Study on Estimation Methods of Applied Stress using Fractography Analysis

156 Study on Estimation Methods of Applied Stress using Fractography Analysis Hideaki Kaneko* 1 Hiroshi Ishikawa* 1 Takashi Konishi* 1 Masahiro Yamada* 1 The damage mode and applied stress must be estimated quantitatively by fractography analysis based on electromicroscopy when causes of structural breakage are studied and improvements introduced. Applied stress estimation method based on the EBS (Electric Back Scattering attern) and fracture roughness with an accuracy of 25%, were developed on the fatigue fracture of nickel-based directionally solidified alloy. 1. Introduction Fractography analysis based on the electron microscope, etc. is carried out to clarify the causes of actual structural breakage. Tabl able 1 shows the present state of the quantitative analysis techniques for fatigue fracture surfaces using electron microscopes. As shown in this table, various quantified evaluation methods have been investigated according to damage modes (1)(2). However, most of these evaluation methods are still merely qualitative. Additionally, estimation methods based on striations are used for quantitative stress evaluation of fatigue fractures, but at present are limited in their applications for material selection and/or estimation stress ranges because striations do not appear in many cases. On the other hand, recently the performance of electron microscopes has been improving rapidly, so that it makes micro region analysis possible. Moreover, studies are being carried out in order to clarify material breakage at an atomic level and estimate remaining life on the basis of the micro changes of material structures. Accordingly, this study has been carried out to discover an applied stress estimation method for inspecting fatigue fracture surfaces using high resolution Electric Back Scattering atterns (EBS) capable of measuring strains in local regions and the three-dimensional Scanning Electric Microscope (SEM) capable of measuring micro-roughness. 2. Applied stress estimation method based on fatigue fracture surfaces Generally, average stress due to centrifugal force, etc. and vibrational stress often overlap on structural members and rotating equipment, therefore, both stresses need to be estimated for observing fracture surfaces. Fig. 1 shows a procedure for estimating stress applied to such a fracture surface. The procedure estimates the vibrational applied stress on the basis of the fracture surface roughness frequency through its roughness parameter and the maximum applied stress adding the stress amplitude to the average stresses based on the plastic deformation size just below the fracture surface. In this study, an accurate stress-analyzing method has been investigated by applying three-dimensional SEM to vibrational applied stress and EBS to the maximum applied stress. Crack propagation rate da/dn Table 1 Review of quantitative analysis technique for fracture surface K Damage mode Brittle fracture Ductile fracture Fatigue failure When striations are clear When striations are not clear Stretched zone Quantifying procedure Striation pitch Crack propagation rate Striation roughness K Stress ratio X-ray half-power band width lastic deformation size Residual strain lastic deformation size Crystal orientation Fracture surface roughness K max K max Observation and measurement methods Stereo observation FRASTA method SEM observation SEM observation Atomic force microscope (AFM) X-ray Channeling pattern method Three-dimensional SEM Laser microscope *1 Takasago Research & Development Center, Technical Headquarters

157 Applied stress Vibrational stress Stress Average stress Time Maximum applied stress Fracture surface profile Fracture surface profile quantified by three-dimensional SEM lastic deformation amount EBS method lastic deformation size ropagating direction ropagating direction Dividing a fracture surface into roughness and frequency, a roughness parameter is computed. Fig. 1 Roughness parameter Applied stress estimation charts Vibrational stress lastic deformation size Maximum stress Applied stress estimation method based on fracture surface analysis (a) lastic strain: small Camera Electron beam Diffraction image Specimen (b) lastic strain: large Fig. 3 Change of EBS image for plastic strain Fig. 2 rinciple of EBS (Electric Back Scattering attern) A diffraction image corresponding to the crystal structure of a specimen is obtained by irradiating an inclined electron beam onto the specimen. 3. Maximum applied stress estimation method based on EBS Solidifying direction 90 o 3.1 EBS equipment and calculating procedure for evaluating parameter Q value This equipment, which is a combination of the EBS of Oxford Instruments Company, UK, and the three-dimensional SEM of Elionix Company, obtains a pseudo-kikuchi pattern produced by the diffraction of an inelastic scattered wave generated by irradiating an electron beam onto a specimen as shown in Fig. 2. The equipment has the feature of being capable of measuring the pseudo-kikuchi pattern at a spatial resolution of 0.5 m and in a short time of 2 seconds. It is known that the pseudo-kikuchi pattern changes its visibility according to the amount of plastic strain, as shown in Fig. 3 (3). Therefore, the method investigated in this study estimates the maximum stress through a quality factor (Q value) parameter, which is digitally expressed by A/D converting the visibility of a pseudo-kikuchi pattern produced on a CCD camera. Fig. 4 Test piece location on a directionally solidified plate 3.2 reparation of a tensile test piece and tensile suspended test sample In order to investigate the relationship between the plastic strain and Q value, round bar tensile test pieces were taken from a nickel-based directionally solidified alloy plate in the crystal growth direction (0 O direction) (Fig Fig. 4). Using these test pieces, the suspended tensile tests were carried out to prepare test samples having different plastic strains. 3.3 Study on observing specimen preparation method In order to measure the plastic strain of suspended tensile test materials, an observation specimen was prepared by slicing each test sample provided in Sec- 0 o

158 1.2 Q Q Quality factor : Measured data : Average value Quality factor ratio Q/Q0 0 1.0 0.8 0.6 0.4 0.2 0 lastic deformation size r p Fracture surface Measuring point 20 40 60 Fig. 5 Relationship between Q value and o plastic strain The Q value indicating the visibility of an EBS image decreases with the increase of plastic strain. Test material: Ni-based directionally solidified alloy 0 o, 90 o Test temperature: Room temperature Loading condition: Fig. 6 R= min max f=30hz R=0.6 to 0.9 Crack propagation range t Slice Forced breakage surface Crack propagation range Electropolishing About 1 mm Q value measurement procedure Fatigue crack propagation test conditions and Q value measurement method Fig. 7 Example measurement of plastic deformation size lastic deformation sizes can be estimated by measuring a change in Q value. lastic deformation size rp Ni-based directionally solidified alloy : 0 o : 90 o Maximum stress amplification coefficient K max (Ma Fig. 8 Relationship between the plastic deformation size and Kmax A good correlation was obtained between the plastic deformation sizes and the maximum stress intensity factor. 1 2 10 20 30 40 50 60 tion 3.2 and then electro-polishing it after removing the processing zone by paper polishing. The optimum condition for electro polishing was decided by selecting the parameters such as electrolyte, voltage, solution temperature, and polishing time. 3.4 lastic strain-measuring procedure and measured results lastic strains were measured at 15 points at a 20 m pitch at a depth of 50 m just below the fracture surface for each suspended tensile test piece. The relationship between the plastic strain and Q value are shown in Fig. 5. The figure shows a good linear relationship between the plastic strain and Q value. 3.5 Measurement of plastic deformation of super alloy fatigue fracture surface Generally, when stress is applied to a crack, a plastic region is produced in the vicinity of the crack according to the applied stress. Accordingly, the applied stress can be estimated if the plastic deformation size can be estimated by measuring the plastic strain. Here, taking a super alloy fatigue fracture surface as an example, a study was performed to discover a plastic deformation size estimation method based on a measured Q value just below the fracture surface. Using the same material as described in Section 3.3 for the test pieces and the CT (Compact Type) test pieces shown in Fig. 6, a fatigue crack propagation test was performed under the load conditions having the maximum stress intensity factor K max kept within a range of 10.2 to 42.8 Ma. Then, slicing the medium part of the CT test piece thickness into a leaflike specimen about 1 mm thick and electro-polishing it, Q value distribution was measured depthwise from the fracture surface using the polished specimen. 3.6 Measured results Fig.7 shows the relationship between the distance from the fracture surface of the specimen at Kmax=21.7 Ma and the dimensionless parameter Q/Q0 (Q 0 is a value such that Q is nearly constant). As shown

159 in the figure, a plastic deformation size rp can be determined because a clear turning point, the boundary point of the plastic deformation region, is indicated. There is a tendency for the plastic deformation region to grow with an increase of the maximum stress intensity factor, which is summarized in Fig.8. It is noticed that there is a linear relationship between them and its incline satisfies a gradient of 1:2 given from the fracture mechanics based on Equation (1). According to the dispersion width shown in Fig. 8, it is also known that a maximum applied stress max can be satisfactorily estimated with a 25% accuracy through Equation (2). where α, y are material constants, where a and f are the Crack length and shape factor, respectively. Roughness profile 80 7060 50 4030 20 10 0 0 102030 40 5060 70 8090 100 110 Detector a Detector c Detector b Detector d Specimen Fig. 9 rinciple of 3D appearance measurement for fracture surfaces A stereo image can be obtained by the four detectors that detect secondary electrons generated by irradiating an electron beam onto the specimen. 4.Vibrational stress estimation method by means of fracture surface roughness 4.1 Fracture surface profile measuring instrument Fig. 9 outlines a three-dimensional SEM measurement instrument. The instrument has four detectors, and when an electron beam is irradiated onto a part of a specimen surface, a secondary electron is emitted from the irradiation part. The amount and direction of the emission changes according to the surface profile of the specimen, the four detectors thereby measure differences in emissions and the surface profile can be determined by quantifying and integrating the angle of the irradiation. The resolution in the height direction is 1 nm. 4.2 Study on roughness parameters and applied stress amplitude estimation results For the roughness profiles of fracture surfaces receiving applied stresses with different amplitudes, using the fatigue crack propagation test pieces prepared in Section 3.5, the roughness horizontal to and that perpendicular to the propagation are measured by three-dimensional SEM. (Magnification: 1 000 times, measuring length: 300 m, measuring pitch: 0.2 m) Then roughness profile data were rearranged and analyzed by various procedures. As a result, the correlations shown in Figs.10 and 11 were found. arameters of both figures are defined by the following equations (3) and (4). = [(Roughness perpendicular to propagation) 2 X Frequency] (3) = Roughness perpendicular to propagation Roughness horizontal to propagation (4) Although S 2 has a binary solution (two K values are given for each S 2.) and has a defect that Step pattern Roughness parameter S2 ( m 2 ) (a) (b) 25% (a) K =2.2Ma= m 2 3 4 5 10 30 50 Stress intensity factor range K (Ma m) 10 m ( ) K=7.8Ma= m Fig. 10 Relationship between the roughness parameter S 2 and K Stress can be estimated from a fracture surface roughness, since there is a correlation between the roughness parameter and stress intensity factor range. Step patterns are produced on the fracture surface in a low K range.

160 Roughness aspect ratio Crack propagating direction Range that step patterns exist in a fracture surface. Roughness aspect ratio = 2 3 4 5 10 20 30 Stress intensity factor range Fig. 11 Relationship between the roughness ratio and K It became possible to estimate the stress at a low K. y Ni-based directionally solidified alloy (0 o direction) Roughness perpendicular to propagation Roughness horizontal to propagation its sensitivity is low in the high-degree K region, combining both S 2 and, stress amplitude a can be estimated over the wide range from a higher to a lower stress. 5. Conclusion Taking nickel-based directionally solidified alloy as an example, a method estimating applied stress by electron microscopy fracture surface analysis was pre- sented and the following three conclusions were given. (1) As a result of applying the EBS method to measurement of local plastic strain just below a fracture surface, plastic deformation sizes can be accurately measured. As a result, a procedure capable of estimating the maximum applied stress within 25% was established. (2) A procedure capable of estimating the stress amplitude satisfactorily within 25% was established by measuring the micro roughness on a fracture surface by three-dimensional SEM and rearranging the measured micro roughness with the roughness parameter S 2. (3) A procedure capable of estimating the stress amplitude in a low stress zone near the threshold of a stress intensity factor range was established by using the aspect ratio parameter of roughness. References (1) Kitagawa, H. et al., Fractography, Baifukan (1977) (2) Fujiwara, M. et al., Quantitative Evaluation of Applied Stress by Surface Roughness for Fatigue Fracture, Journal of the Society of Materials Science, Japan Vol. 40 No. 453 (1991) p.712 (3) Yoshitomi, Y. et al., A Method for Strain Measurement using EC Image Analysis, Journal of the Japan Institute of Metals Vol. 55 No. 1 (1991) pp.22-28