasonic determination of residual stress and the separation from texture effects on AHSS strips*

Advanced high-strength steel (AHSS) enables the automotive industry to increase the stability and crash safety of cars and to reduce weight or CO2 emissions at the same time. Increasing strip speeds and requirements on the lateral homogeneity of the material properties leads to a need for a development of a nondestructive multisensor solution for the quality assurance. The homogeneity of the texture, grain size and the influence of residual stresses in the material is of great importance for the deformation behavior and decisive for material processing, such as deep drawing or welding. Current in-line NDT systems determine only a subset of the required parameters and do not assess their homogeneity across the strip width.

#### **Figure 9.**

*Set-up of an electromagnetic acoustic Rayleigh wave transducer for generating variable trace wavelengths (after [23]).*

In this context, Fraunhofer IZFP developed a hybrid test system for the in-line inspection of AHSS consisting of 3MA and ultrasonic TOF measurements using EMAT.

thermomechanical loads, which, depending on the axle load and the route profile, lead to high energy input in the form of heat. In addition, faulty, non-opening brakes cause the material to overheat, which, in turn, results in compressive stress being converted into tensile stress that may increase until rim failure occurs. There are various systems that determine these stress values in the industrial environment by means of ultrasonic methods. The procedures and evaluation steps presented here refer to the only system for the fully automatic determination of circumferential residual stresses. This system represents a development of Fraunhofer IZFP and has been used for more than 25 years in maintenance and wheel production,

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

In order to check the wheel for critical stress situations, the acoustic birefringence parallel to the tread is evaluated from the side of the wheel rim. For this task, a linearly polarized shear wave is used, since this wave type exhibits the strongest interaction with the stress in the circumferential direction for the given geometry. The required ultrasonic wave is generated with an EMAT that excites the wave in the ferromagnetic base material of the wheel without a coupling agent (**Figure 11**). Also due to the geometry and surface condition of used wheels, only the relative stress difference with respect to the radial direction of the wheel rim is checked. A measurement of the absolute change in the sound velocity is not possible within the scope of the required accuracy of the sound path determination in the maintenance

When determining the relative stress difference, the measurement of the ultrasonic time of flight of the linearly polarized wave with its direction of oscillation perpendicular to the running surface is chosen as reference, as the stresses in the radial direction do not change over the life of the wheel according to experience. The test as well as the presentation of the results takes place as a depth profile of the tread in the direction of the wheel web. The typical step size of the measurement is 1 mm. **Figure 11** shows the test positions and the wave propagation of the ultra-

Since the acousto-elastic material constant K is known, the measured differences in the ultrasonic time of flight of the two measuring tracks can be converted into a relative stress value between the tangential and the radial direction of the wheel.

*<sup>σ</sup>tan* � *<sup>σ</sup>rad* <sup>¼</sup> <sup>K</sup> *TOFtan* � *TOFrad*

Depending on whether a newly manufactured wheel or the review of a used wheel

*Principle of the stress evaluation of the railroad wheel. The scan is performed in steps of 1 mm. The EMAT*

integral result over the entire traveled sound path, as shown in **Figure 12**.

The result is a stress curve in the depth direction. Each stress value represents an

*TOFrad*

(5)

This is done at each test position according to Eq. (5):

*transceiver with the probe generates a linear polarized shear wave.*

presently in the fourth generation.

*DOI: http://dx.doi.org/10.5772/intechopen.90740*

of the track wheels.

sound schematically.

**Figure 11.**

**45**

The challenge in the case of the ultrasonic inspection is the separation of the different effects from texture and residual stresses on the ultrasonic time of flight. The impact on the ultrasonic wave velocity is ranging in a magnitude of percentage to per mil. The objective of the new approach is the use of different wave modes and types to separate the effects. In thin plates, guided waves can be excited with EMAT. By different alignments of the conductive paths to the magnetic field in EMAT, a simultaneous excitation of guided shear horizontal (SH) waves and Lamb waves is possible. Selecting different excitation frequencies and switching between symmetric and antisymmetric modes of different order could be realized.

Because of its symmetry to the texture direction, the lowest symmetric mode of the SH wave (SH0) could be used to determine the residual stress. The time-offlight measurement of this wave mode in rolling direction (0°) and perpendicular to it (90°) is therefore independent of the influence of texture. The presence of residual stress is reflected in an asymmetrical behavior in the polar plot (see **Figure 10**). Additionally, the SH0 mode is dispersion-free and thus independent of thickness, which means that even slight fluctuations in sheet thickness have no influence on the measuring effect.

If the influence of the residual stress is known, the effect can also be calculated for the other wave modes and types, and finally the influence of texture can be determined.

In order to implement the inspection concept, a special arrangement of the probes is required (see **Figure 10**). Thus, the macro-residual stress is determined as an integral value over the sheet thickness and the travel distance of the wave.

## *3.1.2.4 Residual stress analysis in freight car wheels and research challenges of localized stress evaluation*

Residual stress occurring during operation of components can also be detected and quantified with ultrasonic methods. The examination of residual stress in railway wheels of freight cars is an industrial application of ultrasonic stress evaluation that has been established more than 25 years ago [27]. In the production of new wheels, compressive stresses in the tread in the circumferential direction are generated by well-defined quenching, which should prevent the formation of cracks in the wheel-rail contact zone in case of damage to the surface. However, in the case of block-braked freight car wheels, the running surface is subjected to high

#### **Figure 10.**

*Time of flight of SH0 mode depending on the rotation angle, measured on an AHSS plate (left). Arrangement of probes along the steel strip (right, after [26]).*

#### *Nondestructive Characterization of Residual Stress Using Micromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.90740*

thermomechanical loads, which, depending on the axle load and the route profile, lead to high energy input in the form of heat. In addition, faulty, non-opening brakes cause the material to overheat, which, in turn, results in compressive stress being converted into tensile stress that may increase until rim failure occurs. There are various systems that determine these stress values in the industrial environment by means of ultrasonic methods. The procedures and evaluation steps presented here refer to the only system for the fully automatic determination of circumferential residual stresses. This system represents a development of Fraunhofer IZFP and has been used for more than 25 years in maintenance and wheel production, presently in the fourth generation.

In order to check the wheel for critical stress situations, the acoustic birefringence parallel to the tread is evaluated from the side of the wheel rim. For this task, a linearly polarized shear wave is used, since this wave type exhibits the strongest interaction with the stress in the circumferential direction for the given geometry. The required ultrasonic wave is generated with an EMAT that excites the wave in the ferromagnetic base material of the wheel without a coupling agent (**Figure 11**). Also due to the geometry and surface condition of used wheels, only the relative stress difference with respect to the radial direction of the wheel rim is checked. A measurement of the absolute change in the sound velocity is not possible within the scope of the required accuracy of the sound path determination in the maintenance of the track wheels.

When determining the relative stress difference, the measurement of the ultrasonic time of flight of the linearly polarized wave with its direction of oscillation perpendicular to the running surface is chosen as reference, as the stresses in the radial direction do not change over the life of the wheel according to experience. The test as well as the presentation of the results takes place as a depth profile of the tread in the direction of the wheel web. The typical step size of the measurement is 1 mm. **Figure 11** shows the test positions and the wave propagation of the ultrasound schematically.

Since the acousto-elastic material constant K is known, the measured differences in the ultrasonic time of flight of the two measuring tracks can be converted into a relative stress value between the tangential and the radial direction of the wheel. This is done at each test position according to Eq. (5):

$$
\sigma\_{tan} - \sigma\_{rad} = \mathbf{K} \frac{\text{TOF}\_{tan} - \text{TOF}\_{rad}}{\text{TOF}\_{rad}} \tag{5}
$$

The result is a stress curve in the depth direction. Each stress value represents an integral result over the entire traveled sound path, as shown in **Figure 12**. Depending on whether a newly manufactured wheel or the review of a used wheel

#### **Figure 11.**

*Principle of the stress evaluation of the railroad wheel. The scan is performed in steps of 1 mm. The EMAT transceiver with the probe generates a linear polarized shear wave.*

In this context, Fraunhofer IZFP developed a hybrid test system for the in-line inspection of AHSS consisting of 3MA and ultrasonic TOF measurements

*New Challenges in Residual Stress Measurements and Evaluation*

symmetric and antisymmetric modes of different order could be realized.

The challenge in the case of the ultrasonic inspection is the separation of the different effects from texture and residual stresses on the ultrasonic time of flight. The impact on the ultrasonic wave velocity is ranging in a magnitude of percentage to per mil. The objective of the new approach is the use of different wave modes and types to separate the effects. In thin plates, guided waves can be excited with EMAT. By different alignments of the conductive paths to the magnetic field in EMAT, a simultaneous excitation of guided shear horizontal (SH) waves and Lamb waves is possible. Selecting different excitation frequencies and switching between

Because of its symmetry to the texture direction, the lowest symmetric mode of the SH wave (SH0) could be used to determine the residual stress. The time-offlight measurement of this wave mode in rolling direction (0°) and perpendicular to it (90°) is therefore independent of the influence of texture. The presence of residual stress is reflected in an asymmetrical behavior in the polar plot (see **Figure 10**). Additionally, the SH0 mode is dispersion-free and thus independent of thickness, which means that even slight fluctuations in sheet thickness have no

If the influence of the residual stress is known, the effect can also be calculated for the other wave modes and types, and finally the influence of texture can be

In order to implement the inspection concept, a special arrangement of the probes is required (see **Figure 10**). Thus, the macro-residual stress is determined as an integral value over the sheet thickness and the travel distance of the wave.

*3.1.2.4 Residual stress analysis in freight car wheels and research challenges of localized*

Residual stress occurring during operation of components can also be detected and quantified with ultrasonic methods. The examination of residual stress in railway wheels of freight cars is an industrial application of ultrasonic stress evaluation that has been established more than 25 years ago [27]. In the production of new wheels, compressive stresses in the tread in the circumferential direction are generated by well-defined quenching, which should prevent the formation of cracks in the wheel-rail contact zone in case of damage to the surface. However, in the case of

*Time of flight of SH0 mode depending on the rotation angle, measured on an AHSS plate (left). Arrangement of*

block-braked freight car wheels, the running surface is subjected to high

using EMAT.

determined.

**Figure 10.**

**44**

*probes along the steel strip (right, after [26]).*

influence on the measuring effect.

*stress evaluation*

stresses [29]. This approach is based on the applied stress dependence of signals obtained from magnetic hysteresis loop at different applied load stresses in the elastic range. The magnetic hysteresis curve changes its shape under influence of applied load stresses depending on whether the applied load stresses are compressive or tensile. It has been observed experimentally that magnetic hysteresis curves recorded at different applied load stresses contain two intersection points that are invariant with changing applied stress. A possible explanation of this effect is that the magnetization processes at these points take place by 180° Bloch wall movements only. 180° Bloch walls have short-range stress fields, whereas 90° Bloch walls have long-range stress fields. As the intersection points do not change their position with changing applied stress, they are stress-independent, and therefore the magnetization processes in these points are based on 180° Bloch wall movements only. Parameters that define these intersection points are the related magnetic field strength Hsp and flux density Bsp (**Figure 13**). This means that both parameters Hsp and Bsp characterize the 180° Bloch wall movement only and are affected by shortrange residual stresses or microstructure features that can induce them. Microstructure defects, e.g., second-phase precipitates, or dislocations induce such short-

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

*DOI: http://dx.doi.org/10.5772/intechopen.90740*

Furthermore, micromagnetic measurements have been carried out on cylindrical specimens of 20MnMoNi5-5 steel at superimposed elastic compressive and tensile load stress in the range of 150 MPa up to 200 MPa, and the stress invariant points have been determined automatically. In the first step, stress invariant points were determined on stress-relieved specimens of different microstructures with different mechanical properties. X-ray measurements confirmed that the samples were nearly free from residual stress (the maximum stress observed was 50 MPa). It was found that parameter Hsp depends almost linearly on the yield strength values of those samples (**Figure 14**). In order to induce microstructure changes, the samples have been plastically deformed to 1 and 2% plastic deformation. After each plastic deformation the samples have been investigated by means of the approach described above. It has been observed that the increase of the plastic deformation leads to an increase of Hsp. The change of Hsp with increasing plastic deformation depends on the initial mechanical properties of the samples. In the case of the samples with high yield strength, Hsp increased almost linearly with the percentage

*Hysteresis curves measured as different superimposed load stress levels including the invariant stress points and*

range residual stresses.

**Figure 13.**

**47**

*their corresponding coordinates (after [29]).*

**Figure 12.**

*Typical stress graph of a "R7" wheel in new condition (left) and another wheel of this type in worn and used condition. In each case, tests were performed on each wheel on three positions with an offset by 120°.*

is required, different stress limits were applied, which decide on the further operation of the freight car wheel. **Figure 12** shows a comparison between the residual stress of a new and a used wheel.

Now, block-braked track wheels are experiencing a recurrence, also in passenger transport, as a result of which the wheel developers' desire for improved methods for determining local residual stress is emerging. By fundamentally linking finite element computation and knowledge of ultrasonic wave interactions with sample volume stresses, geometrical and thermomechanical states can be predicted. These predictions represent possible solutions for real stress situations leading to the measured integral stresses. Modeling to predict possible wheel residual stress as a first step is a well-known method [28]. The challenges, however, lie in the combination with sufficiently large amounts of residual integral residual stress data as well as the real geometries investigated. With the help of this data, test systems would be able to identify most likely the stress distribution depending on the wheel geometry, which leads to the present measurement result, and thus to make statements about critical local stresses along the sound propagation path.

This procedure for combining preliminary information as a statistical interpretation aid for metrologically inaccessible information beyond the described application is a research field with high potential for improvements in the informational quality of volumetric residual stress evaluation.

#### **3.2 Characterization of micro-residual stress**

#### *3.2.1 Characterization of micro-residual stress by means of micromagnetic techniques*

#### *3.2.1.1 Volumetric characterization*

Micromagnetic testing methods are based on the fact that the ferromagnetic material behavior is influenced by microstructures as well as by applied load or residual stress. Separation of these two influences in micromagnetics can be carried out by analyzing different interaction mechanisms of magnetic structure with microstructure, on the one hand, and with residual or applied stresses, on the other hand. Moreover, it is well-known that microstructure changes always cause changes in the micro-residual stress distribution. This means that, in fact, separating microresidual stress from macro-residual or load stress indirectly allows for the separation of microstructure from macro-residual stress.

Therefore, a nondestructive micromagnetic testing approach has been developed for the evaluation of material changes independently on the macro-residual *Nondestructive Characterization of Residual Stress Using Micromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.90740*

stresses [29]. This approach is based on the applied stress dependence of signals obtained from magnetic hysteresis loop at different applied load stresses in the elastic range. The magnetic hysteresis curve changes its shape under influence of applied load stresses depending on whether the applied load stresses are compressive or tensile. It has been observed experimentally that magnetic hysteresis curves recorded at different applied load stresses contain two intersection points that are invariant with changing applied stress. A possible explanation of this effect is that the magnetization processes at these points take place by 180° Bloch wall movements only. 180° Bloch walls have short-range stress fields, whereas 90° Bloch walls have long-range stress fields. As the intersection points do not change their position with changing applied stress, they are stress-independent, and therefore the magnetization processes in these points are based on 180° Bloch wall movements only. Parameters that define these intersection points are the related magnetic field strength Hsp and flux density Bsp (**Figure 13**). This means that both parameters Hsp and Bsp characterize the 180° Bloch wall movement only and are affected by shortrange residual stresses or microstructure features that can induce them. Microstructure defects, e.g., second-phase precipitates, or dislocations induce such shortrange residual stresses.

Furthermore, micromagnetic measurements have been carried out on cylindrical specimens of 20MnMoNi5-5 steel at superimposed elastic compressive and tensile load stress in the range of 150 MPa up to 200 MPa, and the stress invariant points have been determined automatically. In the first step, stress invariant points were determined on stress-relieved specimens of different microstructures with different mechanical properties. X-ray measurements confirmed that the samples were nearly free from residual stress (the maximum stress observed was 50 MPa). It was found that parameter Hsp depends almost linearly on the yield strength values of those samples (**Figure 14**). In order to induce microstructure changes, the samples have been plastically deformed to 1 and 2% plastic deformation. After each plastic deformation the samples have been investigated by means of the approach described above. It has been observed that the increase of the plastic deformation leads to an increase of Hsp. The change of Hsp with increasing plastic deformation depends on the initial mechanical properties of the samples. In the case of the samples with high yield strength, Hsp increased almost linearly with the percentage

#### **Figure 13.**

*Hysteresis curves measured as different superimposed load stress levels including the invariant stress points and their corresponding coordinates (after [29]).*

is required, different stress limits were applied, which decide on the further operation of the freight car wheel. **Figure 12** shows a comparison between the residual

*Typical stress graph of a "R7" wheel in new condition (left) and another wheel of this type in worn and used condition. In each case, tests were performed on each wheel on three positions with an offset by 120°.*

*New Challenges in Residual Stress Measurements and Evaluation*

ments about critical local stresses along the sound propagation path.

quality of volumetric residual stress evaluation.

**3.2 Characterization of micro-residual stress**

tion of microstructure from macro-residual stress.

*3.2.1.1 Volumetric characterization*

**46**

Now, block-braked track wheels are experiencing a recurrence, also in passenger transport, as a result of which the wheel developers' desire for improved methods for determining local residual stress is emerging. By fundamentally linking finite element computation and knowledge of ultrasonic wave interactions with sample volume stresses, geometrical and thermomechanical states can be predicted. These predictions represent possible solutions for real stress situations leading to the measured integral stresses. Modeling to predict possible wheel residual stress as a first step is a well-known method [28]. The challenges, however, lie in the combination with sufficiently large amounts of residual integral residual stress data as well as the real geometries investigated. With the help of this data, test systems would be able to identify most likely the stress distribution depending on the wheel geometry, which leads to the present measurement result, and thus to make state-

This procedure for combining preliminary information as a statistical interpretation aid for metrologically inaccessible information beyond the described application is a research field with high potential for improvements in the informational

*3.2.1 Characterization of micro-residual stress by means of micromagnetic techniques*

Micromagnetic testing methods are based on the fact that the ferromagnetic material behavior is influenced by microstructures as well as by applied load or residual stress. Separation of these two influences in micromagnetics can be carried out by analyzing different interaction mechanisms of magnetic structure with microstructure, on the one hand, and with residual or applied stresses, on the other hand. Moreover, it is well-known that microstructure changes always cause changes in the micro-residual stress distribution. This means that, in fact, separating microresidual stress from macro-residual or load stress indirectly allows for the separa-

Therefore, a nondestructive micromagnetic testing approach has been developed for the evaluation of material changes independently on the macro-residual

stress of a new and a used wheel.

**Figure 12.**

micro- or macro-residual stress condition. A measurement technique based on this effect permits the quantitative characterization of residual stress variations without the use of a reference method such as X-ray diffraction. If the superimposed residual stress is of the tensile type, the Barkhausen noise activity of the iron-based materials is more enhanced than in the stress-free condition, and the curves reach their maximum at lower load stresses, that is, the curve shifts to the left-hand side and in the other direction in the case of superimposed compressive stress. In order to determine the micro-residual stresses induced by nanoscale Cu particles only (i.e., to eliminate the influence of macro-residual stress from quenching and microresidual stress from different thermal expansion coefficients of particles and surrounding matrix), micromagnetic measurements have been performed in three steps, which are described in [30, 31]. This procedure permits the volumetric

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

*3.2.1.2 Imaging of local residual stress distribution using Barkhausen noise and eddy*

The fundamental sensor principle of 3MA has been implemented in many technological variants and sizes, even down to where microscopic lateral resolution is reached: The Barkhausen noise and eddy current microscope (BEMI) is a scanning probe device based on miniature micromagnetic sensors [32]. So far, two sensor

• *Ferrite core sensor*: Copper coils wound on a small ferritic core with a 300-nmwide gap facing the sample surface are used for picking up magnetic Barkhausen noise (MBN) during cyclic magnetization of the sample, for characterizing permeability and conductivity in an eddy current (EC) operation mode and for measuring eddy current incremental permeability (ECIP). The MBN, EC and ECIP modes are performed alternatingly using a 3MA controller device. Depending on the material, a lateral resolution of about

• *Point probe:* A needle-shaped ferromagnetic core equipped with a primary (excitation) and a secondary (detection) coil is applied for characterizing local permeability and magnetic field [34]. The sample properties close to the needle tip strongly affect the secondary coil voltage waveform under application of sinusoidal voltage to the primary coil. Point probes deliver isotropic lateral response at a resolution depending on the sharpness of the needle tip. Experiments have proven that some features can be determined with a

For both sensor types, an evaluation software determines the characteristic features from the signals received. As further explained in the previous sections of this contribution, magnetic Barkhausen noise amplitude and magnetic permeability are strongly modulated by local stress for a given material. This leads to a lateral stress-dependent contrast in feature images produced by BEMI. Multiple mathematical and procedural approaches are applied for predicting stress quantitatively in

On the example of locally laser-treated X20Cr13 steel, the stress sensitivity of features obtained with both probe types is demonstrated. The sample shown in **Figure 15(a)** was scanned with a point probe, **Figure 15(b)**, and ferrite core sensor, **Figure 15(c)**. The results, as shown in **Figure 16**, indicate strong stress fields surrounding the laser-treated spots. The actual stress values were determined with

an indirect way, using these micromagnetic features as input.

evaluation of micro-residual stresses.

*DOI: http://dx.doi.org/10.5772/intechopen.90740*

*current microscopy (BEMI)*

10–20 μm is achieved [33].

resolution of around 20 μm [35].

**49**

designs have been implemented as BEMI modules:

**Figure 14.** *Dependency of parameter Hsp on the yield strength Rp0,2 (after [29]).*

of plastic deformation. In the case of the sample with low yield strength, Hsp does not change, whereas in the case of the samples with average yield strength, Hsp changed up to 1% of plastic deformation and after that remained constant. In the case of soft materials, the dislocation density changes only after higher degrees of plastic deformation. The more mechanically soft a material is, the more malleable it is, due to the absence of microstructure defects. Due to this fact, in the case of mechanically soft microstructures, Hsp remains constant for plastic deformation degrees ≤2% and would probably increase at higher plastic deformation degrees. With increasing yield strength (mechanical hardness), the ductility of the materials decreases, and the dislocation density already takes place at smaller plastic deformation degrees. For this reason, Hsp increases in the case of mechanically hard microstructures even after a small plastic deformation (<1%).

Moreover, experiments have shown that for samples containing compressive residual stress, stress invariant points occur only when applying compressive stress, whereas for samples containing tensile residual stress, stress invariant points occur when applying either compressive or tensile stress. This means that the sign of applied stress (compressive or tensile) under which the stress invariant point occurs gives information on the sign of the residual stress in the sample.

In practice, this approach is applicable in the context of a monitoring concept if the operating conditions provide for or permit the variation of the operating pressure. A further possible application of this approach is the characterization of the microstructure in the frame of material development, for example, on a material containing macro tensile stress as a result of processing.

The procedure described above allows for the characterization of micro-residual stress induced by dislocations. Micromagnetic measurement techniques based on the tensile load-dependent maximum of the Barkhausen noise amplitude can be used for the analysis of micro (third kind)-residual stress. Such stresses can be induced, e.g., by nanoscale second-phase precipitates due to the difference in lattice parameters of Cu and Fe. For this purpose, Fe-Cu alloys with well-defined amounts of nanoscale Cu precipitates have been manufactured and investigated. The micromagnetic concept is based on load stress-dependent Barkhausen noise measurements. The maximum of the Barkhausen noise amplitude (MMAX) obtained during one hysteresis cycle at a time is recorded under varied tensile load stresses, leading to an MMAX(σ) curve that has a relative maximum. A shift of this relative maximum along the stress axis can be observed as a measure for the change of the

*Nondestructive Characterization of Residual Stress Using Micromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.90740*

micro- or macro-residual stress condition. A measurement technique based on this effect permits the quantitative characterization of residual stress variations without the use of a reference method such as X-ray diffraction. If the superimposed residual stress is of the tensile type, the Barkhausen noise activity of the iron-based materials is more enhanced than in the stress-free condition, and the curves reach their maximum at lower load stresses, that is, the curve shifts to the left-hand side and in the other direction in the case of superimposed compressive stress. In order to determine the micro-residual stresses induced by nanoscale Cu particles only (i.e., to eliminate the influence of macro-residual stress from quenching and microresidual stress from different thermal expansion coefficients of particles and surrounding matrix), micromagnetic measurements have been performed in three steps, which are described in [30, 31]. This procedure permits the volumetric evaluation of micro-residual stresses.
