Numerical modeling and analytical validation of stress and

Transcription

IPASJ International Journal of Mechanical Engineering (IIJME)
Web Site: http://www.ipasj.org/IIJME/IIJME.htm
Email: editoriijme@ipasj.org
ISSN 2321-6441
A Publisher for Research Motivation........
Volume 3, Issue 4, April 2015
Numerical modeling and analytical validation
of stress and stress intensity factor for SENT
tensile specimen of P265GH steel material
M.LAHLOU1, M.RACHIK2, M.BECHTAOUI3, A.HACHIM4, M. EL GHORBA5
1
Laboratory of Control and Mechanical Characterization of Materials and Structures, National Higher School of Electricity
and Mechanics, BP 8118 Oasis, Hassan II University, Casablanca, Morocco
2
Roberval Laboratory. UTC, Royallieu Research Center. Person street from Roberval, BP20520,60205 Compiègne Cedex,
France
3
ISEM/Higher Institute of Maritims Studies, Laboratory of Mechanics, Km 7 Road El Jadida Casablanca, Morocco
4
ISEM/Higher Institute of Maritims Studies, Laboratory of Mechanics, Km 7 Road El Jadida Casablanca, Morocco
5
Laboratory of Control and Mechanical Characterization of Materials and Structures, National Higher School of Electricity
and Mechanics, BP 8118 Oasis, Hassan II University, Casablanca, Morocco
ABSTRACT
In a material subjected to a mechanical loading, the stress distribution is not uniform in the vicinity of a defect, causing a
stress concentration in this area which result a sudden fracture. Therefore, the effect of the notch is generally reflected by an
increase in stress at the bottom of the notch.
The objective of this paper is to establish a numerical finite element modeling for a SENT tensile specimen (Single Edge Notch
Tension) using CASTEM2013 computer code. The studied material is P265GH steel commonly used in sheet form in boilers
and pressure vessels.
The results show that the stresses exhibit a parabolic trend with a maximum value at the bottom of the notch at first, and then
stress stabilization is noticed at the nominal stress value. The length of the critical notch decreases with increasing stress.
Keywords: Notch, Finite element model, Stress, Stress intensity factor, Pressure vessels.
1. INTRODUCTION
Through the development of information technology, new tool of production have been used in many industrial sectors
that become currently inescapable: numerical finite element modeling; this method is a numerical way to resolve the
problems of mechanical systems which allows determining an approximate solution on a spatial domain [1].
Nevertheless, in metallic structures, cracks are mostly initiated at geometric discontinuities of notches or defects. The
geometric parameters and discontinuities govern cracks initiation or propagation and therefore affect the resistance of
structures during their use [2]. In industry, for economic or security reasons it is seek to know the degree of defects
harmfulness and residual life time of structures; This requires the development of models based on fracture mechanics.
The behavior simulation with FEM has been presented by many authors with the aim to improve the knowledge of
predict trends. A. HACHIM [3,4] presented a finite element based approach to simulate a Double Edge Notch Tension
specimen of S355 Steel; he studied the behavior of the material in the presence of defects. Y.HIROSHI [5] presented
the critical stress intensity factor on SENT specimen. A. EL Hakimi [6] studied the correction function i0, by applying
a constant pressure along the lips of crack. According to the results of the calculations, the integral J in the case of a
defect at the base of the transition is always higher than that of the similar case in a straight tube [7].
In the present article, the P265GH steel used in pressure vessels, and its current specifications, are introduced first. The
tensile properties for selected steel are then evaluated. A numerical finite element modeling based on the tensile
properties has been developed to determine the life prediction. Finally, a parametric study of tenacity was performed.
2. EXPERIMENTATION
To extract the mechanical characteristics of the P265GH steel used in our program, tensile tests of standard specimens
(Figure 1a and 1b) were conducted in different directions of rolling (longitudinal and transversal). The test curves
showing the stress versus elongation are given in Figure 2:
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ISSN 2321-6441
Figure 1-a : Image of the
standard test specimen
Figure 1-b : Dimensions
of the standard test
specimen
Figure 2: Stress strain curve test
By comparing the mechanical characteristics of the specimen in both rolling directions, it is found that there is a
negligible difference between the two curves. The mechanical characteristics of P265GH steel, at the ambient
temperature, are reported in the table1:
Table1. Mechanical properties of the material
Young's modulus
E (MPa
elastic limit:
e (Pa)
2.105
320
Breaking
stress: g
(Pa)
470
Elongation %
Poisson's ratio
ν
35
0,3
We notice that the elongation is about 35% which is higher than 14% required by the CODAP[8]. Therefore, this
P265GH steel used is well adapted for pressurized structures.
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3. NUMERICAL MODELING
The calculation code Cast3m 2013 is used to construct a finite element model to analyze SENT specimen behavior
subjected to tensile stress. In what follows, we describe FE modeling.
3.1Geometry
The geometry and dimensions of the studied specimen are shown in Figure 3. Since the study is restricted to the
I, The specimen was subjected to tensile solicitations.
mode
Figure 3. Geometry and dimensions of the studied specimen
3.2Mesh and boundary conditions
By taking into consideration the symmetry of the problem, only half of the test specimen is discretized. Because the
numerical results are intended for analysis of fracture mechanics, special attention is paid to mesh principally in crack
and its vicinity (Mesh Refinement using Barsoum elements)[9]. Details of the mesh are illustrated in Figure 4a and 4b.
x
Figure 4-a : Mesh
Figure 4-b :Mesh in
the vicinity of a notch
3.3Loading
The simulated load is a tensile solicitation along the longitudinal axis of the specimen. To avoid bending or twisting
parasite and to ensure that the tensile stress is perfectly aligned; it is applied on the specimen via a rigid triangle
indicated by the arrow 4a. The selected loads are calibrated in such a way that the applied nominal stresses are
respectively 148 MPa, 284MPa and 356MPa.
4. RESULTS AND DISCUSSION
4.1Evolution of the stress in the ligament
The curves in Figure5 illustrate the evolution of the stress in the ligament of the specimen, ie, along the x axis of
Figure 4a (origin at the crack bottom) for the three levels of applied stress: Δσ = 148 MPa, 284MPa, 356MPa
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ISSN 2321-6441
Figure 5: Evolution of the Von Mises stress in the ligament of the specimen for the three levels of applied stress (Δσ =
356MPa, 284MPa, 148MPa).
For Δσ = 148 MPa, there are three zones:
 The first zone [0, 0.5mm] (in the vicinity of the notch bottom) corresponds to the interval of stress values [470,
653MPa] .The maximum stress is 653 MPa which exceeds the strength of the material. The stress then decreases
until reaching the breaking stress σg = 470MPa.
 The second zone [0.5, 2mm] matching the stress values that are included in the interval [320, 470MPa]. The stress
is greater than the elastic limit of the material; this zone is the seat of plastic deformations.
 The third zone [2, 25mm] that corresponds to the interval of stress values [148, 320MPa]; We are observing a
slight diminution of stress to stabilize at the applied stress value which is below the elastic limit. Thus, this zone is
elastically deformed.
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ISSN 2321-6441
For Δσ = 284 MPa, there are three zones:
 The second zone [1.7, 4.5mm] matching the stress values that are included in the interval [320, 470MPa]. The
stress is greater than the elastic limit of the material; this zone is the seat of plastic deformations.
 The third zone [4.5, 25mm] that corresponds to the interval of stress values [284, 320MPa]; We are observing a
slight diminution of stress to stabilize at the applied stress value which is below the elastic limit. Thus, this zone is
elastically deformed.
For Δσ = 356 MPa, there are two zones:
 The second zone [3.9, 25mm] that corresponds to the interval of stress values [356, 470MPa]; We are observing a
slight diminution of stress to stabilize at the applied stress value which is above the elastic limit. Thus, this zone is
plastically deformed.
4.2 Evolution of the stress intensity factor
The curves in Figure 6 represent the evolution of analytical and numerical stress intensity factor in the ligament of the
specimen, for the three levels of applied stress: Δσ = 148 MPa, 284MPa, 356MPa.
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Figure 6 : Evolution of stress intensity factor in the ligament of the specimen, for the three levels of applied stress: Δσ
= 148 MPa, 284MPa, 356MPa.
The analysis of the curves in Figure 6 shows that there is a significant increase in the stress intensity factor in function
of the crack propagation and the applied stress. The variation of the numerical stress intensity factor is comparable to
that of the analytical. The values of the critical notch length are reported in table 2.
Table2. The values of the critical notch length depending on the stress levels
the critical notch length
Stress (MPa)
ac (mm)
148
12
284
5
356
2
5. CONCLUSION
In the sectors of unsafe structures such as pressure vessels and in the presence of defect, it is essential to detect precisely
the degree of defect harmfulness. Numerical finite element modeling method is an extremely efficient tool to address
this issue.
A numerical model using Cast3m 2013 is performed on a tensile specimen (SENT) to study the evolution of the stress
and stress intensity factor along the ligament of the specimen for three levels of applied stress (Δσ = 356MPa, 284MPa,
148MPa).
Found results show that the stresses follow a parabolic tendency until reaching a maximum value at the root of the
defect, and then stress stabilization is observed at the nominal stress value. The values of the critical notch length
decrease with the increase of the applied stress.
The finite element model adopted for this work is commonly used and can be extended to real applications.
References
[1] Martin Kempeneers, éléments finis statiquement admissibles et estimation d’erreur par analyse duale, Mémoire de
thèse doctorat Université de Liège Faculté des Sciences Appliquées, 31 mars 2006,
[2] Damien Fournier, Analyse et Développement de Méthodes de Ra nement hp en Espace pour l’Equation de
Transport des Neutrons, Mémoire de thèse doctorat Université de Provence Marseille, 10 octobre 2011,
[3] A. Hachim, Etude numérique et validation expérimentale des mécanismes d’endommagement et de fissuration de
l’acier S355 : application aux équipements sous pression, Mémoire de thèse doctorat, Faculté des Sciences-Aïn
Chock,Casablanca, 27/04/2013
[4] A. Hachim, Numerical Evaluation and Experimental Validation of Stress Concentration and Crack Propagation a
Bi-notched Specimen of Steel S355, International Journal of Research and Reviews in Mechatronic Design and
Simulation (IJRRMDS) Vol. 2, No. 3, September 2012, ISSN: 2046-6234
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ISSN 2321-6441
[5] Hiroshi Yoshihara, Mode I Critical Stress Intensity Factor of MediumDensity Fiberboard Obtained by SingleEdgeNotched Bending Test ,Original scientiﬁ c paper • Izvorni znanstveni rad. Accepted – prihvaceno: 6. 2.
2014.
[6] A. El Hakimi, Numerical and experimental study of the harmfulness of defects in cylindrical and spherical shells
under pressure, Ph.D. Thesis University of Technology of Compiègne, June 30, 2006.
[7] A. Saffih, S. Hariri, Numerical study of elliptical cracks in cylindrers with a thickness transition, International
Journal of Pressure Vessels and Piping, Vol 83, No. 1, pp. 35-41, 2006.
[8] CODAP: Code de Construction des Appareils à Pression non soumis à la flame 2005
[9] Barsoum,Furthur application of quadratic isoparametric elements to linear fracture mechanics of plate bending and
general shells. Int.J.Num.Meth,Engng , 11,167-169. (1976).
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Numerical modeling and analytical validation of stress and

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