ISSN-0125 1759 Vol. 17, No. 2. : 1pril i987 JOURNAL OF ___,, FERROCEMEN T International Ferracement lnfarmatian Center
JOURNAL OF FERROCEMENT
Mar 30, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
JOURNAL OF___,, FERROCEMENT
ISSN 0125 - 1759
Reviewed in: Applied Mechanics Re1•iew
EDITOR-IN-CHIEF Ricardo P. Pama Professor, Structural Engineering
and Const ruction Division Vice-President for Development AIT
Mr. D.J. Alexander
Professor A.R. Cusens
Mr. J . Fyson
Mr. M.E. lorns
Professor S.L. Lee
Professor A.E. Naaman
Professor J.P. Romualdi
Professor S.P. Shah
Professor B.R. Walkus
Mr. D.P. Barnard
Dr. G.L. Bowen
EDITORIAL BOARD
Regional Documentation Center AIT
Alexander and Associates. Consulting Engineering. Auckland , New Zealand. Head, Department of Civil Engineering, University of Leeds, Leeds LS2 9JT, England , U.K.
Fishery Industry Officer (Vessels). Fish Production and Marketing Service, UN-F AO, Rome. Italy .
Fcrrocement In ternational Co., 15 12 Lakewood Drive, West Sacramento, CA 9569 L. U.S.A.
Head, Department of Civil Engineering, National University of Singapore, Kent Ridge Campus, Singapore 5. Department of Civil Engineenng, The University of Michigan. 304 West Engineering Building, Ann Arbor, Ml 48109-1 092 U.S.A.
Professor of Civil Engineering. Carnegie-Mellon University, Pi11sburg, Pennsylvania, U.S.A.
Department of Civil Engineering, Northwestern University, Evans ton Illino is, 6020 I , U.S.A. Department of Civil Engineering, Technical University of Czcsto chowa Malchowskicgo 80. 90-159 Lodz, Poland.
CORRESPONDENTS
Director, New Zealand Concrete Research Association, Private Bag, Porirua. New Zealand.
P.O. Box 2311, Si tka. Alaska 99835, U.S.A.
Associate Professor, Faculty of Agricultural Engineering, Bangladesh Agricultural University, Mymensingh. Bangladesh.
737 Race Lane, R.F.D. No. 1, Marstons Mills, Mass. 02648, U.S.A.
Scientist, Structural Engineering Research Centre (SERC), Roorkee, U.P., India.
Surveyor, Ship Division, Newbuilding, Department for Hull , Oct Norske Veritas, P.O. Box 300, N- 1322 Hovik, Oslo, Norway.
Chief Executive, Dr. BVS Consultants, 76 Third Cross Street Raghava Reddy Colony, Madras 600 095 India. Managing Director. Safety Sealers (Eastern) Ltd. P.O. Box No. 8048 Karachi - 29 Pakistan.
CONTENTS
ABOUTIFIC
EDITORIAL
PAPERS ON RESEARCH AND DEVELOPMENT
11
l1l
Finite Element Analysis of Steel Fibre Reinforced Cement Composites I 07 P. Paramasivam
Prediction of Spacing and Maximum Width of Cracks in Ferrocement Built-Up I-Joists 117 P. Desayi and N. Ganesan
PAPERS ON APPLICATIONS AND TECHNIQUES
Alternative Methods of Construction D. Scott
Pit Latrine L. H. Belz
TIPS FOR AMATEUR BUILDERS
Stern Tubes for Ferrocement Hull A. Lucas and P. Finch
Bibliographic List
Advertisements
131
141
149
153
211 212
Discussion of the technical material published in this issue is open until July I, 1987 for publication in the Journal. The Editor and the Publishers are not responsible for any statement made or any opinion expressed by the authors in the Journal. No part of this publication may be reproduced in any form without permission from the publisher. All corres pondences related to manuscript submission, discussions, permission to reprint, advertising, subscriptions or change of address should be sent to : The Editor, Journal of Ferrocement, IFIC/AIT, G.P.O. Box 2754, Bangkok 10501, Thailand.
The International Ferrocement Information Center (IFIC) was founded in October 1976 at the Asian Institute of Technology under the joint sponsorship of the Institute's Division of Structural Engineering and Construction and the Library and Regional Documentation Center. IFIC was established as a result of the recommendations made in 1972 by the U.S. National Academy of Sciences' Advisory Committee on Technological Innovation (ACT!). IFIC receives financial support from the Government of Australia, Canadian International Develop ment Agency (CIDA), Government of France, Government of New Zealand, and the Interna tional Development Research Center (IDRC) of Canada.
Basically, IFIC serves as a clearing house for information on ferrocement and related materials. In cooperation with national societies, universities, libraries, information centers, government agencies, research organizations, engineering and consulting firms all over the world, IFIC attempts to collect information on all forms of ferrocement applications either published or unpublished. This information is identified and sorted before it is repackaged and disseminated as widely as possible through IFIC's publications, reference and reprographic services and technology transfer activities. All information collected by IFIC are entered into a computerized data base using ISIS system. These information are available on request. In addition, IFIC offers referral services.
A quarterly publication, the Journal of Ferrocement, is the main disseminating tool of IFIC. IFIC has also published the monograph Ferrocement, Do It Yourself Booklets, Slide Presentation Series, State-of-the-Art Reviews, bibliographies and reports. FOCUS, the information brochure of IFIC, is published in 16 languages as part of IFIC's attempt to reach out to the rural areas of the developing countries. IFIC is compiling a directory of consultants and ferrocement experts. The first volume, International Directory of Ferrocement Organizations and Experts 1982-1984, is now available.
To transfer ferrocement technology to the rural areas of developing countries; IFIC organizes training programs, seminars, study-tours, conferences and symposia. For these activities, IFIC acts as an initiator; identifying needs, soliciting funding, identifying experts, and bringing people together. So far, IFIC has successfully undertaken training programs for Indonesia and Malaysia; a regional symposium and training course in India; a seminar to introduce ferrocement 'in Malaysia; another seminar to introduce ferrocement to Africans; study-tour in Thailand and Indonesia for African officials; the Second International Sympo sium on Ferrocement and a Short Course on Design and Construction of Ferrocement
'Structures. Currently, IFIC is involved in establishing the National Research and Trai'ning Center in Malaysia, National Centre of Ferrocement at the University of Roorkee in India and a Ferrocement Information Network in Asia and Africa. IFIC is now organizing the Ferrocement Corrosion : .An International Correspondence Symposium.
ii
The need to develop technological capacity rapidly in developing countries in consonance with domestic resources and requirements .is essential. Technology which can be easily adapted to local conditions using traditional skills must be identified. Moreover proper adaption, requires technology assessment and evaluation in the light of national capabilities and possible adveFse social and cultural effects.
Ferrocement was adapted to improve the traditional pit latrine in Tonga. An evaluation after four years confirmed the forcast made when selecting the technology-improved environ mental conditions, health attitudes and sanitary practices. This is reported in the paper of L.H. Belz. In the context of labor intensive technology, its adaption in developing countries is not always as simple as expected. D. Scott in his paper "Alternative methods of Construction discussed some of the problems. He asserts that engineers to be able to make a rational choice about the best construction method to be used, has to overcome lack of experience in the method of construction, time constraint to try new techniques and inadequacy of management information on the method.
Researchers and scientists play a central role in technology development. They are essential to improve and adapt the technology to local resources and needs. The papers, "Prediction of spacing and maximum width of cracks in ferrocement built-up I-joints" and "Finite element analysis of steel fibre reinforced cement composites", are results of research undertaken to improve existing technologies. It is important that developing countries developed their technological manpower.
The Editor
Journal of Ferrocement: Vol. 17, No. 2, April 1987 107
Finite Element Analysis of Steel Fibre Reinforced/ Cement Composites*
P. Paramasivam t
A three dimensional finite element analysis based on micromechanics approach has been employed to determine the linear and nonlinear behaviour of steel fibre reinforced cement compo sites under uniaxial loading. Nine numerical models of the composites are presented by varying the parameters such as volume fraction, aspect ratio and geometric arrangement of the fibres. The results obtained from the finite element analysis are compared with the experimental results and discussed.
INTRODUCTION
lt has been well established that fibre reinforced cement composites provide better crack arrest mechanism, increased cracking strength, toughness, improved resistance to thermal shock and higher fatigue strength [1,2]. Prediction of the mechanical properties and micromechanical understanding of this material can be very useful in the design and selection of a composite material for any particular application. Extensive experimental and theoretical investigations have been carried out by many researchers [3-5] to predict the -mechanical properties of cement composites with continuous and discontinuous (short) fibres, in terms of the mechanical and geometrical properties of the constituent materials using the law of mixtures and spacing concepts. These concepts can predict only the first crack and ultimate strength of the com posites, but it is extremely difficult to predict the composite behaviour after the elastic limit and also the interaction between the constituent materials. Therefore finite element analysis has been employed to study the linear and nonlinear behaviour of steel fibre com posites under uniaxial loading.
The finite element method is a powerful numerical tool for composite micromechanics analysis. It has been extensively used to determine the behaviour of ductile matrix-fibre composites with fibre volume content of 20 %-80 % such as polymer or resin-based composites [6, 7]. Most of these analyses were based on axisymmetric and plane strain models. A fully three-dimensional finite element analysis was used by Curiskis [8, 9] to study the microme chanics behaviour of unidirectional ductile-matrix composites with fibre volume of 20 %-80 % and aspect ratio of approximately 10-20. Later this method was extended to brittle-matrix composites, such as cement paste reinforced with steel fibres, under uniaxial loading by Paramasivam et al. [IO]. In their investigation, validity of the technique for low volume fraction of fibres with aspect ratio upto 53 was examined and the numerical results were compared with limited experimental results for only two volume fractions with one aspect ratio of the fibre. In this investigation, fibre composites with different parameters such as volume fraction, aspect ratio and geometric arrangements have been considered and numerical results are compared with experimental results and discussed.
"' Reprinted with permission of the publisher. Published in Structural Engineering and Construction, Advances and Practice in East Asia and the Pacific Vol. 1, Proceedings of the First East Asian Conference on Structural Engineering and Construction.
t Associate Professor, Department of Civil Engineering, National University of Singapore, Singapore.
- I
108 Journal of Ferrocement: Vol. 17, No. 2, April 1987
FINITE ELEMENT METHOD
The finite element programs entitled "SPLIT l" and "SPLIT 2" which were developed by Valliappan and Curiskis [8] have been employed in this study. The constituent materials of the composite (fibre and composite) are represented by 20-node isoparametric elements. The advantage of this concept is that it achieves the analysis efficiently by allowing an arbitary discretization of the elements of different materials, even, with curved boundaries. The con stituents are assumed to be isotropic and a perfect bond is assumed at the interface between the fibre and the matrix:. The elastic-plastic behaviour of the constituents are considered for non linear analysis. The plasticity analysis is based on Von Mises yield criterion with the associated flow rule. The initial stress method [I I, I2] has been used in the iterative technique for the elastic-plastic analysis.
COMPOSITE ANALYSIS
In the real problem of steel fibre reinforced cement composites, the fibres are randomly oriented three dimensionally as shown in Fig. 1 (a). Generally, the mechanical properties of such composites are determined by idealising the fibres in the unidirection using the various expressions for orientation factors [4]. In the present study, the discrete short fibres are arranged in a regular three dimensional triply-periodic array geometry using the orientation · factor. The geometric idealization of the composite is shown in Fig. 1. The fibres are assumed to be identical cylinders with constant length, cross section and geometry with perfect square
(a) Real problem
0 0 0
0 I I 0 :::::::Jlc:::::::::J: C z L ___ J L.-----_J
~x o o ::::i c:::::::::J c=
( b) Row- column arrangement
section
::::J i : c= c:::EJ- - E:::J
:::J c:::::::::J c:::= Longitudinal
Journal of Ferrocement: Vol. 17, No. 2, April 1987 109
packing in the transverse plane. In the longitudinal direction, the fibres are considered either in row and column or staggered arrangement as shown in Figs. 1 (b) and l(c) respectively. The staggered arrangement is probably more like an actual unidirectional composi_te. Because of symmetry, a typical repeating unit such as that indicated by the dashed lines in Fig. l, can be isolated for detailed micromechanics analysis using three dimensional finite element method. The main aspects and details of constraint formulation of the boundary conditions of the finite element formulation are presented in reference (8, 10, 13].
NUMERICAL EXAMPLES
The finite element programmes were used to analyse the mechanical properties of nine different cases of steel fibre reinforced composites as shown in Table I. The first four cases were adopted to investigate the effect of fibre volume fraction on characteristic properties of the
. composites by keeping the aspect ratio (L1/D) constant at 53.6. The next three cases were used by varying the aspect ratio with constant volume fraction of 4 % and the last two cases were used to investigate the effect of geometric arrangements on properties of the com posites. The material properties used in these examples are the same as obtained by Nathan et al. [3] from their experimental investigation and are given in Table 2.
Table 1 Geometric Parameters for Numerical Models.
No. V1(%) L1/D L1 (mm) L2 (mm) a (mm) Model
1 5 53.6 30 4.0 1.43 row-column 2 4 53.6 30 4.0 1.61 row-column 3 3 53.6 30 4.0 1.85 row-column 4 2 53.6 30 4.0 2.77 row-column 5 4 35.7 20 2.67 1.61 row-column 6 4 53.6 30 4.0 1.61 row-column 7 4 71.4 40 5.33 1.61 row-column 8 2 53.6 30 4.0 4.54 staggered 9 3 53.6 30 4.0 3.70 staggered
Table 2 Properties of Constituent Materials (from Ref. 4).
Cement paste Steel fibre
Modulus of elasticity (N/mm2) 1.59 x IQ4 19.65 x 104
Poisson's ratio 0.2 0.4 Ultimate tensile strength (N/mm2) 1.45 374
Crushing strength (N/mm2) 36.16
For the finite element modelling, only one-eighth of the cross section and one quarter of the longitudinal section have been considered. The orientation factor of 0.47 proposed by Nathan et al. [3] is used in for unidirectional idealisation. The finite element divisions of row column and staggered arrangements are shown in Fig. 2. The geometric parameters relevant
110 Journal of Ferrocement: Vol. 17, No. 2, April 1987
arrangement
Symmetry
(b) Staggered arrangement
Fig. 2. Finite element idealisation.
to all the cases are shown in Table I. The mesh with 81 elements associated with 437 nodal points has been employed for the finite element analysis. The composite properties of elastic modulus and Poisson's ratio are tabulated in Tables 3 and 4 for the different volume fraction with constant aspect ratio of 53.6 and for different aspect ratios with constant volume fraction of 4 % respectively. It can be seen that modulus of elasticity of composites are higher for a larger volume fraction and smaller aspect ratio of fibres. The modulus of elasticity for the staggered arrangement is slightly higher than the row-column arrangement. The values of Poisson's ratio are not affected.
Table 3 Composite Properties for Different Volume Fractions and Geometric Arrangements.
Modulus of elasticity Poisson's ratio
V1(%) Lif D (N/mm2)
Row-columm Staggered Row-column Staggered
2 53.6 17502 17896 2.013 2.013 3 53.6 18260 18362 2.019 2.019 4 53.6 18983 2.025 5 53.6 19809 2.030
__ J
v; 4 4 4
L1/D
19 114 2.024 18 983 2.025 18 897 2.024
c
Section DD Section AA Sec.tion BB
Fig. 3. Stress contours-row and column arrangement (VJ = 4%, L 1/D = 53.6).
Section cc Section DD Section AA Section BB
Fig.4. Stresscontours-rowandcolumnarrangement(VJ = 4%,Li/D = 35.7).
111
112 Journal of Ferrocement: Vol. 17, No. 2, April 1987
Typical contours of longitudinal stress in the composite are shown in Figs. 3 and 4 for the longitudinal section as well as the cross section in the case of row-column arrange111ent with V1 =4 % for aspect ratios of 53.6 and 35.7 respectively. The stresses shown have been obtained for an applied stress of unity. The stress contours plotted for the cross sections in Figs 3 and 4 shows the existence of triaxial stress state. It can be seen from the longitudinal section along sections A-A and B-B as shown in Figs. 3 and 4 that stress concentration exists near the fibre end as expected and the stress distribution away from the fibre end is almost uniform and the value is close to the applied load. A comparison of stress values between the row-column and staggered arrangement for the same value of volume fraction and aspect ratio as shown in Figs. 5(a) and 5(b) indicates that the stress concentration in the row-column case is higher than that for the staggered arrangement.
1.0 1.05 1.07 1.21.4 1.6 1.9
(a) Stoggered arrangement
( b) Row - column orrangement
Fig. 5. Stress contours for different geometric arrangement (VJ = 3 %, L 1/ D = 53.6).
The linear and nonlinear behaviour of fibre composites of the nine cases were carried out. The predicted stress-strain curves for the composites with various volume fractions and aspect ratios of the fibres, are plotted in Figs. 6(a) ·to 6(f). These results are compared with experimental values obtained by Nathan et al. [3]. A comparison between the composite properties obtained from the finite element micromechanics analysis and those from the ex perimental investigation of Nathan et al. [3] is given in Tables 5 and 6 for different volume fractions with an aspect ratio of 53.6 and different aspect ratios with a volume fraction of 4 % respectively. It can be seen from the Tables 5 and 6, and Fig. 6 that the numerical results compare favourably with the experimental results. The composites with staggered arrange ment give slightly closer value to the experimental values compared to the row-column ar rangement.
Journal of Ferrocement: Vol. 17, No. 2, April 1987
0 ...---.,...~~~~~~~~~~~ 0
'° '° .n NE g
E..,: "" 0 zo ~..,: ,,, "'o GIN !: l'i ,,, J! ~ ·u;N oo c. '° E-' 8g
ci 0
Steel fibre
"'o QJ q; ;!:N ,,, oO c. U! E oo (.) Cl)
ci 0
Steel fibre
0.16 o.32 0.48 o.64 0.80 o:96 -3
Composite strain x 10
Composite strain x I0- 3
(a) Vt = 2 °/o L1/o = 53.6 (b) Vt= 3 % L1/o: 53.6
0 (g
<t ,,, ,,, 0 QJ N .:: rti ,,, 0
QJ <i: ..., N
0
.... r<l ,,, 0 QJ <t :!:N ,,, 0
g_~ E- 8g
Composite strain x 10- 3
(c) Vf=4% L1/0=53.6
Steel fibre
0 CD
J! ~ ,,, 0 0 U) c....: E oO (.) Cl!
0
0 ~ U)
(d) Vt= 5 °io L1/o = 53.6
~ o Steel fibre ~E ~ ~ g -Numerical z..t
::l ~ QJ r<l ....
0 0
Composite strain x I0- 3
( f ) Vt = 4 % LI /o = 71. 4
Fig. 6. Comparison of numerical and experimental stress-strain curves of the composites.
113
114 Journal of Ferrocement: Vol. 17, No. 2, April 1987
Table 5 Comparison Between Numerical and Experimental Values of First Crack and Ultimate Strength for Different Volume Fractions with L1/D = 53.6.
Stress at first crack (N/mm2) Ultimate stress (N/mm2)
V1(%) Numerical values Experimental Numerical values Experimental
Row-column Staggered results Row-column Staggered results
2 1.60 1.59 1.58 2.05 1.84 1.79 3 1.68 1.76 1.84 2.79 2.72 2.61 4 1.72 2.07 2.98 3.85
5 1.90 2.23 4.94 5.25
Table 6 Comparison between Numerical and Experimental Values of First Crack and Ultimate Strength for Different Aspect Ratios with V1 = 4 %.
L,/D Stress at first crack (N/mm2) ·Ultimate stress (N/mm2)
Numerical Experimental Numerical Experimental
35.7 1.70 1.85 2.39 2.49 53.7 1.72 2.07 2.98 3.85
71.4 1.80 2.17 4.72 4.55
A typical variation of the longitudinal stress near the fibre axis for the composite with V1 = 4 % and different aspect ratios of 53.6 and 35.7 is shown in Figs. 7(a) and 7(b) respec tively. Two curves corresponding to axial stress before yielding (cry = 1.0) and after yielding (…
ISSN 0125 - 1759
Reviewed in: Applied Mechanics Re1•iew
EDITOR-IN-CHIEF Ricardo P. Pama Professor, Structural Engineering
and Const ruction Division Vice-President for Development AIT
Mr. D.J. Alexander
Professor A.R. Cusens
Mr. J . Fyson
Mr. M.E. lorns
Professor S.L. Lee
Professor A.E. Naaman
Professor J.P. Romualdi
Professor S.P. Shah
Professor B.R. Walkus
Mr. D.P. Barnard
Dr. G.L. Bowen
EDITORIAL BOARD
Regional Documentation Center AIT
Alexander and Associates. Consulting Engineering. Auckland , New Zealand. Head, Department of Civil Engineering, University of Leeds, Leeds LS2 9JT, England , U.K.
Fishery Industry Officer (Vessels). Fish Production and Marketing Service, UN-F AO, Rome. Italy .
Fcrrocement In ternational Co., 15 12 Lakewood Drive, West Sacramento, CA 9569 L. U.S.A.
Head, Department of Civil Engineering, National University of Singapore, Kent Ridge Campus, Singapore 5. Department of Civil Engineenng, The University of Michigan. 304 West Engineering Building, Ann Arbor, Ml 48109-1 092 U.S.A.
Professor of Civil Engineering. Carnegie-Mellon University, Pi11sburg, Pennsylvania, U.S.A.
Department of Civil Engineering, Northwestern University, Evans ton Illino is, 6020 I , U.S.A. Department of Civil Engineering, Technical University of Czcsto chowa Malchowskicgo 80. 90-159 Lodz, Poland.
CORRESPONDENTS
Director, New Zealand Concrete Research Association, Private Bag, Porirua. New Zealand.
P.O. Box 2311, Si tka. Alaska 99835, U.S.A.
Associate Professor, Faculty of Agricultural Engineering, Bangladesh Agricultural University, Mymensingh. Bangladesh.
737 Race Lane, R.F.D. No. 1, Marstons Mills, Mass. 02648, U.S.A.
Scientist, Structural Engineering Research Centre (SERC), Roorkee, U.P., India.
Surveyor, Ship Division, Newbuilding, Department for Hull , Oct Norske Veritas, P.O. Box 300, N- 1322 Hovik, Oslo, Norway.
Chief Executive, Dr. BVS Consultants, 76 Third Cross Street Raghava Reddy Colony, Madras 600 095 India. Managing Director. Safety Sealers (Eastern) Ltd. P.O. Box No. 8048 Karachi - 29 Pakistan.
CONTENTS
ABOUTIFIC
EDITORIAL
PAPERS ON RESEARCH AND DEVELOPMENT
11
l1l
Finite Element Analysis of Steel Fibre Reinforced Cement Composites I 07 P. Paramasivam
Prediction of Spacing and Maximum Width of Cracks in Ferrocement Built-Up I-Joists 117 P. Desayi and N. Ganesan
PAPERS ON APPLICATIONS AND TECHNIQUES
Alternative Methods of Construction D. Scott
Pit Latrine L. H. Belz
TIPS FOR AMATEUR BUILDERS
Stern Tubes for Ferrocement Hull A. Lucas and P. Finch
Bibliographic List
Advertisements
131
141
149
153
211 212
Discussion of the technical material published in this issue is open until July I, 1987 for publication in the Journal. The Editor and the Publishers are not responsible for any statement made or any opinion expressed by the authors in the Journal. No part of this publication may be reproduced in any form without permission from the publisher. All corres pondences related to manuscript submission, discussions, permission to reprint, advertising, subscriptions or change of address should be sent to : The Editor, Journal of Ferrocement, IFIC/AIT, G.P.O. Box 2754, Bangkok 10501, Thailand.
The International Ferrocement Information Center (IFIC) was founded in October 1976 at the Asian Institute of Technology under the joint sponsorship of the Institute's Division of Structural Engineering and Construction and the Library and Regional Documentation Center. IFIC was established as a result of the recommendations made in 1972 by the U.S. National Academy of Sciences' Advisory Committee on Technological Innovation (ACT!). IFIC receives financial support from the Government of Australia, Canadian International Develop ment Agency (CIDA), Government of France, Government of New Zealand, and the Interna tional Development Research Center (IDRC) of Canada.
Basically, IFIC serves as a clearing house for information on ferrocement and related materials. In cooperation with national societies, universities, libraries, information centers, government agencies, research organizations, engineering and consulting firms all over the world, IFIC attempts to collect information on all forms of ferrocement applications either published or unpublished. This information is identified and sorted before it is repackaged and disseminated as widely as possible through IFIC's publications, reference and reprographic services and technology transfer activities. All information collected by IFIC are entered into a computerized data base using ISIS system. These information are available on request. In addition, IFIC offers referral services.
A quarterly publication, the Journal of Ferrocement, is the main disseminating tool of IFIC. IFIC has also published the monograph Ferrocement, Do It Yourself Booklets, Slide Presentation Series, State-of-the-Art Reviews, bibliographies and reports. FOCUS, the information brochure of IFIC, is published in 16 languages as part of IFIC's attempt to reach out to the rural areas of the developing countries. IFIC is compiling a directory of consultants and ferrocement experts. The first volume, International Directory of Ferrocement Organizations and Experts 1982-1984, is now available.
To transfer ferrocement technology to the rural areas of developing countries; IFIC organizes training programs, seminars, study-tours, conferences and symposia. For these activities, IFIC acts as an initiator; identifying needs, soliciting funding, identifying experts, and bringing people together. So far, IFIC has successfully undertaken training programs for Indonesia and Malaysia; a regional symposium and training course in India; a seminar to introduce ferrocement 'in Malaysia; another seminar to introduce ferrocement to Africans; study-tour in Thailand and Indonesia for African officials; the Second International Sympo sium on Ferrocement and a Short Course on Design and Construction of Ferrocement
'Structures. Currently, IFIC is involved in establishing the National Research and Trai'ning Center in Malaysia, National Centre of Ferrocement at the University of Roorkee in India and a Ferrocement Information Network in Asia and Africa. IFIC is now organizing the Ferrocement Corrosion : .An International Correspondence Symposium.
ii
The need to develop technological capacity rapidly in developing countries in consonance with domestic resources and requirements .is essential. Technology which can be easily adapted to local conditions using traditional skills must be identified. Moreover proper adaption, requires technology assessment and evaluation in the light of national capabilities and possible adveFse social and cultural effects.
Ferrocement was adapted to improve the traditional pit latrine in Tonga. An evaluation after four years confirmed the forcast made when selecting the technology-improved environ mental conditions, health attitudes and sanitary practices. This is reported in the paper of L.H. Belz. In the context of labor intensive technology, its adaption in developing countries is not always as simple as expected. D. Scott in his paper "Alternative methods of Construction discussed some of the problems. He asserts that engineers to be able to make a rational choice about the best construction method to be used, has to overcome lack of experience in the method of construction, time constraint to try new techniques and inadequacy of management information on the method.
Researchers and scientists play a central role in technology development. They are essential to improve and adapt the technology to local resources and needs. The papers, "Prediction of spacing and maximum width of cracks in ferrocement built-up I-joints" and "Finite element analysis of steel fibre reinforced cement composites", are results of research undertaken to improve existing technologies. It is important that developing countries developed their technological manpower.
The Editor
Journal of Ferrocement: Vol. 17, No. 2, April 1987 107
Finite Element Analysis of Steel Fibre Reinforced/ Cement Composites*
P. Paramasivam t
A three dimensional finite element analysis based on micromechanics approach has been employed to determine the linear and nonlinear behaviour of steel fibre reinforced cement compo sites under uniaxial loading. Nine numerical models of the composites are presented by varying the parameters such as volume fraction, aspect ratio and geometric arrangement of the fibres. The results obtained from the finite element analysis are compared with the experimental results and discussed.
INTRODUCTION
lt has been well established that fibre reinforced cement composites provide better crack arrest mechanism, increased cracking strength, toughness, improved resistance to thermal shock and higher fatigue strength [1,2]. Prediction of the mechanical properties and micromechanical understanding of this material can be very useful in the design and selection of a composite material for any particular application. Extensive experimental and theoretical investigations have been carried out by many researchers [3-5] to predict the -mechanical properties of cement composites with continuous and discontinuous (short) fibres, in terms of the mechanical and geometrical properties of the constituent materials using the law of mixtures and spacing concepts. These concepts can predict only the first crack and ultimate strength of the com posites, but it is extremely difficult to predict the composite behaviour after the elastic limit and also the interaction between the constituent materials. Therefore finite element analysis has been employed to study the linear and nonlinear behaviour of steel fibre com posites under uniaxial loading.
The finite element method is a powerful numerical tool for composite micromechanics analysis. It has been extensively used to determine the behaviour of ductile matrix-fibre composites with fibre volume content of 20 %-80 % such as polymer or resin-based composites [6, 7]. Most of these analyses were based on axisymmetric and plane strain models. A fully three-dimensional finite element analysis was used by Curiskis [8, 9] to study the microme chanics behaviour of unidirectional ductile-matrix composites with fibre volume of 20 %-80 % and aspect ratio of approximately 10-20. Later this method was extended to brittle-matrix composites, such as cement paste reinforced with steel fibres, under uniaxial loading by Paramasivam et al. [IO]. In their investigation, validity of the technique for low volume fraction of fibres with aspect ratio upto 53 was examined and the numerical results were compared with limited experimental results for only two volume fractions with one aspect ratio of the fibre. In this investigation, fibre composites with different parameters such as volume fraction, aspect ratio and geometric arrangements have been considered and numerical results are compared with experimental results and discussed.
"' Reprinted with permission of the publisher. Published in Structural Engineering and Construction, Advances and Practice in East Asia and the Pacific Vol. 1, Proceedings of the First East Asian Conference on Structural Engineering and Construction.
t Associate Professor, Department of Civil Engineering, National University of Singapore, Singapore.
- I
108 Journal of Ferrocement: Vol. 17, No. 2, April 1987
FINITE ELEMENT METHOD
The finite element programs entitled "SPLIT l" and "SPLIT 2" which were developed by Valliappan and Curiskis [8] have been employed in this study. The constituent materials of the composite (fibre and composite) are represented by 20-node isoparametric elements. The advantage of this concept is that it achieves the analysis efficiently by allowing an arbitary discretization of the elements of different materials, even, with curved boundaries. The con stituents are assumed to be isotropic and a perfect bond is assumed at the interface between the fibre and the matrix:. The elastic-plastic behaviour of the constituents are considered for non linear analysis. The plasticity analysis is based on Von Mises yield criterion with the associated flow rule. The initial stress method [I I, I2] has been used in the iterative technique for the elastic-plastic analysis.
COMPOSITE ANALYSIS
In the real problem of steel fibre reinforced cement composites, the fibres are randomly oriented three dimensionally as shown in Fig. 1 (a). Generally, the mechanical properties of such composites are determined by idealising the fibres in the unidirection using the various expressions for orientation factors [4]. In the present study, the discrete short fibres are arranged in a regular three dimensional triply-periodic array geometry using the orientation · factor. The geometric idealization of the composite is shown in Fig. 1. The fibres are assumed to be identical cylinders with constant length, cross section and geometry with perfect square
(a) Real problem
0 0 0
0 I I 0 :::::::Jlc:::::::::J: C z L ___ J L.-----_J
~x o o ::::i c:::::::::J c=
( b) Row- column arrangement
section
::::J i : c= c:::EJ- - E:::J
:::J c:::::::::J c:::= Longitudinal
Journal of Ferrocement: Vol. 17, No. 2, April 1987 109
packing in the transverse plane. In the longitudinal direction, the fibres are considered either in row and column or staggered arrangement as shown in Figs. 1 (b) and l(c) respectively. The staggered arrangement is probably more like an actual unidirectional composi_te. Because of symmetry, a typical repeating unit such as that indicated by the dashed lines in Fig. l, can be isolated for detailed micromechanics analysis using three dimensional finite element method. The main aspects and details of constraint formulation of the boundary conditions of the finite element formulation are presented in reference (8, 10, 13].
NUMERICAL EXAMPLES
The finite element programmes were used to analyse the mechanical properties of nine different cases of steel fibre reinforced composites as shown in Table I. The first four cases were adopted to investigate the effect of fibre volume fraction on characteristic properties of the
. composites by keeping the aspect ratio (L1/D) constant at 53.6. The next three cases were used by varying the aspect ratio with constant volume fraction of 4 % and the last two cases were used to investigate the effect of geometric arrangements on properties of the com posites. The material properties used in these examples are the same as obtained by Nathan et al. [3] from their experimental investigation and are given in Table 2.
Table 1 Geometric Parameters for Numerical Models.
No. V1(%) L1/D L1 (mm) L2 (mm) a (mm) Model
1 5 53.6 30 4.0 1.43 row-column 2 4 53.6 30 4.0 1.61 row-column 3 3 53.6 30 4.0 1.85 row-column 4 2 53.6 30 4.0 2.77 row-column 5 4 35.7 20 2.67 1.61 row-column 6 4 53.6 30 4.0 1.61 row-column 7 4 71.4 40 5.33 1.61 row-column 8 2 53.6 30 4.0 4.54 staggered 9 3 53.6 30 4.0 3.70 staggered
Table 2 Properties of Constituent Materials (from Ref. 4).
Cement paste Steel fibre
Modulus of elasticity (N/mm2) 1.59 x IQ4 19.65 x 104
Poisson's ratio 0.2 0.4 Ultimate tensile strength (N/mm2) 1.45 374
Crushing strength (N/mm2) 36.16
For the finite element modelling, only one-eighth of the cross section and one quarter of the longitudinal section have been considered. The orientation factor of 0.47 proposed by Nathan et al. [3] is used in for unidirectional idealisation. The finite element divisions of row column and staggered arrangements are shown in Fig. 2. The geometric parameters relevant
110 Journal of Ferrocement: Vol. 17, No. 2, April 1987
arrangement
Symmetry
(b) Staggered arrangement
Fig. 2. Finite element idealisation.
to all the cases are shown in Table I. The mesh with 81 elements associated with 437 nodal points has been employed for the finite element analysis. The composite properties of elastic modulus and Poisson's ratio are tabulated in Tables 3 and 4 for the different volume fraction with constant aspect ratio of 53.6 and for different aspect ratios with constant volume fraction of 4 % respectively. It can be seen that modulus of elasticity of composites are higher for a larger volume fraction and smaller aspect ratio of fibres. The modulus of elasticity for the staggered arrangement is slightly higher than the row-column arrangement. The values of Poisson's ratio are not affected.
Table 3 Composite Properties for Different Volume Fractions and Geometric Arrangements.
Modulus of elasticity Poisson's ratio
V1(%) Lif D (N/mm2)
Row-columm Staggered Row-column Staggered
2 53.6 17502 17896 2.013 2.013 3 53.6 18260 18362 2.019 2.019 4 53.6 18983 2.025 5 53.6 19809 2.030
__ J
v; 4 4 4
L1/D
19 114 2.024 18 983 2.025 18 897 2.024
c
Section DD Section AA Sec.tion BB
Fig. 3. Stress contours-row and column arrangement (VJ = 4%, L 1/D = 53.6).
Section cc Section DD Section AA Section BB
Fig.4. Stresscontours-rowandcolumnarrangement(VJ = 4%,Li/D = 35.7).
111
112 Journal of Ferrocement: Vol. 17, No. 2, April 1987
Typical contours of longitudinal stress in the composite are shown in Figs. 3 and 4 for the longitudinal section as well as the cross section in the case of row-column arrange111ent with V1 =4 % for aspect ratios of 53.6 and 35.7 respectively. The stresses shown have been obtained for an applied stress of unity. The stress contours plotted for the cross sections in Figs 3 and 4 shows the existence of triaxial stress state. It can be seen from the longitudinal section along sections A-A and B-B as shown in Figs. 3 and 4 that stress concentration exists near the fibre end as expected and the stress distribution away from the fibre end is almost uniform and the value is close to the applied load. A comparison of stress values between the row-column and staggered arrangement for the same value of volume fraction and aspect ratio as shown in Figs. 5(a) and 5(b) indicates that the stress concentration in the row-column case is higher than that for the staggered arrangement.
1.0 1.05 1.07 1.21.4 1.6 1.9
(a) Stoggered arrangement
( b) Row - column orrangement
Fig. 5. Stress contours for different geometric arrangement (VJ = 3 %, L 1/ D = 53.6).
The linear and nonlinear behaviour of fibre composites of the nine cases were carried out. The predicted stress-strain curves for the composites with various volume fractions and aspect ratios of the fibres, are plotted in Figs. 6(a) ·to 6(f). These results are compared with experimental values obtained by Nathan et al. [3]. A comparison between the composite properties obtained from the finite element micromechanics analysis and those from the ex perimental investigation of Nathan et al. [3] is given in Tables 5 and 6 for different volume fractions with an aspect ratio of 53.6 and different aspect ratios with a volume fraction of 4 % respectively. It can be seen from the Tables 5 and 6, and Fig. 6 that the numerical results compare favourably with the experimental results. The composites with staggered arrange ment give slightly closer value to the experimental values compared to the row-column ar rangement.
Journal of Ferrocement: Vol. 17, No. 2, April 1987
0 ...---.,...~~~~~~~~~~~ 0
'° '° .n NE g
E..,: "" 0 zo ~..,: ,,, "'o GIN !: l'i ,,, J! ~ ·u;N oo c. '° E-' 8g
ci 0
Steel fibre
"'o QJ q; ;!:N ,,, oO c. U! E oo (.) Cl)
ci 0
Steel fibre
0.16 o.32 0.48 o.64 0.80 o:96 -3
Composite strain x 10
Composite strain x I0- 3
(a) Vt = 2 °/o L1/o = 53.6 (b) Vt= 3 % L1/o: 53.6
0 (g
<t ,,, ,,, 0 QJ N .:: rti ,,, 0
QJ <i: ..., N
0
.... r<l ,,, 0 QJ <t :!:N ,,, 0
g_~ E- 8g
Composite strain x 10- 3
(c) Vf=4% L1/0=53.6
Steel fibre
0 CD
J! ~ ,,, 0 0 U) c....: E oO (.) Cl!
0
0 ~ U)
(d) Vt= 5 °io L1/o = 53.6
~ o Steel fibre ~E ~ ~ g -Numerical z..t
::l ~ QJ r<l ....
0 0
Composite strain x I0- 3
( f ) Vt = 4 % LI /o = 71. 4
Fig. 6. Comparison of numerical and experimental stress-strain curves of the composites.
113
114 Journal of Ferrocement: Vol. 17, No. 2, April 1987
Table 5 Comparison Between Numerical and Experimental Values of First Crack and Ultimate Strength for Different Volume Fractions with L1/D = 53.6.
Stress at first crack (N/mm2) Ultimate stress (N/mm2)
V1(%) Numerical values Experimental Numerical values Experimental
Row-column Staggered results Row-column Staggered results
2 1.60 1.59 1.58 2.05 1.84 1.79 3 1.68 1.76 1.84 2.79 2.72 2.61 4 1.72 2.07 2.98 3.85
5 1.90 2.23 4.94 5.25
Table 6 Comparison between Numerical and Experimental Values of First Crack and Ultimate Strength for Different Aspect Ratios with V1 = 4 %.
L,/D Stress at first crack (N/mm2) ·Ultimate stress (N/mm2)
Numerical Experimental Numerical Experimental
35.7 1.70 1.85 2.39 2.49 53.7 1.72 2.07 2.98 3.85
71.4 1.80 2.17 4.72 4.55
A typical variation of the longitudinal stress near the fibre axis for the composite with V1 = 4 % and different aspect ratios of 53.6 and 35.7 is shown in Figs. 7(a) and 7(b) respec tively. Two curves corresponding to axial stress before yielding (cry = 1.0) and after yielding (…
Related Documents
