1.1 Field of the Invention

[0001] The present invention relates to shape memory alloy (SMA) fibres for reinforcing cementitious and non-cementitious composites such as, but not limited to, concrete, mortar and geopolymers. In particular, the invention relates to segmented SMA fibres for reinforcing concrete, mortar or geopolymers. This invention also relates to the use of segmented SMA fibres in cementitious and non-cementitious composites, as well as the use of such composites in load-bearing structures. Furthermore, the invention relates to the use of segmented SMA fibres for re-centring and crack closing in cementitious and non-cementitious composites.

1.2 Background of the Invention

[0002] Cementitious composites, such as concrete are widely used to construct infrastructure, for example buildings and bridges. However, conventional concrete is limited by its low tensile strength and brittle nature which cause it to crack in service. Tensile cracks in concrete can lead to the corrosion of steel reinforcement in reinforced concrete when chloride ions dissolved in water react with the steel reinforcement. This substantially reduces the durability as well as the in-service performance of infrastructure.

[0003] Fibres such as steel, polyvinyl alcohol, carbon, and polypropylene are increasingly used in a bid to overcome the brittleness of concrete as well as enhance its toughness and cracking behaviour (that is, the rates of crack opening and crack propagation). However, these aforementioned fibres do not provide desirable re-centring and crack-closure performance for cementitious composites. For instance, steel fibres are commonly used in the construction industry to control crack propagation by decreasing the opening at the crack tip, known in the art as a ‘bridging mechanism’. However, under tensile stresses, when steel fibres are stressed beyond their yield point, they become permanently deformed; this limits the possibility of re-centring and crack closing with steel fibres in cementitious composites. Most importantly, steel fibres are designed to achieve slip between the fibres and the matrix, a mechanism known in the art as ‘frictional sliding.’ Frictional sliding allows the cementitious composite to dissipate significant energy when loaded with a tensile stress. In essence, a firm fibre-matrix bond is not desirable for steel fibres because it results in sudden rupture at small fibre-matrix slips. Such steel fibre rupture can result in catastrophic failure of structural components. Expressed alternatively, cementitious composites which are designed based on the frictional sliding mechanism cannot exhibit desirable re-centring and crack-closing capabilities since the slip between the fibres and the matrix is unrecoverable. Furthermore, corrosion of the steel fibres after the onset of cracks can lead to micro-spalling of the concrete as well as weakening of the fibres (by reducing the cross-sectional area of the fibres); as might be expected, these occurrences will cause concern about the long-term in-service behaviour of such concrete infrastructure.

[0004] Fibres of various materials featuring unconventional geometries have been explored as potential reinforcement materials in cementitious composites. For example, AU 442751 B2 discloses low carbon hard drawn wires (fibres) having intermittent portions of substantially rectangular configuration in cross section preferably joined by portions of substantially round configuration in cross-section for reinforcing concrete compositions. However, the strain recovery in these low carbon hard drawn fibres is low and the fibres can therefore not be used for re-centring and crack closing in cementitious or non-cementitious composites. US 2012/0146254 A1 discloses a bi-component fibre having a central core and a casing containing different pure polymers or polymer mixtures with grooved surfaces. While these plastic fibres can be used to improve the tensile strength and post-cracking behaviour of cementitious composites, the thickness and/or diameter of plastic fibres reduces considerably under pullout loads, partly due to the low elastic modulus of plastic fibres. The decrease in diameter and/or thickness weakens the fibre-matrix bond, thus the fibre can easily slip out of the matrix. These fibres can therefore not be used for re centring and crack closing in cementitious or non-cementitious composites.

[0005] Segmented steel fibres with a combination of flattened and round segments have also been investigated as reinforcements for cementitious and non-cementitious composites. For example, US 5451471 A discloses a steel fibre with flattened segments at both ends of the fibre. These fibres are provided with a large number of small notches or grooves, possibly as a means of improving the fibre-matrix bond. However, introducing a large number of small notches or grooves to the fibres would not only increase production costs but also be detrimental to the mechanical properties of the steel fibres. Importantly, because the strain recovery in steel fibres is low, the decrease in crack width after unloading occurs only due to recovery of elastic elongation (which is negligible), these steel fibres cannot be used for re-centring and crack closing in cementitious or non-cementitious composites. Similarly, US 2013/0255540 A1 and US 6045910 A disclose configurations of steel fibres with middle portions and anchor age/hook- shaped ends at one or both ends of the middle portion. However, recent research ¹ on the load-slip behaviour of the fibres disclosed in US 2013/0255540 A1 indicated high amounts of slip between the fibres and cementitious matrices, which, though desirable for steel reinforcement, is undesirable where re-centring and crack closing in cementitious or non-cementitious composites is required. For re-centring and crack closing to occur, the slip between the fibres and the matrix must be minimal, as only minimal re-centring and crack closing will be achieved when the slip between the reinforcing fibre and the cementitious or non-cementitious matrix is high. Consequently, the fibres disclosed in US 2013/0255540 A1 cannot be used for re-centring and crack closing in cementitious or non-cementitious composites. Furthermore, the hook-shaped ends of the steel fibres disclosed in US 6045910 A make the fibres prone to entanglement and/or interlocking during mixing, which causes them to agglomerate and form fibre ‘balls’ such that the fibres are dispersed inhomogenously within the cementitious/non-cementitious matrix. Naturally, this will result in a non-uniform fibre distribution within the cementitious/non-cementititious matrix, with some parts of the composite lacking any fibre components, the consequence of which would be a composite lacking uniform mechanical strength. Additionally, the fabrication of hook-shaped ends fibres with different cross-sections may increase fibre production costs. Lastly, as previously described, because these fibres are made from steel, they are unsuitable for use in re-centring and crack closing in cementitious or non-cementitious composites.

[0006] Strain recovery is an intrinsic property of SMA. Therefore, to overcome the limitations of the aforementioned fibres in re-centring and crack closing in cementitious and non-cementitious composites, shape memory effect SMA fibres in various shapes such as straight, loops, star and hooked-end fibres have been used in cementitious composites to provide re-centring and crack-closure capability. Shape recovery in those SMA fibres is activated by heat. Although these SMA fibres showed re-centring and crack-closing capability, the relatively high temperatures used to activate the fibres damaged the cementitious matrix. Furthermore, high temperature activation could adversely affect the fibre-matrix bond behaviour, which is obviously undesirable. Therefore, these fibres cannot be used for re-centring and/or crack closing in cementitious or non-cementitious composites, especially in structural elements. [0007] Furthermore, straight and hooked-end pseudoelastic SMA fibres and SMA strands have also been investigated to preclude the use of heat. However, the usefulness of these fibres is limited by excessive fibre-matrix slip which inhibits significant re-centring and crack-closing in cementitious composites.

1.3 Summary of the Invention

[0008] In light of the shortcomings of existing cementitious composites, there remains an opportunity to develop SMA fibres which: exhibit minimal fibre-matrix slip; are suitable for use in re-centring and crack closing in cementitious or non-cementitious composites; as well as control the cracking performance of cementitious and non-cementitious composites under loading, without requiring heat activation. Additionally, there remains an opportunity to develop cementitious and non-cementitious compositions comprising such SMA fibres.

[0009] In some embodiments, there is provided segmented SMA fibres for reinforcement of cementitious and non-cementitious composites, such as, but not limited to, concrete, mortar and geopolymers.

[0010] The present inventors have surprisingly found that by reinforcing cementitious or non- cemenetitious composites with these segmented SMA fibres, the re -centring and crack closing performance of the composites is significantly enhanced.

[0011] As used herein, the term crack closing in the context of cementitious and non-cementitious composites refers to a substantial reduction in crack width after unloading.

[0012] Similarly, the term re-centring in the context of cementitious and non-cementitious composites refers to the composite’s or structural element’s return to its original/initial position after unloading.

[0013] In some embodiments, there is provided segmented SMA fibres showing good fibre-matrix bond strength in cementitious and non-cementitious composites.

[0014] In some embodiments, there is provided segmented SMA fibres for use in re-centring and crack closing in cementitious and non-cementitious composites. [0015] In some embodiments, there is provided segmented SMA fibres not prone to form balls when mixed in cementitious and non-cementitious composites.

[0016] In some embodiments, there is provided structural components of cementitious and non- cementitious composites comprising segmented SMA fibres at a volume concentration within the range of about 0.25% to 5%. In some embodiments, the structural components of cementitious and non-cementitious composites comprises segmented SMA fibres at a volume concentration within the range of 0.25% to 5%. Preferably, the volume concentration of the segmented SMA fibres in cementitious or non-cementitious composites is in the range 0.5% to 3%.

[0017] In some embodiments, there is a provided a shape memory alloy fibre for reinforcing cementitious and non-cementitious composites. The SMA fibre is straight. The SMA fibre comprises: alternating flat and round segments with a same longitudinal axis. Consecutive flat segments are separated by respective round segments. Anterior and posterior straight ends of a flat segment are connected to the immediately adjacent round segments by respective stepped transition members. The stepped transition members are located at both ends of said immediately adjacent round segments. The SMA fibre comprises curved transition members located on opposing sides of the anterior and posterior straight ends of said flat segment. Each of said stepped transition members is connected to the respective anterior or posterior straight edge of said flat segment through a 90° angle.

[0018] In some embodiments, a width, w, of said flat segments is at least 60% greater than that of said round segments. In some embodiments, the width, w, of the flat segments is within the range of about 60% to 70% greater than that of the round segments. In some embodiments, the width, w, of the flat segments is within the range of 60% to 70% greater than that of the round segments. Preferably, the width, w, of the flat segments is at least 65% greater than that of the round segments.

[0019] The diameter, d, and length, /,·, of the round segments, as well as the width, w, thickness, t, and length, If, of the flat segments, depend on the aspect ratio of the fibre. By aspect ratio, it is meant the proportion of the diameter of the round segments to the total length of the SMA fibre. In some embodiments, the aspect ratio is any value in the range of about 20 to 85. In some embodiments, the aspect ratio is any value within the range of 20 to 85. In some embodiments, the aspect ratio of the shape memory alloy fibre is between 20 and 85. [0020] In some embodiments, the length of the round segments may be in the range of about 0.75 to 1.00 times the length of the flat segments. In some embodiments, the length of the round segments may be in the range of 0.75 to 1.00 times the length of the flat segments. Preferably, the length of the flat and round segments are equal. In some embodiments, the length of the round segments is at least 0.75 times, but not greater than 1.00 times, a length of the flat segments.

[0021] The number of flat and/or round segments may be modified to suit the aspect ratio of the SMA fibre. Preferably, there are six flat segments, to minimise the fibre-matrix slip and achieve the desired pull-out behaviour. In some embodiments, there are at least 6 flat segments.

[0022] In some embodiments, there is provided a shape memory alloy fibre for reinforcing cementitious and non-cementitious composites. The SMA fibre comprises: a straight middle segment with a first end-hook at one end of the straight middle segment and a second end-hook at the other end of the straight middle segment. The first end-hook and the second end-hook are on the same side of a longitudinal axis of the straight middle segment. The first end-hook comprises a first short straight segment which is connected to one end of the straight middle segment through an angle a, said first short straight segment being substantially perpendicular to the longitudinal axis of the straight middle segment. The first end-hook comprises a second short straight segment which is connected to the first short segment and bent away from the first short straight segment through an angle b, said second short straight segment being substantially parallel to the longitudinal axis of the straight middle segment. The first end-hook comprises a third short straight segment which is connected to the second short straight segment through said angle a, said third short straight segment being substantially perpendicular to the longitudinal axis of the straight middle segment. The first end-hook comprises a fourth short straight segment which is bent away from the third short straight segment through said angle b, said fourth short straight segment being substantially parallel to the longitudinal axis of the straight middle segment. The second end-hook comprises another first short straight segment which is connected to the other end of said straight middle segment through said angle a, said other first short straight segment being substantially perpendicular to the longitudinal axis of the straight middle segment. The second end-hook comprises another second short straight segment which is connected to the other first short segment and bent away from the other first short straight segment through said angle b, said other second short straight segment being substantially parallel to the longitudinal axis of the straight middle segment. The second end-hook comprises another third short straight segment which is connected to the other second short straight segment through said angle a, said other third short straight segment being substantially perpendicular to the longitudinal axis of the straight middle segment. The second end-hook comprises another fourth short straight segment which is bent away from the other third short straight segment through said angle b, said other fourth short straight segment being substantially parallel to the longitudinal axis of the straight middle segment.

[0023] In some embodiments, the first end-hook and the second end-hook are on opposite sides of the longitudinal axis of the straight middle segment.

[0024] In some embodiments, a is between 90° and 100° and b is between 260° and 270°.

[0025] In some embodiments, each short straight segment has a length of at least 0.5 mm and a maximum 6 mm.

[0026] In some embodiments, the lengths of the first and third short straight segments are each a minimum of 1.5 mm and the second and fourth short straight segments have equal or different lengths.

[0027] In some embodiments, each end-hook comprises four short straight segments. Each end of the straight middle segment is connected to the immediately adjacent first short straight segment through an interior angle a. The second short straight segment is bent away from the first short straight segment through an exterior angle b. The third short straight segment is connected to the second short straight segment through an interior angle the same as a. Finally, the fourth short straight segment is bent away from the third short straight segment by an exterior angle the same as b to complete the end-hook.

[0028] In some embodiments, a may range between about 90° and 100° while b may range between about 260° and 270°.

[0029] In some embodiments, a may range be within the range of 90° and 100° while b may be within the range of 260° and 270°. Preferably, a is 90° and b is 270°.

[0030] Specifically, the first short straight segment is substantially perpendicular to the longitudinal axis of the straight middle segment while the second short straight segment is substantially parallel to the longitudinal axis of the straight middle segment. Similar to the first short straight segment, the third short straight segment is substantially perpendicular to the longitudinal axis of the straight middle segment while the fourth short straight segment is similar to the second short straight segment by being substantially parallel to the longitudinal axis of the straight middle segment.

[0031] The term “substantially perpendicular” or “substantially parallel” is used to consider the existence of some small or accidental deviation from parallelism or perpendicularity during the manufacturing process of the SMA fibre.

[0032] The length of the short straight segments in the end-hooks depends on the aspect ratio of the fibres.

[0033] In some embodiments, there is provided the use of SMA fibres according to the present invention for load-bearing structures of cementitious and non-cementitious composites.

[0034] In some embodiments, there is provided the use of the described shape memory alloy fibres for re-centring and/or crack closing in cementitious or non-cementitious composites.

[0035] In some embodiments, there is provided a cementitious composite comprising the described shape memory alloy fibres.

[0036] In some embodiments, there is provided a non-cementitious composite comprising the described shape memory alloy fibres.

[0037] In some embodiments, a volume composition of SMA fibres in the cementitious composite or the non-cementitious composite is between 0.25% and 5%.

[0038] In some embodiments, there is provided the use of the cementitious composite or the non- cementitious composite for a load-bearing structure. 1.4 Brief Description of the Drawings

[0039] The invention is described herein with reference to the following non-limiting drawings in which:

[0040] Figure 1 shows schematic illustrations of: (a) a top view; and (b) a 3D side-view of a Type 1 SMA fibre. The expanded insert in Figure 1A shows a 3D oblique view of the Type 1 SMA fibre while the expanded insert in Figure IB shows an enlarged 3D side-view of the Type 1 SMA fibre. In the figures, 100 points to the Type 1 SMA fibre, 110 points to some flat segments of the Type 1 SMA fibre, 120 points to some round segments of the Type 1 SMA fibre, 130 points to a longitudinal axis of the Type 1 SMA fibre, 140 points to a curved transition member of the Type 1 SMA fibre, and 150 points to a stepped transition member of the Type 1 SMA fibre.

[0041] Figure 2 is a schematic illustration of a mould used to manufacture the Type 1 SMA fibre. In Figure 2, 200 points to the mould, 210 points to a moveable top fixture of the mould, 220 points to threaded holes at the top of the moveable top fixture, 230 points to a stationary bottom fixture of the mould, and 240 points to some mould teeth.

[0042] Figure 3 is a schematic illustration of a Type 2 SMA fibre. In Figure 3, 300 points to the Type 2 SMA fibre of length /, 310 points to a straight middle segment of length l _m , 320 points to end-hooks, 330 points to a first short straight segment of length h, 340 points to a second short straight segment of length , 350 points to a third short straight segment of length / ,·, 360 points to a fourth short straight segment of length U, and 370 points to a longitudinal axis of the straight middle segment.

[0043] Figure 4 is a schematic illustration of an alternative embodiment of Type 2 SMA fibre. In Figure 4, 400 points to the alternative embodiment of Type 2 SMA fibre of length /, 410 points to a straight middle segment of length l _m , 420 and 430 point to end-hooks, 440 points to a longitudinal axis of the straight middle segment, 450 and 450a point to first short straight segments of lengths h and U _a , respectively, 460 and 460a point to second short straight segments of lengths l· and h _a , respectively, 470 and 470a point to third short straight segments of lengths h and h _a , respectively, and 480 and 480a point to fourth short straight segments of lengths U and U _a , respectively. [0044] Figure 5 is a schematic illustration of a mould used to manufacture the Type 2 SMA fibre. In Figure 5, 500 points to the mould, 510 points to a moveable top fixture, 520 points to threaded holes, 530 points to a detachable plate, 540 points to a stationary bottom fixture, 550 points to cartridge heaters, and 560 points to a voltage regulator.

[0045] Figure 6 is a schematic illustration of a single fibre pullout test. In Figure 6, 600 points to a cylindrical grip, 610 points to a SMA fibre specimen, 620 points to a fixture system, 630 points to a cubic shaped cementitious matrix, 640 points to small cubes permanently attached to a top platen, 650 points to the top platen, 660 points to a bottom platen, and 670 points to an extensometer.

[0046] Figure 7 illustrates monotonic tensile stress-strain curves for: (a) the Type 1 SMA fibre compared to as-received SMA wire cut to a fibre of predetermined length [equivalent to the length of Type 1 SMA fibre or l+2h+2k for Type 2 SMA fibre (as shown in Figures 3 and 4)]; and (b) the Type 2 SMA fibre compared to as-received SMA wire cut to a fibre of predetermined length [equivalent to the length of Type 1 SMA fibre or l+2h+2k for Type 2 SMA fibre (as shown in Figures 3 and 4)]. In the figures, 700 points to the monotonic tensile stress-strain curve for the Type 1 SMA fibre, 710 points to the monotonic tensile stress-strain curve for the Type 2 SMA fibre, and 720 points to the monotonic tensile stress-strain curve for the respective SMA wires.

[0047] Figure 8 illustrates a pullout load-slip curve under static loading for: (a) the Type 1 SMA fibre; (b) the Type 2 SMA fibre; and (c) the Type 1 SMA fibre, showing its slip failure. In the Figures, 800 points to the pullout load-slip curve for the Type 1 SMA fibre, 810 points to the pullout load-slip curve for the Type 2 SMA fibre, 820 points to stage 1 of the pullout mechanism of the Type 1 SMA fibre, 830 points to stage 2 of the pullout mechanism of the Type 1 SMA fibre, 840 points to stage 3 of the pullout mechanism of the Type 1 SMA fibre, 850 points to stage 4 of the pullout mechanism of the Type 1 SMA fibre, 860 points to rupture of the Type 1 SMA fibre, and 870 points to slip failure of the Type 1 SMA fibre.

[0048] Figure 9 illustrates: (a) re-centring performance of the Type 1 SMA fibre in a Type 1 SMA fibre-reinforced cementitious composite under cyclic pullout loading; and (b) magnification of a highlighted section in (a). In the Figures, 900 points to the re-centring behaviour and 910 points to the permanent fibre-matrix slip, of the Type 1 SMA fibre, respectively. [0049] Figure 10 illustrates: (a) re-centring performance of the Type 2 SMA fibre in a Type 2 SMA fibre -reinforced cementitious composite under cyclic pullout loading; and (b) magnification of a highlighted section in (a). In the Figures, 1000 points to the re -centring behaviour and 1010 points to the permanent fibre-matrix slip, of the Type 2 SMA fibre, respectively.

[0050] Figure 11 illustrates: (a) re-centring performance of a 5D hooked-end steel fibre in a 5D hooked-end steel fibre-reinforced cementitious composite under cyclic pullout loading; and (b) magnification of a highlighted section in (a). In the Figures, 1100 points to the re-centring behaviour and 1110 points to the permanent fibre-matrix slip, of 5D hooked-end steel fibre, respectively.

[0051] Figure 12 illustrates the re-centring capacity at various cycles for Type 1 SMA fibre, Type 2 SMA fibre and 5D hooked-end steel fibre. In Figure 12, 1200 points to the re-centring capacity for Type 1 SMA fibre, 1210 points to the re-centring capacity for Type 2 SMA fibre, and 1220 points to the re-centring capacity for 5D hooked-end steel fibres.

[0052] Figure 13 shows a comparison of the flowability of a plurality of test mixes with EN206:2013 ⁴ slump-flow classes.

[0053] Figure 14 shows the flexural behaviour of a representative beam of a control specimen (CS) of cementitious composite.

[0054] Figure 15 shows the cyclic bending curves, envelopes of the cyclic curves and curves obtained from the static flexural test of beams reinforced with: (a) 0.50% Type 1 SMA fibres; (b) 0.75% Type 1 SMA fibres; and (c) 1.00% Type 1 SMA fibres.

[0055] Figure 16 shows the cyclic bending curves, envelopes of the cyclic curves and curves obtained from the static flexural test of beams reinforced with: (a) 0.50% steel fibres (SFs); (b) 0.75% SFs; and (c) 1.00% SFs.

[0056] Figures 17 shows the cyclic crack mouth opening displacement (CMOD) curves and envelope curves for notched beams reinforced with: (a) 0.50% Type 1 SMA fibres; (b) 0.75% Type 1 SMA fibres; and (c) 1.00% Type 1 SMA fibres. [0057] Figures 18 shows the cyclic crack mouth opening displacement (CMOD) curves and envelope curves for notched beams reinforced with: (a) 0.50% SFs; (b) 0.75% SFs; and (c) 1.00% SFs.

[0058] Figure 19 shows a comparison between Type 1 SMA fibre -reinforced beams and SF- reinforced beams, of the: (a) hysteresis energy dissipated at each cycle; and (b) cumulative dissipated energy.

[0059] Figure 20 shows the variation of residual deformation after unloading for both Type 1 SMA fibre-reinforced beams and SF-reinforced beams.

[0060] Figure 21 shows a comparison of the re-centring capacities, R _re , between Type 1 SMA fibre-reinforced beams and SF-reinforced beams.

[0061] Figure 22 shows the crack closing ratio and maximum crack width up to a deflection of span/100 for: (a) Type 1 SMA fibre-reinforced beams; and (b) SF fibre-reinforced beam.

[0062] Figure 23 shows changes in crack recovery ratio versus maximum CMOD at each cycle in a three-point bend test on notched reinforced beams.

[0063] Figure 24 shows the cracking pattern as recorded by digital image correlation (DIC) at: peak loading (a, c, and e); and after unloading (b, d, and f), at three different displacement amplitudes for Type 1 SMA fibre-reinforced beams.

[0064] Figure 25 shows the cracking pattern as recorded by DIC at: peak loading (a, c, and e); and after unloading (b, d, and f), at three different displacement amplitudes for SF-reinforced beams.

[0065] Figure 26 illustrates the effects of 4D and 5D end-hooks (with 45° bends) in comparison to 3D end-hooks on the pullout resistance of (A) commercially available steel fibres and (B) as- received SMA wires cut into fibres of predetermined lengths [equivalent to l+2h+2k for Type 2 SMA fibre (as shown in Figures 3 and 4)]. 1.5 Detailed Description of the Invention

[0066] Figure 1 shows an embodiment of a Type 1 SMA fibre 100. The Type 1 SMA fibre 100 may be referred to as a first type of SMA fibre. In some embodiments, the Type 1 SMA fibre 100 may be referred to as a pseudoelastic SMA fibre 100. The Type 1 SMA fibre 100 may be used for reinforcing cementitious and non-cementitious composites. The Type 1 SMA fibre 100 comprises alternating flat segments 110 and round segments 120. Furthermore, the Type 1 SMA fibre 100 is straight. The Type 1 SMA fibre 100 is straight so that a longitudinal axis 130 of the flat segments 110 is the same as that of the round segments 120. It is preferred that Type 1 SMA fibres 100 are straight so that they do not form balls during the composite mixing process and can be mixed homogeneously with the matrix. It is also important that the longitudinal axis 130 of the flat segments 110 is the same as that of the round segments 120 to avoid the undesirable effect of bending forces (in contrast to direct tensile loading) acting on the fibres when used for reinforcing cementitious or non-cementitious composites. Such bending forces substantially increase the snubbing effect at the crack face and cause stress concentration, leading to local damage at the crack face. Such damage is disadvantageous where re-centring and crack closing of cementitious and non-cementitious composites by reinforcement fibres is desired. Consecutive flat segments 110 are separated by round segments 120. The anterior and posterior straight ends of a flat segment 110 are connected to the immediately adjacent round segments 120 by stepped tranisition members 150. Stepped transition members 150 are located at both ends of round segments 120 (e.g. the round segments 120 that are immediately adjacent to the relevant flat segment 110). In other words, the round segments 120 comprise stepped transition members 150. In some embodiments, the stepped transition members 150 may be referred to as stepped portions. For example, a stepped transition member 150 may be considered a stepped transition portion of a respective round segment 120. Curved transition members 140 are located on opposing sides of the anterior and posterior straight ends of the flat segments 110. In other words, the flat segments 110 comprise curved transition members 140. In some embodiments, the curved transition members 140 may be referred to as curved transition portions. For example, a curved transition member 140 may be considered a curved transition portion of a respective flat segment 110. A stepped transition member 150 is connected to the anterior or posterior straight edge of a flat segment 110 through a 90° angle. In some embodiments, each relevant stepped transition member is connected to the respective posterior straight edge of a flat segment through a 90° angle. In other words, a curved transition member 140 meets a stepped transition member 150 at a transition. The transition comprises a 90° angle.

[0067] In some embodiments, the width, w, of the flat segments 110 is within the range of about 60% - 70% greater than that of the round segments 120.

[0068] In some embodiments, the width, w, of the flat segments 110 is within the range of 60% - 70% greater than that of the round segments 120. Preferably, the width, w, of the flat segments 110 is at least 65% greater than that of the round segments 120.

[0069] The diameter, d, and length, /,·, of the round segments 120, as well as the width, w, thickness, t, and length, If, of the flat segments 110, depend on the aspect ratio of the fibre. By aspect ratio is meant the proportion of the diameter of the round segments to the total length of the SMA fibre.

[0070] In some embodiments, the aspect ratio of the Type 1 SMA fibre 100 is any value within the range of about 20 to 85.

[0071] In some embodiments, the aspect ratio of Type 1 SMA fibre is any value within the range of 20 to 85. For example, the aspect ratio of the Type 1 SMA fibre 100 may be 20 30, 40, 50, 60, 70, 80 or 85.

[0072] In some embodiments, the length of the round segments 120 may be within the range of about 0.75 to 1.00 times the length of the flat segments 110.

[0073] In some embodiments, the length of the round segments 120 may be within the range of 0.75 to 1.00 times the length of the flat segments 110. Preferably, the length of the flat and round segments are equal. In some embodiments, the length of the round segments 120 is about 0.75, 0.80, 0.90 or 1.00 times the length of the flat segments 110.

[0074] The number of flat and/or round segments may be modified to suit the aspect ratio of the Type 1 SMA fibre 100. In some embodiments, there are at least six flat segments 110. Preferably, there are six flat segments 110, to minimise the fibre-matrix slip and assist in providing the desired pull-out behaviour. The thickness of the flat segments 110 contributes to obtaining the desired pullout behaviour, as small thicknesses result in local shear failure in the matrix leading to undesirable fibre-matrix slip.

[0075] The Type 1 SMA fibre 100 may be manufactured from a SMA wire using any suitable forming process known in the art, for example, deep-drawing. Firstly, the SMA wire is cut to obtain a straight SMA fibre of predetermined length, l. Then using an appropriately shaped mould, the straight SMA fibre is deep-drawn to form the Type 1 SMA fibre 100. An example of an appropriately shaped mould is shown in Figure 2.

[0076] In Figure 2, the mould 200 comprises a moveable top fixture 210, a stationary bottom fixture 220, threaded holes 230 and mould teeth 240. The skilled addressee will understand that the mould can be fabricated from any suitable material known in the art. Preferably, the mould is fabricated from hardened steel to avoid damaging the mould during the deep-drawing process. The straight SMA fibre of length, /, is placed in the gap between the moveable top fixture 210 and the stationary bottom fixture 220. When pressure is applied to the flat surface of the moveable top fixture 210 the straight SMA fibre is pressed towards the stationary bottom fixture 220 and assumes the shape of the gap indentation. The width of the mould teeth 240 determines the length of the flat segments (//) while the distance between adjacent mould teeth 240 determines the length of the round segments (l _r ). The width, w, of the flat segments 110 is determined by the pressure applied to the moveable top fixture 210.

[0077] Figure 3 shows an embodiment of a Type 2 SMA fibre 300. The Type 2 SMA fibre 300 may be referred to as a second type of SMA fibre. In some embodiments, the Type 2 SMA fibre 300 may be referred to as a pseudoelastic SMA fibre 300. The Type 2 SMA fibre 300 may be used for reinforcement of cementitious and non-cementitious composites. The Type 2 SMA fibre 300 comprises a straight middle segment 310 and an end-hook 320 at each end of the straight middle segment 310. In other words, the type 2 SMA fibre 300 comprises a first end-hook 320 and a second end-hook 320. Each end-hook 320 comprises four short straight segments 330, 340, 350 and 360 with lengths U, l·, h and U, respectively. These may be referred to as a first short straight segment 330, a second short straight segment 340, a third short straight segment 350 and a fourth short straight segment 360 respectively. Each end of the straight middle segment 310 is connected to the respective end-hook 320 by the immediately adjacent first short straight segment 330 through an interior angle a. The second short straight segment 340 is bent away from the first short straight segment 330 through an exterior angle b. The third short straight segment 350 is connected to the second short straight segment 340 through an interior angle the same as a. It will, however, be appreciated that in some embodiments, the third short straight segment 350 is connected to the second short straight segment 340 through an interior angle that differs from a. Finally, the fourth short straight segment 360 is bent away from the third short straight segment 350 by an exterior angle the same as b to complete the end-hook 320. It will, however, be appreciated that in some embodiments, the fourth short straight segment 360 is connected to the third short straight segment 350 through an interior angle that differs from b.

[0078] In some embodiments, a is any value in the range of about 90° to 100°.

[0079] In some embodiments, a is any value in the range of 90° to 100°. For example, in some embodiments, a may be 90°, 91°, 92°, 93°, 94°, 95°, 96°, 97°, 98°, 99° or 100°. Preferably, a is 90°.

[0080] In some embodiments, b is any value in the range of about 260° to 270°.

[0081] In some embodiments, b is any value in the range of 260° to 270°. For example, in some embodiments, b may be 260°, 261°, 262°, 263°, 264°, 265°, 266°, 267°, 268°, 269° or 270° Preferably, b is 270°.

[0082] Specifically, the first short straight segment 330 is substantially perpendicular to the longitudinal axis 370 of the straight middle segment 310 while the second short straight segment 340 is substantially parallel to the longitudinal axis 370 of the straight middle segment 310. Similar to the first short straight segment 330, the third short straight segment 350 is substantially perpendicular to the longitudinal axis 370 of the straight middle segment 310 while the fourth short straight segment 360 is similar to the second short straight segment 340 by being substantially parallel to the longitudinal axis 370 of the straight middle segment 310.

[0083] The lengths of the short straight segments in the end-hooks 320 depend on the aspect ratio of the fibres. [0084] In some embodiments, the aspect ratio of Type 2 SMA fibre 300 is any value within the range of about 20 to 85.

[0085] In some embodiments, the aspect ratio of Type 2 SMA fibres is any value within the range of 20 to 85. For example, the aspect ratio of the Type 2 SMA fibre 300 may be 20 30, 40, 50, 60, 70, 80 or 85.

[0086] In some embodiments, the four short straight segments {U, h, h and U) of the Type 2 SMA fibre 300 are of equal length.

[0087] In some embodiments, each short straight segment can have a length in the range of about 0.5 mm and 6 mm.

[0088] In some embodiments, each short straight segment can have a length in the range of 0.5 mm and 6 mm. For example, the length of each short straight segment can be 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm or 6 mm. Preferably, the length of each short straight segment is between

1 mm and 4 mm.

[0089] In a preferred embodiment, the lengths of the first short straight segment 330 and the third short straight segment 350 is at least 1.5 mm while the lengths of the second short straight segment 340 and the fourth short straight segment 360 can be equal or different lengths, albeit at least 1.5 mm.

[0090] Figure 4 shows a Type 2 SMA fibre 400 which is an alternative embodiment of the Type

2 SMA fibre 300. The Type 2 SMA fibre 400 may be referred to as a third type of SMA fibre. In some embodiments, the Type 2 SMA fibre 400 may be referred to as a pseudoelastic SMA fibre 400. In Figure 4, the Type 2 SMA fibre 400 comprises a straight middle segment 410, end-hook 420 at one end of the straight middle segment 410 and end-hook 430 at the other end of the straight middle segment 410. The end-hook 420 may be referred to as a first end-hook. The end-hook 430 may be referred to as a second end-hook. Importantly, end-hooks 420 and 430 are located on opposite sides of the longitudinal axis 440 of the straight middle segment 410. End-hook 420 comprises four short straight segments 450, 460, 470 and 480 with lengths U, h, h and U- These may be referred to as a first short straight segment 450, a second short straight segment 460, a third short straight segment 470 and a fourth short straight segment 480 respectively. End-hook 430 comprises four short straight segments 450a, 460a, 470a and 480a with lengths h _a , h _a , h _a and U _a . These may be referred to as a first short straight segment 450a, a second short straight segment 460a, a third short straight segment 470a and a fourth short straight segment 480a respectively.

[0091] One end of the straight middle segment 410 is connected to end -hook 420 by the immediately adjacent first short straight segment 450 through an interior angle a. The second short straight segment 460 is bent away from the first short straight segment 450 through an exterior angle b. The third short straight segment 470 is connected to the second short straight segment 460 through an interior angle the same as a. It will, however, be appreciated that in some embodiments, the third short straight segment 470 is connected to the second short straight segment 460 through an interior angle that differs from a. Finally, the fourth short straight segment 480 is bent away from the third short straight segment 470 by an exterior angle the same as b to complete the end- hook 420. It will, however, be appreciated that in some embodiments, the fourth short straight segment 480 is connected to the third short straight segment 470 through an interior angle that differs from b.

[0092] The other end of straight middle segment 410 is connected to end-hook 430 by the immediately adjacent first short straight segment 450a through the same interior angle a used in end-hook 420. The second short straight segment 460a is bent away from the first short straight segment 450a through the same exterior angle b used in end-hook 420. The third short straight segment 470a is connected to the second short straight segment 460a through an interior angle the same as a used in end-hook 420. Finally, to complete end-hook 430, the fourth short straight segment 480a is bent away from the third short straight segment 470a by an exterior angle the same as b used in end-hook 420. It will, however, be appreciated that in some embodiments, one or more of these angles may differ from the relevant counterpart angle of the end-hook 420.

[0093] In some embodiments, a is any value within the range of about 90° to 100°.

[0094] In some embodiments, a is any value in the range of 90° to 100°. For example, in some embodiments, a may be 90°, 91°, 92°, 93°, 94°, 95°, 96°, 97°, 98°, 99° or 100°. Preferably, a is 90°.

[0095] In some embodiments, b is any value within the range of about 260° to 270°. [0096] In some embodiments, b is any value within the range of 260° to 270°. For example, in some embodiments, b may be 260°, 261°, 262°, 263°, 264°, 265°, 266°, 267°, 268°, 269° or 270° Preferably, b is 270°.

[0097] Specifically, the first short straight segments 450 and 450a are substantially perpendicular to the longitudinal axis 440 of the straight middle segment 410 while the second short straight segments 460 and 460a are substantially parallel to the longitudinal axis 440 of the straight middle segment 410. Similar to the first short straight segments 450 and 450a, the third short straight segments 470 and 470a are substantially perpendicular to the longitudinal axis 440 of the straight middle segment 410 while the fourth short straight segments 480 and 480a are similar to the second short straight segments 460 and 460a by being substantially parallel to the longitudinal axis 440 of the straight middle segment 410.

[0098] The length of the short straight segments in the end hooks 420 and 430 depends on the aspect ratio of the fibres.

[0099] In some embodiments, the aspect ratio is any value within the range of about 20 to 85.

[00100] In some embodiments, the aspect ratio is any value within the range of 20 to 85. For example, the aspect ratio of the Type 2 SMA fibre 400 may be 20 30, 40, 50, 60, 70, 80 or 85.

[00101] In some embodiments, the four short straight segments in each end-hook (h, , h, U as well as U _a , ha, ha and ha) of the Type 2 SMA fibre 400 are of equal length.

[00102] In some embodiments, each short straight segment can have a length within the range of about 0.5 mm and 6 mm.

[00103] In some embodiments, each short straight segment can have a length within the range of 0.5 mm and 6 mm. For example, the length of each short straight segment can be 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, 5 mm or 6 mm. Preferably, the length of each short straight segment is between 1 mm and 4 mm.

[00104] In a preferred embodiment, the lengths of the first short straight segments 450 and 450a and the third short straight segments 470 and 470a are at least 1.5 mm while the lengths of the second short straight segments 460 and 460a and the fourth short straight segments 480 and 480a can be equal or different lengths, albeit at least than 1.5 mm.

[00105] With regard to Type 2 SMA fibres 300, 400, the term “substantially perpendicular” or “substantially parallel” is used to consider the existence of some small or accidental deviation during the manufacturing process of Type 2 SMA fibres 300, 400. However, ensuring that the deviation is minimal, so that a and b are within the specified ranges, is beneficial because the pullout behaviour of the Type 2 SMA fibres 300, 400 is adversely affected when a is considerably larger than 90° and/or b is considerably smaller than 270°. Type 2 SMA fibres 300, 400 with a considerably larger than 90° and/or b considerably smaller than 270° are susceptible to being pulled out from the matrix without appreciable re-centring and crack-closing performance. Furthermore, composites containing such fibres may exhibit poor performance under cyclic loading. Conversely, when a is considerably smaller than 90° and/or b is considerably larger than 270°, the fibres may hook to one another, forming balls that may not be uniformly dispersed within the matrix.

[00106] The Type 2 SMA fibre 300, 400 may be manufactured from a SMA wire using any suitable forming process or combination of processes known in the art, for example, deep-drawing combined with, followed by, or preceded by heat treatment. Firstly, the SMA wire is cut to obtain a straight fibre of predetermined length, /, then using an appropriately shaped mould, the straight SMA fibre is deep-drawn to form Type 2 SMA fibre 300, 400. Following this, the deep-drawn Type 2 SMA fibre 300, 400 is heat treated so that its ends are permanently deformed to form end- hooks 320 (or end-hooks 420, 430 in the case of the Type 2 SMA fibre 400 shown in Figure 4). The heat treatment may conveniently be performed by fitting cartridge heaters into the mould. However, this can be performed by other means known in the art. An example of a deep-drawing mould fitted with cartridge heaters used for manufacturing Type 2 SMA fibres 300 is shown in Figure 5.

[00107] In Figure 5, the mould 500 comprises a moveable top fixture 510 with threaded holes 520 at its top, a detachable plate 530 which is detachably attached to the base of movable top fixture 510, a stationary bottom fixture 540, and cartridge heaters 550. It will be readily apparent to the skilled addressee that the dimensions of the mould will depend on the desired dimensions of Type 2 SMA fibre 300. Furthermore, the skilled addressee will understand that the mould can be fabricated from any suitable material known in the art. Preferably, the mould is fabricated from hardened steel.

[00108] To manufacture Type 2 SMA fibre 300, firstly, a straight SMA fibre of predetermined length, l, is fixed between the moveable top fixture 510 and detachable plate 530 by a suitable fastening means, such as bolts or screws or any other suitable fastening means known in the art, inserted through threaded holes 520. Following this, the moveable top fixture 510 is gradually pressed onto the stationary bottom fixture 540 to obtain the segmented fibre geometry shown in Figure 3. However, the fibres obtained at this stage are not yet permanently deformed due to the pseudoelastic nature of SMA. The skilled addressee will understand that the segmented fibres can be permanently deformed by any suitable method known in the art. Preferably, heat treatment is used to permanently deform the segmented fibres. This can be done for example, by using cartridge heaters 550 which may be conveniently fitted into the stationary bottom fixture 540 across its entire length (that is, from the anterior face to the posterior face of the stationary bottom fixture 540), preferably in close proximity to where the end-hooks are to be formed. It will be appreciated by the skilled addressee that for the purposes of practising the invention, heat may be provided by any suitable heat source known in the art. It will also be appreciated by the skilled addressee that there may be a single heat source or a plurality of heat sources and that they may be positioned anywhere on: the stationary bottom fixture 540; the moveable top fixture 510; any other part of the mould 500; or separate from but in close proximity to the mould 500.

[00109] A voltage regulator 560 may conveniently be used to control the temperature of the cartridge heaters 550 to avoid high temperatures which may be deleterious to the mechanical properties of the Type 2 SMA fibre 300. During the fabrication of Type 2 SMA fibre 300, cartridge heaters 550 may be maintained at an operating temperature in the range 250°C to 400°C. Preferably, the operating temperature range is between 300°C and 350°C.

[00110] It will be appreciated by the person skilled in the art that, to obtain the segmented fibre geometry shown in Figure 4, the steps of the top fixture 510 and the bottom fixture 540 may be inverted on one side. That is, the bottom fixture 540 may comprise descending steps on one side (when considering the steps in a direction from a central longitudinal axis of the bottom fixture 540, outwards). Similary, the top fixture 510 may comprise complementary steps to enable the formation of the Type 2 SMA fibre 400 illustrated in Figure 4.

2 Examples

2.1 Pullout Behaviour of Type 1 and Type 2 SMA Fibres

[00111] The single fibre pullout test was chosen to determine the re-centring and crack-closing behaviour of Type 1 SMA fibres 100 and Type 2 SMA fibres 300 when embedded in cementitious and non-cementitious matrices. This test is known in the art as a fundamental method of analysing the critical aspects of the overall performance of high performance fibre reinforced cementitious and non-cementitious composites under uniaxial tension or flexure.

2.2 Matrix, Pullout Specimens and Test Setup

[00112] A self-compacting cementitious matrix was chosen to study the fibre-matrix bond behaviour of the Type 1 SMA fibres 100 and Type 2 SMA fibres 300. The properties of the Type 1 SMA fibres 100 and Type 2 SMA fibres 300 used in the experiment are shown in Table 1 and Table 2. The matrix binder was a mix of cement, class-F fly ash, ground-granulated blast-furnace slag and densified silica fume. Fine quartz sand (with particle size below 600 microns) and 3 different sets of crushed aggregates (with particle diameters of <4 mm, <7 mm, and < 10 mm) were incorporated in the matrix as fillers. A polyether-based superplasticiser and a viscosity agent (an aqueous solution based on polysaccharides) were used to control the fresh properties of the matrix. Also, the matrix skeleton was optimised to obtain a high packing density. A slump diameter of 500 mm at 2.7 seconds and a final slump diameter of 750 mm was obtained for the matrix, indicating a suitable matrix for high performance fibre reinforced cementitious and non-cementitious composites. Additionally, a compressive strength of 51.5 MPa was obtained for the matrix after 28 days. Table 1: An overview of Type 1 SMA fibre 100

Table 2: An overview of Type 2 SMA fibre 300

[00113] Cubic pullout samples were prepared by fixing the fibres at the centre of cubic moulds (which had edge lengths of 100 mm), followed by casting the matrix. The embedded length of the fibres was fixed at 30 mm for all samples. The fresh specimens were covered with plastic immediately after casting, then they were stored in a laboratory environment for 24 hours before demoulding. Following this, they were kept in a curing chamber at humidity of 92 ± 2% and temperature of 23 ± 1 °C for 27 days. A minimum of three pullout tests were conducted for each type of SMA fibre.

[00114] The equipment used to conduct the single fibre pullout test is illustrated schematically in Figure 6. The test equipment comprises a grip 600 (which was used to apply a pullout load to the SMA fibre 610) and a fixture system 620 (used to hold the cubic shaped matrix sample 630 in place). The SMA fibre 610 was aligned to the vertical centre line of the load cell by two small half-cylindrical steel segments placed inside the grip. The fixture system was equipped with four small cubes 640 on the top platen 650 and bottom platen 660 to support the SMA fibre specimen 610. Such an arrangement avoids full contact between the top and bottom platen of the fixture system, and hence, eliminates matrix confinement. A precise extensometer 670 (±0.5% reading accuracy) was used to record the displacement between the grip and fixture. This displacement can be interpreted as the sum of fibre deformation and the slip which occurs between the fibre and the matrix. The pullout loading rate was fixed at 0.025 mm/s for both monotonic and cyclic tests to represent a quasi-static condition.

2.3 Static Pullout Behaviour of Type 1 and Type 2 SMA Fibres

[00115] Figure 7 shows the tensile stress-strain response 700 of Type 1 SMA fibre 100 and the tensile stress-strain response 710 of Type 2 SMA fibre 300 compared to the tensile stress-strain response 720 of SMA wire.

[00116] Without wishing to be limited by theory, it is believed that the stress levels corresponding to the initiation ( a ^Ms ) and completion (a ^M f ) of the austenite-martensite transformation increased due to the fibre manufacturing processes. The manufacturing processes also increased the strain, s ^Ms , corresponding to the initiation of the austenite -martensite transformation. However, the strain, e ^M f , corresponding to the completion of the austenite -martensite transformation remained almost unchanged after deep-drawing as well as deep-drawing followed by heat treatment. Furthermore, the ultimate tensile strength, o _u , of the SMA fibres decreased slightly following deep drawing; this however, improved after heat treatment. The elastic modulus of austenite ( E ^A ) remained almost unchanged after deep drawing followed by heat treatment, whereas these processes decreased the elastic modulus of martensite ( E ^M ). An example of experimentally obtained values for these parameters after deep-drawing as well as deep-drawing followed by heat treatment are listed in Table 3.

Table 3: Tensile characteristics of Type 1 and Type 2 SMA fibres compared to SMA wire

Diameter Tensile characteristic

Name d Manufacturing pr _a Ms _£ Ms _a Mf _£ Mf _{Gu E} A _E M

(mm) ocess

(MPa) (%) (MPa) (%) (MPa) (GPa) (GPa)

SMA wire 0.8 548 1.4 622 9.5 1245 58 16.4

Type 1 0.8 628 1.8 698 9.3 1127 14.8 SMA (for round Cold-pressing 58 fibre segment) (14%) (29%) (12%) (2%) (9%) (10%)

Type 2 618 1.7 697 9.8 1431 11.5 SMA 0.8 Heat treatment 58 fibre (13%) (21%) (12%) (3%) (15%) (29%)

Note: The percentage change in each parameter due to manufacturing processes is given in parentheses

[00117] Figure 8a shows the pullout performance 800 of Type 1 SMA fibre 100, Figure 8b shows the pullout performance 810 of Type 2 SMA fibre 300, while Figure 8c shows slip failure 870 of Type 1 SMA fibre 100, under static loading. Without wishing to be limited by theory, it is believed that the pullout mechanism of these fibres comprises four different stages. The stages are specified only for Type 1 SMA fibre 100 in the figures because Type 2 SMA fibre 300 undergoes similar stages.

[00118] In the first stage 820 (stage 1), a sharp increase in pullout load is observed due to the elastic physico-chemical bond between the fibre and matrix, which depends on the matrix packing density and the surface micro-topography of fibres. At this stage, no slip occurs between the fibre and matrix. The fibres start to slip when the fibre-matrix interfacial shear stress reaches the elastic bond strength at a load level of approximately 75 N and 50 N for Type 1 and Type 2 SMA fibres, respectively.

[00119] In the second stage 830 (stage 2), the pullout load increases linearly with a lower gradient compared to stage 1 up to a plateau (stage 3 - 840) at 300 N and 280 N for Type 1 and Type 2 SMA fibres, respectively. Without wishing to be limited by theory, it is believed that the small difference at the plateau load might be attributed to the differences between the effect of cold drawing and heat treatment used to prepare the fibres. The plateau in the pullout diagram corresponds to the austenite-martensite phase transformation of the SMA fibres. The onset and completion of transformation typically occur at a total displacement of about 0.7 mm and 2.4 mm, respectively, for both Type 1 and Type 2 SMA fibres.

[00120] In the fourth stage 850 (Stage 4), the austenite-martensite transformation is completed and a distinct change appears in the slope of the pullout curve. At this stage, the pullout resistance increases while the SMA fibres experience both elastic deformation of martensite and limited fibre-matrix slip. Finally, fibre rupture 860 or large slip between fibre and matrix (called slip failure 870) occurs where the load surpasses 500 N for the tested SMA fibre. For a Type 1 SMA fibre 100, either one of fibre rupture or slip failure may occur, but both failure methods cannot occur simultaneously. Typically, at this point the stress level in the fibres is greater than 1,000 MPa.

[00121] It is noteworthy that the displacements shown in Figure 8 comprises SMA fibre deformation and fibre-matrix slip at all stages except for stage 1.

2.4 Cyclic Pullout Behaviour, Re-centring, and Crack Closure Capacity of Type 1 and Type 2 SMA Fibres

[00122] Figure 9 illustrates the cyclic pullout behaviour of Type 1 SMA fibre 100 while Figure 10 illustrates the cyclic pullout behaviour of Type 2 SMA fibre 300.

[00123] As can be seen in Figure 9b, Type 1 SMA fibre 100 exhibits extraordinary re-centring performance 900 and crack-closing performance, especially at slips less than 3 mm, which is of interest in structural applications. In Figure 10b, Type 2 SMA fibre 300 is shown to exhibit significant re-centring performance 1000. Both types of SMA fibres show remarkable re-centring even after 2 mm displacement, which is understood in the art as a substantial displacement in fibre pullout mechanism. Even at such a large displacement, Type 1 SMA fibre 100 is shown to exhibit significant displacement recovery with very low permanent fibre -matrix slip 910 (Figure 9b). Similarly, Type 2 SMA fibre 300 is shown to exhibit significant displacement recovery with very low permanent fibre-matrix slip 1010 (Figure 10b).

[00124] The re-centring capacity of the fibres, R _re is quantified by Equation (1) at each cycle, where DS _max and DS _res represent the maximum displacement (that is, fibre deformation plus slip) and the residual displacement, respectively. [00125] The re-centring capacity of Type 1 SMA fibre 100 during the second and third cycles (that is, cycles with 2 mm and 3 mm displacement amplitude) was found to be 86% and 77%, respectively. For Type 2 SMA fibre 300, during the second and third cycles, the re-centring capacity was found to be 88% and 84%, respectively.

[00126] Figure 11 shows the pullout load-slip behaviour of commercially available 5D hooked- end steel fibres which are commonly used in the construction industry. When compared to the Type 1 SMA fibre 100 and Type 2 SMA fibre 300 at cycles with similar displacement amplitudes, the 5D hooked-end steel fibres exhibited insignificant re-centring performance 1100 with large permanent slip 1110, in contrast to the behaviour of the Type 1 and Type 2 SMA fibres. During the second and third cycles, the re-centring capacity of the steel fibres was approximately 5% and 3%, respectively.

[00127] Figure 12 compares at various cycles, the re-centring capacity 1200 for Type 1 SMA fibre 100, re-centring capacity 1210 for Type 2 SMA fibre 300 and re-centring capacity 1220 for 5D hooked-end steel fibre. It is evident from Figure 12 that both Type 1 SMA fibre 100 and Type 2 SMA fibre 300 exhibit good re-centring capacity, especially at cycles with amplitudes below 5 mm. Additionally, both Type 1 SMA fibre 100 and Type 2 SMA fibre 300 showed significantly higher re-centring capacities than the 5D hooked-end steel fibres.

2.5 Crack Closing and Re-centring Performance of Cementitious Composites Reinforced with Type 1 SMA Fibres

2.5.1. Cementitious Composite Matrix Mix Design and Specimens

[00128] The mix design of the cement -based matrix used to cast Type 1 SMA fibre 100 reinforced composites is shown in Table 4. The matrix was self-compacting and could be cast with no vibration. The matrix’s binder consisted of ordinary Portland cement, low-calcium fly ash, ground- granulated blast-furnace slag (GGBFS), and densified silica fume. Three types of fillers were used to optimise grading of the matrix skeleton, namely: fine sand; fine aggregate (<4 mm in diameter); and coarse aggregate (<7 mm in diameter and <10 mm in diameter). Polycarboxylic-based high- range water reducer (HRWR), polyether-based superplasticiser (SP), and a viscosity modifying agent (VMA) were used to achieve high flowability and workability with no bleeding and segregation.

Table 4: Weight proportion of cementitious composite matrix ingredients _ Aggregate _

Ceme Fly GGBF Fine . _ Wat HRWR VM a 4 7 10 sp nt ash S sand er A A fume mm mm mm

1 0.89 0.56 0.18 2.3 3.2 1.8 1.8 1.12 0.015 0.004 0.01

[00129] Type 1 SMA fibres 100 and steel fibres (SF) were added to separate matrix structures at fibre dosages of 0.50%, 0.75%, and 1.00% by volume respectively. Therefore, six composites were prepared to cast the required specimens. The composites containing Type 1 SMA fibres 100 are denoted by SMA50, SMA75, and SMA100 for fibre dosages of 0.50%, 0.75% and 1.00%, respectively. Similarly, SF50, SF75, and SF100 denote composites with 0.50%, 0.75% and 1.00% SFs, respectively. The hooked-end SF used was Dramix® 3D (60 mm long) with an aspect ratio of 80, and it was used as-received. Additionally, three control specimens designated as CS were cast for each type of test.

[00130] A 100-litre capacity laboratory pan mixer was used to prepare the composites. Firstly, the solid ingredients were mixed for 1 minute, then 70% water was added and then the whole mixture was mixed for 2 minutes. Next, SP, HRWRA and 20% water were thoroughly mixed and added to the pan, following by 4 minutes of mixing. Following this, the remaining water was mixed with VMA and added to the mixture to control the mixture viscosity. Finally, fibres were added to the mixture and stirred until a uniform fibre distribution was visually observed, typically seen after stirring for 2 to 3 minutes. For each fibre dosage, the fresh mixture was cast in plastic moulds to prepare six 100 x 100 x 400 mm beams for static and cyclic flexural tests, and three cylinders 200 mm (height) x 100 mm (diameter) for compression tests. All specimens were kept in a curing chamber for 28 days at humidity and temperature of 92 ± 2% and 23 ± 1 °C, respectively.

[00131] Fresh properties were quantified based on slump height, slump flow diameter, and the time to reach 500 mm diameter (T500). Six unnotched and six notched beams (100 x 100 x 400 mm) were prepared for the static and cyclic flexural test and the evaluation of the re -centring and crack-closure capability of the composite at each fibre content. For the notched beams, a notch of 16.5 mm depth and 4.5 mm width was cut at their midspan. All the specimens were kept in a curing chamber for 28 days at a humidity and temperature of 92 ± 2% and 23 ± 1 °C, respectively.

2.5.2. Characterisation Procedures for Cementitious Composites

[00132] The flowability of the fresh composites was examined by slump test according to ASTM C143/C143M ² . Slump height, final diameter of spread, and the time when the spread reached 500 mm diameter (T500) was recorded. The measured values were used to calculate the relative slump according to the equation below: where D is the average of slump diameters measured in two perpendicular directions and Do is the base diameter of the slump cone.

[00133] Static and cyclic four-point bend tests on the beams were conducted in displacement control at a rate of 1.0 mm/min using an Instron ^® 5982 electromechanical testing machine. The span length of beams and the distance between loading points was 300 mm and 100 mm, respectively. The midspan deflection of the beams was recorded using an extensometer with an accuracy of ±0.5%. Additionally, static and cyclic flexural tests were conducted on notched beams using a three -point bend setup with a span length of 300 mm.

[00134] The cyclic loading regime consisted of two different parts. In the first part, fifteen loading cycles were defined with a step-wise increasing amplitude of 0.2 mm. It allowed the evaluation of crack-closing and re-centring behaviour of beams at small deflections after cracking. The second part of the loading regime included eight cycles with a step-wise increasing amplitude of 0.5 mm, which allowed for evaluation of the flexural behaviour at large deformations up to failure. The reversed portion of each cycle included a load limit of zero that defined the onset of the next cycle in the loading regime.

[00135] Digital Image Correlation (DIC) equipment for measuring full-field strain and crack opening included a 6000 x 4000 pixels camera and two white light sources. The camera captured sequential images of a field of view equal to 100 mm x 150 mm illuminated by the light sources to avoid any non-uniform light intensity over the view field. The camera lens was set perpendicular and close to the view field to avoid misleading DIC analysis. A reference image was recorded for each specimen with a scale bar before applying the loading regime to scale sequential images during DIC analysis performed by ARAMIS ³ . ARAMIS tracks an overlapping grid of unique facets in sequential images to create a series of data points. Then, the deformation and full-field strain map are built based on the mapped data points ³ .

2.5.3. Fresh Properties of Cementitious Composites

[00136] The slump, flow diameter and flow rate (T500) measured for control mix and composites are shown in Table 5. Regardless of fibre type, the addition of fibres decreased the flowability of mixtures, and it was further reduced by increasing the fibre content of composites. The increase in fibre content increases fibres interaction and restricts the movement of the matrix’s particles. Hence, higher internal friction is induced in the mixture by increasing fibre content, leading to less flowability. At any given fibre content, the reduction in slump flow was slightly lower for samples comprising Type 1 SMA fibres 100 compared to samples comprising SF; this can be attributed to the straight nature of the Type 1 SMA fibres 100. Similar to the flow diameter, the flow rate (T500) also decreased by increasing fibre dosage for both types of fibres.

[00137] Figure 13 shows a comparison of the flowability of the test mix composites, obtained with slump-flow classes defined by EN206:2013 ⁴ for self-compacting mixtures. As per EN206:2013, the control mixture, SMA50, and SF50 were classified in class 2. Increasing the fibre content to 0.75% reduced the flowability of mixtures to class 1 (lowest flowability of EN206:2013’s classifications) for both Type 1 SMA fibres 100 and SFs. Further increasing the fibre content to 1.00% led to a loss in self-compacting characteristics of the mix. Intense interaction between fibres was observed for SMA100 and SF100 during slump tests, locking the aggregates in place and restricting their movement. Based on the results of T500, CS and composites with 0.50% and 0.75% fibres (either Type 1 SMA fibres 100 or SFs) showed a viscosity class of VS2 (T ₅₀₀ > 2.0 s) according to EN206:2013 ⁴ . Table 5: Summary of results obtained from slump tests

Type 1 SMA Flow

Composite SF content Slump T500 fibre content diameter G _R

ID (% volume) (mm) (s) (% volume) (mm)

CS 680 295 2.7 10.5

SMA50 0.50 660 290 3.3 9.9

SMA75 0.75 590 235 4.5 7.7

SMA100 1.00 525 175 16.5 5.9

SF50 0.50 655 290 3.4 9.7

SF75 0.75 580 220 4.9 7.4

SF100 1.00 520 165 18.1 5.7

2.5.4. Flexural Behaviour

[00138] Figure 14, Figure 15 and Figure 16 show the flexural behaviour of CS beams, Type 1 SMA fibre -reinforced beams and SF-reinforced beams, respectively. Figures 15 and 16 also show the envelope of the cyclic curve and the curve obtained from the static flexural test.

[00139] The cyclic curves in the figures show that all fibre reinforced beams exhibited a higher load-bearing capacity compared to the CS beams. The load-bearing capacity increased with increasing fibre content, regardless of fibre type. Additionally, all the fibre reinforced beams cracked during the second cycle and bore increased flexural load after cracking because of the crack-bridging performance of the fibres. This suggests that fibre reinforced beams will exhibit deflection hardening behaviour regardless of fibre type. However, Type 1 SMA fibre-reinforced specimens exhibited the hardening behaviour up to deflections between 2.5 mm to 3.5 mm, significantly larger than that of SF-reinforced specimens (approximately 1.2 mm to 1.5 mm). After a peak point, the hysteresis loops of all the fibre-reinforced beams showed deflection softening behaviour until the experiment was terminated. By increasing the fibre content, SF-reinforced beams experienced a steeper decrease in flexural load at the softening portion, which was not observed in the case of Type 1 SMA fibre -reinforced beams. The static flexural curve was similar to the envelope of the cyclic curve, especially for the initial elastic stage and deflection hardening stage.

[00140] Additionally, Figures 15 and 16 show that the hysteresis energy (i.e. the area enclosed by hysteresis loops), was minimal during the early stage of loading since the beams were in the elastic stage. Without wishing to be limited by theory, it is suggested that as the cycles progressed up to the peak load, cracks propagated while the fibres bridged the cracks. As a result, the fibres partially bore the tensile force acting on the crack planes. This caused fibre deformation as well as fibre slip, and damage gradually accumulated. Consequently, the fibre reinforced beams dissipated significant energy as the cycles progressed. However, the amount of dissipated energy and its trend is different for Type 1 SMA fibre -reinforced beams when compared to SF-reinforced specimens.

[00141] Figures 17 shows cyclic crack mouth opening displacement (CMOD) curves and envelope curves for notched Type 1 SMA fibre -reinforced beams while Figure 18 shows cyclic - CMOD curves and envelope curves for notched SF-reinforced beams.

[00142] The curves in Figure 17 indicate that Type 1 SMA fibres 100 bridged the crack and supported greater loads than the cracking load after cracking. Therefore, as the cycles progressed and the CMOD increased, the level of load borne by the specimen increased, indicating a displacement -hardening behaviour. The increase in load level was sharper, and the load-bearing capacity increased with increases in the Type 1 SMA fibre 100 content. However, CMOD corresponding to peak load decreased with increases in fibre dosage. Thus, SMA75 and SMA100 exhibited a larger slope for the displacement-hardening portion of the load-CMOD curve.

[00143] In contrast, Figure 18 shows that residual CMOD after unloading at a given cycle is larger for SF-reinforced notched beams than for Type 1 SMA fibre -reinforced notched beams. This difference became more pronounced with progressive cycles. Such greater CMOD observed for SF-reinforced notched beams originates from plastic fibre deformation at hooked-ends and large slip between SFs and matrix ¹ . Since these mechanisms are not recoverable, the reduction in crack width after unloading was minimal for SF-reinforced notched beams. The small crack width reduction occurs due to elastic strain recovery in SFs.

[00144] Additionally, notched beams reinforced with SFs reached their peak loads at smaller CMOD, resulting in a lower displacement-hardening portion. Furthermore, the notched SF- reinforced samples experienced a steeper softening load-CMOD response after peak load than notched Type 1 SMA fibre-reinforced beams. 2.5.5. Ultimate Strength and other Flexural Characteristics

[00145] In general, the CS beams exhibited a brittle elastic behaviour, whereas all the fibre- reinforced beams showed ductile behaviours with three different stages; pre-cracking stage (i.e. elastic stage), deflection-hardening stage, and deflection-softening stage. The pre-cracking stage of fibre -reinforced beams was similar to the CS beams since the fibres enhance the post-cracking behaviour of specimens by bridging cracks.

[00146] Table 6 shows a summary of the parameters that define the deflection-hardening stage. These parameters are: peak load ( P _peak ) and its corresponding deflection cumulative dissipated energy up to peak load ( E _peak ); and flexural toughness factor (FT F _peak ). The dissipated energy before cracking (E _pre-c ) is shown in Table 6 to provide a comparison between pre-cracking and deflection-hardening stages. FTF _peak was calculated using equation (3) below: where b and h are the width and depth of the beam, respectively. Equation (3) was obtained by modifying the toughness factor suggested by JSCE SF-4 ⁵ to make it suitable for composites exhibiting deflection-hardening behaviour ⁶ .

Table 6: Summary results for four-point bend tests

6peak Ppeak Epre-c Epeak FTFpeak

Beam ID

(mm) (kN) (N-m (N· m) (kPa)

CS 029 TOO P ^{1 1}

SMA50 040 2L5 L7 650 65

SMA75 3.50 34.5 1.2 135.3 135

SMA100 2.20 41.7 1.8 165.8 165

SF50 L40 2T5 L2 204 23

SF75 1.60 30.4 1.8 24.3 24

SF100 1.20 40.4 1.8 27.3 27

[00147] Table 6 shows that at a given fibre content P _peak of beams reinforced with Type 1 SMA fibres 100 and SFs are comparable whereas S _peak is much larger for Type 1 SMA fibre-reinforced beams. This is due to the large strain capacity of Type 1 SMA fibres 100 (as a result of the austenite-martensite phase transformation) and their firm bond with the surrounding matrix. Such a large deflection at peak load cannot be obtained without a strong fibre -matrix bond since fibre slip inhibits stress development in the fibre and hence phase transformation. Having significantly larger _peak , the composites containing Type 1 SMA fibres 100 can undergo more load cycles without losing their load-bearing capacity. As a result, they exhibit significantly larger E _peak and flexural toughness (measured as FTF _peak ) when compared to SF-reinforced specimens. This showed that, depending on fibre dosage, Type 1 SMA fibre -reinforced cementitious composites exhibited flexural toughness in the range 2.8 to 6 times greater than SF-reinforced cementitious composites at comparable reinforcing fibre dosages.

[00148] It is known in the art that the envelope curve of hysteresis loops can be idealised by a bilinear curve to evaluate the structural behaviour of fibre -reinforced beams in terms of ductility and performance factor ^{7,8, 9} .

[00149] Table 7 shows the bilinear curves for both Type 1 SMA fibre -reinforced beams and SF- reinforced beams. The values in Table 7 indicate that Type 1 SMA fibre -reinforced beams exhibited higher ductility, m, and force reduction performance factor, R, than their SF-reinforced counterparts. For both types of fibres, the increase in fibre dosage in the test range resulted in reduced ductility and larger overstrength factor. These two parameters should be evaluated simultaneously and not separately because the improvement of one of them considered in isolation may not be an indication of better structural performance. The force reduction performance factor considers the effect of ductility and overstrength factor simultaneously and thus may be an indication of overall performance. When this was considered, it was found that the increase in Type 1 SMA fibre 100 content enhanced the force reduction performance factor, whereas it decreased by increasing the SF content.

Table 7: Ductility and performance factors for tested beams based on the envelope curve idealised by a bilinear curve

SMA50 0.41 3.40 15.0 19.5 21.6 8.4 1.3 4.0 5.2

SMA75 0.98 4.74 15.5 32.5 34.5 4.9 2.1 2.9 6.1

SMA100 1.11 5.24 16.1 40.0 43.0 4.7 2.5 2.9 7.3

SF50 0.54 3.57 16.3 22.0 24.6 6.6 1.3 3.5 4.6

SF75 0.68 2.64 16.4 27.0 30.6 3.9 1.6 2.6 4.2

SF100 0.64 1.94 18.1 32.9 40.2 3.0 1.8 2.3 4.1

Note: _y and A _u are deflections corresponding to the yield and ultimate points on the bilinear curve, P _s is the load level at which the envelope curve deviates significantly from the initial elastic portion, P _y is the yield load, m is ductility, W is the overstrength factor, /? _m is ductility performance factor, and R is force reduction performance factor.

[00150] The flexural behaviour of different types of fibre-reinforced beams can also be compared using three -point bend tests on notched fibre-reinforced beams ¹⁰ .

[00151] Table 8 shows the flexural parameters obtained from three-point bend tests on the notched Type 1 SMA fibre-reinforced beams and notched SF-reinforced beams. The results in Table 8 show that in comparison to SF-reinforced beams, Type 1 SMA fibre-reinforced beams reached their peak load at larger CMODs, indicating improved displacement -hardening behaviour after the onset of cracking.

[00152] Additionally, Table 8 shows that in comparison to SF-reinforced beams, Type 1 SMA fibre-reinforced beams exhibited higher residual flexural tensile strength after their peak points. Importantly, Type 1 SMA fibre -reinforced beams failed at remarkably large CMODM, in the range 1.5 to 2.4 times larger than SF-reinforced beams. Beam failure was assumed to be at a flexural strength loss of 20%, which is a typical assumption in the art. Table 8: Summary of flexural parameters obtained from three-point bend tests on notched fibre- reinforced beams f R.peai f R, 1 f R, 2

Notched CMOD _] P _peak f R,3 R,4 P _U CMOD _U

(MP (MPa (MPa beam ID (mm) (kN) (MPa) (MPa) (kN) mm a) ) )

SMA50 2.98 11.3 7.2 4.5 5.9 7.0 6.6 9.0 6.86

SMA75 1.22 20.1 12.8 11.2 12.1 12.4 12.1 16.1 6.48

SMA100 1.60 22.9 14.6 14.3 14.5 14.0 13.6 18.3 6.29

SF50 1.15 17.8 11.3 9.9 10.8 10.7 8.1 14.2 2.82

SF75 1.05 19.5 12.4 11.3 11.8 10.4 9.1 15.6 2.71

SF100 0.72 23.3 14.8 13.9 14.7 14.2 12.9 18.6 3.22

Note: CMODp and P _peak are crack mouth opening displacement and load at peak, respectively, f _ft, peak is equivalent elastic flexural stress peak load, f _{R j} · (j= 1, 2, 3 and 4) is the residual flexural tensile strength at considered CMODs (0.5 mm, 1.5 mm, 2.5 mm and 3.5 mm) according to

EN14651 ¹⁰ , P _u and CMOD _u are the load and CMOD at a flexural strength loss of 20% considered as failure point.

2.5.6. Energy Dissipation Capacity and Residual Deformation

[00153] Figure 19a shows a comparison between Type 1 SMA fibre-reinforced beams and SF- reinforced beams, of the hysteresis energy dissipated at each cycle; and Figure 19b shows a comparison between Type 1 SMA fibre-reinforced beams and SF-reinforced beams, of the cumulative dissipated energy.

[00154] In Figure 19a, the difference between Type 1 SMA fibre-reinforced beams and SF- reinforced beams with regard to dissipated energy is negligible up to a displacement amplitude of 1.8 mm corresponding to the 9th loading cycle. Beyond this amplitude, Type 1 SMA fibre- reinforced beams exhibited a higher capacity in dissipating energy than SF-reinforced beams, a difference which became more obvious with progressive cycles.

[00155] In Type 1 SMA fibre-reinforced beams, the energy is dissipated mainly due to induced tensile strain in the fibre and austenite-martensite phase transformation. The increase in displacement amplitude increases crack width and tensile strain in the fibres for these composites as there is a firm bond between Type 1 SMA fibres 100 and the matrix. Therefore, Type 1 SMA fibres 100 undergo large tensile strain and contribute effectively to energy dissipation. In contrast, SF-reinforced beams dissipate energy mainly due to plastic deformation of the hooked-ends during the fibre pullout process. As the hooked-ends are progressively deformed, the fibre is pulled out from the matrix and loses its capacity to dissipate energy through fibre deformation. Beyond this point, the energy dissipation capacity of SF-reinforced beams does not significantly increase as it is only controlled by fibre-matrix friction ¹ .

[00156] The energy dissipation capacity of structural elements is more beneficial, when they experience small residual deformat ion. Figure 20 shows the variation of residual deformation after unloading as cycles progressed for both Type 1 SMA fibre -reinforced beams and SF-reinforced beams. The results indicate that, after the 3 ^rd cycle, compared to SF-reinforced beams, Type 1 SMA fibre -reinforced beams showed reduced residual deformation. The efficacy of Type 1 SMA fibres 100 in reducing residual deflection compared to SFs was more pronounced as the cyclic displacement amplitude increased. The increase in applied displacement increased crack width, and resulted in larger tensile strain and forward phase transformation in Type 1 SMA fibres 100. After unloading, Type 1 SMA fibres 100 underwent reverse phase transformation, recovered induced tensile strain, partially closed the crack and thereby reduced the residual displacement of the beam. The residual displacement of Type 1 SMA fibre -reinforced beams originated from inevitable slippage between the fibres and the matrix after unloading. However, for SF-reinforced beams, the unrecoverable fibre-matrix slip increased as displacement and crack width increased. Thus, the SF-reinforced beams exhibited higher residual displacement at larger deformations.

2.5.7. Re-centring and Crack Closing Capacity

[00157] Figure 21 shows a comparison between the re-centring capacity, R _re , obtained for beams reinforced with Type 1 SMA fibres 100 and SFs. Type 1 SMA fibre-reinforced beams and SF- reinforced beams showed comparable re-centring behaviour in the first three cycles where deflection was small. However, as the cycles progressed, Type 1 SMA fibre-reinforced beams exhibited remarkably larger R _re compared to SF-reinforced beams. In contrast to SF-reinforced specimens, the re-centring performance of Type 1 SMA fibre -reinforced beams did not degrade considerably by increasing displacement amplitude.

[00158] During the initial cycles ( e.g . 2 ^nd and 3 ^rd cycles in this experiment), the crack width is small (<0.2 mm in this experiment), and the induced strain and stress are low in the fibres bridging the cracks. At this stage, the fibre-matrix slip is minimal and both types of fibres achieve similar strain recovery because they only experience elastic deformation. However, as displacement amplitude and crack width are increased, Type 1 SMA fibres 100 experience large tensile strains and considerably smaller slips than SFs due to their strong mechanical bond with the matrix. Type 1 SMA fibres 100 recover the tensile strain during unloading (through reverse phase transformation); this applies a force on the crack faces and results in crack closing and re-centring for Type 1 SMA fibre -reinforced beams.

[00159] In contrast, SFs undergo unrecoverable plastic deformation at their hooked ends and experience large fibre-matrix slip ¹ . As a result, SF-reinforced beams cannot exhibit significant re centring and crack closing behaviour, especially at large crack widths. Furthermore, an increase in displacement amplitude increases fibre plastic deformation and fibre slip, leading to larger crack widths and plastic deformation for beams. Since these mechanisms are unrecoverable, SF- reinforced beams exhibited severe declines in re-centring capacity with progressive cycles.

[00160] Figure 22 shows the crack closing ratio and maximum crack width obtained for all fibre reinforced beams up to a deflection of span/100.

[00161] It can be seen from Figure 22a, that Type 1 SMA fibres 100 substantially decreased crack width after unloading at both small and large deflections. When the crack width was small (e.g., 0.2 mm in the 2 ^nd cycle), the crack closing ratio obtained for all considered SMA fibre dosages was about 52%.

[00162] In Figure 22a, as the maximum crack width increased due to increasing displacement amplitude, crack recovery ratio showed a slight fluctuation to within a range of 52% to 65% over the considered displacement range. This suggests that the presence of Type 1 SMA fibres imparted substantial crack-closing capability for the beams. As previously explained, the crack-closing ability of Type 1 SMA fibres-reinforced beams originates from both the reverse phase transformation of SMA fibres 100 and strong fibre-matrix bond. After unloading, Type 1 SMA fibres 100 recover the tensile strain and apply forces onto the crack faces, resulting in a substantial reduction in crack width. [00163] In addition, it was found that an increase in the fibre content did not substantially influence the crack closing capacity of Type 1 SMA fibre-reinforced beams. However, it reduced the maximum crack width the beams experienced in each cycle. This was attributed to the development of more cracks in beams with higher fibre content. When, for example, a concrete beam undergoes a particular deflection, the width of cracks in the concrete beam increases to accommodate the deflection. Where there is a smaller number of cracks to accommodate for the particular deflection, each of the smaller number of cracks is of a first size. Where there is a number of cracks that is larger than the smaller number of cracks, each of the larger number of cracks is a second size. Because the larger number of cracks accommodates the same particular deflection, the second size is smaller than the larger size. Thus, the deflection can be accommodated by cracks of a smaller size (i.e. width).

[00164] In contrast, the crack closing ratio of SF-reinforced beams severely decreased with progressive cycles. This ratio was found to be around 15% at a deflection amplitude of span/150 (2 mm). This behaviour was attributed to the unrecoverable plastic deformation and large fibre- matrix slip during the pullout process of SFs ¹ . Similar to Type 1 SMA fibres 100, the increase in SF content did not affect the crack closing ratio but slightly decreased the maximum crack width at each cycle.

[00165] Figure 23 shows changes in crack recovery ratio versus maximum CMOD at each cycle in the three -point bend test on notched reinforced beams. For Type 1 SMA fibre -reinforced beams, the crack closing ratio decreased from 100% to about 60% at a small CMOD of 0.45 mm, beyond which the crack recovery ratio first increased slightly and then decreased gradually. SMA50 showed better crack recovery performance than SMA75 and SMA100 after 1.0 mm CMOD. This could be due to a more uniform fibre distribution at 0.50% SMA fibre content. Non- uniform fibre distribution leads to flaws which are prone to cracking and crack-bridging weaknesses due to insufficient fibres in the crack plane. Thus, smaller crack closing forces are produced by fibres at the crack plane, resulting in a larger residual crack width and lower crack recovery ratio after unloading. In general, SMA fibre -reinforced beams showed a significant crack closing ratio over the entire CMOD range. [00166] In contrast, CMOD recovery in the SF-reinforced beams was vastly different. For these specimens, residual crack width and slip between fibre and matrix significantly increased with progressive cycles. Hence, the crack recovery ratio quickly dropped to within a range of 30% to 20% when CMOD increased up to approximately 2 mm. Beyond this point, the crack recovery ratio continued to decrease gradually until the failure of the specimen. Interestingly, CMOD recovery in SF-reinforced beams was largely independent of fibre content.

2.5.8. Monitoring Crack Recovery with DIC

[00167] Figure 24 and Figure 25 show the cracking pattern (recorded by DIC) after loading and unloading at three different displacement amplitudes for Type 1 SMA fibre -reinforced beams and SF-reinforced beams, respectively.

[00168] The results strongly suggest that at all Type 1 SMA fibre 100 dosages considered in this study, the presence of Type 1 SMA fibres 100 remarkably reduced crack width after unloading. For instance, the maximum crack width of SMA50 corresponding to displacement amplitude of span/300 decreased from 0.80 mm to 0.24 mm, which is even less than the crack width limit at serviceability limit state (0.4 mm to 0.5 mm). The results further demonstrate that an increase in Type 1 SMA fibre 100 dosage did not influence the crack-closing capacity of the beams, instead, it resulted in a much smaller maximum and residual crack width experienced by beams. Increasing fibre content increases the fibres available to effectively limit the progression of the first crack and transfer strain to other parts of the matrix, where new cracks occur when the longitudinal strain is larger than the tensile strain capacity of the matrix. Thus, specimens exhibit multiple-cracking behaviour in which several cracks occur with smaller crack width than single -cracking behaviour.

[00169] In contrast, Figure 25 shows that the use of hooked-end SFs did not provide considerable crack-closing capability to the reinforced beams. For example, compared to SMA50, the maximum crack width in SF50 decreased from 2.70 mm to only 2.38 mm after load removal at the cycle with 2 mm displacement amplitude (span/150). Additionally, the images in Figure 25 strongly suggest that the maximum crack widths of SF-reinforced beams were generally larger than that of Type 1 SMA fibre -reinforced beams, indicating the efficacy of Type 1 SMA fibres 100 in bridging cracks and providing uniform strain distribution over the matrix. 2.6 Summary

[00170] The examples provided show that the disclosed SMA fibres can be used without any other type of reinforcing elements, for re-centring and crack closing in cementitious/non-cementitious composites. It will however, be readily apparent to the skilled addressee that these SMA fibres may also be used in combination with any other type of reinforcing element known in the art, for example, steel rebars. For example, cementitious and/or non-cementitious composites comprising the disclosed SMA fibres can be used for load-bearing structure(s). This may be the case, even where the load-bearing structure(s) include other reinforcing elements such as steel rebars.

[00171] It is noteworthy that the fact that a particular fibre geometry or configuration enhances the pullout resistance (and hence its suitability for re-centring and crack closing) for steel or plastic fibres does not make it obvious that it will improve the bond between SMA fibres and cementitious/non-cementitious matrices as well. This is due to the distinct mechanical properties of SMA. Providing a firm fibre-matrix bond for steel or plastic fibres increases the brittleness of the cementitious/non-cementitious composite. In contrast, SMA fibres require a very strong bond with the cementitious/non-cementitious matrix with minimal fibre-matrix slip to ensure re-centring and crack closing.

[00172] As an example, Figure 26A shows the effects of 4D and 5D end-hooks (with 45° bends) in comparison to 3D end-hooks on the pullout resistance of as-received SMA wires cut into fibres of predetermined lengths [equivalent to the length l+2h+2k for Type 2 SMA fibre (as shown in Figures 3 and 4)] while Figure 26b shows the effects of 4D and 5D end-hooks in comparison to 3D end-hooks on the pullout resistance of commercially available steel fibres. In the figures, it is evident that the use of 4D and 5D end-hooks with 45° bends dramatically improved the fibre- matrix bond strength for steel fibres, whereas their effects on the as-received SMA fibres is insignificant.

[00173] The sharp difference between the as-received SMA fibres and steel fibres is due to the nature of deformation experienced by SMA fibres during the bending-unbending process while the fibre is being pulled out. In consequence, it is clear that SMA fibres need to be designed specifically to achieve the desired bond behaviour beneficial for crack-closing and re-centring behaviour. [00174] Throughout this specification and the claims which follow, unless the context requires otherwise, the word “comprise”, and variations such as “comprises” and “comprising”, will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

[00175] The reference in this specification to any prior publication (or information derived from it), or to any matter which is known, is not, and should not be taken as an acknowledgement or admission or any form of suggestion that that prior art publication (or information derived from it) or known matter forms part of the common general knowledge in the field of endeavour to which this specification relates.

[00176] It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

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