Moving surfaces and interfaces : application to damage, fracture and wearcontact

Claude Stolz; Claude Stolz

doi:10.3934/matersci.2016.3.881

AIMS Materials Science

2016, Volume 3, Issue 3: 881-907. doi: 10.3934/matersci.2016.3.881

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Moving surfaces and interfaces : application to damage, fracture and wearcontact

Claude Stolz ^,

Institut GeM, Ecole Centrale de Nantes CNRS UMR6183, F-44321 Nantes Cedex 3, IMSIAEdF-CEA-CNRS UMR9219, Universit´e Paris Saclay, 828 Bvd Mar´echaux, F-91762 PalaiseauCedex, France

Received: 30 May 2016 Accepted: 12 July 2016 Published: 14 July 2016

The full scenario of the degradation of solids under mechanical loading is described by modelling the gradual loss of rigidity. This common approach is purely local. Another way to describe the damage evolution is to consider the propagation of the surface separating sound material and damaged material. When this surface is moving, a flux of matter is induced, that is useful for describing the loss of material during wear mechanisms or brittle fracture. The article proposes modelling of moving surface and interface in order to describe such behaviours. The problem of evolution is written, analysis of stability and bifurcation of the propagation is also presented. Applications to brittle fracture, transition from fracture to damage and wear contact are briefly investigated.
- moving interface,
- damage,
- wear contact,
- propagation of discontinuities
Citation: Claude Stolz. Moving surfaces and interfaces : application to damage, fracture and wearcontact[J]. AIMS Materials Science, 2016, 3(3): 881-907. doi: 10.3934/matersci.2016.3.881

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Abstract

The full scenario of the degradation of solids under mechanical loading is described by modelling the gradual loss of rigidity. This common approach is purely local. Another way to describe the damage evolution is to consider the propagation of the surface separating sound material and damaged material. When this surface is moving, a flux of matter is induced, that is useful for describing the loss of material during wear mechanisms or brittle fracture. The article proposes modelling of moving surface and interface in order to describe such behaviours. The problem of evolution is written, analysis of stability and bifurcation of the propagation is also presented. Applications to brittle fracture, transition from fracture to damage and wear contact are briefly investigated.

References

[1]	Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46: 1319-1342. doi: 10.1016/S0022-5096(98)00034-9
[2]	Peerlings R, Geers M, de Borst R, et al. (2001) A critical comparison of non-local and gradientenhanced softening continua. Int J Solids Struct 38: 7723-7746. doi: 10.1016/S0020-7683(01)00087-7
[3]	Hakim V, Karma A (2009) A law of crack motion and phase-field models of fracture. J Mech Phys Solids 57: 342-368. doi: 10.1016/j.jmps.2008.10.012
[4]	Bourdin B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. J Elasticity 91: 5-148. doi: 10.1007/s10659-007-9107-3
[5]	Bui HD (1980) Solution explicite d'un problème de frontière libre en élastoplasticité avec endommagement. C R Acad des Sciences de Paris, série B 290: 345-348.
[6]	Bui HD, Ehrlacher A (1980) Propagation dynamique d'une zone endommagée dans un solide élastique fragile en mode III et en régime permanent. C R Acad des Sciences de Paris, Série B 290 : 273-276.
[7]	Gurtin ME (1995) The nature of configurational forces. Arch Rat Mech 131: 67-100. doi: 10.1007/BF00386071
[8]	Dragon-Louiset M, Stolz C (1999) A thermodynamical approach to contact wear. C R Acad des Sciences de Paris, S´erie IIb 327: 1275-1280.
[9]	Bui HD, Dang Van Ky, Stolz C (1981) Variational-principles applicable to rate boundary-valueproblems of elastic-brittle solids with damaged zone. C R Acad des Sciences de Paris, Série II 292: 251-254.
[10]	Pradeilles-Duval RM, Stolz C (1995) Mechanical transformations and discontinuities along a moving surface. J Mech Phys Solids 43: 91-121. doi: 10.1016/0022-5096(94)00061-9
[11]	Stolz C (2007) Bifurcation of equilibrium solutions and defects nucleation. Int J Fracture 147: 103-107. doi: 10.1007/s10704-007-9147-5
[12]	Stolz C (2010) Thermodynamical description of running discontinuties: application to friction and wear. Entropy 12: 1418-1439. doi: 10.3390/e12061418
[13]	Stolz C, Moës N (2012) A new model of damage: a moving thick layer approach. Int J Fracture 174: 49-60. doi: 10.1007/s10704-012-9693-3
[14]	Abeyaratne R, Knowles J (1990) On the driving traction acting on a surface of strain discontinuity in a continuum. J Mech Phys Solids 38: 345-360. doi: 10.1016/0022-5096(90)90003-M
[15]	Son QN, Pradeilles RM, Stolz C (1989) On a regularized propagation law in fracture and brittle damage. C R Acad des Sciences de Paris, Série II 309: 1515-1520.
[16]	Gurtin ME, Podio-Giugli P (1996) Configurational forces and the basic laws for crack propagation. J Mech Phys Solids 44: 905-927. doi: 10.1016/0022-5096(96)00014-2
[17]	Hill R (1986) Energy momentum tensors in elastostatics: some reflections on the general theory. J Mech Phys Solids 34: 305-317. doi: 10.1016/0022-5096(86)90022-0
[18]	Hutchinson J, Thouless MD, Liniger EG (1992) Growth and configurational stability of circular buckling driven film delamination. Acta Metall Mat 40: 295-308. doi: 10.1016/0956-7151(92)90304-W
[19]	Pradeilles RM, Stolz C (1991) Sur le problème d'évolution des solides à changement de phase irréversibles. C R Acad des Sciences de Paris, Série II 313: 297-302.
[20]	Storakers B, Andersson B (1988) Non linear theory applied to delamination in composites. J Mech Phys Solids 36: 689-718. doi: 10.1016/0022-5096(88)90004-X
[21]	Stolz C (2011) Analysis of stability and bifurcation in non-linear mechanics with dissipation. Entropy 13: 332-366. doi: 10.3390/e13020332
[22]	Pradeilles-Duval RM (2004) Quasi-static evolution of delaminated structures: analysis of stability and bifurcation. Int J Solids Struct 41: 103-130. doi: 10.1016/j.ijsolstr.2003.07.006
[23]	Stolz C. (2004), Energy methods in Non linear Mechanics, Lectures Notes 11,Warsawa, IPPT Pan
[24]	Neuber H (1968) A physically non linear notch and crack model. J Mech Phys Solids 16: 289-294. doi: 10.1016/0022-5096(68)90037-9
[25]	Rice J (1966) Contained plastic deformation near cracks and notches under longitudinal shear. Int J Fracture Mech 2: 426-447.
[26]	Stolz C (2015) Asymptotic fields ahead a crack for a class of non-linear materils under mode III. Mechanics of Materials 90: 102-110. doi: 10.1016/j.mechmat.2015.04.005
[27]	Knowles JK, Sternberg E (1980) Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example. J Elasticity 10: 81-110. doi: 10.1007/BF00043136
[28]	Rice J (1967) Stresses due to sharp notch in a work hardening elastic plastic material loaded by a longitudinal shear. J Appl Mech 34: 287-298. doi: 10.1115/1.3607681
[29]	Knowles JK, Sternberg E (1981) Anti-plane shear fields with discontinuous gradients near the tip of a crack in finite elastostatics. J Elasticity 11: 129-164. doi: 10.1007/BF00043857
[30]	Stolz C (2010) Closed form solution for the finite anti-plane shear field for a class of incompressible brittle solids. Comptes Rendus Mécanique 338-12: 663-669.
[31]	Stolz C, Parrilla-Gomez A (2015) Antiplane shear field for a class of hyperelastic incompressible brittle material: analytical and numerical approaches. J Mech Mater Struct 10: 395-410. doi: 10.2140/jomms.2015.10.395
[32]	Dragon-Louiset M (2001) On a predictive macroscopic contact-sliding wear model based on micro-mechanical consideration.. Int J Solids Struct 38: 1625-1639. doi: 10.1016/S0020-7683(00)00065-2
[33]	Bui HD, Dang Van K (1976) Contribution à l'étude théorique du contact élastique d'un frotteur cylindrique glissant sur un massif élastique. Industrie Minérale, No Sp´ecial Rh´eologie IV: 1-8.

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