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Volume 13, Issue 2 Ver. III (Mar- Apr. 2016)
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Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
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During the last decades, several studies on suspension bridges under wind actions have been developed in civil engineering and many techniques have been used to approach this structural problem both in time and frequency domain. In this paper, four types of time domain techniques to evaluate the response and the stability of a long span suspension bridge are implemented: nonaeroelastic, steady, quasi steady, modified quasi steady. These techniques are compared considering both nonturbulent and turbulent flow wind modelling. The results show consistent differences both in the amplitude of the response and in the value of critical wind velocity.
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The veneering porcelain sintered on zirconia is widely used in dental prostheses, but repeated mechanical loadings may cause a fracture such as edge chipping or delamination. In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered components subjected to mixed mode loadings, the accuracy of a new and traditional fracture criteria are investigated. A modified maximum tangential stress criterion considering the effect of T-stress and critical distance theory is introduced, and compared to three traditional fracture criteria. Comparisons to the recently published fracture test data show that the traditional fracture criteria are not able to properly predict the fracture initiation conditions in zirconia/veneer bi-material joints. The modified maximum tangential stress criterion provides more accurate predictions of the experimental results than the traditional fracture criteria
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Size effect of plain concrete beams–an experimental study
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Volume 12, Issue 1 Ver. III (Jan- Feb. 2015)
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The veneering porcelain sintered on zirconia is widely used in dental prostheses, but repeated mechanical loadings may cause a fracture such as edge chipping or delamination. In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered components subjected to mixed mode loadings, the accuracy of a new and traditional fracture criteria are investigated. A modified maximum tangential stress criterion considering the effect of T-stress and critical distance theory is introduced, and compared to three traditional fracture criteria. Comparisons to the recently published fracture test data show that the traditional fracture criteria are not able to properly predict the fracture initiation conditions in zirconia/veneer bi-material joints. The modified maximum tangential stress criterion provides more accurate predictions of the experimental results than the traditional fracture criteria
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Placement of dental implants requires precise planning that accounts for anatomic limitations and restorative goals. Diagnosis can be made with the assistance of computerized tomographic scanning, but transfer of planning to the surgical field is limited. Precise implant placement no longer relies upon so called mental-navigation but rather can be computer guided, based on a three dimensional prosthetically directed plan. Recently, novel CAD/ CAM techniques such as stereolithographic rapid prototyping have been developed to build surgical guides in an attempt to improve precision of implant placement. The purpose of this paper is to discuss the use of scanning equipments to transfer clinically relevant prosthetic information which can be used for fabrication of stereolithographic medical models and surgical guides. The proposed method provides solid evidence that computer-aided design and manufacturing technologies may become a new avenue for custom-made dental implants design, analysis, and production in the 21st century.
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pdf
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In this paper, static analysis of two dimensional functionally graded plates based on three dimensional theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated. The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it shows very good agreement.
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Abstract The paper analyses the size dependency of the fracture energy (GF) and the effective length of fracture process zone (Cf) of concrete determined as per the Bazant’s Size effect method and RILEM Work-of-fracture methods. The fracture parameters (GF,Cf) are determined by measuring the maximum loads of geometrically similar notched plain concrete (M25) specimens of different sizes in a size ratio of 1:5 with different pre-cast notch depths (a/d=0.15, 0.30 and 0.45) under three point bending through load-deflection curves. In each notch depth ratio, 15 beams are cast and tested with 03 similar specimens in each size of the beams. Total beams tested are 45.The variation of both the fracture energy and the effective length of fracture process zone as a function of the specimen size and notch depth is determined using Bazant’s Size effect method and RILEM Work-of-fracture method. Fracture energy and Fracture process zone length determined by Size effect method are found to be decreasing with the increasing notch depth ratios. Fracture energy calculated using Work-of-fracture method is increasing with the increase in size of specimen and decreasing with the increasing notch depth ratios.
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The study of crack behavior in a plate is a considerable importance in the design to avoid the failure. This paper deals with investigation of stress intensity factor, Von-Misesstress (ϬVon-mises),natural frequency, mode shape and the effect of excitation frequency on the finite center cracked plate subjected to uniform tensile loading depends on the assumptions of Linear Elastic Fracture Mechanics (LEFM) and plane strain problem.
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STATIC AND DYNAMIC ANALYSIS OF CENTER CRACKED FINITE PLATE SUBJECTED TO UNIFO...
IAEME Publication
The paper concerns with analytical description of the phenomena observed in stress drop tests, namely, negative increment in plastic and creep deformation due to the sudden decrease in the acting stresses while the net stress remains positive. The model is developed in terms of the synthetic theory of irrecoverable deformation which has been generalized by introducing interplay between the deformation properties of material in the direction of acting load and opposite to it.
Peculiarities of irrecoverable straining in stress-drop test
Peculiarities of irrecoverable straining in stress-drop test
IJERA Editor
Volume 12, Issue 1 Ver. III (Jan- Feb. 2015)
P01213112116
P01213112116
IOSR Journals
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) vol.12 issue.1version.3
Analysis of Stress Distribution in a Curved Structure Using Photoelastic and ...
Analysis of Stress Distribution in a Curved Structure Using Photoelastic and ...
IOSR Journals
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency parameters are evaluated and compared with previous work available in the literature. The good agreement with other available data demonstrates the capability and reliability of the finite element method and the adopted beam model used.
Free vibration analysis of laminated composite beams using fem
Free vibration analysis of laminated composite beams using fem
Osama Mohammed Elmardi Suleiman
1Introduction The purpose of this research work is to study the fatigue related behavior of weld toe and weld root geometrical parameters in fillet welds based on the effective notch stress approach. The fatigue tests of welded structures under fluctuating loads shows that the crack initiation and propagation until the final failure is carried out mostly on the weld toe and weld root. Since the geometrical effect on stress distribution over a part plays a meaningful role in respect to increasing the stress concentration factor value and consequently the risk of failure, in this research the geometrical variables of welding which can be recommended in some case of welding procedures such as weld toe waving and weld root penetration percentage is studied. The fillet weld models under special case of loading and constraint analyzed by three-dimensional linear static analyses of finite element method to define the maximum principal stress distribution in the modeled cases. The fatigue effect of analysis added to model by utilizing the effective notch stress approach, which models the sharp lines in weld toe, and weld root by determined rounded radius of 1 mm for steel material to avoid the geometrical singularity of numerical analysis and take into consideration the fatigue notch factor. The models of this study focus on the variation of stress concentration factor due to weld toe waving geometrical effects defining by two variables of waving width and waving radius in two separate set of models which the weld flank angle has been changed. This leads an understanding to the benefit of varying stress concentration factor on the weld toe between waving tips and waving depths so that the significant decrease of this factor in waving depths can stop the rate of arbitrary initiated crack propagation. That is a crack, which initiated in a susceptible location such as wave tips could be controlled by the waving depths, which have a significantly lower stress. Meanwhile the study continued to analyze the distribution of stress in fillet weld root in respect of the percentage of weld penetration into the base material by the same fatigue 9 method and numerical analyzing tools. The result of this part depicts the usability of analyzing models type applying the effective notch stress approach and can be utilized to define an optimized penetration percentage in the weld root of fillet-welded joints 2Fatiguebasefracture Material properties, relate to the quality control of materials and initial material selection by a designer and employing only a look at the stress-strain analysis will cause the valuable information is lost. There are factors other than exceeding the yield stress and causing plastic deformation, which will affect structures. Fracture is concerned with the initiation and propagation of a crack until the load can no longer be held by the structure. It is well known that most structures will c.
1IntroductionThe purpose of this research work i.docx
1IntroductionThe purpose of this research work i.docx
hyacinthshackley2629
The determination of the stress distribution around Pin-Loaded Holes in Mechanically Fastened Joints is presented to the Engineering Department, University of Technology - Jamaica
Utech Presentation
Utech Presentation
tomlinson_n
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. To know more about modelling of orbital deformation contact to Jehad Al Sukhun at http://drjehadalsukhun.com.
Modelling of orbital deformation - Jehad Al Sukhun and others
Modelling of orbital deformation - Jehad Al Sukhun and others
Dr Jehad Al Sukhun
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury
Dr jehad al sukhun gives modelling of orbital deformation
Dr jehad al sukhun gives modelling of orbital deformation
jehadsukhun
B. Tech Agriculture TOM&MD Module 03
Tom&md notes module 03
Tom&md notes module 03
Ashish Mishra
30120130405011
30120130405011
IAEME Publication
Af4301172180
Af4301172180
IJERA Editor
7538-14320-2-PB
7538-14320-2-PB
Daryush Ebrahimi
C028011017
C028011017
researchinventy
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
E04701035045
E04701035045
ijceronline
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals, yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
International Journal of Engineering Research and Development (IJERD)
International Journal of Engineering Research and Development (IJERD)
IJERD Editor
This small guide introduces a few methods to handle singularities often referred to as ”Hot Spots” in finite element analysis.
How to deal with the annoying "Hot Spots" in finite element analysis
How to deal with the annoying "Hot Spots" in finite element analysis
Jon Svenninggaard
Slip line field method and its application in forming process Final year project work for Manufacturing Process class
Slip Line Field Method
Slip Line Field Method
Santosh Verma
International Journal of Engineering Research and Development
D1082833
D1082833
IJERD Editor
Electrical, Electronics and Computer Engineering, Information Engineering and Technology, Mechanical, Industrial and Manufacturing Engineering, Automation and Mechatronics Engineering, Material and Chemical Engineering, Civil and Architecture Engineering, Biotechnology and Bio Engineering, Environmental Engineering, Petroleum and Mining Engineering, Marine and Agriculture engineering, Aerospace Engineering.
International Journal of Engineering Research and Development
International Journal of Engineering Research and Development
IJERD Editor
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STATIC AND DYNAMIC ANALYSIS OF CENTER CRACKED FINITE PLATE SUBJECTED TO UNIFO...
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Analysis of Stress Distribution in a Curved Structure Using Photoelastic and ...
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Ijetcas14 509
1.
International Association of
Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS) www.iasir.net IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 29 ISSN (Print): 2279-0047 ISSN (Online): 2279-0055 Influence of notch parameters on fracture behavior of notched component M. Moussaoui 1, S. Meziani 2 1 Mechanical Engineering Department, University Ziane Achour, Djelfa 17000- ALGERIA 2 Laboratory of Mechanic, University Constantine 1, Campus Chaab Erssas, Constantine 25000 - ALGERIA Abstract: In the present study, the influence of variation of notch parameters on the notch stress intensity factor KI is studied using CT- specimen made from steel construction. A semi-elliptical notch has been modeled and investigated and is applied to finite elements model. The specimen is subjected to a uniform uniaxial tensile loading at its two ends under perfect elastic-plastic behavior. The volumetric method and the Irwin models are compared using a finite elements method for determined the effective distance, effective stress and relative gradient stress which represent the elements fundamentals of volumetric method. Changing made to notch parameters affect the results of stress intensity factor and the outcomes obtained shows that the increase in size of minor axis reduces the amplitude of elastic-plastic stresses and effective stresses. In lengthy notches, the Irwin model remains constant with very little disturbance of outcomes. Keywords: Notch; effective distance; notch stress intensity factor; effective stress; relative gradient; Irwin I. Introduction The role of stress concentration was first highlighted by Inglis (1913), [9] who gave a stress concentration factor for an elliptical defect, and later by Neuber (1958) [13]. The fracture phenomenon is created by these defects, if the fracture setting reaches the critical value and is observed in any geometric discontinuity. These kinds of failures take place in areas, which are called notches. The notch geometry and other notch characteristics have strong influence on fracture behavior. Notch effect results in the modification of stress distribution owed to the presence of a notch which changes the force flux. Near the notch tip the lines of force are relatively close together and this leads to a concentration of local stress which is at a maximum at the notch tip. In fracture mechanics of cracked structures is dominated by the near-tip stress field, it is characterized by the stress intensity factors which describe the singular stress field ahead of a crack tip and govern the fracture of a specimen when a critical stress intensity factor is reached. Nevertheless, the stress distribution at a notch tip is governed by the notch stress intensity factor (NSIF), which is the basis of Notch Fracture Mechanics [15] for which a crack is a simple case of a notch with a notch radius and notch angle equal to zero. Notch Fracture Mechanics is associated with the volumetric method [21, 23] which postulates that fracture requires a physical volume, in this volume acts an average fracture parameter in term of stress, strain or strain energy density. Several studies are mainly based on the volumetric method and focus on the notches effect, where Allouti et al, have addressed an analysis of these effects on the stress distribution [3]. Effective stresses are determined by two methods, the method of hot surface stresses (HS) and the volumetric method (VM). The model used for the test is done with a thin pipe of ductile material where the plastic relaxation induced a maximum distribution of stresses. The HS method is obtained by a linear extrapolation of the stress distribution for longitudinal or transversal surface defects in pipes under pressure. This interpolation uses discrete points where the stress concentration effect is dominant. The results led to a similarity of effective stress values. Pluvinage et al., analysis the stress distribution at a notch root; they show a pseudo-singularity stress distribution governed by notch stress intensity factor (NSIF), K. The result of this works and others studies indicate that this approach gives a good description in relation with the notch effect [24]. Under cyclic stress, a fatigue phenomenon is created and the damage of the area appears near the notches tips. The application of the volumetric approach has been extended to a problem of fatigue [2] and has been used to analyze fatigue parameters of notched specimens. Damage to the area due to fatigue depends not only on the peak stress at the notch root but also in areas where the damages caused to material accumulates [17]. The volumetric approach is classified as a macro-mechanical model [17, 20]. Its application depends on a number of considerations such as the elastoplastic stress distribution near the root of notch, notch geometry, loading, boundary conditions and the effect of plasticity and stress relaxation near the notch. According to this study a new concept contributes to a fatigue life assessment, based on volumetric approach and the YAO’s concept (stress field intensity, SFI) [21, 22]. The objective of this work is to investigate the effect of short and lengthy notch in fracture behavior in plain specimen. For this purpose an elliptical notch applied to CT-specimen, plane stress, perfect elastic–plastic behavior in steel construction under mode-I loading conditions using two methods especially volumetric and Irwin models [10,11] applied to a notch specimen. The elliptical notch geometry is characterized by two
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 30 dimensional parameters, the minor axis ‘2b’ and the major axis '2a' (Fig.1). The results have been extracted from elastic-plastic finite element code of the castem software to calculate the notch stress intensity factor as compared to the classical Irwin formula and analyzed the stress field that reigns at the notch root. Fig. 1 Parameters of Semi-Elliptical notch II. Finite element models of elliptical and circular notches Fig.2 show the finite element model for elliptical and circular notch used in the elastic and elastic-plastic analysis, having the dimensions 20x20 [mm] with two given values of the major axis, the short length of the notch is 0.5[mm] and the long notch is 6[mm], subjected to a uniform uni-axial tension loading at its two ends with a value 125[MPa]. Figure 2 Finite element models The material has the following mechanical properties: Young's modulus E = 230E03MPa, yield strength 670MPa, Poisson’s coefficient = 0.293. An appropriate refinement of discretization applied by triangular elements with six nodes made around the tip of the notch. Fig 2a. Elliptical notch, Fig.2b Circular notch. Fig.2a elliptical notch Fig.2b circular notch III. Analysis of Elastic-Plastic Stress Field in Notched Bodies The volumetric method has been classified as a critical distance method (TCD) [1, 4]. The main objective in volumetric method is to calculate ‘‘effective distance’’ and ‘‘effective stress’’ via extracted stress distribution at notch roots. The volumetric method takes damage accumulation in local damaged zone into consideration [2]. Investigations into the fatigue failure mechanisms have shown that the accumulation of fatigue damages depends not only on the peak stress at the notch roots but also an average stress in the damage zone and relative stress gradient [17]. In the volumetric method, the aforementioned average stress is named as ‘‘effective stress’’ and it is calculated using an effective distance. Traditionally, the effective distance has been obtained using volumetric bi-logarithmic diagram (Fig. 3). In fact, the stress distribution near notch roots versus ligament in bi-logarithmic diagram linearly behaves in certain zone like cracks [5] and the start point is considered as effective distance, this distance is considered the boundary of the stress relaxation. It can be found by means of the minimum point of relative stress gradient. The relative stress gradient for volumetric method can be written as: x x x x yy yy 1 (1)
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 31 Where (x) and yy(x), are the relative stress gradient, and maximum principal stress, or crack opening stress, respectively. Fig. 3. A typical illustration of elastic-plastic stress along notch ligament and notch stress intensity virtual crack concept including relative stress gradient which signifies the effective distance position The effective stress for fracture is then considered as the average volume of the stress distribution over the effective distance. The bi-logarithmic elastic–plastic stress distribution (Fig. 3) along the ligament exhibits three distinct zones which can be easily distinguished [18]. The elastic–plastic stress primarily increases and it attains a peak value (zone I) then it gradually drops to the elastic plastic regime (zone II). Zone III represents linear behaviour in the bi-logarithmic diagram. It has been proof by examination of fracture initiation sites that the effective distance correspond to the beginning of zone III which is in fact an inflexion point on this bi logarithmic stress distribution [7]. A graphical method based on the relative stress gradient (x) associated the effective distance to the minimum of (x). A. Weight function Weight function deals with stress contribution in elaborated damage accumulation zone; the weight function explicitly depends on stress, stress gradient and distance from notch root in the elaborated zone and implicitly depends on notch geometry, loading type, boundary conditions and material properties [1]. Weight function is essential to distinguish between Stress Field Intensity (SFI) weight function and other weight function concepts which are utilized in Fracture Mechanics based on Green’s function for boundary problem [8, 12]. The weight function should satisfy the following conditions: ) ( , ( )) 1 ) (0, (0)) 1 ) 0 ( , ) 1 max max c r r b a r Three weighting functions have been proposed, available in volumetric method [1]: - Unit weight function: x, 1 - Delta weight function: eff x, x X - Gradient weight function: x, 1 x. An analytical expression allowing the discrete points modelling of the stress distribution is expressed by the polynomial interpolation [1] : n i i yy i x a x 0 ( ) (2) The relative stress gradient can be derived by Eq. (2) as: n i i i n i i yy i yy a x ia x x x x x 0 0 1 1 (3) According to the polynomial formulation, effective distance which corresponds to minimum point of relative stress gradient can be obtained as below: 0 ( ) ( ) 1 1 2 2 2 2 x x x x x x x x yy yy yy yy (4) B. Effective stress The average stress value within the fracture process zone is then obtained by a line method [8] which consists to average the opening stress distribution over the effective distance. One obtains the second fracture criterion
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 32 parameter called the effective stress ef. However, it is necessary to take into account the stress gradient due to loading mode and specimen geometry. This is done by multiply the stress distribution by a weight function (x,); where x is the distance from notch tip and . The effective stress is finally defined as the average of the weighted stress inside the fracture process zone [25,26]: eff x 0 yy eff eff σ (x) (x, χ)dx x 1 σ (5) The volumetric method effective distance can be numerically solved using the presented volumetric method effective distance characteristics equation. With substitution of Eq. (2) into (5) and calculated effective stress, it can be rewritten including unknown weight function as follows: a x x dx X eff X n i i i eff eff ( , ). 1 0 0 (6) The mentioned polynomial stress distribution can be utilized to calculate the effective stress for all proposed weight functions. Eq. (6) can be rewritten using unit weight function as follows [1]: n i i i eff eff eff i a X X 0 1 1 1 (7) By changing the weight function and replacing the unit weight function by delta function ( ) eff x X , the new relationship of effective stress becomes: ( ) eff yy eff X (8) Including another weight function, which uses the relative stress gradient, is taken as: (x, ) 1 x. Effective stress will be [1]: n i i i eff eff n i i i eff eff eff i a X i X a X X 0 2 0 1 2 . 1 1 1 (9) In bi-logarithmic diagram, at limit of zone II and x = Xeff, the notch stress intensity factor is expressed as function of Xeff and eff [6,25]: eff eff 2 .X (10) Where eff , and Xeff are the notch stress intensity factor, the effective stress, and the effective distance respectively. C. Irwin’s models The elastic stress distribution in an elliptical defect was determined by Inglis [9]. Calculating the stress intensity factor (SIF) of a crack can be done without analyzing the singular stresses field near the tip of notch if the crack is replaced by an elliptical notch of the same size. The relationship between KI, max and can be written as [11,14]: 2 lim max 0 (11) Where , max and = b²/a, are stress intensity factor in opening mode, maximum elastic stress, and curvature radius of elliptical notch respectively. In corrected approach, Irwin argued that the presence of a crack tip plastic zone makes the crack behave as if it were longer than its physical size, and the distribution of stress is equivalent to that of an elastic crack with a length (a + rE) that is [19]: ( ) eff E a r (12) Where , a and rE: applied tension, major axis of ellipse and plastic zone size respectively. IV. Analysis of Elastic Stress Field in Notched Bodies Fig. 4 shows an elastic stress distribution analysis of the short and lengthy notch, having a semi-elliptical shape with dimension b equal to 0.1, 1 and 5 [mm] and for the major axis can take the value 0.5mm for short notch, and for lengthy notch having a value equal to 6 [mm]. It shows a comparison of analytically obtained results with those obtained by the finite element method. Various formalisms representing the stress distribution can be found in literature and are presented as follows [16]: Usami 1985: 2 4 max 1 2 3 1 2 1 1 3 x x yy Chen and Pen,1978:
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 33 x yy 8 max Neuber and Weiss1962: x yy 4 max Kujawski,1991 1/ 2 3/ 2 max 2 1 2 1 x x f yy 0.2 2.8 tan / 2 0.2 , 1 0.2 1 ; k x f x if f x if t The results are similar near the end of notch where the stress concentration is high (Fig. 4a, Fig. 4b and Fig. 4c). However, at remote distances from notch bottom, i.e. where the stress gradient is lower, the results obtained by finite element method decrease rapidly towards lower values. It is also known that the flattened notches behave the same way as crack, generate a higher stress concentration, and consequently significant elastic stresses reach maximum values. In the lengthy notches (a=6[mm],b=1mm and 5mm) away from the notch root, stresses are reduced to lower values then the results obtained by Chen Pen , Neuber and Kujawski, decrease regularly and get closer mutually (Fig. 4b and Fig. 4c). If the semi-elliptical notch tends towards a semi-circular notch, the maximum elastic-plastic stresses tend to have lower values.For short notch configurations, the Chen Pen and Neuber results show a convergence those obtained by finite elements, while for lengthy notch, b=1mm Neuber and Kujawski obtained better results and the extent of high stress region becomes smaller ( 1 [mm]) compared to lengthy notches for b=5mm which is less than 2 [mm]. Fig. 4 Elastic stresses distribution, a) Short notch a=0.5mm and b=0.1mm, b) Lengthy notch a=6mm and b=1mm Fig. 4c Elastic stresses distribution, lengthy notch a=6mm and b=5mm On the other hand, in the case of deep notches having an elastic behaviour, increasing the size of minor axis (b) reduces the effect of stress concentration. The elastic distribution of stress gives the maximum value at notch bottom; unlike the maximum of elastic-plastic stress is far from the notch tip.
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 34 V. Analyzing notch stress intensity factor The phenomenon of rupture must indeed be considered in its physical dimension. It requires a certain elaboration volume of process failure [15]. In this volume, a zone is governed by the notch stress intensity factor, which depends at the same time on the effective distance, the effective stress, the relative stress gradient and the weight function. The results obtained are compared with those calculated in accordance to the two Irwin models [10,14]. Figures 5a and 5b show the notch stress intensity factor evolution versus the ratio b/a calculated by using the two Irwin models and the three weight functions: unit, delta and gradient functions. Fig. 5 Evolution the notch stress intensity factor for, a) short notch, a=0.5mm, b) lengthy notch, a=6mm The changes made to notch parameters (a, b and, ) affects the evolution of stress intensity factor versus the ratio b / a. The figures show its variation for elastic-plastic behaviour; (note that the volumetric method was applied initially for brittle materials, the extension of its use to ductile materials has gave the good approximations). Figure 5 depicts at low values of (b / a) i.e. for an open notch. The results calculated by the volumetric method are convergent mutually by approaching each other with the results of Irwin corrected model. In particular the weight gradient function gives approximately the same results with the corrected Irwin model. For a short notch (a = 0.5mm) and beyond a higher ratio (b/a), a divergence in the results of the volumetric method is observed compared to Irwin corrected, but a convergence to the uncorrected Irwin model has appeared. The made of significant plasticizing (Fig.9) that is starting at the bottom of the notch in lengthy notches, the results of volumetric method (VM) describe a similarity of approximation of the results with re-convergence to the uncorrected -Irwin model and excessive divergence from Irwin – corrected. This latter remains constant with very little disturbance of outcomes, we can conclude that the volumetric method is very sensitive to notch parameters variation. Fig. 6 Evolution of the notch stress intensity factor for: a) Opened semielliptical notch; b) Thinned semielliptical notch If a plastific area widens near the end of the notch, the Irwin corrected model can not detect the change that has occurred to the notch stress intensity factor (NSIF) parameters.
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 35 The increase in size of the major axis (a) and the reduction of the minor axis (b) correspond to a deeper and flattened semi-elliptical notch; creating a region where the stress concentration is high and generates an increased stress gradient as a result of the increase of the stress intensity factor values. Thinned and deepened semi-elliptical notches are much more dangerous than short semi-elliptical and semi-circular notches. If the stress gradient is low (b/a high), Figures 6a and 6b show that the results obtained results by VM and irwin corrected model of the SIF-KI are closer and the curves show an identical appearance in Figure 6a. The Irwin corrected model gives converging results with results of unit weight function (Fig. 6a and Fig. 6b). For a short notch, at great stress gradient (b/a low), i.e. decreasing the major axis (a); the results obtained by the three weight functions move away from those obtained by the Irwin corrected model and are approaching to those of Irwin uncorrected model (Fig. 6b). For values of the minor axis b equal to 4 [mm], the elliptical notch is classified as an open notch (Fig. 6a), this gives a rearrangement of stress concentration distribution. The opening of the elliptical notch reduces the stress concentration in the area near the bottom of the notch (increased b / a). Fig. 7 Evolution of the notch stress intensity factor for a semi-circular notch From a high stress gradient, the values obtained using the two Irwin models, diverge excessively relative to the volumetric approach (Fig. 6a). In the semi-circular notch (Fig. 7), the results of SIF, (calculated according to the Irwin corrected model) are intermediate between those obtained by the weight, delta and unit functions for a radius lower than 2 [mm]. VI. Effective Stress and Maximum Elastic-Plastic Stress The effective stress is the average value of the stress distribution over the effective distance, weighted by the relative stress gradient inside the elaboration volume of fracture. Figures 8a and 8b show the evolution of effective stress calculated using the three weight functions (unit, delta and gradient) with the maximum elastic- plastic stress, according to the ratio (b/a), relating to the short and lengthy semi-elliptic notches in order to determine the function which can approximate the maximum elastic-plastic stress. At low values of ( b / a), where the notch tends to flatten the effective stress calculated by the VM and maximum elastic-plastic stress values increases to the peak, and then follow a regular decrease to low values of stress ,where the stress gradient is lower. Fig. 8 Evolution of effective stress & maximum elastic-plastic stress for short notch and lengthy notch
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Moussaoui et al.,
International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 36 In the case of deep notch which develops a high stress, induces a high stress gradient and displays an extensive of lower values (b / a <0.70) (Fig. 8b ), than that of the short notch (b / a <1.2) (Fig. 8a) and the effective stresses calculated by the weight gradient function get closer to stress maximum elastic-plastic. The outcomes of maximums elastic-plastic stress is greater than the effective stresses value calculated by the volumetric approach. The opening of the elliptical notch (b high) reduces the amplitude of the effective stresses and maximum elastic-plastic stresses and brings up a similarity of approximation of the results of effectives stresses calculated by the different weight functions (Fig. 8b). If the minor axis 'b' of semi-elliptical notch increases, the approximation obtained by the three weight functions converge between them for both notch configurations (short and lengthy). Fig. 9 Plastic zone at the tip of the lengthy notch according to VON MISES criterion; notch a=6mm VII. Conclusion In the present study, the volumetric method is investigated and compared with Irwin models using the finite element method to explain the influence of notch parameters variation in weight functions , effective distance, effective stress, and in the stress gradient (consequently on the fracture behaviour). Extension of the application of volumetric method in the case of an elastic-plastic stress distribution has taken into account the effect of these changes made to notch parameters. The main outcomes can be summarized as: Changing the notch parameters (a, b and ) creates stress field disturbances near the notch root. Therefore, it affects the evaluation of the stress intensity factor. Lengthy notches have a significant plasticizing near the notch root, and the corrected- Irwin model remains constant with very little disturbance of outcomes. The volumetric method is very sensitive to notch parameters variation. The outcomes of volumetric method (VM) describe a similarity of approximation of the results with re-convergence to the uncorrected -Irwin model and excessive divergence from the Irwin corrected model. If the notch tends to open, the results achieved through volumetric method and the uncorrected Irwin model, mutually converge. The deeper and flattened notch creates a region where the stress concentration is high and generates an increased stress gradient. The thinned and lengthy semi-elliptical notches are much more dangerous than the short semi-elliptical and semi-circular notches. The results obtained show that the increase in size of minor axis of elliptical notch reduces the amplitude of elastic-plastic stresses and effective stresses. The elastic stress distribution is characterized by maximum stress at the notch root and in the case of elastic-plastic distribution it is characterized by a stress relaxation. VI. References [1] Adib-Rammezani.H, Jeong.J. Advanced volumetric method for fatigue life prediction using stress gradient effects at notch roots, Computational materials science 39: 649-663, 2007 [2] Adib. H, Pluvinage.G,. Theoretical and numerical aspects of the volumetric approach for fatigue life prediction in notched components,. International Journal of fatigue 25: 67-76, 2003 [3] Allouti. M, Jallouf.S, Schmitt.C, Pluvinage.G. Comparison between hot surface stress and effective stress acting at notch-like defect tip in a pressure vessel,. Engineering Failure Analysis 18: 846-854,2011 [4] David Taylor. The theory of critical distances, a new perspective en fracture mechanics. Book. Elsevier, London WC1X 8RR, UK. First edition 2007 [5] Boukharouba.T, Tamine.T, Niu.L, Chehimi.C , Pluvinage.G .The use of notch stress intensity factor as a fatigue crack initiation parameter. Engineering Fracture Mechanics Vol. 52, No. 3: 503-512, 1995 [6] Minor. H. El, Kifaini. A, Louah. M, Azari. Z, Pluvinage.G. ‘Fracture toughness of high strength steel-using the notch stress intensity factor and volumetric approach’,. Structural Safety 25: 35-45, 2003 [7] Hadj Meliani. M, Matvienko. Y. G , Pluvinage.G. Corrosion defect assessment on pipes using limit analysis and notch fracture mechanics,. Engineering Failure Analysis 18: 271–283, 2011 [8] A.E. Green, I.N. Snedden, Proceeding of the Cambridge Philosophical Society 46 159–163 , 1950
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International Journal of Emerging Technologies in Computational and Applied Sciences, 9(1), June-August, 2014, pp. 29- 37 IJETCAS 14-509; © 2014, IJETCAS All Rights Reserved Page 37 [9] Inglis . Stress in a plate due to the presence of cracks and sharp corners,. Trans Inst Naval Architects, 55:219–230, 1913 [10] Jean Lemaitre, Jean-Louis Chaboche. Mécanique des matériaux solides’, © Bordas, Paris. 1988 [11] Livieri Paolo, Segala Fausto, Evaluation of Stress Intensity Factors from elliptical notches under mixed mode loadings,. Engineering Fracture Mechanics 81: 110–119, 2012 [12] J. Rice, International Journal of Solids and Structures 8 751–758, 1972 [13] Neuber .H. Theory of notch stresses,. Springer-Berlin, 1958 [14] Nui. L. S, Chehimi.C , Pluvinage.G. Stress filed near a large blunted tip V-notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials,. Engineering Fracture Mechanics. Pergamos, Vol.49 .No. 3: 325-335, 1994 [15] Pluvinage.G. Fracture and Fatigue Emanating from Stress Concentrators, Université de Metz, . France, KLUWER Academic Publishers, 2003 [16] Pluvinage..G. Fatigue and fracture emanating from notch; the use of the notch stress intensity factor’,. Nuclear Engineering and Design 185: 173-184, 1998. [17] Qylafiku. G., Azari. Z., Kadi. N., Gjonaj. M. , Pluvinage. G. Application of a new model proposal for fatigue life prediction on notches and key-seats,. International journal of fatigue 21: 753-760, 1999. [18] Shi . S. Q.,. Puls. M. P. A simple method of estimating the maximum normal stress and plastic zone size at a shallow notch,. International Journal of Pressure Vessels and Piping, 64(1): 67–71, 1995 [19] Agah Uguz and John W.Martin, materials characterization 37:105-118 ,1996 [20] H. Adib, J. Gilgert, G. Pluvinage. Fatigue life duration prediction for welded spots by volumetric. Method.International Journal of Fatigue 26 81–94, 2004 [21] Weixing. Yao. The prediction of fatigue behaviours by stress field intensity approach,. Acta mechanica solida sinica, 9 (4): 337–349, 1996 [22] Weixing Yao, Bin Ye, Lichun Zheng. A verification of the assumption of anti-fatigue design,. International Journal of Fatigue, 23(3): 271–277, 2001 [23] Weixing Yao. Stress field intensity approach for predicting fatigue life,. International Journal of Fatigue, 15(3): 243–246, 1993 [24] Pluvinage G., Azari Z., Kadi N., Dlouhy I. and Kozak V. Effect of ferritic microstructure on local damage zone distance associated with fracture near notch. Theoretical and Applied Fracture Mechanics 31,149–156, 1999 [25] Vratnica. M, Puvinage. G., Jodin. P., Cvijovic. Z, Rakin. M, Burzic. Z.. Influence of notch radius and microstructure on the fracture behaviour of Al-Zn-Mg-Cu alloys of different purity,. Materials and design 31: 1790-1798, 2010 [26] Zedira.H, Gilgert.J, Boumaza. A, Jodin.P, Azari.Z, Pluvinage.G,. Fatigue life prediction of welded box structures. Strength of Materials. Vol. 36. No 6, 2004
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