Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Properties of steel micro-fiber reinforced cementitious material Yan, Ning 1995

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1995-0176.pdf [ 8.31MB ]
Metadata
JSON: 831-1.0050347.json
JSON-LD: 831-1.0050347-ld.json
RDF/XML (Pretty): 831-1.0050347-rdf.xml
RDF/JSON: 831-1.0050347-rdf.json
Turtle: 831-1.0050347-turtle.txt
N-Triples: 831-1.0050347-rdf-ntriples.txt
Original Record: 831-1.0050347-source.json
Full Text
831-1.0050347-fulltext.txt
Citation
831-1.0050347.ris

Full Text

PROPERTIES OF STEEL MICRO-FIBER REINFORCED CEMENTITIOUS MATERIAL by NING YAN B. Eng., Tianjin University, 1983 M. Eng., Tianjin University, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1995 © Ning Yan, 1995 In p resen t ing this thesis in partial f u l f i lmen t o f t h e r e q u i r e m e n t s f o r an advanced d e g r e e at the Universi ty o f Brit ish C o l u m b i a , I agree that t h e Library shall make it f reely available f o r re ference and s tudy. I fu r ther agree that pe rmiss ion f o r ex tens ive c o p y i n g of this thesis f o r scholar ly pu rposes may be g ran ted by t h e head o f m y d e p a r t m e n t o r by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g o r pub l i ca t i on o f this thesis f o r f inancial gain shall n o t be a l l o w e d w i t h o u t m y w r i t t e n permiss ion . D e p a r t m e n t o f C i v i l E n g i n e e r i n g The Univers i ty o f Brit ish C o l u m b i a Vancouver , Canada Date 30 M a r c h , 1995 DE-6 (2/88) Abstract The addition of micro-fibers improves not only the tensile strain capacity but also the tensile strength of cementitious materials. Among the different types of micro-fibers currently in use, steel micro-fibers which are characterized by high strength, high stiffness and low cost, have great potential to be used in many applications. The fracture properties of steel micro-fiber reinforced cementitious are, however, not well understood and are necessary for optimization. Three aspects of steel micro-fiber reinforced cementitous materials are examined in this thesis: (1) characteristics of bond between steel micro-fiber and cement paste; (2) properties of steel micro-fiber reinforced mortar (SMFRM) under uniaxial tension; and (3) properties of SMFRM in flexure. Single fiber pull-out tests were used to study the characteristics of bond between steel micro-fiber and cement paste. A feed-back controlled system, which could avoid the sudden fracture of specimens at peak load, was installed in the uniaxial tensile tests. Similarly, crack-opening controlled, four-point flexural tests were performed on beams. Data collected from these tests were analyzed by computer programs written in the FORTRAN language. In pull-out tests, the highest peak pull-out load and the highest total energy absorption were obtained when the micro-fiber was aligned in the loading direction. This suggests that the optimum inclined angle of fiber is 0°. The increase of silica fume content in the matrix increased the strength of bond between steel micro-fiber and the cement-based matrix. The results of the uniaxial tensile tests and the flexural tests show, as expected, that the strength and toughness of SMFRM increases wi th an increase in the fiber volume fraction. SMFRM with fibers having larger diameters had higher toughness. The addition of longer fibers in SMFRM ii also yielded higher toughness. But, with longer fibers, the workability of steel micro-fiber mortar mixtures was inadequate. Short thick fibers, on the other hand, were easy to be mixed at high volume fractions (5% or more) without workability problems. While the inclusion of a polymer in cement mortar increased the toughness of SMFRM significantly, an increase in the sand content in cement mortar led to a significant increase in the strength. Overall, the addition of steel micro-fibers improved the properties of cementitious materials dramatically. iii Table of Contents Abstract ii Table of Contents iv List of Tables vii List of Figures viii Acknowledgments xi 1. Introduction 1 2. Bond-Slip Characteristics of Steel Micro-Fibers Bonded to Cement Matrices 4 2.1 Introduction 4 2.2 Literature Review and Research Significance 5 2.3 Experimental Work 10 2.3.1 Materials 10 2.3.2 Specimen Preparation 15 2.3.3 Test Set-Up 21 2.4 Results and Discussion 21 2.4.1 Load-Slip Relations 21 2.4.2 Tensile Strength of the Fibers 23 2.4.3 Critical Length of the Fibers 25 2.4.4 Strength of Bond between Fiber and Matrix 28 2.4.5 Influence of Fiber Orientation 29 2.5 Summary 38 3. Properties of Steel Micro-Fiber Reinforced Mortar in Uniaxial Tension 39 3.1 Introduction 39 3.2 Literature Review and Research Significance 40 3.3 Experimental Work 43 3.3.1 Materials 43 iv 3.3.2 Specimens Preparation 46 3.3.3 Test Plan 47 3.3.4 Test Set-Up 49 3.4 Test Results and Discussions 52 3.4.1 Workability of the Stainless Steel Micro-Fiber Mortar Mixture 52 3.4.2 Tensile Properties of SMFRM 54 3.4.2.1 Effects of Fiber Volume Fraction 54 3.4.2.2 Effects of Fiber Length 56 3.5 Summary 70 4. Properties of Steel Micro-Fiber Reinforced Mortar in Flexure 72 4.1 Introduction 72 4.2 Literature Review and Research Significance 73 4.3 Experimental Work 74 4.3.1 Materials 74 4.3.2 Specimens Preparation 76 4.3.3 Test Plan 80 4.3.4 Test Set-Up 83 4.4 Test Results and Discussions 83 4.4.1 Workability of the Steel Micro-Fiber Reinforced Mortar Mixtures 83 4.4.1.1 Effects of Fiber Volume Fractions, Fiber Length and Fiber Cross-Sectional Area 83 4.4.1.2 Effects of Sand Content and Polymer Addition 84 4.4.2 Flexural Properties 85 4.4.2.1 Effects of Fiber Volume Fraction 85 4.4.2.2 Effects of Fiber Length 85 4.4.2.3 Effects of Fiber Cross-Sectional Area 86 4.4.2.4 Effects of Matrix Properties 87 4.5 Summary 106 5. Conclusions 108 Bibliography 113 Appendix 1. Computer Program: PULOUT.FOR 118 Appendix 2. Computer Program: TENSIL.FOR 120 Appendix 3. Computer Program: BENDING.FOR 124 vi List of Tables Table 2.1 Mix Proportion of Cement Paste Matrix 10 Table 2.2 Cross-Sections of 40 Randomly Chosen Stainless Fibers 14 Table 2.3 Average Cross-Section Areas and Their Corresponding Diameters of the Carbon Steel Fibers 15 Table 2.4 Tensile Strength of Various Fibers 23 Table 2.5 The Behavior of Fibers under a Pull-Out Load 25 Table 2.6 Critical Length of Various Fibers 26 Table 2.7 Bond Strength Values for Various Fibers 28 Table 2.8 Bond-Slip Characteristics at Various Fiber Orientations 30 Table 3.1 Mix Proportions and Compressive Strength of the Mortar Matrix 43 Table 3.2 Properties of Stainless Steel Micro-Fiber 46 Table 3.3 Superplasticizer Dosage 53 Table 3.4 Test Results of Feed-Back Controlled Uniaxial Tensile Tests ..65 Table 3.5 Repetitious Test Results of Feed-Back Controlled Uniaxial Tensile Tests 66 Table 4.1 Mix Proportions of the Three Matrices 74 Table 4.2 Cross-Sectional Areas of the Various Carbon Steel Fibers 75 Table 4.3 Critical Length and Tensile Strength of Fibers 75 Table 4.4 Test Variables Investigated 80 Table 4.5 Workability of Steel Micro-Fiber Mortar Mixture 84 Table 4.6 Flexural Test Results (a) Fiber Length 2 mm 89 (b) Fiber Length 4 mm 90 (c) Fiber Length 10 mm 91 vii List of Figures Figure 2.1 Micro Graph of Stainless Steel Micro-Fiber 12 Figure 2.2 Micro Graph of Carbon Steel Micro-Fiber 13 Figure 2.3 Pull-Out Specimen Molds 16 Figure 2.4 Pull-Out Specimen 17 Figure 2.5 Pull-Out Test Apparatus 19 Figure 2.6 Schematic of Pull-Out Test Frame 20 Figure 2.7 Bond-Slip Curves for Stainless Steel Micro-Fibers 22 Figure 2.8 Bond-Slip Curves for Carbon Steel Micro-Fibers 24 Figure 2.9 Stresses on a Fiber Embedded in Matrix 27 Figure 2.10 Calculation of Maximum Interfacial Bond Strength Developed between Fiber and Matrix 31 Figure 2.11 Influence of Silica Fume Content on the Bond-Slip Curves..32 Figure 2.12 Influence of Fiber Inclination Angle 33 Figure 2.13 Bond-Slip Curves at Various Angles 34 Figure 2.14 Energy vs. Slip Curves for the Various Inclination Angles ..35 Figure 2.15 Matrix after Fiber Pull-Out 36 Figure 2.16 Matrix Scabbing in A Fiber Inclined w.r.t . the Loading Direction 37 Figure 3.1 Typical Tensile Load-Elongation Response of Various Fiber Reinforced Composites 41 Figure 3.2 Grading Curve for Sand 44 Figure 3.3 Fiber Length Distribution 45 Figure 3.4 Specimen for Uniaxial Tensile Tests 48 Figure 3.5 A Feed-Back Controlled Uniaxial Tensile Test in Progress 50 Figure 3.6 Schematic Description of a Feed-Back Controlled Uniaxial Tensile Test 51 viii Figure 3.7 Tensile Stress-Strain Curves for SMFRM with Different Fiber Volume Fractions (Fiber length = 4 mm) 60 Figure 3.8 Tensile Stress-Strain Curves for SMFRM with Different Fiber Volume Fractions (Fiber length = 6 mm) 61 Figure 3.9 Tensile Stress-Strain Curves for SMFRM with Different Fiber Volume Fractions (Fiber length = 10 mm) 62 Figure 3.10 Tensile Stress-Strain Curves for SMFRM with Different Fiber Length (Fiber volume fraction = 1 % ) 63 Figure 3.11 Tensile Stress-Strain Curves for SMFRM with Different Fiber Lengths (Fiber volume fraction = 2%) 64 Figure 3.12 Relationship between Fiber Volume Fraction and Tensile Strength 67 Figure 3.13 Relationship between Fiber Volume Fraction and Toughness Factor 68 Figure 3.14 Schematic of Deformation of Cement Mortar with or without Fiber under a Tensile Load 69 Figure 4.1 Fiber Length Distributions (a) Industry Cut Fibers 77 (b) Laboratory Cut Fibers 78 Figure 4.2 Specimen for Flexural Tests 79 Figure 4.3 Test Set-Up for Flexural Tests 81 Figure 4.4 Schematic of Test Set-Up for Flexural Tests 82 Figure 4.5 Load-Deflection Curves of SMFRM with Different Fiber Volume Fractions (1) 92 Figure 4.6 Load-Deflection Curves of SMFRM wi th Different Fiber Volume Fractions (2) 93 Figure 4.7 Load-Deflection Curves for SMFRM with Different Fiber Lengths (1) 94 Figure 4.8 Load-Deflection Curves for SMFRM ix with Different Fiber Lengths (2) 95 Figure 4.9 Load-Deflection Curves for SMFRM with Different Fiber Cross-Sectional Areas (1) 96 Figure 4.10 Load-Deflection Curves for SMFRM with Different Fiber Cross-Sectional Areas (2) 97 Figure 4.11 Load-Deflection Curves for SMFRM with Different Types of Matrices (1) 98 Figure 4.12 Load-Deflection Curves for SMFRM with Different Types of Matrices (2) 99 Figure 4.13 Influence of Fiber Length on the Strength and Toughness of SMFRM under Flexure 100 Figure 4 .14 Influence of Fiber Cross-Sectional Area on the Strength and Toughness of SMFRM under Flexure 101 Figure 4.15 Influence of Matrix Type on the Strength and Toughness of SMFRM under Flexure 102 Figure 4.16 Influence of Fiber Volume Fraction on Compressive Strength of SMFRM 103 Figure 4.17 Typical Shape of a Deflection-Crack Opening Curve for a Flexural Tests 104 Figure 4.18 Load Crack Opening Curves for SMFRM with Different Fiber Volume Fractions 105 Acknowledgments First and foremost, the author wishes to thank Dr. Nemkumar P. Banthia, supervisor of her thesis. She is very grateful to him for his invaluable guidance, encouragement and support which enabled her to complete her program of graduate studies. Thanks are also due to Professor Sidney Mindess and Professor Arnon Bentur for their suggestions and help. She is grateful to Dr. Cheng Yan for his unstinting help in design and installment of the test systems. The help of Mr. Cesar Chen is also greatly appreciated. Thanks are also due to Mr. Bernie Merkli, Mr. John Wong, Mr. Dick Postgate and Mr. Ron Dolling for their help in preparing the test machines. Finally the author wishes to thank her husband, Sunsheng, and her daughter, Canmon, for their patience, understanding and support. xi 1 1 . Introduction Cementitious materials are one of the most used construction materials in the world. However, their low fracture strength and low tensile strain capacity limit their more extensive applications in construction. One way to overcome this problem is to add randomly distributed ductile fibers in the cementitious material. It has been found that the addition of fiber can dramatically improve the tensile strain capacity of the parent cementitious matrix [ 1 , 3 ] . Over the past twenty years, there has been a steady increase in the use of fiber reinforced cementitious composites in a variety of construction projects, such as highway pavements, roofing sheets, wall panels, dams, shotcrete etc.. At the same time, newer types of fiber are being developed and used in cementitious materials. In addition to the asbestos fiber which was used in early days, a wide variety of other fibers, such as those of steel, glass, carbon, polypropylene, nylon and various natural materials are used in cementitious materials. Fibers conventionally used in cementitious material, which are often called macro-fibers, are usually 0.1-1.0 mm in diameter and 10-60 mm in length. Macro-fibers are usually used in cementitious composites with a 2 maximum dosage of 1.5% by volume in order to keep an acceptable workability. Studies have shown that although the addition of macro-fibers to cementitious materials can control the cracking of the cement-based composites, it can not improve the tensile strength [1]. The role of this kind of fiber is to alter the behavior of cement-based composites after they have cracked, by bridging across the cracks. In recent years, some very fine fibers with dimensions in the same range as those of cement particles (around 0.025 mm), are being investigated in cementitious materials. These micro-fibers not only improve the post cracking 'ducti l i ty' of the cementitious composites but also increase the tensile strength. These fibers are also relatively easy to be mixed in the cementitious mixture. Fiber fraction up to 7% have been investigated[8]. Little effort has so far been made, however, to study the characteristics of bond between steel micro-fiber and cementitious matrix. The effects of fibers geometry and the matrix characteristics on the tensile and flexural properties of SMFRM (steel micro-fiber reinforced mortar) are also not well understood. Need exists to properly characterize and model the strain-hardening and softening that occurs in these composites in uniaxial tension. T h e p u r p o s e s o f t h i s s t u d y w a s t o e x a m i n e t h e f o l l o w i n g t h r e e a s p e c t s o f s t e e l m i c r o - f i b e r r e i n f o r c e d c o m p o s i t e s : (1) T h e c h a r a c t e r i s t i c s o f t h e i n t e r f a c e b e t w e e n s t e e l m i c r o - f i b e r a n d c e m e n t i t i o u s m a t r i x ; (2) T h e p r o p e r t i e s o f s t e e l m i c r o - f i b e r r e i n f o r c e d c e m e n t i t i o u s c o m p o s i t e u n d e r u n i a x i a l t e n s i o n ; D i f f e r e n t f r o m t h e s t r e s s - c o n t r o l l e d , c o n v e n t i o n a l u n i a x i a l t e n s i l e t e s t s , t h e t e s t t e c h n i q u e u s e d in t h i s s t u d y e m p l o y s a f e e d - b a c k c o n t r o l l e d s y s t e m t o r u n t t h e t e s t in d e f o r m a t i o n c o n t r o l in o r d e r t o o b s e r v e t h e real p r e - c r a c k i n g a n d p o s t c r a c k i n g b e h a v i o r o f S M F R M . (3) T h e f l e x u r a l p r o p e r t i e s o f s t e e l m i c r o - f i b e r r e i n f o r c e d ! m o r t a r s . S i m i l a r t o t h e u n i a x i a l t e n s i l e t e s t , t h e l o a d i n g r a t e in t h e s e t e s t s w a s c o n t r o l l e d b y t h e r a t e o f c r a c k - o p e n i n g b y a n L V D T m o u n t e d o n t h e t e n s i l e s i d e o f t h e b e a m s . 4 2. B o n d - S l i p C h a r a c t e r i s t i c s o f S t e e l M i c r o - F i b e r s B o n d e d t o C e m e n t B a s e d M a t r i x 2.1 Introduction The properties of fiber reinforced cementitious materials are determined by those of its components, viz. the matrix, the fiber and the fiber-matrix interface. While the nature and behavior of both fiber and matrix are reasonably well understood, those of the interface are known in less detail. The stress on the matrix is transferred to fiber through the fiber-matrix interface and hence the fiber-matrix interface play a very important role in composite materials. A strong bond can impart composites wi th a high strength and stiffness, whereas a weak bond may improve the ductil ity, while strengths of such composites usually remain low. In this section, the bond-slip characteristics between steel micro-fiber and cement paste matrix are studied through single fiber pull-out tests. Fibers both aligned and inclined w.r.t. load direction are investigated. The effects of fiber length, fiber cross-sectional area and silica fume contents in the matrix are also examined. 5 2.2 Literature Review and Research Significance In composites, bonding at an interface is due to adhesion between fiber and matrix. However, the fibers are often coated with a layer of material which forms a bond between the fiber and matrix. Adhesion can be attributed to five main mechanisms, that is, (1) adsorption; (2) interdiffusion; (3) electrostatic attraction; (4) chemical bonding and (5) mechanical adhesion. The five types of adhesion can occur at the interface either in isolation or in combination to produce the bond [2]. For cementitious composites, mechanical adhesion bond play an important role. Many studies have been conducted in order to understand the behavior of fiber-matrix bond in cementitious composites. These may be further sub-divided as follows: (1) Structure of the Bond Studies reveal that a transition zone, which is approximately 0.05 mm thick, exists between the matrix and the fiber, the strength of which is much less than that of the bulk matrix. As a result, the interface behavior depends mostly on this weak zone rather than on the bulk cement matrix. This weak zone can be strengthened by reducing the water cement ratio, by adding silica fume and also by adding an acrylic polymer or a water-reducing agent [3, 9]. 6 (2) Effects of Fiber Characteristics on the properties of Bond between Fiber and the Matrix Fiber geometry has a significant influence on fiber-matrix bond characteristics. For example, hooked, crimped and other deformed fibers have higher resistance to pull-out than smooth undeformed fibers. A much higher peak pull-out load and pull-out energy can be obtained for the hooked crimped and other deformed fibers [13]. An excessively deformed fiber, however, may break, instead of pulling out, causing significant reduction in the energy absorption [4, 6]. The load vs. pull-out displacement curve from a deformed fiber may show fluctuation after the peak load , which is caused by the fiber with a non-uniform section moving in the surrounding matrix [13]. For steel fibers, the chemical composition, metallurgical microstructure and the strength of the fiber have a significant influence on the pull-out behavior. The strength of the fiber is relatively a more dominating factor than its ductility. For achieving high performance characteristics, fibers need to have a high strength and a moderate ductility rather than a high ductility and a moderate strength [10]. 7 Experiments also reveal that the average interfacial bond strength and stiffness are independent of fiber spacing when fiber spacing is in the range of 10-25 times the fiber diameter [12]. (3) Effects of Matrix Properties on the Characteristics of Fiber-Matrix Bond The pull-out resistance of a fiber is strongly affected by the characteristics of the matrix. As the matrix strength increase, the bond between the fiber and the matrix also increases [13]. The inclusion of silica fume can improve the adhesion bond. However, it may also cause matrix brittleness leading to premature matrix splitting before the full fiber potential is reached [4, 6]. The bond strength can also be increased by adding acrylic polymer or water-reducing agent the [9, 12]. The addition of latex and fly ash to matrix can also increase the peak pull-out load to a varying degree [13]. (4) Effects of Loading Condition and Curing Temperature on Fiber-Matrix Bond An increase in loading rate increase the resistance to pull-out only when deformed fibers are used [4, 6]. Straight fibers appear to be insensitive to the rate of pull-out [4]. Lateral stresses, when present, have a significant influence on fiber debonding and pull-out. With the presence of lateral compression on the 8 fiber, both the interfacial friction at the onset of sliding and the effective interfacial strength are found to increase. A higher lateral compression, however, also results in a more rapid drop of the post-peak pull-out resistance. As a result, the total energy absorption does not improve as drastically as the peak pull-out load [21]. Subzero test temperatures improve the pull-out resistance[4, 6], but low test temperatures also make the fiber-matrix bond more brittle [7]. A lower curing temperature leads to a lower early-age but a higher later-age peak pull-out load than a higher curing temperature [4]. (5) Effects of Fiber Orientation on the Fiber-Matrix Bond A fiber inclined w.r.t . the loading direction carries both normal and flexural stresses. This is different from the aligned fiber which carries only the normal stress. For different fibers, however, the effects of fiber orientation on the bond-slip characteristics are different. While some studies show that the peak pull-out loads for undeformed steel fibers inclined to loading direction are almost as high as those for the aligned fibers, other studies conclude that for the deformed steel fiber that both the peak pull out load and energy absorption are maximized when the fiber is alighted w.r. t . loading direction and an inclined fiber has inferior resistance to pull-out [5]. Furthermore, the studies on the pull-out of inclined synthetic fibers show that both pull-out load and energy absorption increase with an increase in the angle between fiber and the loading [23]. For glass fibers, it was found that the fibers completely fracture at ultimate pullout load when inclined w.r. t . the loading direction [24]. To date, studies on the behavior of fiber-matrix interface have almost always involved macro-fibers with little or no attention given to micro-fibers. Significant effort is needed to extend this to micro-fiber reinforced composites. This section examines the bond-slip characteristics of steel micro-fibers. Four variables including: (1) fiber cross-section; (2) fiber embedded length; (3) fiber orientation and (4) silica fume content in the matrix, are considered. As part of the larger research project, the pullout test is also used to determine the tensile strength and the critical length of the fibers. These are needed in order to interpret the data from uniaxial tensile tests and flexural tests performed on the composites. 10 2.3 Experimental Work 2.3.1 Materials Matrix The mix proportions of the cement paste matrices used for the pull-out tests are shown in Table 2 . 1 . Water cement ratio of 0.35 and silica fume cement ratio of 0.1 and 0.2 were used. Table 2.1 Mix Proportions for the Cement Paste Matrices Matrix Type W/C S.F.*/C S.P.** (ml/100g cement) 1 0.35 0.10 3 2 0.35 0.20 4 n o t e : * S.F. : s i l ica f u m e * * S.P. : superp las t i c izer CSA Type 10 cement and DaracemlOO superplasticizer were used. The superplasticizer meets the requirements for an ASTM C-494 Type G water reducer, high range retarding admixture. Steel Micro-Fibers Two types of steel micro-fiber were used. They were stainless steel fiber and carbon steel fiber. 11 (1) The Stainless Steel Micro-Fiber: The fiber cross-sections were irregular but close to rectangular. Figure 2.1 shows a typical fiber cross-section. The cross-section areas of the fibers varied from one to another. Forty sample fibers were picked up randomly and their cross-sectional dimensions were measured by using a caliper (precision =0 .01 mm). The results are shown in Table 2.2. As seen, the maximum observed cross-section was 0.10mmX0.20mm and the minimum observed was 0 .02mmX0.06mm or 0.03mmX0.04mm. The average cross-section of the fibers measured was 0.04mmX0.10mm. (2) Carbon Steel Micro-Fiber: The fiber cross-sections were irregular. Figure 2.2 shows two typical fiber cross-sections. Based on their sectional areas, these fibers could be classified into four types: T (thick), L (large), M (medium) and S (small). For each fiber type, the cross-sectional areas of four or more fibers were measured from the micrographs and the average cross-sectional area of the fibers and their corresponding equivalent diameters were obtained. Table 2.3 shows these cross-sectional areas and also the equivalent diameters. 1 2 Figure 2.1 Micrograph Showing the Cross-Section of Stainless Steel Micro-Fiber ure 2.2 Micrograph showing the Cross-Sect ion of Carbon Steel Micro-Fiber 14 Table 2.2 Cross-Sectional Dimensions of 40 Sample Fibers Sample No. Cross-section Sample No. Cross-section (mmXmm) (mmXmm) 1 0.04X0.15 21 0.02X0.06 2 0.08X0.06 22 0.05X0.10 3 0.05X0.10 23 0.03X0.04 4 0.10X0.20 24 0.02X0.06 5 0.06X0.10 25 0.06X0.08 6 0.03X0.05 26 0.05X0.06 7 0.03X0.10 27 0.06X0.08 8 0.04X0.06 28 0.06X0.06 9 0.04X0.10 29 0.05X0.08 10 0.06X0.12 30 0.04X0.10 11 0.04X0.10 31 0.02X0.06 12 0.02X0.10 32 0.04X0.10 13 0.03X0.10 33 0.02X0.12 14 0.04X0.08 34 0.02X0.10 15 0.06X0.13 35 0.03X0.07 16 0.06X0.13 36 0.04X0.10 17 0.04X0.18 37 0.06X0.12 18 0.06X0.10 38 0.04X0.10 19 0.02X0.06 39 0.02X0.10 20 0.08X0.14 40 0.03X0.10 15 Table 2.3 Average Cross-Sectional Areas and The Corresponding Equivalent Diameters of the Carbon Steel Fibers Fiber Type Cross-Sectional Area Corresponding Equivalent Diameter (mmXmm) (mm) f 0.0050 0.08 L 0.0020 0.05 M 0.0013 0.04 S 0.0007 0.03 2.3.2 Spec/men Preparation A specially designed mold (Figure 2.3) was used to make the specimens with the dimension of 20mmX40mmX10mm. Each specimen was divided in the center by a plastic separator and a single fiber was passed through a small hole in it (Figure 2.4). The separator was carefully oiled before inserting the fiber in order to minimize the bond between the matrix and the separator. Two casting methods were used to prepare the specimens. Method One: The fiber was placed in the mold first. One side (side 1) of the fiber was left longer than the other side (side 2), i.e. the fiber was not 16 18 placed symmetrically w.r. t . the plastic separator. Fresh cement paste was poured in side 1 of the mold and after setting, the fiber on side 2 was cut to the appropriate length. Cement paste was then poured on this side of mold. Most specimens were cast this way except for those used to investigate the influence of fiber orientation. Method Two: The fiber was cut to the appropriate length and the cement paste was poured on one side (side 1) of the mold up to the hole in the plastic separator. The fiber was then placed in the mold with the same length on both side of separator and then the cement paste was poured on one side. In order to prevent the fiber from moving, the second side was not cast until setting on the first side. All specimens used to investigate the influence of fiber orientation were cast this way. All specimens were demolded on the second day of casting and further cured in water for six more days before testing. 1 9 Figure 2.5 Puil-Out Test Apparatus 2.3.3 The Test Set-Up The test set-up is shown in Figures 2.5 and 2.6. In principle, the pull-out specimen bridged two grips as shown. One side of the specimen grips was fixed to the machine frame and the other, with rollers underneath, was connected to a small motor which drove this grip at a constant speed away from the first grip. A 100N load cell was connected between the roller mounted grip and the driving motor to measure the applied load and an LVDT was connected to measure the displacement. All specimens were tested at a pull-out loading rate of 0.024 mm/s. An X-Y plotter was used to record the load-slip curves. A digitizer was then used to digitize these curves. The data were finally analyzed using a FORTRAN computer program (Appendix 1). 2.4 Results and Discussion 2.4.1 Load-Slip Relations Figure 2.7 shows the load-slip curves for stainless steel micro-fibers wi th cross-sections of 0.08mmX0.22mm (close to the maximum cross-sectional area) and 0.04mmX0.10mm (close to the average cross-sectional area). Notice that the fluctuations in the load values in the larger fiber are 22 more pronounced than those in the curves for the smaller fiber. This is apparently a result of the very uneven surface of the larger fiber. Figure 2.8 shows the bond-slip curves for carbon steel fibers. Only carbon steel fiber 'L ' (Table 2.3) was tested. 2.4.2 Tensile Strength of the Fibers The tensile strength of the fiber can be obtained from a pull-out test. When the embedded length of a fiber exceeds the critical length, the fiber will fracture instead of pulling out. The tensile strength of fiber is then simply the load at fracture divided by the cross-sectional area of the fiber. Table 2.4 shows the tensile strengths of the various fibers. Table 2.4 Tensile Strength of Various Fibers* Fiber Type Cross-sectional Dimension (mmXmm) Area (mm) Tensile Strength (MPa) 0.08X0.22 0.0176 850 Stainless steel 0.08X0.16 0.0128 870 fiber 0.06X0.12 0.0072 750 0.04X0.10 0.0040 1200 0.06X0.06 0.0036 1140 Carbon steel fiber L (see Table 2.3) 0.0020 1000 n o t e : * T h e va lues of tens i le s t r e n g t h in th is table are on ly app rox ima te because it is n o t poss ib le t o prec ise ly measure t h e cross-sec t iona l area o f the f iber . 24 25 Notice that the tensile strengths vary between 750 MPa to 1200 MPa and the fibers with larger cross-sectional areas have smaller tensile strength. This is well expected. 2.4.3 Critical Length of the Fibers When the embedded fiber length is longer than its critical length, the stress in the fiber reaches the ultimate strength of steel and the fiber fractures. On the other hand, when the embedded length of the fiber is shorter than the critical length, fiber pull out is expected to occur. Table 2.5 shows the behavior of stainless steel fibers and carbon fiber 'L ' , wi th different embedded lengths, under a pull-out load. Table 2.5 Behavior of Fibers under a Pull-out Load Fiber Type Cross-Section Embedded Length (mmXmm) 1mm 2mm 3mm 4mm 5mm 6mm Stainless 0.08X0.22 P * P P P o r F F steel fiber 0.04X0.10 P F* F Carbon L steel fiber (see Table 2.3) P P or F P note: * P= Fiber pull-out F= Fiber fractures 26 The critical lengths for the stainless steel fiber and carbon fiber 'L ' obtained directly from these tests are given in Table 2.6. The critical length for the other types of carbon steel fibers, however, can be calculated by assuming that they have the same tensile strength a and bond strength x as for the fiber 'L ' . The relationship between a and T can be seen in Figure 2.9. Assuming I, and d, are critical length and diameter of carbon steel fiber 'L ' respectively and l2 and d 2 are the same for other fibers (say fiber 'T') then, a I x = 21,/d, = 2l 2 /d 2 The critical lengths obtained using this procedure also given in Table 2.6. Table 2.6 Critical Length of the Fibers Fiber Type Cross-Section Critical Length (mmXmm) (mm) Stainless 0.08X0.22 10 steel fiber 0.04X0.10 6 T 6 (analytically) Carbon L 4 steel fiber M 3(analytically) S 2(analytically) 27 X t w—m 03 ro E <D JO +-> c . . c •«-> c ro sz T J 05 T J T J CD £ D) c 03 JC 0) ro o C N C N II ±3 O, b T J C N II b o 03 X3 CD CD E UJ CD LL 03 C o CO CD C/3 CO CD u. «*-» CO CD c\i CD • • • • • Li-28 2.4.4 Average and Maximum Shear Strength of the Bond The average shear strength of bond is the peak pullout load divided by the surface area of the embedded fiber. The relationship between maximum shear strength xmm. and average shear strength xave. is established through shear lag theory [16]: t m . x . / t a v e . = al coth al where, I is embedded fiber length, and a is a constant. as I -> 0, T '•max, Ix = 1 in other words, ^max. ^ave. / 1 -> 0 Table 2.7 Fiber-Matrix Bond Strength Values for Various Fibers Matrix Cross-Section Embedded Length Average Bond Maximum Bond (mmXmm) (mm) Strength (MPa) Strength (MPa) 3.0 4.53 M1 0.08X0.22 5.0 3.23 6.18 (20% L 2.0 4.60 S.F.) 0 .04X0.10 3.0 3.33 7.10 2.0 4.38 0.06X0.12 3.0 3.73 5.66 M2 2.0 3.98 (10% S.F.) 0.06X0.12 3.0 3.60 4.73 29 The concept is illustrated in Figure 2.10 and in Table 2.7 bond strength values are given. There is no apparent effects of fibers cross-sectional area on the average or the maximum bond strength. As expected, the strength of the bond increases with an increase in silica fume content in matrix. This effect can also be seen in Figure 2 .11 . 2.4.5 Influence of Fiber Orientation Specimens with aligned as well as inclined fibers were tested and the test results are shown in Table 2.8 and Figures 2.12-2.14 where the noted inclination angle is the angle between fiber and the loading direction. As seen in Table 2.8, the highest peak load and energy absorption were obtained when the fibers were aligned w.r.t. the loading direction. The slip of the aligned fiber at the occurrence of the peak load, however, is smaller than that of inclined fibers. Additional observations are as follows: (1) It is often that the load drops suddenly at a certain pullout displacement (Figure 2.13). This drop of load is caused possibly by the matrix breaking out at the point where the inclined fiber enters the matrix. Figure 2.15 shows the breakage of matrix for an aligned fiber (a) and an inclined fiber (b) and Figure 2.16 shows the schematic of this process. 30 (2) A greater proportion of aligned fibers fractured as compared to inclined fibers even though they had the same cross-sectional areas and embedded lengths. Table 2.8 Bond-Slip Characteristics at Various Fiber Orientation Fiber Peak Total Slip at Energy at Angle Load Energy Peak Load Peak Load (degree) (N) (N-mm) (mm) (N-mm) 0 3.91 5.92 0.08 0.35 15 2.54 3.25 0.47 0.81 30 2.75 4.06 0.25 0.44 45 2.53 3.92 0.45 0.87 60 3.32 3.84 0.28 0.53 75 3.03 3.45 0.82 1.07 31 V 33 o o 34 35 36 37 o3 -Q CQ L_ c O mmmm O 0) C • mwmi "O o a> •o o c v. 0 n Li-re c .E a) 2 3-O 0 O § 3 O •o r > » CD CB C CD o o .c cu si U) lb CD - t r = | Is n ca o (/) X • mmm mm CB CO OJ 0 k. 3 D) E -I 8 a. cn 0 55 3 8 2.5 Summary Based on the pull out tests described in this section, the following conclusions may be drawn: (1) The tensile strength of the stainless steel micro-fibers is in the range of 750-1200 MPa and their critical length is in the range of 6-10 mm. The bond strength between the stainless steel micro-fiber and the cement paste is between 4.7 MPa and 7.1 MPa. (2) The tensile strength of the carbon steel micro-fibers used in this study is around 1000 MPa and their critical lengths are in the range of 2-6 mm. These fibers develop an average bond strength of 3.92 MPa with a cementitious matrix.. (3) An increase in the silica fume content in the matrix improves the bond. (4) The orientation of fiber had a strong influence on the bond. A fiber aligned to the load direction supported a higher peak pullout load and absorbed greater pull out energy than the inclined fibers. The slip of an aligned fiber at the occurrence of peak load is also smaller than that of an inclined fiber. 39 3. Properties of Steel Micro-Fiber Reinforced Mortar in Uniaxial Tension 3.1 Introduction Previous studies indicate that the addition of steel micro-fibers in cementitious materials improves the tensile strength [25]. The post-cracking behavior of steel micro-fiber reinforced cementitious composite under tension, however, is still not well understood. The test results from stress-controlled direct tensile test [25] are not reliable because of the 'snap-back' of the specimens after cracking. Tensile testing of cementitious composites is a difficult task. Because of the gripping problems, for brittle cementitious materials, one uses indirect tensile test methods, such as the splitting test, trussed beam test, pressurized ring test and the flexural test [27]. Although these tests, especially the splitting test, are widely used for concrete, they have their own limitations because the tensile properties are obtained indirectly. In any case, the behavior of fiber reinforced cementitious materials under direct tension is desired for a thorough understanding of their softening characteristics. For such composites, given their more ductile behavior, it is possible to test them under direct tension [1,25, 30, 31]. 40 This section describes the uniaxial tensile behavior of steel micro-fiber reinforced composites with different volume fraction and different lengths of fibers. In order to observe the real post-cracking behavior of SMFRM, a feed-back controlled system (closed-loop setup) was used in the tests. 3.2 Literature Review and Research Significance The addition of fibers in cementitious materials improves their tensile strain capacity and ductility [ 1 , 3]. When a high (more than 2%) volume fraction of fibers is added, the behavior of the cementitious materials can be fundamentally altered [3, 3 1 , 32]. As a result, cementitious composites with high volume fraction of fibers are often called high performance cementitious composites. Figure 3.1 shows the typical tensile stress-strain curves for high performance and conventional fiber reinforced cementitious composites. While the conventional cementitious composites have only a linear stage followed by the strain softening stage [3, 31] , the tensile stress-stain curves for high performance fiber reinforced cementitious composites have three stages: (1) a linear stage; (2) multiple cracking stage or the pseudo strain hardening stage and (3) localization or the strain softening stage. 41 ra CD W C o a CO CD DC c o Mwmm U) CD 13 C3 C o • MM •*—> c CD > c o O LU • "O CTS O i w CD CD * -- o w 0) S ° w E p CD O O h- t: O CD -o 8 J 8 5; o> o I MM H I c r i cr CO CD MM 3 i i SSSJJS Jo peon 42 With the addition of different types of micro-fibers (e.g. steel, carbon, polypropylene and other fibers), the tensile behavior of the cementitious composites are different. It has been reported [25] that steel micro-fiber provides the most stiffening and the highest strength followed by carbon fiber and then polypropylene fiber. The composite reinforced wi th carbon micro-fibers, on the other hand, had the largest tensile strain capacity. The tensile stress-strain curves of carbon micro-fiber reinforced composites had significant non-linearity after the peak load, while the curves for steel micro-fiber reinforced composites remain almost linearly elastic to fracture with only a nominal pre-peak non-linearity [25]. The lack of ductility in steel micro-fiber reinforced composites in Ref. 25, in addition to being related to fiber geometry and surface characteristics, is also the consequence of the test being performed in the stress-controlled mode, where the machine energy is suddenly released causing sudden fracture of the specimen. To avoid this problem, it has been proposed to use special specimens and test set-ups [35, 36, 37]. The best way to solve the problem of instability is to use a feed-back controlled system in which an LVDT with a short gage length is used to control the specimen crack opening to eliminate the effects of specimen 'snap-back' at the peak load. In this investigation, a feed-back controlled system was designed and installed to test the real tensile behavior of steel micro-fiber reinforced composites. 43 3.3 Experimental Work 3.3.1 Materials Matrix The mix proportion of the cement mortar and its compressive strength are shown in Table 3 . 1 . CSA type 10 cement and Daracem 100 superplasticizer were used. The sand used was very fine and clean playsand. Figure 3.2 shows the gradation curve for the sand. Table 3.1 Mix Proportion and Compressive Strength of the Cement Mortar W/C S/C S.F./C Superplasticizer Compressive Strength * 0.35 0.5 0.2 1.4 - 5 ml/100g C. 56 MPa N o t e : * C o m p r e s s i v e s t r e n g t h ob ta ined us ing cy l indr ica l spec imens ( 4 2 . 5 m m in d iame te r and 8 5 m m in he igh t ) . The va lue l is ted is the average value f o r th ree s p e c i m e n s . Stainless Steel Micro-Fiber The properties of the stainless steel micro-fiber, which were obtained from pull-out tests as described in Section 2, are shown in Table 3.2. 44 46 Table 3.2 Properties of Stainless Steel Micro-Fiber Average Cross-Section Tensile Strength Average Critical Length (mmXmm) (MPa) (mm) 0.04X0.1 700 - 1200 around 6 The fibers were cut to lengths of 4, 6, and 10 mm. It was found difficult to cut the fibers to an uniform length. Figure 3.3 shows the fiber length distributions. As seen, for the 4 mm fiber, most fibers (75.2%) had the length between 4 and 6 mm. Similarly, most 6 mm (68.8%) and 10 mm fiber (71.3%) had lengths between 6 and 8 mm, and between 8 and 10 mm respectively. Several fiber volume fractions were investigated. For the 4 mm fiber, fiber volume fraction of 0.5%, 1.0%, 1.5%, 2.0%, 3 .0% and 5 .0% were used. For the 6 mm and 10 mm fibers, fiber volume fraction of 0 .5%, 1.0%, 1.5% and 2 .0% were used. 3.3.2 Specimen Preparation The mixing procedure for steel micro-fiber reinforced mortar was similar to that of normal cement mortar. First, cement, sand and silica fume were mixed in the mixer. Then water with half the required quantity of 47 superplasticizer were added. Finally, fibers were scattered slowly and evenly into the cement mortar with the mixer running. The mixing was continued for another two minutes after all fibers were added in. The mixture was then poured in the molds. After being cured at room temperature for 24 hours, the specimens were carefully demolded and cured for another 27 days before tested. The shape and dimension of the specimen are shown in Figure 3.4. 3.3.3 Test Plan Fifteen sets of specimens were tested. For the 4 mm fiber, specimens wi th fiber volume fractions of 0.5%, 1.0%, 1.5%, 2.0%, 3 .0% and 5.0% were tested. For the 6 mm and 10 mm fibers, specimens with fiber volume fractions of 0.5%, 1.0%, 1.5% and 2.0% were tested. Plain cement mortar specimens were also tested as the control. To verify the reproducibility of the test results, three additional sets of specimens were cast and tested. These repetitious test used specimens wi th 1.0% of fibers which had length of 4 mm, 6 mm and 10 mm. In each category, at least six specimens were tested. 48 E E E E O) E E LO l l w w 0) 0) "co c (1) 75 • X (0 • 1MB c c 0) E O o a (/) CO a) 3 D) LL •E-E LO CM 49 3.3.4 Test Set-Up The test set-up is shown in Figures 3.5 and 3.6. As mentioned before, the testing machine should be stiff enough to avoid unstable and sudden unloading after the specimen cracks. Although the frame of the test machine used was much stiffer compared to the specimens, the stiffness of the grips and the joints between the machine and the grips were of particular concern. High stiffness steel grips which were much bigger in size than the specimens themselves were used. Rubber or any other flexible materials were avoided in the joints and grips. To prevent bending stress in the specimens, ball-and socket joints were used between machine frame and the grips. The feed-back controlled system was the key part of the test set-up. The tensile strain of the specimen with a gage length of 65 mm were measured by two symmetrically placed LVDTs, each with a sensitivity of 75.5 mv/mm, as shown in Figure 3.6. The strain signal f rom the LVDTs was fed back to the machine which controlled the movement of the machine cross- head so as to keep the strain rate of the specimens at a prescribed value. In this study, two different strain-rates were used. The specimen was first loaded at a strain rate of 2 microstrain per second up to the peak load followed by a higher strain rate of 20 microstrain per second in the descending branch. Figure 3.5 A Feed-Back Controlled Uniaxial Tensile Test in Progress 51 fixed to the frame \//////////////////////\ 65 mm load cell ball-and-socket joint grips signal to the machine system LVDT holders loading direction V//////////X Figure 3.6 Schematic Description of a Feed Back Controlled Uni-axial Tensile Test 52 The system was found to be very sensitive even to minor movements. A small disturbance to the LVDT, for example, a gentle touch to the LVDT during the installation of the specimen, could cause a big movement in the cross-head and disrupt the test suddenly. To overcome this problem, a pneumatic grip system was used. When installing a specimen, the upper part of the specimen was fixed to the top grip first. After properly adjusting the LVDT, the lower part of the specimen was griped quickly by using high pressure air from the pneumatic grip system. The applied tensile load was measured by a load-cell with a capacity of 1600 N. The test results, in the form of applied load vs. LVDT displacement, were recorded by both an X-Y recorder and a computer based data acquisition system. Finally, a FORTRAN computer program (Appendix 2) was written to analyze the data. 3.4 Test Results and Discussion 3.4.1 Workability of the Steel Micro-Fiber Reinforced Mortar Mixtures The workability of the mixtures was affected significantly by the fiber volume fraction and fiber length. The workability of the mixture became worse with an increase in the fiber volume fraction. To keep a good workability, the quantity of the 53 superplasticizer had to be increased with an increase of fiber volume. Table 3.3 shows the quantities of the superplasticizer used. The mixture which contained 5% of 4 mm fiber in spite of a high dosage of superplasticizer was highly unworkable. Table 3.3 Superplasticizer Dosages Fiber volume Fraction (%) Superplasticizer (ml /100g C.) 0 1.2 0.5 1.6 1.0 2.0 1.5 2.4 2.0 2.8 3.0 3.2 5.0 4.5 Mixtures with longer fibers witnessed more fiber balling than those with shorter fibers and an increase in the dosage of the superplasticizer had only a limited effect. In particular, the mixtures with 10 mm fibers were highly unworkable. The dosage of superplasticizer could not exceed 5 ml/100g of cement. The addition of a large quantity of superplasticizer caused the mixture to set too quickly allowing little time for finishing. 54 3.4.2 Tensile Properties of SMFRM The test results are shown in Table 3.4 and Figures 3.7- 3.13. The results from the repetitious tests performed to verify the reproducibility of the data are shown in Table 3.5. 3.4.2.1 Effects of Fiber Volume Fraction Figures 3.7, 3.8 and 3.9 show the stress-strain curves for composites with different fiber volume fractions and lengths of 4, 6 and 10 mm, respectively. Figures 3.12 and 3.13 show the relationships between fiber volume fraction and the tensile strength factor and between fiber volume fraction and the toughness factor. These factors are defined as fol lows: Tensile strength factor = Tensile strength of SMFRM / Tensile strength of plain cement mortar Toughness factor* = Toughness of SMFRM / Toughness of plain cement mortar The figures illustrate clearly that no matter what the fiber length, the tensile strength and toughness of SMFRM increases with an increase in the fiber volume fraction. With an addition of 2% fiber, the tensile strength of the SMFRM can be nearly doubled and the toughness can be improved by a factor of ten. Note also that the elastic modules, the strain at peak-load and the ultimate strain increase with an increase in the fiber volume fraction. T o u g h n e s s w a s measu red by the to ta l area under a s t ress-s t ra in c u r v e . 55 Distinct from the steel macro-fibers, the addition of steel micro-fiber also increases the elastic strength of the cement mortar significantly. Compared to the macro-fiber, for a given fiber volume fraction, micro-fibers wi th their fine size will be much higher in number. Let us consider a small part of the matrix which contains a single fiber (Figure 3.14). When the composite is loaded in tension, the load acts on the matrix and is then transferred through the fiber-matrix interface to the fiber. To maintain strain compatibility, the deformation of the matrix closer to the fiber is constrained. If the number of fibers are large enough and the fibers distributed evenly, the fibers will be very close to each other and the deformation of the whole matrix will be constrained. At a certain stress level, therefore, the corresponding strain in the matrix will be smaller as compared to a plain matrix. In other words, the stress in the composite will be higher when the failure strain of the matrix is reached. Higher elastic strengths can be, therefore, obtained when micro-fibers are used and the higher the number of fibers, the higher the expected elastic strength of the matrix. Similar to the carbon micro-fiber reinforced mortar, steel micro-fiber reinforced mortar depicted significant strain hardening under tension, especially at high fiber volume fractions. The mechanisms of strain hardening of micro-fiber reinforced cementitious composite have been studied by several researchers [8,31]. Like the other cementitious materials, 56 under tension, SMFRM will develop the first crack at a flaw. The presence of fibers at the crack will provide resistance against crack opening. If the number of fibers is sufficiently large, and the fiber and the fiber-matrix interfaces are strong enough, the specimen can absorb more energy and the load can be further increased. With an increase in the load, there will be enough energy to form an additional crack somewhere else in the material. In other words, the energy required to open the first crack is larger than that required to form a new crack. With a further increase in load, more cracks appear and more energy is absorbed. The multiple cracking process is continued until the energy needed to form new cracks is larger than the energy to open the first crack. At this point, process of multiple cracking is terminated and the softening stage is reached. The first crack will continue to open until complete fracture occurs. 3.4.2.2 Effects of Fiber Length Fiber length affects the tensile strength and toughness of SMFRM. Figure 3.10 and 3.11 show the stress-strain curves for fiber lengths of 4, 6 and 10 mm for fiber volume fractions of 1 % and 2%, respectively. At a low volume fraction of 1 %, specimens with 6 mm fibers gave both the highest strength and the highest toughness, followed by those wi th 4 mm fibers and 10 mm fibers. At a higher fiber volume fraction of 2%, the 57 specimens with 6 mm fibers still yielded the highest tensile strength but also the lowest toughness as compared to those with 4 and 10 mm fibers. It was expected that the specimens with shorter fibers would yield higher toughness but also lower strengths and those wi th longer fibers would yield lower toughness and higher strengths. When the fiber length is less than the critical length, more fibers should be pulled out. For a fiber that pulls out, the peak load should be lower and the energy absorption in the process of pull-out should be higher than a fiber that fractures. The test results suggest that the interaction between fiber and matrix in SMFRM is not as simple as expected. The following factors need to be considered: (1) Strength of the Fiber-Matrix Bond and Strength of the Matrix As mentioned before, the workability of SMFRM mixes was affected significantly by the fiber length. Mixtures with 10 mm fibers were hard to be compacted and significant balling occurred during mixing. When the same volume fraction of shorter fibers were used, the mixture were significantly more workable and a higher bond strength between fiber and the matrix and a higher matrix strength are expected. This explains why 10 mm fibers gave lower strength than the 6 mm fibers. (2) Fiber Efficiency When. SMFRM specimens are loaded in tension, the load is transferred from the matrix to the fiber through the fiber-matrix interface. If the fiber 58 length is less than critical, the stress which is transferred to a fiber can never reach the fiber strength. It means that the fibers are not used efficiently. On the contrary, if the fibers are long enough, higher stresses can be supported by the fibers. From this point of view, the specimens with shorter fibers will have lower strengths. This explains the lower strength given by 4 mm fibers as compared to 6 mm fibers. (3) Drop of Load after the Peak Load As the load starts to drop after the peak load, the thicker and shorter fibers slip and the thinner and longer fibers fracture. The stainless steel fibers used in these tests were not uniform in length as well as in cross-section (Figure 3.3 and Table 2.2). For all specimens, both fiber pull-out and fiber fracture with varying proportions will occur at the cracks. Specimens wi th shorter fibers (4 mm) should have more fibers pulling out and less fibers fractured. Specimens with 10 mm fibers, on the other hand, should have more fibers fracture and less fibers pulling out. Specimens with 6 mm fibers may be expected to have equal proportions of fibers pulling out and fracturing. At the peak load, fibers at the cracks are severely stressed and hence some weaker fibers are fractured. After the fracture of these fibers, the load is redistributed to other fibers, which in turn causes others fiber to fracture. 59 This process can be very fast and the load may drop very quickly if the peak load is very high and if the fibers are not strong enough. The above analysis suggests that the increase or decrease in fiber length could have opposing effects on the tensile strength and toughness of SMFRM. On the whole, specimens with 6 mm fibers yield the highest strength, while those with 10 mm fibers yield lowest strength. However, a high strength may have a faster load drop and then results in a lower toughness. Accordingly, when 2% fibers were added, the specimens with 6 mm fibers gave the highest strength but also the lowest toughness. 60 61 cd CL CO CO CD CO d LO ci d ° co -*—< CO CM d LL E E co c cu co £ 2 3 LL O „ .£ E (Q 3 o JO to \t CD c = o> H Q 00 CO CD 3 CO oo CO CM 62 63 64 O E E co Ti-ro c JQJ w CU .o E E E CO i 1 , E o CO J i CO C i jz r leng lengt cu CD .Q co C L CO CO 0 CD d LO d d c 'cc >_ -»—< CO C O d CM d CM C g CO o v . E O = • 1 S I 3 O co J> i -0 I- Q co O ) LL CO CO CD CM 65 to CD I— _CD to c 0 CO X 95 ZD TJ CD C o O o ro co • TJ Cl) CD LL CD . C h-u— O tn 3 CO CD CU to CD H ro I— to c to t gj E T -D C O ° z x i CD ro c E ro. ± i -h ; 3 C O ! TJ ro o c ' r o : ro 2 co to 3 ro to TJ Q L L U S CD - C ro cn ro £ <D • 3 w . c o B I L U C O •5* — LL O > CD O) (-n C fc r <"> E ||CN CD CD CO CO CO icrir 00 CN CO HO CN d 'CO S| CD If) • CN CN |CN CD CN 00 o '|d|< If) CO |CN CO CN i n co -^o 00 CN CD |CN co [co co iri co CD if) i d LO i d LO I d o CN CD CO (O 2> E b O) o • 7= CJ E M ; b w "O CO CD £0 -CD -b • Q . C O ! O CN O i CD ' o f CO TD I CU O i L T J ^ CD -C E c ro C D Q -x: C CL Jg CD^ UU CO CD U I C CN CD CO ci CM CN o CN CO CO CO ICN CN ' CD CO CO CN C D : 67 69 70 3.5 Summary Using the feed-back controlled system, the post-cracking behavior of SMFRM under uniaxial tension is observed and studied. Pseudo-strain hardening occurs when 1 % or more stainless steel fibers are added. With an increase in the fiber volume fraction, the tensile strength, toughness, elastic modules and the strain capacity of SMFRM increase, while the workability of the fresh steel micro-fiber mortar decreases. Fiber length affects the tensile strength and toughness of SMFRM. For a given fiber volume fraction, specimens with 6 mm (close to the average critical length) fibers gave the highest strength, followed by those wi th 4 mm fibers and 10 mm fibers. When fiber volume fraction is small (e.g. 1 % ) , specimens with 6 mm fibers also gave the highest toughness, followed by those with 4 mm fibers and 10 mm fibers. However, at a higher fiber volume fraction (e.g. 2%), specimens with 6 mm fibers gave the lowest toughness, and those with 10 mm fibers gave the highest toughness. Although at a high volume fraction (2%), specimens with 10 mm fibers appear to be more ductile, in the fresh state, the long fibers tend to ball and the workability is poor. The best fiber length from this study, therefore, is 4 mm long. Steel micro-fiber mortars with 2% or 3% of 4 mm stainless steel fibers gave a relatively high tensile strength and toughness 71 and acceptable workability. At addition rate of 5%, although the tensile strength are higher, the increase is not proportional to the fiber volume fraction. A 2% fiber composite with 4 mm fiber appears to be the optimum composite in the end. 72 4. Properties of Steel Micro-Fiber Reinforced Mortar in Flexure 4.1 Introduction The feed-back controlled uniaxial tensile test used in the previous section yielded valuable fundamental data for SMFRM. However, these tests are too complicated and time consuming to be used in the projects involving large number of specimens. Flexural tests, on the other hand, are easily conducted. In this section, data from about 250 specimens with different fiber cross-sectional areas, fiber lengths, fiber volume fractions and sand contents, and polymer contents tested under flexure are described. To prevent the specimens from an unstable sudden failure after the peak load, a crack opening controlled system was employed. 4.2 Literature Review and Research Significance Flexural testing is conducted usually in four point, or, sometimes, in three point loading configuration. Different sizes of specimens and various testing spans are used for different applications. The load deflection curves, which provide useful information on fiber reinforced cementitious 73 composites, are then analyzed for material properties. [1, 8, 15, 44, 45, 47]. Flexural test on micro-fiber reinforced cementitious composites with different type of fibers (carbon fiber, steel fiber, polymer fiber, etc.) have indicated that the tensile and flexural properties of micro-fiber reinforced cementitious composites are significantly superior than the parent matrix. Comparatively, carbon fibers bring about a better improvement in the toughness or energy absorption than steel fibers. Steel fibers, on the other hand, impart higher tensile strengths to the base cement matrices than carbon fibers. Studies also indicated that regardless of the type of micro-fiber used, the strength and toughness of the composites increase wi th an increase in the fiber volume fraction [8, 44, 47]. However, the influences of fiber length, fiber cross-sectional area, and the changes in the matrix mix proportions is not clearly understood. In the experiments of the previous section, only the influence of fiber length was considered. In this section, the influence of fiber type and fiber cross-sectional area will also be investigated using flexural tests. 74 4.3 Experimental Work 4.3.1 Materials Matrix Three types of matrices, in which sand and polymer contents were varied, were used in this study. Table 4.1 reports the mix proportions of these matrices. Table 4.1 Mix Proportion of the Matrices Matrix Type W/C S/C S.F./C S.P. (ml/100 g C.) P/C D/P M1 0.35 1 0.1 1-3 M2 0.35 0.5 0.1 1-3 M3 0.35 1 0.1 1 0.1 0.1 N o t e s : C: C e m e n t ; S: S a n d ; S.F: Sil ica Fume; S.P.: Superp last ic izer ; P: Po lymer ; D: D e f o r m e r . Properties of cement, superplasticizer and sand used here are the same as those used in the specimens for the uniaxial tensile tests. Dry acrylic polymer was used as the polymer additive. To help the acrylic polymer powder to spread out in the cement paste and to reduce the entrapped air, 10% (by weight of polymer) of deformer (Foamblast 390) was added. Steel Micro-Fibers High carbon content steel fibers were used. The fibers had irregular cross-sectional shapes (Figure 2.2). Four different cross-sectional areas of fibers, classified as 'S ' , ' M ' , 'L ' and 'T ' fibers, were used in this study. The cross-sectional areas, which were measured from micrographs, are given in Table 4.2. The tensile strengths and the critical lengths of the fibers, obtained by using the pull-out test, are shown in Table 4.3. Table 4.2 Cross-Sectional Areas of the Fibers Fiber Type* Cross-Sectional Area (mm X mm) S 0.0007 M 0.0013 L 0.0020 T 0.0044 N o t e : * S: Sma l l ; M : M e d i u m ; L: Large; T: Th i ck Table 4.3 Critical Length and Tensile Strength of the Fibers Fiber Type Critical Length Tensile Strength (mm) (MPa) S 2 M 3 1000 L 4 T 6 Fibers were cut to 2 mm, 4 mm and 10 mm in length. For fiber 'T, all three lengths of fibers were cut by the manufacture. For fibers 'S ' , ' M ' and 'L ' , 4 mm and 10 mm fibers were cut in the laboratory and 2 mm fiber was cut by the manufacturer. The fiber length distributions are given in Figure 4.1 (a) and (b). It is clearly noticeable that fibers cut in the laboratory have different length distributions from those cut by the manufacturer. For example, although they were all called '4 mm fiber', the lengths of most 76 laboratory cut fibers range from 4 to 6 mm, while those cut by manufacturer range from 2 to 4 mm. 4.3.2 Specimen Preparation The shape and the dimension of the specimens are shown in Figure 4.2. The specimens were cast and cured using the following procedure: Mix cement, sand, silica fume, polymer and deformer (if used) in the mixer. Add water and a small quantity of superplasticizer. Mix for two minutes. Add more superplasticizer to make the mixture flowable and record the total quantity of superplasticizer used. Introduce the fibers slowly and evenly into the mixture while the mixer is mixing. Mix for another two minutes and then pour the mixture into the molds. Vibrate to compact the mixture in the molds. Cure in the moist condition and room temperature for one day. Demold and then cure in water for another twenty seven days before testing. For those specimens containing polymer or large quantities of the superplasticizer, one additional curing day was needed before demolding because of their slow hardening. 78 79 4.3.3 Test Plan Fifty-five separate sets, with four specimens each, were tested. The test program is shown in Table 4.4. Table 4.4 Test Variables Investigated Fiber Length (mm) Matrix Type Fiber Type Fiber Volume Fraction (%) 2 M1 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 T 0, 1, 2, 5 M2 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 T 0, 1, 2, 5 M3 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 4 M1 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 T 0, 1, 2 M2 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 T 0, 1, 2 M3 S 0, 1, 2 M 0, 1, 2 L 0, 1, 2 10 M1 L 0, 1 T 0, 1, 2 M2 L 0, 1 T 0, 1, 2 Figure 4.3 Test Set-Up of Flexural Tests 82 83 4.3.4 Test Set-Up The four-point flexural test set-up is shown in Figures 4.3 and 4.4. The load applied was measured by a load-cell which had a capacity of 1600 N. The deflection of the beam was measured by an LVDT (LVDT 1) installed on the top of the beam at the mid-span. The movement of the machine cross-head was controlled by the crack opening on the tensile side of the beam through another LVDT ( LVDT 2). Crack-opening rates of 0.2 L i m / sec before the peak load and 2 Lim /sec after the peak load were used. Both LVDTs had a sensitivity of 75.5 mv/mm. The applied load, deflection and crack opening were recorded by both a system for data acquisition and an X-Y plotter. A FORTRAN computer program was written and used to analyze the data (Appendix 3). 4.4 Test Results and Discussion 4.4.1 Workability of the Mixtures 4.4.1.1 Effects of Fiber Length, Fiber Volume Fraction and Fiber Cross-Sectional Area As observed in the previous section, fiber length and fiber volume fractions affect the workability of steel micro-fiber mortar mixture significantly. Fiber thickness also affects the workability. Table 4.5 reports the workability of mixtures with different fiber lengths, fiber volume fraction and fiber cross-sectional areas. Table 4.5 Workability of SMFRM Mixtures Fiber Fiber Fiber Quantity of workability Maximum Type Length Volume S.P. Fiber (mm) Fraction (ml/100 g C. Volume (%) Fraction S 2 1 1.0 A > 2 % 2 1.5 A 4 1 2.0 B 1 % 2 3.0 C M 2 1 1.0 A > 2 % 2 1.5 A 4 1 2.0 B 1 % 2 3.0 C L 2 1 1.0 A > 2 % 2 1.5 A 4 1 1.8 A 2 % 2 2.5 B 10 1 3.0 D < 1 % T 2 1 1.0 A > 5 % 2 1.2 A 5 2.0 A 4 1 1.0 A > 2 % 2 1.5 A 10 1 2.0 B 1 % 2 3.0 D N o t e s : A : ve ry g o o d w o r k a b i l i t y ; B: w o r k a b l e , f iber bal l ing; C: r o u g h , hard t o handle ; D: very r o u g h , very hard t o handle . 4.4.1.2 Effects of Sand Content and Polymer Addition The sand content had no apparent effects on the workability. The addition of polymer made the mixture soft and sticky. For a given f low, mixtures with the polymer needed less superplasticizer. 85 4.4.2 Flexural Properties o f SMFRM The test results are shown in Table 4.6 (a), (b) and (c) and Figures 4 . 5 - 4 . 1 7 . 4.4.2.1 Effects of Fiber Volume Fraction Figures 4.5 and 4.6 show typical load versus deflection plots for cement mortars reinforced with various volume fractions of steel fibers. It is clear that there are significant improvements both in the load carrying capacity and toughness with an increase in the fiber volume fraction. At high fiber volume fractions (5 %) , the load-deflection curves show significant strain hardening and toughness can be fourteen times higher than that of cement mortar without steel fibers (Table 4.6 (a) and Figure 4.13). 4.4.2.2 Effects of Fiber Length Figures 4.7 and 4.8 show the load-deflection curves of SMFRM with different fiber lengths. It can be noted that when fiber cross-sectional areas are different, the effects of fiber length are also different. For example, for the type 'T ' fiber, the specimens with 2 mm fibers gave the highest strength, but the load dropped quickly after the peak load and the lowest toughness was recorded. On the other hand, specimens with 10 mm fibers gave the lowest strength but also the highest toughness. The strength and toughness of composites with 4 mm fibers are between those with 2 mm and 10 mm fibers. Figure 4.13 demonstrates the changes in strength and 86 t o u g h n e s s o f S M F R M w h e n d i f f e r e n t l e n g t h s a n d v o l u m e f r a c t i o n s o f T ' f i b e r a re a d d e d . For t h e o t h e r t y p e s o f f i b e r s (S , M a n d L) , t h e s p e c i m e n s w i t h 2 m m f i b e r s o n c e a g a i n y i e l d e d t h e h i g h e s t s t r e n g t h , b u t n o c l e a r i n f l u e n c e o f f i b e r l e n g t h o n t o u g h n e s s b e c a m e a p p a r e n t . W h e n t h e s e r e s u l t s a re c o m p a r e d w i t h t h e r e s u l t s f r o m t h e p r e v i o u s s e c t i o n ( u n i a x i a l t e n s i o n ) , o n e c a n see t h a t t h e e f f e c t s o f f i b e r l e n g t h o n t h e s t r e n g t h a n d t o u g h n e s s d o n o t a l w a y s f o l l o w t h e s a m e t r e n d in f l e x u r e a n d t e n s i o n . In t h e p r e v i o u s s e c t i o n , it w a s f o u n d t h a t 6 m m ( c l o s e t o t h e c r i t i c a l l e n g t h ) g a v e t h e h i g h e s t s t r e n g t h b u t t h e i n f l u e n c e o f f i b e r l e n g t h o n t o u g h n e s s v a r i e d w i t h t h e f i b e r v o l u m e f r a c t i o n . It s h o u l d be r e c o g n i z e d , h o w e v e r , t h a t s t a i n l e s s s t e e l f i b e r s w i t h d i f f e r e n t s u r f a c e c h a r a c t e r i s t i c s w e r e i n v e s t i g a t e d in t h e p r e v i o u s s e c t i o n as o p p o s e d t o t h e c a r b o n , s t e e l f i b e r s o f t h i s s e c t i o n . 4 . 4 . 2 . 3 E f f e c t s o f F iber C r o s s - S e c t i o n a l A r e a F i g u r e s 4 . 9 a n d 4 . 1 0 s h o w t h e l o a d - d e f l e c t i o n c u r v e s f o r S M F R M w i t h d i f f e r e n t f i b e r c r o s s - s e c t i o n a l a r e a s . F i g u r e 4 . 1 4 s h o w s t h e e f f e c t s o f f i b e r c r o s s - s e c t i o n a l a rea o n t h e f l e x u r a l s t r e n g t h a n d t o u g h n e s s o f S M F R M f o r t h e 2 m m f i b e r . I t c a n b e n o t e d t h a t w i t h a n i n c r e a s e in t h e f i b e r c r o s s -s e c t i o n a l a r e a , t h e t o u g h n e s s o f S M F R M i n c r e a s e s e v e n t h o u g h t h e s t r e n g t h d o e s n o t f o l l o w t h e s a m e t r e n d . T h e h i g h e r t o u g h n e s s f o r S M F R M w i t h t h i c k f i b e r s c a n b e e x p l a i n e d as t h e f o l l o w s : A f t e r t h e p e a k l o a d , t h e l o a d s t a r t s 87 to drop and fibers are either pulled-out or fractured. For a given fiber length, the thicker fiber pulls out while the thinner fiber fractures. The process of pull-out consumes more energy than that of fracture, and thus higher toughness is expected. The somewhat reduced strength of the thicker fiber 'J' (Figure 4.14) is also related to the lack of fiber fractures in their case; fracture requiring a higher load than that of pull-out. 4 .4.2.4 Effects of Matrix Properties Figures 4.11 and 4.12 show the load-deflection curves for SMFRM with different matrices (Table 4.1). Figure 4.15 shows the influence of matrix type on the strength and toughness of SMFRM. With an increase in sand content in matrix (M1: S/C = 1; M2: S/C = 0.5), the elastic strength, as well as the ultimate strength of SMFRM was found to increase. The reason apparently is that a mix with a higher sand content would be more stable and undergo less shrinkage cracking. Also with an increase in the sand content, more water gets absorbed by the sand and consequently, the W/C of the mortar is reduced and a higher strength is recorded. The effect of sand content on the toughness of SMFRM, on the other hand, is not clear. As expected, the addition of polymer (Matrix: M3) improved the toughness of SMFRM significantly. The addition of polymer, however, does not appear to have a clear effect on the strength. 88 The compressive strengths of the various composites are reported in Table 4.6 (a), (b) and (c) and Figure 4.16. Data suggest that the obtained compressive strength are much higher than generally reported for fiber reinforced cementitious composites [42, 45] . The primary reason is the small size of the specimens (25 mm X 25 mm X25 mm) and also the lateral confinement by the loading plates. It can also be noticed that the compressive strength of SMFRM increases with an increase in the fiber volume fraction. The data of crack-opening were also acquired during these tests. Figure 4.17 shows a typical deflection-crack opening curve, which shows t w o straight lines with different slopes separated by the point of first crack in the matrix. The noted linear relation between the deflection and the crack opening confirms the stability of the tests. Figure 4.18 shows a load-crack opening curve. Analysis of the properties of the steel micro-fiber reinforced mortar from fracture mechanics perspective is being conducted using these data , but is out of the scope of this thesis. 89 > co £ tn O ) o CD Q_ CO CN CO ^1 CN 00 i i r i cn CO o co CD 00 1 CD CD O LO LO CD CD LO CD CO led 00 E _ 3 o X CD CD Q E E CN CNl CN CO co CD •<r CN O CO csi CN d o LO o L O CO i cvii -<r o CN CD CD CN CN CN 00 Icsi E CD =J ^. c ^ E ( j c E x <D E CD O -5 O oo CN CD CO LO CD CO 00 CO CD d CO 00 | L O CO CD LO LO CD LO tn " O 3 § u ° Q ro E E CD CN CD CN 00 CO CN LO L O oo 00 00 CD CN I co I CO d co CN CO o 00 E E CN c CD CD tn CO 0 tn CD H ro i _ 13 X CD ro^ CD 0) x i ro o « ro c ^ ^ ° c O CL CL ~— o oo CD o CD CD o CO CD L O o o 00 o o CD O o CO o LO cn o d CO CO CD c CD O E E CO 00 X— ro io CD 00 CD CO CD csi lO CN CD ^ I d o io CD CD LO CD O O C O OO 00 •<r CO CD CO co CD ICN o 3 to 3 ro "o L 7 J £ ro o_ O CN CO CD d CN CO 00 I CO CO 00 CO | L O | CD CN Is-hr CO CN loo CN CN Is-d CN LO CN CD I I s-d CN LO CN ro cn ro . b CD ^ 5 co CN CO CN LO CD o Is-00 CD l^r CD LO I I s-Is-I s-lr-1 LO I CD LO 00 ed! LO CN •^Z CD CO C ro CD CD CL-I O CNlO ;LO oo' o IIs-CO LO 00 co CD CD LO o Is-Is-o LO CN d CO CN CD _ IS CN CN CN CN LO CN CN CN CN LO CN CN CN CD CD L L I— X ' i _ -#-« CD CO CO CO CO LLI 2 O CO CO CN 00 Compressive Strength (MPa) 59.29 82.74 118.59 70.33 106.87 118.59 126.17 122.73 130.31 102.73 82.05 84.12 61.36 84.81 123.42 129.62 126.17 121.35 93.08 103.42 85.49 100.66 111.7 = 71.71 115.14 Maximum Deflect (mm) 0.311 CN LO CD O CD o CD CM CM CO \r o LO LO 2.274 2.134 2.320 0.467 CO CO o r-00 CD CD T— CO N -CD CO r--LO cn 2.164 2.212 0.472 2.045 2.379 1.071 2.080 1.626 2.300 Maximum Crack Opening (mm) 0.193 0.383 1.254 0.617 1.114 1.275 1.368 1.512 1.443 0.275 0.708 1.047 0.971 1.015 1.151 1.264 1.346 1.356 0.364 1.247 1.599 0.751 1.841 0.977 1.292 Deflects at P-load (mm) 0.204 0.249 0.220 0.232 0.270 0.210 0.289 0.273 0.292 0.185 0.306 0.391 0.320 0.180 0.257 0.324 0.178 0.264 0.247 0.340 0.493 0.307 0.336 0.287 0.362 Crack Opens at P-load (mm) 0.056 0.084 0.080 0.078 0.084 0.074 0.092 0.073 0.120 0.055 0.082 0.111 0.072 0.078 0.094 0.124 0.049 0.089 0.071 0.104 0.155 0.088 0.107 0.106 0.112 Toughness (N-mm) 29.06 78.63 108.73 50.17 136.67 88.80 156.36 154.28 255.04 27.84 74.66 144.59 73.39 103.75 107.23 155.32 123.82 263.29 42.11 123.61 212.42 93.97 166.74 99.24 I 242.30 Elastic Modulus (GPa) 27.16 22.56 25.86 24.50 25.27 35.77 28.20 22.65 27.23 23.13 19.38 17.66 20.43 36.59 23.68 23.28 23.59 28.86 22.10 18.98 15.09 21.92 27.42 16.91 21.09 Ultimate Strength (MPa) 7.03 6.91 7.16-6.30 7.41 8.20 8.45 8.12 7.14 5.11 7.19 7.81 6.19 6.67 4.36 8.11 5.08 8.11 6.46 6.85 7.40 7.70 8.64 5.08 7.40 Elastic Strength (MPa) 7.01 6.83 7.09 6.21 7.06 8.04 8.40 7.98 6.60 5.10 6.70 7.73 6.13 6.51 4.22 7.49 5.04 7.95 6.42 6.78 6.81 7.55 8.50 4.88 7.24 ® _^ _ Q O V O LL ^ ^ o CM CM - CM - CM o CM CM - CM - CN o x — CM - CN - CM Fibre Type NONE CO CO _ i _ l h-NONE CO 00 _ l h- h-NONE CO CO _ i _1 Matrix i M2 M3 E E o CO c CD CD X 3 3 CO CD cc "co CD h-"co 1 X 03 U_ CO _<D co I— CD > £ °> CD C Q . 2 o 91 CO 0_ E ^ E a> x a5 <2 Q E E E F ° .E ro co O co c — c E CD p CL 3 o TJlo "5 o-E E Q co o w co cr 0 3 £ ° 1= i— CD - r £ O a i -O to to CD c CO o h-E E o 3 CO ED £ CO D_ O CD SZ CVJ CD . i g 5 co CO CL 4= CO co c _C0 0 co CD _ CD CD .-9 £ LL h-cn CM cn CD llO o CO CO I LO CO I I s -CN O LO CM CO I o LO "3-CN CO CD CD CO CD CO |CM CO CM Is-LO in CM I CM CO LO CO CM CO CD CD co LO CM d CD o CD d l CM CO CO LO o CM CM CD CD IO CO CO o CO CM CD LO o o CD LO LO O m CD o CD LO o CD CD CD O CD CM CD CO d CM o | CM LO CO 00 CO loo CM co I CO o CO LO LO I CM CD CO CD | CM d CM CN loo ] CO CM CM T— CM | CO CM CM co o o CO o CN LO d co CO d io co cd o CO 1^ M Is-LO I I d LO Is-|LO d CO CD I S -o CM CM LU Z o i -ILU z o z I- H CN 92 93 o o o o o o o o o o o o o CO 10 ^fr CO CM i -94 95 E E E E CM , £ B); C C i 0 a) ; k_ k. 1 0 0 n n L O cvi 1 - 0 CO •• © w ' 0 c S ft 3 ft ^ o i _ »— i _ o fo 0 .•9 c -Q CM L O ? 8 ° L O E E, c g 0 "D L L 0 £ 1 a, o | 8 o I* 3% CO • o U) mmam L L 96 LO c\i GO u cu XI I P cu XI cu XI CD XI E E = £ C M 0 O) : 9-c O & co co "cS CM LO E E, c g o Q) «+— CD TJ LO d •g o O LO (0 (0 0) < § o o (!) CO o O n |E o § 5: 0 Q Q • O p -re? • 0 3 U) o o o o CO o o CM o o 97 LO cvi 98 L O 99 100 101 LO c\i CO T -102 103 104 E E, c o ' o a CJ) c "c CD Q_ o o CO O c o t) CD CO CD CD 7= Q 2 co 2 CD CJ) c ' c 0) C L o o ca o o CD 2. CD > 1 ^ E #8 E CD O £ c c 'co o CO | 2 *- CD CD SZ sz +- CD CD X I CD CO £3 105 106 4.5 Summary The experiments in this section provide fundamental information of the behavior of SMFRM in flexure. The following remarks can be made: The flexural strength, toughness and compressive strength of SMFRM increase with an increase in the fiber volume fraction. For the largest diameter fiber, fiber 'T ' , the SMFRM specimens wi th shorter fibers gave a higher strength but usually depicted lower toughness as compared to the longer fibers. For the other fibers (fiber 'S ' , ' M ' , ), SMFRM with shorter fibers again gave higher strength but the influences of fiber length on the toughness was not significant. With an increase in the fiber cross-sectional area, the toughness of SMFRM increases, but strength does not follow a similar trend. With an increase in the content of sand in the matrix, both the elastic and the ultimate strength of SMFRM increase. The effect of sand content on the toughness, however, is not clear. The addition of polymer to the matrix improves the toughness of SMFRM significantly. The influence on strength, however, is not clear. Addition of 1 % of 2 mm and 4 mm steel micro-fibers by volume fraction may improve the strength and toughness of SMFRM to some 107 degree, but the composites essentially stays brittle, particularly when the fibers are small in diameter. With 1 % of 10 mm steel micro-fiber, both the strength and toughness of the SMFRM are increased significantly. From these tests, one can conclude that for SMFRM, longer and thicker fibers provides better mechanical properties. The workability of the mixture, however, is very bad for the 10 mm fiber, particularly when fiber diameter is small. The mixture with 10 mm type 'L ' fibers is highly unworkable even at 1 % by volume fraction of fibers. The best fiber from these tests is the thickest (type 'T') fiber. The mechanical properties of the SMFRM may be improved significantly and the workability of the mixture is adequate with 1-2% of 'T ' fibers which are less than 10 mm in length. The mixtures with 2 mm and 4 mm fibers have good workability even at 5% fibers by volume fraction. The mechanical properties of the resulting SMFRM are also significantly superior to the plain matrix. 5. Conclusions 108 This thesis investigated the behavior of steel micro-fiber reinforced cementitious composites. Three aspects were examined: (1) the behavior of the interface between a steel micro-fiber and the surrounding cementitious matrix; (2) the tensile behavior of the composite; and (3) the flexural behavior of the composite. Routine tests in compression were also carried out. Based on the single fiber pull-out tests conducted to characterize the fiber-matrix interface, the following conclusions can be drawn: (1) The peak loads supported by fibers that are aligned in the direction of loading are higher than those supported by fibers inclined wi th respect to the loading direction. The peak load for an aligned fiber also occurs at a smaller slip than for a inclined fiber. (2) Even from an energy absorption point of view, a fiber aligned wi th respect to the loading direction absorbs a greater amount of energy than one that is inclined. A O 0 inclination with respect to the loading direction, therefore, is the optimal direction. (3) The ultimate bond strength between the stainless steel fiber and cement paste varies from 4.7 MPa to 7.1 MPa. The tensile strength of the steel micro-fibers used is in the range of 750-1200 MPa. 109 (4) An increase in the content of silica fume in the matrix increases both the average interfacial bond strength and the maximum interfacial bond strength. Based on the feed back controlled uniaxial tensile tests aimed at studding the tensile properties of stainless steel micro-fiber reinforced mortar, the following conclusions were drawn: (1) With an increase in the fiber volume fraction, the tensile strength, toughness, elastic modules and the strain capacity of the steel micro fiber reinforced mortar (SMFRM) are found to increase. When the fiber volume fraction is 1 % or higher, pseudo strain-hardening is noted in the tensile stress-strain curves. (2) Fiber length has a significant influence on the tensile strength and toughness of SMFRM. For a given fiber volume fraction, specimens wi th 6 mm (close to the average critical length) fiber gave the highest strength followed by those with the 4 mm fiber and then those with 10 mm fiber. Specimens wi th the 10 mm fiber demonstrated the highest toughness followed by those with the 4 mm and the 6 mm fibers at 2% fiber volume fraction. (3) Although an increase in the fiber volume fraction and the fiber length improves the ductility of SMFRM, high fiber volume fractions and 110 high fiber lengths lead to poor workability in the fresh state. The optimum fiber length, therefore, is 4 mm. By using the 4 mm fiber, while up to 2-3% of fibers can be added to cement mortar to achieve high tensile strength and toughness as well as adequate workability, the optimum properties are obtained at 2% of fiber by volume. Based on the four-point flexural tests performed using a crack opening controlled system, carbon steel micro-fiber reinforced mortars were investigated and the following conclusions were drawn: (1) The flexural strength, toughness, tensile strain capacity and compressive strength of the composite increase with an increase in the fiber volume fraction. (2) With an increase in the fiber cross-sectional area, although the flexural strength is generally not affected, the toughness of the composite is found to increase. (3) For the thickest fiber 'T'(cross-sectional area 0.0044 mm 2), longer fibers gave higher toughness but usually lower flexural strengths as compared to the shorter fibers. (4) With an increase in the sand content in the matrix, the flexural strength of SMFRM increases. The effects of sand content on the toughness of SMFRM, however, are not clear. The addition of polymer in cement I l l mortar improves the toughness of SMFRM significantly, even though a similar influence on flexural strength was not observed. (5) High fiber volume fractions and long fibers make the workability of fresh steel micro-fiber mortar unacceptable. However, with a 2 mm fiber, the mixture has very good workability even at 5% of fibers by volume. The flexural properties of the cement mortars are improved considerably by adding 5% of type 'J' fiber with a length of 2 mm. Closure To sum up, the addition of both stainless steel micro-fiber and carbon steel micro-fiber can improve the ductility of cement mortars significantly. The carbon steel micro-fibers, however, have more practical importance because of their low cost. The effects of fiber length on strength and toughness of SMFRM are different in uniaxial tensile tests than in flexural tests. Partly, this is because different type of fibers and fiber cross-sectional areas were used in these two tests. For the stainless steel micro-fiber reinforced composites, those wi th 2 % of the 4 mm fiber gave the best combination of properties. For the carbon steel micro-fiber, if fiber volume fractions are limited to 2% from economical considerations, the thickest fiber ('T' fiber) with 4 mm length is the best choice. However, when the 2 mm 'T ' fiber is used, fibers can be added up to 5% or more by volume without workability problem. The 112 properties of SMFRM at such a high fiber volume fractions are improved dramatically. 113 Bibliography 1. Bentur A.and Mindess S., Fiber Reinforced Cementitious Composites. Elsevier Applied Science, London and New York, 1991. 2. Hull D., An Introduction to Composite Materials. Cambridge University Press, 1981 . 3. Shah S. P. and Ouyang C , Mechanical Behavior of Fiber-Reinforced Cement-Based Composites. J. Am. Ceram. Soc, 74, 1991 , pp.2727-2753. 4. Banthia N., A Study of Some Factors Affecting the Fiber-Matrix Bond in Steel Fiber Reinforced Concrete. Can. J. of Civil Engineering, Vol .17, No. 4, 1990, pp.610-620. 5. Banthia N. and Trottier J. F., Concrete Reinforced With Deformed Steel Fibers, Part I: Bond-Slip Mechanisms. ACI Materials Journal, September-October, 1992, pp. 435-446. 6. Banthia N., Trottier J . F., and Pigeon M., Fiber Pull Out Mechanisms: Effects of Fiber Geometry, Loading Rate and Sub-zero Temperatures. In Swamy R. N. and Barr B. ed. Fiber Reinforced Cement and Concrete: Recent Developments, 1989, pp. 136-145. 7. Banthia N. and Mani M., Toughness Indices of Steel Fiber Reinforced Concrete at Sub-zero Temperatures. Cement and Concrete Research, Vol. 23, 1993, pp. 863-873. 8. Banthia N. and Sheng J . , Strength and Toughness of Cement Mortars Reinforced with Micro-Fibers of Carbon, Steel and Polypropylene. In Mindess S. ed. Proceedings: The Second Canadian Symposium on Cement and Concrete, 1991 , pp. 75-83. 9. Wei S., Mandel J . A. and Said S., Study of the Interface Strength in Steel Fiber-Reinforced Cement-based Composites. ACI Journal, July- August, 1986, pp. 597-605. 10. Krishnadev M. R., Berrada S., Banthia N. and Trottier J . F., Deformed Steel Fiber Pull-out Mechanics: Influence of Steel Properties. In Swamy R. 114 N. ed. Fiber Reinforced Cement and Concrete, Proceedings of the Forth International Symposium Held by RILEM . E&FN SPON, NewYork, 1992, pp. 390-399. 1 1 . Chanvillard G., Energy Dissipetion during Steel Fiber Pull-out. In Swamy R. N. ed. Fiber Reinforced Cement and Concrete, Proceedings of the Forth International Symposium Held by RILEM. E&FN SPON, NewYork, 1992, pp. 380-389. 12. Mandel J . A., Wei S and Said S., Studies of the Properties of the Fiber-Matrix Interface in Steel Fiber Reinforced Mortar. AC/ Materials Journal, March-April, 1987, pp. 101-109. 13. Naaman A. E. and Najm H., Bond-slip Mechanisms of Steel Fibers in Concrete. AC/ Materials Journal, March-April 1991, pp. 135-145. 14. Lawrence P., Some Theoretical Considerations of Fiber Pull-Out from an Elastic Matrix. Journal of Material Science, 7(1972), pp. 1-6. 15. Banthia N. and Mani M., Toughness Indices of Steel Fiber Reinforced Concrete at Low Temperatures, Low Temperature Effects on Concrete. Proceedings Second Canada/ Japan Workshop, August 1-2, 1991 , Ottawa. 16. Greszuk L.B., Theoretical Studies of the Mechanics of the Fiber-Matrix Interface in Composites. Interfaces in Composites (ASTM), 1968, pp. 43-57. 17. Cooper G.A. and Kelly A., Role of the Interface in the Fracture of Fiber-Composite Materials. Interfaces in Composites (ASTM), 1968, pp. 91-105. 18. Morton J. and Groves G. W., The Cracking of Composites Consisting of Discontinuous Ductile Fibers in a Brittle Matrix-Effect of Fiber Orientation. Journal of Material Science, 9(1974), pp. 1436-1445. 19. Naaman A.E. and Najm H., Bond-Slip Mechanisms of Steel Fibers in Concrete. AC/ Materials Journal, March-April 1991, pp. 135-144. 20. Li Z., Characterization of Interfacial Properties in Fiber-Reinforced Cementitious Composites. J. Am. Ceram. Soc, 74 , pp. 2156-64. 2 1 . Leung C. K. Y. and Geng Y., Effect of Lateral Stress on the Debonding and Pull-out of Steel Fibers in a Cementitious Matrix, Unpublished Manuscript. 115 22. Naaman A. E. and Shah S. P., Pull-Out Mechanism in Steel-Fiber Reinforced Concrete. J. Struct. Eng., 102 [ST8], 1976, pp. 1439-1445. 23. Li V. C , Wong Y. and Backer S., Effect of Inclining Angle, Bundling and Surface Treatment on Synthetic Fiber Pull-Out from a Cement Matrix. Composites, 21 [2], 1990, pp. 132-140. 24. Bartos P., Bond in Glass Reinforced Cement. In Bartos P. ed. Bond in Concrete, Applied Science Publishers, London, U.K., 1982, pp. 60-72. 25. Banthia N., Moncef A. and Sheng J . , Uni-Axial Tension Response of Cement Composites Reinforced with High Volume Fraction of Carbon, Steel and Polypropylene Micro-Fibers. Can. J. Eng., 2 1 , 1994, pp. 999-1011 . 26. Li V.C. and Obla K. H., Effect of Fiber Length Variation on Tensile Properties of Carbon Fiber Cement Composites, Unpublished Manuscript. 27. Dept. of Civil Eng., UBC, Tension Test of Brittle Material, Class Notes for 'Civil Engineering Material I (Civil 220) ' (Banthia N. Ed.), 1993. 28. Naaman A. E. and Homrich J. R., Tensile Stress-Strain Properties of SIFCON. ACI Materials Journal, May-June 1989, pp. 244-251 . 29. Shah S. P., Do Fibers Increase the Tensile Strength of Cement-Based Matrixes?. ACI Materials Journal, November-December 1991 , pp. 595-602. 30. Akihama S., Suenaga T and Nakagawa H., Carbon Fiber Reinforced Concrete. Concrete International, January 1988, pp. 40-47. 3 1 . Tjiptobroto P. and Hansen W., Tensile Strain Hardening and Multiple Cracking in High-Performance Cement-Based Composites Containing Discontinuous Fibers. ACI Materials Journal, January-February 1993, pp. 16-25. 32. Tjiptobroto P. and Hansen W., Model for Predicting the Elastic Strain of Fiber Reinforced Composites Containing High Volume Fractions of Fibers. ACI Materials Journal, March-April 1993, pp. 134-142. 33. Soroushian P., Choi K. B. and Fu G., Tensile Strength of Concrete at Different Strain Rates, In Mindess S. and Shah S. P. ed. Cement-Based Composites: Strain Rate Effects on Fracture, 1986, pp. 87-92. 34. Nammur G. G. and Naaman A. E., Strain Rate Effects on Tensile Properties of Fiber Reinforced Concrete. In Mindess S. and Shah S. P. ed. 116 Cement-Based Composites: Strain Rate Effects on Fracture, 1986, pp. 97-117. 35. Wang Y., Li V. C. and Backer S., Experimental Determination of Tensile Behavior of Fiber Reinforced Concrete. AC/ Materials Journal, September-October 1990, pp. 461-468. 36. Luong M. P., Liu H., Trinh J. L. and Tran T. P., Tensile Properties of Steel Fiber Reinforced Concrete. In Swamy R. N. ed. Fiber Reinforced Cement and Concrete, Proceedings of the Forth International Symposium Held by RILEM, 1992, pp. 343-354. 37. Nanni A., Splitting-Tension Test for Fiber Reinforced Concrete. AC/ Materials Journal, July-August 1988, pp. 229-233. 38. Li V. C , Chan C. M. and Leung C. K. Y., Experimental Determination of the Tension-Softening Relations for Cementitious Composites. Cement and Concrete Research, Vol. 17, pp. 441-452. 39. Li V. C , Postcrack Scaling Relations for Fiber Reinforced Cementitious Composites. Journal of Materials in Civil Engineering, February, 1992, pp. 41-57. 40. Soroushian P. and Baysi Z., Fiber-Type Effects on the Performance of Steel Fiber Reinforced Concrete. AC/ Materials Journal, March-April, 1991 , pp. 129-134. 4 1 . Wafa F. F. and Ashour S.A., Mechanical Properties of High-Strength Fiber Reinforced Concrete. ACI Materials Journal, September-October, 1992, pp. 449- 454. 42. Soroushian P., Khan A. and Hsu J. W., Mechanical Properties of Concrete Materials Reinforced with Polypropylene or Polyethylene Fibers. AC/ Materials Journal, November-December, 1992, pp. 535-640. 43. Brandt A. M., On the Optimal Direction of Short Metal Fibers in Brittle Matrix Composites. J. of Material Science, 20 (1985), pp. 3831-41 . 44. Banthia N. and Sheng J. , Micro-Reinforced Cementitious Materials. Mat. Res. Soc. Symp. Proc. Vol. 2 1 1 , 1991, pp. 25-32. 45. Akihama S., Suenaga T. and Banno T., Mechanical Properties of Carbon Fiber Reinforced Cement Composites. The International Journal of Cement Composites and Lightweight Concrete, Vol. 8, February, 1986, pp. 21-32. 117 46. Banthia N. and Dubeau S., Carbon and Steel Micro-fiber-Reinforced Cement-Based Composites for Thin Repairs. Journal of Material in Civil Engineering, February, 1994, pp. 88-98. 47. Shivaraj S.K., Ramakrishnan V. and Wu G. Y., Properties and Flexural Performance of Steel Fiber Reinforced Refractory Concrete. In Swamy R.N. and Barr B. ed. Fiber Reinforced Cement and Concrete: Recent Developments, 1989, pp. 499-512. 48. Mobasher B., Stang H. and Shah S. P., Micro-Cracking in Fiber Reinforced Concrete. Cement and Concrete Research, Vol. 20, 1990, pp. 665-676. 49. Visalvanich K. and Naaman A.E., Fracture Model for Fiber Reinforced Concrete. AC/ Journal, March-April, 1983, pp. 128-138. 50. Ouyang C. and Shan S.P., Toughening of High Strength Cementitious Matrix Reinforced by Discontinuous Short Fibers. Cement and Concrete Research, Vol. 22, 1992, pp. 1201-1215. Appendix 1 PULOUT.FOR a FORTRAN program used to analyze the data from pull-out tests PROGRAM MAIN DIMENSION Al(5000) , A2 (5000), A22 (5000) ,E(5000) COMMON/DAT/N, All(5000) CHARACTER*18 DATFIL CHARACTER*18 ENEFIL WRITE (*,*) 'INPUT THE DATA FILE NAME' WRITE (*,*) READ (*, '(A18)') DATFIL OPEN (4, FILE=DATFIL, STATUS='OLD') DO 8 1=1,5000 READ (4, * , END=88) A2(I) , A1(I) CONTINUE N=I-1 DO 10 1=1,N A11(I)=0.0975*A1(I) A22(I)=0.025*A2(I) CONTINUE CALCULATE PEAK LOAD AND CORRESPONDING SLIP CALL PKLOAD(PMAX, M) 1=0 1=1 + 1 IF (I .EQ. M) THEN PDIS=A22(I) ELSE GOTO 2 0 END IF CALCULATE ENERGY VERSUS SLIP, TOTAL ENERGY AND ENERGY AT PEAK LOAD E(1)=(A22(2)-A22(1))*(All(2)+A11(1))/2 DO 3 0 J=2,N-1 E(J)=E(J-1)+(A22(J+l)-A22(J))*(All(J+l)+A11(J))/2 IF (J .EQ. M) THEN PENE=E(J) ELSE IF (J .EQ. N-l) THEN TENE=E(J) END IF END IF CONTINUE OUTPUT DATA WRITE (*,*) 'INPUT ENERGY FILE NAME' WRITE (*,*) READ (*, ' (A18)') ENEFIL 119 OPEN (5, FILE=ENEFIL, STATUS='UNKNOWN') WRITE (5, '(A18)') ENEFIL WRITE (5,100) 100 FORMAT (5X, 'SLIP(mm)', 8X, 'ENERGY(N.mm)') DO 40 1=1,N WRITE (5,200) A22(I) , E(I) 200 FORMAT (5X, F8 .5 , 12X, F8.5) 40 CONTINUE CLOSE (5) WRITE (*, '(A18)') DATFIL WRITE (*,310) 310 FORMAT (IX, 'TOTAL ENERGY (N.mm)') WRITE (*,350) TENE 350 FORMAT (3X,F10.4) WRITE (*,410) WRITE (*,420) 410 FORMAT (IX, 'PEAK LOAD', 4X, 'SLIP AT PEAK LOAD' $ ,4X, 'ENERGY AT PEAK LOAD') 420 FORMAT (4X, ' ( N ) ' , 12X, '(mm)',15X, '(N.mm)') WRITE (*,450) PMAX, PDIS, PENE 450 FORMAT (3X, F5.2 , 10X, F5.2, 15X, F5.2) END SUBROUTINE PKLOAD(PMAX, M) COMMON /DAT/ N, All(5000) CALCULATE THE PEAK LOAD AMAX=0 DO 15 1=1,N IF (A l l ( I ) .GT. AMAX) THEN AMAX=A11(I) END IF 15 CONTINUE PMAX=AMAX CALCULATE THE POSITION OF THE PEAK LOAD 1=0 25 1=1+1 IF (A l l ( I ) .EQ. PMAX) THEN M=I ELSE GOTO 2 5 END IF END 120 Appendix 2 TENSIL.FOR a FORTRAN program used to analyze the data from uniaxial tensile tests PROGRAM MAIN DIMENSION P(2000), D(2000), G(12000), Al(12000), A2(12000) COMMON /DATA/ N, Al l (12000) , A22(12000) CHARACTER *2 0 INFIL, OUTFIL WRITE (*,*) 'INPUT THE FILE NAME' WRITE (*,*) READ (*, '(A20)') INFIL WRITE (*,*) 'INPUT THE OUTPUT FILE NAME' WRITE (*,*) READ (*, '(A20)') OUTFIL OPEN (4, FILE=INFIL, STATUS='UNKNOWN') DO 8 1=1,12000 READ (4,*, END=80) A1(I) , A2(I) 8 CONTINUE 80 N=I-1 WRITE (*,*) 'N=',N C SET THE STARTING POINT AND MULTIPLY BY THE COEFICIENTS 10 DO 10 1=1,N A1(I)=A1(I)-A1(1) A2(I)=A2(I)-A2(1) All(I)=A1(I)*0.0013 2/65 A22(I)=A2(I)*1.0543 CONTINUE C CALCULATE THE ULTIMATE STRENGTH AND STRAINS CALL PKLOAD (PMAX, NP) PDIS=A11(NP)*100 UDIS=A11(N)*100 C CALCULATE THE ELASTIC STRENGTH AND THE ELASTIC MODULUS CALL ELASTIC (E, PE, NE, NP, PMAX) C 100 CALCULATE THE TOUGHNESS G(1)=(A11(2)-A11(1))*(A22(2)+A22(1))/2 DO 100 1=2,N-l G(I)=G(I-1)+(A11(I+1)-All(I))*(A22(1+1)+A22(I))/2 CONTINUE TOUGH=G(N-l) C SMOOTH THE CURVE BY AVERAGING THE DATA CALL AVERAGE (P, D, NE, NP, M) C OUTPUT DATA OPEN (5, FILE=OUTFIL, STATUS='UNKNOWN') WRITE (5, '(A20)') OUTFIL 121 WRITE (5, *) WRITE (5, 18) WRITE (5, 19) 18 FORMAT (4X, 'STRAIN', 5X, 'STRESS') 19 FORMAT (6X,'(%)', 6X, '(MPa)') DO 200 1=1,M D(I)=D(I)*100 WRITE (5,28) D(I ) , P(I) 28 FORMAT (2X, F8.4, 3X, F8.4) 200 CONTINUE WRITE (*, '(A20)') OUTFIL WRITE (*,*) WRITE (*,38) WRITE (*,39) 38 FORMAT (IX, 'ELASTIC STRENGTH', 3X, 'ELASTIC MODULUS', $ 3X, 'ULTIMATE STRENGTH') 39 FORMAT (6X, ' (MPa)' , 14X, ' (GPa) ' , 14X, '(MPa)') WRITE (*, 40) PE, E , PMAX 40 FORMAT (5X, F8.4 , 10X, F8.4, 11X, F8.4) WRITE (*, 48) WRITE (*, 49) 4 8 FORMAT (IX, 'PEAK LOAD STRAIN', 3X, 'ULTIMATE STRAIN', $ 3X, 'TOUGHNESS') 49 FORMAT (7X, '(%)', 16X, '(%)', 9X, '(N/mm*mm)') WRITE (*, 50) PDIS, UDIS, TOUGH 50 FORMAT (5X, F8 .4 , 11X, F8.4, 5X, F8.4) END SUBROUTINE PKLOAD (PMAX, NP) COMMON /DATA/ N, Al l (12000) , A22(12000) AMAX=0 DO 15 1=1,N IF (A22(I) .GT. AMAX) THEN AMAX=A2 2(I) END IF 15 CONTINUE PMAX=AMAX 1=0 25 1=1+1 IF (A22(I) .EQ. PMAX) THEN NP=I ELSE GO TO 25 END IF END SUBROUTINE ELASTIC ( E l , PE, NE, NP, PMAX) DIMENSION EE(12000), E(12000) COMMON/ DATA / N, Al l (12000) , A22(12000) NPP=NP/5 IF ((A11(5)-A11(1)) . L T . 0.000001) THEN E(l)=25 ELSE E(1)=(A22(5)-A22(1)) / ((All(5)-All(1))*1000) IF (E(l) . L T . 5 .OR. E(l) .GT. 50) THEN E(l)=25 END IF END IF J=l EE(J)=E(1) DO 3 5 1=1,NPP IF ((All(1*5+5)-All(1*5)) . L T . 0.000001) THEN E(I+1)=25 ELSE E(I+1)=(A22(1*5+5)-A22(1*5))/ ((All(1*5+5)-All(1*5))*1000) IF (E(I+1) . L T . 5 .OR. E(I+1) .GT. 50) THEN E(I+1)=25 END IF END IF IF ( ABS(1-E(I+1)/E(I)) . L E . 5.95) THEN J=J+1 EE(J)=EE(J-1)+E(I) ELSE GO TO 35 END IF CONTINUE NE=J E1=EE(NE)/NE PE=A2 2(NE) IF (PE .EQ. PMAX) THEN WRITE (*,*) 'NO STRAIN HARDENNING' END IF END SUBROUTINE AVERAGE(P, D, NE, NP, M) DIMENSION P(2000), D(2000) COMMON /DATA/ N, All (12000) , A22(12000) NA=(N)/10 NEA=NE/10 NEB=NEA*10 NPA=NP/10 NPB=NPA*10 J=0 DO 45 1=1,NEA 11=10*1 J=J+1 CALL PD(PI, D l , II) P(J)=PI D(J)=DI CONTINUE DO 55 I=NEB+1, NEB+10 J=J+1 P(J)=A22(I) D(J)=A11(I) CONTINUE IF (NEA .EQ. NPA) THEN GO TO 76 END IF DO 65 I=NEA+2, NPA 11=10*1 J=J+1 CALL PD(PI, DI, II) P(J)=PI D(J)=DI CONTINUE DO 75 I=NPB+1, NPB+10 J=J+1 P(J)=A22(I) D(J)=A11(I) CONTINUE CONTINUE DO 85 I=NPA+2, NA 11=10*1 J=J+1 CALL PD (PI, DI, II) P(J)=PI D(J)=DI CONTINUE M=J END SUBROUTINE PD(P, D, II) COMMON /DATA/N, Al l (12000) , A22(12000) I=(II-1)/10 D=(All(10*1+1)+A11(10*1+2)+A11(10*1+3)+All(10*1+4) +A11(10*1+5)+A11(10*1+6)+A11(10*1+7)+A11(10*1+8) +A11(10*1+9)+All(10*1+10))/10 P=(A22(10*1+1)+A2 2(10*1+2)+A22(10*1+3)+A22(10*1+4) +A22(10*1+5)+A22(10*1+6)+A22(10*1+7)+A22(10*1+8) +A22(10*1+9)+A22(10*1+10))/10 END 124 Appendix 3 BENDING.FOR a FORTRAN program used to analyze the data from flexural tests PROGRAM MAIN DIMENSION LOAD1(2500), CRAK1(2500), DEFL1(2500), LOAD(2500), CRAK(2500), DEFL(2500), G(2500), ALOAD(250), ACRAK(250), BLOAD(250), BDEFL(250) REAL LOAD1, LOAD CHARACTER* 2 0 INFILE, OTFIL1, OTFIL2 CHARACTER*1 CHOICE WRITE (*,*) 'INPUT THE FILE NAME' WRITE (*,*) READ (*, '(A20)') INFILE WRITE (*,*) 'INPUT THE LOAD-CRACK OPENING OUTPUT FILE NAME' WRITE (*,*) READ (*, '(A20)') OTFIL1 WRITE (*,*) 'INPUT THE LOAD-DEFLECTION OUTPUT FILE NAME' WRITE (*,*) READ (*, '(A20)') OTFIL2 INPUT THE DATA OPEN (4, FILE=INFILE, STATUS='UNKNOWN') DO 10 1=1,2500 READ (4,*, END=88) CRAKl(I) , LOADl(I) , DEFLl(I) CONTINUE N=I-1 MULTIPLY BY THE COEFFICIENT DO 20 1=1,N CRAK(I)=0.0 01151*CRAK1(I) LOAD(I)=110.7*L0AD1(I) DEFL(I)=0.0 01151*DEFL1(I) CONTINUE WRITE (*,*) READ (*,' SET THE FIRST READING TO BE 'BEAM ROCKING? (Al) ' ) CHOICE IF (CHOICE .EQ. 'Y ' ) THEN DO 6 1=1,N IF ((LOAD(I)-LOAD(1)-150) ME1=I GO TO 5 END IF CONTINUE CONTINUE DO 8 1=1,N IF ((LOAD(I)-LOAD(l)-240) ME2=I GO TO 7 ZERO (Y/N) .GE. 0) THEN GE. 0) THEN 125 END IF 8 CONTINUE 7 CONTINUE EF=(LOAD(ME2)-LOAD(ME1))/(DEFL(ME2)-DEFL(ME1)) DO 9 I=1,ME1-1 DEFL(I)=DEFL(ME1)-(LOAD(ME1)-LOAD(I))/EF 9 CONTINUE END IF IF (CHOICE .EQ. 'N') THEN GO TO 66 END IF 6 6 CONTINUE DO 99 1=1,N DEFL(I)=(-1)*DEFL(I) 99 CONTINUE FSTC=CRAK(1) FSTL=LOAD(1) FSTD=DEFL(1) DO 30 1=1,N CRAK(I)=CRAK(I)-FSTC LOAD(I)=LOAD(I)-FSTL DEFL(I)=DEFL(I)-FSTD 3 0 CONTINUE C CALCULATE THE STRENGTH CALL PKLOAD (PMAX, NP, STREN=12 * PMAX/6 2 5 PCRAK=CRAK(NP) PDEFL=DEFL(NP) UCRAK=CRAK(N) UDEFL=DEFL(N) OF THE BEAM ETC. N, LOAD) C SMOOTH THE LOAD-CRACK OPENING CURVE CALL SMOOTH (LOAD, CRAK, ALOAD, ACRAK, N, M l , NP, NPP1) C SMOOTH THE LOAD-DEFLECTION CURVE CALL SMOOTH (LOAD, DEFL, BLOAD, BDEFL, N, M2, NP, NPP2) DO 4 0 I=NPP2,M2 IF (BDEFL(I) . L T . BDEFL(I- l ) ) THEN BDEFL(I)=BDEFL(I-1) + (BDEFL(1-1)-BDEFL(I) )/8 END IF 40 CONTINUE 50 55 CALCULATE THE ELASTIC MOUDULUS DO 50 I=1,NPP2 IF ((BLOAD(I)-150) .GE. 0) THEN NE1=I GO TO 55 END IF CONTINUE CONTINUE P85=0.85*PMAX DO 60 I=1,NPP2 IF ((BLOAD(I)-P8 5) .GE. 0) THEN NE2=I 126 GO TO 65 END IF 60 CONTINUE 65 CONTINUE CALL ELASTIC (E, NE1, NE2, BLOAD, BDEFL) CALCULATE THE TOUGHNESS G(1)=(DEFL(2)-DEFL(l))*(LOAD(2)+LOAD(1))/2 DO 70 1=2,N-l G(I)=G(I-1)+(DEFL(I+1)-DEFL(I))*(LOAD(1+1)+LOAD(I))/2 70 CONTINUE TOUGH=G(N-l) OUTPUT DATA WRITE (*, 150) WRITE (*, 250) 150 FORMAT (IX,'STRENGTH',2X,'ELASTIC MOUDULUS',2X,'TOUGHNESS') 250 FORMAT (3X, ' (MPa)' , 8X, ' (GPa) ' , 9X, '(N.mm)') WRITE (*, 350) STREN, E , TOUGH 350 FORMAT (IX, F8 .3 , 7X, F6.3 , 7X, F9.3) WRITE (*,450) WRITE (*,550) 450 FORMAT (IX,'CRACK AT P-LOAD',2X,'DEFLECTION AT P-LOAD') 550 FORMAT (6X, '(mm)', 16X, '(mm)') WRITE (*,650) PCRAK, PDEFL 650 FORMAT (4X, F9.7 , 10X, F9.7) WRITE (*,750) WRITE (*,850) 750 FORMAT (IX, 'MAX. CRACK OPENING', 2X, 'MAX. DEFLECTION') 850 FORMAT (8X, '(mm)', 14X, '(mm)') WRITE (*,950) UCRAK, UDEFL 950 FORMAT (7X, F6.4 , 12X, F6.4) OPEN (5, FILE=0TFIL1, STATUS='UNKNOWN') DO 80 1=1,Ml WRITE (5,*) ACRAK(I), ALOAD(I) 8 0 CONTINUE OPEN (6, FILE=OTFIL2, STATUS='UNKNOWN') DO 90 1=1,M2 WRITE (6,*) BDEFL(I), BLOAD(I) 90 CONTINUE END SUBROUTINE PKLOAD (PMAX, NP, N, LOAD) REAL LOAD(2500) AMAX=0.0 DO 100 1=1,N IF (LOAD(I) .GT. AMAX) THEN AMAX=LOAD(I) END IF 100 CONTINUE PMAX=AMAX DO 110 1=1,N IF (LOAD(I) .EQ. PMAX) THEN 127 NP=I GO TO 12 0 END IF 110 CONTINUE 120 CONTINUE END SUBROUTINE SMOOTH (LOAD, DESP, P, D, N, M, NP, NPP) DIMENSION P(250), D(250), LOAD(2500), DESP(2500) REAL LOAD NA=N/10 NB=NA*10 NPA=NP/10 NPB=NPA*10 J=l P(1)=0 D(1)=0 DO 200 1=1,NPA 11=10*1 CALL PD (PI, DI, I I , LOAD, DESP) J=J+1 P(J)=P1 D(J)=D1 200 CONTINUE NPP=J DO 210 I=NPB+l,NPB+2 0 J=J+1 P(J)=LOAD(I) D(J)=DESP(I) 210 CONTINUE DO 22 0 I=NPA+3, NA 11=10*1 CALL PD (PI, DI, I I , LOAD, DESP) J=J+1 P(J)=P1 D(J)=D1 22 0 CONTINUE M=J END SUBROUTINE PD (PI, DI, J , LOAD, DESP) DIMENSION LOAD(2500), DESP(2500) REAL LOAD I=(J-1)/10 P1=(LOAD(10*I+1)+LOAD(10*I+2)+LOAD(10*1+3)+LOAD(10*1+4) $ +LOAD(10*I+5)+LOAD(10*I+6)+LOAD(10*I+7)+LOAD(10*I+8) $ +LOAD(10*I+9)+LOAD(10*I+10))/10 Dl=(DESP(10*1+1)+DESP(10*1+2)+DESP(10*1+3)+DESP(10*1+4) $ +DESP(10*1+5)+DESP(10*1+6)+DESP(10*1+7)+DESP(10*1+8) $ +DESP(10*1+9)+DESP(10*1+10))/10 128 END SUBROUTINE ELASTIC ( E l , NE1, NE2, BLOAD, BDEFL) DIMENSION EE(IOO), E(200), BLOAD(250), BDEFL(250) J=l E(NE1)=14.72*BLOAD(NE1)/BDEFL(NE1) EE(1)=E(NE1) DO 3 00 I=NE1+1, NE2 E(I)=14.72*BLOAD(I)/BDEFL(I) J=J+1 EE(J)=EE(J-1)+E(I) 300 CONTINUE NE=J E1=EE(NE)/(NE*1000) END 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050347/manifest

Comment

Related Items