Temperature effects of shape memory alloys (SMAs) in damage control design of steel portal frames

Abstract

The objective of the present study is to analytically investigate temperature effects of an axial-type seismic damper made of shape memory alloys (SMAs) equipped in steel frames. Based on a modified multilinear one dimensional constitutive model of SMAs, two types of SMAs are employed, which have different stress plateau and different stress growth rate with temperature increase. Temperature effects of SMA dampers on seismic performance upgrading are discussed in three aspects: different environment temperatures; rapid loading rate induced heat generation and different SMA fractions. The analysis indicates that the effect of environment temperature should be considered for the SMA damper in steel frames. However, the rapid loading rate induced heat generation has little adverse effect.

Keywords

damage control design / shape memory alloy / temperature effect

Introduction

The effectiveness of application of smart material of shape memory alloys (SMAs) in seismic design has been demonstrated through many numerical and experimental investigations. Superelasticity is one of the most attractive properties of SMAs. It implies the good structural re-centering ability that can reach large strains but without residual deformation upon unloading. Moreover, in strong earthquakes, hysteretic behaviors are shown in SMAs because of phase to phase transition, and vibration energy would be effectively dissipated [1].

However, the characteristics of superelasticity in SMAs are highly sensitive to temperatures [2]. Usually, this is considered one of the main limitations of SMAs in seismic engineering and much research has focused on the temperature effects of SMAs made damping devices [3-5]. In damage control design of engineering structures, the investigation of temperature effects for SMA dampers should consider two aspects: one is the influence of environment temperature, which leads to different phase transformation plateau, the other is the influence of loading rate induced heat generation, which leads to rising transformation stresses.

In the present study, temperature effects of SMAs in damage control design are investigated. Elasto-plastic time-history analysis is performed in a frame-typed bridge pier with axial-type SMA damping devices using three recommended strong earthquake motions [6]. The SMA damping device is designed by two types of SMAs with different phase transformation plateau and temperature-stress growth rate. In the study, displacement at the top of the steel frame, local strain of critical members near bases and stress-strain relationship of SMA dampers are investigated as performance indices [7].

Temperature effects of SMA materials

As mentioned above, mechanical characteristics of SMA are temperature dependent. As shown in Fig. 1, linear relationship exists between transformation stresses and environment temperatures in the positive and reversal phase transformation processes [1]. The same trend was verified in the differential scanning caborimetry (DSC) experiments.

As described by Wayman and Duerig [2], the transformation critical stresses increase while increasing the temperature, with growth rate ranging from 3 up to 20MPa/°C. In this study, two types of SMAs are investigated: one is NiTi SMAs with growth rate of nearly 6MPa/°C [1], the other is CuAlBe SMAs with growth rate of 2MPa/°C [8]. The critical stresses under investigated temperatures are listed in Table 1.

On the other hand, in high rate loading process such as earthquake, heat generated from phase transformation cannot dissipate rapidly in short time intervals and the temperature in SMAs rises. As Motahari and Ghassemieh suggested [9], the temperature effects induced by heat generation could be simplified to adiabatic process, and the rise of temperature can be expressed as follows:

(1)T_{\mathrm{f}}=T_{\mathrm{s}}{e}^{-\mathrm{\Delta }{s}_{\mathrm{0}}/c},

in which, T_f and T_s represent the final temperature and the start temperature, respectively, c and Δs₀ are effective specific heat and specific entropy increment, respectively.

Modeling of axial-type SMA damper

Constitutive model of SMA material

A modified multilinear one-dimensional constitutive law of SMAs is recently proposed by authors [10], based on a model developed by Motahari and Ghassemieh [9]. Shown in Fig. 2(a) is the multilinear bone curve of SMAs in the austenite state at the reference temperature, in which four transformation stresses, i.e., σ_MS, σ_MF, σ_AS and σ_AF are given and the elastic modulus in the austenite state and martensite state are E_A and E_M, respectively. The superelasticity ability of the SMAs is illustrated and modeled in Fig. 2(a) that the SMAs can dissipate energy and recover to its undeformed shape after a large “plastic” strain in a cyclic loading due to phase transformation between the austenite state and the martensite state.

Modeling of axial-type SMA damper [10]

The axial-type SMA damper considered is shown in Fig. 3, in which two blocks (i.e., Part A and Part B) made of steel can slide past each other and two sets of austenite wire systems and one martensite or low yield steel (i.e., LYS) sheet are kernel material in the damper. Lubricating material is placed at the contact interface of Part A and Part B to reduce friction. The whole SMA damper can be distinctly divided into two components, i.e., the recentering component and the energy dissipation component. The recentering component consists of the two sets of austenite wires A and B, which are in tension only and react in reverse directions because the austenite wires A and B have excellent superelastic ability with relative small hysteretic loop, as shown in Fig. 2(a). And the energy dissipation component is made up of the martensite sheet or LYS sheet that is restrained so that it can afford tension and compression without undergoing buckling and its good energy dissipation ability is also shown in Fig. 2(a). With a combination of the recentering and dissipation components, the working principle of the SMA damper is illustrated and the constitutive model of the damper is shown as Fig. 2(b).

Analysis and discussion

Analytical model of the portal frame steel pier

A benchmark frame model is a simple single deck frame-typed steel pier as shown in Fig. 4. The main frame is made of SM490 steel grade with the yield strength of 315 MPa and the yield strain of 0.00153, and details of the bare frame can be found in a previous study [11]. The height and width of the frame are all 12 m, and the frames and girders have uniform stiffened box sections. Timoshenko beam elements of B21 in the ABAQUS [12] are used in the modeling the frame-typed pier as shown in Fig. 4 that refined meshes of 5 elements are for the critical part at the base of the pier. The yield shear force and top displacement of the bare frame (i.e., without the damping device) are determined from a pushover analysis. Detail of basic dimensions and structural properties of the pier is listed in Table 2.

Three JRA recommended Level 2 ground motions for Ground type II are considered as inputs in the analysis, i.e., JRT-EW-M, JRT-NS-M and FUKIAI-M [6], the records and the corresponding response spectras of the three inputs are shown in Fig. 6 .

The constitutive law proposed in the above section is applied for SMA dampers and the modified two surface model is used for beam elements in the main frame.

Design of SMA damping device

To investigate temperature effects of SMAs, two types of SMAs, i.e., Niti and CuAlBe SMAs, are used here and the critical transformation stresses at investigated temperatures in isothermal process are listed in Table 1. And the temperature increase considering adiabatic process can be obtained by Eq. (1) and the corresponding transformation stresses can be given by interpolation from Table 1. The two thermo-mechanical constants c and Δs₀ are given as 2.12 and -0.35, respectively, which are cited from Motahari and Ghassemieh [9].

The SMA damping device is consisted of two SMA dampers and two steel braces which are assumed to be rigid for simplicity. The geometric parameters and basic properties of the damping device are illustrated in Fig. 5, where l is the whole length of the damping devices, (EA)_SMA and l_SMA are stiffness and length of the SMA damper, respectively, (EA)_b and l_b are stiffness and length of the steel brace, respectively, F_SMA, K_SMA and δ_SMA are lateral yield force, elastic stiffness and displacement of the SMA damping devices, respectively. α_L is the length ratio between the steel brace component and SMA damper.

(2)l=l_{\mathrm{S}\mathrm{M}\mathrm{A}}+l_{\mathrm{b}},

(3){\alpha }_{\mathrm{L}}=l_{\mathrm{b}}/l_{\mathrm{S}\mathrm{M}\mathrm{A}},

As in a previous study of controlled structures, three design factors, i.e., the strength ratio α_F, the stiffness ratio α_K and the displacement ratio α_δ, were proposed as design governing parameters shown below:

(4){\alpha }_F={\displaystyle \frac{F_{\mathrm{y},\mathrm{d}}}{F_{\mathrm{y},\mathrm{f}}}},{\alpha }_{\mathrm{K}}={\displaystyle \frac{K_{\mathrm{y},\mathrm{d}}}{K_{\mathrm{y},\mathrm{f}}}},{\alpha }_{\mathrm{\delta }}={\displaystyle \frac{{\delta }_{\mathrm{y},\mathrm{d}}}{{\delta }_{\mathrm{y},\mathrm{f}}}},

here, F_y,d, K_y,d and δ_y,d are yield strength, elastic stiffness and yield displacement of damping devices, respectively, while F_y,f, K_y,f and δ_y,f are those of main structures.

The basic relationship of lateral force and displacement of the frame can be expressed as follows:

(5)F_{\mathrm{S}\mathrm{M}\mathrm{A}}=K_{\mathrm{S}\mathrm{M}\mathrm{A}}{\delta }_{\mathrm{S}\mathrm{M}\mathrm{A}},

and from the schematic diagram of the SMA damping device in Fig. 5, considering the relations of Eq. (4), K_SMA and δ_SMA can be derived as follows:

(6)K_{\mathrm{S}\mathrm{M}\mathrm{A}}=A_{\mathrm{S}\mathrm{M}\mathrm{A}}\cdot {\displaystyle \frac{\mathrm{1}}{C_{\mathrm{1}}}}{\displaystyle \frac{E_{\mathrm{S}\mathrm{M}\mathrm{A}}{L}^{\mathrm{2}}}{l^{\mathrm{3}}}},

(7){\delta }_{\mathrm{S}\mathrm{M}\mathrm{A}}={\displaystyle \frac{{\sigma }_{\mathrm{S}\mathrm{M}\mathrm{A}}}{E_{\mathrm{S}\mathrm{M}\mathrm{A}}}}{\displaystyle \frac{l^{\mathrm{2}}}{L}}{C}_{\mathrm{1}},

in which

(8)C_{\mathrm{1}}={\displaystyle \frac{\mathrm{2}}{(\mathrm{1}+{\alpha }_L)}},

Substituting Eqs. (6) and (7) into Eq. (5), then we have

(9)F_{\mathrm{S}\mathrm{M}\mathrm{A}}={\sigma }_{\mathrm{S}\mathrm{M}\mathrm{A}}{A}_{\mathrm{S}\mathrm{M}\mathrm{A}}{\displaystyle \frac{L}{l}},

For given α_F and α_K, F_SMA and K_SMA are first obtained from Eq. (4), then the area of SMAs can be calculated from Eq. (9) and the length of the damper from Eqs. (6), (8) and (2) simultaneously. As mentioned in a previous study [13], α_F≥0.8 and α_K ≈ 3 are suggested in such single deck portal frames, so constant α_F of 0.9 and α_K of 3 are used in the study. σ_MS at room temperature of 20°C is set as σ_y,SMA. The elastic modulus E is assumed as 70GPa [9], then the corresponding ϵ_y,SMA can be calculated, and the sizes of SMA dampers are listed in Table 3.

Discussions

To investigate temperature effects of SMA damping devices in steel frames under strong earthquakes, the following performance parameters are to be investigated:

1) top displacement, δ_top;

2) normalized average compressive strain at the base of the pier, ϵ_a/ϵ_y;

3) normalized stress-strain relationship of SMA dampers, ϵ_SMA/ϵ_{y, SMA} and σ_SMA/σ_{y, SMA}.

Effects of environment temperature

Only JRT-EW-M accelerogram is used for the time-history analysis presented in this subsection. The response results are illustrated in Figs. 7-9.

Shown in Fig. 7 are time history responses of the top displacement for the frame models with NiTi and CuAlBe SMA dampers under investigated temperatures. In the models with NiTi dampers, the maximum top displacement in the frame reaches to nearly 2.0δ_y at 0°C, while it is 1.6δ_y at 40°C. However, the maximum top displacement in the models with CuAlBe dampers ranges only from 1.2δ_y to 1.6δ_y. Moreover, it is found that in all the cases the residual top displacement is always very small. In Table 4-5, the absolute values of the maximum top displacement of the investigated frame models with two SMA dampers are listed under different temperatures and strong earthquake inputs. In general, it can be seen that the displacement demands are gradually reduced with the increase of temperatures.

The same trend is also shown in Fig. 8. In the models with NiTi dampers, the maximum average compressive strain at bases is nearly 5.0ϵ_y while it is only 2ϵ_y at 40°C. It is partially because the transformation critial stress of σ_AF is below 0 and it is meant the NiTi SMA damper would lose its work capacity tentatively. In the models with CuAlBe dampers, the maximum average compressive strain at bases slightly decreases from 2.69ϵ_y to 2.12ϵ_y with the drop of temperatures.

Shown in Fig. 9 are stress-strain responses of SMA damping devices at given temperatures, in which the stress and strain are divided by the “yield” stress and “yield” strain (the transformation critial stress σ_MS and strain ϵ_MS at the room temperature of 20°C) to be dimensionless. According to Eqs. (6) and (9), it is considered that the temperature has no effect on the stiffness ratio α_K, but the lower the temperature, the smaller the strength ratio α_F. It is found in the figure that the lower the temperature, the smaller the transformation stress of σ_MS, the larger the strain demand and the larger the energy dissipation. It is also found in the models with CuAlBe dampers that the hysteretic curves are plumper than those in the models with NiTi dampers and the variation of the yielding plateau is much smaller.

From above discussions, it is concluded that the capacity of SMAs is affected by the change of temperatures. Comparing the CuAlBe SMA to the NiTi SMA, because the transformation critical stresses is smaller, and the stress growth rate with temperature is smaller, another conclusion is given that, for the CuAlBe SMA, the temperature effects is less and the damage control effects is better.

Considering temperature effects, how to define a safety coefficient to satisfy the performance requirement, such as ultimate average compressive strain of 2.0ϵ_y [14], should be further investigated.

Effects of rapid loading induced heat generation

Note that the above analysis is performed under the assumption of the isothermal processes that no temperature variation happens under the hysteretic processes. However, if affording rapid loading such as strong earthquake, heat generated from the phase transformation of SMA cannot dissipate in short time, so the temperature rises and it can be investigated by simplifying it as the adabiatic processes expressed in Eq. (1).

The comparisons between results from models with CuAlBe SMAs are shown in Fig. 10. Three strong ground motion inputs FUKIAI-M, JRT-EW-M and JRT-NS-M are employed and four structural performance indices, i.e., the maximum top displacement, the residual top displacement, the maximum average compressive strain at bases, the maximum stress and strain of SMA dampers are examined. In the figure, F, EW and NS represent the three ground motions, I and A stand for the isothermal process and the adiabatic process, respectively. It is found that seismic performances in adiabatic processes are generally slightly less than those in isothermal processes except for the performance of maximum stress in SMA dampers. It is shown that the maximum top displacement in the JRT-EW-M motion is 1.57δ_y in the isothermal process at 20°C while it is 1.42δ_y in the adiabatic process. It is also shown in the JRT-EW-M motion that the average compressive strain is 1.32ϵ_y in the isothermal process at 20°C while it is 1.24ϵ_y in the adiabatic process at 20°C. In SMA dampers, it is noted that the performances of strain drop and the performances of stress rise in the adiabatic process. Similar trends exist in different environment temperatures. It can be thus concluded that the influence of heat generation induced temperature rise has no large influence on working performance of SMA dampers.

Investigation of seismic dampers with SMA-LYS

The energy dissipation capacity of SMAs might not be very large because SMAs usually show nearly elasticity when reach to the transformation critical stress of σ_AF, and the stress of σ_AF is not small in some types of SMAs. In the section of 4.2, the SMA dampers without energy dissipation component are designed and the needed length and area of SMAs are listed in Table 3. Here in the subsection, new seismic dampers consisted of austenite SMA made recentering component and LYS made dissipation component are presented. Half amount of SMAs listed in Table 3 are subsituted to LYS and the detail of structural parameters is shown in Table 4. The response results with or without LYS component are examined at the room temperature of 20°C under various gound motions as employed above.

The comparisons of results are illustrated in Fig. 11. Comparing SMA dampers and the SMA-LYS dampers, it can be found that most performance indices of the SMA-LYS damper are less than the SMA damper except for the residual displacement. Through the stress-strain relationship of the dampers shown in Fig. 12 under the strong earthquake of JRT-NS-M, it would be the reason that much more energy can be effectively dissipated in the SMA-LYS damper. However, the upgrading effect of seismic performance using the SMA-LYS damper is not so obvious, and further investigations should be carried out on the fraction between SMA and LYS in the damper and the optimized strength ratio α_F, the stiffness ratio α_K using such dampers should be explored.

Conclusions

Temperature effects of superelastic SMAs on seismic performance upgrading of civil engineering structures are discussed, which include the environment temperature and the temperature rise induced by rapid loading rate. Based on axial-type SMA dampers with CuAlBe and NiTi SMAs, dynamic numerical simulations have been implemented to evaluate the seismic behavior of a benchmark steel portal frame. Comparisons of the steel frame with SMA dampers under different temperature conditions and different materials are carried out. Following conclusions can be drawn:

1) The capability of seismic performance upgrading in SMA dampers is affected by environment temperatures. Safety coefficient is needed to consider such situations. How to define it should be further investigated.

2) Through application comparisons with two SMA materials, it is thought that both of two SMAs can afford good capability for seismic performance upgrading for the single storey portal steel frames if it is properly designed through the suggested method. It is suggested the selected SMA material with the lower transformation critical stresses and the slower stress growth rate with temperature.

3) Although high rate loading would change mechanical properties of SMAs, it has little influence on damage control in civil engineering. Therefore, analytical simulation with SMAs can be carried out in the isothermal process instead of the adiabatic process.

4) Combination of SMA and LYS into seismic dampers could effectively dissipate energy and recover residual deformation. Further investigation is valuable to explore the optimized fraction between two materials in one seismic damper.

5) Further researches on different types of structures should be carried out in future works, and the optimization of placement of dampers should be further explored.

References

[1] Dolce M, Cardone D. Mechanical behaviour of shape memory alloys for seismic applications 2. Austenite NiTi wires subjected to tension. International Journal of Mechanical Sciences, 2001, 43(11): 2657-2677

[2] Wayman C M, Duerig T W. Engineering Aspects of Shape Memory Alloys. In: Duerig T W, Melton K N, Stockel D, Wayman C M, eds. London: Butterworth-Heinemann Ltd, 1990, 3-20

[3] Attanasi G, Auricchio F, Fenves G L. Feasibility assessment of an innovative isolation bearing system with shape memory alloys. Journal of Earthquake Engineering, 2009, 13(S1): 18-39

[4] Cardone D, Dolce M. SMA-based tension control block for metallic tendons. International Journal of Mechanical Sciences, 2009, 51(2): 159-165

[5] Zhang Y F, Hu X B, Zhu S Y. Seismic performance of benchmark base-isolated bridges with superelastic Cu-Al-Be restraining damping devices. Structural Control and Health Monitoring, 2009, 16(6): 668-685

[6] JRA. Design Specification of Highway Bridges. Part V: Seismic Design, Japan Road Association, Tokyo, Japan, 2002 (in Japanese)

[7] Usami T, Ge H B. Performance-based seismic design methodology for steel bridge systems. Journal of Earthquake and Tsunami, 2009, 3(3): 175-193

[8] Araya R, Marivil M, Mir C, Moroni O, Sepúlveda A. Temperature and grain size effects on the behavior of CuAlBe SMA wires under cyclic loading. Materials Science and Engineering A, 2008, 496(1-2): 209-213

[9] Motahari S A, Ghassemieh M. Multilinear one-dimensional shape memory material model for use in structural engineering applications. Engineering Structures, 2007, 29(6): 904-913

[10] Luo X Q, Ge H B, Usami T. Dynamic numerical simulation of steel frame-typed piers installed with SMA damping devices based on multi-linear one dimensional constitutive model. Advanced Steel Construction, 2010, 6(2): 722-741

[11] Chen Z Y, Ge H B, Usami T. Study on seismic performance upgrading for steel bridge structures by introducing energy-dissipation members. Journal of Structural Engineering, 2007, 53A: 540-549

[12] ABAQUS. ABAQUS Analysis User’s Manual, Dassault Systèmes, 2006

[13] Luo X Q, Ge H B, Usami T. Parametric study on damage control design of SMA dampers in frame-typed steel piers. Frontiers of Architecture and Civil Engineering in China, 2009, 3(4): 384-394

[14] Usami T. Guidelines for Seismic and Damage Control Design of Steel Bridges. Japanese Society of Steel Construction, Tokyo: Gihodo Syuppan Press, Japan, 2006 (in Japanese)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg