7 4. Characterization of ductile tearing resistance Our displacement-based approach focuses on changes in geometry of the whole crack border, instead of considering mainly the near crack-tip displacements, which are given much attention in the current test procedures [9, 10]. Generally, ductile tearing is seen as interplay of seven processes of continuous (virtual) fracture that are represented by the through-life fracture curves. These latter relate to each other on the IFD by imaginary (instantaneous) unloading-reloading cycles. Such cycles are shown as the straight-vertical lines in Fig. 8 passing through the points c and b on the nrelationship. They bounds the Steady State Tearing (SST) stage, when the plastic component s(x)n of the virtual crack opening displacement s(x) is in direct proportion to the extension of the virtual crack tips along the 0x axis (Fig 1). The virtual crack extension is modelled by continuous moving the upper half of a broken-down specimen towards its lower counterpart, as a rigid body. Plane stress tearing is considered from the viewpoint of a “moving crack tip” embedded into a fullydeveloped “moving neck”. We assume that the crack surfaces, in their final shape, contain the entire history of accumulating the plastic deformations within the regions of subsurface damage (Fig. 5b). So, there are good reasons for quantifying the resistance to stable crack extension by the plastic component ψ(х)n of the СТОА-ψ [1-7]. Variations in the value of this angle during the virtual fracture process are determined by the following expression: ψ(х)n = 2d(s(х)n)/dx,. (1) Consequently, the simplified assessment of ductile tearing can be performed using only post-test measurements of the virtual crack opening displacement 2s(x)n. The tensile testing of the MR(T) specimens (Fig. 1c) is the most promising and practical route to assess effects of constraint on ductile tearing in thin sheets of metallic materials. In this case, the global in-plane constraint can be varied merely by changing the distance 2H0 between the rigidly clamped boundaries of a specimen. Experimental results of this and previous studies [1-7] are contradictory to the commonly accepted statement that the constraint effect in plane stress specimens is negligible. A decrease in the specimen aspect ratio H0 / W0 taken together with an increase in the PD width 2W0 elevates Figure 8. The Integrated Fracture Diagram (IFD) derived from test data for three identical MR(T)-1.0-1.0 specimens of the following dimensions: 2W0 = 2H0 = 120mm, 2r0 = 2mm and 2d0 = 0. These tests were conducted without the use of antibuckling guide plates and with forced unloading-reloading cycles.
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