G.J. Parra-Montesinos, H.W. Reinhardt, and A.E. Naaman (Eds.): HPFRCC 6, pp. 381–387. © RILEM 2012
Strain Rate Dependent Tensile Behavior of Ultra-High Performance Fiber Reinforced Concrete
K. Wille 1, S. El-Tawil 2, and A.E. Naaman 2
teacher的音标1
Civil and Environmental Engineering, University of Connecticut, USA 2 Civil and Environmental Engineering, University of Michigan, USA
Abstract. Ultra High Performance Fiber Reinforced Concretes (UHP-FRC) can be designed to resist increasing tensile loading after first matrix cracking, which re-sults from strain hardening tensile characteristics accompanied by multiple crack-ing. Previous investigations carried out under static loading conditions have clear-ly shown that matrix composition, fiber material and geometry as well as fiber volume fraction and fiber orientation influence the strain hardening tensile beha-vior. This paper describes rearch that was conducted to study the direct tensile behavior of UHP-FRC loaded at various speeds. A hydraulic test machine was ud to apply load up to 103 times faster than static loading, i.e. up to a strain rate of 1s 1.0−=ε
. The test tup was designed to permit reliable measurement of di-rect tension test results at the different loading speeds considered, taking into con-sideration a reasonable gage length for multiple crack development while mini-mizing the inertial effects associated with the specimen and attached measurement equipment. The strain rate dependent tensile behavior is analyzed in terms of peak strength, strain at peak strength, hardening modulus and energy absorption capaci-ty prior to softening. The results show the strain rate nsitivity of each of the parameters at fiber volume fractions of 2, 2.5 and 3%.
1 Introduction
Ultra-high performance concretes (UHPC) reprent a class of cement composites characterized by a low water/binder ratio, a high particle packing density, and a compressive strength in excess of 150 MPa (22 ksi). The term UHP-FRC (ultra-high performance fiber reinforced concrete or cement composite) is ud for an UHPC containing fibers. Here straight very high strength steel fibers are ud. The addition of fibers leads to significant improvement in the material ductility under direct tensile loading, which also affects the ductility under compression, shear or torsion. Prior rearch by the authors has shown that the ductility of UHP-FRC can be significantly incread by utilizing a ternary optimization (matrix, fiber, in-terface properties), leading to an energy absorption capacity of
about g =130 kJ/m 3
382 K. Wille, S. El-Tawil, and A.E. Naaman
prior to softening; which exceeds by at least 5 times comparable energy values re-ported by other rearchers [1]. High energy absorption capacity is a result of in-cread post-cracking strength (in excess of 20 MPa) and incread strain capacity at stress-peak (in excess of 0.5%), accompanied by multiple cracking with an av-erage crack spacing as low as 2 mm. The results suggest that such UHP-FRCs have the potential to be particularly uful for structures that could be subjected to extreme events such as blast, impact or ismic loading. Therefore the material’s tensile behavior under higher strain rate loading is of particular interest.
Previous rearch on high performance fiber cement composites (HPFRCC) up to a compressive strength of 84 MPa has clearly shown that the tensile strength [2] as well as the single fiber pull-out resistance [3] is strain rate nsitive. Habel & Gauvreau [4] performed two uniaxial tension tests on UHP-FRC up to a strain rate
of 1s 02.0−=ε
,
which refers to ismic loading or vehicle collision on bridge piers [5], and obtained a 25% increa in tensile strength up to 14 MPa in compar-ison to the tensile strength of 11 MPa under static loading. While limited informa-tion exists about the effect of strain rate on HPFRCC, very little information is available on the rate-dependent behavior of UHP-FRC, which is the motivation for the work reported herein.
母亲劫
2 Specimen Preparation and Testing
The uniaxial tensile behavior of three different UHP-FRCs composites was inves-tigated under four different strain rates. The composites only varied in Their composition is summarized in Table 1, where it can be en that the composites were developed from the ba UHPC by volumetric replacement of some sand by steel fibers. The volume of fiber content varied in f 2.0,2.5,and 3.0%V =. The
UHPC composition in Table 1 is a result of particle packing and strength optimi-zation performed in prior rearch [1, 6]. In order to cover the rate effects asso-ciated with ismic loading, normally considered to be correspond to 1s 1.0001.0−−=ε
中级口译官网[7], four different strain rates of 1s 1.00001.0−−=ε were applied to the specimens using a hydraulic s结束的英文单词
ervo-controlled testing machine (MTS-810). This follows the same procedure reported in a prior study on HPFRCC [2]. Three to six specimens were tested for each ries.
All tests were performed after 28 days of age and no special heat or pressure curing was applied. The workability of the UHP-FRC mixtures was designed to exhibit lf-consolidating properties without the risk of fiber gregation. No vi-bration was applied during or after casting. The workability of the mixes and the casting method preferably aligned the fibers in the direction of loading. The test t-up is shown in (Fig. 1) and simulates a similar t-up described in [8]. Me-chanical anchorage and rotational boundary conditions allowed for quick speci-men installation and alignment. An infrared-bad motion measurement system was ud (Optotrak) with accuracy of up to 0.1 mm, resolution of 0.01mm and a
Strain Rate Dependent Tensile Behavior of UHPFRC 383 maximum marker frequency of up to 4600 Hz. Prior comparison using LVDTs
had proven the accuracy of this system. The nsors are particularly suitable for
high strain rate tests due to their small weight, which introduces negligible inertial effects, and their high frequency. Additionally, the markers could be quickly dep-
loyed, removed and reud.
Table 1. Mixture proportions by weight
UHP-FRC-3%
UHP-FRC-2.5%
UHP-FRC-2%
Type UHPC
七年级下册英语单词
Cement 1.00 1.00 1.00 1.00
Silica Fume 0.25 0.25 0.25 0.25
Glass Powder 0.25 0.25 0.25 0.25
Water 0.19 0.19 0.19 0.19 Superplasticizer1 0.011 0.011 0.011 0.011 Sand A2 0.31 0.29 0.28 0.28
Sand B3 0.72 0.67 0.66 0.65
Fiber4 0.00 0.18 0.22 0.27 Fiber by Vol.% 0 2.0 2.5 3.0
(MPa) 230 248 246 250
f
cube
28
['d
,
]
c
(MPa) 7.4 - 8.5* 15 16.5 18 f
]
succeeding[tension
t
1 solid content;
2 max. grain size 0.2 mm (1/128 in.),centralization
3 max. grain size 0.8 mm (1/32 in.),4
straight steel fiber, length/diameter = 13 mm/0.20 mm, tensile strength ≈ 2600 MPa (377 ksi),
* at first cracking, followed by immediate failure
a) Test b) Specimen geometry and fixture
english teacherFig. 1. Direct tensile test tup ud in this rearch with Optotrak markers on front and
back face of the specimen
384 K. Wille, S. El-Tawil, and A.E. Naaman
3 Test Data Analysis and Results
Fig. 2a shows the tensile stress versus strain curves of the three UHP-FRC-2.5%
specimens tested at a strain rate of 1s 0001.0−=ε
that is considered quasi-static loading. Each curve is then idealized into a best fit polygon made up of 3 g-ments: the first corresponds to the elastic respon, the cond for the strain-hardening behavior and the third for the plateau that occurs just prior to softening (Fig. 2b). The definitions of the tensile parameters are given in Fig. 2b. The idea-lized curves and their parameters are then averaged (Fig. 2c). Fig. 2d compares the averaged idealized curves of UHP-FRC-2.5% at the four different strain rates up
to 1s 1.0−=ε
.
a) Specimens 1-3 experimental data b) Specimen 2 and idealized tensile behavior
c) Idealized tensile behavior of specimens 1-
3 and average curve d) Strain rate dependent idealized tensile be-havior Fig. 2. Analytical procedure for the example of ries UHP-FRC-2.5%
Figs. 3a-f show the values of the various tensile parameters for the idealized aver-age curves at different strain rates for UHP-FRCs with straight steel fibers of 2,
2.5 and 3% fibers by volume. In general it can be obrved that the strain rate ef-fect is not influenced by fiber volume fraction.
Strain Rate Dependent Tensile Behavior of UHPFRC 385
a) Idealized composite cracking stress cc σ b) Elastic modulus c E
c) Post-cracking strength pc σ d) Hardening modulus hc E
idc是什么>veakse) Strain capacity prior softening 2pc ε f) Energy absorption capacity prior softening g Fig. 3. Strain r
ate dependent tensile parameters of UHP-FRC with straight steel fibers of 2, 2.5 and 3% fiber by volume
A strong strain rate dependency is obrved for the stress bad parameters cc σ
and pc σ. The increa in strain rate by 310 up to 1s 1.0−=ε
increas the post-cracking strength by about 20% for all volume fractions. This is in agreement with the preliminary test results reported in [4]. Strain bad parameters like 2pc ε
