Cracking phenomena of brittle films in nanostructure composites analysed by a modified shear lag model with residual strain

A cohesive zone finite element approach to model tensile cracks in thin film coatings

“…In the i + 1' increment the stress in the middle of the region of interest has exceeded the critical value for one of the cohesive zone elements, a new crack is generated, and the σ x x surface stresses go towards zero. This crack progression is consistent with the shear lag models for tensile cracking [Agrawal and Raj 1989;Wojciechowski and Mendolia 1989;Yanaka et al 1998;Chen et al 1999;2000]. From shear lag assumptions and from the above description of the contours in Figure 6, one would expect the cracks always to form at the midpoint between two adjacent cracks.…”

“…However, this expectation is based on the assumption that the stress profile in Figure 6 is unchanged through the thickness of the coating. Uniform stresses along the thickness of the coating are also an underlying assumption in the analytical models referred to above [Agrawal and Raj 1989;Wojciechowski and Mendolia 1989;Yanaka et al 1998;Chen et al 1999;2000]. It was found that the stresses are not uniform through the coating thickness.…”

“…Other research groups have asserted that, as shown in Figure 2b, the interfacial shear stress should have its maximum value located at each end of the intercrack spacing and be zero at the midpoint of the intercrack spacing in the coating [Wojciechowski and Mendolia 1989;Yanaka et al 1998;Chen et al 1999;2000]. The recent analytical work of Yanaka et al [1998] and Wojciechowski and Mendolia [1989], and the experiments and FEA of Chen et al [1999;2000], indicate that the interfacial shear stress distribution is best approximated by a distribution like the one shown in Figure 2b. The applicability of these two different shear stress distributions may be related to how the crack spacing compares to the coating thickness.…”

“…Figure 2. Two different theories predicting the distribution of interfacial shear stresses along the coating-interlayer interface between two cracks when the coating-interlayersubstrate system is subject to tensile loads: (a) sinusoidal distribution with zero stress at the endpoints [Agrawal and Raj 1989], and (b) maximum stress at the endpoints [Chen et al 2000;Yanaka et al 1998;Wojciechowski and Mendolia 1989].…”

“…The previous work with finite element analysis of tensile cracking assumes preexisting cracks by introducing fine notches in the model [Wojciechowski and Mendolia 1989;Yanaka et al 1998;Chen et al 1999;2000;Krishnamurthy and Reimanis 2005]. Few researchers have developed finite element models which can simulate the formation and propagation of tensile cracks and thus predict coating performance.…”