On fracture criteria for dynamic crack propagation in elastic materials with couple stresses. (English) Zbl 1423.74840
Summary: The focus of the article is on fracture criteria for dynamic crack propagation in elastic materials with microstructures. Steady-state propagation of a Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behavior of the material is described by the theory of couple-stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion, and thus it is able to account for the underlying microstructures of the material. Both translational and micro-rotational inertial terms are included in the balance equations, and the behavior of the solution near to the crack tip is investigated by means of an asymptotic analysis. The asymptotic fields are used to evaluate the dynamic J-integral for a couple-stress material, and the energy release rate is derived by the corresponding conservation law. The propagation stability is studied according to the energy-based Griffith criterion and the obtained results are compared to those derived by the application of the maximum total shear stress criterion.
MSC:
| 74R10 | Brittle fracture |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74N15 | Analysis of microstructure in solids |
Keywords:
couple stress elasticity; dynamic fracture; steady-state propagation; energy release rate; fracture criterionReferences:
| [1] | Aifantis, E. C., On the gradient approach - relation to eringen’s nonlocal theory, International Journal of Engineering Science, 49, 1367-1377, (2011) |
| [2] | Andrade, J. E.; Avila, C. F.; Hall, S. A.; Lenoir, L.; Viggiani, G., Multiscale modelling and characterization of granular matter: from grain kinematics to continuum mechanics, Journal of the Mechanics and Physics of Solids, 59, 237-250, (2011) · Zbl 1270.74049 |
| [3] | Aravas, N.; Giannakopoulos, A. E., Plane asymptotic crack-tip solutions in gradient elasticity, International Journal of Solids and Structures, 46, 4478-4503, (2009) · Zbl 1176.74155 |
| [4] | Arfken, G. B.; Weber, H. J., Mathematical methods for physicists, (2005), Elsevier Academic Press San Diego · Zbl 1066.00001 |
| [5] | Askes, H.; Aifantis, E. C., Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures, 48, 1962-1990, (2011) |
| [6] | Askes, H.; Bennet, T.; Gitman, I. M.; Aifantis, E. C., A multi-scale formulation of gradient elasticity and its finite element implementation, (Papadrakakis, M.; Topping, B., Trends in engineering computational technology, (2008), Saxe-Coburg Stirlingshire, UK), 189-208 |
| [7] | Askes, H.; Gitman, I. M.; Simone, A.; Sluys, L. J., Modelling of size effects with gradient-enriched continuum theories, (Borodich, F., IUTAM symposium on scaling in solids mechanics, (2009), Springer), 59-68 · Zbl 1208.74013 |
| [8] | Atkinson, C.; Leppington, F. G., Some calculations of the energy-release rate G for cracks in micropolar and couple-stress elastic media, International Journal of Fracture, 10, 599-602, (1974) |
| [9] | Atkinson, C.; Leppington, F. G., The effect of couple stresses on the tip of a crack, International Journal of Solids and Structures, 13, 1103-1122, (1977) · Zbl 0368.73083 |
| [10] | Bigoni, D.; Drugan, W. J., Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials, ASME Journal of Applied Mechanics, 74, 741-753, (2007) |
| [11] | Budiansky, B., On the elastic moduli of some heterogeneous materials, Journal of the Mechanics and Physics of Solids, 13, 223-227, (1965) |
| [12] | Budiansky, B.; O’Connell, R. J., Elastic moduli of a cracked solid, International Journal of Solids and Structures, 12, 81-97, (1976) · Zbl 0318.73065 |
| [13] | Cosserat, E.; Cosserat, F., Theorie des corps deformables, (1909), Hermann et Fils · JFM 40.0862.02 |
| [14] | Dal Corso, F.; Willis, J. R., Stability of strain gradient plastic materials, Journal of the Mechanics and Physics of Solids, 59, 1251-1267, (2011) · Zbl 1270.74032 |
| [15] | Du, Z.-Z.; Betegon, C.; Hancock, J. W., J dominance in mixed mode loading, International Journal of Fracture, 52, 191-206, (1991) |
| [16] | Du, Z.-Z.; Hancock, J. W., The effect of non-singular terms on crack-tip constraint, Journal of the Mechanics and Physics of Solids, 39, 555-567, (1991) |
| [17] | Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, Proceedings of the Royal Society of London Series A, 241, 376-396, (1976) · Zbl 0079.39606 |
| [18] | Fischer, B., The product of distributions, Quarterly Journal of Mathematics: Oxford, 22, 291-298, (1971) · Zbl 0213.13104 |
| [19] | Fleck, N. A.; Hutchinson, J. W., A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49, 2245-2271, (2001) · Zbl 1033.74006 |
| [20] | Fleck, N. A.; Muller, G. M.; Ashby, M. F.; Hutchinson, J. W., Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42, 475-487, (1994) |
| [21] | Freund, L. B., Dynamic fracture mechanics, (1998), Cambridge University Press · Zbl 0712.73072 |
| [22] | Freund, L. B.; Hutchinson, J. W., High strain-rate crack growth in rate-dependent plastic solids, Journal of the Mechanics and Physics of Solids, 33, 169-191, (1985) |
| [23] | Georgiadis, H. G., The mode III crack problem in microstructured solids governed by dipolar gradient elasticity, static and dynamic analysis, ASME Journal of Applied Mechanics, 70, 517-530, (2003) · Zbl 1110.74453 |
| [24] | Gourgiotis, P. A.; Georgiadis, H. G.; Sifnaiou, M. D., Couple-stress effects for the problem of a crack under concentrated shear loading, Mathematics and Mechanics of Solids, 17, 433-459, (2011) · Zbl 07278872 |
| [25] | Hancock, J. W.; Du, Z.-Z., Two parameters characterization of elastic-plastic crack-tip fields, ASME Journal of Applied Mechanics, 113, 104-110, (1991) |
| [26] | Hashin, Z., The moduli of an elastic solid containing spherical particles of another elastic material, (Olszak, W., Non-homogeneity in elasticity and plasticity, (1959), Pergamon New York), 463-478 · Zbl 0091.38103 |
| [27] | Huang, Y.; Hu, K. X.; Chandra, A., A self-consistent mechanics method for solids containing inclusions and a general distribution of cracks, Acta Mechanica, 105, 69-84, (1994) · Zbl 0811.73048 |
| [28] | Kachanov, M., Elastic solids with many cracks: a simple method of analysis, International Journal of Solids and Structures, 23, 27-43, (1987) · Zbl 0601.73096 |
| [29] | Kachanov, M., Effective elastic properties of cracked solids: critical review of some basic concepts, Applied Mechanics Reviews, 45, 304-335, (1992) |
| [30] | Koiter, W. T., Couple-stresses in the theory of elasticity, I and II, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen - Series B, 67, 17-44, (1964) · Zbl 0124.17405 |
| [31] | Lakes, R. S., Experimental microelasticity of two porous solids, International Journal of Solids and Structures, 22, 55-63, (1986) |
| [32] | Lakes, R. S., Experimental methods for study of Cosserat elastic solids and other generalized elastic continua, (Mühlhaus, H., Continuum models for materials with micro-structure, (1995), John Wiley New York), 1-22 · Zbl 0900.73005 |
| [33] | Lubarda, V. A.; Markenscoff, X., Conservation integrals in couple stress elasticity, Journal of the Mechanics and Physics of Solids, 48, 553-564, (2000) · Zbl 0988.74015 |
| [34] | Mishuris, G.; Piccolroaz, A.; Radi, E., Steady-state propagation of a mode III crack in couple stress elastic materials, International Journal of Engineering Science, 61, 112-128, (2013) · Zbl 1423.74721 |
| [35] | Morozov, N. F., Mathematical problems of theory of cracks, (1984), Nauka Moscow · Zbl 0566.73079 |
| [36] | Obrezanova, O.; Movchan, A. B.; Willis, J. R., Dynamic stability of a propagating crack, Journal of the Mechanics and Physics of Solids, 50, 2637-2668, (2002) · Zbl 1100.74620 |
| [37] | Piccolroaz, A.; Mishuris, G.; Radi, E., Mode III interfacial crack in the presence of couple stress elastic materials, Engineering Fracture Mechanics, 80, 60-71, (2012) · Zbl 1423.74721 |
| [38] | Radi, E., Effects of characteristic material lengths on mode III crack propagation in couple stress elastic-plastic materials, International Journal of Plasticity, 23, 1439-1456, (2007) · Zbl 1134.74399 |
| [39] | Radi, E., On the effects of the characteristic lengths in bending and torsion on mode III crack in couple stress elasticity, International Journal of Solids and Structures, 45, 3033-3058, (2008) · Zbl 1169.74548 |
| [40] | Radi, E.; Gei, M., Mode III crack growth in linear hardening materials with strain gradient effects, International Journal of Fracture, 130, 765-785, (2004) · Zbl 1196.74253 |
| [41] | Roos, B. W., Analitic functions and distributions in physics and engineering, (1969), Wiley New York · Zbl 0186.57902 |
| [42] | Silberschmidt, V., Effect of the microstructure: multi-scale modelling, (Silberschmidt, V., Computational and experimental mechanics of advanced materials, (2009), Springer New York), 225-259 |
| [43] | Smith, D. J.; Ayatollahi, M. R.; Pavier, M. J., On the consequences of T-stress in elastic brittle fracture, Proceedings of the Royal Society of London Series A, 462, 2415-2437, (2006) · Zbl 1149.74390 |
| [44] | Tvergaard, V.; Hutchinson, J. W., Effect of T-stress on mode I crack growth resistance in a ductile solid, International Journal of Solids and Structures, 31, 823-833, (1994) · Zbl 0800.73334 |
| [45] | Willis, J. R., A comparison of the fracture criteria of griffith and Barenblatt, Journal of the Mechanics and Physics of Solids, 15, 151-162, (1967) |
| [46] | Willis, J. R., Fracture mechanics of interfacial cracks, Journal of the Mechanics and Physics of Solids, 19, 335-368, (1971) · Zbl 0329.73070 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
