Top

Arabian Journal for Science and Engineering

Published in:

29-04-2019 | Research Article - Mechanical Engineering

Numerical Analysis of Crack Initiation Direction in Quasi-brittle Materials: Effect of T-Stress

Author: A. S. Fayed

Published in: Arabian Journal for Science and Engineering | Issue 9/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A two-dimensional finite element analysis was adopted to assess the effect of T-stress on predicting crack initiation angle in a quasi-brittle material. Asymmetric semicircular PMMA specimen containing a vertical edge crack subjected to three-point bending was employed. The specimen was assumed as an isotropic and homogeneous material. Relative crack length ratios of 0.3, 0.4, 0.5, 0.6 and 0.7 were examined. Several relative bottom span ratios were included to develop a wide range of mixed-mode I/II loading conditions. The conventional maximum tangential stress (MTS) criterion could not precisely predict the crack initiation angle through the total range of pure mode I to pure mode II. The generalized maximum tangential stress (GMTS) criterion showed a significant effect of T-stress on the numerical prediction of the crack initiation angles in PMMA specimens. In the present study, neglecting the T-stress in the MTS criterion overestimates the crack initiation angle. The numerical predictions using the GMTS criterion showed a good agreement with the relevant experimental data found in the literature. The ability of GMTS in predicting the crack initiation angle is improved by considering the T-stress.

previous article Experimental-Based Multi-objective Optimization of Injection Molding Process Parameters

next article Tensile After Impact Test of Scarf-Repaired Composite Laminates

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Hammouda, M.M.I.; Fayed, A.S.: Modes I/II SIF of a diametrically compressed Brazilian disc having a central inclined crack with frictional surfaces. Fatigue Fract. Eng. Mater. Struct. 41, 856–868 (2018). https://doi.org/10.1111/ffe.12733 CrossRef

Fayed, A.S.: Numerical analysis of mixed mode I/II stress intensity factors of edge slant cracked plates. Eng. Solid Mech. 5, 61–70 (2017). https://doi.org/10.5267/j.esm.2016.8.001 CrossRef

Aliha, M.R.M.; Hosseinpour, G.R.; Ayatollahi, M.R.: Application of cracked triangular specimen subjected to three-point bending for investigating fracture behavior of rock materials. Rock Mech. Rock Eng. 46, 1023–1034 (2013). https://doi.org/10.1007/s00603-012-0325-z CrossRef

Hammouda, M.M.I.; Pasha, R.A.; Fayed, A.S.: Modelling of cracking sites/development in axial dovetail joints of aero-engine compressor discs. Int. J. Fatigue 29, 30–48 (2007). https://doi.org/10.1016/j.ijfatigue.2006.02.049 CrossRef

Lim, I.L.; Johnston, I.W.; Choi, S.K.; Boland, J.N.; Introduction, I.: Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 1-mode I. Int. J. Rock Mech. Min. Sci. 31, 185–197 (1994). https://doi.org/10.1016/0148-9062(94)90463-4 CrossRef

Shahani, A.R.; Tabatabaei, S.A.: Computation of mixed mode stress intensity factors in a four-point bend specimen. Appl. Math. Model. (2008). https://doi.org/10.1016/j.apm.2007.04.001 MATH

Chang, S.H.; Lee, C.I.; Jeon, S.: Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens. Eng. Geol. 66, 79–97 (2002). https://doi.org/10.1016/S0013-7952(02)00033-9 CrossRef

Khan, K.; Al-Shayea, N.A.: Effect of specimen geometry and testing method on mixed mode I–II fracture toughness of a limestone rock from Saudi Arabia. Rock Mech. Rock Eng. 33, 179–206 (2000). https://doi.org/10.1007/s006030070006 CrossRef

Wei, M.D.; Dai, F.; Xu, N.W.; Liu, J.F.; Xu, Y.: Experimental and numerical study on the cracked chevron notched semi-circular bend method for characterizing the mode I fracture toughness of rocks. Rock Mech. Rock Eng. 49, 1595–1609 (2016). https://doi.org/10.1007/s00603-015-0855-2 CrossRef

10.

Mirsayar, M.M.M.; Berto, F.; Aliha, M.R.M.R.M.; Park, P.: Strain-based criteria for mixed-mode fracture of polycrystalline graphite. Eng. Fract. Mech. 156, 114–123 (2016). https://doi.org/10.1016/j.engfracmech.2016.02.011 CrossRef

11.

Elghazel, A.; Taktak, R.; Bouaziz, J.: Combined numerical and experimental mechanical characterization of a calcium phosphate ceramic using modified Brazilian disc and SCB specimen. Mater. Sci. Eng. A 670, 240–251 (2016). https://doi.org/10.1016/j.msea.2016.06.020 CrossRef

12.

Smith, D.J.; Ayatollahi, M.R.; Pavier, M.J.: On the consequences of T-stress in elastic brittle fracture. Proc. R. Soc. A Math. Phys. Eng. Sci. 462, 2415–2437 (2006). https://doi.org/10.1098/rspa.2005.1639 CrossRefMATH

13.

Chong, K.P.; Kuruppu, M.D.: New specimen for fracture toughness determination for rock and other materials. Int. J. Fract. 26, R59–R62 (1984). https://doi.org/10.1007/BF01157555 CrossRef

14.

Xie, Y.; Cao, P.; Jin, J.; Wang, M.: Mixed mode fracture analysis of semi-circular bend (SCB) specimen: a numerical study based on extended finite element method. Comput. Geotech. 82, 157–172 (2017). https://doi.org/10.1016/j.compgeo.2016.10.012 CrossRef

15.

Kuruppu, M.D.; Obara, Y.; Ayatollahi, M.R.; Chong, K.P.; Funatsu, T.: ISRM-suggested method for determining the mode I static fracture toughness using semi-circular bend specimen. Rock Mech. Rock Eng. 47, 267–274 (2014). https://doi.org/10.1007/s00603-013-0422-7 CrossRef

16.

Kataoka, M.; Mahdavi, E.; Funatsu, T.; Takehara, T.; Obara, Y.; Fukui, K.; Hashiba, K.: Estimation of mode I fracture toughness of rock by semi-circular bend test under confining pressure condition. Procedia Eng. 191, 886–893 (2017). https://doi.org/10.1016/j.proeng.2017.05.258 CrossRef

17.

Wu, P.F.; Liang, W.G.; Li, Z.G.; Cao, M.T.; Yang, J.F.: Investigations on mechanical properties and crack propagation characteristics of coal and sandy mudstone using three experimental methods. Rock Mech. Rock Eng. 50, 215–223 (2017). https://doi.org/10.1007/s00603-016-1048-3 CrossRef

18.

Mahdavi, E.; Obara, Y.; Ayatollahi, M.R.: Numerical investigation of stress intensity factor for semi-circular bend specimen with chevron notc. Eng. Solid Mech. 3, 235–244 (2015). https://doi.org/10.5267/j.esm.2015.7.001 CrossRef

19.

Ayatollahi, M.R.; Aliha, M.R.M.; Saghafi, H.: An improved semi-circular bend specimen for investigating mixed mode brittle fracture. Eng. Fract. Mech. 78, 110–123 (2011). https://doi.org/10.1016/j.engfracmech.2010.10.001 CrossRef

20.

Darban, H.; Haghpanahi, M.; Assadi, A.: Determination of crack tip parameters for ASCB specimen under mixed mode loading using finite element method. Comput. Mater. Sci. 50, 1667–1674 (2011). https://doi.org/10.1016/J.COMMATSCI.2010.12.027 CrossRef

21.

Sutton, M.A.; Deng, X.; Ma, F.; Newman Jr., J.C.; James, M.: Development and application of a crack tip opening displacement-based mixed mode fracture criterion. Int. J. Solids Struct. (2000). https://doi.org/10.1016/s0020-7683(99)00055-4 MATH

22.

Hussain, M.; Pu, S.; Underwood, J.: Strain energy release rate for a crack under combined Mode I and Mode II. Fract. Anal. (1974). https://doi.org/10.1520/stp33130s

23.

Khan, S.M.A.; Khraisheh, M.K.: Analysis of mixed mode crack initiation angles under various loading conditions. Eng. Fract. Mech. 67, 397–419 (2000). https://doi.org/10.1016/s0013-7944(00)00068-0 CrossRef

24.

Theocaris, P.S.; Andrianopoulos, N.P.: The T-criterion applied to ductile fracture. Int. J. Fract. (1982). https://doi.org/10.1007/bf01130617 MATH

25.

Ma, F.S., Deng, X.M., Sutton, M.A.A., Newman Jr., J.C., Newman, J.C.: A CTOD-based mixed-mode fracture criterion. In: Mixed-mode crack behavior, pp. 86–110 (1999)

26.

Sajjadi, S.H.; Ostad Ahmad Ghorabi, M.J.; Salimi-Majd, D.: A novel mixed-mode brittle fracture criterion for crack growth path prediction under static and fatigue loading. Fatigue Fract. Eng. Mater. Struct. 38, 1372–1382 (2015). https://doi.org/10.1111/ffe.12320 CrossRef

27.

Maiti, S.K.; Smith, R.A.: Criteria for brittle fracture in biaxial tension. Eng. Fract. Mech. 19, 793–804 (1984). https://doi.org/10.1016/0013-7944(84)90162-0 CrossRef

28.

Wu, X.; Li, X.: Analysis and modification of fracture criteria for mixed-mode crack. Eng. Fract. Mech. 34, 55–64 (1989). https://doi.org/10.1016/0013-7944(89)90242-7 CrossRef

29.

Ayatollahi, M.R.; Berto, F.; Campagnolo, A.; Gallo, P.; Tang, K.: Review of local strain energy density theory for the fracture assessment of V-notches under mixed mode loading. Eng. Solid Mech. 5, 113–132 (2017). https://doi.org/10.5267/j.esm.2017.3.001 CrossRef

30.

Berto, F.; Gomez, J.: Notched plates in mixed mode loading (I + II): a review based on the local strain energy density and the cohesive zone model. Eng. Solid Mech. 5, 1–8 (2017). https://doi.org/10.5267/j.esm.2016.11.002 CrossRef

31.

Aliha, M.R.M.; Ayatollahi, M.R.: Mixed mode I/II brittle fracture evaluation of marble using SCB specimen. Procedia Eng. 10, 311–318 (2011). https://doi.org/10.1016/j.proeng.2011.04.054 CrossRef

32.

Ayatollahi, M.R.; Aliha, M.R.M.: On determination of mode II fracture toughness using semi-circular bend specimen. Int. J. Solids Struct. 43, 5217–5227 (2006). https://doi.org/10.1016/j.ijsolstr.2005.07.049 CrossRefMATH

33.

Ayatollahi, M.R.; Aliha, M.R.M.; Hassani, M.M.: Mixed mode brittle fracture in PMMA: an experimental study using SCB specimens. Mater. Sci. Eng. A 417, 348–356 (2006). https://doi.org/10.1016/j.msea.2005.11.002 CrossRef

34.

Ayatollahi, M.R.; Aliha, M.R.M.M.: Mixed mode fracture in soda lime glass analyzed by using the generalized MTS criterion. Int. J. Solids Struct. 46, 311–321 (2009). https://doi.org/10.1016/j.ijsolstr.2008.08.035 CrossRefMATH

35.

Aliha, M.R.M.M.; Ayatollahi, M.R.: Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion. Int. J. Solids Struct. 49, 1877–1883 (2012). https://doi.org/10.1016/j.ijsolstr.2012.03.029 CrossRef

36.

Ayatollahi, M.R.; Saboori, B.: T-stress effects in mixed mode I/II/III brittle fracture. Eng. Fract. Mech. 144, 32–45 (2015). https://doi.org/10.1016/j.engfracmech.2015.06.070 CrossRef

37.

Smith, D.J.; Ayatollahi, M.R.; Pavier, M.J.: The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading. Fatigue Fract. Eng. Mater. Struct. 24, 137–150 (2001). https://doi.org/10.1046/j.1460-2695.2001.00377.x CrossRef

38.

Mirsayar, M.M.: A new mixed mode fracture test specimen covering positive and negative values of T-stress. Eng. Solid Mech. 2, 67–72 (2014). https://doi.org/10.5267/j.esm.2014.2.006 CrossRef

39.

Mirsayar, M.M.M.; Park, P.: Mixed mode brittle fracture analysis of high strength cement mortar using strain-based criteria. Theor. Appl. Fract. Mech. 86, 233–238 (2016). https://doi.org/10.1016/j.tafmec.2016.07.007 CrossRef

40.

Ayatollahi, M.R.R.; Aliha, M.R.M.R.M.: Fracture toughness study for a brittle rock subjected to mixed mode I/II loading. Int. J. Rock Mech. Min. Sci. 44, 617–624 (2007). https://doi.org/10.1016/j.ijrmms.2006.10.001 CrossRef

41.

Mirsayar, M.M.M.; Joneidi, V.A.A.; Petrescu, R.V.V.V.V.; Petrescu, F.I.T.I.T.; Berto, F.: Extended MTSN criterion for fracture analysis of soda lime glass. Eng. Fract. Mech. 178, 50–59 (2017). https://doi.org/10.1016/j.engfracmech.2017.04.018 CrossRef

42.

Ayatollahi, M.R.R.; Rashidi Moghaddam, M.; Berto, F.: A generalized strain energy density criterion for mixed mode fracture analysis in brittle and quasi-brittle materials. Theor. Appl. Fract. Mech. 79, 70–76 (2015). https://doi.org/10.1016/j.tafmec.2015.09.004 CrossRef

43.

Kaung Jain Chang: On the maximum strain criterion-a new approach to the angled crack problem. Eng. Fract. Mech. 14, 107–124 (1981). https://doi.org/10.1016/0013-7944(81)90021-7 CrossRef

44.

Ayatollahi, M.R.; Abbasi, H.: Prediction of fracture using a strain based mechanism of crack growth. Build. Res. J. 49, 167–180 (2001)

45.

Aliha, M.R.M.; Bahmani, A.; Akhondi, S.: Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens. Eur. J. Mech. A/Solids. 58, 148–162 (2016). https://doi.org/10.1016/j.euromechsol.2016.01.012 CrossRef

46.

Fayed, A.S.: Numerical evaluation of mode I/II SIF of quasi-brittle materials using cracked semi-circular bend specimen. Eng. Solid Mech. 6, 175–186 (2018). https://doi.org/10.5267/j.esm.2018.1.002 CrossRef

47.

Saghafi, H.; Zucchelli, A.; Minak, G.: Evaluating fracture behavior of brittle polymeric materials using an IASCB specimen. Polym. Test. 32, 133–140 (2013). https://doi.org/10.1016/j.polymertesting.2012.09.013 CrossRef

48.

Aliha, M.R.M.R.M.; Berto, F.; Bahmani, A.; Gallo, P.: Mixed mode I/II fracture investigation of Perspex based on the averaged strain energy density criterion. Phys. Mesomech. 20, 149–156 (2017). https://doi.org/10.1134/s1029959917020059 CrossRef

49.

ABAQUS: Analysis user’s guide—Version 6.14. Dassault Systèmes (2013). https://doi.org/10.1177/0886260505276833

50.

Anderson, T.L.: Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton (2017)CrossRefMATH

51.

Erdogan, F.; Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85, 519 (1963). https://doi.org/10.1115/1.3656897 CrossRef

52.

Ayatollahi, M.R.; Aliha, M.R.M.: On the use of Brazilian disc specimen for calculating mixed mode I-II fracture toughness of rock materials. Eng. Fract. Mech. 75, 4631–4641 (2008). https://doi.org/10.1016/j.engfracmech.2008.06.018 CrossRef

53.

Taylor, D.; Merlo, M.; Pegley, R.; Cavatorta, M.P.: The effect of stress concentrations on the fracture strength of polymethylmethacrylate. Mater. Sci. Eng. A 382, 288–294 (2004). https://doi.org/10.1016/j.msea.2004.05.012 CrossRef

54.

Golos, K.; Wasiluk, B.: Role of plastic zone in crack growth direction criterion under mixed mode loading. Int. J. Fract. 102, 341–353 (2000). https://doi.org/10.1023/A:1007663728926 CrossRef

55.

Aliha, M.R.M.; Ayatollah, M.R.; Smith, D.J.; Pavier, M.J.: Geometry and size effects on fracture trajectory in a limestone rock under mixed mode loading. Eng. Fract. Mech. 77, 2200–2212 (2010). https://doi.org/10.1016/j.engfracmech.2010.03.009 CrossRef

56.

Wei, M.D.; Dai, F.; Xu, N.W.; Liu, Y.; Zhao, T.: Fracture prediction of rocks under mode I and mode II loading using the generalized maximum tangential strain criterion. Eng. Fract. Mech. 186, 21–38 (2017). https://doi.org/10.1016/j.engfracmech.2017.09.026 CrossRef

57.

Bahmani, A.; Aliha, M.R.M.: Rock fracture toughness study under mixed mode I/III loading. Rock Mech. Rock Eng. (2017). https://doi.org/10.1007/s00603-017-1201-7

Title: Numerical Analysis of Crack Initiation Direction in Quasi-brittle Materials: Effect of T-Stress
Author: A. S. Fayed
Publication date: 29-04-2019
Publisher: Springer Berlin Heidelberg
Published in: Arabian Journal for Science and Engineering / Issue 9/2019
Print ISSN: 2193-567X
Electronic ISSN: 2191-4281
DOI: https://doi.org/10.1007/s13369-019-03860-4

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 9/2019

Bond Graph Modelling and Simulation of Planar Quadruple Robot with Different Gaits

Effect of the Process Parameters on Machining of GFRP Composites for Different Conditions of Abrasive Water Suspension Jet Machining

Role of the Induced Magnetic Field on Dispersed CNTs in Propylene Glycol Transportation Toward a Curved Surface

Design and Optimization for a New Compliant Planar Spring of Upper Limb Assistive Device Using Hybrid Approach of RSM–FEM and MOGA

Numerical and Experimental Study of the Aerothermal Characteristics in Solar Chimney Power Plant with Hyperbolic Chimney Shape

Augmented Turbulence for Progressive and Efficient Combustion in Biodiesel–Diesel Engine

Premium Partners