zbMATH — the first resource for mathematics

Rate effects on toughness in elastic nonlinear viscous solids. (English) Zbl 1419.74272
Summary: A micromechanics-based constitutive relation for void growth in a nonlinear viscous solid is proposed to study rate effects on fracture toughness. This relation is incorporated into a microporous strip of cell elements embedded in a computational model for crack growth. The microporous strip is surrounded by an elastic nonlinear viscous solid referred to as the background material. Under steady-state crack growth, two dissipative processes contribute to the macroscopic fracture toughness-the work of separation in the strip of cell elements and energy dissipation by inelastic deformation in the background material. As the crack velocity increases, voids grow in the strain-rate strengthened microporous strip, thereby elevating the work of separation. In contrast, the energy dissipation in the background material decreases as the crack velocity increases. In the regime where the work of separation dominates energy dissipation, toughness increases with crack velocity. In the regime where energy dissipation is dominant, toughness decreases with crack velocity. Computational simulations show that the two regimes can exist in certain range of crack velocities for a given material. The existence of these regimes is greatly influenced by the rate dependence of the void growth mechanism (and the initial void size) as well as that of the bulk material. This competition between the two dissipative processes produces a U-shaped toughness-crack velocity curve. Our computational simulations predict trends that agree with fracture toughness vs. crack velocity data reported in several experimental studies for glassy polymers and rubber-modified epoxies.

74-XX Mechanics of deformable solids
PDF BibTeX Cite
Full Text: DOI
[1] Abaqus/Standard User’s Manual, Version 6.3.1, 2002. Hibbit, Karlsson and Sorensen, RI, USA.
[2] Argon, A.S.; Hannoosh, J.G., Initiation of crazes in polystyrene, Philos. mag., 36, 1195-1216, (1977)
[3] Atkins, A.G.; Lee, C.S.; Caddell, R.M., Time-temperature dependent fracture toughness of PMMA, J. mater. sci., 10, 1394-1404, (1975)
[4] Bradley, W.; Cantwell, W.J.; Kausch, H.H., Viscoelastic creep crack growth: a review of fracture mechanical analyses, Mech. time-dependent mater., 1, 241-268, (1998)
[5] Brown, H.R., A molecular interpretation of the toughness of Glass polymers, Macromolecules, 24, 2752-2756, (1991)
[6] Cardwell, B.J.; Yee, A.F., Rate and temperature effects on the fracture toughness of a rubber-modified epoxy, Polymer, 34, 1695-1701, (1993)
[7] Cheng, L.; Guo, T.F., Vapor pressure assisted void growth and cracking of polymeric films and interfaces, Interface sci., 11, 277-290, (2003)
[8] Cheng, L.; Guo, T.F., Void interaction and coalescence in polymeric materials, Int. J. solids struct., 44, 1787-1808, (2007) · Zbl 1109.74045
[9] Chew, H.B.; Guo, T.F.; Cheng, L., Vapor pressure and residual stress effects on mixed mode toughness of an adhesive film, Int. J. fract., 134, 349-368, (2005) · Zbl 1196.74257
[10] Dean, R.H., Hutchinson, J.W., 1980. Quasi-static steady crack growth in small-scale yielding. In: Fracture Mechanics: 12th Conference, ASTM STP 700, American Society for Testing and Materials, pp. 383-405.
[11] Döll, W., Optical interference measurements and fracture-mechanics analysis of crack tip zones, Adv. polym., 52/53, 105-168, (1983)
[12] Du, J.; Thouless, M.D.; Yee, A.F., Effects of rate on crack growth in a rubber-modified epoxy, Acta mater., 48, 3581-3592, (2000)
[13] Duva, J.M.; Hutchinson, J.W., Constitutive potentials for dilutely voided nonlinear materials, Mech. mater., 3, 41-54, (1984)
[14] Estevez, R.; van der Giessen, E., Modeling and computational analysis of fracture of glassy polymers, Adv. polym. sci., 188, 195-234, (2005)
[15] Freund, L.B.; Hutchinson, J.W.; Lam, P.S., Analysis of high-strain-rate elastic – plastic crack growth, Eng. fract. mech., 23, 119-129, (1986)
[16] Guo, T.F.; Cheng, L., Modeling vapor pressure effects on void rupture and crack growth resistance, Acta mater., 50, 3487-3500, (2002)
[17] Guo, T.F.; Cheng, L., Vapor pressure and void size effects on failure of a constrained ductile film, J. mech. phys. solids, 51, 993-1014, (2003) · Zbl 1032.74650
[18] Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media, J. eng. mater. technol., 99, 2-15, (1977)
[19] Hui, C.Y.; Riedel, H., The asymptotic stress and strain field near the tip of a growing crack under creep conditions, Int. J. fract., 17, 409-425, (1981)
[20] Kambour, R.P., A review of crazing and fracture in thermoplastics, J. polym. sci. macromol. rev., 7, 1-154, (1973)
[21] Kinloch, A.J.; Gilbert, O.G.; Shaw, S.J., A mechanism for ductile crack growth in epoxy polymers, J. mater. sci., 21, 1051-1056, (1986)
[22] Kramer, E.J.; Berger, L.L., Fundamental processes of craze growth and fracture, Adv. polym. sci., 91/92, 1-68, (1990)
[23] Kumar, R.K.; Narasimhan, R.; Prabhakar, O., Dynamic growth of tensile cracks by ductile and brittle fracture mechanisms in a viscoplastic material, Acta metall. mater., 40, 1563-1572, (1992)
[24] Landis, C.M.; Pardoen, T.; Hutchinson, J.W., Crack velocity dependent toughness in rate dependent materials, Mech. mater., 32, 663-678, (2000)
[25] Leblond, J.B.; Perrin, G.; Suquet, P., Exact results and approximate models for porous viscoplastic solids, Int. J. plasticity, 10, 213-235, (1994) · Zbl 0821.73022
[26] Peirce, D.; Shih, C.F.; Needleman, A., A tangent modulus method for rate dependent solids, Comput. struct., 18, 875-887, (1984) · Zbl 0531.73057
[27] Scott, J.M.; Wells, G.M.; Phillips, D.C., Low temperature crack propagation in an epoxide resin, J. mater. sci., 15, 1436-1448, (1980)
[28] Sha, Y.; Hui, C.Y.; Ruina, A.; Kramer, E.J., Continuum and discrete modeling of craze failure at crack tip in a glassy polymer, Macromolecules, 28, 2450-2459, (1995)
[29] Sha, Y.; Hui, C.Y.; Ruina, A.; Kramer, E.J., Detailed simulation of craze fibril failure at a crack tip in a glassy polymer, Acta mater., 45, 3555-3563, (1997)
[30] Shih, C.F.; Xia, L., Modelling crack growth resistance using computational cells with microstructurally-based length scale, Astm stp, 1244, 163-190, (1995)
[31] Tijssens, M.G.A.; van der Giessen, E., A possible mechanism for cross-tie fibril generation in crazing of amorphous polymers, Polymer, 43, 831-838, (2002)
[32] Wang, T.C.; Qin, J.L., Constitutive potential for void-containing nonlinear materials and void growth, Acta mech. solida sin., 2, 129-146, (1989)
[33] Webb, T.W.; Aifantis, E.C., Oscillatory fracture in polymeric materials, Int. J. solids struct., 32, 2725-2743, (1995) · Zbl 0869.73059
[34] Wilkinson, D.S.; Ashby, M.F., Pressure sintering by power law creep, Acta metall., 23, 1277-1285, (1975)
[35] Xia, L.; Shih, C.F., Ductile crack growth—I: a numerical study using computational cells with microstructurally-based length scales, J. mech. phys. solids, 43, 233-259, (1995) · Zbl 0879.73047
[36] Xia, L.; Shih, C.F.; Hutchinson, J.W., A computational approach to ductile crack growth under large scale yielding conditions, J. mech. phys. solids, 43, 389-413, (1995) · Zbl 0875.73192
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.