Study on bond-slip behavior at the interface between Fe-SMA and concrete after thermal activation

Abstract

This study investigates the residual bond behavior of thermally activated Fe-SMA/concrete interfaces through 39 groups of 117 single-shear specimens, considering adhesive type, adhesive thickness, bond length, heating temperature, thermal cycles, and substrate strength. Results show that high-temperature-resistant epoxy adhesives retained acceptable bond capacity after short-term exposure up to 200°C, and failure in concrete specimens was governed mainly by surface concrete spalling rather than adhesive failure. The interfacial ultimate load increased with adhesive thickness, bond length, and substrate strength, but decreased with increasing adhesive elastic modulus and heating temperature. Within the tested range, a 1 mm adhesive thickness, a low-modulus heat-resistant adhesive, and a 150 mm bond length are recommended for practical use. Among the candidate constitutive models, the Nakaba model best described the test results, and a temperature-dependent parameterization was established for the investigated range.

Keywords

Fe-SMA bond-slip behavior single-shear test thermal activation constitutive model

Introduction

As existing structures age, externally bonded strengthening has become increasingly important in civil engineering. Fe-SMA is particularly attractive because its shape memory effect enables thermally activated recovery stress and thus jackless prestressing, offering a simple and adaptable strengthening strategy for concrete and steel structures (Abdulkareem et al., 2023; Hong et al., 2018; Qiang et al., 2023; Sato et al., 1982).

Interface bond performance is crucial to the composite action of reinforcement systems, involving interactions among the adhesive, reinforcement, and substrate. Early studies on FRP-concrete interfaces showed that bond behavior is governed by chemical adhesion, friction, and mechanical interlocking, and is mainly affected by bond length, material stiffness, and interface parameters (Chen et al., 2023; Hawileh et al., 2015; Kurtoglu et al., 2022; Li et al., 2021; Lv et al., 2025). Subsequent studies established classical bond-slip models for interfacial failure analysis and design (Lu et al., 2005). However, these studies mainly concerned FRP or aluminum systems (Abuodeh et al., 2021), whereas Fe-SMA exhibits distinct interfacial behavior because of its nonlinear constitutive response and thermally activated characteristics.

Existing studies on the Fe-SMA/concrete interface mainly involve embedded, near-surface mounted (NSM), and externally bonded systems. In embedded and NSM applications, ribbed Fe-SMA bars can achieve high bond strength, with failure mode governed mainly by cover thickness, substrate strength, and bar diameter (Fawaz and Murcia-Delso, 2020; Schranz et al., 2020). Owing to its nonlinear stress-strain behavior, Fe-SMA also differs from steel and FRP in interfacial stress transfer and bond ductility (Wang et al., 2021). In externally bonded systems, bond performance depends mainly on adhesive thickness, bond length, and adhesive type, which also affect failure mode and stress distribution (Qiang et al., 2025). Since the bonded interface is usually the weakest part of the system, several bond-slip models for Fe-SMA interfaces have been developed based on FRP theories (Jiang et al., 2025).

Thermal activation is an essential step in Fe-SMA strengthening and fundamentally affects interfacial performance. Activation at about 160–300°C may reduce the stiffness and strength of structural adhesives, thereby weakening the interface, while temperature gradients and thermal stresses may also induce initial interfacial damage or delamination (Enns and Gillham, 1983). Previous studies have shown that Fe-SMA can generate effective recovery stress at about 200–300°C (Czaderski et al., 2014; Izadi et al., 2018; Shahverdi et al., 2016; Zhang et al., 2022), but adhesive softening or degradation during heating may cause bond slip and prestress loss (Li et al., 2023; Qiang et al., 2024). To improve interfacial stability, bolt-adhesive hybrid connections have been proposed, although they may introduce stress concentration and durability concerns (Dong et al., 2024).

Overall, existing studies have clarified the feasibility of Fe-SMA reinforcement and provided important information on its bond behavior in different connection systems. However, these studies have different research emphases. Previous studies on embedded or near-surface-mounted Fe-SMA bars mainly focused on bar-concrete interaction, cover splitting, pull-out behavior, and transfer length, rather than the adhesive-mediated interface of externally bonded Fe-SMA strips. Studies on adhesively bonded Fe-SMA joints have mainly addressed Fe-SMA-to-steel interfaces or Fe-SMA/concrete bonded joints under room-temperature or non-activated conditions, in which the degradation of the adhesive layer during thermal activation was not the primary concern. In addition, existing FRP-based bond-slip models provide useful theoretical references, but they do not explicitly consider the nonlinear stress-strain response of Fe-SMA, the recovery-stress activation process, or the temperature-dependent degradation of structural adhesives. Therefore, their direct application to thermally activated Fe-SMA/concrete interfaces remains uncertain.

Based on this background, this study investigates the residual bond behavior of externally bonded Fe-SMA strips on concrete after short-term thermal activation. A total of 39 groups of 117 single-shear specimens were tested to examine the effects of adhesive type, adhesive thickness, bond length, heating temperature, thermal cycles, and substrate strength on failure mode, ultimate load, strain transfer, shear stress distribution, and bond-slip response. Compared with previous Fe-SMA bond studies, the present work provides a broader parametric evaluation of thermally activated Fe-SMA/concrete adhesive interfaces and identifies the combined effects of adhesive thermal resistance, adhesive modulus, bond length, and concrete substrate strength. Furthermore, a temperature-related parameterization of the Nakaba bond-slip model is established to describe the residual bond-slip behavior within the investigated range.

Test scheme

Test materials

Each specimen consisted of a substrate block, an Fe-SMA plate, and a structural epoxy adhesive.

The concrete substrate block has dimensions of 300 mm × 100 mm × 100 mm and design strengths of C30/C40/C60. The respective mass mix ratios (W:C:S:G), average compressive strength, and splitting tensile strength are shown in Table 1. For the Q235 steel substrate, which has dimensions of 300 mm × 100 mm × 20 mm, 235 MPa and 420 MPa denote the nominal yield strength and tensile strength, respectively.

Table 1.

Substrate parameters.

Substrate type	W:C:S:G	Compressive strength (MPa)	Splitting tensile strength (MPa)
C30	0.38:1:1.11:2.72	37.5	2.9
C40	0.41:1:1.35:2.41	45.7	3.7
C60	0.33:1:1.10:2.10	67.6	4.35

The Fe-SMA plate has dimensions of 200 mm × 50 mm × 3.5 mm, with a Young’s modulus of 180 GPa, an elongation at break of 13%, a yield strength of 560 MPa, and a tensile strength of 840 MPa.

Three structural adhesives were used: 3M DP420 (Type A), a heat-resistant low-modulus adhesive; 3M DP490 (Type B), a heat-resistant high-modulus adhesive; and Fischer FC-SRS (Type C), a commonly used epoxy adhesive for externally bonded concrete-steel systems. Their elastic moduli were 2.36, 12.8, and 3.6 GPa, ultimate strengths were 31.0, 55.7, and 38 MPa, and glass transition temperatures were 150, 120, and 60°C, respectively.

Specimen design

A total of 117 specimens were designed in 39 groups, with three identical specimens in each group for averaging, considering adhesive type (A, B, C), adhesive thickness (0.5, 1, 2 mm), bond length (50, 70, 150, 200 mm), heating temperature (20, 150, 200, 250, 300°C), thermal cycles (1, 10, 20, 50), and substrate strength (C30, C40, C60 concrete, and Q235 steel). In addition to the regular parametric design, specially considered cases included room-temperature unheated specimens, steel-substrate specimens, and multi-cycle specimens. Detailed parameters are listed in Table 2, and the single-shear configuration is shown in Figure 1.

Table 2.

Specimen design.

Specimen number	Type of adhesive	Adhesive layer thickness (mm)	Bond length (mm)	Heating temperature (°C)	Type of substrate
A-1-50-200-C30	A	1	50	200	C30
A-1-70-200-C30	A	1	70	200	C30
A-1-100-200-C30	A	1	100	200	C30
A-1-150-200-C30	A	1	150	200	C30
A-1-200-200-C30	A	1	200	200	C30
A-0.5-50-200-C30	A	0.5	50	200	C30
A-0.5-70-200-C30	A	0.5	70	200	C30
A-0.5-100-200-C30	A	0.5	100	200	C30
A-0.5-150-200-C30	A	0.5	150	200	C30
A-0.5-200-200-C30	A	0.5	200	200	C30
A-2-50-200-C30	A	2	50	200	C30
A-2-70-200-C30	A	2	70	200	C30
A-2-100-200-C30	A	2	100	200	C30
A-2-150-200-C30	A	2	150	200	C30
A-2-200-200-C30	A	2	200	200	C30
A-1-100-20-C30	A	1	100	20	C30
A-1-100-150-C30	A	1	100	150	C30
A-1-100-250-C30	A	1	100	250	C30
A-1-100-300-C30	A	1	100	300	C30
B-1-50-200-C30	B	1	50	200	C30
B-1-70-200-C30	B	1	70	200	C30
B-1-100-200-C30	B	1	100	200	C30
B-1-150-200-C30	B	1	150	200	C30
B-1-200-200-C30	B	1	200	200	C30
B-1-100-20-C30	B	1	100	20	C30
B-1-100-150-C30	B	1	100	150	C30
B-1-100-250-C30	B	1	100	250	C30
B-1-100-300-C30	B	1	100	300	C30
C-1-100-20-C30	C	1	100	20	C30
C-1-100-150-C30	C	1	100	150	C30
C-1-100-200-C30	C	1	100	200	C30
C-1-100-250-C30	C	1	100	250	C30
C-1-100-300-C30	C	1	100	300	C30
A-1-100-200-C40	A	1	100	200	C40
A-1-100-200-C60	A	1	100	200	C60
A-1-100-200-Q235	A	1	100	200	Q235
A-1-100-200*10-C30	A	1	100	200*10	C30
A-1-100-200*20-C30	A	1	100	200*20	C30
A-1-100-200*50-C30	A	1	100	200*50	C30

Note. In the table, “A, B, C” represent adhesive types, while “C30, C40, C60, Q235” represent substrate material strengths; “A-1-100-200*20-C30” represents Adhesive A, an adhesive layer thickness of 1 mm, a bond length of 100 mm, a heating temperature of 200 °C, 20 thermal cycles, and a C30 concrete substrate.

Figure 1.

The single-shear specimen configuration.

To ensure engineering relevance, the parameter ranges were selected based on previous studies and practical applications. Bond length and adhesive thickness were chosen according to reported effective bond ranges of Fe-SMA/FRP bonded systems and preliminary observations, so as to cover both the ascending and plateau stages of load transfer. The activation temperature of 150–300°C was adopted to represent the typical recovery-stress development range of Fe-SMA while considering the performance of high-temperature-resistant epoxy adhesives. Thermal cycling was introduced to simulate repeated temperature exposure in service, and the substrate strength covered common concrete and steel grades used in practice. Overall, the parameter design balanced literature evidence and engineering feasibility.

Both single-shear and double-shear tests are typical methods for evaluating shear performance (Jiang et al., 2020). They involve fixing the specimen while applying a force parallel to the specimen to the Fe-SMA plate bonded to its surface, thereby inducing bond shear stress at the interface. The single-shear test can better simulate the shear force and eccentric load generated when the Fe-SMA plate is anchored at the bottom of the beam in actual engineering. Considering the structural characteristics of externally prestressed systems (Shahverdi et al., 2016), the single-shear test is selected for this study.

Test methods and equipment

The Fe-SMA plates were wire-cut, mechanically polished, cleaned with acetone, and lightly abraded with fine-grit sandpaper, while the concrete bonding surfaces were transversely roughened. After drying, the Fe-SMA plates were bonded to the concrete substrates with structural adhesive. A 0.2 mm K-type thermocouple was embedded at the center of the adhesive layer to monitor the interfacial temperature during heating. Custom PTFE molds and steel balls were used to control adhesive thickness and position. After bonding, all specimens were cured at room temperature for seven days.

After fabrication, the adhesive thickness was determined from the measured total specimen thickness by subtracting the thicknesses of the concrete block and Fe-SMA plate. A custom-made electrical device was used for heating. Once the Fe-SMA surface reached the target temperature measured by an infrared thermometer, it was held for 30 s and the current was then automatically cut off, while the embedded K-type thermocouple recorded the interfacial temperature.

A 3D-DIC system was used to measure the full-field strain and displacement on the Fe-SMA surface (Pan et al., 2009). After heating and cooling, the surface was prepared with a white matte base coat and random black speckles. Images were recorded at 1 Hz during loading and processed to obtain the displacement and strain fields.

All tests were conducted using a 500 kN electro-hydraulic servo testing machine (Figure 2). A specially designed fixture was used to apply the unsymmetrical eccentric tensile load required for the single-shear configuration. Before formal loading, a 2 kN preload was applied at 1 kN/min. The specimens were then loaded under load control at 1 kN/min until failure.

Figure 2.

Shear test setup.

Test results and analysis

Failure mode

For the Fe-SMA/concrete interface, three typical failure modes can be identified: (a) Fe-SMA/adhesive interfacial debonding, usually caused by insufficient bond quality due to an excessively thin adhesive layer, uneven application, or an overly smooth Fe-SMA surface; (b) adhesive layer failure, in which the adhesive fails in shear and its strength is more fully utilized, commonly in high-strength concrete or steel substrates, but also in non-heat-resistant adhesives after thermal damage; and (c) concrete surface spalling with coarse aggregate exposed, indicating that the adhesive remained intact while failure occurred in the surface concrete, i.e., the interfacial capacity exceeded the tensile resistance of the concrete surface layer.

Among the concrete specimens, the majority (72 specimens) showed Type c failure, characterized by concrete surface shearing with exposed coarse aggregate while the adhesive remained intact. The peak shear stress in these specimens was 3–5 MPa, exceeding the corresponding concrete tensile strength (2.9–4.35 MPa), indicating a mixed shear-tension failure. Under eccentric single-shear loading, stress concentration at the loading end caused the principal tensile stress to exceed the concrete tensile capacity before the adhesive reached its full shear strength (Ramirez et al., 2021; Smith and Teng, 2001), showing that adhesive performance was not the governing factor. Another 24 concrete specimens exhibited mixed Type b + c failure, confirming sufficient bond length and adhesive thickness. By contrast, Q235 specimens failed mainly in Type b mode, with peak shear stress of 10–20 MPa and much higher ultimate load, indicating that the intrinsic shear strength of the adhesive can be fully mobilized only when the substrate is sufficiently strong. A few C30 specimens (9 specimens) showed Type a or a + c failure, mainly because of excessively thin or uneven adhesive layers. Key results are shown in Figure 3.

Figure 3.

Typical failure modes.

Ultimate load

Table 3 lists the measured thickness of the adhesive layer (

t_{m}

), the measured temperature of the adhesive layer (

T_{m}

), the maximum shear stress (

τ_{\max}

), the relative slip at the loading end (

s_{0}

), the ultimate load (

F_{u}

), and the failure mode for all specimens. To more clearly illustrate the ultimate load patterns, bar charts of ultimate load under different parameters were plotted separately.

Table 3.

Test results.

Specimen number	$t_{m}$ (mm)	$T_{m}$ (°C)	$τ_{\max}$ (MPa)	$s_{0}$ (mm)	$F_{u}$ (kN)	Failure mode
A-1-50-200-C30	1.05	172	2.42	0.102	12.05	a + c
A-1-70-200-C30	1.04	170	3.07	0.112	15.07	c
A-1-100-200-C30	1.02	165	3.69	0.128	18.16	c
A-1-150-200-C30	1.03	173	4.02	0.143	20.03	c
A-1-200-200-C30	1.02	172	4.22	0.153	20.96	b + c
A-0.5-50-200-C30	0.47	171	1.72	0.082	8.44	a
A-0.5-70-200-C30	0.49	176	2.15	0.090	10.57	c
A-0.5-100-200-C30	0.52	178	2.63	0.102	12.79	c
A-0.5-150-200-C30	0.47	181	2.85	0.114	14.37	c
A-0.5-200-200-C30	0.48	178	3.02	0.122	14.97	c
A-2-50-200-C30	2.04	165	2.98	0.124	14.59	c
A-2-70-200-C30	2.05	164	3.66	0.136	18.29	c
A-2-100-200-C30	2.03	162	4.35	0.155	21.56	c
A-2-150-200-C30	2.03	160	4.86	0.173	24.22	b + c
A-2-200-200-C30	2.04	162	5.02	0.185	24.85	b + c
A-1-100-20-C30	1.01	21	4.03	0.142	20.01	c
A-1-100-150-C30	0.98	112	3.87	0.135	19.08	c
A-1-100-250-C30	0.98	215	3.52	0.122	17.24	c
A-1-100-300-C30	1.02	261	3.36	0.116	16.46	b + c
B-1-50-200-C30	1.03	170	2.18	0.089	10.53	a + c
B-1-70-200-C30	1.03	172	2.72	0.098	13.25	c
B-1-100-200-C30	1.02	175	3.35	0.111	15.97	c
B-1-150-200-C30	1.02	169	3.58	0.124	17.53	c
B-1-200-200-C30	1.03	168	3.67	0.133	17.99	b + c
B-1-100-20-C30	1.01	20	3.56	0.123	17.53	c
B-1-100-150-C30	0.98	110	3.42	0.117	16.67	c
B-1-100-250-C30	0.97	210	3.12	0.106	15.10	c
B-1-100-300-C30	1.03	257	2.99	0.101	14.41	b + c
C-1-100-20-C30	1.02	22	2.72	0.170	22.01	c
C-1-100-150-C30	1.02	117	1.93	0.102	15.74	c
C-1-100-200-C30	1.04	173	1.68	0.068	13.60	b
C-1-100-250-C30	0.98	215	0.92	0.051	7.07	b
C-1-100-300-C30	0.96	248	0.67	0.034	4.82	b
A-1-100-200-C40	0.97	172	4.36	0.143	20.50	b + c
A-1-100-200-C60	0.99	173	4.83	0.179	22.79	b + c
A-1-100-200-Q235	1.02	161	17.83	0.224	35.96	b
A-1-100-200*10-C30	1.03	171	3.73	0.131	17.61	c
A-1-100-200*20-C30	1.03	173	3.82	0.134	17.29	c
A-1-100-200*50-C30	0.98	170	3.92	0.138	16.71	c

As shown in Figure 4(a), under identical conditions, the ultimate load increases with the bond length. When the bond length exceeds 100 mm, the effect of further increasing the bond length on the ultimate load gradually diminishes. For A-1-50-200-C30, ultimate load increments were 25.03%, 20.54%, 10.26%, and 4.69% for bond length increases of 50→70 mm, 70→100 mm, 100→150 mm, and 150→200 mm, respectively.

Figure 4.

Ultimate loads under different parameters.

The ultimate load increases with the increase in adhesive layer thickness. For A-0.5-100-200-C30, ultimate load increments were 42.03% and 18.70% for the adhesive layer thickness increases of 0.5→1.0 mm, and 1.0→2.0 mm.

Increasing the bond length from 50 mm to 100 mm significantly enhances the ultimate load capacity. However, further increases in bond length yield diminishing returns, indicating the existence of an effective bond length (Chen and Teng, 2001) beyond which load capacity gains become negligible. Sensitivity analysis of ultimate load to design parameters is presented in Table 4.

Table 4.

Sensitivity analysis of ultimate load to design parameters.

Design parameters	Range of variation (mm)	Reference specimen	Ultimate load (kN)	Load increase (%)	Key factors
Bond length	50→70	A-1-50-200-C30	12.05→15.07	25.03	Significant load increase before reaching the effective bond length
Bond length	100→150	A-1-100-200-C30	18.16→20.03	10.26	Reduced marginal gain as the bond length approaches the effective bond length
Adhesive thickness	0.5→1.0	A-0.5-100-200-C30	12.79→18.16	42.03	Marked improvement in bond capacity with increasing adhesive thickness
Adhesive thickness	1.0→2.0	A-1-100-200-C30	18.16→21.56	18.70	Diminishing improvement in bond capacity at larger adhesive thickness

For practical applications, a bond length of 150 mm is recommended to provide a sufficient safety margin, while an adhesive thickness of 1 mm appears to be the most effective and economical choice. Thicker adhesive layers provide little further increase in ultimate load because they also increase eccentricity (Lenwari et al., 2006). In C30 specimens, most failures were concrete surface peeling, indicating that adhesive shear strength was no longer the governing factor. These results confirm the feasibility of the investigated heat-resistant adhesives for Fe-SMA-to-concrete bonding under the short-term thermal activation considered here, although additional end or hybrid anchorage may still be beneficial to improve reliability and reduce local concrete damage (Khalil et al., 2022).

As the heating temperature increased, the ultimate load gradually decreased, but the reduction was much smaller for the two heat-resistant adhesives than for the non-heat-resistant adhesive. For Type A adhesive, the ultimate load decreased by 4.65%, 9.25%, 13.84%, and 17.74% at 150, 200, 250, and 300°C, respectively, compared with 20°C. For Type C adhesive, the corresponding reductions were 28.50%, 38.20%, 67.90%, and 78.10%, as shown in Figure 4(b). For Type A and B adhesives, the ultimate load remained relatively stable even when the adhesive-layer temperature exceeded 150°C, with only about a 10% reduction at 200°C, whereas Type C showed a 38.2% reduction under the same condition.

This difference is attributed to the better thermal resistance of high-temperature epoxy adhesives. When heated above Tg, their elastic modulus and strength decrease because of the transition from a glassy to a rubbery state, but under the present short-duration heating regime, the deterioration was governed mainly by reversible thermal softening rather than irreversible chain decomposition (Aleb and Abu-Thabit, 2025). Accordingly, the investigated high-temperature-resistant adhesives retained acceptable bond performance after short-term thermal activation.

In addition, after 10, 20, and 50 thermal cycles at 200°C, the ultimate load decreased by only 3.12%, 4.79%, and 7.98%, respectively, relative to a single 200°C cycle, indicating that low-cycle thermal exposure did not fundamentally alter the bond-slip evolution within the tested range, as shown in Figure 4(c).

Adhesive type also had a significant effect on ultimate load. Owing to their greater flexibility and ductility, low-modulus adhesives were more favorable for strengthening applications (Wang et al., 2017). At an adhesive thickness of 1 mm and a heating temperature of 200°C, the ultimate load of Type A adhesive was 10%–20% higher than that of Type B for all bond lengths, as shown in Figure 4(d).

The ultimate load also increased with substrate strength, as shown in Figure 4(e). For A-1-100-200-C30, it increased by 12.87% from C30 to C40 and by 11.16% from C40 to C60, while the largest increase, 57.83%, occurred when the substrate changed from C60 concrete to Q235 steel, because the steel surface was not damaged and failure occurred only within the adhesive layer.

Fe-SMA strain distribution

Based on the DIC analysis results, axial strain data for the Fe-SMA in each specimen can be obtained (Zhang et al., 2006). Figure 5 shows the axial strain evolution of the Fe-SMA in specimen A-1-150-200-C30 during loading. Figure 5(a) displays the load-displacement curve, while Figure 5(b) presents the full-field axial strain contours of the Fe-SMA obtained from the DIC measurements at different loading stages. Point A represents the initial phase, while points B–F represent various loading phases. The vertical axis indicates the distance from the measurement point to the loading end.

Figure 5.

Axial strain distribution of Fe-SMA in A-1-150-200-C30.

Overall, all Fe-SMA plates exhibit similar strain variation patterns:

At zero loading, axial strain in the Fe-SMA plate is zero. During the initial loading phase, strain first appears at the loading end and gradually increases while propagating toward the free end. At this stage, the Fe-SMA plate, structural adhesive, and concrete work synergistically, resulting in a linear load-displacement curve. At point C, the load reaches its maximum value, coinciding with the peak axial strain of the Fe-SMA plate occurring at the loading end. Upon entering the interfacial peeling stage, the peak strain value stabilizes, and the peak strain zone continuously expands from the loading end toward the free end. However, near the free end, the strain rapidly decreases, and no significant strain is recorded at the free end throughout the entire loading process.

This indicates that debonding initiated at the loaded end and gradually propagated toward the free end, whereas the region beyond the effective bond length carried negligible interfacial stress. This demonstrates that each specimen possesses an effective bond length; beyond this length, stress transfer ceases.

Figure 6 shows the axial strain distribution curves for Fe-SMA plates with three different bond lengths. 1# Section represents the free end, and the number gradually increases towards the loading end. The maximum number represents the section at the loading end. During the initial loading phase, significant strain occurs only at the loading end. At this stage, the materials work synergistically, resulting in a linear curve trend. As the load increases, slippage occurs between the Fe-SMA plate and the concrete, leading to a decrease in interfacial stiffness and a nonlinear increase in the curve. Upon reaching the ultimate load, a rapid increase in strain occurs, resulting in specimen failure.

Figure 6.

Axial strain distribution curves with different bond lengths.

Interface shear stress analysis

The distribution of interfacial shear stress reflects stress transfer between the Fe-SMA plate and the substrate, and local shear stress serves as a key parameter characterizing the bond-slip relationship at the interface. The local interfacial shear stress was calculated from the axial strain gradient of the Fe-SMA plate based on force equilibrium:

τ_{i} = E_{f} t_{f} \frac{d ε_{i}}{d x}

(1)

where

E_{f} = 180 GPa

and

t_{f} = 3.5 mm

are the elastic modulus and thickness of the Fe-SMA plate, respectively;

ε_{i}

is the axial strain of the Fe-SMA plate obtained from DIC, and

x

is the coordinate along the bonded length. In the discrete DIC analysis,

\frac{d ε_{i}}{d x}

was calculated from the strain difference between adjacent measurement points.

Figure 7 shows the interfacial shear stress distribution curves for each specimen. The concrete and steel substrates exhibited distinct shear-stress distributions.

Figure 7.

Interfacial shear stress distributions for different bond lengths and substrate types.

Concrete specimens (brittle failure): The shear stress distribution shows a gradually expanding parabolic shape. After reaching the peak, the shear stress at the loading end drops immediately to zero, indicating brittle fracture of the concrete surface. Once the principal tensile stress induced by eccentric loading exceeds the concrete tensile strength, cracks propagate rapidly and cause sudden failure. The maximum parabolic width corresponds to the effective bond length, beyond which stress is no longer transferred. For the tested concrete specimens, the effective bond length was approximately 80–100 mm, and the peak shear stress was generally 3–5 MPa.

Steel specimens (ductile failure): The shear stress distribution resembles a peak moving toward the free end. When the shear stress at the loading end drops to zero, local failure initiates, but the peak continues to shift toward the free end with little change in curve shape. This migrating peak reflects ductile softening of the adhesive layer, in which load is progressively redistributed to undamaged regions after local shear failure. The effective bond length was about 100–120 mm, and the peak shear stress ranged from 10 to 20 MPa.

The difference between concrete specimens and steel specimens lies in the following: For concrete specimens, the adhesive layer is sufficiently tough such that it does not fail upon reaching the specimen’s ultimate load, while failure occurs at the concrete surface (Kashfuddoja and Ramji, 2013). For steel specimens, the substrate strength is sufficiently high such that adhesive failure typically occurs, starting from the loading end and progressively propagating toward the free end.

Type A adhesive, with a lower elastic modulus, showed better performance mainly because its greater deformability promoted stress redistribution (Ahmed and Kodur, 2011). Under eccentric single-shear loading, high-modulus Type B adhesive caused severe local stress concentration and earlier brittle concrete failure, whereas low-modulus Type A adhesive allowed greater interfacial slip and a longer effective stress transfer zone. As a result, the low-modulus adhesive improved both ductility and ultimate load capacity.

Interface load-slip relationship curve

During actual loading, neither strain nor stress is transmitted to the free end, so the relative slip at the specimen’s free end is nearly zero. The local slip was obtained by integrating the axial strain of the Fe-SMA plate along the bonded length:

s_{i} = \int_{0}^{x_{i}} ε (x) d x

(2)

where

s_{i}

is the relative slip at position

x_{i}

. Because the strain and slip near the free end were negligible during the tests, the free end was taken as the reference point for slip calculation. In the discrete calculation, the integral was evaluated numerically using the DIC strain data.

A typical load-slip curve exhibits three distinct stages:

(1) Elastic stage: At low loads, the load-slip curve increases linearly as the interface materials work synergistically;

(2) Softening stage: As load increases, the load-slip curve exhibits nonlinear growth, with slip occurring at the interface and stiffness weakening;

(3) Peeling stage: After peeling occurs at the loading end, the load increase is not significant, but the relative slip has increased sharply, ultimately leading to specimen failure.

Figure 8 shows load-slip curves under different structural adhesives, bond lengths, concrete grades, and heating temperatures. Low-modulus adhesives improve ductility, giving larger slip and higher maximum load. Bond length has little effect on initial stiffness, but shorter bond lengths enter softening earlier, whereas longer bond lengths produce larger slip. Higher concrete strength reduces slip, while higher heating temperature accelerates bond-slip development by degrading adhesive stiffness and shear strength.

Figure 8.

Interface load-slip relationship curve.

Bond-slip constitutive model

Bond-slip scatter plot

The bond-slip constitutive model establishes the relationship between interfacial shear stress and relative slip, forming the core foundation for further investigation of the Fe-SMA/concrete interface. The calculation methods for interfacial shear stress and relative slip were presented earlier. Figure 9 displays the bond-slip scatter plot.

Figure 9.

Bond-slip scatter plots.

The figure reveals distinct ascending segments and interfacial softening descending segments across all specimens:

(1) The initial straight-line rise in the ascending segment corresponds to the elastic stage, characterized by low load and slip values;

(2) Prior to reaching the peak, interfacial stiffness gradually diminishes, leading to a nonlinear ascending segment;

(3) Upon entering the descending segment, interfacial damage occurs, causing a decline in load-bearing capacity;

(4) The final segment approaches a horizontal line, indicating interfacial debonding.

The test results indicate that increasing the adhesive layer thickness enhances the maximum interfacial shear stress. As the bond length increases, both the maximum interfacial shear stress and the maximum slip increase. The adhesive elastic modulus has the most significant influence on the shape of the scatter plots, flattening the ascending branch and enlarging the envelope area.

Bond-slip model

Existing studies suggest that bond-slip models for externally bonded plate-to-concrete interfaces have certain cross-material transferability. Models originally developed for FRP–concrete interfaces (Lu et al., 2005) have been adopted or modified for aluminum alloy plate–concrete and steel plate–concrete interfaces with satisfactory agreement (Chen et al., 2023). This is because these interfaces are commonly governed by adhesion, friction, mechanical interlocking, and progressive damage evolution. Therefore, classical bond-slip frameworks can be used as a rational basis for the Fe-SMA/concrete interface, provided that temperature-related parameters are introduced to account for thermal activation and adhesive degradation. In this study, the bilinear model, hyperbolic-type model, and Nakaba model (Nakaba et al., 2001) were selected to fit the experimentally derived bond-slip data, as shown in Figure 10. In these models, $τ$ is the local interfacial shear stress, $s$ is the local slip, $τ_{\max}$ is the peak shear stress, $s_{0}$ is the slip corresponding to $τ_{\max}$ , and $s_{u}$ is the ultimate slip at which the residual shear stress approaches zero.

Figure 10.

Bond-slip model comparison.

The bilinear model is expressed as follows:

\frac{τ}{τ_{\max}} = \frac{s}{s_{0}}, 0 \leq s \leq s_{0}

(3)

\frac{τ}{τ_{\max}} = \frac{s_{u} - s}{s_{u} - s_{0}}, s_{0} < s \leq s_{u}

(4)

This model is simple and provides a clear physical interpretation of the ascending elastic branch and the descending softening branch. However, because both branches are linear, it cannot capture the gradual stiffness degradation observed in the nonlinear ascending stage.

The hyperbolic-type model is written as:

\frac{τ}{τ_{\max}} = {(\frac{s}{s_{0}})}^{a}, 0 \leq s \leq s_{0}

(5)

\frac{τ}{τ_{\max}} = \exp [- b (\frac{s}{s_{0}} - 1)], s > s_{0}

(6)

where

a

and

b

are regression coefficients controlling the curvature of the ascending and descending branches, respectively.

The Nakaba model is expressed as:

\frac{τ}{τ_{\max}} = \frac{n (s / s_{0})}{n - 1 + {(s / s_{0})}^{n}}

(7)

where

n

is a dimensionless shape parameter and

n > 1

. This form satisfies

τ = τ_{\max}

when

s = s_{0}

. A larger

n

generally corresponds to a steeper ascending branch and a more concentrated post-peak softening response. The equation was checked against the original formulation of Nakaba et al. and was used consistently in the following parameter identification.

As shown in Figure 10, the Nakaba and hyperbolic models capture both linear and nonlinear ascending behavior, whereas the bilinear model cannot represent the stiffness reduction in the nonlinear stage. In the descending stage, the bilinear model fails to simulate interfacial softening, and the hyperbolic model shows larger deviation and greater parameter complexity. Overall, the Nakaba model best reproduces the complete bond-slip process.

To quantitatively compare the fitting performance of the candidate bond-slip models, the coefficient of determination (R²) and root mean square error (RMSE) were calculated for the bilinear, hyperbolic, and Nakaba models, as summarized in Table 5. The values in Table 5 are the statistical averages obtained from curve-by-curve fitting of the experimentally derived bond-slip relationships, rather than from a single pooled curve. The bilinear model gave an average R² of 0.82 and an RMSE of 1.15 MPa, mainly because it cannot represent the nonlinear stiffness degradation before the peak or the gradual post-peak softening. The hyperbolic-type model improved the fitting accuracy, with an average R² of 0.91 and an RMSE of 0.68 MPa, but it still showed noticeable deviation in the descending branch for several specimens. The Nakaba model provided the best overall agreement, with an average R² of 0.97 and an RMSE of 0.42 MPa. Therefore, the Nakaba model was selected as the basic form for the subsequent parameterization.

Table 5.

Quantitative comparison of candidate bond-slip models.

Model	R²	RMSE (MPa)
Bilinear model	0.82 ± 0.05	1.15 ± 0.12
Hyperbolic-type model	0.91 ± 0.03	0.68 ± 0.09
Nakaba model	0.97 ± 0.02	0.42 ± 0.08

Although no published data are available for the heated Fe-SMA/concrete interface, experimental results from the non-heated Fe-SMA/concrete interface (Zhang et al., 2026), the FRP/concrete interface (Lu et al., 2005), and the aluminum alloy plate/concrete interface (Jiang et al., 2020) were used for validation. In addition, the improved exponential Teng model (Chen and Teng, 2001; Zhang et al., 2026) and the classical three-segment model for the FRCM (Fiber Reinforced Cementitious Matrix)/concrete system (Zou et al., 2020) were introduced for comparison, as shown in Figure 11. The results indicate that the general form of the Nakaba bond-slip law remains applicable to several externally bonded interface systems, although the governing parameters and failure mechanisms are material-dependent. On this basis, the present study extends the Nakaba model to the thermally activated Fe-SMA/concrete interface.

Figure 11.

Comparison with bond-slip data from other material systems.

To facilitate engineering application and finite element implementation, the three key parameters of the Nakaba model, namely $τ_{\max}$ , $s_{0}$ , and $n$ , were further expressed as functions of the adhesive elastic modulus $E_{a}$ , the glass transition temperature of the adhesive $T_{g}$ , the measured adhesive-layer temperature $T_{m}$ , and the measured concrete splitting tensile strength $f_{t, s p}$ . The splitting tensile strength was adopted because the dominant failure mode of the concrete specimens was concrete surface spalling or mixed shear–tension failure near the adhesive–concrete interface. Therefore, $f_{t, s p}$ is more directly related to the interfacial failure mechanism than the concrete compressive strength.

The normalized thermal exposure index $θ_{T}$ was defined as:

θ_{T} = \frac{T_{m} - T_{r e f}}{T_{g} - T_{r e f}}

(8)

where

T_{r e f} = 20 ° C

is the reference ambient temperature. The value of

θ_{T}

represents the relative thermal exposure level of the adhesive layer with respect to its glass transition temperature.

The peak interfacial shear stress $τ_{\max}$ was expressed as:

τ_{\max} = τ_{\max, r e f} {(\frac{f_{t, s p}}{f_{t, s p, r e f}})}^{β} {(\frac{E_{a}}{E_{a, r e f}})}^{- α_{E}} \exp (- λ θ_{T})

(9)

The slip corresponding to the peak interfacial shear stress $s_{0}$ was expressed as:

s_{0} = s_{0, r e f} {(\frac{E_{a}}{E_{a, r e f}})}^{- η} \exp (- ζ θ_{T})

(10)

The shape parameter $n$ was expressed as:

n = n_{r e f} {(\frac{E_{a}}{E_{a, r e f}})}^{- ρ} (1 + ξ θ_{T})

(11)

where

E_{a, r e f} = 2.36 GPa

is the elastic modulus of the Type A adhesive;

f_{t, s p, r e f} = 2.9 MPa

is the measured splitting tensile strength of the C30 concrete;

τ_{\max, r e f} = 4.0 MPa

s_{0, r e f} = 0.142 mm

, and

n_{r e f} = 2.0

are the reference bond-slip parameters identified from the baseline specimen (A-1-100-20-C30) at room temperature. The fitted sensitivity coefficients are

α_{E} = 0.04

β = 0.50

λ = 0.10

η = 0.08

ζ = 0.016

ρ = 0.20

, and

ξ = 0.005

Before regression, all variables were normalized by their reference values to reduce scale effects. The parameter identification was performed in a stepwise manner. First, the reference parameters $τ_{\max, r e f}$ , $s_{0, r e f}$ , and $n_{r e f}$ were determined from the baseline room-temperature specimen. Then, the coefficients controlling $τ_{\max}$ , $s_{0}$ , and $n$ were identified separately using nonlinear least-squares regression. A normalized sensitivity analysis was further conducted by varying each input variable within the tested range while keeping the other variables at their reference values. The results showed that the peak shear stress was mainly governed by adhesive elastic modulus, concrete splitting tensile strength, and thermal exposure, whereas the peak slip and the shape parameter were more sensitive to adhesive stiffness and thermal exposure. This trend is consistent with the observed failure modes and strain-transfer behavior. Because the experimental matrix was designed for controlled parametric comparison rather than statistically independent random sampling, conventional confidence intervals may overstate the statistical reliability of the fitted coefficients. Therefore, the coefficients are interpreted as deterministic calibration parameters within the tested range, and their robustness is discussed through the normalized sensitivity trends rather than through confidence intervals.

The exponent $β$ represents the contribution of the concrete splitting tensile resistance to the peak interfacial shear stress. The coefficient $α_{E}$ accounts for the adverse effect of adhesive stiffness mismatch, because a higher adhesive modulus tends to increase local stress concentration near the loaded end. The coefficient $λ$ describes thermal softening of the adhesive as the measured adhesive-layer temperature approaches its glass transition temperature. The parameters $η$ and $ζ$ describe the influence of adhesive stiffness and thermal exposure on the slip corresponding to the peak interfacial shear stress. The parameters $ρ$ and $ξ$ control the evolution of the shape parameter $n$ , reflecting changes in the curvature and post-peak softening characteristics of the bond-slip curve.

The regression accuracy of the parameterized model was evaluated by comparing the predicted and fitted values of $τ_{\max}$ , $s_{0}$ , and $n$ . The R² values for $τ_{\max}$ , $s_{0}$ , and $n$ were 0.95, 0.91, and 0.92, respectively, and the corresponding RMSE values were 0.20 MPa, 0.015 mm, and 0.35. These results indicate that the proposed parameterization provides acceptable prediction accuracy within the tested range.

Scope and limitations of the proposed model

The proposed parameterized Nakaba model was established based on the present Fe-SMA/concrete interface tests and is applicable mainly to externally bonded Fe-SMA plates using epoxy structural adhesives, conventional concrete substrates with strengths ranging from C30 to C60, and the short-term thermal activation protocol adopted in this study. The model should be interpreted as a residual bond-slip model after short-term thermal activation rather than a general durability model.

The effective bond length and failure mechanisms reported in this study are also specific to the present specimen geometry, adhesive thickness, substrate preparation, eccentric single-shear loading configuration, and heating procedure. In particular, the observed effective bond length of approximately 80–100 mm for concrete substrates and the dominant concrete surface spalling failure mode should not be directly extrapolated to other heating durations, sustained elevated-temperature exposure, long-term relaxation conditions, or field environments involving humidity, freeze–thaw action, fatigue loading, or sustained service loads.

Although repeated heating at 200°C for up to 50 cycles caused less than an 8% reduction in the ultimate load and did not fundamentally change the bond-slip evolution, the number of thermal cycles was not introduced as an explicit variable in the proposed model. Therefore, the model may be used only as a first-order approximation for limited repeated activation under the tested conditions. Further tests are required to validate its applicability to long-term thermal cycling, sustained high-temperature exposure, and coupled thermo-mechanical environmental actions. In addition, the Q235 steel comparison specimens exhibited adhesive-layer failure rather than concrete surface spalling, and therefore the proposed parameterized model should not be directly extended to steel or other non-concrete substrates.

Conclusion

Focusing on the interface between Fe-SMA and concrete, this study investigates the effects of different adhesive types, adhesive layer thickness, bond length, heating temperature, number of thermal cycles, and substrate strength on interface failure modes, ultimate load, strain distribution, shear stress distribution, load-slip curves, and bond-slip curves, and a bond-slip constitutive model is established. The key conclusions are as follows:

(1) The high-temperature-resistant epoxy adhesive retains more than 80% of the interfacial load-bearing capacity after short-term exposure to 200°C and 50 thermal cycles. Its bonding performance is not the dominant limiting factor for the interfacial load-bearing capacity within the tested parameter range.

(2) For practical applications, a 1 mm adhesive thickness and a low-modulus heat-resistant adhesive are favorable for enhancing interfacial performance. A bond length of 150 mm can be adopted as a conservative engineering recommendation with an allowance for safety reserve. Additional anchorage may be considered when higher connection reliability is required.

(3) The interfacial ultimate load increases with adhesive thickness, bond length, and substrate strength, but decreases with increasing adhesive elastic modulus and heating temperature. Among the investigated variables, substrate strength and heating temperature showed particularly pronounced effects on the ultimate load.

(4) Interfacial failure is governed by brittle spalling of the concrete surface, whereas steel specimens exhibit a more ductile failure mode. The peak shear stress shifts from the loading end toward the free end along the bonded length.

(5) The bond-slip relationship exhibits a typical nonlinear evolution, and there exists an effective bond length, which determines the upper limit of the interface bearing capacity.

(6) A temperature-dependent bond-slip constitutive model based on the Nakaba model is established. The model is applicable to concrete substrates with strengths ranging from C30 to C60, epoxy structural adhesives, and short-term thermal activation conditions. It captures the elastic, softening, and debonding stages, and enables explicit formulation in terms of adhesive elastic modulus, concrete splitting tensile strength, and thermal exposure.

Footnotes

ORCID iDs

Dongxiang Zhang

Hui Qian

Author contributions

Dongxiang Zhang: Methodology, Investigation, Writing – original draft, Visualization, Data curation.

Hui Qian: Conceptualization, Funding acquisition.

Zekai Su: Writing – review & editing.

Jiajie Wang: Writing – review & editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by Key Research and Development Program of Henan Province [grant numbers 251111241100]; China Construction Seventh Engineering Bureau Technology R&D Program [grant numbers CSCEC7b-2024-Z-17].

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Abdulkareem

Oukaili

Al-Mahaidi

(2023) Shear capacity investigation of RC concrete beams using self-prestressing Fe-based shape memory alloys strips. Results in Engineering 18: 101204. https://doi.org/10.1016/j.rineng.2023.101204

Abuodeh

Abdalla

Hawileh

(2021) Flexural strengthening of RC beams using aluminum alloy plates with mechanically-fastened anchorage systems: an experimental investigation. Engineering Structures 234: 111969. https://doi.org/10.1016/j.engstruct.2021.111969

Ahmed

Kodur

VKR

(2011) Effect of bond degradation on fire resistance of FRP-strengthened reinforced concrete beams. Composites Part B: Engineering 42(2): 226–237. https://doi.org/10.1016/j.compositesb.2010.11.004

Aleb

Abu-Thabit

(2025) TransTg: a new transformer model for predicting glass transition temperature of polymers from monomers’ molecular structures. Neural Computing & Applications 37(4): 2733–2746. https://doi.org/10.1007/s00521-024-10532-4

Chen

Teng

(2001) Anchorage strength models for FRP and steel plates bonded to concrete. Journal of Structural Engineering 127(7): 784–791. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:7(784)

Chen

Huang

Jiang

, et al. (2023) Experimental study on bond-slip performance of aluminum alloy plate-concrete interface by double-lap shear test [in Chinese]. Journal of Civil & Environmental Engineering 45(5): 181–190. https://doi.org/10.11835/j.issn.2096-6717.2021.153

Czaderski

Shahverdi

Brönnimann

, et al. (2014) Feasibility of iron-based shape memory alloy strips for prestressed strengthening of concrete structures. Construction and Building Materials 56: 94–105. https://doi.org/10.1016/j.conbuildmat.2014.01.069

Dong

Sun

, et al. (2024) Experimental investigation on anchoring and bonding properties between Fe-SMA strip and concrete. Construction and Building Materials 438: 137141. https://doi.org/10.1016/j.conbuildmat.2024.137141

Enns

Gillham

(1983) Time–temperature–transformation (TTT) cure diagram: modeling the cure behavior of thermosets. Journal of Applied Polymer Science 28(8): 2567–2591. https://doi.org/10.1002/app.1983.070280810

10.

Fawaz

Murcia-Delso

(2020) Bond behavior of iron-based shape memory alloy reinforcing bars embedded in concrete. Materials and Structures 53(5): 114. https://doi.org/10.1617/s11527-020-01548-y

11.

Hawileh

Abu-Obeidah

Abdalla

, et al. (2015) Temperature effect on the mechanical properties of carbon, glass and carbon–glass FRP laminates. Construction and Building Materials 75: 342–348. https://doi.org/10.1016/j.conbuildmat.2014.11.020

12.

Hong

Lee

Yeon

, et al. (2018) Flexural response of reinforced concrete beams strengthened with near-surface-mounted Fe-Based shape-memory alloy strips. International Journal of Concrete Structures and Materials 12(1): 45. https://doi.org/10.1186/s40069-018-0279-y

13.

Izadi

Ghafoori

Shahverdi

, et al. (2018) Development of an iron-based shape memory alloy (Fe-SMA) strengthening system for steel plates. Engineering Structures 174: 433–446. https://doi.org/10.1016/j.engstruct.2018.07.073

14.

Jiang

Huang

Liu

, et al. (2020) Research on bond-slip performance of aluminum alloy plate-concrete interface based on double-shear test [in Chinese]. Engineering Mechanics 37(S1): 287–295. https://doi.org/10.6052/j.issn.1000-4750.2019.04.S052

15.

Jiang

Jia

, et al. (2025) Mechanical performance and bond-slip model of adhesively bonded joints between Fe-SMA and concrete. International Journal of Adhesion and Adhesives 142: 104085. https://doi.org/10.1016/j.ijadhadh.2025.104085

16.

Kashfuddoja

Ramji

(2013) Whole-field strain analysis and damage assessment of adhesively bonded patch repair of CFRP laminates using 3D-DIC and FEA. Composites Part B: Engineering 53: 46–61. https://doi.org/10.1016/j.compositesb.2013.04.030

17.

Khalil

Elkafrawy

Abuzaid

, et al. (2022) Flexural performance of RC beams strengthened with pre-stressed iron-based shape memory alloy (Fe-SMA) bars: numerical study. Buildings 12(12): 2228. https://doi.org/10.3390/buildings12122228

18.

Kurtoğlu

Anil

Çevik

(2022) A machine‐learning‐based constitutive bond‐slip model for anchored CFRP strips externally bonded on concrete members. Structural Concrete 23(3): 1828–1844. https://doi.org/10.1002/suco.202100647

19.

Lenwari

Thepchatri

Albrecht

(2006) Debonding strength of steel beams strengthened with CFRP plates. Journal of Composites for Construction 10(1): 69–78. https://doi.org/10.1061/(ASCE)1090-0268(2006)10:1(69)

20.

Ning

(2021) Debonding failure of bonded interface in CFRP-strengthened steel plates [in Chinese]. Acta Materiae Compositae Sinica 38(12): 4090–4105. https://doi.org/10.13801/j.cnki.fhclxb.20210317.003

21.

Chatzi

Czaderski

, et al. (2023) Influence of activation temperature and prestress on behavior of Fe-SMA bonded joints. Construction and Building Materials 409: 134070. https://doi.org/10.1016/j.conbuildmat.2023.134070

22.

Teng

, et al. (2005) Bond-slip models for FRP sheets/plates bonded to concrete. Engineering Structures 27(6): 920–937. https://doi.org/10.1016/j.engstruct.2005.01.014

23.

Liu

Yuan

(2025) Experimental study and theoretical constitutive model for bond stress-slip relationship between high-strength stainless steel reinforcement and concrete. Construction and Building Materials 492: 143120. https://doi.org/10.1016/j.conbuildmat.2025.143120

24.

Nakaba

Kanakubo

Furuta

, et al. (2001) Bond behavior between fiber-reinforced polymer laminates and concrete. ACI Structural Journal 98(3): 359–367. https://doi.org/10.14359/10224

25.

Pan

Qian

Xie

, et al. (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Measurement Science and Technology 20(6): 062001. https://doi.org/10.1088/0957-0233/20/6/062001

26.

Qiang

Jiang

, et al. (2023) Strengthening mechanisms and research progress of steel and concrete beams strengthened with iron-based shape memory alloys [in Chinese]. Structural Engineers 39(6): 214–228. https://doi.org/10.15935/j.cnki.jggcs.2023.06.013

27.

Qiang

Wang

, et al. (2024) Constitutive model and activation recovery performance of Fe-SMA: experimental and theoretical study. Construction and Building Materials 420: 135537. https://doi.org/10.1016/j.conbuildmat.2024.135537

28.

Qiang

Chen

Jiang

, et al. (2025) Bond-slip failure characteristics of Fe-SMA-steel adhesively bonded joints. International Journal of Adhesion and Adhesives 138: 103941. https://doi.org/10.1016/j.ijadhadh.2025.103941

29.

Ramírez

FMG

De Moura

MFSF

Moreira

RDF

, et al. (2021) Experimental and numerical mixed-mode I + II fracture characterization of carbon fibre reinforced polymer laminates using a novel strategy. Composite Structures 263: 113683. https://doi.org/10.1016/j.compstruct.2021.113683

30.

Sato

Chishima

Soma

, et al. (1982) Shape memory effect in γ⇄ϵ transformation in Fe-30Mn-1Si alloy single crystals. Acta Metallurgica 30(6): 1177–1183. https://doi.org/10.1016/0001-6160(82)90011-6

31.

Schranz

Czaderski

Vogel

, et al. (2020) Bond investigations of prestressed, near-surface-mounted, ribbed memory-steel bars with full bond length. Materials & Design 196: 109145. https://doi.org/10.1016/j.matdes.2020.109145

32.

Shahverdi

Czaderski

Motavalli

(2016) Iron-based shape memory alloys for prestressed near-surface mounted strengthening of reinforced concrete beams. Construction and Building Materials 112: 28–38. https://doi.org/10.1016/j.conbuildmat.2016.02.174

33.

Smith

Teng

(2001) Interfacial stresses in plated beams. Engineering Structures 23(7): 857–871. https://doi.org/10.1016/S0141-0296(00)00090-0

34.

Wang

Pang

(2017) Effect of structural adhesive types on bond performance of CFRP plate-steel interface [in Chinese]. Journal of Suzhou University of Science and Technology (Engineering and Technology Edition) 30(4): 45–48. https://doi.org/10.3969/j.issn.1672-0679.2017.04.008

35.

Wang

Hosseini

Ghafoori

(2021) Experimental study on Fe-SMA-to-steel adhesively bonded interfaces using DIC. Engineering Fracture Mechanics 244: 107553. https://doi.org/10.1016/j.engfracmech.2021.107553

36.

Zhang

Luo

Arola

(2006) Displacement/strain measurements using an optical microscope and digital image correlation. Optical Engineering 45(3): 033605. https://doi.org/10.1117/1.2182108

37.

Zhang

, et al. (2022) Iron-based shape memory alloys in construction: research, applications and opportunities. Materials 15(5): 1723. https://doi.org/10.3390/ma15051723

38.

Zhang

Jiang

Qiang

, et al. (2026) Synergistic load-carrying mechanism of adhesive and bolts in hybrid joints between Fe-SMA and concrete. Construction and Building Materials 514: 145496. https://doi.org/10.1016/j.conbuildmat.2026.145496

39.

Zou

Sneed

D’Antino

(2020) Full-range behavior of fiber reinforced cementitious matrix (FRCM)-concrete joints using a trilinear bond-slip relationship. Composite Structures 239: 112024. https://doi.org/10.1016/j.compstruct.2020.112024