Abstract
The present paper investigates the employment of coarse meshes in evaluating the T-stress with the displacement method. Several finite element analyses have been carried out with different mesh refinements and accuracies. Mode I and mixed mode I/II loadings have been considered in finite element analyses. Under mode I loading, single and double edge notched geometries have been considered, while plate with central crack has been considerd for mixed mode loading condition. The analyses are compared with the results by the well-nown stress based approach, and showed that the displacement method permits the evaluation of the T-stress with the employment of coarse meshes. By the way, several precautions must be taken when dealing with coarse and very coarse meshes.
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References
McClintock, F.A., Plasticity Aspect of Fracture, Fracture an Advanced Treatise, Vol. III, Liebowitz, H., Ed., New York: Academic Press, 1971, pp. 47–225.
O’Dowd, N.P. and Shih, C.F., Family of Crack-Tip Fields Characterized by a Triaxiality Parameter-I. Structure of fields, J. Mech. Phys. Solid., 1991, vol. 39, pp. 989–1015. doi 10.1016/0022-5096(91)90049-T
O’Dowd, N.P. and Shih, C.F., Family of Crack-Tip Fields Characterized by a Triaxiality Parameter-II. Fracture Applications, J. Mech. Phys. Solid., 1992, vol. 40, pp. 939–963. doi 10.1016/0022-5096(92)90057-9
Shih, C., O’Dowd, N., and Kirk, M., A Framework for Quantifying Crack Tip Constraint, Constraint Effects in Fracture, West Conshohocken, PA: ASTM Int., 1992, pp. 2–19. doi 10.1520/STP18020S
Ayatollahi, M.R., Rashidi Moghaddam, M., Razavi, N., and Berto, F., Geometry Effects on Fracture Trajectory of PMMA Samples under Pure Mode-I Loading, Eng. Fract. Mech., 2016, vol. 163, pp. 449–461. doi 10.1016/j.engfracmech.2016.05.014
Rashidi Moghaddam, M., Ayatollahi, M.R., Razavi, N., and Berto, F., Mode II Brittle Fracture Assessment Using an Energy Based Criterion, Phys. Mesomech., 2017, vol. 20, no. 2, pp. 142–148.
Williams, M.L., On the Stress Distribution at the Base of a Stationary Crack, J. Appl. Mech., 1957, vol. 24, pp. 109–114. doi 10.1115/1.3640470
Hancock, J., Reuter, W., and Parks, D., Constraint and Toughness Parameterized by 7, West Conshohocken, PA: ASTM Int., 1993. doi 10.1520/STP18021S
Sumpter, J.D.G., An Experimental Investigation of the T Stress Approach, ASTM STP 1171, 1993, pp. 492–502. doi 10.1520/STP18042S
Sherry, A.H., France, C.C., and Goldthorpe, M.R., Compendium of T-Stress Solutions for Two and Three Dimensional Cracked Geometries, Fatig. Fract. Eng. Mater. Struct., 1995, vol. 18, pp. 141–155. doi 10.1111/j.1460-2695.1995.tb00148.x
Chen, Y.Z., Integral Equation Methods for Multiple Crack Problems and Related Topics, Appl. Mech. Rev., 2007, vol. 60, no. 172. doi 10.1115/1.2750671
Larsson, S.G. and Carlsson, A.J., Influence of NonSingular Stress Terms and Specimen Geometry on Small-Scale Yielding at Crack Tips in Elastic-Plastic Materials, J. Mech. Phys. Solid., 1973, vol. 21, pp. 263–277. doi 10.1016/0022-5096(73)90024-0
Leevers, P.S. and Radon, J.C., Inherent Stress Biaxiality in Various Fracture Specimen Geometries, Int. J. Fract., 1982, vol. 19, pp. 311–325. doi 10.1007BF00012486
Ewing, P.D., Swedlow, J.L., and Williams, J.G., Further Results on the Angled Crack Problem, Int. J. Fract., 1976, vol. 12, pp. 85–93. doi 10.1007/BF00036011
Knesl, Z., Evaluation of the Elastic T-Stress Using a Hybrid Finite Element Approach, Int. J. Fract., 1994, vol. 70, pp. R9–R14. doi 10.1007/BF00018140
Cardew, G.E., Goldthorpe, M.R., Howard, I.C., and Kfouri, A.P., On the Elastic T-Term, in Fundamental Deformation and Fracture, Bilby, B.A., Miller, K.J., and Willis, J.R., Eds., Sheffield: Cambridge University Press, 1984, pp. 465–476.
Kfouri, A.P., Some Evaluations of the Elastic T-Term Using Eshelby’s Method, Int. J. Fract., 1986, vol. 30, no. 301–315. doi 10.1007/BF00019710
Fett, T., A Green’s Function for T-Stresses in an Edge-Cracked Rectangular Plate, Eng. Fract. Mech., 1997, vol. 57, pp. 365–373. doi 10.1016/S0013-7944(97)00034-9
Maleski, M.J., Kirugulige, M.S., and Tippur, H.V, A Method for Measuring Mode I Crack Tip Constraint under Static and Dynamic Loading Conditions, Exp. Mech., 2004, vol. 44, pp. 522–532. doi 10.1007/BF0-2427964
Olsen, P.C., Determining the Stress Intensity Factors Kt, Kjj and the T-Term Via the Conservation Laws Using the Boundary Element Method, Eng. Fract. Mech., 1994, vol. 49, pp. 49–60. doi 10.1016/0013-7944(94)90110-4
Sladek, J., Sladek, V., and Fedelinski, P., Contour Integrals for Mixed-Mode Crack Analysis: Effect of Nonsingular Terms, Theor. Appl. Fract. Mech., 1997, vol. 27, pp. 115–127. doi 10.1016/S0167-8442(97)00013-X
Seed, G.M. and Nowell, D., Use of the Distributed Dislocations Method to Determine the T-Stress, Fatigue Fract. Eng. Mater. Struct., 1994, vol. 17, pp. 605–618.
Ayatollahi, M.R., Pavier, M.J., and Smith, D.J., Determination of T-Stress from Finite Element Analysis for Mode I and Mixed Mode I/II Loading, Int. J. Fract., 1998, vol. 91, pp. 283–298. doi 10.1023/A:1007581125618
Westergaard, H.M., Bearing Pressures and Cracks, J. Appl. Mech., 1939, vol. 61, pp. A49–A53. doi 216756690
Irwin, G.R., Fracture, in Elasticity and Plasticity, Flügge, S., Ed., Berlin-Heidelberg: Springer, 1958, pp. 551–590. doi 10.1007/978-3-642-45887-3_5
Anderson, T.L., Fracture Mechanics: Fundamentals and Applications, Taylor & Francis, 2005.
Bueckner, H., A Novel Principlefor the Computation of Stress Intensity Factors, 1970.
Yang, Y.Y., Effect of the Regular Term on the Stress Field in a Joint of Dissimilar Materials under Remote Mechanical Load, Arch. Appl. Mech., 1999, vol. 69, pp. 364–378. doi 10.1007/s004190050227
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Original Text © M. Acanfora, P. Gallo, N. Razavi, M.R. Ayatollahi, F. Berto, 2018, published in Fizicheskaya Mezomekhanika, 2018, Vol. 21, No. 1, pp. 30–40.
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Acanfora, M., Gallo, P., Razavi, N. et al. Numerical Evaluation of T-stress under Mixed Mode Loading Through the Use of Coarse Meshes. Phys Mesomech 21, 124–134 (2018). https://doi.org/10.1134/S1029959918020054
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DOI: https://doi.org/10.1134/S1029959918020054