• U-shaped geometry

For each geometry, a twin sample was provided.

The 3MA probe was manually and step vice moved along a measuring trace from the middle of the bottom (position 0 according to **Figure 7**) along the wall to the die radius (position 8 according to **Figure 7**). Hereby the samples have been magnetized parallel to the die (or punch) radius by using a magnetization frequency of 250 Hz and a magnetization field strength of 10 A/cm. For each measuring position, 41 measuring parameters derived from upper harmonic analysis, Barkhausen noise analysis, incremental permeability analysis and eddy current impedance analysis were recorded.

The graph in **Figure 7** shows the behavior of the micromagnetically determined residual stress on a rectangular geometry, a rectangular geometry trimmed on the small sides of the part and a U-shaped geometry. In the range between positions 4 and 5 cm, a decisive decrease of tensile residual stresses after cutting free is observed. Due to the cutting process and the resulting relief of tensile residual stress, the deep drawn part shows a clear spring-back and hence an increase of the spring-back angle Δα. The U-shaped sample shows a quite homogenous distribution of stress in a low level along the measured line. Due to the missing sidewall, the sample can expand when taken out from the deep drawing tool, and therefore the

spring-back angle increases, and the stress level stays small.

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

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

ular to the rolling direction) concerning the formula

the existing stress states.

point, were applied.

**Figure 8.**

**41**

*3.1.2 Characterization of macro-residual stress by means of ultrasonic techniques*

In this paragraph, a study regarding integral biaxial stress conditions at rolled aluminum sheets for a stretched (0.5%) and an unstretched condition is presented and discussed in order to show the influence of the stretching process on residual stress relief. As for aluminum, the ultrasound velocity is almost equally affected by rolling texture and stress of the material—whereas for steels the ultrasound velocity is affected approximately 10 times more due to the rolling texture compared to stress conditions—these effects need to be separated from each other to determine

Under the assumption that the stress component along the thickness direction

**Figure 8** shows the distribution of the measured relative TOF changes of the two polarized shear waves due to the two principal stress directions (in and perpendic-

TOF perpendicular to the rolling direction � <sup>1000</sup>

(1)

can be neglected due to the texture, the two principal stress directions in and perpendicular to the rolling direction can be determined having information of two directional TOF dependencies. In order to easily implement measurements, an EMAT in impulse-echo mode (cf. **Figure 3** middle) using a center frequency of 2.5 MHz, three bursts and a bandpass filter generating ultrasonic shear waves propagating across the thickness of the sheets, polarized in and perpendicular to the rolling direction by turning the transducer around its own axis at each measuring

*Relative* TOF ½ �¼ ‰ TOF in rollingdirection � TOF perpendicular to the rolling direction

*Distribution of relative TOF measurements at a stretched (0.5%) sheet (left) and an unstretched sheet (right).*

For a quantitative determination of residual stress, a calibration procedure is necessary. For the calibration, generally the micromagnetic measuring parameters are correlated to real stress values at a corresponding position, which are measured by a reference method. Bases on these calibration data, a numerical function is generated, which is able to calculate stress values out of the micromagnetic measuring parameters. For the calibration of the shown example, the Barkhausen noise values which yielded the best results out of all the 3MA values were correlated with the tangential component of the residual stress values measured by X-ray diffractometer (XRD). As the samples have been magnetized parallel to the die (or punch), the magnetic measurements are mostly sensitive to the tangential component of the residual stress.


#### **Figure 6.**

*Examined shapes and correlated spring-back angle Δα (two samples for each shape). The labels below the photos relate to the legend in* **Figure 7** *[9].*

#### **Figure 7.**

*Residual stress distribution determined micromagnetically by 3MA on a rectangular geometry (A001, A003), a rectangular geometry trimmed on the small sides of the part (A002, A004) and a U-shaped geometry (B001, B002) along a measuring trace from the center of the part bottom (position 0) down to the die radius (position 8) [9].*

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

The graph in **Figure 7** shows the behavior of the micromagnetically determined residual stress on a rectangular geometry, a rectangular geometry trimmed on the small sides of the part and a U-shaped geometry. In the range between positions 4 and 5 cm, a decisive decrease of tensile residual stresses after cutting free is observed. Due to the cutting process and the resulting relief of tensile residual stress, the deep drawn part shows a clear spring-back and hence an increase of the spring-back angle Δα. The U-shaped sample shows a quite homogenous distribution of stress in a low level along the measured line. Due to the missing sidewall, the sample can expand when taken out from the deep drawing tool, and therefore the spring-back angle increases, and the stress level stays small.

#### *3.1.2 Characterization of macro-residual stress by means of ultrasonic techniques*

In this paragraph, a study regarding integral biaxial stress conditions at rolled aluminum sheets for a stretched (0.5%) and an unstretched condition is presented and discussed in order to show the influence of the stretching process on residual stress relief. As for aluminum, the ultrasound velocity is almost equally affected by rolling texture and stress of the material—whereas for steels the ultrasound velocity is affected approximately 10 times more due to the rolling texture compared to stress conditions—these effects need to be separated from each other to determine the existing stress states.

Under the assumption that the stress component along the thickness direction can be neglected due to the texture, the two principal stress directions in and perpendicular to the rolling direction can be determined having information of two directional TOF dependencies. In order to easily implement measurements, an EMAT in impulse-echo mode (cf. **Figure 3** middle) using a center frequency of 2.5 MHz, three bursts and a bandpass filter generating ultrasonic shear waves propagating across the thickness of the sheets, polarized in and perpendicular to the rolling direction by turning the transducer around its own axis at each measuring point, were applied.

**Figure 8** shows the distribution of the measured relative TOF changes of the two polarized shear waves due to the two principal stress directions (in and perpendicular to the rolling direction) concerning the formula

$$\text{Relative TOF} \left[ \text{\%o} \right] = \frac{\text{TOF in rolling direction - TOF perpendicular to the rolling direction}}{\text{TOF perpendicular to the rolling direction}} \times 1000$$

(1)

**Figure 8.** *Distribution of relative TOF measurements at a stretched (0.5%) sheet (left) and an unstretched sheet (right).*

• U-shaped geometry

component of the residual stress.

*photos relate to the legend in* **Figure 7** *[9].*

were recorded.

**Figure 6.**

**Figure 7.**

*8) [9].*

**40**

For each geometry, a twin sample was provided.

*New Challenges in Residual Stress Measurements and Evaluation*

The 3MA probe was manually and step vice moved along a measuring trace from the middle of the bottom (position 0 according to **Figure 7**) along the wall to the die radius (position 8 according to **Figure 7**). Hereby the samples have been magnetized parallel to the die (or punch) radius by using a magnetization frequency of 250 Hz and a magnetization field strength of 10 A/cm. For each measuring position, 41 measuring parameters derived from upper harmonic analysis, Barkhausen noise analysis, incremental permeability analysis and eddy current impedance analysis

For a quantitative determination of residual stress, a calibration procedure is necessary. For the calibration, generally the micromagnetic measuring parameters are correlated to real stress values at a corresponding position, which are measured by a reference method. Bases on these calibration data, a numerical function is generated, which is able to calculate stress values out of the micromagnetic measuring parameters. For the calibration of the shown example, the Barkhausen noise values which yielded the best results out of all the 3MA values were correlated with the tangential component of the residual stress values measured by X-ray diffractometer (XRD). As the samples have been magnetized parallel to the die (or punch), the magnetic measurements are mostly sensitive to the tangential

*Examined shapes and correlated spring-back angle Δα (two samples for each shape). The labels below the*

*Residual stress distribution determined micromagnetically by 3MA on a rectangular geometry (A001, A003), a rectangular geometry trimmed on the small sides of the part (A002, A004) and a U-shaped geometry (B001, B002) along a measuring trace from the center of the part bottom (position 0) down to the die radius (position*

at 297 measuring points at a stretched (left) and an unstretched sheet (right) of 30 mm thickness and a flat profile of 2 m � 4 m.

combinations of the second- and the third-order elastic constants, the quotients of which define weighting factors for the corresponding main stress directions [13].

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

Following, an innovative approach is described in order to determine depthresolved stress conditions using EMATs generating Rayleigh waves in transmission

Rayleigh waves operating at different frequencies in a time multiplex using the same transducers. The general EMAT concept is explained for ferromagnetic materials here, but it can be applied to non-ferromagnetic ones as well, by modifying the transducer set-up. It is based on the superposition of a perpendicular bias magnetic field B0 and a high-frequency field generated by a meander-shaped coil that is wound on the ferromagnetic comb structure (**Figure 9**). The generated trace wavelength, λs, is defined as the distance of two neighboring wires wound into the grooves of the comb having the same current direction. By winding the coil on just every second or third tooth, respectively, by segmenting the coil into several single coils for each comb tooth using an additionally adequate electrical connecting, the

A smart layout of the transducers offers the opportunity to generate and receive

As the penetration depth of a Rayleigh wave is approximately in the range of one

wavelength [24], different depth ranges can be achieved. Approaching specific evaluation algorithms comparable to the one mentioned in [25], stress conditions in different depths can be resolved. Since the stress dependence of the ultrasound velocity of a Rayleigh wave is less than for longitudinal and transversal wave types

due to the elliptic polarization, the stress resolution is comparatively small.

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

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.

*Set-up of an electromagnetic acoustic Rayleigh wave transducer for generating variable trace wavelengths*

*3.1.2.2 Depth-resolved measurements*

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

mode in ferromagnetic or conductive materials.

trace wavelength can be varied (λS1, λS2, λS3).

*on AHSS strips*

**Figure 9.**

**43**

*(after [23]).*

In both diagrams displayed in **Figure 8**, the superimposed influence of the rolling texture and the residual stress state is contained in each measurement point. In order to separate them from each other, the texture needs to be determined by measurements at selected measuring points that have to be cut out in order to relieve the stress condition or at a comparative sample of the same microstructure in a stress-relief heat-treated condition. Afterwards, quantitative stress values can be calculated using the TOF values and the acousto-elastic constants evaluated in tensile tests [13]. Under the assumption of an even distribution of the texture due to the rolling process, the shapes of the measurement results of **Figure 8** reflect the residual stress distribution for the stretched (0.5%) and the unstretched sheet originating from the two principal stress directions.

## *3.1.2.1 Evaluation of absolute stress in the two principal stress directions for platelike products*

For the determination of individual values of two principal stress components at sheets, an additional information concerning the local thickness of the sheets is necessary compared to the approach mentioned above. The principle described in this paragraph can, therefore, be applied using a newly developed hybrid EMAT.

Due to the excitation mechanism, the hybrid EMAT is linked conductively to non-ferromagnetic materials. This kind of EMAT generates two different ultrasonic waves in a time multiplex at the same measurement point. On the one hand, a shear wave propagating across the thickness of the sheet oscillating perpendicular to its direction of propagation is generated, and on the other hand, a longitudinal wave propagating across the thickness oscillating in the same direction is generated.

Depending on the position of the transducer, the anisotropy of the shear wave velocity can be evaluated by turning the transducer around its axis. Since the TOF of the longitudinal wave is not affected by any stress condition across the thickness of the sheet, there is no significant anisotropy for this wave type. Thereafter, reliable information on the thickness of the sheet can be obtained at each measurement point.

Using the evaluated thickness for a stress-free state determined by the longitudinal wave and information on the anisotropy of the two shear waves oscillating in and perpendicular to the rolling direction, the shear wave velocities can be determined. Afterwards, the two main stress states Vij and Vik can be calculated according to Eqs. (3) and (4) below, using the shear wave velocities evaluated previously.

$$\frac{\upsilon\_{ii} - \upsilon\_L}{\upsilon\_L} = \frac{A}{C} \cdot \sigma\_i + \frac{B}{C} \cdot \left(\sigma\_j + \sigma\_k\right) \tag{2}$$

$$\frac{\upsilon\_{\vec{v}\rangle} - \upsilon\_T}{\upsilon\_T} = \frac{D}{K} \cdot \sigma\_i + \frac{H}{K} \cdot \sigma\_{\vec{j}} + \frac{F}{K} \cdot \sigma\_k \tag{3}$$

$$\frac{\upsilon\_{ik} - \upsilon\_T}{\upsilon\_T} = \frac{D}{K} \cdot \sigma\_i + \frac{F}{K} \cdot \sigma\_j + \frac{H}{K} \cdot \sigma\_k \tag{4}$$

In Eqs. (2)–(4), σi, σ<sup>j</sup> and σ<sup>k</sup> represent the components of a normalized stress tensor, and vL and vT define the ultrasound velocity of a longitudinal (L) and transverse (T) wave for a stress-free condition. v (with its two indices) denotes the ultrasonic velocity for different directions of propagation (first index) and oscillation (second index) for a stress-affected state. A, B, C, D, H, F and K are

combinations of the second- and the third-order elastic constants, the quotients of which define weighting factors for the corresponding main stress directions [13].
