A mode III Dugdale crack interacting with a non-elliptical inhomogeneity with internal uniform stresses

2019 ◽  
Vol 216 ◽  
pp. 106495
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Mode Iii ◽  
Elliptical Inhomogeneity ◽  
Dugdale Crack

scholarly journals Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a mode III crack

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180304 ◽  
Author(s):  
Xu Wang ◽  
Liang Chen ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Singular Integral Equations ◽  
Infinite Matrix ◽  
Mode Iii ◽  
Mode Iii Crack ◽  
Elliptical Inhomogeneity ◽  
Internal Stress Field ◽  
Uniform Stress Field ◽  
Cauchy Singular Integral ◽  
Mapping Techniques

Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that it is possible to maintain a uniform internal stress field inside a non-elliptical elastic inhomogeneity embedded in an infinite matrix subjected to uniform remote stress despite the fact that the inhomogeneity interacts with a finite mode III crack. The crack can be modelled either as a Griffith crack or as a Zener–Stroh crack. Our analysis further indicates that the existence of the crack plays a key role in influencing the shape of the corresponding inhomogeneity but not the internal uniform stress field inside the inhomogeneity. Numerical examples are presented to demonstrate the solution.

scholarly journals Antiplane–inplane shear mode delamination between two second-order shear deformable composite plates

2016 ◽  
Vol 22 (3) ◽  
pp. 259-282 ◽  
Author(s):  
András Szekrényes
Keyword(s):  
Plate Theory ◽  
Plate Thickness ◽  
State Space Model ◽  
Boundary Surface ◽  
Plate Boundary ◽  
Composite Plates ◽  
Second Order ◽  
Shear Mode ◽  
Mode Iii ◽  
Double Plate System

The second-order laminated plate theory is utilized in this work to analyze orthotropic composite plates with asymmetric delamination. First, a displacement field satisfying the system of exact kinematic conditions is presented by developing a double-plate system in the uncracked plate portion. The basic equations of linear elasticity and Hamilton’s principle are utilized to derive the system of equilibrium and governing equations. As an example, a delaminated simply supported plate is analyzed using Lévy plate formulation and the state-space model by varying the position of the delamination along the plate thickness. The displacements, strains, stresses and the J-integral are calculated by the plate theory solution and compared with those by linear finite-element calculations. The comparison of the numerical and analytical results shows that the second-order plate theory captures very well the mechanical fields. However, if the delamination is separated by only a relatively thin layer from the plate boundary surface, then the second-order plate theory approximates badly the stress resultants and so the mode-II and mode-III J-integrals and thus leads to erroneous results.

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