A stress-concentration-formula generating equation for arbitrary shallow surfaces

Medina, Hector

doi:10.1016/j.ijsolstr.2015.06.006

Cited by 20 publications

(11 citation statements)

References 20 publications

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“…Analyzing a sinusoidal surface perturbation of a stressed solid at the macrolevel, Gao (1991) has shown that even a slightly undulating surface can generate significant stress concentration that can induce fracture before the bulk stress reaches a critical level. Similar results have been analytically obtained for cycloid-shaped surfaces ( Chiu and Gao, 1993 ), arbitrary weakly curved surfaces ( Grekov and Kostyrko, 2015;Grekov and Makarov, 2004;Medina, 2015;Medina and Hilderliter, 2014;Vikulina et al, 2010 ), and interfaces ( Grekov, 2004( Grekov, , 2011Grekov and Kostyrko, 2013 ).…”

Section: Introductionsupporting

confidence: 84%

“…Quite a number of them are reviewed in Bashkankova et al (2015) . Recently, based on this method, Medina and Hilderliter (2014) and Medina (2015) have derived stress concentration formulas for different slightly curved surfaces at the macrolevel and Mohammadi et al (2013) have presented derivations that relate both a periodic and a random roughness to the effective surface elastic behaviour. Unlike all cited papers, our perturbation technique, based on the original equation in complex potentials, similar to (14) , leads either to the same explicit equation or the same integral equations in an approximation of any order.…”

Section: Boundary Perturbation Proceduresmentioning

confidence: 99%

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Surface effects in an elastic solid with nanosized surface asperities

Grekov

Kostyrko

2016

International Journal of Solids and Structures

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a b s t r a c tThe effects of surface elasticity and surface tension on the stress field near nanosized surface asperities having at least one dimension in the range 1-100 nm is investigated. The general two-dimensional problem for an isotropic stressed solid with an arbitrary roughened surface at the nanoscale is considered. The bulk material is idealized as an elastic semi-infinite continuum. In accordance with the Gurtin-Murdoch model, the surface is represented as a coherently bonded elastic membrane. The surface properties are characterized by the residual surface stress (surface tension) and the surface Lame constants, which differ from those of the bulk. The boundary conditions at the curved surface are described by the generalized Young-Laplace equation. Using a specific approach to the boundary perturbation technique, GoursatKolosov complex potentials, and Muskhelishvili representations, the boundary value problem is reduced to the solution of a hypersingular integral equation. Based on the first-order approximation, some numerical results in the case of a periodic shape of the surface and the analysis of the influence of surface stress, surface tension, the surface shape, and the size of the asperity on the hoop stress at the surface are presented. It is found that the surface tension alone produces a high level of stress concentration, much more than can be reduced by surface stress arising as a result of deformation. The stress formula obtained by Gao (1991) for sinusoidal surfaces at the macrolevel is extended to nanosized surface asperities.

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Section: Introductionsupporting

confidence: 84%

Section: Boundary Perturbation Proceduresmentioning

confidence: 99%

Surface effects in an elastic solid with nanosized surface asperities

Grekov

Kostyrko

2016

International Journal of Solids and Structures

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“…The maximum stress concentration occurs at the base of the dimple. Based on the analytical solution for stress concentration factor in sinusoidal shallow surface, 41,42 the maximum stress concentration factor, K t , can be related to depth and width of the dimple as

K_{t} = 1 + 4 π \frac{a}{w} .

This gives us the value of K t as 1.15. Then, from Equation 3), the K f was calculated to be 1.12.…”

Section: Resultsmentioning

confidence: 99%

Fatigue performance of laser shock peened Ti6Al4V and Al6061‐T6 alloys

Maharjan¹,

Chan²,

Ramesh³

et al. 2020

Fatigue Fract Eng Mat Struct

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Propagation of fatigue crack in laser shock peened metallic component is retarded by introduction of deep compressive residual stresses during the process. Apart from large compressive residual stress build‐up near the surface, surface topography is also significantly altered during laser shock peening. However, a systematic evaluation of the individual effects of residual stresses and surface topography as well as their interaction effects on fatigue crack initiation and growth is still lacking. This study investigates the effect of laser shock peening on near‐surface properties of Ti6Al4V and Al6061‐T6 alloys and how these changes dictate their overall fatigue performance. Microstructure, surface topography, hardness and residual stress state of the alloys are investigated before and after peening, and four‐point bending fatigue tests are performed to obtain Wöhler curves (S‐N curves) for each case. The results show that both surface residual stresses and surface topography influence the fatigue life of a component. Compressive residual stresses were induced to a depth beyond 1 mm for both alloys. Fatigue life of Ti6Al4V alloy increased by at least 1.28 times after laser shock peening due to the introduction of deep compressive residual stresses with minimal change in surface topography. By contrast, the improvement is nominal for Al6061‐T6 alloy due to the surface roughening effect introduced by laser peening, which results in early crack initiation and negates the beneficial effect of compressive residual stresses.

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“…In the case of zero-order approximation, F 0 = 0 and we arrive to the homogeneous equations (13), which have only trivial solution τ (0) (x 1 ) = 0 corresponding to the problem of bimaterial with perfectly flat interface Γ (0) and piecewise uniform stress state:…”

Section: Fig 1 a Model Of Bimaterials With Slightly Perturbated Intementioning

confidence: 99%

“…In past decades, a number of studies have been conducted, where the stress concentration caused by surface or interface irregularities was considered [6][7][8][9][10][11][12][13][14]. But these studies have been focused on the case of macroscale roughness and didn't take into account the surface/interface stress, assuming it insignificant compared to the external loading.…”

mentioning

confidence: 99%

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

Shuvalov¹,

Vakaeva²,

Shamsutdinov³

et al. 2020

Vestnik SPbSU. Applied Mathematics. Computer Science. Control P

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Based on the Gurtin-Murdoch surface/interface elasticity theory, the article investigates the effect of nonlinear terms in the boundary perturbation method on stress concentration near the curvilinear bimaterial interface taking into account plane strain conditions. The authors consider the 2D boundary value problem for the infinite two-component plane under uniaxial tension. The interface domain is assumed to be a negligibly thin layer with the elastic properties differing from those of the bulk materials. Using the boundary perturbation method, the authors determined a semi-analytical solution taking into account non-linear approximations. In order to verify this solution, the corresponding boundary value problem was solved using the finite element method where the interface layer is modelled by the truss elements. It was shown that the effect of the amplitude-to-wavelength ratio of surface undulation on the stress concentration is nonlinear. This should be taken into account even for small perturbations. It was also found that the convergence rate of the derived solution increases with an increase in the relative stiffness coefficient of the bimaterial system and, conversely, decreases with an increase of the amplitude-to-wavelength ratio.

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A stress-concentration-formula generating equation for arbitrary shallow surfaces

Cited by 20 publications

References 20 publications

Surface effects in an elastic solid with nanosized surface asperities

Surface effects in an elastic solid with nanosized surface asperities

Fatigue performance of laser shock peened Ti6Al4V and Al6061‐T6 alloys

The effect of nonlinear terms in boundary perturbation method on stress concentration near the nanopatterned bimaterial interface

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