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.

Using the Multi-Parameter Fracture Mechanics for more Accurate Description of Stress/Displacement Crack Tip Fields

2013 ◽  
Vol 586 ◽  
pp. 237-240 ◽  
Author(s):  
Lucie Šestáková
Keyword(s):  
Stress Distribution ◽  
Fracture Mechanics ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Singular Term ◽  
Crack Tip ◽  
Higher Order ◽  
Precise Description ◽  
Accurate Knowledge ◽  
Higher Order Terms

Most of fracture analyses often require an accurate knowledge of the stress/displacement field over the investigated body. However, this can be sometimes problematic when only one (singular) term of the Williams expansion is considered. Therefore, also other terms should be taken into account. Such an approach, referred to as multi-parameter fracture mechanics is used and investigated in this paper. Its importance for short/long cracks and the influence of different boundary conditions are studied. It has been found out that higher-order terms of the Williams expansion can contribute to more precise description of the stress distribution near the crack tip especially for long cracks. Unfortunately, the dependences obtained from the analyses presented are not unambiguous and it cannot be strictly derived how many of the higher-order terms are sufficient.

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.

The Stress Concentration Factor (Kt) and Fatigue Crack Behavior on the Relative Defect Location in Monolithic Aluminum versus GLARE

2006 ◽  
Vol 321-323 ◽  
pp. 952-956
Author(s):  
Cheol Woong Kim ◽  
Kwang Lae Kim ◽  
Won Pyung Lee ◽  
Sung Hyuk Lee ◽  
Seok Heo
Keyword(s):  
Experimental Study ◽  
Fatigue Crack ◽  
Stress Concentration ◽  
Stress Distribution ◽  
Crack Initiation ◽  
High Strength ◽  
Defect Location ◽  
Crack Behavior ◽  
Glass Fiber Reinforced ◽  
Made In

To analyze the stress distribution and the crack initiation due to the location of the defects, artificial defects were made on the different locations of the high strength monolithic Al and GLAss fiber REinforced laminate (GLARE). Experimental study shows that the defect location in the vicinity of the circular hole was changed from ° = 90 4 θ to ° = 0 1 θ , the stress concentration was increased. The stress concentration of GLARE was about 15% higher than that of the monolithic Al. When the defect was at ° = 30 2 θ , Multi Site Damage (MSD) crack was found in the monolithic Al but not in GLARE. Instead of MSD crack, a delamination was made in GLARE and that it resulted in the prevention against the second crack initiation.

Empirical Formula for Stress Intensity Factor of Crack Initiated from an Interface Edge

2013 ◽  
Vol 645 ◽  
pp. 377-380
Author(s):  
Zhen Yang
Keyword(s):  
Stress Intensity ◽  
Numerical Analysis ◽  
Fracture Mechanics ◽  
Stress Field ◽  
Empirical Formula ◽  
Evaluation Method ◽  
Singular Stress ◽  
Edge Singularity ◽  
Singular Stress Field ◽  
Interface Edge

Bi-material has been widely used in engineering. Due to the edge singularity, failure usually occurs from interface edge. For the evaluation of such failures, fracture mechanics approach is considered useful to avoid the edge singularity, by introducing an edge crack with various directions. However, this evaluation method is inconvenient for engineering application due to its complicity. In this paper, based on a huge amount of numerical analysis, an empirical formula of stress intensity factors (SIFs) for cracks initiated from the interface edge with various directions and crack length has been proposed. Since the cracks initiated from the interface edge is induced and dominated by the edge singular stress field, which can be characterized by the singular order and the corresponding stress intensity coefficient (SIC), this empirical formula relates their SIFs with the SIC and singular order of the edge singular stress field. With this empirical formula, it is possible to evaluate the fracture occurring from the interface edge by fracture mechanics approach, only with the numerical analysis of non-cracked bonded dissimilar materials.

Crack onset assessment near the sharp material inclusion tip by means of modified maximum tangential stress criterion

2017 ◽  
Author(s):  
Ondej Krepl ◽  
Jan Klusák
Keyword(s):  
Stress Concentration ◽  
Crack Initiation ◽  
Tangential Stress ◽  
Maximum Tangential Stress ◽  
Reinforced Composites ◽  
Singular Stress ◽  
Stress Criterion ◽  
Maximum Tangential Stress Criterion ◽  
Particle Reinforced Composites ◽  
Material Discontinuities

In the case of particle reinforced composites, where the particles are in a form of sharp material inclusions, singular stress concentration exists on each tip of each inclusion. This is due to the geometric and material discontinuities between matrix and particle. These points of stress concentration are susceptible of crack initiation and thus often responsible for failure of the whole structure. The modified maximum tangential stress criterion is employed in order to predict crack onset conditions.

Relation of Textural Stress and Rock Failure of Diversion Tunnel

2011 ◽  
Vol 243-249 ◽  
pp. 3685-3688
Author(s):  
Rui Gao
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Stress Field ◽  
Multivariate Regression ◽  
Large Scale ◽  
Regression Method ◽  
Rock Failure ◽  
Hydropower Station ◽  
Diversion Tunnel ◽  
The Stability

The textural stress has great effect on the stability of rock. According to the measured geo-stress data, through FEM and combined with the linear multivariate regression method, the geo-stress field was conducted. Using these methods, a diversion tunnel of a large-scale hydropower station was analyzed to study the stress distribution. It was shown that the stress concentration was located at the bottom of the wall and the arch top, the stress in the wall was little and the failure happened at the bottom of the wall and the arch top, then the bottom board and some areas far from the tunnel. Under the condition without considering textural stress, the stress concentration area located in the wall and the failure happened at the bottom of the wall, then in the middle of the wall and at the arch top.

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