In the Rockwell hardness test, the measure of the hardness is not an indentation surface but an indentation depth. Either a carbide ball or a rounded diamond cone with a tip angle of 120° and a tip radius of 0.2 mm serves as the indenter. The indentation depth can be read directly from a dial gauge via the traverse path of the testing machine.

In the Rockwell hardness test, an indenter is pressed into the material to be tested. The indentation depth serves as a measure of the hardness!

The measuring process of the Rockwell test is carried out in three steps. First, the indenter is placed on the surface to be tested with a so-called preload F₀ of 98 N. In this way, the influences of possible setting processes in the sample and any clearance in the measuring instrument can be compensated. After the preliminary test force has been applied for a short time, the dial gauge is set to zero (reference level). The actual hardness value can then be determined.

The actual test load F₁ is applied in addition to the preload and the indetor penetrates the material with the total force F=F₀+F1. The test load to be set is taken from table books depending on the indenter and the material to be tested.

After the indenter has penetrated the material with a given total force, the test force F₁ is removed again. Finally, the material is only stressed by the preload F₀ and the indenter is slightly raised again by the elastic material behavior of the sample. However, contact with the sample remains. The remaining indentation depth h (in mm) while maintaining the preload F₀ is finally measured and used to determine the hardness value.

Depending on the indenter (diamond cone or carbide ball), the unit-less hardness value HR can be determined using the following formulae:

\begin{align}
\label{rockwellhaertewert_1}
&\boxed{HRC, HRA =100-\frac{h}{0.002}} ~~~~~\text{Rockwell hardness for diamond cone} \\[5px]
\label{rockwellhaertewert_2}
&\boxed{HRB, HRF =130-\frac{h}{0.002}} ~~~~~\text{Rockwell hardness for carbide ball} \\[5px]\end{align}

Testing with diamond cones

For diamond cones, the hardness value is obtained from a reference depth of 0.2 mm. Depending on how far the penetrated indenter reaches this reference depth, a corresponding hardness is assigned to the material. The complete penetration of the indenter to the reference depth obviously means a very soft material; this is assigned a hardness value of 0. If, however, the diamond cone does not penetrate the material at all, an extremely hard material is present, to which the full hardness value 100 is assigned. The scale follows an even subdivision of 0.002 mm (2 µm), so that reaching half the reference depth also corresponds to half the maximum hardness value (Rockwell hardness value 50). When diamond cones are used, the Rockwell scale is thus divided into 100 degrees of hardness.

The testing method with a diamond cone is particularly suitable for very hard materials such as hardened or tempered steels. Apart from special procedures, the preload is 98 N (10 kp). The actual test load can vary depending on the application.

In process variant C, the specimen is subjected to a test load of 1373 N (140 kp). However, especially when testing thin sheets, there is a risk that the material will only bulged out on the opposite side due to the high test force and thus falsify the measurement result.  For this reason, variant A was introduced for diamond cone testing, which operates with a reduced test force of 490 N (50 kp). In addition, there is the less common variant D, in which the hardness value is determined using a test load of 883 N (90 kp). For its determination also equation (\ref{rockwellhaertewert_1}) is used.

Note that in practice Rockwell hardness is not determined by equation (\ref{rockwellhaertewert_1}) and (\ref{rockwellhaertewert_2}) but read directly from a calibrated scale.

Testing with carbide balls

However, when testing relatively soft materials, the diamond cone would penetrate far too deeply into the material and would lie outside the reference depth of 0.2 mm. Therefore, soft surfaces are tested with carbide balls and the reference depth is extended to 0.26 mm. However, the division of the degrees of hardness in steps of 0.002 mm is maintained. This results in hardness values in the theoretical range of 0 (full indentation depth to 0.26 mm) to 130 (no indentation depth) when using carbide balls.

When using a carbide ball for hardness testing, a main distinction is made between process variants B and F. In contrast to diamond cone testing, they are suitable for softer metals such as construction steels or brass. The ball has a diameter of 1.5875 mm (=1/16 inches). In all process variants the preload is 98 N (10 kp). The procedures differ again only in the actual test load. In variant B the test load is 883 N (90 kp) and in variant F the test load is 490 N (50 kp). Due to its reduced test load, process variant F is particularly suitable for very soft materials such as copper or thin sheets.

Comparability of hardness values

Hardness values obtained with different process variants cannot be compared with each other. In addition, the hardness value obtained with a certain process method must lie within a certain range. For values outside this range, the method should be changed because the indenter has either penetrated too strongly or too weakly into the material.

• HRC: 20 to 70
• HRA: 20 to 88
• HRB: 20 to 100
• HRF: 60 to 100

Advantages and disadvantages

The advantage of Rockwell hardness testing is the relatively short testing time and good automation capability, as the measured values are determined directly from the indentation depth without optical measurement under a microscope. This process is therefore particularly suitable for automated production.

A disadvantage of the Rockwell process is the relatively small depth range. Even small indentations in the material can lead to significant deviations in the indentation depth and thus in the hardness value. In addition, it is particularly difficult to differentiate between materials with high hardness values due to the small differences in depth.

Indication of the hardness value

The standard-compliant specification of Rockwell hardness consists of the hardness value and the test method.

For the Vickers hardness test, a square base pyramid with a opening angle of 136° is used as the indenter (opening angle = angle between two opposite surfaces of the pyramid). The angle was chosen so that the Vickers hardness values are comparable to a certain degree with the Brinell hardness values (applies to approx. 400 HBW or 400 HV). The diamond pyramid is pressed into the material surface with increasing force and maintained for about 10 to 15 seconds when the desired test force is reached. As with the Brinell hardness test, the ratio of test force F and indentation surface A (pyramid surface area) serves as hardness value for the Vickers method:

\begin{align}
\label{vickershaerte}
&HV=\frac{0.102 \cdot F}{A} \\[5px]
\end{align}

In the Vickers hardness test, a four-sided diamond pyramid is pressed into the material to be tested. The indentation surface left behind serves as a measure of the hardness value!

The factor 0.102 again comes from the no longer used unit “kilopond” (see Brinell hardness test). The indentation surface can be determined from the diagonals of the indentation left behind. With this indentation diagonal \(d\) (in mm) and the test force \(F\) (in N), the Vickers hardness value HV is then determined as follows:

\begin{align}
\label{vickershaertewert}
&\boxed{HV =\frac{0.1891 \cdot F}{d^2}} ~~~~~\text{Vickers hardness} \\[5px]
\end{align}

The indentation diagonal \(d\) is determined by the mean value of the two diagonals \(d_1\) and \(d_2\) at right angles to each other:

\begin{align}
\label{durchmesserdiagonale}
&\boxed{d=\frac{d_1+d_2}{2}} \\[5px]
\end{align}

Validity

To avoid the risk of material bulging on the opposite side of the sample, the thickness should not fall below a certain minimum value. The minimum thickness depends on the expected hardness of the material and the test load.

In addition, the distance \(a\) from the center of the indentation to the edge of the sample should be at least 2.5 times the value of the indentation diagonal \(d\) to prevent the material from flowing sideways:

\begin{align}
\label{mindestrandabstand}
&\boxed{a \ge 2.5 \cdot d} \\[5px]
\end{align}

Furthermore, the distance between two adjacent indentations for steel and copper samples should be at least as far apart as three times the diagonal length of an indentation (six times for aluminum samples). This is to eliminate the influence of work hardening phenomena around the area of the indentation.

\begin{align}
\label{mindestprobenabstand}
&\boxed{\Delta a \ge 3 \cdot d} \\[5px]
\end{align}

Comparability of hardness values

In contrast to a ball (as in Brinell hardness test), a pyramid always provides to a certain extent geometrically similar indentations even with different test loads. Thus, with identical samples, the double force also leads to a double indentation surface. As a ratio of force and indentation surface, the hardness value is therefore always identical despite different test loads*. However, the independence of the hardness value from the test load does not apply to low test loads. In this case, the elastic deformation accounts for a larger proportion of the total deformation. As a result, the remaining pyramid indentation is smaller and thus pretends a higher hardness value.

*) This is not the case with Brinell hardness test. There the double force (higher load factor) would lead to a different hardness value for the same ball used. 

Therefore, Vickers hardness values should only be compared with each other if they were determined with the same test loads. A harder material always requires higher test loads than a softer material. Depending on the expected hardness of the material, different test load ranges are prescribed. A distinction is made between three ranges of loads.

On the one hand, the so-called macro test range with test loads between 49.03 N (5 kp) and 980.7 N (100 kp), within which the hardness values are practically independent of the test load (“macrohardness”).

On the other hand, the micro test range is differentiated between 1.961 N (0.2 kp) and 29.42 N (3 kp). Such a load range is used for thin surface layers and sheet metals as well as for finished parts in order not to damage the components too much (“microhardness”).

In special cases, the nano test range between 0.098 N (0.01 kp) and 1.961 N (0.2 kp) is also used (“nanohardness”). The pyramid tip used offers an additional advantage over the ball in the Brinell process, since the pyramid-shaped indentation leaves sharper edges even at low indentation depths and can thus be better measured. At low indentation depths, therefore, the accuracy of the Vickers test increases compared to the Brinell hardness test.

In contrast to the Brinell hardness test, the Vickers test method is suitable for all hardness ranges, i.e. from very soft to very hard materials. In addition, this method can also be used for thin sheets or thin surface layers, which makes it a universal hardness testing method.

The Vickers hardness test is suitable for soft to very hard materials and especially for thin sheets!

Indication of the hardness value

The standard-compliant specification of Vickers hardness consists of the hardness value, the test force and the application time. The latter can be omitted with the standard time of 10 to 15 seconds.

Both the Brinell and Vickers hardness test use the indentation surface left behind as a hardness measure. The indentation geometry is determined by a light microscope. This usually requires a glossy surface so that the indentation is clearly visible. It may be necessary to polish the sample before testing. Therefore, these processes are generally not suitable for automated production. For this reason, the Rockwell hardness test was developed.

Introduction

In many applications, components should have not only a high strength but also a high wear resistance. This generally applies whenever two or more components are in moving contact with each other. These include, for example, gears, shafts, bolts, pins, etc.

High wear resistance ultimately means a hard surface, so that the surface is not damaged in contact with adjacent components and thus wear is kept to a minimum. For this reason, characteristic values are required to characterize the hardness of a material. In order to obtain such parameters, hardness must first be defined:

Indentation hardness is the resistance of a material to penetration by an indenter (indentation resistance)!

According to this definition, all hardness testing methods are ultimately based on the same principle. An indenter (e.g. ball, cone, pyramid, etc.) is pressed with a certain force into the material surface to be tested. The indentation hardness value is determined from the indentation left behind.

Depending on the material to be tested and the given boundary conditions, different hardness tests have developed, whose respective measured values generally cannot be converted into one another. Therefore, hardness values can only be compared if they have been obtained by identical test procedures. The most important procedures and their advantages and disadvantages are explained in more detail below:

• Brinell hardness test (explained in this article)
• Vickers hardness test
• Rockwell hardness test

Specially prepared specimens or real components can be used for hardness testing, provided that their functionality is not impaired due to the indentation left behind.

Determination of the hardness

In Brinell hardness testing, a hard metal ball (carbide ball) is pressed into the material surface to be tested within approximately 10 seconds as the force increases. The applied test force is maintained for 15 to 20 seconds so that the material can settle during this time and the measurement provides reproducible and comparable test results. The indentation left behind on the material surface is then determined under a light microscope. The ratio of testing force \(F\) and the indentation surface \(A\) (spherical segment) serves as a measure for the Brinell hardness value HBW:

\begin{align}
\label{brinellhaerte}
&HBW=\frac{0.102 \cdot F}{A}  \\[5px]
\end{align}

With the Brinell hardness test, a carbide ball is pressed into the material. The indentation surface left behind serves as a measure of the hardness!

The factor 0.102 in the equation is due to the unit “kilopond” or “kilogram-force” (1 kp ≙ 9.807 N), which was used in the past but is no longer permissible today. Therefore, the unit kilopond was replaced by the physically correct unit “Newton” with the corresponding conversion factor of 0.102 (=1/9.807).

The indentation surface \(A\) can be determined by the diameter \(D\) of the penetrator ball and by the indentation diameter \(d\) left behind using the following formula:

\begin{align}
\label{kugelsegment}
&A=\frac{\pi}{2} \cdot D \cdot \left(D-\sqrt{D^2-d^2} \right)  \\[5px]
\end{align}

By combining equation (\ref{kugelsegment}) and equation (\ref{brinellhaerte}), the unit-less Brinell hardness HBW is calculated as a function of the applied penetration force \(F\) (in N) and the ball diameter \(D\) (in mm) and the indentation diameter \(d\) (in mm) as follows:

\begin{align}
\label{brinellhaertewert}
&\boxed{HBW =\frac{0.204 \cdot F}{\pi \cdot D \cdot \left(D-\sqrt{D^2-d^2} \right)}}  ~~~~~\text{Brinell hardness} \\[5px]
\end{align}

Due to the anisotropy in the deformation behavior, it can happen that there is no exactly circular imprint on the material surface. Then the indentation diameter \(d\) is determined from the mean of two indentation diameters \(d_1\) and \(d_2\) at right angles to each other:

\begin{align}
\label{durchmesser}
&\boxed{d=\frac{d_1+d_2}{2}}  \\[5px]
\end{align}

Validity

To prevent the material from being pushed over the edge of the specimen during testing and therefore pretending a lower hardness value, the center of the indentation should be at least as far from the edge as 2.5 times the diameter of the indentation.

\begin{align}
\label{mindestabstand}
&\boxed{a \ge 2.5 \cdot d}  \\[5px]
\end{align}

If several hardness tests are carried out on one single specimen, care must be taken to ensure that the indentations do not fall below a minimum distance from each other. Otherwise, the measurement result would be influenced by hardening phenomena that occur around the respective indentations. This distance should not be less than 3 times the indentation diameter.

\begin{align}
\label{mindestabstand_proben}
&\boxed{\Delta a \ge 3 \cdot d} \\[5px]
\end{align}

In order to obtain comparable results, the indentation diameter \(d\) should not be smaller than 24 % and not larger than 60 % of the indenter diameter \(D\):

\begin{align}
\label{mindestdurchmesser}
&\boxed{0.24 \cdot D \le d \le 0.6 \cdot D} \\[5px]
\end{align}

If the indentation diameters are too large and lie in the range of the test ball diameter, the test ball is pressed too deeply into the material. A further penetration then hardly produces a larger indentation diameter, which then leads to no longer reproducible hardness values due to measurement inaccuracies in the diameter determination.

If, on the other hand, the indentation diameter is too small compared to the test ball diameter used, however, the ball is hardly pressed into the material. Blurred edges are the result, from which it is very difficult to determine the indentation diameter left behind. Due to the low deformation, elastic portions are particularly high, so that the indentation diameter decreases relatively strongly when the ball is lifted off. The hardness values obtained from small indentation diameters are no longer valid, as well as those from large diameter values.

Load factor

For the above mentioned reasons of too much or too little penetration, the surface pressure between the ball and material sample must therefore not be too high and not too low. Comparable results for different materials are only given if the test was carried out with the same stress intensity. Due to the larger surface area, larger test balls also require higher test forces compared to smaller test balls, in which the forces are distributed over a smaller surface.

In order to do justice to this fact, the so-called load factor \(B\) is defined. The load factor is ultimately defined by the ratio of test load to test ball surface and can be regarded as a kind of “surface pressure”:

\begin{align}
\label{beanspruchungsgrad}
&\boxed{B =\frac{0.102 \cdot F}{D^2}} ~~~~~\text{load factor} \\[5px]
\end{align}

For comparability of the hardness values obtained with different test balls on different materials, the load factor \(B\) must have the same value in all cases!

The factor 0.102 results again from the obsolete unit “kilopond”. In contrast to softer materials, hard materials must be tested with a higher load and thus with a higher load factor in order to maintain the diameter range according to the equation (\ref{mindestdurchmesser}).

The load factor is standardized to the values 1 – 2.5 – 5 – 10 – 15 – 30. Depending on the expected hardness, reference values for the load factor used can be found in the table books. The test force \(F\) (in N) to be set can then be determined with equation (\ref{beanspruchungsgrad}) depending on the dimensionless load factor \(B\) and the selected ball diameter \(D\) (in mm).

Test balls

Sintered carbide balls with a standardized diameter of 10 mm, 5 mm, 2.5 mm, 2 mm or 1 mm are available as test balls for Brinell hardness testing. Small diameters are necessary for thinner sheets, as balls that are too large would only bulge out the material on the opposite side of the sheet. In principle, the sample thickness \(s\) should be at least 8 times the penetration depth \(h\):

\begin{align}
\label{mindestprobendicke}
&\boxed{s \ge 8 \cdot h} ~~~~~\text{minimum thickness of the sample} \\[5px]
\end{align}

Large test balls are also not suitable for determining the hardness of thin surface layers. In such cases, there is a risk that the surface layer will only be pressed into the underlying base material.

Larger ball diameters are necessary when testing coarse-grained, heterogeneous microstructures (e.g. cast iron). Due to the large sphere, as many individual (heterogeneous) structural components as possible are involved in the deformation, resulting in a hardness value that covers the entire microstructure and not just individual phases. This testing of heterogeneous microstructures is a big advantage of Brinell hardness testing. In principle, however, it is only suitable for soft to medium-hard materials.

Brinell hardness testing is particularly suitable for thicker, heterogeneous materials in the low to medium hardness range! Thin sheets cannot be tested with the Brinell hardness test!

The Brinell hardness test is not suitable for very hard materials or hardened surface layers because the ball does not penetrate sufficiently into the material. Higher test loads are not the solution at this point, as this leads to deformation of the carbide ball. The flattening of the ball results in a larger indentation diameter and thus pretends a softer material.

Even very thin sheets cannot be tested due to the aforementioned bulging of the material on the opposite side of the sheet. In order to close this gap, a new hardness test method was developed by Vickers, which is explained in a separat article.

Indication of the hardness value

The standard-compliant specification of Brinell hardness consists of the hardness value (HBW), the ball diameter (in millimeters), the test force (in kiloponds) and the application time (in seconds). These values are given without units and separated by slashes. The indication of the time can be omitted if the test was performed with the standard application time of 10 to 15 seconds.

Empirical relationship between tensile strength and hardness for non-alloy steels

For unalloyed and low-alloyed steels there is an empirical relationship between the Brinell hardness HBW and the tensile strength \(\sigma_u\). This relationship means that the tensile strength (in N/mm²) corresponds approximately to 3.5 times the Brinell hardness value:

\begin{align}
\label{zugfestigkeit_brinell}
&\boxed{R_m \approx 3.5 \cdot \text{HBW}} \\[5px]
\end{align}

With eddy current testing, electrically conductive materials can be examined for pores, inclusions and cracks in the area near the surface. Layer thickness and microstructure tests are also possible with this method.

Eddy current testing is based on the principle of electromagnetic induction. For this purpose, a constantly changing magnetic field (primary field) is first generated in an field coil by an alternating current.

This alternating magnetic field induces an annular current flow near a metallic surface, also known as eddy current. This eddy current also changes constantly in accordance with the alternating primary magnetic field of the field coil. The eddy currents can be regarded analog to the circular currents of the field coil and thus also generate a magnetic field (secondary field).

The secondary magnetic field induced in the workpiece by eddy currents is directed in the opposite direction to the external primary magnetic field of the field coil (Lenz’s law). The secondary field thus weakens the primary field and a somewhat weaker overall magnetic field is produced.

Depending on how good or bad the surface to be tested conducts the current, more or less strong eddy currents are formed. This in turn has a direct effect on the strength of the secondary field and thus on the overall field. The magnetic properties of the surface to be tested also influence the secondary field and thus the overall field. At cracks, pores or other inclusions, the electrical and magnetic properties usually change very strongly, so that the total magnetic field changes there. The change of the magnetic field serves as proof of defects.

Note that ultimately only the overall magnetic field actually exists physically. The primary field and the secondary field itself do not exist, since they superpose and only the overall field will be present.

In order to detect the overall field or rather its change, the induction effect is again used. The constantly changing overall field creates an induction voltage in induction coil which is implemented in a detector. This induction voltage in the induction coil ultimately serves as a measurement value, since the induction voltage at the induction coil also changes as the overall magnetic field changes.

The induction coil is integrated directly inside the field coil. To increase the measurement sensitivity, two induction coils can also be connected against each other. In this case, it is not the induction voltage of the induction coil that is measured, but the much more sensitive difference in the two induction coil voltages.

Introduction

Like the dye penetrant inspection, magnetic particle inspection is also a method for examining surface defects such as cracks. In contrast to the dye penetrant inspection, flaws near the surface that do not reach directly to the surface can also be localized. Magnetic particle testing can only be applied to ferromagnetic materials and is based on the principle of deflecting magnetic field lines at defects. A distinction is made between two inspection methods, which are explained in more detail below:

• magnetic field flow method
• current flow method

Magnetic field flow method

First, the component to be examined is thoroughly cleaned and the test site magnetized with a yoke. Magnetic field lines are formed in the component between the ends of the yoke. In the crack-free state, the field lines run in a straight line and parallel to each other near the surface.

However, at imperfections such as cracks, a stray magnetic field is created, which causes the magnetic field lines to be increasingly forced out of the interior of the workpiece. In this area, there is a particularly large magnetic effect on the surface. Iron particles applied to the surface therefore adhere well to these imperfections.

After magnetization, a ferromagnetic iron oxide powder is applied as test medium, which is mixed with an oil-based fluorescent carrier liquid (test suspension). By adding the fluorescent agent, the flaws can be made particularly visible under ultraviolet light.

For optimum flaw resolution, the defect should be aligned perpendicular to the magnetic field lines so that the effect of a magnetic stray field is as large as possible. Elongated Cracks that are parallel to the magnetic field direction, however, can hardly be made visible due to the low scattering effect. However, in order to detect even such unfavourable defects, the test benches can be switched to the current flow mode at the touch of a button. This method will be explained in more detail in the next section.

Current flow method

Instead of “flooding” the workpiece directly with a magnetic field, a current flow is first generated in the workpiece. For this purpose, an electric field is introduced via the yoke instead of a magnetic field. Due to the electrical conductivity of the metallic workpiece, an electrical current is generated. This current flow in turn causes a magnetic field whose field lines form concentrically to the current flow (“magnetic field of a current-carrying wire”).

Compared to the magnetic flow method, the magnetic field is now perpendicular aligned to it, so that even the previously unfavourably oriented flaws can now be optimally resolved.

The dye penetrant inspection (or liquid penetrate inspection) can be used to visualize surface defects of components. Since the component to be examined is not damaged during the inspection, the dye penetrant method is one of the non-destructive material tests. This method is mainly used to inspect possible cracks, e.g. on turbine blades.

The surface under inspection is first thoroughly cleaned to remove dirt or other deposits from the cracks. The very low-viscosity colorant (flaw detection ink) is then applied. Due to the capillary effect, the flaw detection ink penetrates deeply into the cracks.

After an exposure time of about 10 minutes, the surface can be cleaned with a special cleaner. However, only the surface is cleaned, while the low-viscosity colorant remains in the cracks due to the strong capillary effect.

In order to make the ink and thus the cracks ultimately visible, a dye developer is now applied. The developer sucks the ink liquid out of the cracks and combines with it. Under visible or ultraviolet light, the cracks appear very clearly and can be assessed.

The dye penetrant method requires that defects reach to the surface so that they can be penetrated with the detection ink. Flaws below the surface of the workpiece cannot be detected with this method. In the case of ferromagnetic materials, however, magnetic particle inspection can be used here.

Only cracks that reach the surface can be inspected with the dye penetrant method!

Introduction

Ultrasonic testing is a non-destructive testing technique because the workpieces or components to be tested are not damaged during the test. If there are no complaints after the test, the component can continue to be used. Ultrasonic tests are therefore often used for weld inspections.

The most common form of ultrasonic testing is based on the pulse-echo method. Acoustic waves in the ultrasonic range with typical frequencies between 0.2 MHz and 100 MHz are induced pulse-like into the workpiece to be tested by a probe. The pulse duration is usually a few microseconds. These sound pulses propagate in the workpiece with characteristic sound velocity (depending on the material). At locations where the propagation speed of the ultrasonic pulses changes, the sound waves are reflected. This is then referred to as an echo.

Echoes occur particularly at imperfections such as pores, cavities or cracks, since the speed of sound in the metal structure is approximately 10 to 20 times higher than that of air. Such reflection points are also referred to as reflectors. In contrast to flaw echos (or defect echos), reflections also occur on the rear wall of the test material (backwall echo).

The sound pulses reflected from the backwall or from imperfections are registered by a receiver. From the elapsed time between emission of a sound pulse and registration of a flaw echo, the location (depth) of the echo point and thus the position of the imperfection can be determined, provided that the propagation speed of the sound waves is known (depending on the material). It should be noted that the measured time results from twice the distance until the echo location is reached, since the sound pulse needs the same time for the return path after reflection.

In ultrasonic testing, sound pulses are passed through the workpiece, which are reflected at imperfections (flaw echo). In this way, defects can non-destructively be localized!

In order that the probe can induce the ultrasonic pulses into the workpiece and the entire sound pulses are not already reflected on the outside of the test material (input echo), the entire area of the probe must rest completely on the workpiece surface. However, due to the surface roughness of each workpiece or probe, this is not easily possible. For this reason, a gel-like coupling agent is applied to the workpiece. This completely wets the surface of the probe and the workpiece, thus enabling the sound pulses to be emitted and received again with low reflection. In order to achieve the necessary coupling effect in special automated processes, the entire component can also be immersed in water.

Coupling agent is used to introduced the ultrasonic waves into the workpiece with low reflection and to receive them again with low reflection!

When inspecting workpieces, the probes used are particularly important and must be carefully selected depending on the application. In order to better understand the different requirements on the probes, the generation and propagation of ultrasound is described in the next sections.

Generation and reception of ultrasound

The principle of ultrasonic generation is based on the piezoelectric effect. Historically, piezoelectricity was first discovered on quartz (silicon dioxide, \(SiO_2\)). It was found that mechanical stress (compressive or tensile stress) leads to a shift of the charge concentrations in the atomic structure of the quartz. Electric dipoles are formed, which lead to a voltage between the top and the bottom of the quartz. Not only silicon dioxide but also many other materials such as artificially produced ceramics show a piezoelectric effect. Such materials are generally referred to as piezoelectric crystals.

The piezoelectric effect is the generation of a voltage by mechanical deformation of certain materials (piezoelectric crystals)!

The piezoelectric effect can also be reversed! This means that when an external voltage is applied, the crystal is deformed. Depending on the polarity, the piezoelectric crystal is either compressed or stretched. This reciprocal piezoelectric effect (or indirect piezoelectric effect) can therefore be used to convert electrical energy into mechanical energy.

If an alternating voltage is applied to a piezoelectric crystal, the compressive and tensile stresses alternate permanently. As a result, the crystal oscillates. The forced oscillation frequency goes hand in hand with the frequency of the alternating voltage. This forced oscillation is particularly strong when the AC voltage frequency corresponds to the natural frequency of the crystal. In such a case resonance occurs and the piezoelectric crystal oscillates at maximum. The natural frequency of the crystal depends mainly on its geometry. Thus, the natural frequency of the crystal can be adjusted to the desired value by changing the geometry.

When exposed to an alternating voltage, the piezoelectric crystal oscillates like a diaphragm of a loudspeaker, and transmits these oscillations either to the surrounding air or, as in the case of ultrasonic testing, to the component to be tested. In this case, the piezoelectric crystal serves as a transmitter of (ultra)sonic waves.

By applying a high-frequency alternating voltage to a piezoelectric crystal, it carries out vibrations in the ultrasonic range and thus serves as a transmitter of ultrasonic waves!

Piezoelectric crystals can also serve as a receiver of sound waves. When sound waves hit the piezoelectric crystal, they cause compressive and/or tensile stresses inside (in the same way that the human eardrum is stimulated by sonic wave). The electrical voltage connected to the deformation serves directly as a receive signal. Piezoelectric crystals therefore serve both to generate and to receive ultrasonic waves.

Propagation of ultrasound

Depending on the medium, sound waves can propagate in different ways. In gaseous, liquid or solid materials, sound waves can propagate in the form of pressure fluctuations. The matter particles are compressed locally (“positive pressure”) and dilated (“negative pressure”) and transfer the corresponding impulse to the adjacent particles. The oscillation direction of the individual particles is identical to the direction of propagation of the wave. In this case one also speaks of longitudinal waves (also called compressional wave or compression wave).

In longitudinal waves, the individual particles oscillate longitudinally to the direction of wave propagation!

Besides the longitudinal wave propagation, there is another possibility of sound propagation in solids. In addition to compaction or dilution, the material can also undergo a “lateral” displacement (analogous to the swinging up and down of a rope). Such a lateral displacement has an effect on the adjacent particles, which also experience a force directed sideways and are thus gradually made to oscillate. In this case, the oscillation direction of the individual particles is perpendicular to the direction of the wave propagation. Such a wave is referred to as s a transverse wave (shear wave).

In transverse waves (shear waves), the individual particles oscillate transversely to the direction of wave propagation.

Transverse waves can only propagate in media in which the individual particles are elastically connected to their neighboring particles by binding forces. Only then can the individual particles “entrain” the neighbouring particles as they move up and down. Consequently, this only applies to solids, as there are sufficient intermolecular binding forces compared to liquids and gases.

In solids, sound can propagate both as longitudinal wave and as transverse wave; in liquids and gases, however, only as longitudinal wave.

The propagation velocity of a sonic wave is called speed of sound. The speed of sound depends primarily on the medium in which the sound propagates. The velocity at which the individual particles oscillate back and forth (called particle velocity) has no influence on the propagation velocity of the wave. The particle velocity only determines the frequency of the sound wave. However, this does not cause the wave to propagate faster or slower. Strictly speaking, the speed of sound also depends on the temperature of the medium. In the case of solids, it must also be taken into account whether the sound wave propagates as longitudinal or transversal wave.

The speed of sound depends mostly on the medium in which it propagates!

Ultrasonic probes

The principle of emitting and receiving ultrasonic waves is technically implemented in ultrasonic probes. Different probes have developed depending on the application. The most important ones will be discussed in more detail in the following sections.

Normal probes

The simplest type of probes are so-called normal probes. These probes have only one single piezoelectric element (transducer), which is switched alternately as transmitter and receiver.

During the emission of an ultrasonic pulse, reception is basically not possible. Only when the ultrasonic pulse has been fully transmitted, the piezoelectric element can be switched back to the receive mode after a short damping period of the oscillating piezoelectric crystal. During this period of time, the emitted ultrasonic pulse has already propagated in the test material and may have already been reflected at imperfections. However, the probe could not receive these reflected waves at all, since the probe was not yet switched to “receive mode”.

This period of time within which no signal can be received is also referred to as dead time. The dead time is composed of the transmission time of an ultrasonic pulse and the damping time until the oscillations of the piezoelectric crystal have settled before the probe can be switched to receive mode. In connection with the speed of sound, the dead time results in a so-called dead zone below the workpiece surface. Imperfections within this dead zone cannot be detected by the probe.

Normal probes alternately transmit and receive ultrasonic waves; they are not suitable for testing near-surface imperfections due to the resulting “dead zone”!

To keep the dead zone to a minimum, the probe should switch to receive mode as quickly as possible after emitting the ultrasonic pulses. For this the vibrating piezoelectric crystal must be strongly damped after the emission. For this reason, a damping block (backing) is located at the rear of the crystal, which stops the vibrations as quickly as possible after the emitting pulse. At the same time, oscillations of the entire probe (due to sound waves radiated from the rear of the piezoelectric element) is avoided.

As mechanical protection, the piezoelectric crystal is separated from the workpiece surface or from the applied coupling agent by a wear resisting plate. This protection layer prevents damage to the piezoelectric element during ultrasonic testing. In addition to the coupling agent, the wear resisting plate itself provides good sound coupling to the workpiece. Probes for smooth workpiece surfaces are usually equipped with harder (more wear-resistant) protective layers, while for rough surfaces rather softer (less sound dissipative) protective layers are used.

Delay line probes

The normal probes cause a relatively large dead zone just below the workpiece surface. However, a high resolution near the surface is indispensable when inspecting near-surface imperfections or when measuring layer thicknesses.

For this reason, probes can be equipped with an integrated delay line that largely shifts the dead zone out of the test material. In this context one also speaks of delay line probes oder delay line transducers. The delay line is made of sound-conductive plastic. A matching layer is located between the piezoelectric element and the delay line. This ensures good sound transmission with good damping properties at the same time, so that a separate damping block can often be omitted.

Delay line transducers have an integrated delay line within which the “dead zone” is shifted out of the workpiece surface and thus also near-surface imperfections can be detected!

When using delay line probes, reflections always occur when the emitted beam enters or leaves the the delay line. This can lead to unfavorable signal overlaps with a possible flaw echo. For this reason, the TR-probes described below have been developed.

Transmitter-Receiver probes (TR probes)

In Transmitter-Receiver probes (TR probes for short), transmitter and receiver are integrated at once and acoustically separated from each other by a sound barrier. These probes can be used to transmit and receive simultaneously by separate control units. Due to the acoustic barrier, the transmitting pulse does not leave a disturbing echo for the receiver from the delay line. This enables the detection of near-surface imperfections and the measurement of thin wall thicknesses.

So that a flaw echo does not occur at the transmitter but can be detected at the receiver, the sound pulse must be radiated slightly obliquely into the workpiece. This is the only way that the flaw echo can reach the spatially separated receiver again at an angle. For this reason, the transmitter and receiver are slightly tilted towards each other. However, a dead zone forms, within which the flaw echoes are reflected past the receiver. The more the transmitter and receiver are tilted, the smaller the dead zone becomes, but deeper imperfections cannot be resolved as well.

The depth of the maximum resolution lies at the intersection of the acoustic axes of the transmitter and receiver. This is where the measurement sensitivity is greatest. At a relatively steep inclination, the greatest measurement sensitivity is therefore very close to the surface and the dead zone is relatively small. However, due to the small overlap of the sound paths, the sensitivity decreases considerably at deviating depths. A good resolution over longer distances can be achieved by smaller angles of inclination, but this increases the dead zone.

Transmit-Receive probes (TR probes) can transmit and receive ultrasonic waves simultaneously. Depending on the inclination of transmitter and receiver, the measurement sensitivity can be optimized to a certain depth!

When determining the flaw depth, it should be noted that TR probes cause a V-shaped sound path in the workpiece. The sound path and propagation time of the ultrasonic signal are therefore greater for TR probes than for normal probes. Furthermore, it should be noted that, due to the inclined intromission of sound, refraction occurs at the interface to the test material, i.e. the incident beam changes its direction as soon as the sound wave enters the workpiece (refraction is a general phenomenon of waves when penetrating a medium with a changed propagation velocity)!

Angle probes

The inspection of weld seams requires an oblique intromission of sound so that the interface between weld seam and base material can be examined for cracks. For this reason, angle probes were developed which radiate the sound waves into the workpiece at a certain angle. Frequently used intromission angles are 45°, 60° and 70°.

Angle probes are particularly suitable for the inspection of weld seams due to the oblique scanning!

In general, angle probes are equipped with delay lines, which are then also referred to as delay wedges. Angle probes can also be equipped with TR probes, so-called angle transmit-receive probes (angle TR probe).

In addition, a change in angle by refraction is connected to the inclined intromission of sound. Since the emitted sound waves usually propagate slower in the delay wedge (or in the wear resisting plate) than in the workpiece, a refraction away from the normal of the boundary takes place. Furthermore, the sound wave no longer propagates as a longitudinal wave but as a transverse wave. The longitudinal wave component is totally reflected at the boundary due to the greatly differing propagation velocity.

Phased array probes

Phased array probes are basically made up of a multitude of individual transducers. Such probes are therefore also referred to as group transducers. In a group there are e.g. 16, 32, 64 or more oscillators. The individual transducers can be controlled separately in time. This allows a wide range of applications since the transmission characteristics can be specifically influenced. Phased array probes can only be used with special testing devices that have the appropriate software and hardware to control the probes.

Phased array probes contain a large number of individually controllable transducers. This allows the transmission characteristic to be specifically influenced!

The basis for influencing the transmission characteristic is Huygens principle, which states that the envelopes of the individual ultrasonic waves form the new wave front.

The animations below show different timing controls. If the transducers are controlled one after the other, an angular acoustic irradiation is obtained. The sound field can also be permanently swivelled during the test. The flaw (also called discontinuity) then becomes visible at different angles and allows a limited indication of the flaw size. This is usually not easily possible with simple probes.

Furthermore, with phased array probes the ultrasonic waves can be focused to a certain depth. The focus can also change over time, so that it moves permanently through the test sample.

Advantages, disadvantages and limitations of ultrasonic testing

Ultrasonic testing is not only used for detecting flaws but also for wall thickness measurement or for measuring the layer thickness of components subject to wear. It is particularly important for weld seam inspection by using an angle probe. Ultrasonic testing can be easily automated and, in comparison to the X-ray process, carried out without protective equipment. Test depths of several meters are theoretically possible depending on the acoustic properties of the test sample.

In addition to the flaw detection, ultrasonic testing also takes place for wall thickness and layer thickness measurements!

Although the position of a flaw can be determined very reliably with ultrasonic testing, the flaw size cannot be determined easily. A laminar flaw should be scanned as perpendicular as possible in order to be able to resolve it optimally. In order to estimate at least the approximate flaw dimension, the flaw should be scanned from different angles. The resulting flaw echo can then be compared with the echoes of reference flaws. Phased array probes can perform this function of the different beam angles to a limited extent. However, such a comparison method does not provide a 100% reliable statement.

Depending on the spatial orientation of the flaws, they are difficult to detect. Likewise, the flaw size is usually not clearly determinable!

The resolution of possible flaws is limited depending on the ultrasonic frequency used. Flaws that are smaller than half the wavelength of the ultrasonic pulses can no longer be physically resolved. As the wavelength decreases with increasing frequency, smaller flaws can therefore only be resolved by higher sound frequencies. However, the higher the frequency, the higher the sound absorption, so that the high-frequency ultrasonic pulses may not be able to reach deeper flaws.

Only flaws that are larger than half the wavelength of the ultrasonic waves can be physically resolved!

Sheets for deep-drawing applications must have very good cold formability, i.e. they must be able to be strongly deformed without cracking. Corresponding deformation characteristics from the tensile test such as elongation at break and reduction in area have only limited significance at this point, since the tensile test permits only low degrees of deformation due to the relatively massive specimen. Sheets, on the other hand, are formed many times more strongly and are subject to a multi-axial stress during loading.

For this reason, sheets are subjected to a special technological test, the so-called cupping test (according to Erichsen), to characterize their deep-drawing capability. A steel ball with a diameter of 20 mm is pressed into a plate, which is held in position by a blank holder. As the force increases, the ball is pressed in more and more and the sheet metal bulges out – in contrast to the Brinell hardness test – on the opposite side. The maximum depth \(f\) to which the steel ball is pressed, without cracking the sheet metal, is used to assess the deep-drawing capability. The cupping test can be used to test sheets up to 3 mm thick.

But not only the deepening is used to characterize the deep-drawing ability but also the appearance of the deep-drawn sample. Thus, the sheet surface may become very roughened during the test, which can be undesirable in some cases despite good deepening.

In the creep rupture test, material samples are subjected to a constant stress at elevated temperature and the strain is measured as a function of time. In some cases, however, such as for bolted connections, the loading at high temperatures is just the other way round. After the screw has been tightened, the screw shaft is subjected to constant strain, while creep causes the stress to decrease over time. This “stress relief” is also called relaxation and gradually leads to the screw becoming “loose”.

In order to assess such a relaxation behavior of materials, samples are clamped and stretched in a fixed device at elevated temperature in so-called stress-relaxation tests. The strain is maintained constantly by the clamping while the temporal drop of the stress is measured. The characteristic value obtained from the relaxation test is called the relaxation strength.

The relaxation strength indicates for a certain temperature to which value the stress falls at a given strain after a certain time!

Creep

If components are subjected to a constant tensile load under normal conditions below the yield point, this usually results in a constant (elastic) elongation over time. Above the yield point, plastic deformations occur, which, however, can come to an halt due to strain hardening effects. Under normal conditions, no further expansion of the component will occur in this case either. Despite plastic deformation, the component does not fracture. However, these behaviours only apply on condition that the component is not exposed to excessively high temperatures. Materials often behave differently at elevated temperatures!

At elevated temperatures, the material is usually “softened” and both the yield strength and tensile strength decrease. Up to certain temperatures, this can be demonstrated in the tensile test with heated samples. The yield strengths obtained at elevated temperatures are then referred to as hot yield strengths.

Elastic stress limits above which plastic deformations occur at elevated temperatures are referred to as hot yield strengths!

However, the hot yield strengths can only be used as a basis for dimensioning of components if the creep described below cannot occur or can at least be neglected.

For example, high temperatures can cause materials to lose their elastic limit under prolonged stress. The material lengthens irreversibly over a longer period of time, no matter how low the tension will be. This plastic deformation over a longer period of time at elevated temperature and under static stress is also referred to as creeping.

Creep is the irreversible deformation of a material at elevated temperatures, even at the lowest stresses!

The cause of creep is explained in more detail in the section Creep mechanism. Creep always increases with the following influencing variables:

• load intensity,
• load duration
• temperature

In tensile tests, creeping cannot really be measured, since the specimen is deformed relatively quickly under rapidly increasing stress to fracture. The time-controlled creeping is then not relevant. This also applies to the hot yield strengths determined in heated tensile tests!

For this reason, special tests have to be carried out which are run at elevated temperature for a relatively long period of time under constant tensile stress, so that creeping can be detected and measured. These so-called creep rupture tests or stress rupture tests can cover a period of several years (!) in long-term tests. The creep rupture test is of great importance, for example, for materials for turbine blades or for screws of pressure vessels.

The creep rupture test (stress rupture test) is used to measure the high-temperature strength of materials that are subjected to constant stress at elevated temperatures over a longer period of time.

Note that the phenomenon of creep also occurs at relatively low temperatures. However, the processes required for such a creeping are usually so slow that creeping at room temperature has no practical importance for metallic materials. Only in the range from approx. 40 % of the melting temperature (in Kelvin) is a technically relevant creeping to be expected. For structural steels, this means temperatures above approx. 400 °C.

Creep curve

In the stress rupture test, the time \(t\) at constant temperature is determined, which leads at a given stress \(\sigma\) to a certain plastic strain \(\epsilon\) or to fracture of the specimen. If the plastic deformation of the sample is additionally measured at regular intervals (creep strain), this test variant is then referred to as creep rupture test. This procedure is repeated on several identical specimens with different stresses, whereby the test temperature remains unchanged in all cases. The obtained temporal course of the creep strains are also referred to as creep curves.

In the stress rupture test, the duration until the specimen breaks is determined at constant stress and temperature. In the creep rupture test, the temporal course of the creep strain is recorded too (creep curves)!

From the creep curves, the time leading to a certain plastic strain or fracture can then be transferred to a separate time-stress diagram. This type of diagram is also referred to as creep diagram. For a given period of use, the stress can be determined from this diagram which leads to a certain creep strain (creep strain limit or creep limit for short) or to fracture of the specimen (creep strength). Note that creep diagrams only ever apply to a certain temperature!

A creep limit in the specification \(R_{p1/10,000h/400°C}\) = 170 N/mm² means that the material lengthens plastically by 1 % at a temperature of 400 °C when subjected to a stress of 170 N/mm² for 10,000 hours. The specification of a creep strength of \(R_{m/10,000h/500°C}\) = 74 N/mm² means that the material can withstand a stress of 74 N/mm² at a temperature of 500 °C for a total of 10,000 hours before it fractures.

Note that with creep rupture tests there are no permanent strengths as with fatigue tests, i.e. the specimen will sooner or later always suffer plastic deformation or breakage, no matter how low the stresses.

Creep mechanism

The reasons for creep are thermally activated processes. Thus, diffusion processes take effect at high temperatures. Due to the increasing change of location of the atoms, pinned dislocations on obstacles can be released by climbing or cross-slipping and move on to other slip planes (dislocation gliding). This results in irreversible deformation processes even at low stresses.

In addition, above the recrystallisation temperature, the grain boundaries change due to the diffusing atoms. The grain boundaries begin to move and the grains shift. This grain boundary sliding also contributes to the gradual deformation of the microstructure under load. Grain boundary sliding is particularly pronounced in microstructures with many grain boundaries, i.e. fine-grained microstructures. By means of a coarse-grained structure, however, grain boundary sliding can be reduced.

All the processes mentioned above, such as dislocation gliding and grain boundary sliding, are diffusion-controlled and therefore always take up a certain amount of time. For this reason, the irreversible deformation process (creep) only becomes noticeable over a longer period of time.

In principle, creep can come to a halt due to work hardening, provided the temperature is below the recrystallisation temperature. In such cases, fine-grained microstructures show better strength values than coarse-grained microstructures due to grain boundary hardening. Above the recrystallisation temperature, however, strain-hardening effects are absent due to the steadily formation of new grains, so that a permanent creep to fracture can be observed. Due to the better resistance to grain boundary sliding, coarse-grained microstructures show better strength values than fine-grained materials. For this reason, grain boundary-free materials are used for thermally and mechanically highly stressed turbine blades (single-crystalline nickel-based superalloys).

Coarse-grained or even grain boundary-free materials (single crystals) are particularly suitable for high-temperature applications!

Creep stages

Creep curves provide important information about the temporal dynamics of creep, i.e. how creep progresses over time. Depending on whether the creep test is carried out below or above the recrystallisation temperature, the creep process can be stopped by strain hardening (curve 1) or it will inevitably lead to fracture (curves 2 and 3). In general, three stages can be distinguished in the creep curves.

Stage I is called primary creep or transition creep and is characterized by a gradual decrease in creep speed. The slowing down of the creep speed is caused by hardening effects due to the accumulation of dislocations. Especially at relatively low temperatures, this stage I is very pronounced.

Finally, as elongation or time progresses, a dynamic equilibrium between the hardening effects through dislocation accumulation and the softening effects through dislocation gliding will develop. This stage II is also referred to as secondary creep or stationary creep and is therefore characterized by a constant creep speed. This stage accounts for a large proportion of the total service life of the sample at elevated temperatures and therefore plays a very important role.

With increasing elongation, pores form in the material over time and creep resistance decreases. This results in an accelerated creep strain which causes cracks in the material. This stage III is also known as tertiary creep and is characterized by a significant increase in creep speed which finally ends in the fracture of the sample. Tertiary creep usually covers only a relatively short time measured in relation to the total service life of the sample.