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On the stress distribution near the tip of a sharp notch
Ostratický, Jakub ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
The notch is a stress concentrator from the point of view of elasticity theory and the knowledge of the description of this stress in the vicinity of its tip is necessary for the correct functionality of a wide range of mechanical components and products. The stress at the tip of the notch is singular and it is technically impossible to prevent the initiation of cracks in its vicinity. However, it is known from fracture mechanics that the initiation and propagation of cracks is not influenced by the magnitude of the stress at their tips, but its intensity characterized by the so-called stress intensity factor. In the case of a notch, it is a generalized stress intensity factor or simply the amplitudes of the singular parts of the stress filed. These coefficients cannot be determined directly from the results of widely used numerical methods such as FEM, but it is necessary to use linear fracture mechanics methods based on the asymptotic solution of the equilibrium equations in elasticity. The presented work deals with the case of a symmetric sharp notch in an isotropic material under the mode I or II loadings. The stress singularity and the related stress intensity factor at the notch tip are analysed and evaluated. The derived asymptotic solution is compared with the results obtained from the FEM analysis.
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The Influence of Specimen Thickness on Crack Initiation in the Tip of General Singular Stress Concentrator
Kopp, Dalibor ; Řoutil,, Ladislav (referee) ; Malíková, Lucie (referee) ; Klusák, Jan (advisor)
Geometrical discontinuities, like sharp notches, appear in constructions and engineering structures and lead to stress concentrations. These technical objects are very dangerous due to the fact that they reduce the structural conformity and can lead to crack initiation. Technical objects are not always designed as homogenous bodies but can consist of two or more materials with sharp notches on the interface of these materials. The influence of free surface on crack initiation conditions is studied and assessed by means of 3D model of sharp and bi-material notches with finite thickness. Stress fields around the singular stress concentrators are calculated with finite element method and the results are evaluated by means of criterion of critical quantity. This approach is easy applicable and can be used in combination with the knowledge of basic material properties and results of finite element analysis of the assessed notches. In order to estimate weather crack will initiate from the middle of the observed notched specimen or from its free surface, the value of averaged critical applied stress was introduced. With this value it’s possible to determine the location of crack initiation thru the sample thickness. Thru the ratio of values of critical applied stress in the middle and on the free surface of the observed specimen it’s possible to quantify the influence of the free surface on the location of crack initiation. With the use of this approach it’s shown, that the location of crack initiation depends on more parameters, loading direction, the notch opening angle and the sample thickness. In case of bi-material notches it depends also on the ratio of young modulus.
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On the stress distribution near the tip of a sharp notch
Ostratický, Jakub ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
The notch is a stress concentrator from the point of view of elasticity theory and the knowledge of the description of this stress in the vicinity of its tip is necessary for the correct functionality of a wide range of mechanical components and products. The stress at the tip of the notch is singular and it is technically impossible to prevent the initiation of cracks in its vicinity. However, it is known from fracture mechanics that the initiation and propagation of cracks is not influenced by the magnitude of the stress at their tips, but its intensity characterized by the so-called stress intensity factor. In the case of a notch, it is a generalized stress intensity factor or simply the amplitudes of the singular parts of the stress filed. These coefficients cannot be determined directly from the results of widely used numerical methods such as FEM, but it is necessary to use linear fracture mechanics methods based on the asymptotic solution of the equilibrium equations in elasticity. The presented work deals with the case of a symmetric sharp notch in an isotropic material under the mode I or II loadings. The stress singularity and the related stress intensity factor at the notch tip are analysed and evaluated. The derived asymptotic solution is compared with the results obtained from the FEM analysis.
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The Influence of Specimen Thickness on Crack Initiation in the Tip of General Singular Stress Concentrator
Kopp, Dalibor ; Řoutil,, Ladislav (referee) ; Malíková, Lucie (referee) ; Klusák, Jan (advisor)
Geometrical discontinuities, like sharp notches, appear in constructions and engineering structures and lead to stress concentrations. These technical objects are very dangerous due to the fact that they reduce the structural conformity and can lead to crack initiation. Technical objects are not always designed as homogenous bodies but can consist of two or more materials with sharp notches on the interface of these materials. The influence of free surface on crack initiation conditions is studied and assessed by means of 3D model of sharp and bi-material notches with finite thickness. Stress fields around the singular stress concentrators are calculated with finite element method and the results are evaluated by means of criterion of critical quantity. This approach is easy applicable and can be used in combination with the knowledge of basic material properties and results of finite element analysis of the assessed notches. In order to estimate weather crack will initiate from the middle of the observed notched specimen or from its free surface, the value of averaged critical applied stress was introduced. With this value it’s possible to determine the location of crack initiation thru the sample thickness. Thru the ratio of values of critical applied stress in the middle and on the free surface of the observed specimen it’s possible to quantify the influence of the free surface on the location of crack initiation. With the use of this approach it’s shown, that the location of crack initiation depends on more parameters, loading direction, the notch opening angle and the sample thickness. In case of bi-material notches it depends also on the ratio of young modulus.
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