Enhanced Mechanical Properties of Fe–Mn–Si–Cr Shape Memory … · 1Department of Functional Machinery and Mechanics Shinshu University, Ueda 386-8567, Japan 2Department of Mechanical

Materials Transactions, Vol. 43, No. 5 (2002) pp. 974 to 983Special Issue on Smart Materials-Fundamentals and Applicationsc©2002 The Japan Institute of Metals

Enhanced Mechanical Properties of Fe–Mn–Si–Cr ShapeMemory Fiber/Plaster Smart Composite

Yoshimi Watanabe1, Eiichi Miyazaki1, ∗ and Hiroshi Okada2

1Department of Functional Machinery and Mechanics Shinshu University, Ueda 386-8567, Japan2Department of Mechanical Engineering, Kagoshima University, Kagoshima 890-0065, Japan

This paper reports the fabrication method and mechanical properties of a shape memory alloy (SMA) fiber/plaster smart composite, whichcan be used in architectural and civil engineering applications. Fe–Mn–Si–Cr SMA fibers are subjected to pretensile strain at room temperature,and are embedded into plaster matrix. The Fe–Mn–Si–Cr SMA fiber/plaster composites are then heated up to 250◦C (above As) to generate acompressive residual stress in the matrix. Three-point bending test is performed for the mechanical property characterization. Fiber pull-outtest is also conducted to evaluate the bonding strength at interface between SMA fiber and plaster matrix. Finite element analyses are carriedout to have some further insights on the experimental results. It is found that the bending strength of the composites enhances with increasinglevel of pretensile strain. By using the inexpensive Fe–Mn–Si–Cr SMA fibers for the reinforcement of the SMA composite, one can obtainmaterials for practical engineering applications at low cost.

(Received November 20, 2001; Accepted February 8, 2002)

Keywords: smart material, shape memory alloy (SMA) composite, Iron-Manganese-Silicon-Chromium shape memory alloy, fiber, plaster,residual stress, three-point bending test, fracture, fiber pull-out test, finite element analysis

1. Introduction

The residual stress in a composite is mainly caused by themismatch of the thermal expansion coefficient between thematrix and reinforcement, when the composite fabricated athigh temperature is cooled down to room temperature. Theeffect of the residual stress induced by the thermal expansioncoefficient mismatch on the mechanical properties of com-posite has been studied.1, 2) It was shown that the compressiveresidual stress enhances the mechanical properties of the com-posites. If the composites are reinforced by the shape memoryalloy (SMA) fiber that shrinks in the matrix, one can introducean artificial compressive residual stress along the direction ofthe shrinkage. Then the mechanical properties of compositeswill be improved significantly.

Recently, much attention has been paid to the developmentof SMA composites.3–7) For example, Furuya et al.3) haveproposed a design concept of NiTi SMA fiber/Al compos-ite. Mechanical properties of NiTi SMA fiber/CFRP havebeen studied by Jang et al.7) The motivation of this researchis to develop an SMA fiber/plaster composite which will becommercially applicable for architectural and civil engineer-ing materials applications. For this purpose, the NiTi SMA isnot suited, since the NiTi SMA is unacceptably expensive.

Meanwhile, it is known that some Fe–Mn–Si alloys withsuitable composition exhibit a good shape memory effect ofa one-way type with the temperature hysteresis as large as500◦C, governed by the fcc (γ ) ↔ hcp(ε) transformation.8, 9)

Fe–Mn–Si alloys appear to be commercially applicable ow-ing to their inexpensiveness and excellent workability. Withaddition of Cr, it is possible to achieve a good corrosion resis-tance, which enhances commercial significance to this type ofalloy.10) Therefore, by using the Fe–Mn–Si or Fe–Mn–Si–CrSMA for reinforcement of the SMA composite, one can pro-duce practically and economically sounded engineering ma-

∗Graduate Student, Shinshu University.

terials.In this study, Fe–27.2 mass%Mn–5.7 mass%Si–5 mass%Cr

SMA fibers are subjected to pretensile strain at room temper-ature (below Md temperature), and are embedded into plas-ter matrix. Then the Fe–Mn–Si–Cr fiber/plaster compositesare heated to 250◦C (above As) to generate the compressiveresidual stress in the matrix. The bending strength of the com-posites is tested at room temperature. Fiber pull-out test isalso conducted to evaluate the bonding strength at interfacebetween SMA fiber and plaster matrix. Moreover, finite ele-ment analyses are carried out to have some further insights onthe experimental results. In addition, potential applications ofthis composite are discussed.

2. Experimental Procedures

2.1 Fe–Mn–Si–Cr shape memory alloyThe composition (in mass%) of the SMA fiber used in this

investigation was Fe–27.2Mn–5.69Si–5.02Cr–0.047C. Theas-received material, in the form of 1 mm diameter fiber, wassubjected to heat treatment in vacuum at 950◦C for 20 min,followed by air cooling to room temperature in order to ob-tain a single phase austenite microstructure (shape memorytreatment).

In order to assess the shape memory effect of the Fe–Mn–Si–Cr SMA fiber used for the composite, the ratio of shaperecovery versus annealing temperature curves were obtained.Tensile tests were carried out on a screw-driven test machineat a strain rate of 0.03 mm/min. Tensile strains of 1%, 2% and3% were given, respectively, at room temperature. Follow-ing the tensile deformation, each specimen was annealed attemperatures ranging from 100 to 450◦C for 20 min for everyinterval 50◦C. Point markings were introduced by a micro-Vickers hardness tester for determination of length changesdue to tensile deformation and heat treatment.9)

Enhanced Mechanical Properties of Fe–Mn–Si–Cr Shape Memory Fiber/Plaster Smart Composite 975

2.2 Fabrication of SMA fiber/plaster compositeThe fabrication process and the strengthening mechanism

of a plaster matrix composite by use of the shape memoryeffect of the Fe–Mn–Si–Cr alloy are summarized in Fig. 1.(1) Shape memory treatment was given to the Fe–Mn–Si–Cr

SMA fibers to memorize the straight shape (Fig. 1(a)).(2) The SMA fibers were subjected to pretensile strain at

room temperature (below the Md temperature) (Fig.1(b)).

(3) The SMA fibers were embedded into plaster plus watermatrix (Fig. 1(c)). The volume fraction of fiber is 0.03.The dimensions of the specimen are shown in Fig. 2.Since the humidity and the temperature have effects onthe solidification of plaster,12) they were fixed to be 58%and 20◦C, respectively, during the fabrication of com-posite. Specimens were dried at 20◦C for 2 days aftersolidification of the plaster matrix, and were kept in adryer at 40◦C for 2 hours before the heat treatment. (Fab-rication of an SMA fiber/plaster composite)

(4) The SMA fiber/plaster composites were heated to 250◦C(above As) to generate the compressive residual stress inthe matrix along the fiber axis (Fig. 1(d)).

2.3 Three-point bending testA three-point bending test was performed using a screw-

driven test machine at a crosshead speed of 2 mm/min.Figure 2 also shows the three-point bending test setup, wherethe lower span length of the bending test specimen was60 mm. The specimen was loaded until fracture occurred, andbending strength was calculated from the load-stroke curves.The number of bending tests was more than five for each con-dition.

2.4 SMA fiber pull-out testTo evaluate the bonding strength at interface between SMA

fiber and plaster matrix, fiber pull-out test was also conducted.After SMA fiber was subjected to pretensile strain at roomtemperature, one SMA fiber was embedded into the center ofplaster matrix with 20 mm × 20 mm × 80 mm in size. Thistest piece was heated to 250◦C for the shape recovery to oc-cur for the SMA fiber. Figure 3 shows a schematic illustra-tion of SMA fiber pull-out test. The fiber pull-out test wasperformed using a screw-driven test machine at a crossheadspeed of 1 mm/min.

3. Results and Discussion

3.1 Shape memory effect of Fe–Mn–Si–Cr SMA fiberFigure 4 shows the shape recovery strain versus anneal-

ing temperatures for the SMA fiber subjected to 1, 2 and 3%pretensile strains. In all cases, the ratio of shape recoveryis nearly constant above 400◦C. Note that the shape mem-ory effect decreased with increasing pretensile strain, whichagrees with the previous results.8, 11) Since the ratio of shape

Fig. 3 Schematic illustration of SMA fiber pull-out test.

Fig. 2 Specimen configuration and dimensions for three-point bendingtest.

Fig. 1 Design concept of the Fe–Mn–Si–Cr SMA fiber/plaster matrix com-posite.

976 Y. Watanabe, E. Miyazaki and H. Okada

bending strength as a function of the amount of preten-sile strain. The bending strength of the plaster specimenis also shown in this figure. The bending strength of the

3.2 Fracture behavior of plaster matrixA typical macrograph of plaster without the SMA fiber

(plaster specimen) after three-point bending test is shown inFig. 5. And a typical bending load as a function of compres-sion stroke curve is shown in Fig. 6. As can be seen, theplaster without SMA fiber shows brittle fracture. A signifi-cant fracture toughness enhancement may be achieved by thefiber reinforcement.

3.3 Fracture behavior of SMA fiber/plaster compositeIn Fig. 7, an example of the fractured SMA fiber/plaster

composite after three-point bending test is shown. Figures8(a), (b), (c) and (d) show examples of bending load ver-sus compression stroke curves for the composites with 0%,1%, 2% and 3% pretensile-strained SMA fiber, respectively.These composites are hereafter abbreviated as 0%-, 1%-,2%- and 3%-composites, respectively. The bending load in-creases with increasing compression stroke up to 1.5–2.0 mmin the given examples, and then decreases slowly. Sincethe composite with 0% pretensile-strained SMA fiber (0%-composite) shows ductile fracture compared with plasterspecimen, we can conclude that the SMA fibers play an im-portant role on improvement of the fracture toughness of plas-ter.

Using the load-stroke curves obtained, Fig. 9 plots the

recovery at 250◦C for 1, 2 and 3% pretensile-strained spec-imens are 0.79, 0.55 and 0.41, respectively, shrinkages ofSMA fibers with 80 mm length are 0.63 mm for 1% preten-sile strain, 0.88 mm for 2% pretensile strain and 0.98 mm for3% pretensile strain.

Fig. 6 Typical bending load versus compressive stroke curve for plasterspecimen.

Fig. 7 Macrograph of 2%-composite after three-point bending test.

Fig. 8 Examples of bending load versus compression stroke curves for thecomposites with 0% (a), 1% (b), 2% (c) and 3% pretensile-strained SMAfiber (d), respectively.

Fig. 5 Macrograph of plaster specimen after three-point bending test.

Fig. 4 Fraction of recovery strain plotted against annealing temperature.


displacement curve to be slightly nonlinear. To carry out theanalysis, a commercial finite element software ABAQUS13)

was used. Linear axisymmetric solid element with four inte-gration points (CAX413)) was adopted. The elastic modulusof plaster was determined so that the slope of applied load-

some useful insights on the failure mechanisms of SMAfiber/plaster matrix specimen were obtained. In this section,we will discuss, 1) general observations, and 2) where andwhen fracture at the interface region initiates based on stressdistributions.

The boundary conditions and model descriptions are illus-trated in Fig. 11. The axisymmetric finite element model isshown in Fig. 12. When SMA fiber undergoes strain recov-ery due to the shape memory effect, the stress distributionand deformation of the specimen only due to the strain re-covery without any external loadings are computed, and thenSMA fiber is pulled in upward direction. When the analy-sis for strain recovery of SMA fiber is carried out, no dis-placement constraints on the specimen is specified except forones that suppress rigid body motion. Then, displacement atthe top end of SMA fiber incrementally increases. Contactbetween the jig and the plaster is accounted for by using acontact algorithm. It is noted that since the contact condi-tion is specified between the jig and the specimen, geometricnonlinear analyses are carried out though the materials arelinear. As specimen is loaded, the area of contacting sur-face may change, therefore it is expected for applied load-

Fig. 9 Bending strengths of the plaster specimen and composite specimens.

Fig. 10 Experimentally measured applied load-displacement curve duringSMA fiber pull-out test.

Fig. 11 Analysis model for SMA fiber pull-out test.

These phenomena will be discussed with the results of finiteelement analyses.

3.5 Finite element analysis for fiber pull-out experimenton SMA fiber/plaster composite

The finite element analyses were carried out to havesome further insights on the experimental results. Thoughonly elastic analyses were carried out in this investigation,

3.4 Experimental results of SMA fiber pull-out testFigure 10 shows applied load-displacement curves mea-

sured during SMA fiber pull-out test. The maximum values offiber pull-out load increases with increases in the amount ofpretensile strain. At the same time, fracture displacement alsoincreases with increases in the amount of pretensile strain.

0%-composites is less than 3 MPa, although that of 2%-composites is about 4.5 MPa. In this way, the bendingstrength of the composites increases with increasing the levelof pretensile strain. Note that the bending strength of the 0%-composites is equal to that of the plaster specimen. There-fore, the improvement of the bending strength does not occurby SMA fiber reinforcements themselves but by compressiveresidual stress introduced by shape memory effect of SMAfibers.

It is noteworthy that the bending strength of the 3%-composites is smaller than that of 2%-composites. This de-crease may be attributed to the imperfect bonding at inter-face between SMA fiber and plaster matrix. If the 3%-composite had sufficient bonding strength, the 3%-compositeshould show larger bending strength compared with the 2%-composite. In fact, the scatter of the data for 3%-compositesis found to be considerably greater than those for other com-posites, and greater scatter means presence of composite withlarge bending strength. Although the data is not presentedhere, it was also found that the bending strength increasedwith increasing the volume fraction of SMA fibers. As al-ready mentioned before, SMA fibers themselves do not en-hance the bending strength. Therefore, this phenomenon mayalso be attributed to the overall bonding strength at interfacebetween SMA fiber and plaster matrix.


displacement curve obtained by finite element analysis for thecase without strain recovery matches the initial elastic slopeof experimental applied load-displacement curve. Mechani-cal properties of materials are given in Table 1.

In Figs. 13 and 14, typical shear stress distributions in thecross section of the specimen are presented. In Fig. 13, shearstress distribution without the strain recovery is presented. Alarge magnitude of shear stress is generated in the interface

Fig. 12 Fig. 13 Fig. 14

Fig. 12 Finite element model for SMA fiber pull out test.

Fig. 13 Shear stress distribution and deformation without strain recovery of SMA at displacement 0.5 mm (unit of stress: MPa).

Fig. 14 Shear stress distribution and deformation with strain recovery (1.2%) (a) before loaded and (b) at displacement 0.5 mm (unit ofstress: MPa).

Table 1 Mechanical properties of SMA fiber and Plaster.

Young’s modulus Poisson’s ratio

SMA fiber 126 GPa 0.3

Plaster 34 MPa 0.1


Fig. 18. Fibers are placed in plaster matrix in the y directionand their strain recoveries due to the shape memory effectare modeled by specifying initial strains. They are ε I

yy andε I

xx = ε Izz = −0.5ε I

yy in x3 and the other directions, respec-tively. ε I

33 was set to be 0, −0.8% and −1.2% (for 0, 0.8%and 1.2% of strain recovery, respectively). The values −0.8%and −1.2% of initial strain ε I

yy roughly correspond to the casesof 1% pretensile strain with 79% strain recovery ratio (1%-composite) and 3% pretensile strain with 41% strain recoveryratio (3%-composite), respectively.

recovery ratio, the magnitude of shear stress at the bottom ofthe specimen is about 1.6 MPa before it is loaded. This mag-nitude of shear stress is similar to or just below the fracturestress of 1.7 MPa. The magnitude of shear stress at the topportion decreases rapidly as the specimen is loaded, whereasthat at the bottom gradually increases. This implies that thefracture of specimen would occur from the bottom also andthen the stress at the top increases and reaches the fracturestress. Thus, the fracture is considered to progress from boththe bottom and top of the specimen. Therefore the regionof progressive material damage is much larger than previouscases. This phenomenon can be explained in another way thatthe bonding between the SMA fibers and plaster matrix be-comes imperfect because the large magnitude of stress wouldinduce a damage at the interface.

3.6 Finite element analysis for three-point bending ex-periment on SMA fiber/plaster composite

Finite element analyses on the three-point bending exper-iments were also conducted using a fully three dimensionalmodel. Linear eight noded brick element with eight integra-tion points was adopted. There are a total of 16800 elementsand 18291 nodes. Analyses were carried out by using an in-house finite element program (see, for example, Hughes14)

for finite element method). Boundary conditions, which arespecified to carry out the analyses on the three-point bend-ing specimen and the plane of visualization, are shown inFig. 17. Only a quarter of the specimen was modeled forthe finite element analyses because of the symmetry. Me-chanical properties of SMA fiber and plaster matrix, that aredetermined in the fiber pull out analysis, are used and are al-ready given in Table 1. In this analysis, small strain linearelasticity is assumed. The finite element model is shown in

creases but the slopes of the curves are much less than thoseat the top.

From the experiment (Fig. 10), nonlinear deformation inthe case without the strain recovery of SMA fiber seems to be-come significant when the applied load reaches about 150 N.Corresponding applied displacement, which is obtained fromthe finite element analysis, is about 0.32 mm. The shear stressin the interface region between SMA fiber and plaster is about1.7 MPa (Fig. 15). This shear stress is considered to inducethe damage of plaster at the interface region or fracture at theinterface between plaster and SMA fiber.

When the specimen is tested after SMA recovered a strainfor about 0.8%, corresponding experimental data is availablein Fig. 10 that is the case of 1% pretensile strain and 79%recovery ratio. The magnitude of shear residual stress at theinterface between fiber and plaster at the top and bottom of thespecimen is about 1.1 MPa (Figs. 15 and 16). This magnitudeof shear stress is considered to be below the fracture stress,which was seen in the analysis without shape memory effect.When the specimen is loaded, the shear stress at the top ofspecimen rapidly increases and reaches to the fracture stress,and the strength of the specimen is enhanced for about 50 Nor little less. In the experiment, an enhancement of similarmagnitude is seen in Fig. 10. The fracture of specimen isconsidered to initiate from its top region.

When the strain recovery is about 1.2%, which roughly cor-responds to the case of 3% pretensile strain and 41% strain

region at the top end of plaster. In Fig. 14, stress distribu-tion after the strain recovery, without any loading and whenSMA fiber is pulled, is presented for 1.2% strain recovery.Displacement at the top of SMA fiber is 0.5 mm. The signs ofthe shear stresses at the top and bottom are opposite to eachother.

Figure 15 shows the shear stress at the interface region be-tween SMA fiber and plaster at the top of specimen, whichare plotted against the applied displacement. Figure 16 showsthose at the bottom of specimen. Shear stress at the top,which is induced by the strain recovery of SMA fiber, is op-posite to that induced by applied displacement. Therefore, inFig. 15, as applied displacement increases the sign of shearstress changes. In other words, the magnitude of shear stressdecreases initially, becomes zero and keep increasing as theapplied displacement increases. Shear stress at the bottomof specimen keeps increasing as the applied displacement in-

Fig. 15 Shear stress at the top interface region between SMA fiber andplaster.

Fig. 16 Shear stress at the bottom interface region between SMA fiber andplaster.


The analyses were carried in two steps. First, a problemwith specified initial strains is solved without any externalloadings. Second, a beam bending analysis is carried outwithout any initial strains. The results of these two prob-lems are superposed and the solutions for three-point beambending problems with specified initial strains are obtained.Applied load is given by prescribed nodal displacements in−z direction and are adjusted so that the total force applied tothe specimen equals 300 N. It is noted that the superpositionof solutions is possible because the problems are linear andelastic.

First, we look into the effects of strain recovery of SMAfibers. A typical deformation of the plane of visualizationdue to the strain recovery of 0.8% in SMA fibers is depictedin Fig. 19 (1%-composite). Intensive deformations are seenat the intersections of beam end free surface and SMA fibers.

A typical distribution of shear stress τyz in plaster matrix inthe plane of visualization is depicted in Fig. 20 for the case ofstrain recovery of 1.2% (3%-composite). This case was cho-sen so that the shear stress has a significant magnitude. Rel-atively large magnitude of shear stress at the intersection ofSMA fibers and beam free surface is seen. The results, whichare depicted in Figs. 19 and 20, indicate that the compres-sive initial strain of SMA fibers causes stress concentrationsat the intersections of SMA fiber and beam free surface. Thesame phenomenon was also seen in the analyses on the fiberpull out specimen, as already described. The magnitudes ofstress concentration are rather weak for SMA reinforced beamthan for the fiber pull out specimen. This is because SMAfibers are much more populated in the composite beam thanin the fiber pull out specimen. The mechanisms causing thestress concentrations are considered to be the same for boththe cases.

Next, some discussions on the results of beam bendinganalysis are presented. We first discuss on the bending defor-mation of beam without any strain recovery of SMA fibers.In this case, the beam behaves as a fiber reinforced compositematerial (0%-composite). In Figs. 21 and 22, the distributionsof normal stress σyy and shear stress τyz in the plane of visu-alization of beam along with its deformation are presented. Arelatively large magnitude of tensile stress is seen at the bot-tom center of the beam in Fig. 21. Also, a large magnitude ofshear stress τyz is seen around SMA fibers above the support(Fig. 22).

When the strain recovery of SMA fibers is included, thedistributions of stresses change. The distributions of normalstress σyy and shear stress τyz are depicted in Figs. 23 and 24,when 0.8% compressive initial strain is given to SMA fibers(1%-composite). As seen in Fig. 23, normal stress at the bot-tom center of the beam is in compression due to the presenceof initial strains in SMA fibers. Comparing Figs. 22 and 24,the region of relatively large magnitude of shear stress τyz isseen to enlarge towards the end surface of the beam whenthe strain recovery is assumed. Stress distributions, whenthe magnitude of the strain recovery is further increased tobe 1.2%, are shown in Figs. 25 and 26 (3%-composite). Thevalue of normal stress σyy is mostly negative throughout thebeam. Even at the bottom center of the beam, the stress isnegative and its value is relatively large. The region of strongmagnitude of shear stress τyz further enlarges and reaches tothe end surface of the beam.

Based on the results of the finite element analyses, wecan discuss on the failure mechanisms of three-point bend-ing specimens. Normal stress σyy at the bottom center of thebeam is positive (in extension) when the strain recovery ofSMA fibers is not assumed, and the normal stress turns tonegative (compression) as the magnitude of the strain recov-ery increases. This implies that without the strain recovery,the failure of the specimen may initiate from its bottom cen-ter due to the tensile stress. When the magnitude of the strainrecovery increases, the compressive normal stress at the bot-tom center of the specimen prevents failure initiation. On theother hand, as seen in the analyses on the fiber pull out exper-iment, stress concentration occurs at the intersection of SMAfibers and beam end free surface when the strain recovery isassumed. Relatively large magnitude of shear stress τyz is seen

Fig. 17 Boundary conditions for the analysis of three-point bending exper-iment using the finite element method and the plane of visualization.

Fig. 18 Finite element mesh for the analysis of three-point bending exper-iment.

Fig. 19 Deformation of the beam due to SMA strain recovery of 0.8%(1%-composite). The deformation is magnified by 10 times.


Fig. 21 Distribution of normal stress σyy when the specimen is bent without any SMA strain recovery (0%-composite).

Fig. 20 Distribution of shear stress τyz induced by SMA strain recovery of 1.2% (3%-composite). The deformation is magnified by 10times.

Fig. 22 Distribution of shear stress τyz when the specimen is bent without any SMA strain recovery (0%-composite).


Fig. 23 Distribution of normal stress σyy when the specimen is bent with SMA strain recovery of 0.8% (1%-composite).

Fig. 24 Distribution of shear stress τyz when the specimen is bent with SMA strain recovery of 0.8% (1%-composite).

Fig. 25 Distribution of normal stress σyy when the specimen is bent with SMA strain recovery of 1.2% (3%-composite).


strain recovery of SMA fibers, is clearly seen in the finite ele-ment analyses for three-point bending specimens. The resid-ual stress is so large that in some cases stress remains to be incompression even when the specimens are subject to the ap-plied load. This may have caused the change of failure modeof three-point bending specimen.

(6) Since the price of Fe–Mn–Si–Cr SMA fibers is rela-tively low, one can obtain actual and economical SMA com-posites for engineering applications by using Fe–Mn–Si–CrSMA fibers.

Acknowledgements

The authors would like to acknowledge the support of theGrant-in-Aid for COE Research (10CE2003) by the Ministryof Education, Science, Sports and Culture of Japan.

REFERENCES

1) K. Wakashima, Y. Suzuki and S. Umekawa: J. Comp. Mater., 13 (1979)288–302.

2) R. J. Arsenault and M. Taya: Acta Metal. 35 (1987, 651–659.3) Y. Furuya, A. Sasaki and M. Taya: Mater. Trans., JIM 34 (1993) 224–

227.4) Y. Yamada, M. Taya and R. Watanabe: Mater. Trans., JIM 34 (1993)

254–260.5) Y. Furuya: J. Intell. Mater. Sys. Struc. 7 (1996) 321–330.6) J. B. Berman and S. R. White: Smart Mater. Struct. 5 (1996) 731–743.7) B.-K. Jang, N. Toyama, J.-H. Koo and T. Kishi: Inter. J. Mater. Prod.

Tech. 16 (2001) 117–124.8) A. Sato, E. Chishima, K. Soma and T. Mori: Acta Metal. 30 (1982)

1177–1183.9) Y. Watanabe, Y. Mori and A. Sato: J. Mater. Sci. 28 (1993) 1509–1514.

10) B. H. Jiang, L. Sun, R. Li and T. Y. Hsu: Scr. Metall. Mater. 33 (1995)63–68.

11) M. M. Reyhani and P. G. McCormick: Mater. Sci. Eng. A160 (1993)57–61.

12) The Society of Gypsum and Lime, Japan (Eds.), Handbook of gypsumand Lime. Tokyo: Gihodo Shuppan Co., Ltd., 1972 (in Japanese).

13) Hibitt, Karlsson & Sorensen, Inc., ABAQUS/Standard Users ManualV. 5.6, Pawtucket, RI, USA, 1996.

14) T. R. J. Hughes: The Finite Element Method, General PublishingCompany, LTD., Toronto, Canada, 1987.

Fig. 26 Distribution of shear stress τyz when the specimen is bent with SMA strain recovery of 1.2% (3%-composite).

at the interface between SMA fiber and plaster matrix abovethe support, and would interact with the stress concentrationat the beam end free surface. This means that the strain recov-ery would intensifies the magnitude of stress concentrationand enlarges its region. Thus, as the strain recovery increases,the location of failure initiation would shift from the bottomcenter to the location of large magnitude of shear stress τyz

(above the support). The mode of failure initiation would alsoshift from matrix fracture due to tensile stress to shear frac-ture at the interface between SMA fiber and the plaster ma-trix. The shear stress at the interface intensifies as the strainrecovery increases and may dominate the initiation of failure.This phenomenon can be explained in another way that theinduced residual stress would make the bonding between theSMA fibers and plaster matrix imperfect. There should be anoptimum amount of strain recovery of SMA fibers making thecomposite the strongest.

4. Summary

(1) The fracture toughness of plaster could be improvedby fiber reinforcements.

(2) It is also found that the bending strength of the com-posite increases with increasing level of pretensile strain inthe SMA fiber.

(3) The fact that the scatter of the data for 3%-compositesis considerably greater than those for other composites im-plies imperfect bonding at interface between SMA fiber andplaster matrix for 3%-composites.

(4) When the strain recovery of SMA fibers is assumed, aconsiderable magnitude of stress concentration in plaster ma-trix around the fibers at the vicinity of free surface is foundin the finite element analyses. The stress concentration in-tensifies as the amount of strain recovery increases. Thus,some damage which makes the bonding between the SMAfibers and plaster matrix imperfect. This observation supportthe experimental result that the data scatter for 3%-compositewas greater than that for other specimens.

(5) Compressive residual stress, which is induced by the

Documents

Enhanced Mechanical Properties of Fe–Mn–Si–Cr Shape Memory … · 1Department of Functional Machinery and Mechanics Shinshu University, Ueda 386-8567, Japan 2Department of Mechanical