10−2 10−1 100 101 102 103 k t1/κ 10−5 10−4 10−3 10−2 10−1 100 101 102 P(k,t) t(−1−2ζ)/κ −2.2 Figure 4: Family-Vicsek scaling: The dependence of the scaling function P(k;t)t (1+2 )= with kt 1= . This data collapse gives an estimate of the dynamic exponent =1:2. In Fig. 4, the scaling function P(f;t)t (1+2 )= is plotted as function of kt 1= fordi erenttimesfrom 0:03s to 7:11s. This data collapse provides an estimate of the dynamic exponent = 1:2 and the roughness exponent = 0:6[1].Weemphasizethattheexponentmaybedi erentfromthedynamic exponentobtainedfromaninitially atfront.Howeverthesubtractiontechniquepresentedhereisthe only one experimentally accessible. The latter value of the roughness exponent has been extensively checked for fronts at rest over a larger range of scales (5 mto 50mm) [18]. The roughness exponent has also been measured after loading, when the fracture front had come to a complete rest. During each loading stop, the microscope was translated along the front and neighboring pictures were taken. By assembling up to 20 pictures we obtained front up to 2 14 data points [18]. We found a self-aÆne crack front over more than three decades using several techniques[18]. The result of thepowerspectrumoftheself-aÆnepro leaveragedoverninefrontsisshowninFig.5.The ttedline corresponds to a roughness exponent of 0.64. The roughness exponents obtained in our experiment is not consistent with most present theoretical models or simulations [8, 21, 11, 22]. However the theoretical model proposed by Ramanathan and Fisher [12] in which they solve the elastic problem of a planar tensile crack in a heterogeneous medium with a full elastodynamic description is consistent with our experimental work. In the ideal case where the toughness is not dependent of the velocity, they predict a roughness exponent of =0:5 consistent with our experiments. This model contains elastic waves, and in particular crack front waves which will create stress overshoot along the fracture front. The results are also consistent with a recent quasi static simulation by Hansen et. al [16] (see this proceeding) who found =0:6 and =0:9. Conclusion Thefastdynamicsofthelocalscaleisverydi erentfromthedynamicsonlargescalecharacterizedby 4
RkJQdWJsaXNoZXIy MjM0NDE=