engleski

Investigation of Crack Opening in Isotropic Strain Hardening Material

The thin infinite plate with an embedded straight crack of a length 2a is considered. The plate is uniaxially loaded in its plane with uniformly distributed continuous load in a direction perpendicular to the crack plane. The plate material is ductile so the small plastic zones around the crack tips are formed. Also, it is assumed that the plate material possesses a property of isotropic strain hardening. The strain hardening of the material is non-linear and it obeys the Ramberg-Osgood relation. The different stages of strain hardening of plate material are modeled by varying the parameters yy∞∞σ=σα and n in the Ramberg-Osgood's analytical expression. So, it is assumed that the strain hardening exponent n takes the values n = 3, 5, 7, 10, 25 and ∞. The stress intensity factor (SIF) of the cohesive stresses coh(pKar+ is determined by means of Green's functions method. The crack tip and crack centre opening, or any arbitrary point at the crack surface, is determined by means of the displacement field of the points lying on the crack surface. The problem is formulated fully exactly and its solution is looked for by means of commercial software „Mathematica“. If it is assumed an appearance of small plastic zone around crack tip then it is possible to find an exact analytical solution expressed in a form of special gamma-functions . If the assumptions about small plastic zone are not introduced, then it is possible to give the solution by means of special hypergeometric functions .

Crack opening; isotropic strain hardening material; small plastic zone; strain hardening exponent; cohesive stresses; stress intensity factor; method of Green´s functions; commercial software „Mathematica“; gamma-function; hypergeometric function

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