11 Direct and Simultaneous Extraction of Mixed-Mode Traction-Separation Relations 81 11.3 Analysis and Results From [2], when the balanced condition is met, the J-integral for mode I and II can be expressed in terms of the far-field measurements explicitly as JI D b D P1 D1 P2 D2 . 1 2/ ; (11.1) JII Db A 4 h1 D1 P.h2 2 Ch1 1/ ; (11.2) where b AD 1 A1 C 1 A2 C h2 1 4D1 C h2 2 4D2 1 , Ai D Eihi 1 vi 2 . The local CTOD can also be computed using far-field measurements through following equations, ı n D. 1 2/ C a3 6 P1 D1 P2 D2 a. 1 2/ ; (11.3) ı t D 1 2 .h1 1 Ch2 2/ h1 4D1 Pa2; (11.4) where ı n ; ı t are the normal and shear CTODs, respectively. Then the traction-separation relation can be obtained by taking derivatives of J-integral with respect to local CTODs. ( D @JI @ı n , D @JII @ı t ). It should be noted here that for the ENF specimens, the force distributed to each beam is challenging to measure due to spatial limitations. Therefore, the NCOD were measured using IR-COI to provide force measurements on top adherend (P1) using relationship derived from Eq. (11.3) since the total force is measured (PDP1 CP2), P1 D b D P D2 C 6 a3 ı n C. 1 2/a : (11.5) The extracted TSR for mode-mix angle of D26.97ı are shown in Fig. 11.3. In the normal TSR, an initially stiffening response was observed. In the past, the response prior to the maximum traction has been universally represented by linearly elastic behavior. Time constraints have not allowed further investigation to determine if the stiffening behavior is elastic. A stiffening response is certainly consistent with rubber-like behavior and may relate to randomly oriented polymer chains in Fig. 11.3 Extracted TSR for ELS specimen with silicon as substrate ( D26.97ı)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==