Review of non-destructive measuring methods for the assessment of surface integrity: a survey of new measuring methods for coatings, layered structures and processed surfaces

Precision Engineering 23 (1999) 9 –33

Review of non-destructive measuring methods for the assessment of surface integrity: a survey of new measuring methods for coatings, layered structures and processed surfaces G. Goch a,*, B. Schmitz b, B. Karpuschewski c, J. Geerkens b, M. Reigl d, P. Sprongl b, R. Ritter b a

Fachgebiet Meß-, Steuerungs- und Regelungstechnik, Hochschulring 20, D-28359 University of Bremen, Germany b Institut fu¨r Lasertechnologien in der Medizin und Meßtechnik, Ulm, Germany c Institut fu¨r Fertigungstechnik und Spanende Werkzeugmaschinen, University of Hannover, Germany d Siemens AG, Ulm, Germany Manuscript received 16 March 1998; accepted 9 June 1998

Abstract Even though the near-surface areas of precisely manufactured parts represent only a few percent of the workpiece’s material volume, they influence its functional behaviour, quality and lifetime significantly. Therefore, sensors and measuring principles able to detect material changes, damage and process influences in the near-edge zone are of increasing importance. However, they have to meet industrial purposes concerning accuracy, measuring time, robustness and costs. In addition, they should work non-destructively and should offer the capability for integration in a production line. © 1999 Elsevier Science Inc. All rights reserved.

As the X-ray, sound propagation and Raman spectroscopy techniques were explained in detail in [1] by Brinksmeier, this contribution takes special emphasis on other non-destructive methods: photothermal, micromagnetic and SNAM-based (Scanning Near-Field Acoustic Microscopy) microhardness measurement. They cover thin near-surface layers from the sub-micrometer to the millimeter-range. Namely the photothermal techniques including various detector-options have gained a substantial progress during the last five years, promising a broad spectrum of measuring abilities. Today, photothermics are applied to a wide spectrum of well-known and new materials, all kinds of layeredstructure measurements concerning coatings (thickness, adhesion strength, local disturbances), hardness profiles, residual stresses, wear, thermal influences, and various manufacturing techniques, affecting the near-surface zone. The contribution concludes by the SNAM-technique, allowing simultaneously a surface and a new microindentational inspection.

* Corresponding author. E-mail: [email protected].

1. Introduction New capabilities in machining processes, a continuing miniaturization and tolerances down to the nanometer scale have lead to material treatments and depths of cut, affecting only very thin layers next to the surface. The more the over-all volume of a miniaturized product or its affected zone is scaled down in precision engineering, the more these near-surface areas influence its functional behaviour, quality and lifetime, even though they represent only a few percent of the workpiece’s volume. Therefore, industrially applicable sensors and measuring principles detecting material changes, damages and process influences in the near-edge zone are of increasing importance. However, they should work non-destructively and meet, at least, current standards concerning accuracy, measuring time, robustness and costs.

2. New measuring principles Since the state-of-the-art of non-destructive measuring methods was summarized by E. Brinksmeier at the ASPEMeeting in 1989 [1], special interest is focused on measuring devices and methods suitable for an installation in or

0141-6359/99/$–see front matter © 1999 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 6 3 5 9 ( 9 8 ) 0 0 0 2 1 - X

10

G. Goch et al./Precision Engineering 23 (1999) 9 –33

near to a production line, i.e. others than pure laboratory instruments. Only a few measuring methods offer a direct access to the surface and sub-surface properties, especially if a non-destructive inspection of thin layers is required. Indirect measuring methods correlate the interesting mechanical, structural or chemical surface properties with easier accessible quantities, depending on the detecting principle. Photothermal, micromagnetic and SNAM-based inspections (see sections 3, 4 and 5, respectively) belong to the latter indirect methods, correlating the material and structural properties of the near-edge zone with its thermal, electromagnetic or mechanical material parameters and their spatial distribution. The three mentioned groups of measuring principles cover thin near-surface layers from the sub-micrometer to the millimeter-range. Additionally, photothermics can be applied to new materials like ceramics and special coatings. All these applications require new measuring and evaluation methods, able to discover new types of deviations (e.g. cracks, adhesion defects, material parameter profiles). Corresponding to the down-scaled thickness of the relevant near-surface layer, the requested measuring resolution and uncertainty must be reduced, too. Due to the importance of the edge zone and a widely stated lack of experience with processing new materials, there is an urgent need to improve manufacturing control, quality inspection and the wearbehaviour concerning all kinds of coatings, edge hardening, sub-surface damages and residual stresses.

3. Photothermal inspection of the near-surface zone 3.1. Physical principles In a photothermal experiment, heat is generated by the interaction between an intensity-modulated tightly focused light beam (e.g. realized in Fig. 1 by an Ar-laser with an acousto-optic modulator) and an extended, three-dimensional sample [2–5]. Absorption and subsequent deexcitation-relaxation release heat energy that may be distributed throughout a large region of the sample or be confined to a small area such as the surface of an opaque solid. Thus, experiments with a resolution in a microscopic scale can be realized [6]. The corresponding thermal response of the periodically heated object can be detected by different sensing devices. The detector signals imply information about the thermal material parameters, layer structures, type and distribution of hidden sub-surface defects [7–9]. In photothermal radiometry (PTR), an infrared detector (Fig. 2); e.g. a Joule-Thomson cooled MCT-device (Mercury-Cadmium-Telluride), monitors the variations of the surface temperature [10,11]. The emitted IR-radiation is imaged onto the detection plane by suitable optics. For real samples, various measuring conditions affect the measured IR-flux (optical material properties, absolute temperature of

Fig. 1. Photothermal experimental set-up.

the surrounding, surface roughness, heat flow from the sample’s surface to the surrounding gas, etc.). Usually, these influences are ignored in non-destructive photothermal applications, since only the signal changes during a lateral scanning across the surface or during a frequency sweep at one surface spot reveal the subsurface structures. Therefore, phase sensitive lock-in amplifiers record amplitude and phase of the detector signals with respect to the excitation beam, which can be scanned across the sample by a 2-D stage (Fig. 1 and e.g. Fig. 12b). The Optical Beam Deflection (OBD) (Fig. 3a and the

Fig. 2. Excitation of thermal waves and their IR detection.

G. Goch et al./Precision Engineering 23 (1999) 9 –33

11

Table 1 Thermal diffusion length for different materials and modulation frequencies

Fig. 3. Photothermal detecting principles: a) Optical Beam Deflection (OBD, ‘Mirage-effect’), b) Interferometric detection.

commercially available compact setup labelled ‘Mirage MonoBloc’ in Fig. 1) detects the local thermal response of the periodically heated solid by the deflection of a lowpower probe laser beam, crossing the air region adjacent to the heated surface spot in grazing incidence [12,13]. One of the two deflection contributions (normal or transverse component) is measured by a four quadrant diode. The OBDsensor needs much more adjustment attendance, leading to a significantly higher sensitivity compared to the PTRsystem. On the other hand, lower adjustment error influences of the PTR-sensor means more robustness in terms of adverse industrial environments. Therefore, PTR-detection should be preferred for applications in or near to a production line. Fig. 3b shows the interferometric detection principle [14], which is even more sensitive than the OBD-detector,

Material

Diffusion length for 1 Hz

Diffusion length for 1 kHz

Copper Steel 16MnCr5 Air

6.0 mm 2.0 mm 2.6 mm

190 mm 64 mm 83 mm

but again causes high adjustment efforts. Fig. 4 summarizes some other photothermal interaction phenomena reported in literature [7,15]. Except the photoreflection system (semiconductors, [16,17]), the piezoelectric detection schemes [18,19] and the photoacoustic cell [20,21], they are of minor importance for precision engineering processes. The detectability of deviations in the thermal material properties can be enhanced by using contrast functions of the amplitude and phase [8,22,23]. They compare the photothermal readings obtained from a defect or a thermal alteration with the background signal of the surrounding, homogeneous material. In order to reconstruct the depth and profiles of thermal changes, contrast signals as a function of the modulation frequency f are recorded (frequency sweep). 3.2. Theoretical description of the heat diffusion process The basic equation (1) named thermal diffusion equation (TDE) enables to quantify photothermal signals. Its solution describes the heat diffusion process, i.e. the temperature distribution T(x, t) with its spatial and time dependency after a thermal load (from the exciting laser beam) [24 –26] [Eq. (1)].

S

The temperature distribution within the sample depends on the spatial distribution of the thermal parameters thermal conductivity k, specific heat c and mass density r. In general, an analytical solution for (1) cannot be achieved, only for special cases and regarding some restrictions. For a periodic excitation with a certain modulation frequency, thermal waves propagate within the sample. Their penetration depth is given by Eq. (2) as the thermal diffusion length m, which depends on the thermal parameters of the sample and is inverse proportional to the square root of the exciting frequency f [Eq. (2)]:

m5

Fig. 4. Spectrum of photothermal interaction phenomena.

D

d d d k ~x! T~x, t! 2 r ~x!c~x! T~x, t! 5 2Q~x, t! dx dx dt (1)

Î

2a v

(2)

with the thermal diffusivity a 5 k /(rc) and v 5 2pf. Typical values for the thermal diffusion length are shown in Table 1. Thus, by varying the modulation frequency, photothermal detectors can ‘look inside’ a surface zone

12

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 6. Depth dependence of the thermal impedance in the one-dimensional case: (1) coated system, (2) coated system with a thermal contact resistance, (3) thermal transition zone.

Fig. 5. Excitation and detection areas for the one-dimensional photothermal problem.

down to a variable depth, without contact, non-destructively, with a microscopic lateral resolution and very quickly. The analytical solutions of the TDE cover a wide range of applications. Each requires a specialized model concerning the investigated near-surface properties, their correlation with thermal parameters, the theoretical heat propagation within the sample and the expected resulting signal response recorded by the photothermal detectors. For some applications, analytical models are available since several years, solving problems like layer thickness determination [27–30], adhesion strength inspection [31], diffusivity measurements [32–37] or the detection of local disturbances [8,22,23,38 – 41]. However, many other applications require an extended numerical treatment such as the finite-element method (FEM) or the finite-difference method (FDM) [42, 43], allowing to compare the predicted 2- or 3-dimensional heat flow in the sub-surface zone with the measured photothermal responses, recorded at the sample’s surface. Measuring tasks concerning hardness depths and profiles, residual stresses, cracks, remaining traces induced by manufacturing tools, damages caused by material processing and defect identification belong to the latter application spectrum [44 –51]. 3.3. Layer thickness determination If the excitation beam covers a large area compared to the thermal diffusion length m, whereas the detection spot extends less than m, the TDE is reduced to a one-dimensional problem (Fig. 5). This simplification of Eq. (1) matches applications like homogeneous samples, layered systems concerning thickness and delaminations and depth dependent material changes (e.g. one-dimensional hardness description). It requires an opaque (surface absorbing) sample or, vice versa, the optical penetration depth must be much smaller than the thermal diffusion length m.

For typical photothermal experiments, a periodically modulated excitation Q(z, t) 5 Q(z) z eivt is used. Looking at the oscillating part, which is the only one to be registered during measurement, the TDE is reduced to [Eq. (3)]:

S

D

d iv d k ~ z! T~ z! 2 T~ z! 5 2Q~ z! dz dz a ~ z!

(3)

Within a homogeneous sample, the temperature distribution follows [Eq. (4)] T~ z, t! 5 T 0e 2z/m cos~ v t 2 z/ m 2 p /4!

(4)

describing damped thermal waves with a penetration depth according to the thermal diffusion length m and an oscillation in time and space. Even this simple example shows that photothermal detectors always register two independent signals at the surface (z 5 0) : a (damped) temperature amplitude oscillating at the modulation frequency v, and a phase shift between excitation and thermal response. For the homogeneous sample, the phase shift at the surface remains constant (2p/4). For a non-homogeneous sample, the depth dependence of the thermal parameters (e.g. the thermal conductivity or, as shown in Fig. 6, the thermal impedance) may follow one of the shapes shown in Fig. 6 [30]: a simple coating (graph 1), a thermal contact resistance (graph 2, modelling e.g. an adhesion defect or a delamination) as well as a continuous transition of the thermal impedance (graph 3). The resulting temperature distribution and therefore the measured surface temperature (amplitude and phase) depend on the two combined materials, the coating thickness and any possible thermal contact resistance in between. For a photothermal characterization of unknown objects, the latter sample properties have to be extracted from the measured data. Optically opaque surfaces or interfaces like curve (1) and (2) in Fig. 6 characterize a change of the material properties without transition. These mechanical alterations (e.g. grain boundaries, microstructural pattern or coating-substrate boundaries) are correlated with abrupt changing thermal properties and, therefore, become detectable by photothermal means. For further discussions, the sample in Fig. 6

G. Goch et al./Precision Engineering 23 (1999) 9 –33

13

Fig. 7. Photothermal layer thickness determination for graphal on aluminium by frequency sweeps a) calculated phase contrasts b) measured phase contrasts c) calibration curves obtained from Fig. b.

may consist of a substrate (index s) with infinite thickness and a single layer coating (index c) with the thickness d. For simplification, the radiative energy is absorbed at the surface and is completely converted into heat. On each boundary, the thermal waves are reflected or transmitted, depending on the reflection coefficient Scs. This leads to the complex surface temperature Tc(x 5 0) [Eq. (5)] T c ~ x 5 0! 5

I 0 1 1 S cs e 22scd 2 ks c 1 2 S cs e 22scd

where

sc 5

Î

i2 p f r c k

(5)

denotes the thermal wave propagation constant (or ‘the thermal diffusion coefficient’, in mm21) of the coating and I0 describes the intensity of the exciting laser beam. The reflection coefficient Scs is given by [Eq. (6)] es ec S cs 5 es 11 ec 12

(6)

so-called ‘contrast’-signals: amplitude contrast, calculated from the quotient of the two signal amplitudes, and phase contrast, evaluated by subtracting the two signal phase shifts (both with respect to the excitation). Fig. 7a and b show the calculated (a) and measured (b) phase contrasts on a steplike coating substrate transition, realized by different layers of graphal (a solid lubricant) on aluminium, assuming Scs 5 20.9, approximately. Comparisons with destructive tests confirmed the thickness values. By extracting calibration curves (Fig. 7c) from the results of Fig. 7b, a quick, nondestructive and non-contacting layer thickness determination is available, offering microscopic lateral resolution, a thickness detection range from approximately 1 mm to several 100 mm and a very broad spectrum of object materials. Several environmental or process-related conditions, namely at the coating-bulk interface, affect the thickness determination. If the thermal contact between the layer and the substrate is disturbed, a finite temperature difference DT occurs across the thin boundary zone. The physical quantity, which describes such a defect, is the thermal contact resistance Rbd. The thermal wave reflection coefficient Scs must be extended by the contact resistance, modifying Eq. (6) to [Eq. (7)]:

where

12

e s ~1 1 i! 1 e R Îv ec Î2 s bd

e i 5 Îk i r i c i

S csd 5

is the thermal effusivity and the index i is c or s. Comparing the two photothermal signals obtained from the layered sample (limited coating thickness) and a homogeneous sample (infinite coating thickness) leads to two

This thermal contact resistance affects the thermal wave in the same way as a very thin air gap. The increased

e s ~1 1 i! 11 1 e R Îv ec Î2 s bd

(7)

14

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 10. Experimental set-up for photothermal radiometric measurements. Fig. 8. Photothermal phase contrast of layered system (graphal on aluminium) with and without a thermal contact resistant, induced by a thin PTFE layer in between.

reflectivity causes an enhanced temperature response on the surface and a phase shift of the reflected thermal wave. Fig. 8 shows some experimental results obtained with or without a PTFE-layer at the coating-bulk interface, inducing a significant thermal contact resistance. Obviously, the frequency sweep for the sample including a contact resistance yields similar results as a much larger coating: the layer appears to be thicker (about 2 . . . 4 times). Fortunately, this effect is big enough to separate it clearly from any reasonable thickness deviation, occurring at regular industrial coating processes. Fig. 9 illustrates other influences on the layer-bulk interface. Organic soiling like oil (Fig. 9a) affects the thickness determination only to a minor degree, depending on the surface roughness and the thus ‘trapped’ undesired contamination. Contrasting to this, surface roughness may cause significant deviations at the photothermal thickness determination (Fig. 9b). Its influence must be separated by a geometrical surface measurement before coating [52]. The thickness determination of a lacquer layer on steel is of a very high importance in the automobile industry for corrosion prevention. A constant layer thickness is requested all over the body. In order to install an effective control of the manufacturing process, the lacquer thickness should be measured right after its application, i.e. in the wet state. Photothermal measurements meet these requirements,

since they operate, additionally to their non-destructive performance, in a remote, non-contacting manner. Similar advantages can be expected for powder-based coating processes (laser sintering, enamelling, powder rolling). The model, based on the assumptions in Fig. 6 and the Eq. (5)–(7), combined with a small and robust experimental set-up (Fig. 10) has already proved its suitability in many industrial applications. Even effects like wear can be treated photothermally with this elementary theory, allowing to estimate or, at least, to compare the depth of wear-induced material changes with respect to an unaffected surface. Fig. 11b shows the frequency sweep of a phase contrast, measured at the flank of a used involute gear. The two basic phase signals yielding this contrast (difference) were obtained in the middle and at the outer edge of the flank, i.e. inside and outside the tooth contact area recognized by visible wear traces (Fig. 11a) [53]. 3.4. Adhesion strength determination Several photothermal experiments were performed on 1.2 mm thick, galvanically deposited nickel/palladium coatings on 0.3 mm thick copper alloy sheets (Fig. 12). These systems are used for semiconductor devices, e.g. for heat sinks. Adhesion problems, affecting the later bonding ability, occur, if dark spots in the microscopic image indicate a defect on the surface, a delamination or imperfection at the interface. In order to assess the quality of the

Fig. 9. Disturbing influences at the layer-bulk interface, obtained from graphal on aluminium a) interface with or without thin oil film b) surface roughness of bulk before coating.

G. Goch et al./Precision Engineering 23 (1999) 9 –33

15

Fig. 13. Theoretical (lines) and measured (dots) phase signal at a contact resistance between a Cu-bulk and Ni/Pd coating. Fig. 11. Photothermal measurement of flank wear at a used gear a) measuring points for phase contrast inside and outside tooth contact area (visible wear) b) phase contrast obtained from marked spots in Fig. a above.

raw material before application to semiconductor circuits, these defects should be characterized by optical and thermal methods. Exemplarily for other similar results, Fig. 12a and b show the optical and photothermal phase image of a scanned area 320 mm * 270 mm. Obviously, some extended ‘thermal defects’ could be detected. But not all of them are discovered in the optical image. Only radiometric measurements determine the real defect extensions, e.g., the wide

defected area in Fig. 12b is almost invisible in the optical microscopic image, Fig. 12a. In order to characterize the defect, frequency sweeps close to and far away from the defected areas were carried out. One example is plotted in Fig. 13 and compared with the theoretically calculated phase contrast curves. Obviously, a thermal contact resistance between the Ni-layer and the copper substrate, assumed as an air gap of 0.1 mm, fits the best to the measured values. The influence of the delamination or disbonding on the heat propagation is clearly resolved. In particular, these curves indicate a decreased heat-flux at the interface between coating and substrate, resulting in an increased reflection and phase shift of the thermal wave.

Fig. 12. a) Optical microscopy of a Nickel/Palladium coating on a Copper base showing some possible defects (scanned area: 320mm * 270 mm) b) Photothermal radiometric phase mapping of a defect, caused by a disbonding between a Nickel/Palladium coating and a Copper base material (scanned area: 320mm * 270 mm).

16

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 15. Influences of surface preparation for hard metals before TiNcoating on photothermal results.

Fig. 14. Photothermal phase signal of a Ni-Cu layered sample with a high (without passivation) and a low adhesive strength (with passivation).

However, it is difficult to prove that the assumption of an air gap is ‘true’. The same photothermal behaviour could also originate from a corrosion or contamination of the copper sheet by other materials. Here, an a-priori knowledge about the coating process or additional inspections are necessary to exclude other possible interpretations of the results. Thus, in good agreement with the model of Fig. 6, graph 2, disbonding and adhesion defects can be described as a thermal resistance that influences the heat propagation and leads to a temperature rise at the surface. In order to confirm this statement by inducing an adhesion defect intentionally, the surface of the copper substrate was passivated before the nickel plating. Fig. 14 shows that the zero-crossing-point of the phase curve occurs at lower frequencies for the passivated sample. Modeling the passivation by a thermal contact resistance, similar to Fig. 3, the measurements (dots) are in a good agreement with the theory (lines) and with a destructive tensile test of the adherence force. Problems of adhesion strength occur, when coating hardmetal or ceramic tools with wear-resistant layers like TiN. Since the bulk cutting material needs a size and shape finishing after sintering, some grinding, polishing, cleaning and other manufacturing steps precede the final coating process. Due to this surface preparation, adhesion problems occur, which sensitively react on the parameters of the preceding process (e.g. grain size, water-blasted, microblasted). Focusing on hard metal tools, these phenomena can be explained by the different behaviour of cobalt and carbides during the grinding. Carbide grains are removed from the surface, where softer cobalt fills up the hollows, resulting in an optically smooth surface after grinding. But, these cobalt particles adhere not strong enough to the bulk material. They have to be removed by ‘knocking’ them out of the surface (waterblasting, micro-blasting), since a regular cleaning shows an insufficient (or even worse) result. In terms of the thermal parameters, these blasting processes change the cobalt content in the nearest surface zone,

where, additionally, the influence of the ‘bombardment’ results in slight structure distortions (forming, stress). As illustrated in Fig. 15, photothermal signals of the TiNcoated products reflect these different surface treatments of the substrates. Investigations carried out by long-term cutting tests showed that this result correlates to the adhesion strength of the coating [54]. Photothermics, therefore, may offer a regular inspection and prediction of the adhesion quality to be expected for a coating layer, even before this coating is performed, leading to a reduction of waste and unexpected failures during cutting. 3.5. Three-dimensional description If three-dimensional treatment or local variations of material properties occur or if the lateral heat flow cannot be neglected, a 3-D-solution of Eq. (1) is necessary, as e.g. for thermal microscopy, examinations of ceramics after thermal and mechanical treatment or wear. Even influences of the finite excitation beam diameters may require a spatial description of the heat propagation within the sample, in order to interpret the recorded photothermal signals properly. Due to the structure of the TDE (1), this 2-D respectively 3-D-problem has to be described numerically, e.g. by the finite-element method (FEM) or the finite-difference method (FDM, [42,43]). Fig. 16 illustrates the principle of the FDM for the

Fig. 16. Discretization of the continuous temperature T at discrete grid points zi [42].

G. Goch et al./Precision Engineering 23 (1999) 9 –33

17

Fig. 17. Hardness and thermal parameters: a) decrease of the thermal conductivity of pure iron by alloy elements [55], b) inverse relationship between hardness and the thermal conductivity k.

one-dimensional case: Here, the TDE (1) is reduced to an ordinary differential equation with spatially dependent coefficients. The sample to be calculated (and its surrounding air) is described within the interval [z0, zN] on a regular grid with the stepsize h 5 (zN 2 z0)/N between N 1 1 grid points (Fig. 16). The temperature derivatives to the depth coordinate z within the reduced TDE (3) (periodical excitation) are replaced by difference quotients at the inner grid points zi [Eq. (8)] T i9 5

1 ~2T i21 1 T i11! 2h T i0 5

1 ~T 2 2T i 1 T i11! h 2 i21

(8)

Additionally, at the boundaries z0 and zN the oscillating part of the temperature vanishes, since the surrounding environment is at (constant) room temperature. This leads to a set of equations for the N 1 1 grid points. Using this formalism, the calculation of the temperature distribution is possible by the solution of a large set of linear equations. Since the coefficient matrix of the equation system shows a tri-diagonal structure (i.e. most of the coefficients are zero except the three main diagonals) special solution algorithms may reduce calculation time. Extending this method to a non-regular three-dimensional grid, almost any kind of photothermal problem can be treated [42]. Heat propagation in objects with rotational symmetry and with axial excitation can be

Fig. 18. Photothermal hardness measurement a) laser-hardened specimen with Vickers and radiometric inspection b) photothermal phase contrasts at tracks 1 to 8, reference: track 9 c) calibration curve obtained from b.

18

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 20. Calibration curve for the photothermal determination of the compound layer thickness after nitriding. Fig. 19. Remote radiometric measurement at surfaces with difficult access, e.g. helical gears.

described by cylinder coordinates, reducing the TDE to a 2-D problem. 3.6. Photothermal hardness measurement Microstructural changes, as they appear in the steel hardening process (e.g. in the austenite/martensitic phase conversion at case hardening) occur together with modifications of the thermal properties, i.e. the increasing hardness in a near edge layer causes a decrease of the thermal conductivity in this zone. Therefore, hardness becomes detectable by photothermal means (Fig. 17) [55]. As a first approach, a specimen as illustrated in Fig. 18a was prepared, containing nine laser-induced hardened traces (track 1 to 9). As a calibration measurement, their hardness depth and profile was obtained by Vickers tests, performed on a transverse cut of the sample (illustrated at track 9). Subsequently, the same sample was inspected with the radiometric sensor from the unaffected top side, with almost no sample preparation (sometimes a slight remove of any scaled layer). Fig. 18b shows the phase contrast signals, where the zero-crossings (as expected according to Eq. (2)) of the individual frequency sweeps appear in a strongly decreasing order, corresponding to the hardness depth. Therefore, a calibration curve (Fig. 18c) can easily be constructed. Similar procedures were repeated for all other known hardening processes like case hardening, nitriding, carbonitriding leading to promising results concerning measuring times, accuracy, robustness and costs. Thus, the use of photothermal calibration curves (destructively obtained Vickers data versus photothermal data) offers a simple and practical approach for the hardness depth or compound layer thickness determination. As experienced with a first prototype designed for industrial purposes (Fig. 23), this non-destructive principle is ready for integration in a production line. Besides its non-contact manner, the remote performance of measurement and the high (microscopic) lateral resolu-

tion offers inspection abilities, where other non-destructive methods like micromagnetics, eddy current or acoustic principles fail. Fig. 19 sketches out the radiometric inspection of a gear flank, which is not accessible for any other nondestructive hardness detector, known as yet. One special problem in hardness inspection is related to the compound layer thickness of carbonitrided steel. Carbonitriding belongs to the thermochemical treatments, established in manufacturing industry since a long time. The formation of a thin compound layer at the surface can be described as a stoechiometric carbonitride (FexCyNz). In many cases, its very high surface hardness, high corrosionresistance and very good wear properties characterize decisively the component properties. Usually, the thickness of a compound layer is measured destructively at an inspected sample. Photothermal radiometry now offers to measure the thickness non-destructively at each manufactured component. Fig. 20 shows the photothermal calibration curve (phase) for carbonitrided 20MnCr5 steel, enabling to measure the compound layer thickness fast, accurate, independent of the individual sample geometry and without any special sample preparation. In order to evaluate the shape of the hardness profile, several analytical and numerical models for a theoretical prediction of the photothermal signals were developed in the last five years [42,45,46,48,50,51,56]. The accuracy and the field of possible applications increase with the mathematical complexity and computation time of these models. Numerical methods like the FDM [42,43] also offer a 3-D evaluation of the photothermal signals. 3.6.1. Model by Thoen [56] The model proposed by Thoen assumes that the thermal conductivity inclines from the surface value k1 within the depth 2d# linearly to the value k0 of the bulk material (Fig. 21a) [Eq. (9)]:

k ~ z! 5 k 1 1

k0 2 k1 2d#

for

z # 2d#

(9)

The analytical solution of the TDE (1) includes several Bessel functions. The wide transition zone and the finite

G. Goch et al./Precision Engineering 23 (1999) 9 –33

19

modulation frequencies, the photothermally covered nearsurface layer is at first limited to its outer edge, described by the first depth value d# 9 and a corresponding diffusivity a19. Then, by decreasing the modulation frequency step by step, the covered layer increases due to Eq. (2). Since in each step the upper part of this (deeper) inspection zone was evaluated before, the measured data give access to the new values d# 0 and a10 for the lower region. This procedure is repeated for frequencies down to a few Hz or below. It enables to calculate and reconstruct any profile of the thermal diffusivity. Fig. 21. Profiles of thermal parameters: a) linear function of the thermal conductivity (Thoen), b) profile of the thermal diffusivity (Mandelis), c) piecewise linear profile of the thermal conductivity (Friedrich and Walther), d) arctangent shaped profile of the thermal conductivity (authors).

gradient at the surface lead to simulated photothermal signals up to very high frequencies (graph a, Fig. 22), which do not meet experimental results because the simulation does not predict a zero-crossing of the graph for phase contrast versus modulation frequency. At least, this model is suitable for a quick and easy determination of hardness depth. 3.6.2. Model by Mandelis [45] This model assumes the thermal diffusivity a (and thus also the thermal conductivity k) to increase by a nearly exponential graph from the surface value a1 to the bulk value a0 (Fig. 21b) [Eq. (10)]:

S

a ~ z! 5 a 1

#

1 1 De 2z/d 11D

D

2

(10)

with a diffusivity parameter D 5 Îa 1/ a 0 2 1. Again, an analytical solution is available. The model of Mandelis faces the same restrictions as the model of Thoen. But in addition, it extends the formalism to more complicated functions of the diffusivity, including a reconstruction of the hardness profile: Starting with high

Fig. 22. Phase contrasts of the thermal parameters profiles corresponding to fig. 21 ([43]).

3.6.3. Model by Walther [30,50] Walther et al. improved the model of Thoen by introducing a linear transition between the constant values k1 and k0 at the surface and the substrate, which meets experiments of hardened steel. The thermal conductivity follows (Fig. 21c) [Eq. (11)]

k~z! 5 k1 1

k0 2 k1 ~z 2 d1! for d1 # z # d2 d2 2 d1

(11)

The analytical solution leads to modified Bessel functions [30]. Any piecewise linear profile can be derived by linking profiles as in Eq. (11) together. Again, a reconstruction of the thermal conductivity profile is possible, following a similar procedure as explained for the Mandelis model. 3.6.4. Model by the authors [42,43] Since hardening belongs to the diffusion processes, a smooth profile for the thermal conductivity will be a more probable approximation. The authors used an arctangent shaped profile for the thermal conductivity. They assumed its width by a 80% transition of the total conductivity step height (Fig. 21d) [Eq. (12)]:

k ~ z! 5

k0 1 k1 1 arctan 2 3

S

D

tan~0.8 p / 2! k0 2 k1 ~2z 2 d 1 2 d 2! d2 2 d1 p

(12)

Using the FDM as described in section 3.5 enables to solve the TDE (1) for this conductivity profile. Simulation results point out that the evaluated difference between the profile of Walther and the arctangent shaped profile is within the range or less than the actually available measuring uncertainty. In addition, unique values of d1 and d2 cannot be derived from a photothermal measurement, only the mean depth d# . A convenient measuring set-up (Fig. 23) typically consists of an intensity modulated CO2 laser beam as the excitation source. The light is focussed onto the sample’s surface by a concave mirror. Since the CO2 laser operates in the infrared region, the system provides a pilot (diode) laser for adjustment, which was not necessary for the set-up of Fig. 10. Several mirrors collect the infrared radiation and

20

G. Goch et al./Precision Engineering 23 (1999) 9 –33

ical procedure developed for micromagnetic hardness determination (see section 4) is regarded as the most promising approach to solve this problem. Contrasting to this future research, the detection of local defects like hardening and cooling shadows (gas bubbles locally inhibiting cooling), weak spots or pitting (point like defects on worn gear flanks) can already run off automatically today, using a system like Fig. 7, since lateral scans offer a microscopic resolution. 3.7. Residual stress measurement Fig. 23. Measuring setup for photothermal hardness measurements.

guide it to an IR detector, recording the surface temperature directly. The collinear excitation and detection reduce the adjusting efforts to a minimum, which again meets the industrial applications. In order to verify and compare these models, aiming at a non-destructive evaluation of hardness profiles, a case hardened shaft of low carbon steel 16MnCr5 was inspected and evaluated, applying mainly Eq. (12) within a FDM calculation [57]. The real hardness profile, determined by a Vickers test for comparison, has a mean profile depth of about 0.8 mm (Fig. 24a). Then, a photothermal measurement was carried out (circles in Fig. 24b). The evaluation algorithm (FDM simulation) aims at a parameter estimation of the (unknown) mean hardness depth. An iterative approximation of the photothermal data (circles in Fig. 24b) by the simulated phase signal (solid line in Fig. 24b), regarding this mean depth as one degree of freedom leads to the (destructively confirmed) value of 0.8 mm. The resulting FDM data for the reconstructed conductivity profile is shown in Fig. 24a. Actual research efforts are concentrated on the separation of disturbing influences at the photothermal hardness profile evaluation, such as grinding belts, scaled layers, surface carbon austenite content, and residual stress (section 3–7). A multi-parameter approximation similar to a numer-

Residual stresses result from permanent elastic strains of the material lattice (tensile or compressive, i.e. expansion or contraction), which may e.g. originate from crystallographic changes, nitriding or layered systems with different physical properties. For many applications, residual stresses play an important role regarding constant quality and lifetime of parts under mechanical load and wear, since these inner stresses superimpose with the mechanically induced stress during application [58]. They may lead to an unpredictable behaviour and to sudden damages of the parts [59,60]. In terms of accuracy, residual stresses influence the geometry, which leads for precision engineering purposes to the strong requirement of predicting and controlling all stress phenomena. Furthermore, modern manufacturing techniques aim at precisely induced residual stress distributions within the surface layer in order to improve a part’s performance. However, the generation of residual stresses rather sensitively responds to a variety of parameters in precision manufacturing like grinding, rolling and hard-turning processes. Because their mechanisms are not completely understood yet, the demand for in-line measuring techniques arises. Photothermics offer the potential to perform stress measurements continuously and contactless in a non-destructive manner, in or near to production lines. Again, as explained before e.g. at the hardness inspection, the desired process or material parameters are detected by a simultaneously occurring variation of the thermal parameters. Via this correlation, residual stress also becomes detectable by photother-

Fig. 24. Case hardened shaft: a) hardness profile from Vickers indentation test and reconstructed profile of the thermal conductivity, b) measured phase contrast (o) and simulated phase contrast for the identified parameters (-).

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 25. Dependency of the phase contrast on the modulation frequency in residual stress measurements.

mal investigation. As a first experiment, radiometric measurements were carried out on elastic stresses, mechanically induced on a clamped metal strip. Thus, on the upper and lower side of the strip, predictable tensile (.0) and compressive stresses (,0) at three different values (75, 150 and 225 N/mm2) were induced. Frequency-scan measurements have been performed on both sides of the sample. Fig. 25 shows the resulting frequency dependent phase contrasts. With an increasing modulation frequency (i.e. according to Eq. (2) with a decreasing penetration depth of the thermal wave) compressive and tensile stress conditions can clearly be distinguished, since phase contrasts in the range of 5 degrees can easily be measured. Even though residual and elastic stresses have different origins, these results encourage further investigations using photothermal techniques for stress detection and evaluation. In order to illustrate the clear correlation between the photothermal signals and the stress values, Fig. 26 shows the phase-contrast at a modulation frequency of 58 kHz and the amplitude-contrast at 15 kHz. In a second step, measurements on hard-turned surfaces were carried out. For the production of e.g. drive shafts, hard-turning is one of the most promising processes in

21

Fig. 27. left: Radiometric phase signals of drive shafts with tensile (2) and compressive (1) residual stress, turned with a worn tool (2) or a new tool (1); right: Phase contrast (difference) signal ‘2-1’.

precision engineering, weighing surface quality, diameter accuracy and manufacturing costs. However, due to the wear condition of the turning tools, both compressive and tensile residual stresses may appear in the surface zone, affected by the cutting process. While compressive stresses are regarded as advantageous in terms of load stability and later performance, tensile stresses may lead to breakdown failures during enhanced loads. Fig. 27 summarizes radiometric measurements of two hard-turned shafts, one produced with a new turning tool and a second one cut with a worn tool. From X-ray measurements as described in [1,61,62], the actual surface stress values and orientation of part 1 (compressive) and 2 (tensile) were known. The phase signals of both samples are shown in Fig. 27. A significant contrast between these two phase graphs can be stated. As a minimum result, the contrast signals clearly distinguish the sign of an actual stress condition in a surface layer (i.e. compressive or tensile), which is one of the most important decisions concerning the maximum load and lifetime estimation. It qualifies photothermal techniques especially for production control on hard turning machines, where tools beyond a certain wear condition may cause a sign-change in surface stress. 3.8. Photothermal investigations of advanced ceramics

Fig. 26. Amplitude and phase contrast for different stress values induced by a varying load.

During the last few years, advanced ceramic materials gathered an increasing importance in manufacturing technologies [63]. This is mainly due to their good performance concerning hardness, ductility and wear resistance yielding e.g. increased manufacturing speeds using ceramic tools. With respect to their further applicability, reliability and functionality, advanced ceramics have to fulfil high demands on shape, accuracy and surface finishing. For most applications, grinding with diamond wheels represents the final step during the manufacturing process of ceramic parts, especially for tools. During this process, the diamond grains

22

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 28. a) Cracks and plastic deformations due to an abrasive diamond grain b) Illustration of plastic zones and cracks formed by Vickers indentations in brittle materials.

can induce micro-cracks and plastic deformations in the surface region of the ceramics. This may increase the probability of damages, when the ceramic part is exposed to any load. Actually, several groups investigate the idea to heal these micro-cracks by laser heating of the surface after the grinding process. The plastic deformation results in micro-structural changes as well as the micro-cracks influence any heat propagation in the affected region. Therefore, photothermal measuring techniques, to some extend, will yield information about the changed mechanical or structural properties of the surface and near surface region [42]. Fig. 28a reflects the mechanical impact on a near-edge zone during grinding or polishing a ceramic surface [64]. Due to the mechanical and thermal load, brittle fracture, surface defects, cracks and subsurface damages can be induced by the material removal and increased material compression. Local pressures and heat in the contact zones during the machining process cause plastic deformations. Since all these phenomena significantly influence the mechanical strength and affect the later use of ceramics, their effects on material properties have to be determined—nondestructively and contactless. As all changes appear in nearsurface layers and since they are, as explained above, combined with variations of the thermal properties, they can be detected by photothermal means. In order to investigate the extent of correlation between the manufacturing influences on ceramics (mechanical or laser material processing) and the thermal variations in near-surface altered zones, a sample preparation procedure is required, causing similar locally distributed inhomogeneities on and beneath the sample’s surface as the grinding process. It should be performed under laboratory conditions, preferably without a grinding machine tool. According to Fig. 28a, the ‘indentation fracture mechanics’ approach [64], realized by a Vickers hardness check, is mostly regarded as a reasonable choice. Since the Vickers test is supposed to simulate the dynamic interactions, caused by a grinding grain (e.g. cracks, delaminations, alterations of microcrystalline structures, varied material densifications,

porosity, etc.), with the quasi-static flaw system produced by a sharp indenter, it is sometimes labelled as a ‘model’ for the grinding process. Even though the validity of this assumption is, of course, limited (e.g. the occurrence of residual stress phenomena on ground surfaces cannot be explained by this model), Vickers indentation marks represent a suitable test object for first photothermal investigations of ceramics. A Vickers indenter was pressed with various forces (HV2 - HV50) into flat polished ceramic samples (Silicon Nitride Si3N4 WIDIANIT 2000 or Alumina Al2O3) and, for comparison purposes, into hard metal samples (WC-Co TTI25, Cermet THM) [49]. Fig. 29 illustrates exemplary a typical result, obtainable by scanning the detector (OBD or PTR) across the indentation area and by recording both, the amplitude or the phase signal. Obviously, the photothermal image shows a remarkable signal variation at the areas surrounding the Vickers distorted surface. Also, cracks starting in the rectangular corners (also traceable in the optical microscopic images) are clearly resolved. Near the edges the phase angle decreases by several degrees. Contrasting to these thermal images, no comparable

Fig. 29. Vickers (HV30) deformed area: Phase image of an OBD-measurement; Vickers indenter (163 degrees) pressed into Si3N4 (WIDIANIT 2000); area 800mm*640 mm.

G. Goch et al./Precision Engineering 23 (1999) 9 –33

23

Fig. 30. Phase (left) and amplitude (right) contrasts as functions of the modulation frequency for differently loaded Vickers indented areas.

structure could be resolved in the optical images— except the Vickers indentation square and the cracks rising from the four corners. Moreover, the increased amplitude and phase signals in the neighborhood outside the Vickers mark do not correspond to any optically visible change. These results indicate that due to the mechanical load the thermal flux into the sample is disturbed. The reasons for this behaviour are not yet completely understood. Probably, there are parallel subsurface median cracks below the sample’s surface. Or, the changes of the thermal properties correlate to modifications of the microcrystalline structure. Both effects might originate from the mechanical load. The cracks starting near the rectangular corners (Fig. 29) support the first explanation, whereas the wide area of altered photothermal signals even outside the Vickers square refers to the second one. In order to clarify this question, frequency sweeps of the amplitude and phase have been measured for various loads (HV2 to HV30), near and far away from the Vickers marks (at corresponding spots on all samples). The contrasts (‘near’ minus ‘far’, or respectively, ‘near’ by ‘far’) are shown in Fig. 30, indicating that both, the amplitude and the phase contrasts carry information about the inner structure and the varying thermal properties near the surface. The zero-crossings in the phase signal occur at decreasing frequencies for increasing loads, indicating (section 3.3) that the mechanically affected zone extends deeper for an enhancing load. For the quantitative interpretation of these results in terms of depth and profile of material changes, again a model is required, correlating thermal parameters to the several objective material parameters, describing the grinding respectively the Vickers impacts. According to Eq. (1) and (3), a changed thermal behaviour of the near-edge zone mainly originates from a decreased heat conductivity, since the density r and the heat capacity c of the ceramic material remains almost unaffected, even in the plastically formed zone (Fig. 28). This assumption is well agreed in literature. More precisely, the changed conductivity should be labelled as an ‘appearing’ or ‘effective’ heat conductivity, since it macroscopically summarizes all the possible (partly microscopic) near-surface effects, caused by the indenter or by the grinding grain, respectively. A more detailed and individual

Fig. 31. Reconstructed heat conductivity profiles of ceramic samples, loaded with different forces.

simulation of the phenomena, appearing at ground surfaces, is actually not available, since, contrasting to the hardness measurements of steel (section 3–5), neither the clear identification of the contributing effects nor their quantitative estimation with other, maybe destructive methods, is possible as yet. Nevertheless, the lone assumption of a depth-depending conductivity profile (r, c 5 const.) yields interesting, quantitative results, first evaluated with the Walther-model [41, 50] and confirmed by FDM calculations [43] (section 3–5). Knowing the unaffected thermal parameters of WIDIANIT 2000 (k0 5 0.29 W cm21 K 21, r*c 5 1.46 J K 21 cm23) the inversion procedure enables to reconstruct the depth profile of the heat conductivity, assuming r*c being constant. Obviously, a considerable decrease in k has been induced by the mechanical load. As supposed before, an increase of the load also increases the depths of reduced thermal conductivity. This may be due to a stress-induced plastic deformation followed by a network of optically invisible microcracks inhibiting the penetration of the thermal waves. Fig. 31 shows that photothermal inspections enable to estimate non-destructively and quickly the total depth of an affected ceramic surface zone and, to some extend, its internal structure, at least concerning heat propagation. Further research efforts will be necessary to map these clearly resolved profiles to convenient objective parameters, describing grinding impacts on ceramic near-edge zones. Additionally, it should be mentioned that the thickness of the distorted areas, the (most probably) plastically deformed zones, appear to extend considerably deeper (about three times) than the depths of the indenter hollows. The origin of this result is not completely understood, as yet. The reduction of k directly at the surface keeps constant for all loads applied, whereas the reduced thermal conductivity inside deeper regions depends on the load. This effect might indicate, that the thermal diffusion in deeper layers is obstructed mainly by microcracks while the near-surface region is mainly influenced by pressure densifications or plastic deformations.

24

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 34. Alteration of the domain structure due to external influence.

Fig. 32. Photothermal radiometric phase map of a laser treated ceramic surface.

Extending the application area on ceramics to other manufacturing processes, photothermal measurements enable to characterize laser modified surfaces. Several experiments on different Si3N4-ceramics were carried out. Since at regular ambient conditions every surface is covered by a thin layer of water, a pulsed Er:YAG laser was chosen as excitation source. An Er:YAG laser emits light at 2.94 mm wavelength, where water has a very high absorption coefficient. Almost all the laser light is absorbed in a very thin layer, resulting in a very strong thermal pulse, which leads to the surface modifications. Afterwards, the samples were examined by photothermal means as explained before. The photothermal phase scan (Fig. 32) reveals a highly inhomogeneous surface. Areas of lowered thermal conductivity are marked by darkened spots. Only a minor part of these inhomogeneities was visible under an optical microscope, whereas some optically visible spots were not detected in the photothermal image, indicating that an optical inspection is not sufficient for the assessment of processed ceram-

Fig. 33. Frequency sweep on a laser treated ceramic (Widianit), phase contrast.

ics. The phase contrast graph (Fig. 33) at low modulation frequencies indicates variations over a deep range within the sample. They were interpreted as an increased subsurface fracture, caused by the laser irradiation, requiring (in this case) a milder treatment to improve the surface integrity. Several other experiments were carried out on hard metals. Similar results showed that the depth and the profile of material changes due to different loads might be reconstructed from photothermal experiments. The model-based reconstruction of thermal conductivity profiles from photothermal signals enables to estimate the impacts on mechanically and laser treated ceramic surfaces. The results justify the assumption that the physical properties of the ceramic samples have been changed in the surroundings of the Vickers or laser treated areas. The impacts yield changes of thermal properties and, hence, become detectable by photothermal techniques.

4. Micromagnetic measuring methods 4.1. Physical principle Magnetic measuring principles correlate the objective surface zone parameters to a simultaneously appearing change of the electromagnetic material properties. Thus, these methods are restricted to materials with reasonable electrical conductivity (e.g. eddy current measuring methods) and ferromagnetic properties (magnetic and micromagnetic methods). Nevertheless, all ferromagnetic, ferrimagnetic and antiferromagnetic materials show a strong interaction between the magnetic dipoles and Weiss domains. Since they cover a large spectrum of technically very important workpieces, micromagnetics have gained a substantial progress during the last 10 years, due to intensive research work. These investigations were mainly focused on the non-destructive measurement of hardness and residual stress layers [1,65– 69]. Since many years it is well known, that the coercivity, saturation magnetization and the magnetic remanence occurring on a hysteresis loop are significantly affected by hardness or mechanical stresses and deformation. Fig. 34

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 35. a) hysteresis loop, b) signal pattern of Barkhausen noise, c) magnetic orientation and Blochwall.

shows the influence of macro stresses on the domain structure. The main reason for stress-induced Blochwall motions are changing elastic energy densities. On principle, a ferromagnetic body reacts on the increase of the elastic energy density due to macro stresses with a change of shape to minimize the internal energy concentration. This reaction is called magnetoelastic response to mechanically induced stresses [70]. To visualize the effects, an initially stress-free demagnetized ferromagnetic single crystal is set under stresses. Under tensile stresses the areas with magnetization directions parallel to the stresses are growing, whereas the perpendicular areas are decreasing until they completely disappear (Fig. 34). With compressive stresses the effects are opposite, areas with perpendicular orientation increase displacing parallel areas. If an external magnetization with an orientation parallel to the tensile stresses is superimposed, an increase of the area with an orientation parallel to the magnetization direction is detected. A further increase of the excitation field is leading to a progressing wall movement until the anti-parallel area is completely deleted. This effect of parallel orientation due to superposition of tensile stresses and magnetization is thus leading to the same increased Blochwall movements. Under compressive stresses the magnetization is causing a rotation of the areas in the direction of the excitation field. Therefore the resulting effects on the Blochwall are contrary and reduce the movement activity [71]. This behavior can be used to explain the hysteresis loop of ferromagnetic materials, Fig. 35. For magnetostrictive positive materials (i.e. they are lengthened in the direction of an external magnetic field) like all iron-based specimens the hysteresis loop is narrowed under tensile stresses. The Blochwalls, which separate adjacent ferromagnetic domains with different local magnetization directions, are set under movement due to an external magnetic field (Fig. 35). As a result the total magnetization of the sample is changing (Fig. 35b). With a small coil at the surface of the test workpiece the change of the magnetization can be registered as an electrical pulse. This magnetization change is not a continuous process, rather the Blochwalls move in single sudden jumps (Fig. 35a). Prof. Barkhausen was the first to observe this phenomenon in 1919. In honor of him the obtained

25

signal, added of all jump movement pulses, is called Barkhausen noise. The magnetization process is characterized by the well known hysteresis loop (Fig. 35a). Irreversible Blochwall motions lead to remaining magnetization without any field intensity H, called remanence Br. For eliminating this remanence, the application of a certain intensity of field, the coercivity HC, is necessary. The Barkhausen noise is damped in the material due to the depth it has to pass. The main reason is the eddy current damping effect, which influences the electromagnetic fields of the moving Blochwalls. The presence and the distribution of elastic stresses in the material influence the Blochwalls to find the direction of easiest orientation to the lines of magnetic flux. Subsequently, the existence of compressive stresses in ferromagnetic materials reduces the intensity of the Barkhausen noise, whereas tensile stresses will increase the signal (Fig. 34, Fig. 35b). In addition to these stress sensitive properties, also the hardness and structure state of the workpiece influence the Barkhausen noise. To separate the different material characteristics of a manufactured workpiece, different quantities deduced from the Barkhausen noise signal must be taken into consideration. 4.2. Available measuring systems Several measuring set-ups are suitable to map the various applications. The first one works according to the transformer principle. Conventionally, a larger exciting coil surrounds the test object, driving the material under inspection periodically along a full or partial hysteresis loop B(H), depending on the applied magnetic field intensity H and the frequency f. The measuring object itself represents the core of the transformer. A second probing coil registers the magnetic flux density B, which depends on the magnetic excitation, the geometry and relative position of both coils, the part geometry and its relative position within the exciting field. Thus, a precise and robust evaluation of the actual hysteresis B(H) of the sample, avoiding field distribution and geometrical influences, can only be expected, if the test object completely fills up the inner volume of the exciting coil. This restriction limits its application range to small, simple geometries, preferably with axial symmetry, and to integrating measurements. Lateral deviations of surface parameters are not detectable, whereas a depth measurement from the mm- to the mm-range is achievable. Additionally, this set-up requires a careful calibration procedure, where not only the material (including batch deviations), but also the size and shape have to match the calibration samples precisely. However, for a regular quality inspection device in a mass production line, these efforts might appear acceptable, since— once installed—the test procedure runs off fast and fully automatic. The most important set-up is based on a small sensor unit with integrated excitation and detection equipment. Fig. 36 gives an schematic view of the components of such a sensor system. The driving magnetic field, excited by a magnet in

26

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 38. Surface integrity classification in consideration of different heat treatments.

Fig. 36. Set-up for magnetic Barkhausen noise measurement.

close contact to the surface, is registered by a Hall-probe. A small coil is detecting the electrical pulses due to Blochwall motions. These two systems are integrated in a receiver sensor with a minimum contact area of approximately 16 mm2. The necessary magnet can either be integrated in the sensor unit or separated. The depth of penetration can be varied by different analyzing frequencies. It is possible to vary the exciting and the analyzing frequency range to achieve a minimum penetration depth of about 10 mm [72–76]. Fig. 37 shows a signal of the Barkhausen noise measurement with such a set-up. Two rectified curves deduced from the upper and lower slope of the hysteresis loop can be evaluated using any kind of computer based systems. A variety of quantities can be used to describe the surface integrity state. Especially by using the Hall-probe as a second sensor it is possible to detect not only the coercivity, but also the distortion of the tangential magnetizing field H. This is one additional possibility to include quantities independent from the pure Barkhausen noise measurement to describe the material properties. The distortion of the tangential field is recommended to be used for case hardening depth (chd) determination [73–75]. Also the incremental

Fig. 37. Magnetic quantities evaluated from the Barhausen.

permeability can be deduced without hardware changes. With just one further coil integrated in the sensor unit the system can be extended to a multi frequency eddy-current analyzer. At the moment prototype systems with this multi parameter configuration are tested to achieve the best surface integrity characterization [76]. The measuring time of all these systems is very short. The quantities are available within a few seconds depending on the measuring parameters. But in any case the sensor has to be adapted to the workpiece geometry. It must be possible to magnetize the material in a sufficient way and to set the sensor unit on the interesting area of the part. 4.3. Measuring results and further developments As already stated one of the limiting factors to micromagnetic surface integrity analysis is the dependence of the signal on hardness, structure and stresses of the material. Especially batch deviations of heat treated steels often lead to severe characterization problems. Still the most important process to manufacture precise parts from hardened steel is grinding. Due to demands for higher productivity, this process may cause thermal damage of the ground workpiece, which cannot be accepted in any case. Thus, grinding is predestined to be monitored by micromagnetic techniques. In a lot of different investigations the residual stress state was identified to be the most sensitive quantity to thermal damage [e.g. 77]. Fig. 38 shows the results of extensive grinding tests with different corundum wheels on case hardened steel 16MnCr5 with varying case hardening depths (chd). The heat treatment variation was determined by destructive indenter measurements on equally treated copy samples. The specific material removal rate Qw9 was changed from roughing to finishing conditions (1– 8 mm3/ mms). By using a sensor system according to Fig. 36 and taking into account the different heat treatments by measuring the distortion of the magnetizing field it is possible to classify the ground surfaces in three main areas. The resulting residual stresses of these workpieces were measured for calibration purposes by conventional X-ray techniques. Be-

G. Goch et al./Precision Engineering 23 (1999) 9 –33

27

Fig. 40. Set-up for micromagnetic in-process measurement. Fig. 39. Correlation of Barkhausen noise amplitude and etching results.

sides faultless workpieces which have only compressive residual stresses and definitely damaged parts with tensile stresses of more than 200 MPa a transitional area can be found. A decision whether parts with this result can be accepted or have to be rejected depends on the later use. The residual stress state in this transition area can either be slightly compressive or tensile. For workpieces with a high dynamical load this result can not be accepted, parts without critical demands can still be mounted. The measuring time to achieve the X-ray results is approximately 50 hours, the micromagnetic quantities are available within 60 minutes. Also extensive industrial applications of this sensor system were performed, Fig. 39. Planet wheels of a truck gear box were ground with an electroplated CBN grinding wheel at constant specific material removal rate of 5 mm3/mms. The lifetime of these wheels is limited by thermal damage induced by grinding of the flanks. With the increasing wear of the grinding wheel due to the increasing number of ground workpieces without changing the wheel the energy in the zone of contact is significantly influenced. The increasing amount of heat penetration into the workpiece is leading to an increase of residual stresses in the workpieces. The highest Barkhausen amplitudes are found for the highest workpiece number. All gears without thermal damage (detected by etching tests) lead to low Barkhausen amplitudes. As seen in Fig. 38 again specific thresholds for this mass production can be determined. It is obvious that all workpieces which were classified as “thermally damaged” lead to high Barkhausen amplitudes. High Barkhausen signal levels of more than 5 V also occurred for parts where the etching test did not point out the damage. This difference of the Barkhausen results can be explained by the depth of penetration. While the etching test is limited to pure surface damages the micromagnetic system is able to detect subsurface defects depending on the frequency range. Most recent investigations are concentrating on the development of in-process micromagnetic systems. The sensor is mounted in an external grinding machine and touching the workpiece during the manufacturing process, Fig.

40. An oil or emulsion resistant design and excellent wear protection is required to withstand the loads during grinding. First successful tests were already performed, with further development of hardware and software components this technique has even the potential to be used for process control [76].

5. Contactless topography and microhardness measurements using scanning near-field acoustic microscopy (SNAM) 5.1. Introduction Particularly in ultraprecision engineering, the three-dimensional characterization of finished surfaces and the microhardness in near-surface layers becomes increasingly important, since the microgeometric structure, roughness, and the resistance against abrasive wear influence extensively the functionality and lifetime. Just as with optical techniques, the Scanning Near-Field Acoustic Microscopy (SNAM) can be used as a contactless and non-destructive technique to inspect the topography, profile and roughness of a surface [78 – 80]. Recent projects also showed that the SNAM approach is suitable to measure microhardness of very thin layers and/or sensitive surfaces. Herein, the main advantage consists in the reduced preparation of the surfaces, where polishing the samples as requested for the more conventional hardness inspections is no longer necessary, including ground, milled or turned surfaces. Since the depth of the indentation is very small, the SNAM-microhardness measuring technique may be considered as a ‘minimal intruding’ or ‘almost non-destructive’ method. 5.2. Principle of the near-field acoustic effect Scanning near-field acoustic microscopy is one type of scanning probe technique [81,82]. The basic set-up is shown in Fig. 41. A vibrating tip attached to a quartz tuning fork works as a distance sensor. If the tip approaches to the

28

G. Goch et al./Precision Engineering 23 (1999) 9 –33

resonator, whereas d2 (D2) characterizes the viscous friction of air in the gap between the tip (position x) on the lower quartz leg (mass m) and the sample. The second one dominates in the near-field close to a sample’s surface. The damping therefore depends on the working distance d between tuning fork and surface [Eq. (13)] and [Eq. (14)]. x¨ 1 2 d x˙ 1

F k x 5 e ivt m m

(13)

D1 D2 1 2m 2m

(14)

where Fig. 41. Principle of the Scanning Near-Field Acoustic Microscopy (SNAM).

surface, both the resonance frequency and the oscillation amplitude decrease. Theoretically, a hydrodynamic model describes these two effects (Fig. 42). Due to an acoustic wavelength of approximately 10 mm (for 32 kHz excitation frequency of the fork) and a working distance of about 100 nm (Fig. 42b), the air between the specimen and the vibrating tip is pressed out and sucked in again periodically (Fig. 42c). Thus, the tip’s movements yield a viscous damping. In order to image the surface topography, the sensor scans across the surface in a constant distance (i.e. constant damping). Experimental comparisons carried out with a stylus instrument, an optical sensor and the SNAM principle (Fig. 43, Table 2) showed a very good correlation between mechanical and acoustical tracing. The SNAM-technique is therefore expected to extend the actual abilities of surface metrology significantly. 5.3. Theoretical aspects of the near-field acoustic effect In order to explain the near-field acoustic effect theoretically, a simple model assumes an harmonic and damped oscillator, excited by a driving force amplitude F and oscillating with the frequency v 5 2pf. Two damping effects must be considered (Fig. 42): d1 (D1) characterizes the internal losses and the acoustic emission of the free running

d 5 d1 1 d2 5

k: spring constant The hydrodynamic model assumes a die vibrating perpendicularly to the flat surface under normal environmental conditions (atmospheric pressure, humidity etc.). The periodic movement of this die in the viscous and incompressible gas phase (section 5.2) yields a damping effect that affects both the amplitude and the vibration frequency of the tuning fork. Therefore, a distance dependent interaction between the probe and sample can be detected while scanning the sample’s surface. Thus, the surface microgeometry can be imaged along the moved track. According to Eq. (14), the damping factor d1 can be determined indirectly via the quality factor Q and the resonance frequency v0 of the resonating quartz. The damping factor d2 is calculated by the friction-induced energy loss of the air flow (viscosity h) in the gap, integrated over one oscillation period [Eq. (15a)] and [Eq. (15b)].

d1 5

v0 2Q

(15a)

and

d2 5

3 ph R 4v

(15b)

4k Î~d 02 2 A n2! 3

R: effective radius (in m) of the tip (represented by a die in Fig. 42b and c), corresponding to the tip curvature of the tuning fork (Fig. 41) Finally, the solution of the differential equation leads to the relationship between the mean distance position d0 of the quartz leg or the tip, respectively, and the relative change between the near-field amplitude An (damped) and the far-field amplitude Af (undamped) of the tuning fork [Eq. (16)]

ÎS

d 02 5 A n2 1 3

D

An 3 ph R 4v Q 2k Af 2 An

2

(16)

5.4. Measuring system Fig. 42. Hydrodynamic model of the near-field acoustic effect. a) externally excited damped spring-mass system, b) simplified model for the hydrodynamic friction, c) air gap and vibrating quartz tip.

Fig. 41 shows a block diagram of a commercially available SNAM instrument. Usually, the probe scans the sample’s surface at a constant vibration amplitude, comparable

G. Goch et al./Precision Engineering 23 (1999) 9 –33

29

Fig. 43. Comparison between SNAM and stylus measurement on a calibrated roughness standard.

to the non-contact mode of a scanning force microscope. The electrical vibration amplitude is obtained via a rectifier and compared to a reference voltage. The amplified difference voltage controls a PZT-actuator that keeps a constant distance between the tip and the sample’s surface. But, due to the inevitable hysteresis of a piezo transducer, the input voltage of the z-actuator images the actual vertical position of the tip only by a residual error, depending on the voltage level. In order to avoid this, a second selected piezo transducer with an identical characteristic is connected to the z-voltage of the control loop, driving the ferrite core of a solenoid. The latter inductive sensors are commercially available for tactile stylus instruments, showing an extremely low linearity error (less than 1nm). The output voltage of the solenoid is monitored, while the tip scans laterally across the sample’s surface. 5.5. Surface measurement results Fig. 43 shows comparisons between the SNAM technique and a standardized stylus instrument. They give an idea about the achievable accuracy and the degree of consistency. See Table 2. Apart from a slightly increased noise level, the results coincide to a very high degree and the deviations are much less than the measurement uncertainty. Further measurements on other calibrated standards have proved the comparability and reproducibility of the SNAM method.

Fig. 44. Comparisons of SNAM and stylus measurements on a soft surface (silicone).

Besides a good agreement in terms of accuracy, the SNAM-method offers several decisive advantages, due to its non-contacting principle. Fig. 44 is an example from investigations on soft surfaces (e.g. rubber, lacquer). The same track was measured twice. While the contacting tip of the stylus instrument removes or shifts particles of the surface by being pressed into it, the SNAM technique yields fully reproducible results. Contactless measurements also enable to inspect scratch sensitive optical surfaces (mirrors and lenses) and extremely hard materials like sintered carbide, ceramics or diamond surfaces in addition to soft surfaces such as skin and plastic coatings. In SNAM measurements, contrasting to autofocus inspections, no mirroring effects or variations in the refrac-

Table 2 Comparisons between the conventionally measured roughness and the SNAM results, all values are in mm Roughness parameter

Nominal values

Stylus TKL 100

SNAM

Ra Rz Rt

0.28 0.95 0.97

0.28 0.95 0.96

0.28 1.00 1.09

Fig. 45. Area scan across the front end of an optical fibre plug, area: 1.25*1.25 mm2.

30

G. Goch et al./Precision Engineering 23 (1999) 9 –33

Fig. 47. SFM-scan of a SNAM-indentation.

Fig. 46. Microhardness measurement on a turned surface; a) profile before the indentation; b) profile after the indentation; c) subtraction profile.

tion index affect the results. An area scan across the frontend of an optical fibre plug illustrates this option in Fig. 45. Obviously, the fibre exceeds the upper metallic plane. Such a sample would cause significant errors at autofocus or other optical measurements due to the considerable difference in the refractive index and absorption coefficient between the glass fibre and the outer metallic material. 5.6. Principle of microhardness measurements with the SNAM Conventional hardness measurements (such as Brinell, Vickers and Rockwell) determine the material resistance via the indentation of a diamond tip. The mentioned procedures are standardized and extensively used in industry. They all belong to the indirect measuring methods, correlating hardness with the applied force and geometric features of the resulting indentation marks. Thus, every conventional hardness inspection technique needs, additionally to a careful calibration, a smooth, preferably flat and polished, surface [83]. As a major disadvantage, this sample preparation alters the material and geometrical properties in the near-edge zone. Especially in precision and ultraprecision engineering with a relevant layer thickness in the mm- and sub-mmrange, the preparation-induced material changes may cause significant measuring errors. SNAM-microhardness measurements avoid the time-

consuming, cost-intensive, accuracy-decreasing and, sometimes, even destroying preparation steps. The SNAM-microhardness approach leads to a threestep inspection procedure [84]. First, the surface topography is imaged at a certain track (Fig. 46a). Due to the nondestructive principle and due to conventionally available guide ways, allowing a tracing repeatability in the nm- and sub-nm-range, the identical measuring track can be retrieved at a low error, excluding any significant displacement of the sensor or damage to the surface or the tip. So, as a second step, the vibrating tip is pressed (during its second scan along the same profile) several times into the inspected surface with a controlled and reproducible force. Thus, a few small indentations are generated within the line probed before (Fig. 46b). Third, mapping the same line again and subtracting line 1 from line 2 results in the indentation profile alone (Fig. 46c). Consequently, the measuring technique can be used for inspecting the surface and microhardness simultaneously. 5.7. Experimental results of microhardness measurements The extensions and depths of the indentations are very small. The damaged zones are not enlarged by any preparation procedures. The already discussed results of Fig. 46 were obtained on a conventionally turned surface. Similar results were achieved with milled, ground and drilled surfaces. Fig. 47 shows the highly resolved 3-D view of a SNAM-indentation, performed by a SFM measurement. Comparing Fig. 48a (zoom of SNAM indentation in Fig. 46c) and Fig. 48b (SFM-measurement) both registered at one indentation mark, confirms that the SNAM-evaluated indentation profiles fulfil high accuracy standards, even without any sample polishing. Experimental verifications on different solid materials (copper, zinc, brass, aluminium and bronze) proved that the depths and widths of the SNAM-indentations correlate with the Vickers hardness measurements. A strong dependency of the measured indentation depths upon the (conventionally obtained) hardness confirmed that the depths and the widths of the indentations depend on the applied load in the expected linear relationship. Furthermore, some investigations on very thin and soft galvanic layers on a hard substrate showed the expected bulk material influences.

G. Goch et al./Precision Engineering 23 (1999) 9 –33

31

support in preparing this paper. Also the support of Prof. Dr. R. Hocken, University of North Carolina (UNC), CharlotteUSA, and Prof. Dr. E. Brinksmeier, University of BremenGermany is gratefully appreciated. References

Fig. 48. Detailed profile of one SNAM-indentation; a) zoom of fig. 46; b) measured with a SFM-instrument.

6. Conclusions This paper gives a survey about the state-of-the-art of photothermal, micromagnetic and near-field acoustic measurements meeting industrial purposes. All of them are non-destructive and non-contacting measuring methods correlating the material and structural properties of the near-edge zone with thermal, electromagnetic and/or mechanical parameters and their spatial distribution. They have gained a substantial progress during the last 10 years, due to intensive research work. Today they cover a wide spectrum of materials, coating features (thickness, adhesion strength, local disturbances), hardness profiles, residual stresses and wear. Due to the increasing importance of thin near-surface layers from the sub-micrometer to the millimeter-range, they are supposed to improve manufacturing control, quality inspection and wear behaviour estimation for all kinds of coatings, edge hardening, sub-surface damages and residual stresses. Several prototypes and recently commercially available instruments are actually tested under industrial environments, promising a substantial progress for the assessment of surface integrity in the near future.

Acknowledgements The authors wish to gratefully acknowledge the research cooperation with Prof. Dr. H.K. To¨nshoff and A. Mohlfeld, Institut fu¨r Fertigungstechnik und Spanende Werkzeugmaschinen (IFW), University of Hannover-Germany, leading to some of the results presented herein above, and their

[1] Brinksmeier E. State-of-the-art of non-destructive measurement of subsurface material properties and damages. Prec Eng 1989;11(4):211–24. [2] Busse G, Walther HG. Photothermal non-destructive evaluation of material with thermal waves. In: Mandelis A, Editor. Progress in photothermal and photoacoustic science and technology. New York: Elsevier, 1992, 207–98. [3] Munidasa M, Mandelis A. Photothermal imaging and spectroscopy. In: Mandelis A, editor. Progress in photothermal and photoacoustic science and Technology. New York: Elsevier, 1992, 299 –367. [4] Mandelis K, Michaelian H. Special section on photoacoustic and photothermal science and engineering. Opt Eng 1997;36(2):301–534. [5] Mandelis A, editor. Nondestructive evaluation (NDE), progress in photothermal and photoacoustic science and technology. Englewood Cliffs, New Jersey: PTR Prentice Hall, 1994. [6] Ash EA. Scanned image microscopy. London: Academy Press, 1980. [7] Hartikainen J, Jaarinen J, Luukkala M. Microscopic thermal wave non-destructive testing. Advances in Optical and Electron Microscopy 1991;12:313–59. [8] Seidel U. Quantitative Auswertung Photothermischer Messungen zur Erkennung und Charakterisierung von Inhomogenita¨ten in Festko¨rpern. PhD Thesis, Jena: Friedrich-Schiller-Universita¨t, 1996. [9] Schmitz B, Goch G. Charakterisierung von Oberfla¨chen und randnahen Bereichen mit photothermischen Meßverfahren, Jahrbuch Oberfla¨chentechnik, Band 52. Zielonka A, editor. Heidelberg, Germany: Hu¨thig Verlag, 1995, 239 – 81. [10] Kanstad SO, Nordal PE. Experimental aspects of photothermal radiometry. Can J Phys 1986;64:1155– 64. [11] Schmitz B, Geerkens J, Goch G. Photothermal radiometry and beam deflection studies—a metrological tool for material characterization and manufacturing control. In: Harding KG, Stahl HP, editors. Industrial optical sensing and metrology: applications and integration, Bellingham, Washington, USA: SPIE-P Series 1993;2066:41–52. [12] Boccara AC, Fournier D, Jackson WB, Amer NM. Photothermal deflection spectroscopy and detection. Appl. Optics 1981;20:1333– 44. [13] Murphy JC, Aamodt LC. Photothermal spectroscopy using optical beam probing: Mirage effect. J Appl Phys 1980;51:4580 – 8. [14] Walther HG, Friedrich K, Haupt K, Muratikov K, Glazov A. New phase interference technique applied for sensitive photothermal microscopy. Appl Phys Lett 1990;57:1600 –1. [15] Almond DP, Patel PM. Photothermal science and techniques, physics and its applications. London, Great Britain: Chapman and Hill, 1996. [16] Rosencwaig A, Opsal J, Smith WL, Willenborg DL. Detection of thermal waves through optical reflectance. Appl Phys Lett 1985;46: 1013–5. [17] Ehlert A, Kerstan M, Lundt H, Huber A, Helmreich D, Geiler HD, Karge H, Wagner M. Selected applications of photothermal and photoluminescence heterodyne techniques for process control in silicon wafer manufacturing. Opt Eng 1997;36(2):446 –58. [18] Jackson W, Amer N. Piezoelectric photoacoustic detection: theory and experiment, J Appl Phys 1980;51:3343–53. [19] Tam AC. Applications of photoacoustic sensing techniques. Rev. Modern Physics 1986;58(2):381– 431. [20] Rosencwaig A. Photoacoustics and photoacoustic spectroscopy, New York, NY, USA: John Wiley, 1980. [21] West GA. Photoacoustic spectroscopy. Rev. Scientific Instr. 1983;54: 797– 817. [22] Friedrich K, Haupt K, Seidel U, Walther HG. Definition, resolution, and contrast in photothermal imaging. J Appl Phys 1992;72(8):3759 – 64.

32

G. Goch et al./Precision Engineering 23 (1999) 9 –33

[23] Seidel U, Haupt K, Walther HG, Burt J, Bein BK. Analysis of the detectability of buried inhomogeneities by means of photothermal microscopy. J Appl Phys 1994;75(9):4396 – 401. [24] Carslaw HS, Jaeger JC. Conduction of heat in solids, 2nd ed. London: Oxford University Press, 1959. [25] Rosencwaig A, Gersho A. Theory of the photoacoustic effect in solids. J Appl Phys 1976;47:64 –9. [26] Murphy J, Aamodt LC, Spicer JWM. Principles of photothermal detection in solids. In: Mandelis A, editor. Progress in photothermal and photoacoustic science and technology, New York: Elsevier, 1992, 41–94. [27] Bennett CA, Patty RR. Thermal wave interferometry: a potential application of the photoacoustic effect. Appl Opt 1982;21(1):49 –54. [28] Patel PM, Almond DP. Thermal wave testing of plasma-sprayed coatings and a comparison of the effects of coating microstructure on the propagation of thermal and ultrasonic waves. J Mater Science 1985;20:955– 66. [29] Egee M, Dartois R, Marx J, Bissieux C. Analysis of semi-transparent layers by modulated photothermal radiometry: Application to the bonding and thickness control of enamel coatings. Can J Phys 1986; 64(9):1297–302. [30] Friedrich K, Seidel U, Walther HG, Karpen W, Busse G. Proposal for photothermal characterization of boundaries between layer and substrate. Res Nondestr Eval 1993;5:31–9. [31] Ritter R, Reick M, Schmitz B, Goch G. Nondestructive and contactless evaluation of surface coatings and adhesion defects by photothermal radiometry. SPIE, 1996;2782:662–73. [32] Kuo PK, Lin MJ, Reyes CB, Favro LD, Thomas RL, Kim DS, Zhang Shu-Yi, Inglehart LJ, Fournier D, Boccara AC, Yacoubi N. Mirageeffect measurement of thermal diffusivity, Part I: Experiment. Can J Phys 1986;64(9):1165–7. [33] Kuo PK, Sendler ED, Favro LD, Thomas RL. Mirage effect measurement of thermal diffusivity, part II. Theory. Can J Phys 1986; 64(9):1168 –71. [34] Rantala J, Wei L, Kuo PK, Jaarinen J, Luukala M, Thomas RL. Determination of thermal diffusivity of low-diffusivity materials using the mirage effect method with multiparameter fitting. J Appl Phys 1993;73(6):1333– 44. [35] Salazar A, Sanchez-Lavega A, Ocariz A. Photothermal characterization of anisotropic materials with buried principal axes. Opt Eng 1997;36(2):391–9. [36] Glazov A, Muratikov K. Simulations of photodeflection measurements of thermal diffusivity of solids, wave optics approach. J Appl Phys 1994;76(6):3279 – 84. [37] Power JF, Schweitzer MA. Diffraction theory of the impulse mirage effect. Opt Eng 1997;36(2):521–34. [38] Goch G, Seidel U, Schmitz B, Walther HG. Applications of the photothermal measurement techniques for the detection of subsurface defects and thermal inhomogeneities. Proceedings of the XIII IMEKO World Congress, Torino, Italy. From Measurement to Innovation, September 1994, Vol. 2, Padua, Italy: CLEUP (Cooperative Libraria Editrice Universita` di Padova, 1504 –9. [39] Reigl M, Gapp M, Schmitz B, Stein J, Goch G, Seidel U, Walther HG. Investigations of subsurface structures and buried inhomogeneities by photothermal radiometry, quantitative infrared thermography QIRT 94, Balageas D, Busse G, Carlomagno GM, Editors. Sorrent, Italy 1996, 232–7. [40] Seidel U, Haupt K, Walther HG, Burt J, Munidasa M. An attempt towards quantitative photothermal microscopy. J Appl Phys 1995; 78(3):2050 – 6. [41] Seidel U, Lan TTN, Walther HG, Schmitz B, Geerkens J, Goch G: Quantitative characterization of material inhomogeneities by thermal waves. Opt Eng 1997;36(2):376 –90. [42] Goch G, Reigl M. Application of the finite-element-method and the finite-difference-method to photothermal inspections. J Appl Phys 1996;79:9084 –9.

[43] Reigl M. Methoden zur Quantifizierung photothermischer Signale. PhD thesis, Universita¨t Ulm, 1997. [44] Vidberg J, Jaarinen J, Riska DO. Inverse determination of the thermal-conductivity profile in steel from thermal surface data. Can J Phys 1986;64:1178 – 83. [45] Mandelis A, Peralta SB, Thoen J. Photoacoustic frequency-domain depth profiling of continuously inhomogeneous condensed phases: theory and simulations for the inverse problem. J Appl Phys 1991; 70:1761–70. [46] Ma TC, Munidasa M, Mandelis A. Photoacoustic frequency-domain depth profilometry of surface-layer inhomogeneities: Application to laser processed steels. J Appl Phys 1992;71:6029 –35. [47] Munidasa M, Ma TC, Mandelis A, Brown SK, Mannik L. Nondestructive depth-profiling of laser-processed Zr-2.5Nb alloy by IR photothermal radiometry. Mater Sci Eng 1992;A159:111– 8. [48] Fivez J, Thoen J. Thermal waves in materials with linearly inhomogeneous thermal conductivity. J Appl Phys 1994;75:7696 –9. [49] Goch G, Geerkens J, Reick M, Schmitz B. Analysis of surface layer variations by photothermal means. J Physique IV, 1994;C7-4:319 –22. [50] Lan TTN, Seidel U, Walther HG. The determination of microstructural depth profiles by means of photothermal measurements: Theory. J Appl Phys 1995;77:4739 – 45. [51] Lan TTN, Seidel U, Walther HG, Goch G, Schmitz B. Experimental results of photothermal microstructural depth profiling. J Appl Phys 1995;78(6):4108 –11. [52] Goch G, Ritter R, Schmitz B. Haftungsuntersuchungen an Beschichtungen mit photothermischer Radiometrie, IX. Oberfla¨chenkolloquium, Chemnitz 1996, 415–26. [53] Goch G, Seidel U, Schmitz B, Reigl M, Walther HG, Lan TTN. Photothermal hardness measurement for shafts, bearings and gears, VDI-Ber. 1996;1230:1031– 42. [54] Karpuschewski, B. Private communication concerning experiments, carried out at the IFW-institute University Hannover-Germany 1997. [55] Spur G, Sto¨ferle T. Handbuch der Fertigungstechnik, Band 4/2, Wa¨rmebehandeln. Munich-Germany: Carl Hanser Verlag, 1987. [56] Mandelis A, Schoubs E, Peralta SB, Thoen J. Quantitative photoacoustic depth profilometry of magnetic field-induced thermal diffusivity inhomogeneity in the liquid crystal octylcyanobiphenyl. J Appl Phys 1991;70(3):1771–7. [57] Reigl M, Ku¨mpel J, Goch G. Finite-difference-method for depthprofiling of photothermal measurements. Proceedings of the “Quantitative Infrared Thermography (QIRT 96)”, Stuttgart Germany 1996; Pisa Italy, Eurotherm Series No. 50, Edizioni ETS, 1997. [58] Kloos KH. Eigenspannung, Definition und Entstehungsursachen. Z Werkstofftech 1979;10:293–302. [59] Macherauch E. Eigenspannungen, Materialpru¨f. 1978;20:28 –33. [60] Hauk V, Hougardy E, Macherauch E, Tietz H-D. Residual stresses, report of DGM Informationsgesellschaft mbH, Germany, 1993. [61] Eigenmann B, Macherauch E. Ro¨ntgenographische Untersuchung von Spannungszusta¨nden in Werkstoffen, Teil I. Mat.-wiss. U Werkstofftech 1995;26:148 – 60. [62] Eigenmann B, Macherauch E. Ro¨ntgenographische Untersuchung von Spannungszusta¨nden in Werkstoffen, Teil II. Mat.-wiss. U Werkstofftech 1995;26:199 –216. [63] To¨nshoff HK, Trumpold H, Brinksmeier E, Wobker HG. Evaluation of surface layers of machined ceramics. Ann CIRP 1989;38(2):699 –708. [64] Malkin S, Ritter JE. Grinding mechanisms and strength degradation for ceramics. J Eng Ind 1989;111:167–74. [65] Crostak HA, Bischoff W, Polaud B. Induktive Pru¨fverfahren, at survey 89/1 angewandte Technik, Wegweiser fu¨r die zersto¨rungsfreie Pru¨fpraxis. 1989; 16 –25. [66] Theiner WA, Altpeter I, Becker R. Zersto¨rungsfreie Ermittlung der Einha¨rtetiefe nach Randschichtha¨rten, Ha¨rterei-Technische Mitteilungen. 1989;44(4):231–5. [67] Crostak HA, Bischoff W. Stand und Mo¨glichkeiten der zersto¨rungsfreien Qualita¨tssicherung, Ha¨rterei-Technische Mitteilungen. 1989; 44(4):221–30.

G. Goch et al./Precision Engineering 23 (1999) 9 –33 [68] Fru¨hauf B. Magnetinduktive Pru¨fgera¨te, Erfahrungen aus der Sicht des industriellen Anwenders, Ha¨rterei-Technische Mitteilungen. 1994;49(4):231–5. [69] Grotz K, Steidinger R. Magnetinduktive Werkstoffpru¨fung, eine wirkungsvolle Methode zur Qualita¨tspru¨fung in der Produktion, Bleche Rohre Profile, 1990;37(11):858 – 61. [70] Theiner WA, Grossmann J, Repplinger W. Zersto¨rungsfreier Nachweis von Spannungen insbesondere Eigenspannungen mit magnetostriktiv angeregten Ultraschallwellen, Messung der Magnetostriktion mit DMS bzw. mittels des Barkhausenrauschens, Report of Deutsche Gesellschaft fu¨r Zersto¨rungsfreie Pru¨fung, Germany, 1980;245–354. [71] Tiitto S. On the influence of microstructure on magnetization transitions in steel, Acta Politechnica Scandinavica, Applied Physics Series 119, Helsinki 1977. [72] Qualimax, Zersto¨rungsfreie Ermittlung von Ha¨rte und Ha¨rtetiefe. Report of C. Stiefelmayer company, Denkendorf-Germany, 1996. [73] Karpuschewski B, Teiner WA. Eht-Messung: Zersto¨rungsfreie Bestimmung der Einha¨rtungstiefe an Zahnra¨dern, Final Report of Research Project No. 161, Forschungheft der Forschungsvereinigung Antriebstechnik e.V., 1994, 425. [74] Karpuschewski B. Mikromagnetische Randzonenanalyse geschliffener einsatzgeha¨rteter Bauteile, PhD Thesis, Universita¨t Hannover 1995, Fortschritt-Berichte VDI, Reihe 8, Meß-, Steuerungsund Regelungstechnik Nr. 498. [75] Pitsch H. Die Entwicklung und Erprobung der Oberwellenanalyse im Zeitsignal der magnetischen Tangentialfeldsta¨rke als neues Modul des 3MA-Ansatzes, Report of IzfP. Saarbru¨cken—Germany, Nr. 900107-TW, 1990.

33

[76] To¨nshoff HK, Karpuschewski B, Regent C, Hinkenhuis H. Potentiale ¨ berwachung und Regelung von Schleifprozessen, Schleiftechder U nik im Wettbewerb, Schleiftechnisches Kolloquium, Aachen—Germany 1997, 8/1-13. [77] Brinksmeier. Prozeß- und Werkstu¨ckqualita¨t in der Feinbearbeitung, Habilitationsschrift, University Hannover—Germany 1991. [78] Guethner P, Fischer U, Dransfeld K. Scanning near-field acoustic microscopy, Appl Phys 1989;B48:89 –92. [79] Goch G, Volk R. Contactless surface measurements with a new acoustic sensor. Ann CIRP 1994;43(1):487–90. [80] Goch G, Pelzmann A, Volk R, Schmitz B. Contactless surface investigations with the near-field acoustic effect. In: Bonis M, Alayli Y, Revel P, McKeown PA, Corbett J. editors. International progress in precision engineering, Proceedings 8th IPES, Compie`gne-France 1995, 170 –3. [81] Binning G, Rohrer H, Gerber C, Weibel E. Surface studies by scanning tunneling microscopy. Phys Rev Lett 1882;49:57– 61. [82] Gu¨ntherodt H.-J., Wiesendanger R, editors. Scanning tunneling microscopy, Vol. I-III. In: Springer Series in Surface Science. BerlinGermany: Springer Verlag, 1994. [83] Dengel D. Zur Problematik der Ha¨rtepru¨fung du¨nner Hartstoffschichten, 8. Internationales Symposium Ha¨rtepru¨fung in Theorie und Praxis, VDI Ber. 1990;804:11–27. [84] Schmitz B, Kra¨mer I, Goch G, Volk R. Microhardness measurements with a scanning near-field acoustic microscope. In: Kunzmann H, Wa¨ldele F, Wilkening G, Corbett J, McKeown P, editors. Proceedings of the 9th international precision engineering seminar, BraunschweigGermany 1997, 153–5.