×

Dynamic fibre sliding along debonded, frictional interfaces. (English) Zbl 1149.74375

Summary: The problem is considered of a fibre that is driven dynamically, by compression at one end, into a matrix. The fibre is not initially bonded to the matrix, so that its motion is resisted solely by friction. Prior work based on simplified models has shown that the combination of inertial effects and friction acting over long domains of the fibre-matrix interface gives rise to behaviour that is far more complex than in the well-known static loading problem. The front velocity may depart significantly from the bar wave speed and regimes of slip, slip/stick and reverse slip can exist for different material choices and loading rates. Here more realistic numerical simulations and detailed observations of dynamic displacement fields in a model push-in experiment are used to seek more complete understanding of the problem. The prior results are at least partly confirmed, especially the ability of simple shear-lag theory to predict front velocities and gross features of the deformation. Some other fundamental aspects are newly revealed, including oscillations in the interface stresses during loading; and suggestions of unstable, possibly chaotic interface conditions during unloading. Consideration of the experiments and two different orders of model suggest that the tentatively characterized chaotic phenomena may arise because of the essential nonlinearity of friction, that the shear traction changes discontinuously with the sense of the motion, rather than being associated with the details of the constitutive law that is assumed for the friction. This contrasts with recent understanding of instability and ill-posedness at interfaces loaded uniformly in time, where the nature of the assumed friction law dominates the outcome.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adams, G.G. 1998 Steady sliding of two elastic half-spaces with friction reduction due to interface stick-slip. <i>J. Appl. Mech.</i>&nbsp;<b>65</b>, 470–475.
[2] Andrews, D.J. 1976 Rupture velocity of plane strain shear cracks. <i>J. Geophys. Res.</i>&nbsp;<b>81</b>, 5679–5687.
[3] Bao, G. & Suo, Z. 1992 Remarks on crack-bridging concepts. <i>Appl. Mech. Rev.</i>&nbsp;<b>24</b>, 355–366.
[4] Broberg, K.B. 1994 Intersonic bilateral slip. <i>Geophys. J. Int.</i>&nbsp;<b>119</b>, 706–714.
[5] Budiansky, B., Hutchinson, J.W. & Evans, A.G. 1986 Matrix fracture in fiber reinforced ceramics. <i>J. Mech. Phys. Solids</i>&nbsp;<b>34</b>, 167–189, (doi:10.1016/0022-5096(86)90035-9).
[6] Burridge, R. 1973 Admissible speeds for plane-strain self-similar shear cracks with friction but lacking coercion. <i>Geophys. J. R. Astron. Soc.</i>&nbsp;<b>35</b>, 439. · Zbl 0272.73022
[7] Burridge, R., Conn, G. & Freund, L.B. 1979 The stability of a rapid mode II shear crack with finite cohesive tractions. <i>J. Geophys. Res.</i>&nbsp;<b>85</b>, 2210–2222.
[8] Cochard, A. & Rice, J.R. 2000 Fault rupture between dissimilar materials: ill-posedness, regularization, and slip-pulse response. <i>J. Geophys. Res.</i>&nbsp;<b>105</b>, 25891–25907, (doi:10.1029/2000JB900230).
[9] Cox, B.N. 1990 Interfacial sliding near a free surface in a fibrous or layered composite during thermal cycling. <i>Acta Metall. Mater.</i>&nbsp;<b>38</b>, 2411–2424, (doi:10.1016/0956-7151(90)90253-D).
[10] Cox, B.N. & Marshall, D.B. 1994 Concepts for bridged cracks in fracture and fatigue. <i>Acta Metall. Mater.</i>&nbsp;<b>42</b>, 341–363, (doi:10.1016/0956-7151(94)90492-8).
[11] Cox, B.N. & Sridhar, N. 2001 Universal bridging laws for cracks in creeping media. <i>Advances in fracture research, Proc. Int. Conf. on Fracture</i>, ICF10, Honolulu. Oxford: Elsevier.
[12] Cox, B.N., Dadkhah, M.S., James, M.R., Marshall, D.B., Morris, W.L. & Shaw, M.C. 1990 On determining temperature dependent interfacial shear properties and bulk residual stresses in fibrous composites. <i>Acta Metall. Mater.</i>&nbsp;<b>38</b>, 2425–2433, (doi:10.1016/0956-7151(90)90254-E).
[13] Cox, B.N., Sridhar, N. & Beyerlein, I. 2001 Inertial effects in the pullout mechanism during dynamic loading of a bridged crack. <i>Acta Mater.</i>&nbsp;<b>49</b>, 3863–3877, (doi:10.1016/S1359-6454(01)00241-5).
[14] Gao, H., Huang, Y. & Abraham, F.F. 2001 Continuum and atomistic studies of intersonic crack propagation. <i>J. Mech. Phys. Solids</i>&nbsp;<b>49</b>, 2113–2132, (doi:10.1016/S0022-5096(01)00032-1). · Zbl 1093.74510
[15] Hutchinson, J.W. & Jensen, H.M. 1990 Models of fiber debonding and pullout in brittle composites with friction. <i>Mech. Mater.</i>&nbsp;<b>9</b>, 139–163, (doi:10.1016/0167-6636(90)90037-G).
[16] Lapusta, N. & Rice, J.R. 2003 Nucleation and early seismic propagation of small and large events in a crustal earthquake model. <i>J. Geophys. Res.</i>&nbsp;<b>108</b>, (doi:10.1029/2001JB000793).
[17] Marshall, D.B. 1992 Analysis of fiber debonding and sliding experiments in brittle matrix composites. <i>Acta Metall.</i>&nbsp;<b>40</b>, 427–441, (doi:10.1016/0956-7151(92)90391-Q).
[18] Marshall, D.B., Cox, B.N. & Evans, A.G. 1985 The mechanics of matrix cracking in brittle-matrix fiber composites. <i>Acta Metall.</i>&nbsp;<b>33</b>, 2013–2021, (doi:10.1016/0001-6160(85)90124-5).
[19] Massabò, R. & Cox, B.N. 1999 Concepts for bridged mode II delamination cracks. <i>J. Mech. Phys. Solids</i>&nbsp;<b>47</b>, 1265–1300, (doi:10.1016/S0022-5096(98)00107-0).
[20] McCartney, L.N. 1987 Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites. <i>Proc. R. Soc. A</i>&nbsp;<b>409</b>, 329–350.
[21] Needleman, A. 1999 An analysis of intersonic crack growth under shear loading. <i>J. Appl. Mech.</i>&nbsp;<b>66</b>, 847–857.
[22] Needleman, A. & Rosakis, A.J. 1999 The effect of bond strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces. <i>J. Mech. Phys. Solids</i>&nbsp;<b>47</b>, 2411–2445, (doi:10.1016/S0022-5096(99)00012-5). · Zbl 0982.74059
[23] Nikitin, L.V. & Tyurekhodgaev, A.N. 1990 Wave propagation and vibration of elastic rods with interfacial frictional slip. <i>Wave Motion</i>&nbsp;<b>12</b>, 513–526, (doi:10.1016/0165-2125(90)90022-V). · Zbl 0725.73054
[24] Prakash, V. 1998 Frictional response of sliding interfaces subjected to time varying normal pressures. <i>J. Tribol.</i>&nbsp;<b>120</b>, 97–102.
[25] Prakash, V. & Clifton, R.J. 1993 Time resolved dynamic friction measurements in pressure-shear. <i>Experimental techniques in the dynamics of deformable solids: applied mechanics division</i> (ed. Ramesh, K.T.), pp. 33–47, New York: ASME
[26] Ranjith, K. & Rice, J.R. 2001 Slip dynamics at an interface between dissimilar materials. <i>J. Mech. Phys. Solids</i>&nbsp;<b>49</b>, 341–361, (doi:10.1016/S0022-5096(00)00029-6).
[27] Rosakis, A.J., Samudrala, O. & Coker, D. 1999 Cracks faster than the shear wave speed. <i>Science</i>&nbsp;<b>284</b>, 1337–1340, (doi:10.1126/science.284.5418.1337).
[28] Sridhar, N., Yang, Q.D. & Cox, B.N. 2003 Slip, stick and reverse slip characteristics during dynamic fiber pullout. <i>J. Mech. Phys. Solids</i>&nbsp;<b>51</b>, 1215–1241, (doi:10.1016/S0022-5096(03)00035-8). · Zbl 1077.74526
[29] Weertman, J.J. 1980 Unstable slippage across a fault that separates elastic media of different elastic constants. <i>J. Geophys. Res.</i>&nbsp;<b>85</b>, 1455–1461.
[30] Xia, K., Rosakis, A.J. & Kanamori, H. 2004 Laboratory earthquakes: the sub-rayleigh-to-supershear rupture transition. <i>Science</i>&nbsp;<b>303</b>, 1859–1859, (doi:10.1126/science.1094022).
[31] Zheng, G. & Rice, J.R. 1998 Conditions under which velocity-weakening friction allows a self-healing versus cracklike mode of rupture. <i>Bull. Seismol. Soc. Am.</i>&nbsp;<b>88</b>, 1466–1483.
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.