Probabilistic Analysis of Notched Micro Specimen Under Three-Point Loading

2005 ◽  
Author(s):  
S. Ekwaro-Osire ◽  
M. P. H. Khandaker ◽  
K. Gautam
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Probabilistic Analysis ◽  
Stress Singularity ◽  
Beam Specimen ◽  
Mems Devices ◽  
Mode Iii ◽  
Notch Angle ◽  
Notch Stress ◽  
Geometric Variation

Stress singularity arises in MEMS devices due to sudden geometric and material variation. Sharp notches are common example of sudden geometric variation, which often occurs during the fabrication process of MEMS components. The magnitude of the stress field induced due to stress singularity is given by the value of the notch stress intensity, K. The stress intensity is depended on the notch geometry and the type of loading (mode I, mode II and mode III). Fracture failure at the notch occurs when notch stress intensity reach fracture toughness, KC. An electrostatically actuated test device used for the analysis of a notched micro beam specimen under three-point loading will be presented. The objective of this study was to investigate the effect of geometric configuration on the stress field around singularity for a micro beam specimen by asymptotic, numerical and probabilistic analysis. The scope of work is fourfold. First, the effect of notch angle on the strength of the singularity is determined using two different asymptotic analysis methods — complex potential method and Airy stress function method. Second, the effect of the angular variation (for different notch angle) on the influence coefficients is determined using analytical methods. Third, the effect of the notch angle and depth on the stress intensity factor is determined using finite element methods and contour integral method. Fourth, the probabilistic analysis of maximum stress developed in the micro beam specimen is performed.

Stress Intensity Factors for Cracks Emanating from a Notch under Shear-Mode Loading

2018 ◽  
Vol 774 ◽  
pp. 48-53
Author(s):  
Jana Horníková ◽  
Pavel Šandera ◽  
Stanislav Žák ◽  
Jaroslav Pokluda
Keyword(s):  
Stress Intensity ◽  
Critical Length ◽  
Shear Mode ◽  
Mode I ◽  
Mode Ii ◽  
Mode Iii ◽  
Loading Mode ◽  
Notch Stress ◽  
Notch Geometry ◽  
Mode Ii Loading

The influence of the notch geometry on the stress intensity factor at the front of the emanating cracks is well known for the opening loading mode. The critical length of the crack corresponding to a vanishing of the influence of the notch stress concentration can be approximately expressed by the formula aI,c = 0.5ρ(d/ρ)1/3, where d and ρ are the depth and radius of the notch, respectively. The aim of the paper was to find out if this formula could be, at least nearly, applicable also to the case of shear mode loading. The related numerical calculations for mode II and III loading were performed using the ANSYS code for various combinations of notch depths and crack lengths in a cylindrical specimen with a circumferential U-notch. The results revealed that, for mode II loading, the critical length was much higher than that predicted by the formula for mode I loading. On the other hand, the critical lengths for mode I and mode III were found to be nearly equal.

A Novel Closed-Form Calculation of the Stress Intensity Factor for a Crack in a Residual Stress Field

2006 ◽  
Vol 524-525 ◽  
pp. 83-88
Author(s):  
Jeffrey Meng Lee Tan ◽  
Michael E. Fitzpatrick ◽  
Lyndon Edwards
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Closed Form ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Residual Stress Field ◽  
Crack Problems

Exact closed-form stress intensity factor (SIF) solutions have been developed for a mode- I through-thickness cracks in an infinite plate. Centre-crack problems have been analysed comprehensively in the literature, but the focus has been on the effect of simple loading about the crack centre. In the current work, the formula of Sih-Paris-Erdogan has been extended to consider the SIF difference on the left and right crack tips, under the local influence of general asymmetric and symmetric stress field. Exact SIF magnification factors convenient for computations have been derived that simultaneously circumvent the problem of crack-tip stress singularity. The solutions so obtained are applied to generate the residual SIFs that would act on a crack growing under the influence of the residual stress fields associated with welded plates and cold-worked holes using the measured residual stress profiles.

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

Mixed Mode Stress Singularities in Anisotropic Composites

1999 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Intensity ◽  
Asymptotic Solution ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Free Edge ◽  
Complex Conjugate ◽  
Circular Path ◽  
Intensity Factors ◽  
Element Analysis ◽  
Anisotropic Elastic

Abstract Multi-material wedges composed of fully anisotropic elastic sectors generally show intrinsic coupling of the anti-plane and in-plane modes of deformation. Each anisotropic sector has three complex conjugate pairs of material eigensolutions whose form of expression depends on five distinct types of anisotropic materials. Continuity of the displacements and the tractions across the sector interfaces and the traction-free conditions on two exterior boundary edges determine an infinite sequence of eigenvalues and eigensolutions of the multi-material wedge. These eigensolutions are linearly combined to match the traction-boundary data (generated by global finite element analysis of the structure) on a circular path encircling the singularity. The analysis method is applied to a bimaterial wedge near the free edge of a four-layer angle-ply laminate, and to a trimaterial wedge surrounding the tip of an embedded oblique crack in a three-layer composite. Under a uniform temperature load, the elasticity solution based on the eigenseries yields interfacial stresses that are significantly different from the asymptotic solution (given by the first term of the eigenseries), even as the distance from the singularity decreases to subatomic scales. Similar observations have been found previously for isotropic and orthotropic multi-material wedges. This raises serious questions with regard to characterizing the criticality of stress singularity exclusively in terms of the asymptotic solution and the associated stress intensity factors or generalized stress intensity factors.

On notch fracture mechanics

2021 ◽  
Vol 87 (2) ◽  
pp. 56-64
Author(s):  
G. Pluvinage
Keyword(s):  
Fracture Toughness ◽  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plastic Zone ◽  
Fracture Resistance ◽  
Notch Radius ◽  
Notch Stress Intensity Factor ◽  
Blunt Notch ◽  
Notch Stress

Different stress distributions for an elastic behavior are presented as analytical expressions for an ideal crack, a sharp notch and a blunt notch. The elastic plastic distribution at a blunt notch tip is analyzed. The concept of the notch stress intensity factor is deduced from the definition of the effective stress and the effective distance. The impacts of the notch radius and constraint on the critical notch stress intensity factor are presented. The paper ends with the presentation of the crack driving force Jρ for a notch in the elastic case and the impact of the notch radius on the notch fracture toughness Jρ,c. The notch fracture toughness Jρ,c is a measure of the fracture resistance which increases linearly with the notch radius due to the plastic work in the notch plastic zone. If this notch plastic zone does not invade totally the ligament, the notch fracture toughness Jρ,c is constant. This occurs when the notch radius is less than a critical one and there is no need to use the cracked specimen to measure a lower bound of the fracture resistance.

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