*3.1.2.2 Depth-resolved measurements*

at 297 measuring points at a stretched (left) and an unstretched sheet (right) of

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

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

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 measure-

For the determination of individual values of two principal stress components at

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

*B*

*H <sup>K</sup>* � *<sup>σ</sup><sup>j</sup>* <sup>þ</sup>

*F <sup>K</sup>* � *<sup>σ</sup><sup>j</sup>* <sup>þ</sup>

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 oscilla-

*<sup>C</sup>* � *<sup>σ</sup><sup>j</sup>* <sup>þ</sup> *<sup>σ</sup><sup>k</sup>*

*F*

*H*

(2)

*<sup>K</sup>* � *<sup>σ</sup><sup>k</sup>* (3)

*<sup>K</sup>* � *<sup>σ</sup><sup>k</sup>* (4)

*vii* � *vL vL*

*vij* � *vT vT*

*vik* � *vT vT*

¼ *A <sup>C</sup>* � *<sup>σ</sup><sup>i</sup>* <sup>þ</sup>

¼ *D <sup>K</sup>* � *<sup>σ</sup><sup>i</sup>* <sup>þ</sup>

¼ *D <sup>K</sup>* � *<sup>σ</sup><sup>i</sup>* <sup>þ</sup>

tion (second index) for a stress-affected state. A, B, C, D, H, F and K are

30 mm thickness and a flat profile of 2 m � 4 m.

*New Challenges in Residual Stress Measurements and Evaluation*

originating from the two principal stress directions.

*products*

ment point.

previously.

**42**

Following, an innovative approach is described in order to determine depthresolved stress conditions using EMATs generating Rayleigh waves in transmission mode in ferromagnetic or conductive materials.

A smart layout of the transducers offers the opportunity to generate and receive 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 trace wavelength can be varied (λS1, λS2, λS3).

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.
