COMPRESSION STRENGTH OF CONTINOUS STEEL FIBER REINFORCED POLYMERS - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS COMPRESSION STRENGTH OF CONTINOUS STEEL FIBER REINFORCED POLYMERS L.P. Mikkelsen*, J.I. Bech, F.N. Jespersen Material Research Division, Risø DTU, Technical University of Denmark, Roskilde, Denmark * Corresponding author(lapm@risoe.dtu.dk) Keywords : Kink-bands, Finite elements, Steel fibers, Composites, Non-linear material laws X 2 1 General Introduction The compression behavior of unidirectional steel fiber composites has been studied as a part of a b larger study exploring possible applications of steel H � fiber reinforced polymers. In contradiction to glass X 1 � and carbon fibers, the mechanical properties of steel fibers are rather ductile and after the yielding point highly non-linear. An important compression failure L mode in unidirectional composites is kink-band Fig.1. Initial horizontal fiber misalignments. formation. For conventional unidirectional fiber composite the fiber misalignment and plastic The finite element model has been used to predict deformation of the matrix material plays the the kink-band formation in a block of material under important roles in the kink-band formation [1,2]. compression. In order to facilitate the kink-band Taken into account the weak elastic non-linearity of failure mode, a small imperfection has been carbon fibers, only a negligible influence on the introduced in the initial aligned fibers as a small kink-band formation has been identified [3]. On the fiber waviness as shown in Fig. 1. The waviness has other hand, general structural buckling is known to  , along a band a maximal miss-alignment angle, m be influenced significantly on material non- width in the center of the material block. The band linearity’s where the buckling load depends on the has the width b and is inclined with an angle,  , instantaneous stiffness of the material. Steel fibers with respect the vertical direction of the block of optimized with respect to the tensile strength may do material [8]. to the Bauschinger effect show a low yield stress in Both the steel fibers and the polymer matrix material compression, see e.g. [4]. This may influence the are modeled using a standard isotropic power law compression failure of the composite significantly hardening elastic-plastic material law following a J 2 - [5]. flow theory. From this, we have that both the fiber and the matrix material in the composites are given 2 Numerical model by individual Young’s modulus, E , Poisson’s ratio, ν , initial yield stress,  , and a hardening exponent, Based on the individual non-linear elastic-plastic y behavior of the fiber and matrix material, the n . Together with the fiber volume fraction of the compression failure is predicted using a plane strain composite, c f , this sums up to 9 material parameters 2-D smeared-out incremental composite material in total for the composite. model formulated for finite strains and rotations by The two incremental given material laws are Christoffersen and Jensen [6-7] and implemented in combined into a smeared-out incremental composite the commercial finite element code Abaqus by law by using the Voigt and Reuss classical model, Sørensen, Mikkelsen and Jensen [8] as a user respectively, working along and transverse to the defined material using the UMat user interface. instantaneous fiber-directions in the composite [6].

3 Material behaviour followed by a non-linear loading curve, which after yield in the matrix material will follow a strongly Based on non-linear steel fiber tensile curves, the non-linear loading shortening path including non-linear composite tensile curve and the non- extensive shearing of the matrix material, load-drop linear composite compression curve, the and snap-back behavior giving a very imperfection compressive non-linearity of the steel fiber has been sensitive behavior on the material level. If the plastic extracted. In principle it should also be possible to yielding of the matrix material is suppressed, only a extract the non-linear behavior of the matrix material monotonic increasing load are predicted. A from the tensile and compression test before failure, observation also found using other material but do to the low matrix stiffness compared with the parameters [9]. In the case of larger initial fiber fiber stiffness, the polyester matrix properties has misalignments, only matrix yielding is observed. been taken from the literature. Assuming a power- law hardening behavior of the following form 0.25 φ = 1 φ = 2   φ = 5    0.2 ,  Fiber yield y E Matrix yield      = n (1)     0.15 1 1 P/(AE m )    y       1 , >       y E n n      y 0.1 the set of representative material parameters for 0.05 compression used in the study is shown in Table 1. For all cases analyzed, the fiber volume fraction is c  0 taken to be . Do to the fact that the steel 0.4 f 0 0.005 0.01 0.015 0.02 fiber material has been optimized in tension with a ∆ L/L Fig.2. Compressive elastic-plastic material response rather high yield stress and tensile strength on of one linear element. approximately 2GPa and 3GPa respectively with a n  hardening exponent on , the corresponding 10 compression yield strength is found to be significant 4 Kink-band predictions lower but with a significant steeper hardening curve In order to include the possibility of strain localization in the finite element model, a   E n y rectangular block of material with a height over Fiber 200GPa 0.3 700MPa 2 L  H length ratio on / 3/10 under axial compression Matrix 3GPa 0.4 35MPa 5  has been simulated using 30 100 4-noded linear Table 1. Elastic-plastic compressive power-law elements. The unidirectional fiber orientation hardening material parameters for the constituents includes a small fiber misalignment with a smooth variation as shown earlier in Fig. 1. In the specific Fig. 2 show the material response of a block of case, the imperfections parameters has been chosen material when compressed in the horizontal  ,  and     b L  to resulting in a fiber 5 5 / 2 m direction. The initial fiber mis-orientation with misalignment variation as shown in Fig. 3 where the respect to the horizontal direction is in the range  .       contours shows the angle levels  . The simulations are performed using one 1 ,2 ,3 ,4 and 5    [1 ;5 ] Earlier simulations [8], shows only a weak influence 4-noded element why a homogenous deformation of the  angle and the b value on the kink band state is obtained. In Fig. 2, it can be seen that for formation. On the other hand there is a strong small initial fiber mis-orientations, the yielding of  influence of the maximum misalignment angle the fibers will occurs before matrix material which m  f f   m m E E on the kink-band formation and the load carrying are also indicated by the fact that / / y y capacity. in the specific case. The fiber yielding will be