Partition of mixed-mode fractures in 2D elastic orthotropic laminated beams under general loading

Abstract

An analytical method for partitioning mixed-mode fractures on rigid interfaces in orthotropic laminated double cantilever beams (DCBs) under through-thickness shear forces, in addition to bending moments and axial forces, is developed by extending recent work by the authors (Harvey et al., 2014). First, two pure through-thickness-shear-force modes (one pure mode I and one pure mode II) are discovered by extending the authors' mixed-mode partition theory for Timoshenko beams. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II energy release rate (ERR) correction factor. Both correction factors closely follow an elegant normal distribution around a symmetric DCB geometry. The principle of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a general loading condition, including bending moments, axial forces, and through-thickness shear forces. Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations.

Spallation of thin films driven by pockets of energy concentration

“…By using Eqs. (20) and (22), the initiation of unstable growth, which is assumed to coincide with the buckling condition, is found at…”

“…Similarly, 2D elasticity partition theory [15][16][17][18][19][20] gives the mode I and II ERRs as where the subscript 2D denotes 2D elasticity partition theory. It is seen from Eqs.…”

“…As mentioned earlier, Refs. [23][24][25] show, using data from extensive fracture testing [26][27][28][29][30][31], that the partition theory based on Euler beam or classical plate theory [12][13][14] gives very accurate predictions of interface fracture toughness for macroscopic mixed-mode fracture while the partition theories based on Timoshenko beam theory or the first-order sheardeformable plate theory [12][13][14] and 2D elasticity [15][16][17][18][19][20] give poor predictions. The very latest studies [11,32], however, show that the 2D elasticity partition theory gives accurate predictions for the delamination behavior of micro-scale and nano-scale thin films.…”

“…[11]. Second, to develop analytical mechanical models for PEC-driven delamination based on the classical and the first-order shear-deformable plate mixed-modefracture partition theories [12][13][14] in addition to the analytical mechanical model [11] which was based only on the 2D elasticity mixed-mode-fracture partition theory [15][16][17][18][19][20]. The mechanical model for delamination with straight edges is developed in Section 2 while the model for delamination with circular edges is developed in Section 3.…”

“…16) to(20) except for swapping the subscript x -coordinate for the r -coordinate. The bubble energy at growth in Eq.…”