*3.2.1.2 Imaging of local residual stress distribution using Barkhausen noise and eddy current microscopy (BEMI)*

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 designs have been implemented as BEMI modules:


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 an indirect way, using these micromagnetic features as input.

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

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

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

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

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

microstructures even after a small plastic deformation (<1%).

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

*New Challenges in Residual Stress Measurements and Evaluation*

**Figure 14.**

**48**

gives information on the sign of the residual stress in the sample.

containing macro tensile stress as a result of processing.

applied stress, while the stress axis just presents the applied stress. As the separation of the effect of residual and applied stress for MBN is not possible, the stress axis is adjusted to show the sum of applied and residual stress. This is achieved by horizontally aligning the curves in their respective maxima. As shown in **Figure 17(b)**, the MMAX(σ) curves of the pre-deformed samples were moved to the MMAX(σ) curve of the non-deformed sample in such a way that all the maxima were aligned under the maximum of the MMAX(σ) curve of the non-deformed sample [20]. The residual stress σ<sup>R</sup> of each sample is then measured based on the peak shift compared

where σtot., σapp., and σ<sup>R</sup> are total, applied, and residual stresses, respectively. After modification of the stress axis, the modified stress and MMAX parameters are used as input for a regression analysis in order to determine a polynomial expression

**Figure 18** shows the MMAX(σ) curves before and after adjustment for nondeformed, 1 and 3% pre-deformed high-strength steel, respectively, and **Figure 19** shows the relation between measured and estimated stress after calibration. The measured stress values are obtained by the summation of the applied stress determined by the load cell of the tensile machine and the residual stress of the sample calculated by means of the shift between the peak positions at the MMAX(σ) curves (**Figure 18**). The estimated stress values show the residual stress calculated by

Determination of the residual stress distribution in an arbitrary area with high lateral resolution is possible using BEMI calibrated with RESTMAB (**Figure 20**)

*(a) Schematic MMAX(σ) curves for non- and pre-deformed material; (b) curves after horizontal alignment in*

*(a) Measured MMAX(σ) curves; (b) adjusted MMAX(σ) curves for the calibration process [20].*

for the relation between MBN parameters and (total) stress.

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

*σtot:* ¼ *σapp:* þ *σ<sup>R</sup>* (7)

to this reference, using Eq. (7):

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

means of the RESTMAB procedure.

**Figure 18.**

**51**

**Figure 17.**

*the respective maxima [20].*

**Figure 15.**

*(a) Photo of X20Cr13 steel sample with laser-heated spots (scale unit is millimeters) [35]. (b) Photo of point probe [35]; (c) photo of ferrite core sensor (Fraunhofer IZFP).*

#### **Figure 16.**

*(a) Scan of point probe feature VPEAK in the area marked in* **Figure 15(a)***; (b) the same VPEAK scan with narrow grey scale value range exposing stress fields around the laser-treated spots; (c) magnetic Barkhausen noise peak MMAX of two laser-hardened spots inside the framed area [33, 35].*

X-ray diffraction and indicated peak stresses M ranging from �300 MPa up to +600 MPa.

The novel micro-residual stress mapping method based on magnetic Barkhausen noise (RESTMAB) approach allows for a nondestructive estimation of microresidual stress of ferromagnetic materials without any help from conventional stress measurement methods. Moreover, RESTMAB is a timesaving approach for quantitative stress determination with BEMI.

As previously mentioned, the position of the maximum of the MMAX(σ) curve is proportional to micro-residual stress (**Figure 17(a)**). As an example, the micro-residual stress inside a pre-deformed sample is calculated using Eq. (6):

$$
\sigma\_R = \sigma\_{c\text{rit.}(n)} - \sigma\_{c\text{rit.}(p)} \tag{6}
$$

where σ<sup>R</sup> is the residual stress and σcrit.(n) and σcrit.(p) are the applied stresses in the maximum of the MMAX(σ) curve for the non- and pre-deformed samples, respectively.

RESTMAB works based on the information extracted from the MMAX(σ) curve and using regression analysis for calibration. The residual stress and the MMAX values are the inputs of the regression analysis. However, the MMAX(σ) curves require an adjustment prior to calibration. This adjustment is required because the MBN response is related to the sum of applied and residual stress. In other words, the MBN output shows the effect of residual stress and applied stress at the same time. Therefore, the MMAX values in **Figure 17(a)** are affected by the residual and

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

applied stress, while the stress axis just presents the applied stress. As the separation of the effect of residual and applied stress for MBN is not possible, the stress axis is adjusted to show the sum of applied and residual stress. This is achieved by horizontally aligning the curves in their respective maxima. As shown in **Figure 17(b)**, the MMAX(σ) curves of the pre-deformed samples were moved to the MMAX(σ) curve of the non-deformed sample in such a way that all the maxima were aligned under the maximum of the MMAX(σ) curve of the non-deformed sample [20]. The residual stress σ<sup>R</sup> of each sample is then measured based on the peak shift compared to this reference, using Eq. (7):

$$
\sigma\_{\text{tot.}} = \sigma\_{app.} + \sigma\_{\text{R}} \tag{7}
$$

where σtot., σapp., and σ<sup>R</sup> are total, applied, and residual stresses, respectively. After modification of the stress axis, the modified stress and MMAX parameters are used as input for a regression analysis in order to determine a polynomial expression for the relation between MBN parameters and (total) stress.

**Figure 18** shows the MMAX(σ) curves before and after adjustment for nondeformed, 1 and 3% pre-deformed high-strength steel, respectively, and **Figure 19** shows the relation between measured and estimated stress after calibration. The measured stress values are obtained by the summation of the applied stress determined by the load cell of the tensile machine and the residual stress of the sample calculated by means of the shift between the peak positions at the MMAX(σ) curves (**Figure 18**). The estimated stress values show the residual stress calculated by means of the RESTMAB procedure.

Determination of the residual stress distribution in an arbitrary area with high lateral resolution is possible using BEMI calibrated with RESTMAB (**Figure 20**)

#### **Figure 17.**

X-ray diffraction and indicated peak stresses M ranging from �300 MPa up to

*noise peak MMAX of two laser-hardened spots inside the framed area [33, 35].*

*(a) Scan of point probe feature VPEAK in the area marked in* **Figure 15(a)***; (b) the same VPEAK scan with narrow grey scale value range exposing stress fields around the laser-treated spots; (c) magnetic Barkhausen*

*(a) Photo of X20Cr13 steel sample with laser-heated spots (scale unit is millimeters) [35]. (b) Photo of point*

noise (RESTMAB) approach allows for a nondestructive estimation of microresidual stress of ferromagnetic materials without any help from conventional stress

measurement methods. Moreover, RESTMAB is a timesaving approach for

proportional to micro-residual stress (**Figure 17(a)**). As an example, the micro-residual stress inside a pre-deformed sample is calculated using Eq. (6):

quantitative stress determination with BEMI.

*probe [35]; (c) photo of ferrite core sensor (Fraunhofer IZFP).*

*New Challenges in Residual Stress Measurements and Evaluation*

The novel micro-residual stress mapping method based on magnetic Barkhausen

As previously mentioned, the position of the maximum of the MMAX(σ) curve is

where σ<sup>R</sup> is the residual stress and σcrit.(n) and σcrit.(p) are the applied stresses in

RESTMAB works based on the information extracted from the MMAX(σ) curve and using regression analysis for calibration. The residual stress and the MMAX values are the inputs of the regression analysis. However, the MMAX(σ) curves require an adjustment prior to calibration. This adjustment is required because the MBN response is related to the sum of applied and residual stress. In other words, the MBN output shows the effect of residual stress and applied stress at the same time. Therefore, the MMAX values in **Figure 17(a)** are affected by the residual and

the maximum of the MMAX(σ) curve for the non- and pre-deformed samples,

*σ<sup>R</sup>* ¼ *σcrit:*ð Þ *<sup>n</sup>* � *σcrit:*ð Þ *<sup>p</sup>* (6)

+600 MPa.

**Figure 16.**

**Figure 15.**

respectively.

**50**

*(a) Schematic MMAX(σ) curves for non- and pre-deformed material; (b) curves after horizontal alignment in the respective maxima [20].*

**Figure 18.** *(a) Measured MMAX(σ) curves; (b) adjusted MMAX(σ) curves for the calibration process [20].*

distribution as well as the plastic zone in front of a crack tip. Similar BEMI scans of a crack tip were reported by Altpeter et al. [32]; however, in their approach, BEMI

Residual stresses on the microscale require ultrasonic methods, which are characterized by a low interaction volume and high frequencies. A common method in research is scanning acoustic microscopy (SAM), which uses high-frequency ultrasonic waves >100 MHz to achieve lateral resolution in the range of 50–100 microns. By increasing the frequencies up to 1 GHz, the resolution is further improved. Surface waves or near-surface waves excited by such microscopes are used to determine the sound velocity and to map two-dimensional surface stress states [36]. To determine the absolute stress values, the sound velocity for the phase of the material to be examined must first be determined in calibration experiments, usually in tensile tests with parallel ultrasonic measurement. Since this can be a problem especially with polycrystalline materials due to local orientation differences, the

Based on the range of materials that can be examined, the use of a SAM is determined solely by the sound-damping properties [37]. Thus, therefore polymers and ceramic materials can be examined. Due to the small working distance and the sensitive sapphire or fused quartz lenses, a high surface quality and thus prepara-

Although the method has meanwhile lost in importance, current material developments in the field of functionalized and smart materials pose new

SAM could be a useful extension, for example, to investigate non-metallic materials that are functionalized by the introduction of microscopic residual

challenges for the test methods that are used to describe their condition. Here, the

In this contribution, nondestructive methods are discussed with respect to their ability to characterize residual stresses. It is shown that there are approaches and testing situations where both ultrasonic and micromagnetic techniques are able to (at least quantitatively) determine residual stress. Nevertheless, the contribution clarifies that ultrasonic techniques are mainly used to determine macro-residual stress, whereas micromagnetic techniques are mainly used to determine microresidual stresses. Most presented techniques, such as BEMI, 3MA, different EMAT applications, etc., are available for industrial use. New challenges can be found especially in the context of a depth-resolved determination of residual stresses.

The authors would like to thank the German Research Society for the financial support of research activities under grants Al 442/5-2, SCHM 746/71-2 and KI

Moreover, the authors would like to thank the Federal Ministry for Economic Affairs and Energy for the financial support of research activities under grant

*3.2.2 Characterization of micro-residual stress by means of ultrasonic techniques*

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

method is also often used to represent only local anisotropy.

was calibrated using XRD data.

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

tion are necessary.

stress fields.

**4. Conclusions**

**Acknowledgements**

1135/2-2.

1501523.

**53**

#### **Figure 19.**

*Relation between measured residual stress and estimated residual stress with RESTMAB for high-strength steel [20].*

#### **Figure 20.**

*(a) Micro-residual stress distributions measured with the calibrated BEMI using the RESTMAB for 1% predeformed sample. (b) Line scan extracted from the scan, in which it shows different orders of residual stresses measured with the calibrated BEMI for high-strength steel [20].*

#### **Figure 21.**

*Residual stress distribution in front of a crack tip in high-strength steel using BEMI calibrated by means of RESTMAB. The overlaying sketch in dark gray shows the notch and crack [20].*

illustrates the calibrated BEMI scan of pre-deformed sample of the high-strength steel, in which it shows the stress distributions of the sample in the scan area.

In another application, BEMI calibrated with RESTMAB was used to determine the stress distribution in front of a fatigue crack tip. **Figure 21** illustrates the stress distribution as well as the plastic zone in front of a crack tip. Similar BEMI scans of a crack tip were reported by Altpeter et al. [32]; however, in their approach, BEMI was calibrated using XRD data.

## *3.2.2 Characterization of micro-residual stress by means of ultrasonic techniques*

Residual stresses on the microscale require ultrasonic methods, which are characterized by a low interaction volume and high frequencies. A common method in research is scanning acoustic microscopy (SAM), which uses high-frequency ultrasonic waves >100 MHz to achieve lateral resolution in the range of 50–100 microns. By increasing the frequencies up to 1 GHz, the resolution is further improved. Surface waves or near-surface waves excited by such microscopes are used to determine the sound velocity and to map two-dimensional surface stress states [36]. To determine the absolute stress values, the sound velocity for the phase of the material to be examined must first be determined in calibration experiments, usually in tensile tests with parallel ultrasonic measurement. Since this can be a problem especially with polycrystalline materials due to local orientation differences, the method is also often used to represent only local anisotropy.

Based on the range of materials that can be examined, the use of a SAM is determined solely by the sound-damping properties [37]. Thus, therefore polymers and ceramic materials can be examined. Due to the small working distance and the sensitive sapphire or fused quartz lenses, a high surface quality and thus preparation are necessary.

Although the method has meanwhile lost in importance, current material developments in the field of functionalized and smart materials pose new challenges for the test methods that are used to describe their condition. Here, the SAM could be a useful extension, for example, to investigate non-metallic materials that are functionalized by the introduction of microscopic residual stress fields.
