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StructuralStructural IntegrityIntegrity Procedia100 (2016) 000–000 Procedia (2016) 066–073
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XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal
Finite element prediction of stress-strain fields on sandwich Finite element prediction of stress-strain fields on sandwich composites XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal composites a a R. Martins , L. Reisof , R. Marat-Mendesa,b,* Thermo-mechanical modeling a a a high pressure R. Martins , L. Reis , R. Marat-Mendesa,b,* turbine blade of an IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal airplane gas turbine engine Department of Mechanical Engineering, ESTSetúbal, Instituto Politécnico de Setúbal, Estefanilha, 2914-761 Setúbal, Portugal IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal a
b
a
Department of Mechanical Engineering, ESTSetúbal, Instituto Politécnico de Setúbal, Estefanilha, 2914-761 Setúbal, Portugal
b
P. Brandãoa, V. Infanteb, A.M. Deusc*
Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal fields of the sandwich core during bending tests. Finite The bmain objective of this study was the assessment of the stress-strain IDMEC, Department of Mechanical Superior Técnico,fields Universidade deused Lisboa, Av. 1, 1049-001 Lisboa, The main objective of this study was Engineering, the assessment of the stress-strain of the coreRovisco during bending tests. Finite element models (FEM) using Siemens NX10 andInstituto digital image correlation (DIC) weresandwich to predict the Pais, behavior of sandwich Portugal element (FEM) Siemens NX10 andcore digital image correlation (DIC) were used length to predict the behavior of sandwich beams inmodels 3 and 4 point using bending. TwoEngineering, different thickness and two different sandwich beams) with c CeFEMA, Department of Mechanical Instituto Superior Técnico, Universidade de Lisboa, Av. (short Roviscoand Pais,long 1, 1049-001 Lisboa, beams fiber in 3 reinforced and 4 pointpolymer bending. Two different core thicknessThe andnumerical two different sandwich length (shortelement and long beams) with basalt (BFRP) faces were simulated. simulation using 3D finite were compared Portugal basalt fiber reinforced polymer (BFRP) werepreviously simulated.byThe numerical simulation 3D finite element simulations were compared and validated with experimental results faces obtained DIC. This work validatedusing innovative numerical and and validated techniques with experimental results obtained previously bycomposite DIC. Thissandwich work validated and experimental for determining stress-strain fields in beams innovative subjected tonumerical bending. simulations The correlation experimental techniques for determining fields inand composite sandwich beams subjected to bending. correlation Abstract between experience and analysis allowed stress-strain a better knowledge understanding of the complex stress-strain fieldsThe along the core between experience and analysis allowed a better knowledge and understanding of the complex stress-strain fields along the core thickness of sandwich beams in bending. thickness sandwich beamsmodern in bending. During oftheir operation, aircraft engine components are subjected to increasingly demanding operating conditions, especially the high Published pressure turbine (HPT)B.V. blades. Such conditions cause these parts to undergo different types of time-dependent © 2016 The Authors. by Elsevier © 2016, PROSTRone (Procedia Structural Integrity) Hosting by Elsevier Ltd.element All rightsmethod reserved.(FEM) was developed, in order to be able to predict degradation, ofPublished which is creep. AScientific model the finite © 2016 The under Authors. by Elsevier B.V.using Peer-review responsibility of the Committee of PCF 2016. Peer-review under responsibility of the Scientific Committee of PCF 2016. the creep under behaviour of HPT of blades. Flight data recordsof(FDR) for a specific aircraft, provided by a commercial aviation Peer-review responsibility the Scientific Committee PCF 2016. company, were used toSandwich obtain thermal and mechanical data4PB for three different flight cycles. In order to create the 3D model Keywords: FEM, Composite beams, stress-strain fields, 3PB, needed FEM, for the FEM analysis, HPT stress-strain blade scrap was3PB, scanned, Keywords: Composite Sandwich abeams, fields, 4PB and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. overall Introduction expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a 1. Introduction model can be useful in the goal of predicting turbine blade life, given a set of FDR data.
Structural sandwich panels consist of three main structural components: two flat or lightly profiled thin faces are Structural sandwich panels consist ofThe three mainand structural components: two flat or lightly faces and are bonded relatively light strong stiff thin faces provide flexural load profiled bearing thin capacity © 2016toThe Authors. thick Published bycore. Elsevier B.V. bonded to relatively thick light core. The strong and stiff thin faces provide flexural load bearing capacity and Peer-review responsibility of the Scientific Committee PCF with 2016.adequate shear strength and stiffness transfers rigidity of theunder panel. The low density and flexible thickofcore rigidity of the panel. the Thetwo lowfaces. density flexible thick core structural with adequate shear strength and high stiffness transfers shear loads between Theand result is a composite element with relatively load-bearing Keywords: Pressure Turbine Method; 3D structural Model; Simulation. shear loads High between the two Blade; faces.Creep; The Finite resultElement is a composite element with relatively high load-bearing
* *
Corresponding author. Tel.: +351265790000; fax: +351265790043. Corresponding Tel.: +351265790000; fax: +351265790043. E-mail address:author.
[email protected] E-mail address:
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2452-3216 © 2016 The Authors. Published by Elsevier B.V. 2452-3216 © 2016 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby Scientific Committee of PCF 2016. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the Scientific Committee of PCF 2016. E-mail address:
[email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 © 2016, PROSTR (Procedia Structural Integrity) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of the Scientific Committee of PCF 2016. 10.1016/j.prostr.2016.02.010
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capacity and bending stiffness showed by Davies (2001). Different face and core materials can be used in sandwich structures depending the practical employment. Among the non-metallic materials the composites are the modest utilized ones, because of its high elasticity while improves weight-bending stiffness. One of these fascinating materials with extraordinary properties is the basalt fiber that is a novel kind of inorganic fiber manufactured from the extrusion of melted basalt rock and is commercially available. In this paper the stress–strain behavior of BFRP face materials in short and long sandwich beams under three- and four-point bending were compared and analyzed with FEM and DIC. Nomenclature 𝑣𝑣 𝜀𝜀𝑥𝑥𝑥𝑥
Displacement along y direction [mm] Strain along x direction
2. Experiment 2.1. Material Basalt fiber reinforced polymer (BFRP) composite was used on the sandwich structures as face materials. The core was induced with polyurethane plates with two different thicknesses: 20 mm and 30 mm, enabling a wider range of tests and results to be analyzed. The composite sandwiches with BFRP faces and polyurethane core were hand lay-up (HLU) with vacuum bag during 24hours with 850mPa of pressure and ambient temperature. Thus, four layers of 2x2 twill per side with layup [(0/90)/(45/-45)]4 of basalt fiber fabric BasaltexTM BAS 220.1270.T were cut into rectangular sections (430mm x 780mm) and added to polyurethane core with epoxy resin Sicomin SR1500 and SD2505 hardener. Afterwards specimens with 390mm x 70mm were cut with a diamond circular saw as by ASTM C393-00. The composite sandwiches with BFRP faces and polyurethane core were hand lay-up (HLU) with vacuum bag during 24hours with 850 mPa of pressure and ambient temperature. Thus, four layers of 2x2 twill per side with [(0/90)/(45/-45)]4 lay-up of basalt fiber fabric BasaltexTM BAS 220.1270.T were merged to polyurethane core with epoxy resin Sicomin SR1500 and SD2505 hardener to obtain rectangular plates (430 mm x 780 mm). Afterwards specimens with 390 mm x 70 mm were cut with a diamond circular saw as by ASTM C393-00. The main properties of the materials used in this work are presented in Table 1 and Table 2. Table 1. Material Properties
Resin SR1500 + SD2505 Basalt (twill) 220.1270.T Polyurethane
Composite BFRP
2.2. Testing
Density (kg⁄𝑚𝑚3 ) 1454
Density (𝑘𝑘𝑘𝑘⁄𝑚𝑚3 )
Poisson
1.0
0.26
2.8
0.35
40
0.33
𝜈𝜈12 = 𝜈𝜈13 0.31
Elastic modulus (𝐺𝐺𝐺𝐺𝐺𝐺) 3.2 78
Shear modulus (𝐺𝐺𝐺𝐺𝐺𝐺) -
16
3.2
0.13 𝑐𝑐 = 20 𝑐𝑐 = 30
−3
0.0106
𝐸𝐸33 (𝐺𝐺𝐺𝐺𝐺𝐺)
-
-
4 ∙ 10
Table 2. BFRP Properties 𝐸𝐸11 = 𝐸𝐸22 (𝐺𝐺𝐺𝐺𝐺𝐺)
Thickness (𝑚𝑚𝑚𝑚)
𝐺𝐺12 = 𝐺𝐺13 = 𝐺𝐺23 (𝐺𝐺𝐺𝐺𝐺𝐺) 2.7
Thickness
Fiber Volume Fraction (%)
𝑡𝑡 = 1
49
Three point bending (3PB) and four point bending (4PB) tests according to ASTM C 393-00 standard (Fig. 1) were applied to the prepared sandwiches to measure the flexural properties such as core shear stress, face-sheet compressive and tensile strains and deflections. All specimens were tested and load vs. displacement results were
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recorded using a Instron 3369 universal testing machine equipped with a 10 kN load cell with a crosshead displacement rate of 2 mm/min. Both situations: short- and long-beam conditions were tested as by ASTM C 393–00 and Teixeira de Freitas, S. (2012). In the 4PB test the short- and long-beam were induced with the application of a quarter and a third span length (Fig. 1b and Fig. 1c). This way, 90mm and 250mm span lengths were used in the 20 mm core thickness specimens and 136 mm and 340 mm span lengths were adopted in the 30 mm core thickness for mutually 3PB and 4PB tests.
a
b
c
Fig. 1. Scheme of applied loads: (a) 3PB (mid-span loading); (b) 4PB (quarter-point loading); (c) 4PB (third-point loading).
An encoding was created based on the assignment of characters “SB” (Sandwich with BFRP faces), followed by the numbers “20” or “30” (for the core thickness of 20 or 30mm) then the type of test ("3PB" or "4PB") and span length ("90mm", "136mm", "250mm" and "340mm"). 2.3. DIC measurement Digital image correlation (DIC) software using VIC2D system has been used in this work for assessment of strains and displacements of the numerical results obtained from finite element modeling (FEM). Prior to that the surfaces of the specimens were coated with thin layer of white acrylic paint. Using an airbrush, carbon black paint is sprayed over the white surfaces, creating random black and white artificial speckle pattern. The 2D DIC optical system consists of a CCD camera that captures images of an experimental test and by software that makes the correlation. The longitudinal section of the specimen between the supports was defined as an area of interest (AOI) and the values of 21 and 5 were assigned for the subset and for the step, respectively (which defining the partitions to be analyzed) (VIC 2D, 2009). In the end of the analysis, the program provides information about the displacements and strains in each direction, through a color gradient representing ranges of displacement or other selected variables, as well as a statistical treatment of the data in the interest zone previously selected, namely the maximum value observed. Sequences of images are collected as the displacement control progresses from 1, 2 and 3mm. The images collected during the experiments are then processed using VIC2D to estimate the displacement and strain fields. 3. Finite element strain calculation A three-dimensional solid FEM is developed using a commercial finite element code according to Siemens NX10 (2014). A typical finite element mesh of 3PB and 4PB sandwich specimens can be visualized in Fig. 2a) and Fig. 2b) respectively. The FEM was meshed with 8-node hexahedral solid-body elements CHEXA(8). The polyurethane core and the BFRP faces were modeled with 5 mm of element size in the width. It was adopted for the thickness and length directions an element size of 1 mm and 0.75 mm for the basalt faces and for the core respectively. Details of element sizes can be seen in Fig. 2a).
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b) Fig. 2. Finite element modeling of: a) 3PB; b) 4PB.
4. Results and discussion 4.1. Displacement results Fig. 3 and Fig. 4 illustrates typical 𝑣𝑣 displacement contour obtained with 3 mm of crosshead displacement control under 3PB and 4PB tests respectively. Both situations were analyzed: FEM and VIC for short- and longbeam. Qualitatively both of them compare well.
a)
b)
c)
d)
Fig. 3. 𝑣𝑣 displacement contour obtained under 3PB with 3mm of displacement control: a) FEM short beam; b) VIC2D short beam; c) FEM long beam; d) VIC2D long beam.
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a)
b)
c)
d)
5
Fig. 4. 𝑣𝑣 displacement contour obtained under 4PB with 3mm of displacement control: a) FEM short beam; b) VIC2D short beam; c) FEM long beam; d) VIC2D long beam.
From these analyses it is clear that the VIC2D and the FEM can capture the 𝑣𝑣 displacement properly, this can be proven by Fig. 5 where it is visible the comparison of displacement under 3PB test where in general the FEM presents 10 % higher displacement than VIC2D. 3.500�
Displacement�(mm)�
3.000� 2.500� 2.000�
FEM�
1.500�
VIC�
1.000� 0.500� 0.000�
4.2. Strain results
sb20_90�
sb20_250�
sb_30_136�
sb_30_340�
Fig. 5. Comparison of 𝑣𝑣 displacement obtained under 3PB with 3mm of displacement control.
Strain plot results obtained by FEM and VIC can be visualized in Fig. 6 and Fig. 7 for 3PB and 4PB respectively. In both tests short- and long-beam analyses are present. The pressure distribution under applied loads highlights with the red areas. Juntikka et al. (2007) showed that sandwich structures are in general sensitive to localized loads. An applied compressive load will cause the exposed face sheet to deform locally and, as the load increases, indentation will eventually occur induced by core compression failure, so the pressure distribution under the applied load depends on the bending stiffness of the face sheet. As the displacement plots, also strain plots qualitatively compare well.
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a)
c)
71
b)
d)
Fig. 6. 𝜀𝜀𝑥𝑥𝑥𝑥 displacement contour obtained under 3PB with 3mm of displacement control: a) FEM short beam; b) VIC2D short beam; c) FEM long beam; d) VIC2D long beam.
a)
b)
c)
d)
Fig. 7. 𝜀𝜀𝑥𝑥𝑥𝑥 displacement contour obtained under 4PB with 3mm of displacement control: (a) FEM short beam; (b) VIC2D short beam; (c) FEM long beam; (d) VIC2D long beam.
R. Martins et al. / Procedia Structural Integrity 1 (2016) 066–073 R. Marat-Mendes/ Structural Integrity Procedia 00 (2016) 000–000
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Fig. 8 and Fig. 9 present the 𝜀𝜀𝑥𝑥𝑥𝑥 distribution along the normalized mid-span length along the thickness of the specimens with 3mm of 𝑣𝑣 deformation under 3PB and 4PB tests respectively. Fig. 8a) and Fig. 9a) are related to short-beam and Fig. 8b) and Fig. 9b) to long-beam. In all the plots red lines corresponds to FEM and black lines to VIC2D. From these analyses it can be pointed out that the basalt sandwich is extremely locally deformable resulting in a redistribution of the stresses nearby the applied load region. This is the reason for the higher strains observed in the top face of the basalt sandwich specimens in the 3PB tests (Fig. 8). The short-beam under 4PB exhibits higher (negative) strains suggesting compression zones. 1�
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0.9�
0.9�
0.8�
0.8�
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0.6� SB_20_90_3PB_VIC�
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SB_30_136_3PB_VIC� SB_20_90_3PB_FEM�
0.4�
SB_30_136_3PB_FEM�
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SB_30_340_3PB_VIC� SB_20_250_3PB_FEM� SB_30_340_3PB_FEM�
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0�
0.002�
0.004�
xx�
0.006�
0.008�
0.01�
0.012�
0.014�
xx�
a)
b)
Fig. 8. Comparison of FEM and VIC 𝜀𝜀𝑥𝑥𝑥𝑥 along thickness at mid span length under 3PB with 3mm of displacement control: a) 3PB-short beam; b) 3PB-long beam. 1�
1�
0.9�
0.9�
0.8�
0.8�
-0.005�
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0.5�
-0.0015�
-0.001�
-0.0005�
0�
0�
0.0005�
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b)
Fig. 9. Comparison of FEM and VIC 𝜀𝜀𝑥𝑥𝑥𝑥 along thickness at mid span length under 4PB with 3mm of displacement control: a) 4PB-short beam; b) 4PB-long beam.
5. Conclusions 3PB and 4PB tests of sandwich panels have been performed with BFRP to estimate the behavior of short and long beams. The present study involved experimental investigation using digital image correlation and numerical simulation in order to obtain the displacement and strain fields of core materials when subjected to bending tests. The displacements obtained from FEM and VIC2D for the same set of input images have been compared and are found to be a close match with each other. The strain results showed that the polyurethane sandwiches with basalt faces are locally deformable by the constraints especially in the 3PB. Also short beams present higher compression strains due to the shear effects less prevalent in the longer ones.
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Acknowledgements This work was supported by FCT, through IDMEC, under LAETA, project UID/EMS/50022/2013. References ASTM C393-00., 2000. Standard Test Method for Flexural Properties of Sandwich Constructions. Annual Book of the ASTM Standards, American Society for Testing and Materials, PA, USA. Davies, J.M., 2014. Lightweight Sandwich Construction. Blackwell Science, Oxford. Juntikka, R., Hallstrom, S., 2007. Shear Characterization of Sandwich Core Materials Using Four-point Bending. Journal of Sandwich Structures and Materials, 9, 67. Siemens NX., 2014. Siemens NX version 10 user’s manual. Providence: Siemens Product Lifecycle Management Software Inc; 2014. Teixeira de Freitas, S., 2012. Steel plate reinforcement of orthotropic bridge decks. PhD Thesis, TU Delft, Delft University of Technology. VIC2D, 2009. VIC2D Reference Manual Correlated Solutions.
