مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

اثر طول ترک اولیه بر چقرمگی شکست مود I در PMMA با استفاده از روش شبه فشرده کششی

نوع مقاله : پژوهشی اصیل

نویسندگان
شهربانو صیادی 1
علیرضا باغبانان 2
مرتضی جوادی 3
جوردی دلگادو-مارتین 4
حمید هاشم الحسینی 5
1 دانشکده مهندسی معدن، دانشگاه صنعتی اصفهان
2 دانشکده مهندسی معدن، دانشکاه صنعتی اصفهان
3 دانشکده مهندسی معدن، نفت و ژئوفیزیک، دانشگاه صنعتی شاهرود
4 مدرسه مهندسی عمران، دانشگاه اکرونیا
5 دانشکده مهندسی عمران، دانشگاه صنعتی اصفهان
10.22034/mme.23.9.543
چکیده
چقرمگی شکست مود I، بعنوان یک مشخصه در فرآیند آغاز و گسترش ترک، ویژگی مهمی در مصالح بشمار می­آید. در این مطالعه به بررسی اثر طول ترک اولیه بر چقرمگی شکست مود I پرداخته شده است. بدین­منظور نمونه­هایی از جنس پلیمر پلی­متیل متاکریلات با استفاده از روش شبه فشرده کششی، تحت بارگذاری قرار گرفته­ است. جهت پایش توزیع میدان تغییرشکل در حین آزمایش و بررسی اثر تغییر طول ترک اولیه بر نحوه توزیع تغییرشکل در نمونه، از روش برهم­نگاری تصاویر دیجیتالی بعنوان ابزار کمکی استفاده شده است. نتایج حاصل از آزمایش­ها در قالب نمودارهای بار بر حسب جابجایی و زمان بررسی شده و مقدار چقرمگی شکست مود I در هریک از مقادیر طول ترک اولیه مورد ارزیابی قرار گرفته است. استفاده از روش شبه فشرده کششی در این مطالعه امکان بررسی و مقایسه مناسبی از کار انجام شده بر روی نمونه در مراحل پیش از شکست و پس از شکست را فراهم کرده است. نتایج این مطالعه نشان می­دهد؛ طول ترک اولیه بعنوان یکی از کلیدی ترین فاکتورهای موثر بر رفتار شکست بوده به گونه ای که با افزایش طول ترک اولیه، میزان انرژی جذب شده تا لحظه شکست، وسعت ناحیه گسترش ترک (FPZ)، تمرکز کرنش در نوک ترک، بار بیشینه و چقرمگی شکست مود I کاهش می یابد. بر اساس مقایسه نتایج حاصل از این مطالعه، قطر مناسب برای آزمایش شبه فشرده کششی در حدود 50 میلی متر بوده که برای این قطر نمونه، طول ترک اولیه بین 5/11 الی 5/15 میلی متر پیشنهاد می شود.
کلیدواژه‌ها
چقرمگی شکست مود I
روش شبه فشرده کششی
روش برهم نگاری تصاویر دیجیتال
طول ترک اولیه
پلی متیل متاکریلات

موضوعات

عنوان مقاله English

Effect of Initial Crack Length on Mode I Fracture Toughness of PMMA Using Pseudo Compact Tension Test

نویسندگان English

SHAHRBANOU SAYADI 1
ALIREZA BAGHBANAN 2
MORTEZA JAVADI 3
JORDI DELGADO-MARTIN 4
HAMID HASHEMALHOSSEINI 5
1 Department of mining engineering, Isfahan University of Technology
2 Department of mining engineering, Isfahan university of technology
3 Faculty of Mining, Petroleum & Geophysics Engineering, Shahrood University of Technology
4 School of civil engineering, Universidade da Coruña
5 Department of civil engineering, Isfahan University of Technology
چکیده English

Mode I fracture toughness (KIC) is one of the most important parameters in fracture mechanics, which represents the ability of a material containing a pre-existing defect to resist tensile failure. In this paper, the crack length effect on the mode I fracture toughness of an isotropic homogeneous material was investigated. For this purpose, several disc shaped PPMA samples were loaded in pure tension by performing pseudo-compact tension (pCT) tests. Digital image correlation (DIC) method was utilized to assess and monitor the distribution of the deformation field during the tests. DIC results were also used to compare the effect of crack length on the deformation field variation in samples. Very good agreement was found between the KIC values estimated in this study and those reported in the past for the similar material; indicating that the pCT method is convenient for the assessment of KIC. The experimental results also show that the initial crack length has a tangible impact on KIC, although the magnitude of its influence is closely related to material structure and type. According to the tests results, an increase in the initial crack length leads to increase the ultimate displacement at failure point, decrease the maximum load and the amount of absorbed energy until the moment of failure, and finally decrease the mode I fracture toughness of the material. Results of this study show that the pCT method configuration is useful for testing PMMA and may be useful for testing other materials suitable amenable of molding such as mortar, concrete and ceramics. According to the comparison of the results, in the optimum range of sample diameter, about 50 mm, the initial crack length is suggested between 11.5 to 15.5 mm for the PMMA.

کلیدواژه‌ها English

Mode I Fracture Toughness
Pseudo-Compact Tension Method
Digital Image Correlation Method
Initial Crack Length
PMMA
[1] Chong, K.P., Kuruppu, M.D., (1984) New specimen for fracture toughness determination of rock and other materials. Int. J. Fract.; 26:59-62.
[2] Kuruppu, M.D., (1997) Fracture toughness measurement using chevron notched semi-circular bend specimen. Int. J. Fract.; 86: L33-L38.
[3] ISRM commission on testing methods, (2017) Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens. Int J Rock Mech Min Sci Geomech Abstr. 10(2).
[4] ISRM Testing Commission, (1988) Suggested methods for determining the fracture toughness of rock. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 25:71–96.
[5] Kuruppu, M.D., Obara, Y., Ayatollahi, M.R., Chong, K.P., Funatsu. T. (2014) ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen Rock Mech Rock Eng 47:267–74.
[6] Gogotsi, GA. (2003). Fracture toughness of ceramics and ceramic composites. Ceramics International, 29(7), 777–784.
[7] ASTM C1421-99, Standard Test Method for the Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature.
[8] G.A. Gogotsi, GA., (2002) Fracture toughness studies on ceramics and ceramic particulate composites at different temperatures, in: J.A. Salem, G.D. Quinn, M.G. Jenkins (Eds.), Fracture Resistance Testing of Monolithic and Composite Brittle Materials (ASTM STP 1409), American Society for Testing and Materials, West Conshohocken, PA, 199–212.
[9] Lubauer, J.; Belli, R.; Lorey, T.; Max, S.; Lohbauer, U.; Zorzin, J.I., (2022) A split-Chevron-Notched-Beam sandwich specimen for fracture toughness testing of bonded interfaces. J. Mech. Behav. Biomed. Mater. 131, 105236.
[10] Awaji, H.; Sakaida, Y., (1990) V-Notch Technique for Single-Edge Notched Beam and Chevron Notch Methods. J. Am. Ceram. Soc. 73, 3522–3523.
[11] Zhang, Z., (2002) An empirical relation between mode I fracture toughness and the tensile strength
of rock. Int. J. Rock Mech. Min. Sci. 39(3): 401–406.
[12] Muñoz-Ibáñez, A., Delgado-Martín, J., Costas, M., Rabuñal-Dopico, J., Alvarellos-Iglesias, J., Canal-Vila. J., (2020) Mode I fracture toughness determination in rocks using a pseudo-compact tension (pCT) test approach Rock Mech Rock Eng., 53:3267-85.
[13] Ayatollahi MR, Akbardoost J (2014) Size and geometry effects on rock fracture toughness: mode I fracture. Rock Mech Rock Eng. 47:677–687
[14] Ayatollahi MR, Moghaddam MR, Razavi SMJ, Berto F (2016) Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading. Eng Fract Mech 163:449–461.
[15] Tutluoglu, L., Keles, C., (2012) Effects of geometric factors on mode I fracture toughness for modified ring tests. Int J Rock Mech Min Sci. 51:149‐161.
[16] Ghouli, S., Bahrami, B., Ayatollahi, M.R. et al., (2021) Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test. Rock Mech Rock Eng 54, 4041–4058.
[17] Zhang, S., An, D., Zhang, X., Yu, B., Wang, H., (2021) Research on size effect of fracture toughness of sandstone using the center-cracked circular disc samples. Eng. Fract. Mech. 251.
[18] Wei, M-D., Dai, F., Xu, NW., Zhao, T., Liu, Y., (2017) An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. Int J Rock Mech Min Sci. 99:28–38.
[19] Justo J, Castro J, Cicero S et al (2017) Notch effect on the fracture of several rocks: application of the theory of critical distances. Theor Appl Fract Mech 90:251–258.
[20] Bahadori, R.; Ayatollahi, M.R.; Cicero, S.; Álvarez, J.A., (2021) Geometry Effects on Mode I Brittle Fracture in VO-Notched PMMA Specimens. Polymers, 13, 3017.
[21] Zhang, S., Wang, L. & Gao, M., (2020) Experimental and Numerical Study of the Influence of Prefabricated Crack Width on the Fracture Toughness of NSCB Specimens. Rock Mech Rock Eng 53, 5133–5154.
[22] Aliha, MRM., Ayatollahi, MR., (2014) Rock fracture toughness study using cracked chevron notched Brazilian disc specimen under pure modes I and II loading-A statistical approach. Theor Appl Fract Mech 69:17–25.
[23] Fahimifar, A., Heidari Moghadam, R., (2017) An Experimental and Numerical Study on the Effect of Loading Type and Specimen Geometry on Mode-I Fracture Toughness of Rock. AUT Journal of Civil Engineering, 1(1): 45-54.
[24] Zhou, L., Zhu, ZM., Qiu, H., et al (2018) Study of the effect of loading rates on crack propagation velocity and rock fracture toughness using cracked tunnel specimens. Int J Rock Mech Min Sci 112:25–34.
[25] Zhou, J., Wang, Y., Xia, Y., (2006) Mode-I fracture toughness of PMMA at high loading rate,Journal of Material Science, 41 (24), 8363-8366.
[26] Weerasooriya, T., Moy,M P., Casem, D., Cheng, M., Chen, W., (2006) Fracture toughness for PMMA as a function of loading rate.
[27] Dehghani B, Faramarzi L (2019) Experimental investigations of fracture toughness and crack initiation in marble under different freezing and thermal cyclic loading. Constr Build Mater 220:340–352.
[28] Justo, J., Castro, J., Cicero, S., (2020) Notch effect and fracture load predictions of rock beams at different temperatures using the theory of critical distances. Int. J. Rock Mech. Min. Sci., 125, 104161.
[29] Zejin, y., Zhang, C., (2019) Mode I Fracture Toughness Test and Fractal Character of Fracture Trajectory of Red Sandstone under Real-Time High Temperature, Advances in Materials Science and Engineering.
[30] Torabi, AR., Jabbari, M., Akbardoost, J., (2020) Scaling effects on notch fracture toughness of graphite specimens under mode I loading, Engineering Fracture Mechanics, 235.
[31] Zhang, N., Hedayat, A., Bolaños, HG., Tunnah, J., González, JJ., Salas Álvare, GE., Estimation of the mode I fracture toughness and evaluations on the strain behaviors of the compacted mine tailings from full field displacement fields via digital image correlation, Theor Appl Fract Mech, 2021 ;11 4 :103014 .
[32] Muñoz-Ibáñez, A., Delgado-Martín, J., Juncosa-Rivera, R., (2021) Size effect and other effects on mode I fracture toughness using two testing methods Int J Rock Mech Min Sci 143C 104785.

[33] Huddhar, A., Desai, A., Sharanaprabhu, CM., Kudari, SK., Gouda, PSS., (2016) Studies on effect of pre-crack length variation on Inter-laminar fracture toughness of a Glass Epoxy laminated composite. IOP Conference Series. Materials Science and Engineering, 149: 012161.
[34] Xiao, P., Li, D., Zhao, G., Liu, M., (2021) Experimental and Numerical Analysis of Mode I Fracture Process of Rock by Semi-Circular Bend Specimen. Mathematics, 9, 1769.
[35] Torabi, A.R., Saboori, B., Keshavarz S., Ayatollahi, M.R., (2018) Brittle failure of PMMA in the presence of blunt V-notches under combined tension-tear loading: Experiments and stress-based theories, Polymer Testing, 72, 94-109.
[36] Sanchez, F.J., Elices, M., Valiente, A., (2001) Cracking in PMMA containing U-shaped notches. Fatigue & Fracture of Engineering Materials & Structures. 23, 795-803.
[37] ASTM, (2012) E399-12: Standard test method for linear-elastic plane strain fracture toughness of metallic materials. West Conshohocken, PA: ASTM International.
[38] Backers, T., Stephansson, O., (2012) ISRM suggested method for the determination of mode II fracture toughness. Rock Mechanics and Rock Engineering 45:1011–1022.
[39] Backers, T., Fardin, N., Dresen, G., Stephansson, O., (2003) Effect of loading rate on Mode I fracture toughness, roughness and micromechanics of sandstone. International Journal of Rock Mechanics and Mining Sciences 40:425–433.
[40] Huang, X., Liu, Z., & Xie, H., )2013) Recent progress in residual stress measurement techniques. Acta Mechanica Solida Sinica, 26(6), 570-583.
[41] Yates, J.R., Zanganeh, M., Tai, Y.H., )2010) Quantifying crack tip displacement fields with DIC Engineering Fracture Mechanics, 77, 2063–2076.
[42] Zhang, R., He, L., (2012) Measurement of mixed-mode stress intensity factors using digital image correlation method. Optics and Lasers in Engineering, 50, 1001–1007.
[43] Chang, S.H., Lee, C.I., Jeon, S. 2002. Measurement of rock fracture toughness under mode I and II and mixed mode conditions by using disc type specimens. Eng. Geol. 66, 79-97.
[44] Zhang J, Little DN, Grajales J, You T, Kim Y-R (2017) Use of Semicircular Bending Test and Cohesive Zone Modeling to Evaluate Fracture Resistance of Stabilized Soils. Transportation Research Record: Journal of the Transportation Research Board 2657:67–77.
[45] Ayatollahi, MR., Saboori, B., (2015) A new fixture for fracture tests under mixed mode I/III loading Eur J Mech A/Solids 51 67-76.
مهندسی مکانیک مدرس
دوره 23، شماره 9
شهریور 1402
صفحه 543-551