3 Experimental Observations on the Fracture of Metals 33 Fig. 3.16 Plot of the ratio w/wo corresponding to the top view of the shape of the specimen after fracture Table 3.1 Data corresponding to fracture process t s Liso mm ε E 1 ×10−4 34.06 3.70 8.00 20.86 1.75 11 15.68 0.75 9.4 3.9 Fracture Process In Sect. 3.8, the propagation of the structural instability from the point of view of geometrical changes is analyzed. In what follows, the transition from propagation to fracture will be considered. First, it is necessary to look at some notation clarification. The plots of Fig. 3.15 correspond to the center line of the specimen of Fig. 3.14, and the peak of the isoderivatives are located very close to the axis of maximum contraction of the specimen (Fig. 3.13b). Since this center line is an axis of symmetry of the specimen, it coincides with the principal directions of the stresses and strains in this section. That is, the center line of the family V(x,P) coincides with the y-coordinate. Hence, we can write εv ≈ε E 1 (3.23) Equation (3.23) indicates that the value of the iso-derivative in the finite differences sense is equal to the Eulerian principal direction along the axis of symmetry of the specimen. Equation (3.23) provides the principal iso-derivative along the centerline of the specimen and extends to most of the depth of the specimen. However, at the edges of the specimen, Eq. (3.23) is no longer valid and the plotted values correspond to derivatives including contribution of the rigid body rotations [20]. The data of Fig. 3.14 corresponding to the fracture process are shown in Table 3.1. The first column gives the recording times t, the second column gives the length of the segments Liso where the iso-derivatives are different from zero and the third column gives the peak values of the iso-derivatives. At t =34.06, the maximum load has been reached. The region where the rate of change of the iso-derivatives is different from zero is given in the second column. In the following time intervals, the segments where the iso-derivatives are different from zero keep narrowing. This fact indicates that the local deformation increases at smaller segments in size until the fracture takes place. It is interesting to see that the crack in this specimen is perpendicular to the axis of the specimen. That is in the language of Fracture Mechanics and in the approximation of the plane stress condition, the crack corresponds to a mode-1 fracture, although in reality the fracture surface is a 3D surface. Mode-1 fracture indicates that the axial force remains at the centroid of the specimen. In the experimental observation of wide bands, in most of the cases the wide bands are inclined with respect to the center line. To analyze this case of wide band propagation, the specimen called specimen 1 of Fig. 3.17 [10] will be examined. In
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