Shape memory alloy-carbon fiber reinforced polymer system for strengthening fatigue-sensitive metallic structures

Engineering Structures 171 (2018) 190–201

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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Shape memory alloy-carbon fiber reinforced polymer system for strengthening fatigue-sensitive metallic structures Bo-Tong Zhenga, Mossab El-Tahanb, Mina Dawoodc,

T

⁎

a

Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China Dar Al-Handasah, Giza, Egypt c Department of Civil and Environmental Engineering, University of Houston, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Fatigue Crack Composites Repair Debonding Numerical modeling

This paper provides an overview of the basic elements, course of development, experimental evaluation, and numerical simulation of a thermally activated shape memory alloy (SMA) and carbon fiber reinforced polymer (CFRP) composite system for fatigue repair or retrofit of metallic structures. Nickel titanium niobium (NiTiNb) SMA wires, which are able to generate 400 MPa recovery stress upon thermal loading and maintain that stress level at a wide range of temperatures, was adopted to apply compressive stresses near the crack. Monotonic bond behavior of single and multiple SMA wires to CFRP was investigated; the debonding onset load and maximum capacity were quantified. The fatigue behavior of patches consisting of multiple wires bonded to CFRP was studied. Results indicated that the system could maintain 80% of the recovery stress, after up to 2 million load cycles, so long as the maximum applied stress was below the debonding onset level. A fatigue strengthening system, using such multiple SMA wire system as underlay and CFRP patch as overlay, was applied to fatigue sensitive steel plates for fatigue life improvement evaluation. The average fatigue life of the patched steel plates was over 26 times longer than that of the unpatched plates tested at the same load range. Finally, a numerical framework was developed to simulate the fatigue crack growth in steel plates patched with such strengthening system and was validated by the experimental data. The findings suggest that the proposed system could be a promising alternative to traditional techniques for fatigue crack repair.

1. Introduction

crack initiation followed by mode I crack propagation has also been investigated [10–12]. Prestressed FRP patches were found to be more effective for fatigue life enhancement than non-prestressed patches [13]. Huawen et al. [14] conducted 14 fatigue tests of double-edge notched steel plates that were strengthened with prestressed CFRP laminates. CFRP with prestress levels of 600, 1000 and 1200 MPa increased the fatigue lives of the steel plates by 0.7, 1.7 and 3.4 times, respectively, those of nonprestressed laminates. Hosseini et al. [15] reported the use of prestressed CFRP to completely halt the fatigue crack in tensile steel plates. In the study, using non-prestressed ultra-high modulus CFRP, the fatigue life increased by over four times. Prestressing the CFRP fully arrested the crack. Various types of prestressed bonded and unbonded reinforcement systems have been developed and extensively investigated [16,17]. Prestressing externally bonded or unbonded FRP plates usually require hydraulic jacks and heavy fixtures [13]. Most prestressed CFRP strengthening systems involve mechanical end-anchors to prevent premature debonding during stressing [18]. In Hosseini et al. [15], the prestressed CFRP strips were anchored to the substrate by means of

Fatigue strengthening of metallic elements has progressively become a major research topic for the use of fiber reinforced polymer (FRP) composites since the early experimental and numerical studies [1–3]. Relevant research has since covered various target structural components, strengthening configurations, different metallic materials, and fatigue cracking modes. Non-prestressed FRP has proved effective in strengthening plated members [4,5], very large crane girders [6], and steel beams [7]. Hu et al. [8] analyzed the CFRP strengthened steel plates and beams, with existing fatigue cracks or fatigue sensitive details, taking into account the fatigue crack induced debonding, and developed a computer program for the design of CFRP fatigue repairs. In addition to mode I crack propagation, crack propagation in orthotropic connections of members in metallic bridges, so-called distortioninduced fatigue, involves mode III cracking. This was investigated in [9], where CFRP plates were used to successfully increase the fatigue life by 4 to 10 times, for different stress ratios, compared to unstrengthened specimens. In-plane mixed mode, i.e. mode I and mode II, ⁎

Corresponding author. E-mail addresses: [email protected] (B.-T. Zheng), [email protected] (M. El-Tahan), [email protected] (M. Dawood).

https://doi.org/10.1016/j.engstruct.2018.05.046

0141-0296/ © 2018 Elsevier Ltd. All rights reserved.

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(a) 500

(b)

Cooling

Stress (MPa)

Stress (MPa)

400 300 200 100

Test

1200 900 Before activation-1 Before activation-2 Before activation-3 After activation-1 After activation-2 After activation-3

600 300

Manufacturer

0 -150 -100 -50

0 50 100 150 200 250 Temperature (oC)

0 0

0.1

0.2 0.3 0.4 Strain (mm/mm)

0.5

Fig. 1. Mechanical properties of NiTiNb wires: (a) thermo-mechanical behavior of single NiTiNb SMA wire; (b) stress–strain relationship before and after thermal activation.

fatigue life improvement. Finally, a numerical framework is introduced to simulate the fatigue crack growth (FCG) of the steel members that are reinforced with the developed system. The comprehensive review of the entire course of development, experimental evaluation, and numerical simulation of the novel system altogether highlights the connections among the elements and enables new perspectives for comparison and understanding, which were inaccessible previously by examining the individual elements separately. The strengthening mechanism of the developed SMA-CFRP system, and, to a broader sense, of any fatigue strengthening approach using prestressed CFRP, was assessed and expounded theoretically, in Section 4, and experimentally, in Section 5, for the first time. The experimental observations, the consequent inference, and the numerical simulation of the fatigue crack induced debonded region elaborate and validate the grounds for modeling of fatigue crack growth analysis in FRP patched metal through cycle-by-cycle approach, i.e. a series of static models.

steel anchor plates with 12 bolts, which altogether could generate 518 kN of anchorage force. The prestressing apparatus, in this study, consisted of a reaction frame, two tension rods, clamping systems and hydraulic jacks. Chen et al. [19] studied the fatigue strengthening, using prestressed-, non-prestressed- and high-modulus-CFRP, of rectangular-hollow-section steel beams with notches in the tension area. While the prestressed CFRP was the most effective system, the task of prestressing the CFRP was a major challenge that limited the potential to exploit the high tensile strength of the CFRP. In this application, the prestressing apparatus was larger than the steel beam itself. The size and complexity of the fixtures needed to apply prestressing forces is a primary barrier to the feasible adoption of the technique. Shape memory alloy (SMA) materials exhibit a unique thermo-mechanical response. The shape memory effect has been exploited to develop composites that are able to actively tune their mechanical response through thermal activation [20–22]. In these applications, the thermally induced recovery forces in the SMA modulate the properties of the composite. The bond between SMA materials and CFRP has been evaluated to understand the failure mechanism [23] and to develop a model to predict the critical parameters [24,25]. Ternary nickel-titanium-niobium (NiTiNb) SMA have been developed to ensure a wide thermal hysteresis with high activation temperatures and low reverse transformation temperatures [26], making them well suited for applications that require sustained recovery forces over a wide temperature range [27]. Iron-based SMAs (Fe-SMAs) possess similar wide thermal hysteresis traits and are promising for civil engineering applications. Fe-SMAs were used to strengthen reinforced concrete beams; the FeSMA provided 350 MPa of prestress and the cracking load of the beam was increased by 200% [28]. An anchorage system for the application of Fe-SMA strips on steel plates was developed [29]. Using the anchorage system, the Fe-SMA strips were attached to steel plates and thermally activated; the resulting recovery stress in the SMA was 370 MPa, and the corresponding compressive strain in the steel was 90 × 10−6 mm/mm [30]. This paper describes a novel thermally activated SMA-CFRP composite system for extending the fatigue life of cracked or crack-sensitive metallic structures. The system consists of two layers of externally bonded composites: an underlay containing multiple SMA wires that is able to apply compressive stress to the metallic substrate, and an overlay CFRP patch that reduces the stress range in the metallic substrate. The single SMA wire behavior, and its bond to CFRP matrix is presented. A multiple wire SMA-CFRP system was monotonically tested to examine the effectiveness of multiple wires in a single patch. The characterization of the system was concluded through a series of fatigue tests to assess the stability of the recovery stress under high cycle fatigue loading. Based on the full understanding of the SMA-CFRP composite patch, a strengthening system was implemented onto edge-notched steel plates to investigate the effectiveness of the approach for

2. Monotonic behavior of SMA-CFRP bond Single and multiple SMA wires were pulled-out of a CFRP patch to investigate the monotonic bond behavior. The thorough understanding provides grounds for investigating the fatigue behavior of SMA-CFRP bond hence developing the strengthening system. 2.1. NiTiNb SMA The developed system employs a NiTiNb SMA with wide thermal hysteresis to apply prestressing forces to steel elements. The wires in this study were provided with a diameter of 0.77 mm and a grit blasted surface. The wires were received in the martensitic phase with a 5% residual strain, at room temperature. According to the manufacturer (Intrinsic devices Inc.), the austenitic start (As), austenitic finish (Af), martensitic start (Ms), and martensitic finish (Mf) temperatures, of the NiTiNb, are 47 °C, 165 °C, −65 °C and −120 °C, respectively. Fig. 1(a) illustrates the temperature vs. recovery stress relationship of the wires during heating and cooling. A 254 mm long SMA wire was restrained between two grips of a rigid testing frame. The force in the wire was measured using an 1100 N load cell. To remove slack in the wire a seating load of 8.9 N was applied before activation. The wire was activated by running a controlled current in the wire through two electrodes; the temperature of the wire was measured by thermocouples that were bonded to the wire between the two electrodes. Heating the wire, from room temperature to 160 °C, induced an increasing recovery stress of up to 400 MPa. When the wire was cooled to room temperature, the 400 MPa recovery stress was retained as shown in the figure. The dashed line in the figure shows the theoretical temperature-recovery stress relationship below 25 °C. Six samples of the wires were tested to failure under tension. The first three were tested at room 191

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CFRP

Metal tab

25

51

[mm]

Fig. 2. Single SMA wire pull out specimen.

temperature in the as received condition, i.e. before activation. While the other three wires were activated to a temperature of 165 °C while being unrestrained then cooled to room temperature before testing, i.e. after activation. Fig. 1(b) shows the stress–strain data of the six tests. The initial tangent modulus of elasticity before and after activation were 45 and 67 GPa, respectively. The ultimate stress and ultimate strain were 1160 MPa, and 0.360 mm/mm before activation, and 1140 MPa and 0.467 mm after activation.

384

419

425

432

479

513

578

268 [MPa]

400

Debonding onset

200 0 0

0.1 0.2 0.3 Displacement from 51 mm exten. [mm]

0.4

Fig. 4. DIC measurements and stress displacement relationship for single wire pull out specimen.

Fig. 3. Fig. 4 displays a succession of longitudinal strain contours of a representative pull out specimen as obtained from the DIC system. Examining the contours and corresponding loads indicates the presence of a strain concentration near the SMA wire, which gradually grew as load increased, and propagated along the length of the wire indicating the initiation and propagation of debonding. The concentration initiated as soon as tension was applied to the wire, as the load was transmitted from the wire to the CFRP patch. The concentration expanded along the embedded wire as the load increased, implying the growth of the shear transfer region along the embedded wire. At a tensile stress level of 432 MPa the concentration propagated away from the edge of the patch indicating the initiation and propagation of debonding. The stress-displacement relationship in Fig. 4 suggests that after debonding there was frictional contribution to the NiTiNb wire-CFRP bond as indicated by the positive slope of the stress–deflection response after debonding. This was confirmed through numerical simulations [33]. The interfacial shear stress distribution along the wire was simulated through a numerical model, in which the interface was modelled using cohesive zone [33]. A trilinear bond-slip relationship was adopted to incorporate the friction contribution after complete cohesive debonding. Fig. 5 summarizes the results of the pull-out tests for different embedment lengths. The figure presents both the stress at the onset of debonding and the ultimate capacity of the pull-out specimens. The results indicate that the debonding stress is independent of the embedment length, for the tested range, while the ultimate capacity generally increased as the embedment length increased. This suggests that the cohesive effective length of the bond is less than 25 mm. The debonding onset stress measured in the wire was 400 MPa. The recovery stress achieved from thermal activation of the wire was also 400 MPa. Thus, activation of the wire must be conducted with care so as to avoid

2.2. Single wire-CFRP bond The monotonic bond behavior of a single NiTiNb wire embedded in a CFRP patch was studied through pull-out tests. The test specimen, shown schematically in Fig. 2, was fabricated by means of a wet lay-up technique. A 0.77 mm diameter NiTiNb wire was sandwiched between two layers of dry carbon fabric, with predetermined embedment length. The fabric was saturated with epoxy resin, clamped lightly, and left to cure at room temperature for at least 24 h. The elastic modulus, tensile strength and ultimate strain of the epoxy resin for wet lay-up were obtained by coupon tests according to ASTM D638 [31] and were found to be 2.6 GPa, 54 MPa and 0.023 mm/mm, respectively. The elastic modulus of the cured CFRP, obtained from tension coupons tested according to ASTM D3039 [32], is 87 GPa. The cured CFRP patch, with a thickness of approximate 1 mm, was trimmed to 25 mm width. The end opposite to the SMA wire was bonded with aluminum tabs, on both sides, to facilitate mechanical gripping during testing. A total of nine such specimens, with three repetitions for each of the three embedment lengths, 25, 51 and 102 mm, were fabricated and tested. More details of these pull out tests can be found in [33]. The pull-out samples were loaded in displacement control at a rate of 0.4 mm/min. The samples were instrumented using two extensometers, one with a gauge length of 51 mm measuring the wire-toCFRP slip, and another with a gauge length of 13 mm measuring the elongation of the exposed portion of the wire. The surface of the CFRP patch was observed using an ARAMIS digital image correlation (DIC) system, which captured stereoscopic images of the specimen at 1 Hz, throughout the loading process. Post-processing of these images provided the full-field strain response at the surface of the patch throughout the loading sequence. The entire test setup is illustrated in

1200

Stress [MPa]

13 mm Extensometer Pullout specimen

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Ld

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NiTiNb wire

51 mm Extensometer ARAMIS DIC cameras

Capacity Debonding

800

400

0 0

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Fig. 5. Debonding onset and maximum stresses of the tested coupons with different embedment lengths.

Fig. 3. Setup of single wire pullout test. 192

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38 mm

10 NiTiNb SMA wires

76 CFRP only (Grip area)

102

102 mm

102

76

NiTiNb Wires embedded in CFRP

Wires only

NiTiNb Wires embedded in CFRP

CFRP only (Grip area)

Fig. 6. Multiple wire test specimen containing 10 SMA wires.

4 3 2

Phase I

Force [kN]

Test 1 Test 2

Phase II

debonding of the wire from the FRP under activation alone. The maximum capacity of the wire comprises of both cohesive and frictional contributions. Therefore, longer embedment lengths should result in higher ultimate capacities. It appears, however, that the specimens with a development length of 51 mm have higher capacities than those with a development length of 102 mm. This anomaly may be attributed to a slight curvature of the embedded portion of the wire, which was observed exclusively for the samples with 51 mm development lengths; this slight curvature of the wires was expected to have provided supplemental anchorage thereby resulting in higher pullout capacity.

1 0

2.3. Multiple wire-CFRP bond

0

50

100

150

Temperature

To investigate the effectiveness of a multi-wire patch, ten 0.77 mm diameter NiTiNb wires were embedded into CFRP patches as shown in Fig. 6. The spacing between neighboring wires was equal to the wire diameter. The central 100 mm long segment of the wires was intentionally left exposed to facilitate thermal activation, which can alternatively be achieved by applying an electrical current to the wire, as conducted in the single wire test in Section 2.1, or by using a forced air heating device. The former approach controls the temperature in the wire more precisely, but is inconvenient in heating multiple wires simultaneously. The latter is simple and effective in heating multiple wires. The CFRP patches should not be heated during the activation of the exposed SMA wires to avoid softening of the resin matrix at elevated temperatures. A test regarding the thermal transfer through the SMA wires was conducted [34]. In the test, a SMA wire was heated using two electrodes; the temperature along the wire was measured. The temperature between the electrodes was maintained at 120 °C for over 10 min, and the temperature of the wire immediately outside the electrodes remained at room temperature. This indicates that the thermal transfer of the SMA wire at 120 °C is negligible. Therefore, in order to prevent the CFRP patch from being heated during thermal activation of the exposed SMA wires, no special measure is needed when the wires are heated using electrodes. If forced air heating is used to activate the wires thermal insulation of the CFRP patch is recommended. A combination of glass fiber batt insulation and foil tape was successfully used to insulate the CFRP [35]. The ends of the CFRP patches were sandwiched with aluminum tabs for gripping purposes. Additional details are available in [34]. The testing included two phases. In phase one the specimen was gripped in the testing frame using displacement control such that the grips remained fixed. The exposed segment was then heated, using a digital control forced-air heating device. Subsequently, the heating source was removed, and the wires were cooled to room temperature. The temperature of the wires was measured using thermocouples and synchronized with the measured load that was obtained from the load cell in the test frame. Fig. 7 presents the measured force-temperature response of the multi-wire patch. When the temperature reached

200

250

[oC]

Fig. 7. Recovery force and bearing capacity for multiple wire system.

200 °C, the resulting recovery force was above 2000 N; when the wires cooled back to room temperature, 1750 N recovery force was retained. The resulting recovery force was equivalent to an average tensile stress in the SMA wires of 370 MPa, which is comparable to the results of the individual wire activation suggesting good load sharing among individual wires. In phase two, the specimen was loaded up to failure, which occurred due to pull-out of the wires from the CFRP patch. The average failure load of two patches was 3250 N, which was about twice the recovery force indicating a sufficient margin of safety. This also suggests that the individual wire pull-out tests provided a conservative estimate of the ultimate pull-out capacity. 3. Fatigue behavior of multiple wire system To quantify the reduction of the recovery stress in the SMA wires due to fatigue loading, 12 SMA-CFRP multiple wire specimens were tested under cyclic loading with different loading ranges. The test specimens were the same as those that were tested in the monotonic test and shown in Fig. 6. All the specimens were tested under sinusoidal fatigue loading, with constant maximum and minimum loads at a loading frequency of 10 Hz. The patches were tested until failure or up to two million cycles. To prevent debonding of the SMA wires in the patch, the maximum stress in the wires should be limited to 320 MPa based on the previous testing. The patches were tested in three groups as outlined in Table 1. In each group the minimum stress was the target activation stress in the wires while the maximum stress represented the stress due both to activation and the anticipated effect of additional live load. In the first group the maximum stress in the wires during the fatigue cycles was limited to 320 MPa to prevent debonding of the wires at all stages of loading. Three different stress ranges, corresponding to three different live load levels, were considered as outlined in the table. In the second group the minimum stress was kept below 320 MPa to 193

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1

Group

Min stress [MPa]

Max stress [MPa]

Replicates

1

250 250 250 250 390

270 300 320 450 590

2 3 3 2 2

2 3

Normalized prestress

Table 1 Matrix for multiple wire fatigue testing.

prevent debonding during activation while the maximum average stress was greater than 320 MPa. In the third group the minimum stress was greater than 320 MPa so as to capture the effect of debonding during activation. Additional details are available in [36]. During testing the specimens were first gripped in a servo-hydraulic testing frame, with a capacity of 22 kN, and subjected to a minimal seating load. Subsequently, the wires were heated, in a controlled manner, until the average stress (determined from the recovery force measured by the load cell) reached the predetermined minimum stress listed in Table 1. Thereafter, a hybrid loading protocol, including both displacement and load control, was employed to exert designed fatigue loading as follows as illustrated in Fig. 8. At the outset, the position of the actuator was set as baseline, and the recovery force carried by the specimen was equivalent to the predetermined minimum stress. Successively, 500 fatigue load cycles were applied to the specimen in load control. During these load controlled fatigue cycles, the maximum and minimum loads applied to the specimen were maintained unchanged, as shown in Fig. 8(a). The piston positions corresponding to the maximum and minimum loads, however, gradually shifted, as shown in Fig. 8(b), due to the relaxation of the specimen. After the 500 fatigue load cycles, displacement control was used to return the piston to the baseline position, as shown in Fig. 8(b). The degradation of the recovery force in the system was evaluated based on the measured force required to maintain the actuator at the baseline position which corresponds to the original position at the time of activation of the wires, as shown in Fig. 8(a). Fig. 9 shows the normalized recovery stress level against the number of fatigue cycles, in log scale, for all of the tested specimens. The recovery stresses of the samples in Group 1 decreased gradually in the first 0.5 million fatigue cycles to 90%, 85%, and 80% of the initial values for each of the three applied stress ranges. From 0.5 to 2 million fatigue cycles, the recovery force remained effectively constant as shown in Fig. 9. The specimens in Groups 2 and 3, however, completely lost the recovery stress after 100,000 and 30,000 cycles, respectively. The results suggest that in order to maintain the recovery force of the patches at an acceptable level, the maximum stress of the SMA wires should be less than the stress at the onset of debonding during every phase of the fatigue loading. The measured recovery stress degradation of the multiple wire system was attributed to the recovery stress loss of

G.1 250-270 MPa G.1 250-300 MPa G.1 250-320 MPa

0.4

G.2 250-450 MPa

0.2

G.3 390-590 MPa

0.1

Number of cycles

1

[x106]

Fig. 9. Recovery stress degradation under fatigue loading for all the tested specimens.

the SMA wires and the degradation of the SMA-CFRP interface. It was reported that the recovery stress of a Fe-SMA material, after 2 million fatigue cycles, decreased by 20% due to transformation-induced relaxation under high cycle fatigue loading [37,38]. A similar effect is hypothesized here, although the magnitude cannot be explicitly determined due to the additional possibility of deterioration at the CFRP/ SMA interface. 4. Primary mechanisms of the SMA-CFRP patch The multiple SMA wires patch, as an underlay, and a CFRP overlay, together compose a fatigue strengthening system. This SMA-CFRP system exploits two mechanisms, in combination, to extend the fatigue life of fatigue sensitive details as follows. The maximum stress, σmax, determines the length at which fracture occurs, i.e. acr,. Fracture failure occurs when the stress intensity factor near the crack approaches the critical stress intensity factor, KIC, as:

KIC = Fσmax πacr

(1)

where F is a geometric coefficient. In a fatigue problem, the stress range, Δσ, can be input into Eq. (1) in place of the maximum stress, σmax, to determine the SIF range, ΔKI, which can subsequently be input into a crack growth model to determine crack growth rate, da/dN. Put together, the SMA-CFRP patching system extends the fatigue life of a crack sensitive detail by decreasing the crack propagation rate and increasing the distance that the crack must propagate in order for fracture to occur, as illustrated qualitatively in Fig. 10. The presence of the SMA wires applies a compressive pre-stress force near the crack thereby reducing the magnitudes of the maximum and minimum stresses at the crack sensitive detail. Due to its relatively low stiffness compared to the

(b) Load control Disp. control

Fatigue load

0.6

0 0.01

Inital recovery force

Piston position

(a)

0.8

Degradation of recovery force

Baseline Load control Disp. control Time

Time

Fig. 8. A schematic illustration of the hybrid load–displacement control loading protocol: (a) load vs. time; (b) piston position vs. time. 194

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cured CFRP overlay was approximate 1 mm; Fig. 11(f) shows the steel plate with completed repair using the developed fatigue strengthening system. Prior to activating the SMA wires, a strain gauge and a thermocouple were installed on each side of the steel substrate to record the strain in the steel and temperature of the SMA wires. Fig. 12 plots the average compressive stress, calculated from the measured average strain in the steel, and the measured temperature of the SMA wires, against time. The dashed lines are temperature measurements on two sides of the specimen, while the solid line is the average compressive stress. By activating the first side to near 100 °C and cooling down to room temperature at 25 °C, an average compressive stress of 11 MPa was achieved in the steel. The temporary decrease of the compressive stress along with the increasing temperature was attributed to the thermal expansion of SMA wires and the steel, which counteracted the recovery stress. As the wires and the steel cooled to room temperature, the effective recovery stress increased to 11 MPa compressive stress as the thermal expansion dissipated. By activating the second underlay on the other side of the steel plate, the resulting average compressive stress in the steel reached 17 MPa. This is equivalent to an average of 255 MPa recovery stress in the SMA wires on both sides of the steel plate. This equivalent recovery stress is lower than that was achieved in the 10wire patch, 370 MPa, and even lower than the single wire test, 400 MPa. This was done deliberately by heating the wires to 100 °C, as a conservative measure to avoid debonding of the wires from the CFRP during fatigue loading, which would have been an undesirable failure mode. Due to specimen imperfections and the activation process, i.e. heating the SMA wires on one side before heating those on the other side, the resulting stresses of the SMA wires on both sides of the steel were not identical having a maximum mismatch of 30%. This was embodied by the slightly asymmetric beach marks with respect to the mid-thickness plane on the fracture surface; more details are available at [35].

Fig. 10. Different fatigue strengthening scenarios.

steel element, the SMA underlay reduces the maximum applied stress, σmax, but not the stress range, Δσ. The presence of the CFRP overlay bridging the crack detail adds additional stiffness thereby reducing the magnitudes of the maximum and minimum stresses proportionally. The maximum stress, σmax, and the stress range, Δσ, near the crack are thus both reduced. It is noteworthy that Fig. 10 illustrates scenarios that are applicable to members with relatively small applied loads at the time of strengthening. This can be achieved by shoring the structure, or removing as much of the dead load as possible from the structure, leaving only self-weight for example. In other cases, the presence of the patches would have a similar effect on the maximum stresses, but not on the minimum stresses. Moreover, the reason that the SMA wires alone, in Fig. 10, result in little reduction of the stress range is due to the small relative stiffness of the SMA wires compared to the other components of the system. Using SMA materials with higher modulus or using a substantially larger amount of SMA materials could further improve the response due to the ability of load sharing. 5. Fatigue testing of steel element with different strengthening scenarios

5.2. Testing program

Single edge-notched steel plates were tested to assess the effectiveness of the SMA-CFRP patches. To quantify the influence of each component of the system, companion specimens were patched with SMA multiple wire underlay patches only and CFRP overlay patches only.

The experimental program consisted of twelve single edge-notched steel specimens. Four configurations of specimens were prepared, each corresponding to a strengthening scenario shown in Fig. 10, and tested under high-cycle tension–tension fatigue loading. The four groups are: (i) the ‘Steel’ group, consisting of un-strengthened plain steel control specimens, (ii) the ‘SMA’ group, consisting of steel plates that were patched only with the activated underlay layer, (iii) the ‘CFRP’ group, consisting of steel plates that were patched only with the CFRP overlay layer, and (iv) the ‘SMA-CFRP’ group, consisting of steel plates that were patched with both the SMA underlay and CFRP overlay layers. Three replicates were prepared for each group. All the coupons were tested under a 100 kN load range, 0.1 load ratio, and 10 Hz frequency sinusoidal fatigue loading. The beach marking technique was used to measure the crack length at different stages of the fatigue loading. All of the steel plates that were used in this research were fabricated from one batch of material to minimize inter-sample variability. The average measured elastic modulus, yield stress, and room-temperature Charpy V-notch energy of the steel are 200 GPa, 400 MPa, and 67 J respectively [39,40]. The elastic modulus, tensile strength and ultimate strain of the structural paste adhesive are 2.26 GPa, 34 MPa and 0.018 mm/mm, respectively. Based on the stiffnesses of the steel and CFRP, and considering the 17 MPa compressive stress induced by the SMA, the resulting nominal stress ranges for the four groups of specimens are shown in Fig. 13. In Figs. 13–15, the names ‘Steel’, ‘SMA’, ‘CFRP’, and ‘SMA-CFRP’ correspond to the bare steel plates, steel plates bonded with SMA underlay only, steel plates bonded with CFRP only, and steel plates bonded with both SMA underlay and CFRP overlay, respectively. The plain steel specimens were subjected to 100 kN load range with 0.1 load ratio directly, therefore, σmax and σmin were 172 and 17 MPa, respectively.

5.1. Installation of the strengthening system Fig. 11 illustrates the installation of the strengthening system. Fig. 11(a) shows the 914 mm long × 102 mm wide × 6.4 mm thick bare steel plate, with a 6.4 mm deep, 60 degree edge notch at the center of one edge. Both surfaces were sandblasted, and cleaned using acetone and 70% cleaning alcohol, prior to bonding of the 46-wire underlay. Fig. 11(b) shows the underlay patch being bonded to one side of the steel plate, with the exposed SMA wires placed over and perpendicular to the anticipated crack path, using a viscous structural adhesive. The SMA wires were thermally activated after the adhesive was cured, as shown in Fig. 11(c). The CFRP tabs of the underlay were thermally isolated, using glass fiber insulation and aluminum foil tape, to prevent debonding between the SMA wires and the CFRP tab, and between the CFRP tab and steel substrate. The exposed SMA wires were gradually heated, using a digitally controlled forced-air heating gun, and then left to cool to room temperature. In so doing, the resin matrix of the CFRP tab, i.e. the saturating resin epoxy, and the adhesive paste between the CFRP tab and the steel substrate, remained unheated. The same procedure was repeated to the underlay on the other side. Thereafter, the SMA wires were covered with the adhesive paste, as shown in Fig. 11(d), which was allowed to cure prior to installing a CFRP overlay layer. Two layers of carbon fabric were bonded on each side of the plate using wet lay-up technique, as shown in Fig. 11(e). The thickness of the 195

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(a) Sandblasted surface

(b)

60o edge notch (c)

Pasty adhesive

SMA wires

Heating gun Fiber glass insulation

CFRP

(d)

SMA wires

CFRP

(e) SMA wires filled with pasty adhesive

wet lay-up of CFRP overlay

(f) Cured CFRP overlay

Fig. 11. Steps of installation of the strengthening system.

(b)

(c)

Strain gauge (both sides)

Temperature (oC)

150

Strain gauge (both sides)

100

Thermocouple (both sides)

20

Compressive stress Thermocouple 1 Thermocouple 2

15 10

50

5

0 0

250

500 Time (s)

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0 1000

Compressive stress(MPa)

(a)

Fig. 12. Thermal activation: (a) location of the strain gauge; (b) thermal isolation and location of the thermocouple; (c) temperatures in the SMA wires and average compressive stress in the steel.

Steel

SMA

CFRP

SMA-CFRP

Fatigue life [Number of cycles] Thousands

180

Stress [MPa]

140 100 60 20 -20

2000

1500

1000

500

0

Fig. 13. Nominal stress ranges in the steel for different groups.

Steel For the SMA group, the stiffness of the SMA wires, compared to that of the steel section, was negligible. Thus, the stress range was the same, 155 MPa whereas the maximum and minimum stresses were each reduced by 17 MPa to 155 and 0 MPa, respectively. The stress ratio in the steel was thus zero. For the CFRP group the stiffness of the CFRP overlays on the two sides was altogether about 14% that of the entire section. As a result, the maximum and minimum stresses were each

SMA

CFRP

SMA-CFRP

Fig. 14. Fatigue lives of all the tested specimens.

reduced by 14% to 148 and 15 MPa, respectively for the CFRP group and the stress ratio remained 0.1. Lastly, the SMA-CFRP group experienced stress reduction of 14%, in addition to the 17 MPa compressive stress. Consequently, the σmax and σmin were 131 and −2 MPa (compressive), respectively, for SMA-CFRP group. The corresponding stress 196

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SMA-CFRP

The crack growth rate of the SMA group is slightly lower than that of the steel group, indicating that the SMA underlay slightly reduced the stress ratio of the steel substrate and the effective stress range (although the applied stress range remained the same). This was achieved by reducing the minimum stress in the steel substrate to below the threshold stress. The CFRP group, exhibited a drastic crack growth rate reduction, compared to the steel group, and much longer maximum crack length, around 80 mm. The SMA-CFRP strengthening configuration reduced the crack growth rate even further and prolonged the maximum crack length up to 94 mm, noting that the width of the steel plate was 101 mm. The synergistic effect of the activated SMA wires and the CFRP overlay is evident.

2.0

1.0

0.0 0

20

40 60 Crack length [mm]

80

100

6. Interfacial bond performance under fatigue loading

Fig. 15. Crack growth rates of all the tested specimens at different crack lengths.

The effectiveness of the SMA-CFRP system depends on the bond between all the various components of the system: SMA wires to CFRP tab, CFRP tab to steel, and CFRP overlay to steel. The bond behavior was monitored during the fatigue loading both visually and based on strains measured at the surface of the CFRP using the DIC system.

ratio was −0.015. Additional details are presented in [35]. 5.3. Results and discussions Fig. 14 displays the measured fatigue lives of all of the tested coupons. The bare steel plates exhibited an average fatigue life of 47,435 cycles prior to fracture. Steel plates that were strengthened with the SMA underlay exhibited an average fatigue life of 78,957 cycles, which was 1.7 times that of the control specimens. The slight fatigue life improvement of the SMA group, compared to steel group, represents the characteristics that the stress range remains effectively unchanged while the maximum stress is reduced by 17 MPa and hence the fatigue life improvement is modest. The coupons that were patched with the CFRP overlay exhibited an average fatigue life of 412,750 cycles, which was 8.7 times that of the unpatched coupons. Referring to Fig. 13, the CFRP overlay reduced both the stress range and maximum stress, of the steel substrate, thereby achieving much higher fatigue life improvement than the SMA underlay alone. The distinction between the strengthening effects of SMA and CFRP groups indicates that, to a moderate extent, stress range reduction is more effective than maximum stress reduction in extending fatigue life. Finally, the coupons, strengthened with both the SMA underlay and the CFRP overlay, exhibited an average fatigue life of 1,254,632 cycles, which was over 26 times that of the control coupons. It is worth noting, however, that the scatter of the fatigue lives of SMA-CFRP coupons was significant. This is attributed to the fabrication-workmanship difference among the specimens. Nonetheless, the lowest fatigue life, of the SMA-CFRP group, was 862,284 cycles, which was still more than 18 times that of the control group. Comparing the fatigue performances of the CFRP and SMA-CFRP groups, for which the CFRP overlays were identical, indicates that the SMA underlay increased the fatigue life by three times. In contrast, without the CFRP overlay, the SMA underlay only increased the fatigue life by 1.7 times. Moreover, the fatigue life of the steel coupon with both the CFRP overlay and SMA underlay is greater than the summation of the fatigue lives of steel coupons patched with only the overlay and only the underlay. These collectively illustrate the synergistic effect between the compressive stress, contributed by the activated SMA wires, and the stiffness enhancement, provided by the CFRP overlay. They also illustrate the combined effect of the slower crack growth rate and a longer crack growth path. Fig. 15 plots the crack growth rates, da/dN, at different crack lengths, for all tested coupons, categorized according to strengthening configurations. The crack growth rate was determined, according to ASTM E647 [41], from the measured crack lengths and corresponding number of fatigue cycles. The data points, for which the crack growth rates are higher than 3.0 × 10−6 m/cycle, are not plotted in the chart, for distinguishability purpose, without compromising meaningful information. At any given crack length, as seen in the chart, da/dN is clearly ordered, from high to low as Steel, SMA, CFRP and SMA-CFRP.

6.1. SMA to CFRP tab and CFRP tab to steel substrate bonds Before rupture of the steel substrate, no debonding was observed. Upon rupture of the steel plate, pull-out of SMA wires from the CFRP tab was observed, while the CFRP tab to steel bond remained intact. Fig. 16(a) shows the typical overview of a fractured SMA specimen, where the steel substrate fractured in the middle and the SMA wires pulled out of the CFRP tabs. Fig. 16(b) shows a close view of the SMA wires to CFRP tab entrance, the pull out of the SMA wires can be distinguished from the surface appearance: the lackluster surface indicates the initially exposed portion, whereas the glossy portion indicates the initially embedded portion that was pulled out upon failure. Fig. 16(c) shows a close view of the CFRP tab to steel substrate bond after failure. Scrutinizing the interfacial bond along the edges indicated no sign of debonding; such conclusion applies to all 12 CFRP tabs, four tabs per each specimen, of the SMA underlay strengthened specimens. The observations imply that the SMA to CFRP tab and CFRP tab to steel bond were reliable during fatigue loading. The final pull-out of SMA wires,

(a (b)

SMA wires pull-out

CFRP tab

(c)

CFRP tab

Steel plate

Fig. 16. Failure of steel plate bonded with SMA underlay: (a) overview of the ruptured specimen; (b) pull-out of SMA wires from CFRP tab; (c) intact bond between CFRP tab and steel plate. 197

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(a

(b)

(c

-6

(d)

Strain gradient [10 m/m/m]

LED light Strain concentration Debonded region High shear stress

Cameras

LED light

Specimen

Fatigue cracks

Fig. 17. Strain measurement analysis: (a) test specimen monitored by DIC system; (b) strain contour of a SMA-CFRP specimen; (c) strain contour of a CFRP specimen; (d) strain gradient computed from the DIC strain measurements.

patched steel elements [42]. This framework includes the sequential static loading models described above. Each static model outputs the SIF at the crack tip at a given stage during the fatigue loading while considering the CFRP overlay, interfacial debonding, and, if applicable, the compressive stress provided by the SMA wires. Using the calculated SIFs at different crack lengths, the entire crack growth curve can be obtained by applying a suitable crack growth model.

yet intact CFRP tab to steel bond, is attributed to the much higher bond capacity, of the tab to substrate, compared to those of SMA wires to tab. 6.2. Crack induced CFRP overlay debonding The CFRP overlay to steel substrate-bonds, of the SMA-CFRP and CFRP specimens were monitored using a DIC system through the entire fatigue loading. Fig. 17(a) shows the test setup, in which the whole surface of the reinforcement was observed using the DIC system cameras, while the specimen was subjected to fatigue loading. The frequency at which the cameras took pictures, of the specimens, was determined by the estimated fatigue life of the specimens in question in a way that the total number of stereoscopic image sets was around 200. Fig. 17(b) and (c) show the longitudinal strain contours, of SMA-CFRP and CFRP specimens respectively, at their intermediate fatigue life stage, superimposed on the high definition pictures of the specimens. As the elapsed number of loading cycles for each captured image was known, the crack length associated to the images was deduced, in the post-processing, from the beach marks on the fracture surface. The crack location is thereby labeled in Fig. 17(b) and (c). Similar strain concentrations, enclosing the crack, were observed for both specimens. The shape of the concentrations resembles the underlying crack in a way that the vertex is at the vicinity of the crack tip whereas the opening mouth at the edge of the CFRP overlay. The edges of the concentrations were, initially curved when the crack length was relatively small, and progressively straightened when the crack length increased. Such strain concentrations indicate the interfacial debonding induced by the fatigue crack; this conclusion is supported by the analysis of the gradient of the longitudinal strain on the surface of the CFRP. Fig. 17(d) shows a 3D contour of the strain gradient for a SMACFRP specimen, at a stage when the observed crack length was 70 mm. The strain gradient is proportional to the interfacial shear stress, as can be easily deduced from the equilibrium, of a CFRP overlay element, shown in Fig. 17(d). Therefore, the area where the strain gradient is relatively high, in the 3D contour, suggests high interfacial shear stresses, whereas those areas where the strain gradient is near zero indicate minimal interfacial shear stress. The near-zero stress area bounded by the high stress ‘border’ corresponds to the strain concentrations in Fig. 17(b) and (c). The stress is near zero because the interface debonded. The shear stresses are high at the debonding front where the majority of the stress transfer occurs. The area outside the high stress ‘border’ has near zero stress as the interfacial shear stresses dissipate away from the debonding front. Consequently, the debonded region can be determined experimentally from the DIC measurements.

7.1. Treatment of small crack growth Since the steel plates tested in this research were not pre-cracked but machined with an edge notch, the crack initiation and the small crack propagation stages (typically when crack length is smaller than 1 mm) were considered. The crack growth for small cracks and long cracks are inherently different. Thus linear elastic fracture mechanics (LEFM) cannot be directly applied to small cracks. This research adopts an equivalent initial flaw size (EIFS) method [43] to apply a unified crack growth model to both small and long cracks. The EIFS is a virtual initial crack length, from which a long crack propagation model can be initiated to predict the fatigue life thereby yielding the same results as the experimentally obtained fatigue life, in which the crack initiated from an actual initial crack length and propagated accordingly. The EIFS for the current study was calibrated experimentally as 28 × 10−6 m, by using long crack propagation model to predict the fatigue life of the control specimens and comparing the results with experimental data. Details of EIFS calibration can be found in [42]. For crack lengths that are smaller than 250 × 10−6 m, the crack was considered a small crack, and the SIF, Ksmall was calculated using the following equation rather than finite element (FE) model described later: (2)

Ksmall = 1.12KT σ πa

where KT is the stress concentration factor of the stress raiser, σ is the stress in the steel substrate, a is the crack length. KT of the 60° V-shaped single notched plate under pure tension was calculated as [44]:

KT =

(Kts−1)(Ktd−1) (Kts−1)2 + (Ktd−1)2

+1

Kts = (1.035 + 0.0261η−0.1451η2 + 0.0842η3) KtE KtE = (1.121−0.2846η + 0.3397η2−0.1544η3) KtH KtH = 1 + 2/ η,η = Ktd =

ρ/c

β1 − 2β2 1−

β2 (b − c ) / ρ + 1

(3)

where Kts and Ktd are stress concentration factors of a shallow notch and a deep notch, KtE and KtH are components for calculating Kts, η is a geometric constant, ρ is the radius of the notch root, β1 and β2 are geometric constants defined in [44] (excluded here for brevity). The notch root radius, ρ, was measured using a Mitutoyo Radius Gage Set

7. Numerical simulation A numerical framework was established to simulate the FCG of the 198

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1.E-1

800

Δa/ΔN (mm/cycle)

Ksmall,max (MPa·mm 1/2)

1000

600 400

Steel CFRP

200

y = 3E-14x3.2884 R² = 0.9267

1.E-2

1.E-3

1.E-4

SMA-CFRP 0

0 EIFS50

100

150

200

1.E-5

250

100

Crack length, a (×10-6mm) Fig. 18. Maximum SIFs for small cracks of specimens with different strengthening configurations.

10,000

Fig. 20. Calibration of crack growth parameters C and m.

elements with edge nodes shifted to the quarter point along the edges. The cracked face was modeled as free boundary condition whereas the uncracked face symmetric boundary condition. Fig. 19(c) shows the calculated maximum SIFs at different crack lengths for steel, CFRP and SMA-CFRP groups. The irregular shapes of the CFRP and SMA-CFRP curves are caused by the application of the debonded region to the SIF model. It is seen that SMA-CFRP coupons exhibited much lower maximum SIF values than those in the CFRP group. The fracture toughness of the steel was taken conservatively as 2000 MPa·mm1/2, in the fatigue life prediction at which point facture was assumed to take place.

with measuring scale of 0.254–12.7 mm. The measured radius of the edge notch in this research was 0.5 mm, thereby the stress concentration factor, KT, was determined as 5.38. The calculated maximum-SIF for small cracks, Ksmall,max, at different crack lengths, of steel, CFRP and SMA-CFRP groups, are shown in Fig. 18. The maximum-SIF reduction for the CFRP group compared with the steel group is due to the reduced maximum stress caused by the load sharing of CFRP overlay. The further reduction of the SIF for the SMA-CFRP group is due to the applied prestress, which was implemented in the model by subtracting the compressive stress from the stress in the steel, σ. The minimum SIF can be easily obtained by multiplying the maximum SIF by the stress ratio in the steel.

7.3. Crack growth curve generation Once the SIFs at different stages were calculated, the entire crack growth curve was obtained by applying the crack growth relationship to convert the SIF range into a corresponding crack growth rate. The modified power relationship proposed by [46] was used to calculate the crack growth rate based on the calculated SIF for both the small crack and long crack stages:

7.2. Long crack treatment The SIFs for long cracks were calculated using two sequential FE models. Fig. 19(a) shows the debonding prediction from a FE model using a bilinear traction separation cohesive zone model to simulate the FRP-steel interface. Details of the model are available in [45,42]. The image shows the contour of the damage parameter, λ, for which a value equal to 1.0 indicates that debonding has taken place. The debonded region was then implemented in a second model in which the bonded CFRP was modeled with a perfect bond to the underlying steel and the unbonded CFRP was modeled with a free interface. The second model is used to calculate the SIF at the crack tip, as shown in Fig. 19(b). The stress singularity at the crack tip was represented using classical 3D, wedge-shaped crack tip elements, which are collapsed 20-node

(a

1,000

ΔK (MPa·mm 1/2)

da

= C (ΔK eff )m = C (U ΔK )m ⎧ ⎪ dN ⎨ ΔK = Kmax−Kmin ⎪U = U (R) ⎩

(4)

where ΔK and ΔKeff are the SIF range and effective SIF range, respectively, U is the stress intensity range ratio, which is dependent on the stress ratio R [47]. For steel the variable U was empirically related to the stress ratio R as U = 0.75 + 0.25R [48]. The entire crack growth

(b)

(c)

Klong,max (MPa·mm 1/2)

2000 1500 1000 Steel CFRP

500

SMA-CFRP 0 0

20

40

60

80

100

Crack length, a (mm)

Fig. 19. (a) FE prediction of the debonding (b) FE model for SIF calculation; (c) calculated max SIF for different groups. 199

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Crack length, a (mm)

100 80 60 40 20 0 10000

100000 N (cycles)

1000000

Steel-1 Steel-2 Steel-3 Steel-prediction CFRP-1 CFRP-2 CFRP-3 CFRP-prediction SMA-CFRP-1 SMA-CFRP-2 SMA-CFRP-3 SMA-CFRP-prediction

Fig. 21. Comparison of the FCG prediction and experimental data.

highlighted the synergistic effects of the SMA and CFRP. The SMA underlay reinforcement, that only applied compression to the steel plate without changing the stress range, achieved the minimum fatigue life improvement of 1.7 times. The CFRP overlay reinforcement, which only reduced the stress range, exhibited moderate fatigue life improvement of 8.7 times. The combined system resulted in a fatigue life improvement of over 26 times. This was attributed to the combined effect of a slower crack growth rate and a longer critical crack length at which fracture occurred. The interfacial behavior observed during the fatigue loading of the CFRP and SMA-CFRP groups of specimens indicate that the SMA to CFRP and CFRP tab to steel bond were intact. Whereas the CFRP overlays were observed to have crack induced interfacial debonding. Experimental observation indicates that the debonded region can be identified using DIC measurements and implies that the fatigue loaded FRP-metal system can be reasonably simulated by a series of static models. Finally, a numerical framework was established, which incorporates interfacial debonding, prestressing, and small crack propagation, to simulate the FCG in steel plates with different strengthening scenarios. The prediction was validated by the experimental data. The success of this framework supports the conclusion that the SMA-CFRP patching system is a promising alternative for repair and retrofit of cracked and crack-sensitive metallic structures. The developed system is advantageous due to its ease of installation and activation. Nevertheless, the prefabrication of the system itself is delicate and complicated. Additionally, the cost of the selected SMA material is high relative to other construction materials. This should be considered in the comparison between such a system and other repair or strengthening techniques.

curve was divided to approximately 20 segments; the number of fatigue cycles needed to reach the end of each segment, Ni, was calculated as: i−1

Ni =

∑ j=0

aj + 1−aj C (U ΔK |a = aj )m

(5)

The crack growth rate constants C and m, were determined as 3.38 × 10−14 and 3.29 respectively, using the da/dN vs. ΔK data of unpatched steel specimens and the least-squares method [49], as shown in Fig. 20. Fig. 21 compares the predicted FCG curves to the measured results, plotted in the log domain. The close agreement between the prediction and experimental data validates the conclusions drawn from the experimental observations that the influence of the CFRP-underlay and CFRP-steel debonding, during fatigue loading, can be considered discretely using a static model. It also demonstrates that the EIFS method is adequate for including crack initiation and small crack propagation stages in fatigue life prediction. 8. Concluding remarks This research provides an overview of a new approach to fatigue crack repair in metallic structures. The new system integrates SMA wires and CFRP sheets to provide a synergistic approach to extending fatigue life. The SMA wires provide compressive stresses along the crack path while the bonded CFRP materials provide additional stiffness thereby reducing the stress range around the crack. The new system has the potential to provide a novel solution to fatigue strengthening of metallic structures. Wide thermal hysteresis NiTiNb SMA wires, which generate and maintain 400 MPa recovery stresses upon thermal loading, were adopted for this system. The anchorage of such SMA wires to target structures was realized through CFRP tabs, therefore, the single wire- and multiple wire-bond performances between SMA and CFRP were investigated experimentally. Results revealed that the debonding onset stress, of SMA-CFRP bond was independent of the embedment length within the range of dimensions and properties studied. The multiple wire system could generate comparable average recovery stresses to the single wire scenario indicating good load sharing among the wires. Fatigue testing of the multiple wire system indicated that in order to maintain the recovery stresses at acceptable levels throughout the fatigue loading, the maximum stress exerted on the SMA wires should be less than the debonding onset stress. The fundamental mechanism of fatigue strengthening, considering the synergistic contributions of the SMA and CFRP, was articulated. Three strengthening scenarios are summarized considering the effects of compression stresses and stress range reduction independently and together. Steel plates with three reinforcement scenarios were tested in fatigue to assess the effectiveness of the system. The results were consistent with the fundamental mechanisms presented, and further

Acknowledgement The authors acknowledge the donation of CFRP materials by Fyfe Co. LLC, Mitsubishi Plastics Composites America Inc. and Sika Corporation U.S., and epoxy materials by Huntsman Advanced materials, LLC. Funding This work was supported by the National Science Foundation [CMMI award numbers 1100954 and 1126540] and the Department of Civil and Environmental Engineering at the University of Houston. References [1] Jones SC, Civjan SA. Application of fiber reinforced polymer overlays to extend steel fatigue life. J Compos Constr 2003;7:331–8. http://dx.doi.org/10.1061/(ASCE) 1090-0268(2003)7:4(331). [2] Tavakkolizadeh M, Saadatmanesh H. Fatigue strength of steel girders strengthened

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