Elastic–plastic analysis of interaction between an interface and crack in bi-materials

Belhouari, M.; Amiri, A.; Mehidi, A.; Madani, K.; Bouiadjra, B. Bachir

doi:10.1177/1056789513493646

Cited by 15 publications

(10 citation statements)

References 61 publications

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“…For the plane problem of a bi-material plate with a crack normal at the interface, the J integral can be approximated by the following expression [40]:…”

Section: Resultsmentioning

confidence: 99%

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Three-dimensional finite element analysis of a crack normal to and terminating at a bi-material interface

Mehidi

Kaddouri

Belhouari

et al. 2014

J Braz. Soc. Mech. Sci. Eng.

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eigenfunction expansion technique. Zak and Williams [1] showed that the stress field singularity at the tip of a crack perpendicular to an interface or terminating at the interface is of order r −λ , where λ is the real part of the eigenvalue and depends on the elastic properties of the bi-material. Bogy [2] investigated the stress singularity of an infinite crack terminating at the interface with an arbitrary angle of different material components. Cook and Erdogan [3] used the Mellin transform method to derive the governing equation of a finite crack perpendicular to the interface and obtained the stress intensity factors (SIFs). The authors found that the power singularity of stress around the crack tip is not −1/2. Erdogan and Biricikoglu [4] solved the problem of two bounded half planes with a crack going through the interface. Wang and Chen [5] used photoelasticity to determine the stress distribution and the stress intensity factors of a crack perpendicular to the interface [6-8], and also used finite element to analyze cracks perpendicular to bimaterial in a finite elastic body. Chen [9] used the body force method to determine the stress intensity factors for a normal crack terminating at a bi-material interface. Chen et al.[10] used the dislocation simulation approach to investigate the crack tip parameters for a crack perpendicular to an interface in a finite solid. He and Hutchinson [11] also considered cracks approaching the interface at oblique angles. Lin and Mar [6] presented a finite element analysis of the stress intensity factors for cracks perpendicular to the bi-material interface. Chang and Xu [12] presented the singular stress field and the stress intensity factors solution for an inclined crack terminating at a bi-material interface. A theoretical description of the stress singularity at an inclined crack terminating at an anisotropic bi-material interface was proposed by Lin and Sung [13]. Wang and Stahle [14,15] used the dislocation simulation approach to investigate a crack perpendicular to and terminating at the Abstract The objective of the present work is to investigate the interaction between interfaces and cracks normal to and terminating at a metal/alumina interface. The behavior is analyzed by the determination of the J integral and the plastic zone at the crack tip using the three-dimensional finite element methods. The effects of the thickness of the metal/alumina were highlighted. The obtained results allow us to deduce mathematical relations, giving the variation of the J integral and the plastic zone as a function of the crack position and the bi-materials thickness.

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“…For the plane problem of a bi-material plate with a crack normal at the interface, the J integral can be approximated by the following expression [40]:…”

Section: Resultsmentioning

confidence: 99%

“…The extents of the plasticized zones were given using the Von Mises criterion. The approximate solution of the maximum radius of plastic zone in bi-dimensional crack problem is [40]: The radius of the plastic zone at the crack tip R 0 can be expressed as follows:…”

Section: Resultsmentioning

confidence: 99%

Three-dimensional finite element analysis of a crack normal to and terminating at a bi-material interface

Mehidi

Kaddouri

Belhouari

et al. 2014

J Braz. Soc. Mech. Sci. Eng.

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“…The model of a bridged slit experimentally confirmed (Brocks and Cornec, 2003; Cox and Marshall, 1994; Needleman, 1990) for composite materials is used. A series of papers (Alsheghri and Abu Al-Rub, 2016; Belhouari et al., 2014; Fan et al., 1998; Hasanov, 2012; Maiti and Geubelle, 2006; Mirsalimov, 2009, 2016; Mirsalimov and Mustafayev, 2014, 2015, 2016a, 2016b; Mirsalimov and Rustamov, 2013; Mir-Salim-zada, 2014; Mir-Salim-zada, 2015; Mir-Salim-zada, 2017; Mir-Salim-zade, 2016; Mir-Salim-zade, 2018; Mir-Salim-zadeh, 2010; Mustafayev, 2014; Zhou and Wei, 2014) were devoted to study thestress state of cracked bodies with regard to existence of tractions between faces and possibility of their contact. Fan et al.…”

Section: Introductionmentioning

confidence: 99%

“…It is assumed that on some parts of contact zone faces grip occurs, and on rest part of contact zone faces slippage may occur. The objective of Belhouari et al. (2014) is to investigate the interaction between interfaces and cracks in metal/alumina bi-materials.…”

Section: Introductionmentioning

confidence: 99%

Partial closure of the periodic system of variable width bridged slits in an isotropic medium under compression

Мирсалимов

2019

International Journal of Damage Mechanics

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The problem of compression of an isotropic medium by a periodic system of variable width slits comparable with elastic deformations is considered. The slit faces are under internal pressure. It is considered that the slits have end zones wherein material's tractions act. It is accepted that interaction of the slit's surface under applied loads may reduce the formation of contact zones of their surfaces. The formation of several contact areas of faces of each slit is studied. Therewith, it is considered that on some parts of a contact area there happens stick of the faces, on the remaining part there may happen slippage. The problem of equilibrium of a periodic system of slits with partially contacting faces under compressing load is reduced to the problem of linear conjugation of analytic functions. Determination of unknown parameters characterizing partial closing of a periodic system of variable width slits is reduced to the solution of the system of singular integro-differential equations. The contact stresses, the tractions in bonds between the slit faces in the end zones, the sizes of the contact areas, the adhesion and end zones are studied.

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“…Within the framework of poroplasticity and continuum damage mechanics, some elastoplastic damage coupled models have been proposed. Main features, such as the elastic degradation due to microcracks, coupling between plastic deformation and induced damage, the influence of water saturation on plastic flow and damage evolution, as well as the variation of permeability with induced damage, are taken into account (Belhouari et al., 2014; Bui et al., 2016; Ciantia and Prisco, 2016; Hu et al., 2013; Jia et al., 2010; Jia et al., 2010; Ma et al., 2016; Pereira and Arson, 2013; Shao et al., 2006; Zhang et al., 2013). However, these studies mostly concern single influencing factor and the elastoplastic damage property of rock mass under the coupling effect of water and petrol environment is rarely concerned.…”

Section: Introductionmentioning

confidence: 99%

An elastic–plastic damage model considering capillary effect for petrol–water saturated sandstone

Yang

Luo

et al. 2017

International Journal of Damage Mechanics

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The mechanical behavior of surrounding rock mass is key important to the water-sealed petrol storage caverns because of the two phase environment. To investigate the strength and damage mechanism of rock mass under petrol–water immersion circumstance, an elastic–plastic damage constitutive model is proposed. The deformation work of rock mass is derived according to the mixture theory and averaging methods. In order to further study the capillary action influence of petrol–water liquid phase on the strength and stiffness of rock mass, the plastic yield condition considering petrol–water circumstance is proposed. Then, the stress–strain increment expression under the influence of both liquid and solid phase is deduced through the consistency condition. Meanwhile, the damage conditions of the rock mass under tensile and compressive stress differ a lot, so the rock mass damage model under petrol–water circumstance is established combining the tensile and compressive damage criterion and the damage evolution law. The proposed constitutive model is adopted to simulate the mechanical property and damage evolution feature of rock mass under axial compression. The results suggest that the increase in the petrol pressure leads to the improvement of the axial strength for rock mass and meanwhile, the occurrence of damage is also advanced. In addition, the elastic–plastic property of the rock material has been well developed below the stress peak point during this process. Ultimately, the proposed elastic–plastic damage constitutive model was verified by making comparisons between the theoretical calculating results and experimental results.

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Elastic–plastic analysis of interaction between an interface and crack in bi-materials

Cited by 15 publications

References 61 publications

Three-dimensional finite element analysis of a crack normal to and terminating at a bi-material interface

Three-dimensional finite element analysis of a crack normal to and terminating at a bi-material interface

Partial closure of the periodic system of variable width bridged slits in an isotropic medium under compression

An elastic–plastic damage model considering capillary effect for petrol–water saturated sandstone

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