**2. Theoretical background on the used nondestructive methods**

### **2.1 Micromagnetic techniques**

#### *2.1.1 Magnetic structure*

The prerequisite for the application of micromagnetic nondestructive testing methods is a ferromagnetic behavior of the material to be tested. Such ferromagnetic materials have a characteristic domain structure. Here, the domains represent areas spontaneously magnetized up to saturation, which are separated from each other by the so-called Bloch walls [3]. The alignment of the magnetization vectors of the domains is statistically distributed over a ferromagnetic sample in the nonmagnetized state in such a way that their total effect is completely neutralized. The magnetic structure of iron-based ferromagnetic materials consists of two kinds of Bloch walls, 180° Bloch walls and 90° Bloch walls. The indicated angle represents the angle between the magnetization vectors in two neighboring domains. The 180° Bloch walls have short-range stress fields resulting in their strong interaction with microstructure inhomogeneity situated locally (dislocations or precipitates) or micro-residual stresses. The 90° Bloch walls have long-range stress fields that cause a strong interaction with microstructure heterogeneities stretched out over hundreds of microns and more (microstructure phases) or residual stresses of the second or first kind.

Under the influence of an external magnetic field, ferromagnetic materials align the magnetization vectors of the domains in the direction of the external magnetic field. The domains also change the structure under the influence of stresses. Known processes, Bloch wall movements and rotations of the domain magnetization vectors, cause these changes. The underlying effect is magnetostriction and the Villari effect. Magnetostriction describes the change in length of a ferromagnetic material during magnetization. A distinction is made between materials with positive and negative magnetostriction, depending on whether a sample lengthens or shortens in the field direction. The magnitude of the change in length depends on the direction of the magnetic field relative to the crystal axes. The Villari effect describes the reversal case that an elastic change in geometry causes a change in magnetization state. The cause of the effects lies in the spin-orbit coupling [4, 5].

#### *2.1.2 Magnetic hysteresis*

With an external alternating field magnetization of ferromagnetic materials, there is no clear correlation between the magnetic field strength H and the magnetic flux density B. This means that the magnetization of a ferromagnetic material depends not only on the external field strength (H) but also on the time course of the magnetization [4, 5]. If the magnetic field strength H is increased in a

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

non-magnetized ferromagnetic material, the magnetic flux density B increases in its surroundings. If the field strength is reduced to zero again, the magnetic flux density remains at a value unequal to zero. The ferromagnetic material retains some residual magnetism (remanence). With periodic magnetization, a ferromagnetic material reacts with a hysteretic relation of flux density B and magnetic field H (see **Figure 1**) [4, 5]. With continuous periodic magnetization, the hysteresis curve is traversed once with each magnetization period.

The reason for the occurrence of hysteretic behavior is the interaction of Bloch walls and microstructure. The Bloch wall motion is discontinuous throughout the magnetization process, as the Bloch walls are pinned by existing lattice defects, and each pinning has to be overcome by increasing applied magnetic field. Lattice defects in the microstructure such as grain boundaries, dislocations and precipitates represent energetic minima for the Bloch walls. This causes the Bloch walls to tear loose abruptly and move until a pinning site of higher strength is reached.

Stresses affect the magnetic hysteresis behavior of ferromagnetic materials. In magnetostrictively positive materials (such as most ferromagnetic steels), tensile stress causes an increase of the differential susceptibility and a narrower hysteresis (HC shift toward smaller values) and vice versa for compressive stresses. Magnetostrictively negative materials behave contrary to positive materials [4, 5, 7].

#### *2.1.3 Magnetic Barkhausen noise*

Although best expressed as a tensor, industrial practice often demands for simplified residual stress values regarding one or a few relevant directions, such as those

as it affects the product geometry and processability (strip steel being just one example), the tendency to crack appearance (e.g., after hardening or forming) as well as the fatigue lifetime. The present contribution discusses micromagnetic and ultrasonic techniques that are industrially applied for nondestructive stress

**2. Theoretical background on the used nondestructive methods**

The prerequisite for the application of micromagnetic nondestructive testing methods is a ferromagnetic behavior of the material to be tested. Such ferromagnetic materials have a characteristic domain structure. Here, the domains represent areas spontaneously magnetized up to saturation, which are separated from each other by the so-called Bloch walls [3]. The alignment of the magnetization vectors of the domains is statistically distributed over a ferromagnetic sample in the nonmagnetized state in such a way that their total effect is completely neutralized. The magnetic structure of iron-based ferromagnetic materials consists of two kinds of Bloch walls, 180° Bloch walls and 90° Bloch walls. The indicated angle represents the angle between the magnetization vectors in two neighboring domains. The 180° Bloch walls have short-range stress fields resulting in their strong interaction with microstructure inhomogeneity situated locally (dislocations or precipitates) or micro-residual stresses. The 90° Bloch walls have long-range stress fields that cause a strong interaction with microstructure heterogeneities stretched out over hundreds of microns and more (microstructure phases) or residual stresses of the

Under the influence of an external magnetic field, ferromagnetic materials align the magnetization vectors of the domains in the direction of the external magnetic field. The domains also change the structure under the influence of stresses. Known processes, Bloch wall movements and rotations of the domain magnetization vectors, cause these changes. The underlying effect is magnetostriction and the Villari effect. Magnetostriction describes the change in length of a ferromagnetic material during magnetization. A distinction is made between materials with positive and negative magnetostriction, depending on whether a sample lengthens or shortens in the field direction. The magnitude of the change in length depends on the direction of the magnetic field relative to the crystal axes. The Villari effect describes the reversal case that an elastic change in geometry causes a change in magnetization

With an external alternating field magnetization of ferromagnetic materials, there is no clear correlation between the magnetic field strength H and the magnetic flux density B. This means that the magnetization of a ferromagnetic material depends not only on the external field strength (H) but also on the time course of the magnetization [4, 5]. If the magnetic field strength H is increased in a

state. The cause of the effects lies in the spin-orbit coupling [4, 5].

Residual stress has significant impact on product quality and useful service life,

most critical under the expected service load.

*New Challenges in Residual Stress Measurements and Evaluation*

measurement.

**2.1 Micromagnetic techniques**

*2.1.1 Magnetic structure*

second or first kind.

*2.1.2 Magnetic hysteresis*

**34**

The analysis of magnetic Barkhausen noise (MBN) is based on a discovery by Barkhausen [8]: Abrupt changes in local magnetization caused by the discontinuous Bloch wall motion can be picked up inductively as a series of voltage pulses (noise) induced into a coil that is placed close to the material surface. The location of the highest density of these impulses is in relation to the magnetic hysteresis near the coercive force HC, since this is where most Bloch wall jumps occur. The voltage pulses can be amplified, filtered and rectified for evaluation. The envelope of the filtered and rectified noise signal can be recorded as a function of the magnetization field strength, resulting in a so-called Barkhausen noise profile curve M(H) (see **Figure 2**). The magnetic Barkhausen noise has a characteristic dependence on

**Figure 1.** *Hysteresis curve (HC, coercivity; BR, remanence) [6].*

inverse piezoelectric effect: an electrical voltage is applied to a solid (in this case usually ceramics) which leads to a deformation of the material and an excitation of ultrasonic waves. The (direct) piezoelectric effect is used to receive ultrasonic waves. In order to transfer the ultrasound into the specimen (and to receive it), a couplant is needed. In this regard, mostly water and oil are used. Depending on the situation, this implies disadvantages, such as a contamination of the specimen by the couplant and the limited excitation of wave modes. Nevertheless, piezoelectric ultrasound is widely used as a wide range of frequencies can be generated [11]. Electromagnetically excited ultrasound presents an advantageous alternative to conventional ultrasound testing, especially in rough environments or when special wave modes are to be excited. In principle, an electromagnetic acoustic transducer (EMAT) is consisting of a magnet and a radio frequency coil. The ultrasonic sources are induced in the material surface by alternating electromagnetic fields. Thus, on the one hand, no couplant is needed, and small lift-offs between specimen and transducers are acceptable. On the other hand, electromagnetic ultrasound can only be excited in electrically conductive materials, and the range of frequencies that can

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

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

In order to perform measurements, regardless of the excitation mode, transducers are required to send and to receive ultrasonic waves. In this regard, different set-ups are feasible. **Figure 3** shows three typical set-ups that are used to measure the so-called ultrasonic time of flight (TOF), which denotes the time the wave (white) propagates from a transmitter (T) through a medium (green) to a receiver (R). Using reflection mode (see **Figure 3**, middle), generally, a transducer is chosen that serves as transmitter and receiver, and the generated wave is reflected at a medium boundary before it propagates back to the receiver. In addition to the TOF, the amplitude of the transmitted or reflected signal is recorded. If the thickness of the specimen is known, it is also possible to measure the velocity of

In addition to the ability to detect flaws, cracks, etc., ultrasonic techniques are

*Three typical set-ups to perform ultrasonic measurements: T denotes the transmitter and R denotes the receiver, and the specimen is marked in green. Left, transmission mode; middle, reflection mode; right, transmission*

often used to determine stresses. Reason for this is that all tension and strain changes in materials are subject to the so-called acousto-elastic effect which raises measurable changes regarding the velocity of propagation of ultrasonic waves [13]. Hence, measurements of ultrasonic velocity of propagation are used to detect emerging material and stress changes. Depending on the applied wave modes (longitudinal, transverse (SH, SV)) and their propagation and polarization direction in relation to the stress direction, additional changes of the measured ultrasonic TOF occur (**Figure 4**). The accuracy of evaluated stresses using ultrasonic TOF measurements is mainly determined by two factors, that is, the accuracy of the determined acousto-elastic constants and the accuracy of the measured TOF. According to [14] typical TOF measurements lead to an accuracy in the stress determination of

be generated is limited [12].

propagation.

**Figure 3.**

*mode.*

**37**

#### **Figure 2.**

*Stress dependence of the magnetic Barkhausen noise profile curve for a single ferromagnetic sample in a tensile/ compressive test in elastic strain range, without a change in the mechanical hardness (after [9]).*

mechanical stresses (see **Figure 2**), which makes it suitable for the nondestructive determination of residual stresses.

#### *2.1.4 Micromagnetic multiparameter microstructure and stress analysis (3MA)*

Micromagnetic multiparameter microstructure and stress analysis (3MA), developed at the Fraunhofer IZFP, is a solution for the quantitative determination of quality-deciding target parameters such as stress as well as hardness, hardening depth (CHD, SHD or NHD), ductile-to-brittle transition temperature (DBTT), yield and ultimate strength. 3MA uses a combination of several micromagnetic measuring methods such as upper harmonic analysis, Barkhausen noise analysis, incremental permeability analysis and eddy current (EC) impedance analysis [10]. The reason for using more than one measuring method for material characterization is the increased robustness against disturbing influences such as material inhomogeneity or surface treatment (similar to the benefits of having different human senses). The 3MA device generates the drive voltages for the magnetization coil and the eddy current coil in the sensor. The 3MA sensor includes an electromagnet, which excites an alternating magnetic field in the ferromagnetic sample, which, in turn, shows micromagnetic effects (see Section 2.1.2). In the most widespread implementation of 3MA, these effects are registered with a Hall probe and coils included in the sensor as well. Other implementations evaluate the current and voltage at the exciter coil. After preamplification, the measured signals are processed in the 3MA device and a controlling PC. This results in a kind of "magnetic fingerprint" which is used for quantitative and qualitative material characterization. For mechanical-technological material characterization, 3MA has to be calibrated on a well-defined calibration set of samples (with known target properties, e.g., stress or hardness).

#### **2.2 Ultrasonic techniques**

Among nondestructive methods, ultrasonic methods are the most and widely used ones. Reasons for this are the applicability to almost all materials and the wide range of wall thicknesses that can be tested. In order to excite ultrasonic waves, two main principles are used. Conventional ultrasonic testing is based on the use of the

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

inverse piezoelectric effect: an electrical voltage is applied to a solid (in this case usually ceramics) which leads to a deformation of the material and an excitation of ultrasonic waves. The (direct) piezoelectric effect is used to receive ultrasonic waves. In order to transfer the ultrasound into the specimen (and to receive it), a couplant is needed. In this regard, mostly water and oil are used. Depending on the situation, this implies disadvantages, such as a contamination of the specimen by the couplant and the limited excitation of wave modes. Nevertheless, piezoelectric ultrasound is widely used as a wide range of frequencies can be generated [11]. Electromagnetically excited ultrasound presents an advantageous alternative to conventional ultrasound testing, especially in rough environments or when special wave modes are to be excited. In principle, an electromagnetic acoustic transducer (EMAT) is consisting of a magnet and a radio frequency coil. The ultrasonic sources are induced in the material surface by alternating electromagnetic fields. Thus, on the one hand, no couplant is needed, and small lift-offs between specimen and transducers are acceptable. On the other hand, electromagnetic ultrasound can only be excited in electrically conductive materials, and the range of frequencies that can be generated is limited [12].

In order to perform measurements, regardless of the excitation mode, transducers are required to send and to receive ultrasonic waves. In this regard, different set-ups are feasible. **Figure 3** shows three typical set-ups that are used to measure the so-called ultrasonic time of flight (TOF), which denotes the time the wave (white) propagates from a transmitter (T) through a medium (green) to a receiver (R). Using reflection mode (see **Figure 3**, middle), generally, a transducer is chosen that serves as transmitter and receiver, and the generated wave is reflected at a medium boundary before it propagates back to the receiver. In addition to the TOF, the amplitude of the transmitted or reflected signal is recorded. If the thickness of the specimen is known, it is also possible to measure the velocity of propagation.

In addition to the ability to detect flaws, cracks, etc., ultrasonic techniques are often used to determine stresses. Reason for this is that all tension and strain changes in materials are subject to the so-called acousto-elastic effect which raises measurable changes regarding the velocity of propagation of ultrasonic waves [13]. Hence, measurements of ultrasonic velocity of propagation are used to detect emerging material and stress changes. Depending on the applied wave modes (longitudinal, transverse (SH, SV)) and their propagation and polarization direction in relation to the stress direction, additional changes of the measured ultrasonic TOF occur (**Figure 4**). The accuracy of evaluated stresses using ultrasonic TOF measurements is mainly determined by two factors, that is, the accuracy of the determined acousto-elastic constants and the accuracy of the measured TOF. According to [14] typical TOF measurements lead to an accuracy in the stress determination of

#### **Figure 3.**

*Three typical set-ups to perform ultrasonic measurements: T denotes the transmitter and R denotes the receiver, and the specimen is marked in green. Left, transmission mode; middle, reflection mode; right, transmission mode.*

mechanical stresses (see **Figure 2**), which makes it suitable for the nondestructive

*Stress dependence of the magnetic Barkhausen noise profile curve for a single ferromagnetic sample in a tensile/*

Micromagnetic multiparameter microstructure and stress analysis (3MA), developed at the Fraunhofer IZFP, is a solution for the quantitative determination of quality-deciding target parameters such as stress as well as hardness, hardening depth (CHD, SHD or NHD), ductile-to-brittle transition temperature (DBTT), yield and ultimate strength. 3MA uses a combination of several micromagnetic measuring methods such as upper harmonic analysis, Barkhausen noise analysis, incremental permeability analysis and eddy current (EC) impedance analysis [10]. The reason for using more than one measuring method for material characterization is the increased robustness against disturbing influences such as material inhomogeneity or surface treatment (similar to the benefits of having different human senses). The 3MA device generates the drive voltages for the magnetization coil and the eddy current coil in the sensor. The 3MA sensor includes an electromagnet, which excites an alternating magnetic field in the ferromagnetic sample, which, in turn, shows micromagnetic effects (see Section 2.1.2). In the most widespread implementation of 3MA, these effects are registered with a Hall probe and coils included in the sensor as well. Other implementations evaluate the current and voltage at the exciter coil. After preamplification, the measured signals are processed in the 3MA device and a controlling PC. This results in a kind of "magnetic fingerprint" which is used for quantitative and qualitative material characterization. For mechanical-technological material characterization, 3MA has to be calibrated on a well-defined calibration set of samples (with known target

Among nondestructive methods, ultrasonic methods are the most and widely used ones. Reasons for this are the applicability to almost all materials and the wide range of wall thicknesses that can be tested. In order to excite ultrasonic waves, two main principles are used. Conventional ultrasonic testing is based on the use of the

*2.1.4 Micromagnetic multiparameter microstructure and stress analysis (3MA)*

*compressive test in elastic strain range, without a change in the mechanical hardness (after [9]).*

*New Challenges in Residual Stress Measurements and Evaluation*

determination of residual stresses.

**Figure 2.**

properties, e.g., stress or hardness).

**2.2 Ultrasonic techniques**

**36**

**Figure 4.** *Relative change in the ultrasound velocity with the elastic tensile strain of a metallic sample: Schematic sketch (after [13]).*

approx. 20–50 MPa. In order to measure a change of approx. 1% in the TOF, a stress change of approx. 100 MPa is needed. This, however, can only be understood as a rule of thumb as it strongly depends on the used wave mode and the material to be characterized. Measurements of steel rolls showed that longitudinal waves are more sensitive to stress changes than transversal waves: while a change in the stress state of 135 MPa caused a change of 1% in the TOF of the used transversal wave, a change in the stress state of only 87 MPa caused a change of 1% in the TOF of the used longitudinal wave [14].

**3.1 Characterization of macro-residual stress**

*Nondestructive Characterization of Residual Stress Using Micromagnetic…*

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

*Three kinds of residual stress over several grains: σ<sup>R</sup>*

*represents stress variations within a grain (after [15]).*

for the nondestructive characterization of stress states.

geometries are:

**39**

**Figure 5.**

*across several grains, σ<sup>R</sup>*

• Rectangular geometry

In order to investigate the influence of stress and strain during the deep drawing process on spring-back, six samples with three different rectangular geometries (160 mm 80 mm), as shown in **Figure 6**, were produced. The three

• Rectangular geometry, trimmed on the small sides of the part in order to remove the influence of the corners on the sample (decreasing stiffness)

*3.1.1 Characterization of macro-residual stress by means of micromagnetic techniques*

In the frame of a research project funded by the German Research Foundation (DFG), the residual stress distribution in deep drawn components was examined by means of the micromagnetic method 3MA [9], which is described in Section 2.1.4. The focus of this research project was the examination of high-strength steels in deep drawing, which are increasingly used within the construction of automotive parts due to the reduction of weight with simultaneous enhancement of safety. The reduction of weight is an important contribution to the reduction of primary energy consumption in transportation and so finally adds a contribution to the reduction of CO2 emissions. However, the application of high-strength steels in deep drawing processes is related to an increase of spring-back. Spring-back is one important criteria for accuracy of the shape geometry. One reason for spring-back is the redistribution of residual stresses when the part is taken from the forming tool [21]. On the other side, the material properties and the deep drawing process parameters are also influencing the spring-back behavior [22]. One aim of the abovementioned project was the determination of the residual stress and its distribution in the deep drawing components with the target to control the process parameters in order to avoid spring-back. The following example demonstrates the correlation between residual stress and spring-back and the potential of the micromagnetic 3MA method

*II represents a shorter-range average (i.e., representing one grain or crystal), and σ<sup>R</sup>*

*<sup>I</sup> represents the average stress over a longer range, that is,*

*III*

### **3. Micro- and macro-residual stresses**

Looking into publications accepted by most researchers and engineers, residual stresses are categorized according to the length scale. In this context, a simple classification categorizes residual stresses into macro- and micro-residual stress [15, 16]. Macroscopic residual stresses are stress distributions whose range is several orders of magnitude greater than the microstructure of the material. This type of residual stresses originates, for example, from shot peening, bending, welding and cold hole punching. Microscopic residual stresses, on the other hand, are based on microstructural misfits between phase constituents and grains which can occur as a side effect of phase transformation, intergranular stresses and plastic deformation, for example [17].

According to [2, 15, 18, 19], residual stresses may be distinguished more precisely. The first type or first kind (σ<sup>R</sup> I ) is the equivalent of macro-residual stresses the volume average stresses—which has a range of some millimeters. The second type or second kind (σ<sup>R</sup> II) analog to micro-residual stresses results from the heterogeneity of grains in polycrystalline materials and is defined as the mean stress value equilibrated inside a grain. The third kind (σ<sup>R</sup> III) as (sub)micro-residual stress contains all stresses at any point inside a grain which equilibrate on a scale of several atoms [18–20]. **Figure 5** shows a schematic summary of the three kinds of stresses.

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

#### **Figure 5.**

approx. 20–50 MPa. In order to measure a change of approx. 1% in the TOF, a stress change of approx. 100 MPa is needed. This, however, can only be understood as a rule of thumb as it strongly depends on the used wave mode and the material to be characterized. Measurements of steel rolls showed that longitudinal waves are more sensitive to stress changes than transversal waves: while a change in the stress state of 135 MPa caused a change of 1% in the TOF of the used transversal wave, a change in the stress state of only 87 MPa caused a change of 1% in the TOF of the

*Relative change in the ultrasound velocity with the elastic tensile strain of a metallic sample: Schematic sketch*

*New Challenges in Residual Stress Measurements and Evaluation*

Looking into publications accepted by most researchers and engineers, residual

According to [2, 15, 18, 19], residual stresses may be distinguished more pre-

geneity of grains in polycrystalline materials and is defined as the mean stress value

the volume average stresses—which has a range of some millimeters. The second

contains all stresses at any point inside a grain which equilibrate on a scale of several atoms [18–20]. **Figure 5** shows a schematic summary of the three kinds of

) is the equivalent of macro-residual stresses—

III) as (sub)micro-residual stress

II) analog to micro-residual stresses results from the hetero-

I

stresses are categorized according to the length scale. In this context, a simple classification categorizes residual stresses into macro- and micro-residual stress [15, 16]. Macroscopic residual stresses are stress distributions whose range is several orders of magnitude greater than the microstructure of the material. This type of residual stresses originates, for example, from shot peening, bending, welding and cold hole punching. Microscopic residual stresses, on the other hand, are based on microstructural misfits between phase constituents and grains which can occur as a side effect of phase transformation, intergranular stresses and plastic deformation,

used longitudinal wave [14].

**Figure 4.**

*(after [13]).*

for example [17].

stresses.

**38**

type or second kind (σ<sup>R</sup>

**3. Micro- and macro-residual stresses**

cisely. The first type or first kind (σ<sup>R</sup>

equilibrated inside a grain. The third kind (σ<sup>R</sup>

*Three kinds of residual stress over several grains: σ<sup>R</sup> <sup>I</sup> represents the average stress over a longer range, that is, across several grains, σ<sup>R</sup> II represents a shorter-range average (i.e., representing one grain or crystal), and σ<sup>R</sup> III represents stress variations within a grain (after [15]).*

#### **3.1 Characterization of macro-residual stress**

### *3.1.1 Characterization of macro-residual stress by means of micromagnetic techniques*

In the frame of a research project funded by the German Research Foundation (DFG), the residual stress distribution in deep drawn components was examined by means of the micromagnetic method 3MA [9], which is described in Section 2.1.4. The focus of this research project was the examination of high-strength steels in deep drawing, which are increasingly used within the construction of automotive parts due to the reduction of weight with simultaneous enhancement of safety. The reduction of weight is an important contribution to the reduction of primary energy consumption in transportation and so finally adds a contribution to the reduction of CO2 emissions. However, the application of high-strength steels in deep drawing processes is related to an increase of spring-back. Spring-back is one important criteria for accuracy of the shape geometry. One reason for spring-back is the redistribution of residual stresses when the part is taken from the forming tool [21]. On the other side, the material properties and the deep drawing process parameters are also influencing the spring-back behavior [22]. One aim of the abovementioned project was the determination of the residual stress and its distribution in the deep drawing components with the target to control the process parameters in order to avoid spring-back. The following example demonstrates the correlation between residual stress and spring-back and the potential of the micromagnetic 3MA method for the nondestructive characterization of stress states.

In order to investigate the influence of stress and strain during the deep drawing process on spring-back, six samples with three different rectangular geometries (160 mm 80 mm), as shown in **Figure 6**, were produced. The three geometries are:

