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Scanning positron microscopy: Non-destructive imaging of plastic deformation in the micrometer range
CIRP Annals - Manufacturing Technology 57 (2008) 537–540
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Scanning positron microscopy: Non-destructive imaging of plastic deformation in the micrometer range M. Haaks Helmholtz Institut fu¨r Strahlen- und Kernphysik, Rheinische Friedrich-Wihelms-Universita¨t Bonn, Nussallee 14-16, 53115 Bonn, Germany Submitted by L. Cronja¨ger (1), Dortmund, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Defect Fatigue Image
Positron annihilation spectroscopy (PAS) provides extreme sensitivity for the detection of lattice defects from a concentration of 10 6 defects per atom. PAS is a versatile and non-destructive tool for the study of plasticity and fatigue in solid-state materials. Scanning positron microscopy (SPM) expands the capabilities of PAS into the micron range. Recent results of defect imaging by SPM on plastically deformed and fatigued metals and semiconductors will be presented in this paper. A new method estimating the remaining useful life of fatigued components by employing the S-parameter as a precursor for failure will be introduced. ß 2008 CIRP.
1. Introduction Already in the 1950s it was realized, that positron annihilation spectroscopy (PAS) is a versatile tool for detecting vacancy-like defects and dislocations. These defects constitute an open volume, which acts as an attractive potential for positively charged particles. Due to its diffusive motion the positron acts as a probe on the atomic scale scanning about 106 lattice positions. Hence, from a defect concentration of 10 6 per atom the annihilation signal is significantly changed. For an overview about the possibilities of PAS in material research see for example [1–5]. Nowadays PAS is an established method in the fields of defect analysis and non-destructive material testing. 2. Positron annihilation spectroscopy The interaction of positrons with matter can be divided into four sections: thermalisation, diffusion, trapping, and finally, annihilation. Implanted in condensed matter, a positron looses all its kinetic energy within a few picoseconds and reaches thermal equilibrium with the lattice (Ekin = 3/2 kBT 0.04 eV at room temperature (RT); kB is the Boltzmann-factor) [6,7]. This time scale is rather short compared to its lifetime in matter (from about 100 ps in metals to several ns in polymers). For monoenergetic positrons from a slow positron beam the implantation profile reaches its maximum a few micrometer below the surface and can be described by a Mahkov-function [8]. For instance, at a positron energy of 30 keV the implantation depth is 1 mm for ferrous alloys and 3.5 mm for aluminium alloys, respectively. Once thermalised, the positron diffuses through the lattice and behaves like a free particle. Repelled from the positively charged nuclei, its probability of presence has a maximum in the interstitial regions of the lattice [9], while its motion can be described as a three-dimensional random-walk [10]. The 0007-8506/$ – see front matter ß 2008 CIRP. doi:10.1016/j.cirp.2008.03.109
positron is highly mobile, having a diffusion constant at RT in the order of 10 4 m2 s 1. Every open volume in the lattice, causing a local increase of the distance of the atomic positions, acts as an attractive potential for the diffusing positron. For instance, one atomic vacancy forms a deep positron trap with a binding energy around 1 eV due to the absent repulsion by the missing nucleus. Fig. 1 shows the potential well of an edge-dislocation with an associated vacancy-like defect (jog), which is a typical potential landscape the positron sees in a plastically deformed metal. For a detailed discussion of positron trapping in open volume defects see e.g. [11]. Once trapped in a vacancy-like defect, a positron cannot escape since its kinetic energy at RT is too small to overcome the barrier. When the positron annihilates with an electron, the rest mass of both particles is transformed into two g-quanta of 511 keV emitted anti-parallel, in the center-of-mass-system. By transformation into the laboratory system the longitudinal component of the electron momentum causes a Doppler shift in the g-energy (Doppler broadening of annihilation radiation (DBAR)) while the transversal component evokes a perturbation of the 1808 angular correlation (angular correlation of annihilation radiation (ACAR)). Here the momentum of the thermalised positron (40 meV) can be neglected in comparison to the electron momentum (1–10 eV). The contribution of electrons with low momenta to the Doppler broadening is quantified by a shape parameter of the momentum distribution, the S-parameter, which is defined as the integral over the central area of the annihilation peak (AS) normalised by the total counts in the peak (A). Fig. 2 shows the annihilation spectra of positrons in pure iron in the well annealed and the cold rolled state, both normalised to the same area. Due to the missing core electrons, the electron momentum density at the vacancy site is lower than in the undisturbed lattice, so a higher density of vacancies leads to a higher S-parameter,
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
538
Fig. 1. Potential well – seen by a positron – of an edge-dislocation with an associated vacancy-like defect (jog).
since an increasing fraction of positrons is trapped in vacancies and annihilates there. Using PAS the concentration of dislocations, jogs, vacancies and vacancy clusters can be detected non-destructively with high sensitivity. The sensitivity limit can be estimated for one-phase systems to be
Fig. 3. Design of the Bonn positron microprobe (BPM).
for dislocations and vacancies, respectively [12]. Hence, every change in the S-parameter reflects a change in the defect density, with respect to the sensitivity limits.
downward by 908 into the entrance plane of a SEM condenser zoom. An objective lens focuses the beams onto the sample, which is mounted on a motorized table that is laterally movable with an accuracy of 1 mm. The positron beam diameter can be adjusted between 5 and 200 mm. Since there is no need for an additional focusing by a strongly inhomogeneous magnetic field, the sample position is field-free, which allows the study of ferromagnetic materials. The annihilation radiation is recorded by a highresolution germanium-detector, mounted below the sample position. The BPM is a laboratory instrument that can be employed for automated measurement series similar to a SEM.
3. The Bonn positron microprobe
4. Measuring plasticity by the S-parameter
Many effects of plastic deformation and material fatigue show a strongly inhomogeneous defect distribution over the sample volume. Hence, for an understanding of these processes by the means of positron annihilation it is crucial to advance to a spatial resolution in the micron range. The Bonn positron microprobe (BPM) [13] provides a fine focused positron beam in the micron range with adjustable beam energy and a beam diameter down to some micrometers (see Fig. 3). The BPM is a combination of a tiny positron source (22Na) with a small phase space and a conventional scanning electron microscope (SEM). Positron and electron source are mounted on the opposite sites of a magnetic prism which bends both beams
In plastic deformation the production of dislocations and vacancies is always interconnected. Jog-dragging of screw dislocations and the annihilation of edge dislocations are very effective processes for the production of vacancies and vacancylike defects. During tensile or fatigue testing the dislocation density and hence, the vacancy density rises by several orders of magnitude from the well-annealed state until fracture occurs. Experiments [14] as well as numerical calculations [15] have shown that perfect dislocations have a binding energy for positrons around 0.1 eV, so a thermalised positron would hardly be trapped. Experimentally measured positron lifetimes being characteristic for dislocations differ significantly from lifetimes obtained for defectfree materials and are almost equal to the characteristic lifetimes for vacancies. Trapping into dislocations obviously forms an intermediate state, from which the positron is trapped by the deep potential of the associated vacancy. Hence, the dislocation density is observed indirectly by the S-parameter via the associated vacancies. The sensitivity of the S-parameter to plasticity in metals and semiconductors has been shown in several experiments. For instance, tensile tests on ferrous alloys show a linear correlation of the S-parameter on the true strain, beyond a sensitivity threshold which corresponds to the transition from elastic to plastic deformation [16,17]. As a verification of the PAS method, laterally resolved studies on plasticity in the ferritic carbon steel AISI 1045 were performed after deformation in a three-point bending test. The local effects of deformation were investigated by scanning the sample using PAS (S-parameter) and Debye–Scherrer diffraction (reflection broadening) at exactly the same positions. Comparing both methods, a linear correlation between the lattice distortion of a-iron and the S-parameter was found [18].
1:5 108 cm
2
C disl 5:4 1010 cm
1:2 10
6
C vac 4:3 10
1:4 10
7
C clust 3:3 10
2
4
(1) (2)
4
Fig. 2. Definition of the S-parameter.
(3)
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
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5. Scanning positron microscopy Many effects of plastic deformation and material fatigue show a strongly inhomogeneous defect distribution over the sample surface. Hence, for an understanding of these processes by means of positron annihilation it is crucial to advance to a microscopic resolution. Scanning positron microscopy (SPM) opens a direct and non-destructive insight to defect distributions in the micron range. In the next sections some examples of SPM from material research are presented. 5.1. High speed cutting During cutting processes the surface and the subsurface regions of a workpiece are influenced mechanically and also thermally. With increasing cutting speed the cutting forces decrease, but the heat production is more localised and will lead to high temperatures. In order to analyze the influence of the cutting parameters on the remaining deformation in the emerging surface after cutting, test series were performed on the carbon steel AISI 1045. The samples were accelerated towards a fixed tool and the cutting process was interrupted rapidly by the impact on an fixed stopper. Thus, a snapshot of the cutting at a given speed is obtained. Exemplary, Fig. 4 shows a SPM image of chip and chip root prepared with 1200 m min 1. The S-parameter is coded in colors and overlaid half-transparent on an SEM image. Here blue equals to the annealed state, while red denotes the maximum defect density. The highest deformation is found in the chip (red area), but also the shear zones can be distinguished (green in the chip root). On the right side of the chip local annealing due to friction heat is obvious (green area). The remaining deformation in the freshly emerging surface can be obtained from the image in the region the tool has past. Outside the deformation zones no damage is observed [19]. 5.2. Cyclic plastic zone at fatigue cracks In front of the tip of a fatigue crack in the direction of crack propagation one finds a zone of reversed plastic flow, the cyclic plastic zone. During crack propagation the plastic zone is driven through the material leaving back a plastic wake at the sides of the crack. Size and shape of the cyclic plastic zone can be estimated by numerical methods. Fig. 5 shows a SPM image of the plastic zone and the plastic wake at the crack tip of a fatigue crack produced in rotating bending geometry in the titanium alloy TiAl6V4. The test was stopped, when a visible crack approached on the surface. The data were taken on the superficies surface of the samples waist. The crack tip is located at the origin of the coordinate system. The position of the fatigue crack is symbolised by a dashed black line. The plastic zone shows a necking in the direction of crack
Fig. 4. SPM image of deformation zones and the remaining deformation of a AISI 1045 sample after HSC.
Fig. 5. SPM image of a fatigue crack tip in TiAl6V4 (constrained axes).
propagation and two wings at both sides in 458 direction. This matches the theoretical butterfly-like shape of a fatigue plastic zone as calculated by fracture mechanics. 5.3. Plasticity in gallium arsenide Scratches on the surface of an undoped semi-insulating GaAs wafer have been produced by a wedge-shaped single diamond grain at high speed. The subsurface damage has been analyzed by the BPM. Areas of damage can be identified, which have been characterized both by conventional SEM (Fig. 6b) and the PAS (Fig. 6a and c). The latter reveals indications of plastic deformation due to the trace of created defects observed. The investigations show high defect densities in the nonabrasive region (areas 1 and 2) indicated by an S-parameter of 1.040. Going from this first impact region to the abrasive region in the scratch (area 3), we observe a more brittle behaviour: The Sparameter decreases to about 1.020. Even though GaAs is a brittle material at normal conditions, it undergoes a brittle-to-ductile transition under hydrostatic pressure. The plastic behaviour obvious in areas 1 and 2 can be explained by the pressure caused by the diamond tool before penetrating the surface [20]. 6. Fatigue failure prediction The conventional way to estimate the remaining useful life of a component is still based on a series of destructive tests
Fig. 6. Scratch on GaAs wafer surface.
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
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subsurface layer a few microns below the surface. The concept of the critical S-parameter will afford an easy way to predict fatigue failure in the near future. Acknowledgment The authors like to acknowledge Karl Maier for fruitful discussions and his support in the presented projects.
References
Fig. 7. Fatigue failure prediction employing the S-parameter.
(Wo¨hler-method). The necessary effort can be reduced significantly by assessing the useful life of individual parts by means of positron annihilation. Since the density of defects rises during fatigue, it can be employed as a precursor for the final state of failure, which is accessible experimentally in a non-destructive way by measuring the S-parameter [16,17]. Material failure occurs when a critical defect density is reached locally. The corresponding critical S-parameter Scrit can be obtained at the plastic zone in direct vicinity to the crack tip of a fatigue crack in the same material. When the dependency of the Sparameter to the load cycle number is known for a certain material the point of failure can be predicted by measuring the S-parameter only in the very beginning of fatigue (103 cycles). This approach was validated by a blind test on fatigued flat-bar samples of AISI 1045 having a central bore hole. The distribution of the VonMieses-stress was calculated using finite-element methods (FEM), to identify the area maximally affected by fatigue. The S-parameter was measured on several samples, while neither the load amplitude nor the number of fatigue cycles were known. Fig. 7 shows the prediction diagram. The critical Sparameter Scrit was obtained from a SPM image of a fatigue crack in AISI 1045 [21]. Extrapolation was done assuming a linear increase of the S-parameter with the logarithm of the cycle number. The predicted failure (Fig. 7, red line) and the measured failure (Fig. 7, black line) are in an excellent agreement. 7. Summary Positron annihilation spectroscopy is a versatile and nondestructive tool for the study of lattice defects in solid-state materials. According to the extraordinary sensitivity of positrons for open volume defects, low concentrations of lattice defects (Cvac 10 6) can be detected. Scanning Positron Microscopy (SPM) gives insight to defect distributions on the microscopic scale in the
[1] Goldanski VI (1968) Positron Annihilation. Atomic Energy Review 6:183– 383. [2] West R (1973) Positron Studies of Condensed Matter. Advances in Physics 22:263–383. [3] Hautoja¨rvi P (1979) Positrons in Solids Topics in Current Physics, vol. 12. Springer, Berlin. [4] Smedskjaer LC, Fluss MJ, (1983) Experimental Methods of Positron Annihilation for the Study of Defects in Metals.Mundy JN, et al. (Eds.) Methods of Experimental Physics, vol. 21. Academic Press, New York. [5] Schultz PJ, Lynn KG (1988) Interaction of Positron Beams with Surfaces, Thin Films and Interfaces. Reviews of Modern Physics 60:701–778. [6] Ritchie RH (1959) Interaction of Charged Particles with a Degenerate FermiDirac Electron Gas. Physical Review 114:644–654. [7] Perkins A, Carbotte JP (1970) Effect of Positron–Phonon Interaction on Positron Motion. Physical Review B 1:101–107. [8] Ghosh VJ (1995) Positron Implantation Profiles in Elemental and Multilayer Systems. Applied Surface Science 85:187–195. [9] Brandt W, Paulin R (1972) Positron Diffusion in Solids. Physical Review B 5:2430–2435. [10] Puska M, Nieminen R (1994) Theory of Positrons in Solids and on Solid Surfaces. Reviews of Modern Physics 66:841–899. [11] Frank W, Seeger A (1974) Theoretical Foundation and Extension of the Trapping Model. Applied Physics 3:61–66. [12] Staab TEM, Krause-Rehberg R, Kieback B (1999) Positron Annihilation in Finegrained Materials and Fine Powders—An Application to the Sintering of Metal Powders. Journal of Material Science 33:3833–3851. [13] Greif H, Haaks M, Holzwarth U, Ma¨nnig U, Tongbhoyai M, Wider T, Maier K, Bihr H, Huber B (1997) High-resolution Positron-annihilation Spectroscopy with A New Positron Microprobe. Applied Physics Letters 71:2115–2117. [14] Seeger A (1974) The Study of Defects in Crystals by Positron Annihilation. Applied Physics 4:183–199. [15] Ha¨kkinen H, Ma¨kinen S, Manninen M (1990) Edge Dislocations in fcc Metals: Microscopic Calculation of Core Structure and Positron States in Al and Cu. Physical Reviews B 41:12441–12453. [16] Bennewitz K, Haaks M, Staab T, Eisenberg S, Lampe T, Maier K (2002) Positron Annihilation Spectroscopy—A Non-destructive Method for Lifetime Prediction in the Field of Dynamical Material Testing. Zeitschrift fur Metallkunde 93:778– 783. [17] Haaks M, Maier K (2005) Predicting the Lifetime of Steels. in Albeverio S, Jentsch V, Kantz H, (Eds.) Extreme Events in Nature and Society. Springer, Berlin, pp. 209–232. [18] Haaks M, Mu¨ller I, Schoeps A, Franz H (2006) Spatially resolved Deformation Studies on Carbon Steel employing X-rays and Positron Annihilation. Physica Status Solidi A 203/4:R31–R33. [19] Haaks M, Plo¨ger J (2005) Abbildung der Scha¨digung in der Randzone mit Positronen als Sondenteilchen. in To¨nshoff HK, Hollmann C, (Eds.) Hochgeschwindigkeitsspanen metallischer Werkstoffe. Wiley-VCH, Weinheim, pp. 89–111. [20] Zamponi C, Ma¨nnig U, Staab TEM, Maier K, Eichler S, Hammer R (2003) Point Defects as Result of Surface Deformation on a GaAs Wafer. Applied Physics Letters 83:4128–4130. [21] Eich P, Haaks M, Sindelar R, Maier K (2007) Spatially Resolved Defect Studies on Fatigued Carbon Steel, Spatially Resolved Defect Studies on Fatigued Carbon Steel. Proceedings of the ICPA-14, Physica Status Solidi C, vol. 4, 3465– 3468.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp
Scanning positron microscopy: Non-destructive imaging of plastic deformation in the micrometer range M. Haaks Helmholtz Institut fu¨r Strahlen- und Kernphysik, Rheinische Friedrich-Wihelms-Universita¨t Bonn, Nussallee 14-16, 53115 Bonn, Germany Submitted by L. Cronja¨ger (1), Dortmund, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Defect Fatigue Image
Positron annihilation spectroscopy (PAS) provides extreme sensitivity for the detection of lattice defects from a concentration of 10 6 defects per atom. PAS is a versatile and non-destructive tool for the study of plasticity and fatigue in solid-state materials. Scanning positron microscopy (SPM) expands the capabilities of PAS into the micron range. Recent results of defect imaging by SPM on plastically deformed and fatigued metals and semiconductors will be presented in this paper. A new method estimating the remaining useful life of fatigued components by employing the S-parameter as a precursor for failure will be introduced. ß 2008 CIRP.
1. Introduction Already in the 1950s it was realized, that positron annihilation spectroscopy (PAS) is a versatile tool for detecting vacancy-like defects and dislocations. These defects constitute an open volume, which acts as an attractive potential for positively charged particles. Due to its diffusive motion the positron acts as a probe on the atomic scale scanning about 106 lattice positions. Hence, from a defect concentration of 10 6 per atom the annihilation signal is significantly changed. For an overview about the possibilities of PAS in material research see for example [1–5]. Nowadays PAS is an established method in the fields of defect analysis and non-destructive material testing. 2. Positron annihilation spectroscopy The interaction of positrons with matter can be divided into four sections: thermalisation, diffusion, trapping, and finally, annihilation. Implanted in condensed matter, a positron looses all its kinetic energy within a few picoseconds and reaches thermal equilibrium with the lattice (Ekin = 3/2 kBT 0.04 eV at room temperature (RT); kB is the Boltzmann-factor) [6,7]. This time scale is rather short compared to its lifetime in matter (from about 100 ps in metals to several ns in polymers). For monoenergetic positrons from a slow positron beam the implantation profile reaches its maximum a few micrometer below the surface and can be described by a Mahkov-function [8]. For instance, at a positron energy of 30 keV the implantation depth is 1 mm for ferrous alloys and 3.5 mm for aluminium alloys, respectively. Once thermalised, the positron diffuses through the lattice and behaves like a free particle. Repelled from the positively charged nuclei, its probability of presence has a maximum in the interstitial regions of the lattice [9], while its motion can be described as a three-dimensional random-walk [10]. The 0007-8506/$ – see front matter ß 2008 CIRP. doi:10.1016/j.cirp.2008.03.109
positron is highly mobile, having a diffusion constant at RT in the order of 10 4 m2 s 1. Every open volume in the lattice, causing a local increase of the distance of the atomic positions, acts as an attractive potential for the diffusing positron. For instance, one atomic vacancy forms a deep positron trap with a binding energy around 1 eV due to the absent repulsion by the missing nucleus. Fig. 1 shows the potential well of an edge-dislocation with an associated vacancy-like defect (jog), which is a typical potential landscape the positron sees in a plastically deformed metal. For a detailed discussion of positron trapping in open volume defects see e.g. [11]. Once trapped in a vacancy-like defect, a positron cannot escape since its kinetic energy at RT is too small to overcome the barrier. When the positron annihilates with an electron, the rest mass of both particles is transformed into two g-quanta of 511 keV emitted anti-parallel, in the center-of-mass-system. By transformation into the laboratory system the longitudinal component of the electron momentum causes a Doppler shift in the g-energy (Doppler broadening of annihilation radiation (DBAR)) while the transversal component evokes a perturbation of the 1808 angular correlation (angular correlation of annihilation radiation (ACAR)). Here the momentum of the thermalised positron (40 meV) can be neglected in comparison to the electron momentum (1–10 eV). The contribution of electrons with low momenta to the Doppler broadening is quantified by a shape parameter of the momentum distribution, the S-parameter, which is defined as the integral over the central area of the annihilation peak (AS) normalised by the total counts in the peak (A). Fig. 2 shows the annihilation spectra of positrons in pure iron in the well annealed and the cold rolled state, both normalised to the same area. Due to the missing core electrons, the electron momentum density at the vacancy site is lower than in the undisturbed lattice, so a higher density of vacancies leads to a higher S-parameter,
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
538
Fig. 1. Potential well – seen by a positron – of an edge-dislocation with an associated vacancy-like defect (jog).
since an increasing fraction of positrons is trapped in vacancies and annihilates there. Using PAS the concentration of dislocations, jogs, vacancies and vacancy clusters can be detected non-destructively with high sensitivity. The sensitivity limit can be estimated for one-phase systems to be
Fig. 3. Design of the Bonn positron microprobe (BPM).
for dislocations and vacancies, respectively [12]. Hence, every change in the S-parameter reflects a change in the defect density, with respect to the sensitivity limits.
downward by 908 into the entrance plane of a SEM condenser zoom. An objective lens focuses the beams onto the sample, which is mounted on a motorized table that is laterally movable with an accuracy of 1 mm. The positron beam diameter can be adjusted between 5 and 200 mm. Since there is no need for an additional focusing by a strongly inhomogeneous magnetic field, the sample position is field-free, which allows the study of ferromagnetic materials. The annihilation radiation is recorded by a highresolution germanium-detector, mounted below the sample position. The BPM is a laboratory instrument that can be employed for automated measurement series similar to a SEM.
3. The Bonn positron microprobe
4. Measuring plasticity by the S-parameter
Many effects of plastic deformation and material fatigue show a strongly inhomogeneous defect distribution over the sample volume. Hence, for an understanding of these processes by the means of positron annihilation it is crucial to advance to a spatial resolution in the micron range. The Bonn positron microprobe (BPM) [13] provides a fine focused positron beam in the micron range with adjustable beam energy and a beam diameter down to some micrometers (see Fig. 3). The BPM is a combination of a tiny positron source (22Na) with a small phase space and a conventional scanning electron microscope (SEM). Positron and electron source are mounted on the opposite sites of a magnetic prism which bends both beams
In plastic deformation the production of dislocations and vacancies is always interconnected. Jog-dragging of screw dislocations and the annihilation of edge dislocations are very effective processes for the production of vacancies and vacancylike defects. During tensile or fatigue testing the dislocation density and hence, the vacancy density rises by several orders of magnitude from the well-annealed state until fracture occurs. Experiments [14] as well as numerical calculations [15] have shown that perfect dislocations have a binding energy for positrons around 0.1 eV, so a thermalised positron would hardly be trapped. Experimentally measured positron lifetimes being characteristic for dislocations differ significantly from lifetimes obtained for defectfree materials and are almost equal to the characteristic lifetimes for vacancies. Trapping into dislocations obviously forms an intermediate state, from which the positron is trapped by the deep potential of the associated vacancy. Hence, the dislocation density is observed indirectly by the S-parameter via the associated vacancies. The sensitivity of the S-parameter to plasticity in metals and semiconductors has been shown in several experiments. For instance, tensile tests on ferrous alloys show a linear correlation of the S-parameter on the true strain, beyond a sensitivity threshold which corresponds to the transition from elastic to plastic deformation [16,17]. As a verification of the PAS method, laterally resolved studies on plasticity in the ferritic carbon steel AISI 1045 were performed after deformation in a three-point bending test. The local effects of deformation were investigated by scanning the sample using PAS (S-parameter) and Debye–Scherrer diffraction (reflection broadening) at exactly the same positions. Comparing both methods, a linear correlation between the lattice distortion of a-iron and the S-parameter was found [18].
1:5 108 cm
2
C disl 5:4 1010 cm
1:2 10
6
C vac 4:3 10
1:4 10
7
C clust 3:3 10
2
4
(1) (2)
4
Fig. 2. Definition of the S-parameter.
(3)
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
539
5. Scanning positron microscopy Many effects of plastic deformation and material fatigue show a strongly inhomogeneous defect distribution over the sample surface. Hence, for an understanding of these processes by means of positron annihilation it is crucial to advance to a microscopic resolution. Scanning positron microscopy (SPM) opens a direct and non-destructive insight to defect distributions in the micron range. In the next sections some examples of SPM from material research are presented. 5.1. High speed cutting During cutting processes the surface and the subsurface regions of a workpiece are influenced mechanically and also thermally. With increasing cutting speed the cutting forces decrease, but the heat production is more localised and will lead to high temperatures. In order to analyze the influence of the cutting parameters on the remaining deformation in the emerging surface after cutting, test series were performed on the carbon steel AISI 1045. The samples were accelerated towards a fixed tool and the cutting process was interrupted rapidly by the impact on an fixed stopper. Thus, a snapshot of the cutting at a given speed is obtained. Exemplary, Fig. 4 shows a SPM image of chip and chip root prepared with 1200 m min 1. The S-parameter is coded in colors and overlaid half-transparent on an SEM image. Here blue equals to the annealed state, while red denotes the maximum defect density. The highest deformation is found in the chip (red area), but also the shear zones can be distinguished (green in the chip root). On the right side of the chip local annealing due to friction heat is obvious (green area). The remaining deformation in the freshly emerging surface can be obtained from the image in the region the tool has past. Outside the deformation zones no damage is observed [19]. 5.2. Cyclic plastic zone at fatigue cracks In front of the tip of a fatigue crack in the direction of crack propagation one finds a zone of reversed plastic flow, the cyclic plastic zone. During crack propagation the plastic zone is driven through the material leaving back a plastic wake at the sides of the crack. Size and shape of the cyclic plastic zone can be estimated by numerical methods. Fig. 5 shows a SPM image of the plastic zone and the plastic wake at the crack tip of a fatigue crack produced in rotating bending geometry in the titanium alloy TiAl6V4. The test was stopped, when a visible crack approached on the surface. The data were taken on the superficies surface of the samples waist. The crack tip is located at the origin of the coordinate system. The position of the fatigue crack is symbolised by a dashed black line. The plastic zone shows a necking in the direction of crack
Fig. 4. SPM image of deformation zones and the remaining deformation of a AISI 1045 sample after HSC.
Fig. 5. SPM image of a fatigue crack tip in TiAl6V4 (constrained axes).
propagation and two wings at both sides in 458 direction. This matches the theoretical butterfly-like shape of a fatigue plastic zone as calculated by fracture mechanics. 5.3. Plasticity in gallium arsenide Scratches on the surface of an undoped semi-insulating GaAs wafer have been produced by a wedge-shaped single diamond grain at high speed. The subsurface damage has been analyzed by the BPM. Areas of damage can be identified, which have been characterized both by conventional SEM (Fig. 6b) and the PAS (Fig. 6a and c). The latter reveals indications of plastic deformation due to the trace of created defects observed. The investigations show high defect densities in the nonabrasive region (areas 1 and 2) indicated by an S-parameter of 1.040. Going from this first impact region to the abrasive region in the scratch (area 3), we observe a more brittle behaviour: The Sparameter decreases to about 1.020. Even though GaAs is a brittle material at normal conditions, it undergoes a brittle-to-ductile transition under hydrostatic pressure. The plastic behaviour obvious in areas 1 and 2 can be explained by the pressure caused by the diamond tool before penetrating the surface [20]. 6. Fatigue failure prediction The conventional way to estimate the remaining useful life of a component is still based on a series of destructive tests
Fig. 6. Scratch on GaAs wafer surface.
M. Haaks / CIRP Annals - Manufacturing Technology 57 (2008) 537–540
540
subsurface layer a few microns below the surface. The concept of the critical S-parameter will afford an easy way to predict fatigue failure in the near future. Acknowledgment The authors like to acknowledge Karl Maier for fruitful discussions and his support in the presented projects.
References
Fig. 7. Fatigue failure prediction employing the S-parameter.
(Wo¨hler-method). The necessary effort can be reduced significantly by assessing the useful life of individual parts by means of positron annihilation. Since the density of defects rises during fatigue, it can be employed as a precursor for the final state of failure, which is accessible experimentally in a non-destructive way by measuring the S-parameter [16,17]. Material failure occurs when a critical defect density is reached locally. The corresponding critical S-parameter Scrit can be obtained at the plastic zone in direct vicinity to the crack tip of a fatigue crack in the same material. When the dependency of the Sparameter to the load cycle number is known for a certain material the point of failure can be predicted by measuring the S-parameter only in the very beginning of fatigue (103 cycles). This approach was validated by a blind test on fatigued flat-bar samples of AISI 1045 having a central bore hole. The distribution of the VonMieses-stress was calculated using finite-element methods (FEM), to identify the area maximally affected by fatigue. The S-parameter was measured on several samples, while neither the load amplitude nor the number of fatigue cycles were known. Fig. 7 shows the prediction diagram. The critical Sparameter Scrit was obtained from a SPM image of a fatigue crack in AISI 1045 [21]. Extrapolation was done assuming a linear increase of the S-parameter with the logarithm of the cycle number. The predicted failure (Fig. 7, red line) and the measured failure (Fig. 7, black line) are in an excellent agreement. 7. Summary Positron annihilation spectroscopy is a versatile and nondestructive tool for the study of lattice defects in solid-state materials. According to the extraordinary sensitivity of positrons for open volume defects, low concentrations of lattice defects (Cvac 10 6) can be detected. Scanning Positron Microscopy (SPM) gives insight to defect distributions on the microscopic scale in the
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