3 Experimental Observations on the Fracture of Metals 29 hd = dσ dε (3.20) If Eq. (3.20) is positive, it indicates an increase of the load carrying capability of the specimen. The hardening process may be the result of many different variables, but the net effect is that a positive σ for an increment of a strain ε indicates that the material can take an increasing load. The condition for maximum load that the specimen shown in Fig. 3.7 corresponds in Fig. 3.8 to dσ dε = 0 (3.21) Equation (3.21) is an indication that the specimen has reached the maximum load and the subsequent negative values of the slope shown in Fig. 3.8, (e) indicates a softening. The softening can be the result of material changes or geometrical changes or a result of both effects. Considering that the carrying load capability is given by P=σA, it follows: dσ dε = 1 A dP dε (3.22) In the case of tensile specimens, structural instability manifests through a process denoted in the literature with the generic name of necking, a sizable change of the cross section of the specimen that follows the yielding of the material, a reduction of the cross-sectional area of the specimen. The actual shape of σ =f (ε) depends on many different variables. In the case of very ductile specimens, maximum load is followed by an immediate softening of the material, a negative slope. The necking process depends on the geometry of the specimen, loading process, and molecular structure of the metal among the main variables. Since our objective is the interpretation of the patterns of iso-derivative fringes, let us analyze patterns that can provide further clues on this process. Changes of geometry caused by plasticity are directly connected to dislocation dynamics and hence on molecular structure of considered metals. That is, in the last instance, this process involves the active systems of slip lines that can produce geometry changes compatible with a given molecular structure adapting to the applied solicitation and generating the strain hardening required to balance the applied load until this process is no longer viable. In order to link images captured by a high-speed camera to mechanisms that lead to the onset of fracture utilizing available experimental observations, it is interesting to start with an interpretation of a sequence of recorded images. This is done in Fig. 3.11 with a scheme that graphically relates events at the molecular level and the recorded behavior of a tensile specimen. The patterns shown in Fig. 3.11 [2] correspond to a tensile specimen made of an aluminum alloy A5052H112. The specimen gage length is Lo = 150 mm, width is wo = 25 mm, thickness is to = 2 mm, ratio width to thickness is rwt =wo/to =12.5, and pulling speed of the machine is vpm =5.83μm/s. Figure 3.11 represents actual observations of the tensile specimen together with a schematic representation of the process leading to the fracture of the specimen after it has yielded. The tensile specimen is fixed at one end and the testing machine displaces the other end at the mentioned uniform crossbeam speed. At the beginning of the test, the pulled end generates elastic waves that are reflected at the fixed end, and the stresses of the specimen is cyclically increased. In the plot motion picture frames vs. applied load of Fig. 3.11, the loading process corresponds to points in the interval labelled (a)–(b), elastic range. At point (b), the onset of plasticity takes place, and a wide band appears at the loading end and propagates towards the fixed end; this band is called in the literature Lüders band. The front end of the band makes angles typically from 32◦ to±7◦ (see Fig. 3.10). The band represents the localized plastic deformation described at the beginning of the section. The band propagates with a speed that is related to the speed of motion of the loading machine. In Fig. 3.11, it is assumed that due to symmetry conditions, if the specimen is homogeneous, propagation of the band decelerates to a stop at the center of the specimen where remains stationary and the process of fracture unfolds. The maximum load has been reached, point (d). In the neighborhood of (d), crack propagation begins. If iso-derivative fringes are recorded (Fig. 3.11), the process of fracture causes an unloading of the specimen, and the iso-derivative fringes re-appear in the specimen. The last frame reproduced in Fig.3.11 shows the broken specimen beyond point (e), and the fracture pattern makes an angle of 24◦ with the horizontal direction. Figure 3.11 contains a symbolic representation of dislocations motion in the metal of the specimen. A discontinuity appears at the external edge of the specimen. The edge dislocation represent the presence of defects in the structure. At (a), when the elastic loading starts dislocations although present in the specimen are not activated. At (b), the dislocations begin their motion under the applied shear forces. Since the specimen is polycrystalline, these events take place in grains whose orientation is favorable to the motions of dislocations (frames (b)–(c)). At a given point in the specimen loading, enough dislocations have joined together to reach the free surface of the specimen and merge with the roughness of the surface. This
RkJQdWJsaXNoZXIy MTMzNzEzMQ==