Detection of delamination in thermoplastic CFRP weld parts using eddy current testing and induction heating

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1 11th European Conference on Non-Destructive Testing (ECNDT 214), October 6-1, 214, Prague, Czech Republic More Info at Open Access Database Detection of delamination in thermoplastic CFRP weld parts using eddy current testing and induction heating Koichi MIZUKAMI 1, Yoshihiro MIZUTANI 1, Akira TODOROKI 1, Yoshiro SUZUKI 1 1 Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology; Tokyo, Japan Phone: ; kmizukam@ginza.mes.titech.ac.jp Abstract This paper presents a new eddy current based method for detecting delamination in thermoplastic CFRP welded zones. Although eddy current testing (ET) has an advantage of short-time testing, it has been difficult for conventional ET to detect delamination. In this study, induction heating assisted eddy current testing (IHAET) is proposed. In IHAET, surface of the CFRP is heated by the driver coil and a hot spot is produced at the top external surface of the delamination zone since delamination acts as an additional thermal resistance. Electrical conductivity of the hot spot is larger than that of intact zones due to temperature dependency of electrical conductivity of carbon fiber and pickup coils for electrical conductivity measurement can identify the location of the delamination. Experimental studies carried out on CF fabric / PPS show the validity of IHAET and detected 45mm 2 penetrated delamination in 2mm depth in 4mm thick weld part by using a statistical diagnosis. Keywords: eddy current testing (ECT), thermal NDT, thermoplastic composite, CFRP 1. Introduction In recent years, Carbon Fiber Reinforced Plastics (CFRP) has been widespread in aviation and automobile industries due to its potential of weight saving. Especially, thermoplastic CFRP in which thermoplastic resin are used as matrix attracts considerable attention. When compared to thermoset CFRP, thermoplastic CFRP has advantages of improved toughness, weldability, repairbility, recyclability and shorter processing time [1-6]. Particularly, welding of thermoplastic CFRP has great advantages of low-cost and rapid production over conventional joining methods such as mechanical fastening and adhesive bonding [2,5]. During welding process, delamination occurs between welded CFRP parts for several reasons: release of stored elastic energy in the deformed carbon fiber bundles when the viscosity of the matrix decreases, expansion of entrapped air, thermal stresses, excessive squeeze flow of resin due to excessive pressure, insufficient squeeze of air in bond line due to insufficient pressure [1]. For detecting delamination in thermoplastic CFRP welded zones, ultrasonic testing is conventionally adopted as a nondestructive testing method. However, since ultrasonic testing requires use of coupling agent and long scanning time, the time cost on nondestructive testing is very high [7,8], which prevents making the most of the thermoplastic CFRP s advantage of low-cost and rapid production. Thus, nondestructive technique which can detect delamination in welded zones in a short time is in great demand. Eddy current testing (ET) is a nondestructive testing method applied to electrically conductive materials including CFRP. Since ET has advantages such as high sensitivity, noncontact inspection and rapid scanning [9], ET can be considered for appropriate short-time testing method for thermoplastic CFRP weld parts. Although studies on detection of defects in carbon fibers by ET have been reported [1-14], it is difficult for conventional ET to detect delamination. In general, ET detects distortion of eddy current flow caused by a defect. However, since delamination is parallel to eddy current, delamination barely affects eddy current flow [13,14]. Thus, the purpose of this study is to develop a new eddy current testing method for detecting delamination. In order to detect delamination, we propose induction heating assisted eddy current testing (IHAET). IHAET is a new testing method which combines induction heating with eddy current testing. Induction heating is conducted to produce a hot spot above the delamination. Electrical conductivity of the delamination zone is different from that of the intact zone due to

2 temperature dependency of electrical conductivity [15]. Since ET can be used for measurement of electrical conductivity of the tested material, the hot spot can be detected by ET and the location of the delamination can be identified. IHAET has advantages of short time delamination detection in CFRP and has potential to detect both delamination and defects in fiber. In this paper, we investigate feasibility of IHAET through experiments. In addition, statistical diagnosis to distinguish defective zone and intact zone is discussed. 2. Induction heating assisted eddy current testing (IHAET) Fig. 1 shows the schematic illustration and photographs of IHAET sensor. IHAET sensor is composed by a driver coil and pickup coils placed between drive windings. These coils are patterned on the polyimide film by etching. IHAET sensor is a flexible sensor which can be used as surface-mounted or embedded sensor. Thus, IHAET sensor can inspect curved materials reducing lift off effect and can be inserted to weld equipment. In IHAET, surface of the weld part is heated by eddy current induced by the driver coil. Fig. 2 shows the general behavior of heat fluxes inside the weld part. From the viewpoint of heat transfer, delamination acts as an additional thermal resistance through the thickness direction due to trapped air and delamination produces a hot spot on the top external surface of the weld part. Fig. 3 shows temperature characteristic of the electrical resistance in in-plane direction of woven CFRP from room temperature. As shown in Fig. 3, resistance of woven CFRP decreases linearly as temperature increases, which indicates that electrical conductivity of woven CFRP increases with temperature. Therefore, hot spot has higher electrical conductivity. On the other hand, pickup coils sense magnetic field from drive current and eddy current. Since eddy current depends on electrical conductivity of the tested material, 13 Polyimide film Pickup coils Driver coil Unit: mm (b) 13 Thermoplastic CFRP weld part Weld defect (delamination) (a) (c) Fig. 1 (a) Schematic illustration of the IHAET sensor mounted on the thermoplastic CFRP weld part, (b) 3 channels IHAET sensor, (c) 5 channels IHAET sensor Unit: mm IHAET sensor Weld defect (delamination) Hot spot Heat flux Higher electrical conductivity Fractional Change in resistance ΔR/R y = -.477x R² = Temperature change ΔT [ ] Fig. 2 General behavior of heat fluxes inside the thermoplastic CFRP weld part. Fig. 3 Fractional change of in-plane resistance of woven CFRP from room temperature.

3 impedance Z p of the pickup coil (Z p is defined as Z p = Output voltage of the pickup coil V out / Drive current I) can extract information pertaining to electrical conductivity of the tested material. The higher the frequency of the drive current is, the smaller the skin depth of eddy current becomes and eddy current can be concentrated in the vicinity of the surface. Therefore, using high frequency drive current makes it possible to measure electrical conductivity in the vicinity of the surface of the weld part. During induction heating, impedance change of the pickup coil at the delamination zone is different from that of intact zone. Thus, location of the delamination can be identified by comparing impedance changes of pickup coils. Advantage of IHAET over ultrasonic testing is that IHAET can detect delamination in shorter time as no coupling agent and scanning time are required. Especially, IHAET sensor can inspect weld part covered by non-conductive pressure board and vacuum bag of weld equipment by inserting IHAET sensor. For instance, when IHAET sensor is inserted under the pressure board or the vacuum bag in induction welding, weld part can be inspected in welding process and reduction of time cost can be expected. When compared to thermography testing, IHAET is superior in terms of inspection of covered materials and the potential of high sensitivity detection of flaw of fibers like conventional ET. 3. Materials and experimental setup 3.1 Specimens of thermoplastic CFRP weld part Fig.4 shows the configuration of the specimen of thermoplastic CFRP weld part with a simulated penetrated delamination. The weld part is fabricated by welding carbon fiber fabric / PPS plates. Fig. 5 shows the schematic illustration of the specimen fabrication. 2mm thick thermoplastic CFRP plates are pressed between 29 C hot plates. Applied pressure is approximately 5kPa. Supporting jigs are placed on the both sides of the thermoplastic CFRP to prevent excessive squeeze flow of thermoplastic resin. In order to simulate delamination, 5 thick polyimide film is inserted between thermoplastic CFRP plates before welding. The width of the polyimide film is w d and penetrated delamination with width of w d can be simulated as Fig. 4 shows by removing the polyimide film after welding is completed. In this study, four samples coded D, D1, D15 and D2 are fabricated. Table 1 shows the tested specimens and size of their simulated delamination. Width of delamination simulated in D, D1, D15 and D2 are mm, 1mm, 15mm, and 2mm respectively. D is the specimen with no delamination. 3 Simulated defect zone 15 w d CF Fabric / PPS weld part 4. Unit: mm Fig. 4 Configuration of the specimen of thermoplastic CFRP weld part with a simulated defect: simulated defect is penetrated delamination with width w d. Hot plate (29 ) Pressure ( 5kPa) Polyimide film (width: w d, thickness:5μm) CF fabric / PPS (thickness:2mm) Supporting jig Fig. 5 Fabrication of the specimen of thermoplastic CFRP weld part with a delamination. Weld part is fabricated by hot press and defect is simulated by inserting a polyimide film between welded CFRP before welding. The polyimide film is removed after the welding is completed.

4 Table 1 Specimens and their size of penetrated delamination Code Width of delamination w d [mm] Area of delamination [mm 2 ] D D1 1 3 D D Experimental setup Measurement of surface temperature distribution In order to verify that delamination produces a hot spot, surface temperature distribution of the specimen with a simulated defect is measured during induction heating. Fig. 6 shows the experimental setup for surface temperature distribution measurement. As Fig. 6 shows, the driver coil cut off from IHAET sensor in Fig. 1 is attached to the specimen D2. To produce a hot spot, eddy current have to be concentrated at upper part of the specimen above the bond line. Since eddy current distribution is strongly dependent on the frequency of the drive current, it is necessary to determine the drive frequency which can concentrate eddy current above the bond line. According to 1D analysis of electromagnetic wave, eddy current density J attenuates in thickness direction exponentially as Eq. (1) shows [16]....(1)...(2) where, is eddy current density at the surface of the tested material, is depth from the surface of the tested material and is defined as skin depth.,, denote magnetic permeability of the tested material, electrical conductivity of the tested material, drive frequency respectively. In the case of woven CFRP, is in-plane conductivity and =14S/m is substituted for Eq. (2). At =3MHz, skin depth is calculated as =2.8 mm, which indicates that eddy current attenuates to 5% at z=2mm, and to 24% at z=4mm. Therefore, a large fraction of eddy current is concentrated above the delamination in case of 4mm weld part at =3MHz. 127Vpp, 3MHz sinusoidal voltage is applied to the driver coil for induction heating. Sinusoidal voltage supplied from arbitrary waveform generator (NI PXI bit 1MS/s) is amplified by high speed bipolar amplifier (NF Corporation HSA411) and is applied to the driver coil. Surface temperature distribution of the specimen is measured by IR camera (FLIR Systems Inc. FLIR i7) during induction heating. IR camera Driver coil Specimen D2 127Vpp 3MHz Fig. 6 Experimental setup for measurement of surface temperature of specimen D2 during induction heating Delamination detection Fig. 7 shows the experimental setup for delamination detection using IHAET sensor in Fig. 1. IHAET sensor is attached to the specimen by using a doubled sided tape to reduce the variation of lift off. As Fig. 7 (a) and (b) shows, 3 channels sensor has three pickup coils A~B, and 5 channels sensor has five pickup coils A~E. Since penetrated delaminations of specimens D1, D15, D2 are simulated at the center of the specimens, pickup coil B is on the delamination zone in case of 3 channels measurement and pickup coil C is on the

5 delamination zone in case of 5 channels measurement. In this experiment, specimen D, D1, D15, D2 are tested. 127Vpp, 3MHz sinusoidal voltage is applied to the driver coil to heat the specimen and output voltage of pickup coils are measured by multichannel oscilloscope (Pico Technology Picoscope 4424, 12bit 2MS/s) during induction heating. Drive current is also measured and impedance Z p of each pickup coils are calculated as Z p = Output voltage of the pickup coil V out / Drive current I. Delamination (width:w p ) 127Vpp 3MHz Delamination (width:w p ) 127Vpp 3MHz A B C A B C D E 3 channels IHAET sensor Specimen 5 channels IHAET sensor Specimen (a) (b) Fig. 7 Experimental setup for delamination detection: (a) 3 channels measurement, (b) 5 channels measurement. 4. Results and discussion 4.1 Surface temperature distribution The result of the experiment in Fig. 6 is shown in Fig. 8. Fig. 8 shows the resulting temperature distribution of the specimen D2 obtained from IR camera 3 seconds after induction heating is started. Since induction heating is localized in the proximity to the rectangular drive coil, specimen is heated not uniformly but in rectangular shape as Fig. 8 shows. In spite of non-uniform heating, surface temperature of delamination zone is higher than intact zone. Although heat transfers not only in thickness direction but in in-plane direction in case of rectangular heating like Fig. 8, it is verified that thermal resistance due to delamination can produces clear hot spot. Delamination zone (width w p =2mm) t=3s [ ] Fig. 8 Surface temperature distribution of the specimen D2 3 seconds after induction heating is started. 4.2 Pickup coil response and statistical diagnosis Fig. 9 shows an example of the fractional change in pickup coil impedance during induction heating when specimen D is tested in 3 channels measurement. denotes the initial value of the pickup coil impedance at t=, and denotes change of the pickup coil impedance from initial value. During induction heating, impedance of the pickup coil decreases and curve can be fitted with quadratic polynomial as shown in Fig. 9. Thus, is expressed as following function of time t.... (3)

6 Where,, and are coefficients of the quadratic polynomial. According to Fig. 9, impedance of the pickup coils decreases as temperature of the tested material increases. Since delamination produces a hot spot, decrease of impedance of the pickup coil on delamination zone is larger than that of intact zone. Then, curve of the pickup coil on the delamination zone is different from intact zone and coefficient, and at delamination zone is different from intact zone. When the specimen with no delamination is inspected, coefficients, and of of each pickup coil are all equivalent ideally. On the other hand, when the specimen with a delamination is inspected, only coefficients of at delamination zone is different and of delamination zone can be distinguished. Thus, location of delamination can be identified by testing statistically the equivalency of coefficients, and of of each pickup coil. Fractional change in impedance ΔZp/Zp ΔZp/Zp = 9.56E-8t 2-5.4E-5t E-4 R² =.99 Measured Impedance Quadratic approximation Time t [s] Fig. 9 Fractional change in pickup coil impedance during induction heating. Impedance change is fitted with a quadratic polynomial. In order to statistically distinguish intact zone and delamination zone, SI-F method (System Identification - F test method) is adopted as a statistical diagnosis method [17-19]. SI-F method consists of system identification by response surface methodology (RSM) and equivalency testing by F test. Response surface is the approximation function that expresses the relationship between a response and input variables. In the delamination detection by IHAET senor, response is and input variable is time t. Response is approximated with polynomial function of input variables in most cases in RSM. In this study, is approximated with a polynomial function of time t as Eq. (3) shows. Equivalency of two response surface is tested by F-test. In this study, testing equivalency of two response surface corresponds to testing equivalency of coefficients, and of of two pickup coils. In the F-test for equivalency testing, F-statistics expressed as Eq. (4) is calculated [17,18]....(4) where, RSS is residual sum of square. When that equivalency of two response surfaces of of pickup coils 1 and 2 is tested, RSS with subscripts 1 and 2 are RSS of response surface of of pickup coil 1 and 2. RSS with subscript means RSS of the response surface regressed with all data obtained from pickup coil 1 and 2. and are number of data for regression of response surface of of pickup coil 1 and 2 respectively. p denotes the number of coefficients of response surface. In this study, three coefficients, and are used for quadratic approximation, thus, p=3. If the two response surfaces are equivalent, F-statistics follows F distribution of degree of freedom of (p, n-2p).

7 According to central limit theorem, average of F-statistics obtained from r times calculation of F-statistics is in the following range at 99%....(5) where, and are expected value and standard deviation of F respectively. z is the significance level determined from the confidential interval of 99%. Therefore, if average F satisfies Eq. (5), equivalency of the two response surface is accepted. If two response surfaces are not equivalent, average F has large value exceeding the range of Eq. (5) due to large in Eq. (4). 4.3 Results of delamination detection Specimens D, D1, D15 and D2 are inspected by using IHAET sensor and SI-F method. Fig. 1 shows the fractional change in impedance of three pickup coils obtained from 3 channels measurement on specimen D. Since D is the specimen with no delamination, temperature change of three measurement points accord with each other, thus, of pickup coils A, B, C are also according with each other as Fig. 1 shows. Moreover, although pickup coil A and C are closer to short sides of the rectangular driver coil, of pickup coil A, B, and C accords with each other. This result indicates that short sides of the driver coil are sufficiently distant from pickup coils not to affect measurement results. Fig. 11 shows the fractional change in impedance of three pickup coils obtained from 3 channels measurement on specimen D2. As Fig. 11 shows, decrease of impedance of the pickup coil B is larger than A and C. Since delamination zone produces a hot spot, decrease of impedance of the pickup coil at the delamination zone is larger than that of intact zone. Therefore, measurement point with larger decrease of the pickup coil impedance can be identified as a delamination zone. Fractional change in impedance ΔZp/Zp A(Intact) B(Intact) C(Intact) Time t [s] Fig. 1 Fractional change in impedance of pickup coils A, B, C obtained from 3 channels measurement on specimen D. Fractional change in impedance ΔZp/Zp A(Intact) B(Defective) C(Intact) Time t [s] Fig. 11 Fractional change in impedance of pickup coils A, B, C obtained from 3 channels measurement on specimen D2. Fig. 12 and Fig. 13 show the results of SI-F method on D and D2 obtained from 3 channels measurement. In this study, response surface obtained from pickup coil A is considered a standard response surface assuming that pickup coil A is at intact zone, which means that average F is calculated for three equivalency test in case of 3 channels measurement: response surface obtained from pickup coil A and pickup coil A, pickup coil B and pickup coil A, pickup coil C and pickup coil A. In the calculation of average F, = =1 and r =1, then, average F is in the range shown in Eq. (6) if the two response surfaces are equivalent....(6)

8 As shown in Fig. 12, average F of all equivalency tests satisfies Eq. (6). Therefore, equivalency of the impedance change of all pickup coils is accepted statistically and the specimen D can be judged as the specimen with no delamination. On the other hand, Fig. 13 shows that equivalency test of response surface obtained from pickup coil B and A does not satisfy Eq. (6). Equivalency of the impedance change of pickup coil B and A is statistically rejected. Thus, pickup coil B is judged to be on the delamination zone which has different temperature from intact zone Average F 3 2 Average F A-A B-A C-A Fig. 12 Result of the SI-F method on the specimen D obtained from 3 channels measurement. A-A B-A C-A Fig. 13 Result of the SI-F method on the specimen D2 obtained from 3 channels measurement. Fig. 14 and Fig. 15 show the results of SI-F method on the specimen D15 and D1 obtained from 3 channels measurement. As Fig. 14 shows, equivalency of response surface obtained from pickup coil B and A is rejected and pickup coil B is judged to be on the delamination like the specimen D2. On the other hand, in the case of SI-F method on the specimen D1 shown in Fig. 15, equivalency of the impedance change of all pickup coils is accepted and D1 is judged as the specimen with no delamination. In order to improve the spatial resolution, 5 channels measurement is carried out on the specimen D1. Fig. 16 and Fig. 17 show the fractional change in impedance of pickup coils A, B, C, D, E and the result of the SI-F method on the specimen D1 obtained from 5 channels measurement. However, in Fig. 16, impedance change of pickup coil C cannot be distinguished from that of other pickup coils. Furthermore, as shown in Fig. 17, equivalency of the impedance change of all pickup coils is accepted and D1 is judged as the specimen with no delamination like the case of 3 channels measurement. Therefore, it is considered that 1mm width delamination cannot cause clear temperature difference between intact zone and delamination zone. In conclusion, at best 45mm 2 penetrated delamination can be detected by using IHAET sensor and SI-F method Average F 3 2 Average F A-A B-A C-A A-A B-A C-A Fig. 14 Result of the SI-F method on the specimen D15 obtained from 3 channels measurement. Fig. 15 Result of the SI-F method on the specimen D1 obtained from 3 channels measurement.

9 Fractional change in impedance ΔZp/Zp A(Intact) B(Intact) C(Defective) D(Intact) E(Intact) Average F Time t [s] Fig. 16 Fractional change in impedance of pickup coils A, B, C obtained from 5 channels measurement on specimen D1. A-A B-A C-A D-A E-A Fig. 17 Result of the SI-F method on the specimen D1 obtained from 5 channels measurement. 5. Conclusion In this study, induction heating assisted eddy current testing (IHAET) is proposed as a new eddy current based nondestructive technique for detection of delamination in thermoplastic CFRP weld parts. In IHAET, temperature difference is caused between intact zone and delamination zone by induction heating, and the temperature difference is detected by eddy current testing utilizing the temperature dependency of electrical conductivity. Experimental studies verified that delamination produces a hot spot during induction heating of the driver coil of the IHAET sensor, and change of the pickup coil impedance on the delamination zone is larger than intact zone. Delamination zone can be identified by comparing the changes of impedance of pickup coils. In order to judge whether the tested material has a delamination or not, SI-F method is introduced for statistical diagnosis. By using SI-F method, 45mm 2 penetrated delamination in 2mm depth in 4mm thick CF fabric / PPS weld part was detected. However, specimen with 3mm 2 penetrated delamination is judge to be intact and the 3mm 2 delamination cannot be detected even though smaller pickup coils are used for improvement of the spatial resolution. References 1. C. Ageorges and L. Ye, Fusion Bonding of Polymer Composites, Springer, (22). 2. Anahi Pereira da Costa, Edson Cocchieri Botelho, Michelle Leali Costa, Nilson Eiji Narita, José Ricardo Tarpani, A Review of Welding Technologies for Thermoplastic Composites in Aerospace Applications, Journal of Aerospace Technology, Vol. 4, No. 3, (212), pp C. Ageorges, L. Ye, M. Hou, Advances in fusion bonding techniques for joining thermoplastic matrix composites: a review, Composites: Part A, Vol. 32, (21), pp R. Rudolf, P. Mitschang, M. Neitzel, Induction heating of continuous carbon-fibrereinforced thermoplastics, Composites: Part A, Vol. 31, (2), pp T.J. Ahmed, D. Stavrov, H.E.N. Bersee, A. Beukers, Induction welding of thermoplastic composite an overview, Composites: Part A, Vol. 37, (26), pp Thomas Bayerl, Miro Duhovic, Peter Mitschang, Debes Bhattacharyya, The heating of polymer composites by electromagnetic induction A review, Composites: Part A, Vol. 57, (214), pp Carol Lebowitz, Reza Zoughi, Jane W.M. Spicer, and Robert Osiander, Comparison of Ultrasonic, Microwave and Photothermal Imaging of Defective Graphite-Epoxy

10 Composite Panels, SPIE proceedings Vol. 2944, (1996). 8. F. Aymerich, S. Meili, Ultrasonic evaluation of matrix damage in impacted composite laminates, Composites: Part B, Vol. 31, (2), pp Ladislav Janousek, Zhenmao Chen, Noritaka Yusa, Kenzo Miya, Excitation with phase shifted fields-enhancing evaluation of deep cracks in eddy-current testing, NDT&E International Vol. 38, (25), pp Henning HEUER, Martin H. SCHULZE, Norbert MEYENDORF, High Resolution Inspection of Carbon Fiber Materials by Eddy Current Techniques, NDT in Aerospace 21, Mo.2.A.3, (21). 11. Henning Heuer andmartin H. Schulze, Eddy Current Testing of Carbon Fiber Materials by High Resolution Directional Sensors, 211 CANSMART CINDE IZFP, (211). 12. R. Lange and G. Mook, Structural analysis of CFRP using eddy current methods, NDT&E International Vol. 27, (1994), pp M. P. DE GOEJE and K. E. D. WAPENAAR, Non-destructive inspection of carbon fibre-reinforced plastics using eddy current methods, Composites, Vol. 23, No. 3, (1992), pp Gerhard Mook, Rolf Lange and Ole Koeser, Non-destructive characterization of carbonfibre-reinforced plastics by means of eddy-currents, Composites Science and Technology, Vol. 61, (21), pp Kosuke Takahashi and H. Thomas Hahn, Investigation of temperature dependency of electrical resistance changes for structural management of graphite/ polymer composite, Journal of Composite Materials, Vol. 45, (211), pp Akira Todoroki, Skin effect of alternating electric current on laminated CFRP, Advanced Composite Materials, Vol. 21, Nos. 5-6, (212), pp Akira Todoroki, The effect of number of electrodes and diagnostic tool for monitoring the delamination of CFRP laminates by changes in electrical resistance, Composites Science and Technology, Vol. 61, (21), pp A Iwasaki, A Todoroki, T Sugiya, S Izumi and S Sakai, Unsupervised statistical damage diagnosis for structural health monitoring of existing civil structures, Smart Materals and Structures, Vol. 14, (25), pp. S154-S Yoshiro SUZUKI, Akira TODOROKI, Yoshihiro MIZUTANIand Ryosuke MATSUZAKI, Impact Damage Detection in CFRP Using Statistical Analysis of Resistance-Temperature Characteristics, Journal of Solid Mechanics and Materials Engineering, Vol. 5, No. 1, (211), pp

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