Stress concentration near stiff inclusions: Validation of rigid inclusion model and boundary layers by means of photoelasticity

Misseroni, D.; Corso, F. Dal; Shahzad, S.; Bigoni, Davide

doi:10.1016/j.engfracmech.2014.03.004

Cited by 55 publications

(15 citation statements)

References 29 publications

(50 reference statements)

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“…Photoelastic investigations [21,28] confirm the severe stress fields theoretically predicted for materials containing stiff inclusions and show that these fields may yield failure instead of reinforcement for composite materials [11,17,23,29]. Therefore, the results given in the present article show possibilities of greatly enhancing the strength of composites through the careful design of the inclusion shapes, thus opening the way to the realization of ultra-strong materials.…”

Section: Some Of the Above Concepts Are Elucidated Insupporting

confidence: 79%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

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Stress field solutions and Stress Intensity Factors (SIFs) are found for n-cusped hypocycloidal shaped voids and rigid inclusions in an infinite linear elastic plane subject to nonuniform remote antiplane loading, using complex potential and conformal mapping. It is shown that a void with hypocycloidal shape can lead to a higher SIF than that induced by a corresponding star-shaped crack; this is counter intuitive as the latter usually produces a more severe stress field in the material. Moreover, it is observed that when the order m of the polynomial governing the remote loading grows, the stress fields generated by the hypocycloidal-shaped void and the star-shaped crack tend to coincide, so that they become equivalent from the point of view of a failure analysis. Finally, special geometries and loading conditions are discovered for which there is no stress singularity at the inclusion cusps and where the stress is even reduced with respect to the case of the absence of the inclusion. The concept of Stress Reduction Factor (SRF) in the presence of a sharp wedge is therefore introduced, contrasting with the well-known definition of Stress Concentration Factor (SCF) in the presence of inclusions with smooth boundary. The results presented in this paper provide criteria that will help in the design of ultra strong composite materials, where stress singularities always promote failure. Furthermore, they will facilitate finding the special conditions where resistance can be optimized in the presence of inclusions with non-smooth boundary.

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Section: Some Of the Above Concepts Are Elucidated Insupporting

confidence: 79%

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Shahzad

Corso

Bigoni

2016

J Elast

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“…The above results coincide with experimental observations of high concentrations and singularities in the stress fields within elastic materials [17,18,35,36].…”

Section: Numerical Results and Discussionsupporting

confidence: 90%

“…Photoelasticity is very helpful in investigating the stress state near inclusions. The results show that the singular stress field predicted by the linear elastic solution for an inclusion can be generated in reality with great accuracy [17]. The inclusions form a thin material that constituted a rigid line inclusion, embedded in a linear elastic body to produce an inhomogeneous stress state.…”

Section: Introductionmentioning

confidence: 91%

Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

Pahlaviani

Mkhitaryan

2015

Mathematical Problems in Engineering

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The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.

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“…The interplay between stress inhomogeneities and singularities generated at inclusion corners is important in the design of ultra-resistant composites, as stress singularities are known to be detrimental to strength. In fact, an extreme stress concentration, leading to material failure, has been shown by experiments to represent the counterpart of the mathematical concept of singularity [19,20]. The determination of the conditions leading to stress relief around inclusions may introduce new perspectives in the development of composite materials.…”

Section: Introductionmentioning

confidence: 99%

Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part I: Formulation and full-field solution

Corso

Shahzad

Bigoni

2016

International Journal of Solids and Structures

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An infinite class of nonuniform antiplane shear fields is considered for a linear elastic isotropic space and (non-intersecting) isotoxal star-shaped polygonal voids and rigid inclusions perturbing these fields are solved. Through the use of the complex potential technique together with the generalized binomial and the multinomial theorems, full-field closed-form solutions are obtained in the conformal plane. The particular (and important) cases of star-shaped cracks and rigid-line inclusions (stiffeners) are also derived. Except for special cases (addressed in Part II), the obtained solutions show singularities at the inclusion corners and at the crack and stiffener ends, where the stress blows-up to infinity, and is therefore detrimental to strength. It is for this reason that the closed-form determination of the stress field near a sharp inclusion or void is crucial for the design of ultra-resistant composites.

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Stress concentration near stiff inclusions: Validation of rigid inclusion model and boundary layers by means of photoelasticity

Cited by 55 publications

References 29 publications

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Hypocycloidal Inclusions in Nonuniform Out-of-Plane Elasticity: Stress Singularity vs. Stress Reduction

Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part I: Formulation and full-field solution

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