Analytical-Numerical Determination of Stress Distribution around a Tip of Polygon-Like Inclusion

2016 ◽  
Vol 713 ◽  
pp. 94-98
Author(s):  
Ondřej Krepl ◽  
Jan Klusák ◽  
Tomáš Profant
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Numerical Procedure ◽  
Plane Elasticity ◽  
Necessary Condition ◽  
Singular Stress ◽  
Reliable Assessment ◽  
Generalized Stress Intensity Factors ◽  
Stress Behaviour

A stress distribution in vicinity of a tip of polygon-like inclusion exhibits a singular stress behaviour. Singular stresses at the tip can be a reason for a crack initiation in composite materials. Knowledge of stress field is necessary condition for reliable assessment of such composites. A stress field near the general singular stress concentrator can be analytically described by means of Muskhelishvili plane elasticity based on complex variable functions. Parameters necessary for the description are the exponents of singularity and Generalized Stress Intensity Factors (GSIFs). The stress field in the closest vicinity of the SMI tip is thus characterized by 1 or 2 singular exponents (1 - λ) where, 0<Re (λ)<1, and corresponding GSIFs that follow from numerical solution. In order to describe stress filed further away from the SMI tip, the non-singular exponents for which 1<Re (λ), and factors corresponding to these non-singular exponents have to be taken into account. Analytical-numerical procedure of determination of stress distribution around a tip of sharp material inclusion is presented. Parameters entering to the procedure are varied and tuned. Thus recommendations are stated in order to gain reliable values of stresses and displacements.

Evaluation of the Bonding Strength at the Three-Dimensional Vertex in Silicon-Resin Joints

2009 ◽  
Author(s):  
Hideo Koguchi ◽  
Masato Nakajima
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Boundary Element ◽  
External Force ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Singular Stress ◽  
Singular Stress Field ◽  
Element Method ◽  
Silicon Resin

Portable electric devices such as mobile phone and portable music player become compact and also their performance improves. High density packaging technology such as CSP (Chip Size Package) and Stacked-CSP is needed to realize advanced functions. CSP is a bonded structure composed of materials with different properties. A mismatch of material properties may cause stress singularity at the edge of interface, which lead to the failure of bonding part in structures. Singular stress field in residual thermal stresses occurs in a cooling process after bonding the joints at a high temperature. In the present paper, the strength of interface in CSP consisted of silicon and resin is investigated. Boundary element method and an eigen value analysis based on finite element method are used for evaluating the intensity of singularity of residual thermal stresses at a vertex in a three-dimensional joint. Three-dimensional boundary element program based on the fundamental solution for two-phase isotropic body is used for calculating the stress distribution in the three-dimensional joint. Angular function in the singular stress field at the vertex in the three-dimensional joint is calculated using eigen vector determined from eigen analysis. The strength of bonding at the interface in several silicon-resin specimens with different thickness of resin is investigated analytically and experimentally. Stress singular analysis applying an external force for the joints is firstly carried out. After that, singular stress field for the residual thermal stresses varying material property of resin with temperature is calculated. Combining singular stress fields for the external force and the residual thermal stress yields a final stress distribution for evaluating the strength of interface. A relationship between the external force for delamination in joints and the thickness of resin is derived. Finally, a critical intensity of singularity for delamination between silicon and resin is determined.

Study of the Stress Distribution Around an Orthotropic Bi-Material Notch Tip

2009 ◽  
Vol 417-418 ◽  
pp. 385-388 ◽  
Author(s):  
Jan Klusák ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Stress Distribution ◽  
Orthotropic Material ◽  
Stress Singularity ◽  
Singular Stress ◽  
Theoretical Approaches ◽  
Singularity Exponents ◽  
Reliable Assessment ◽  
Final Stress ◽  
General Geometry ◽  
Numerical Approaches

Knowledge of the stress distribution is the first and necessary step for the reliable assessment of construction with a geometrical or material discontinuity. General geometry and orthotropic material characteristics of both material components lead to singular stress distribution with general stress singularity exponents different from ½. For the final stress field determination both analytical and numerical approaches are utilised. The results of the theoretical approaches are compared to results from finite element method.

Asymptotic Analysis for the Singular Stress Behaviour around an Interface Edge of Dissimilar Power-Law Hardening Materials Joint

2011 ◽  
Vol 462-463 ◽  
pp. 1290-1295
Author(s):  
Md. Arefin Kowser ◽  
Yoshio Arai ◽  
Wakako Araki
Keyword(s):  
Asymptotic Analysis ◽  
Power Law ◽  
Order Approximation ◽  
Stress Singularity ◽  
Higher Order ◽  
Singular Stress ◽  
Deformation Plasticity ◽  
Stress Behaviour ◽  
Interface Edge

An asymptotic analysis for singular stress fields around an interface-edge of dissimilar power-law hardening materials joint has been presented under plane strain condition and J2 deformation plasticity theory. Both the balance of force and the continuity of displacement are satisfied on the interface. In the higher order approximation, the nonlinear effective stress term was expanded by Taylor series. An iteration method is proposed for the determination of singular fields around interface edge. Multiple stress singular terms exist for in the higher order approximation. The order of stress singularity has a dependency with the combination of hardening exponents, .

Determination of Residual Stress Distribution in Sensitive and Insensitive Materials

1993 ◽  
Author(s):  
Shahriar Jahanian
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Nuclear Reactor ◽  
Numerical Procedure ◽  
Residual Stress Distribution ◽  
Sensitive Material ◽  
Negative Effect ◽  
Temperature Dependent Properties ◽  
Transient Thermal

Abstract One of the important factors to be considered in design is the residual stress distribution in the component. The positive or negative effect of these stresses plays an important role in the life of components. The unexpected failure of the components latter determined to be attributed to the residual stress distribution is not uncommon. Often in the design of nuclear reactor coolant system and components, the level of residual and transient thermal stress distribution is an important factor to be considered. Obviously the level of these stresses depend on the fact that if the material is sensitive (material with temperature dependent properties or insensitive. In this paper an infinite hollow cylinder is considered as an example. A theoretical study, which predict the thermoelastoplastic and residual stress distribution is presented. A quasi static and uncoupled thermoelastoplastic analysis based on incremental theory of plasticity is developed and a numerical procedure for successive approximation is presented. The problem is solved for both case of sensitive and insensitive material. The level of residual and thermoelastoplastic stress for both cases are compared and discussed in detail.

Multi-Parameter Based Stress Distribution in Vicinity of Sharp Material Inclusion Tip

2016 ◽  
Vol 258 ◽  
pp. 169-173
Author(s):  
Ondřej Krepl ◽  
Jan Klusák
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Fracture Mechanics ◽  
Stress Field ◽  
Crack Initiation ◽  
Electronic Components ◽  
Precise Description ◽  
Singular Stress ◽  
Stress Concentrators

General Singular Stress Concentrators (GSSCs) which exhibit singular stress concentration are often responsible for crack initiation and thus failure of the component. The GSSC of the type of bonded bi-material junction occurs in a variety of technical applications including but not limited to sharp material inclusions, silicate based composites and electronic components. The GSSC cannot be assessed by means of standard fracture mechanics. Approaches of generalized fracture mechanics require precise description of stress distribution near the stress concentration points. In order to determine the stress field accurately, the paper incorporates the multi-parameter based description.

Determination of Stress Intensity Factors for an Interfacial Crack in a Bi-Material by Digital Photoelasticity

2004 ◽  
Vol 1-2 ◽  
pp. 139-146
Author(s):  
M. Ravichandran ◽  
K. Ramesh
Keyword(s):  
Stress Intensity ◽  
Stress Field ◽  
Stress Intensity Factors ◽  
Interfacial Crack ◽  
Intensity Factors ◽  
Singular Stress ◽  
Singular Stress Field ◽  
Digital Photoelasticity ◽  
Least Squares Approach

The main sources of error in the determination of stress intensity factors (SIFs) for an interface crack in a bi-material by conventional photoelasticity are the measurement of the positional co-ordinates of the data point and the fringe order. In the present work, use of two digital photoelasticity methods for collecting these data is discussed. SIFs are evaluated using constant radius method and a least squares approach based on the singular stress field equation. The need for developing a multi-parameter stress field solution for evaluating SIF is highlighted.

A Comparison of Two Direct Methods of Generalized Stress Intensity Factor Calculations of Bi-Material Notches

2008 ◽  
Vol 385-387 ◽  
pp. 409-412 ◽  
Author(s):  
Jan Klusák ◽  
Tomáš Profant ◽  
Michal Kotoul
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Homogeneous Medium ◽  
Direct Methods ◽  
Singular Stress ◽  
Generalized Stress Intensity Factor ◽  
Generalized Stress Intensity Factors ◽  
Material Discontinuities

The study of bi-material notches is becoming a topical problem as they can model geometrical or material discontinuities efficiently. Assessing the conditions for crack initiation in bimaterial notches makes it necessary to calculate the generalized stress intensity factors H. In contrast to the determination of the K factor for a crack in an isotropic homogeneous medium, for the ascertainment of a generalized stress intensity factor (GSIF) there is no procedure incorporated in the calculation systems. The calculation of these fracture mechanics parameters is not trivial and requires certain experience. Nevertheless, the accuracy of the H-factor calculation directly influences the reliability of the assessment of the singular stress concentrators. Direct methods of the estimation of H factors usually require choosing the length parameter entering into the calculation. Two types of direct methods of calculating the GSIFs are presented, tested and mutually compared. Recommendations for reliable estimation of H factors are suggested.

scholarly journals Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

2021 ◽  
Vol 11 (15) ◽  
pp. 6931
Author(s):  
Jie Liu ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Stagnation Point ◽  
Analytical Solutions ◽  
Wide Spectrum ◽  
Momentum Conservation ◽  
Stagnation Point Flow ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Special Cases

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

Determination of the temperature stress field in a plexiglas plate

1972 ◽  
Vol 3 (6) ◽  
pp. 743-744
Author(s):  
F. V. Dolinskii ◽  
V. A. Marakhovskii
Keyword(s):  
Stress Field ◽  
Temperature Stress ◽  
Plexiglas Plate
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