is modeled as three main parts; the specimen,the striker, components was assumed to be isotropic and homogenous. ndition of an actual Charpy rig (i.e.Instron ...
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
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ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 4, July - August (2013), pp. 377-386 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com
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THREE DIMENSIONAL NONLINEAR FINITE ELEMENT MODELING OF CHARPY IMPACT TEST Fadi A. Ghaith*, Fahad A. Khan Department of Mechanical Engineering, Heriot-Watt University, Dubai Campus, P O Box 294345, United Arab Emirates
ABSTRACT In this paper, a three-dimensional Finite Element (FE) model was performed to simulate the impact test ofnormalized carbon steel and aluminum specimens. The model specifications were developed according to ASTM E-23 standard requirements. Also the established FE model took into account all sources of non-linearity such as geometric, material and contact nonlinearities. A failure criterion is assumed to be at 10 % of plastic strain based on the tensile experiment data. Based on the simulation results, it was found that the absorbed energy required for fracture of the steel and aluminum specimens under the impact load at room temperature are44.6J and 20.4J, respectively. In comparison with the corresponding values resulted from the experimental Charpy impact test, the percentage of error didn’t exceed 7 % for both steel and aluminum specimens. Also this paper demonstrated the influences of the notch depth and shape on the absorbed energyby conducting the relevant parametric studies. Finally, the importance of the present 3-dimensional model over the 2dimensional model was demonstrated in terms of applicability, accuracy and reliability. Keywords: Charpy test, impact energy, nonlinear, finite element, three dimensional. 1. INTRODUCTION The failure of engineering materials is an undesirable event for several reasons; that include safety of human lives and economic losses. Therefore impact testing techniques were established so as to ascertain the fracture characteristics of materials. Charpy impact test involves measuring the energy consumed in breaking a notched specimen simply supported at both ends when it is hammered by a swinging pendulum. The presence of a notch simulates the pre-existing cracks found in large structures and increases the probability of brittle fracture. Charpy impact testing is a low-cost and reliable test method, which is commonly required by the construction codes for fracture of critical structures such as bridges and pressure vessels. It took from about 1900 to 1964, for impact 377
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME test technology and procedures to reach the levels of accuracy and reproducibility so that they could be broadly applied, started from Charpy tests in 1905 up to the issue of the revised Standard of ASTM E-23 in 1964. Many researchers developed simple mathematical models to describe the impact phenomena [1, 2], but some of themdidn’t address the geometric and contact nonlinearities while other studies were limited to the lumped analysis. Recently, Computer simulation method has been developed in order to accurately simulate the fracture phenomena that can be considered during impact test. Belytschko and Bartel [3] research is considered one of the earliest work in developing a nonlinear transient analysis for large scale deformation using the finite element analysis. Full three dimensional analyses of the failure modes in Charpy impact test was carried out by Mathur et al. [4]. This workaimed to investigate the influence of the specimen dimensionson the plastic straining at the notch. It was found that there are some three-dimensional effects in that material failure grows more rapidly at the center of the specimen than near the free surface end of the notch. Also it was found that the force against time dependence predicted by the plane strain computations produced a reasonably good approximation of the corresponding three-dimensional results. Tvergaard and Needleman [5] investigated the ductile-brittle transition for a weld by means of numerical analyses of Charpy impact specimens. The material response was characterized by an elastic-visco-plastic constitutive relation for a porous plastic solid, with adiabatic heating due to plastic dissipation. The predicted work to fracture showed a strong sensitivity to the location of the notch relative to the weld, with the most brittle behavior for a notch close to the narrow heat affected zone. This analysis illustrated the strong dependence of the transition temperature on stress triaxiality. Lorriot [6] proposed an experimental method based on the specimen displacement measurement using laser sensor in order to determine the actual specimen loading in instrumented impact test. The prediction resulting from this approach was compared with results deduced from dynamic analysis of impact tests with mass-spring model. Altenhof et al. [7] focused on their research on the development of a material model for the AM50A magnesium alloy, which is frequently used in the automotive industry. Computer model was developed and validated through experimental setup and numerical simulation of standardized Charpy and tensile tests. The material model was further used to predict the behavior of an AM50A magnesium alloy steering wheel armature by performing experimental and numerical impact tests. Chao et al. [8] examined the advanced high strength steels (AHSS) that gradually adopted in vehicle structures as lightweight materials in the past years. In this work, results from Charpy V-Notch impact tests on dual phase 590 (DP590) steel were presented and tests were conducted at temperatures ranging from 120°C to 90 °C and DBTT was determined.Rubio-Gonzalez et al. [9] performed an analysis of dynamic fracture toughness of pre-fatigued materials using the split Hopkinson bar apparatus. This setup had been arranged to measure the dynamic loads acting on notched and pre-fatigued bend specimens made of AISI 4140-T steel and A6061-T6 aluminum. Same metal specimens with identical properties were used in the FE simulation presented in this work for the purpose of validation. Ghaith [10] developed a two-dimensional FE model to estimate the impact energy required for the fracture of carbon steel AISI 4140 specimen. Also he was able to estimate the Ductile to Brittle Transition Temperature (DBTT) by estimating the impact energy at different temperatures. In the present work, a three dimensional model with appropriate and realistic assumptions was developed to represent the actual practice of Charpy impact test using finite element analysis (i.e. Abaqus 6.1, Explicit). The geometry was modeled according toASTM E-23 [11]. The main objective of this work is to estimate numerically the impact energy required for the fracture of normalized steel and Aluminum specimens and to compare the obtained results with the corresponding experimental ones at common test conditions.Anothercontribution of this work is to investigate the effects of varying the notch depth and shapeon the absorbed energy.
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 2. FINITE ELEMENT MODEL the striker, and the The impact test apparatus is modeled as three main parts; the specimen,the supports. The material of all components was assumed to be isotropic and homogenous. homogenous.This model inherits the properties and condition ndition of an actual Charpy rig (i.e.Instron (i.e. SI-1K3). 2.1.Geometry The dimensions of both steel and aluminum specimens were assigned according to ASTM E23 requirements as illustrated by Fig. 1. The presence of a notch may simulate the pre-existing pre cracks found in large structures, noting that concentrated stresses are developed on such sharp corners. In order to investigate the influence of the shape of the notch on the fracture, two shapes were selected; V-notch and U-notch notch as described later in section 3.3.
Fig.1. Geometry of the testing specimen (mm) As the main focus of this study is towards the mechanical and material properties of the specimen, the striker is modeled as a rigid body.The mass of the striker was set to30.24 kg and the density was selected just to match the mass of the pendulum in the actual test.According to ASTM E23 standard, the round und pointed face of the striker that strikes the specimen is designed as a fillet with a radius equivalent ivalent to the distance of the V-notch V (i.e. 1.6567 mm). Fig. 2 shows the shape and important dimensions of the striker.
Fig.2. Illustration of the striker from sketch to extrusion
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 2.2.Material properties In this work, AISI 4140-tempered steel and A6061-T6aluminumweresimulated for the purpose of prediction ofthe absorbed energyresulted from impact test. Table 1 shows the physical properties of both test specimens. Table1.Physical properties of the tested specimens Yeild Density Poisson’s Young’s 3 ratio modulus strength (kg/m ) (GPa) (MPa) AISI 4140-T Steel 8030 0.3 207 655 Aluminum A6061 2700 0.33 80 276 Specimen
Ultimate tensile strength (MPa) 1020 310
In the current FE analysis, the bilinear isotropic hardening material model(i.e. a piecewise linear plasticity model)was used to describe the stress/strain relationship of the normalized steel. Such a model is used widely in automotive industry to its ease implementation. Fig. 3 shows the stress-strain curves for both steel and aluminum. 2.3.Computational model setup After introducing the geometry, assigning the material via sections and assembling the individual parts, it is necessary to define the parameters of the computational simulation.
Fig.3.Stress-strain curve for AISI 4140-T steel and aluminum A6061 Firstly, since the model deals with a time dependent problem (i.e. impact), Dynamic/Explicit step was utilized. In order to consider the contact effects, two types of contact interactions were defined; specimen- to- support contact and striker –to- specimen impact. These contact interactions 380
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME were assigned with a frictional interaction property. Regarding the boundary conditions, a coupling constraint was assigned to the striker which restricted the striker’s movement only to towards the specimen (i.e. y-direction). As the main objective is to simulate the actual practice of Charpy impact test, the mass of the striker and the gravity field were considered. It should be recognized that the velocity of the striker was set according to a realistic ‘high latch’ velocity of an actual Charpy rig. 3. RESULTS AND DISCUSSION Numerical analysis was carried out based on the developed FE model described in section 2. This analysis aimed to predict numerically the absorbed impact energy required for fracture of both steel and aluminum specimens as well as the influence of notch shape and depth on the absorbed energy. The fundamental step of any FE analysis is to check the mesh convergence and to assign the most appropriate mesh size. Fig. 4 shows that the mesh is converged at an overall No. of elements equals to 64683. However, a mesh of element numbers 214678 was selected as common for all simulation runs to guaranteethe required accuracy especially around the notch.
Fig.4. Illustration of mesh convergence 3.1. Impact energy The impact energy required for fracture for both AISI 4140-T steel and aluminium A6061-T6 were predicted by considering the area under the force-displacement curve. The displacement has been estimated directly from the FE simulation. Fig. 5 show the Von Mises stresses and corresponding displacements for steel specimen at the maximum permissible plastic strain of 10 %. Fig. 6 shows the force-displacement diagram for the steel specimen. The area under the curve represents the absorbed energy required for fracture which equals 46.64 J. In order to validate the FE findings, the obtained impact energy was compared with the corresponding experimental Charpy impact test. It was found that the impact energy of a V-notch AISI 4140-T steel is 50 J [14]. Hence, the percentage of error that is observed in the suggested FE model is6.6 %only.
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
(a)
(b) Fig.5. (a) Von Mises stresses for steel specimen (b) corresponding displacement distribution
Fig.6. Force-displacement curve for AISI 4140-T steel specimen Similar analysis was carried out for aluminum A6061-T6 specimen. The main findings are summarized in Table 2. The obtained results showed generally that the established FE model was able to capture the impact energy accurately of steel and aluminum specimen with very slight difference if compared to the actual Charpy impact test.
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME Table 2. Estimated impact energy and relevant parameters Impact Impact energy Max. Von Max. Energy Error generated Percentage Specimen MisesStress displacement calculated from (MPa) (mm) using FE (%) experimental simulation setup AISI 4140-T 982.3 1.502 46.64 50 -6.6 Steel Aluminum 376.6 1.303 20.4 21.7 6 A6061 3.2.Influence of the notch depth on the absorbed energy In order to check the influence of the notch depth, numerical run has been performedfor the case in which the V-notch increased by 1.5 % compared to the standard dimension. Fig.7 shows the notch geometry for both cases. Fig. 8 shows the absorbed energy versus the notch depth for AISI 4140. The obtained results demonstrated that as the depth of the notch increases, the absorbed energy decreases accordingly. In other words, the specimen tends to fracture faster and easier in case of higher notch depth. It should be mentioned that according to ASTM E 23 standard, changing the notch depth by 1.5% can give an energy change of up to 8%. On the other hand, the obtained numerical results showed a difference of about 10.1% which is still quite close to the ASTM standards,
Fig.7. Notch geometry at different depths
Fig.8. Absorbed energy versus the V-Notch depth for a AISI 4140-T Steel specimen 383
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 3.3.Influence of the notch shape on the absorbed energy The main objective of this part is to investigate the effect of the notch shape on the absorbed energy required for fracture of AISI 4140-T steel. Hereafter, V-Notch and U-Notch were considered. The dimensions for both notch shapes are shown schematically by Fig. 9.
Fig.9. Dimensions of V-Notch andU-Notch Table 3 shows a comparison between the V-notch and U-notch in terms of absorbed energies, relevant stresses and deformationswhich were generated from two different simulation runs. Based on the obtained results, the absorbed energy required for the fracture of U-Notch specimen is higher than that of a V-Notch by 15.5%. This is due to the fact that V-notch is considered as higher stress concentrator compared to U-notch. Table 3. Comparative study of the absorbed energy results of a V-Notch and U-Notch steel specimens V-Notch AISI 4140-T Steel Specimen
U-Notch AISI 4140-T Steel Specimen
Stress in the Specimen (MPa)
982.3
Stress in the Specimen (MPa)
Displacement in the Specimen (mm)
1.502
Displacement in the Specimen (mm)
Impact Energy absorbed at fracture
46.64 J
Impact Energy Absorbed at fracture
871.2
0.9
54 J
3.4.Comparative study between the conducted 3D analysis and 2D approximation The main objective of this section is to check the applicability and accuracy of using 2dimensional approximation in comparison with the most comprehensive 3-dimensional model. For this purpose, pure 2D plain strain Charpy impact model was designed. For simplicity, the striker was replaced by an acting point impact force. The stress and displacement contours for AISI 4140 specimen are shown in Fig.10.
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
Fig.10. (a) Von Mises stresses forAISI 4140 under the impact influence using 2D model (b) Corresponding displacement contours For the sake of comparison, the simulation results obtained from 2D and 3D analyses are summarized in Table 4. It was shown that 2D model was insufficient to predict accurate values of the impact energy as the percentage of error reached 50.8 % compared to the corresponding values generated from the actual test, whereas for 3D model it is only 6.7 %.This can be explained if we considered that the one point impact force acts as very high stress concentrator in the case of 2D model, while for 3D model, the impact force applied by the striker has certain impact surface areaand less generated stresses accordingly. 2D Model
3D Model Specimen Material: AISI 4140-T Steel 982.3 Stress in the Specimen (MPa) Displacement in the Specimen (mm)
1.502
Impact Absorbed Energy: 46.64 J Percentage Error: 6.6 %
Specimen Material: AISI 4140-T Steel Stress in the Specimen (MPa) Displacement in the Specimen (mm)
982 0.792
Impact Absorbed Energy: 24.6 J Percentage Error: 50.8 %
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME 4. CONCLUSIONS In this work, a 3-dimensional FE model of Charpy impact test was developed. The model was designed under the influence of the ASTM E 23standard and considered the effects of geometric, material and contact nonlinearities. The proposed model was implemented to investigate the absorbed energy required for fracture under the impact load ofAISI 4140 steeland aluminum specimens. The obtained results showed that the developed model was able to predict the absorbed energy accurately when appropriate mesh size was selected. In comparison with the absorbed energy values resulted from the practical Charpy test, it was found that the obtained FE results have minimal percentage of errors of 6.71 % and 6 % for steel and aluminum, respectively.Moreover, this study included wide variety of parametric studies which aimed to investigate the influences of notch depth and shape on the absorbed energy required for fracture. The obtained results showed that increasing the notch depth by 1.5 % of the standard dimension, may lead to decrease the absorbed energy of 10 %. This was found matching the ASTM E 23 section concerned with the uncertainty due to specimen dimension. The obtained 3D model in this study showed superiority over the 2D model approximation in term of the accuracy of the estimated absorbed energy. REFERENCES [1] [2]
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