Dynamic Crack Growth Normal to an Interface in Bi-Layered Materials: An Experimental Study Using Digital Gradient Sensing Technique

Abstract

The dynamic fracture behavior of layered architectures is experimentally studied. Specifically, crack penetration, trapping, and branching at an interface are examined. A newly introduced optical technique called Digital Gradient Sensing (DGS) that quantifies elasto-optic effects due to a non-uniform state of stress is extended to perform full-field measurements during the fracture event using ultrahigh-speed photography. By exploiting the richness of two simultaneously measured orthogonal stress gradient fields, a modified approach for extracting stress intensity factors (SIFs) is implemented for propagating crack-tips under mixed-mode conditions. The method is first calibrated using a quasi-static experiment complemented by finite element simulations before implementing it for studying dynamic mixed-mode fracture mechanics of layered configurations. The layered systems considered consist of two PMMA sheets bonded using an acrylic adhesive with the interface oriented normally to the initial crack propagation direction. Interfaces are characterized as ‘strong’ and ‘weak’ by their crack initiation toughness. The dynamic fracture of monolithic PMMA sheet is also studied in the same configuration for comparison. The crack growth and fracture parameter histories of propagating cracks are evaluated. The interface is shown to drastically perturb crack growth behavior resulting in higher dissipation of fracture energy by exciting crack trapping, branching, and mixed-mode growth mechanisms.

Appendices

Appendix 1

Mixed-Mode FE Simulation

A complementary quasi-static finite element simulation of the mixed-mode tension experiment was carried out using ABAQUS® software. The model was discretized into 4589 four node bilinear plane stress quadrilateral elements. The local seeding around the crack-tip was used to generate a fine mesh in the crack-tip vicinity. Table 1 shows the material properties of PMMA used in the simulation. The discretized model and the boundary conditions used are shown in Fig. 21. Displacements corresponding to the cross-head speed during the experiment were imposed at one end of the specimen in a series of steps. A local coordinate system aligned with the crack direction was defined for post-processing the data. The crack opening (COD) and crack sliding (CSD) displacements were extracted along the two crack faces. This was repeated for each displacement step. The apparent mode-I and mode-II SIFs, (K _I ) _app and (K _II ) _app at each displacement step were computed using [26],

$$ {\left({K}_I\right)}_{app}=\frac{E\sqrt{2\uppi}}{4\sqrt{r}}{u}_{y^{\prime }};\left(r,\uptheta =\uppi \right) $$

(19)

$$ {\left({K}_{II}\right)}_{app}=\frac{E\sqrt{2\uppi}}{4\sqrt{r}}{u}_{x^{\prime }};\left(r,\uptheta =\uppi \right) $$

(20)

where E is the elastic modulus, (r, θ) are the crack-tip polar coordinates, u _y ′ is the half COD and u _x ′ is the half CSD of the crack flanks. By extrapolating the linear portion of (K _I ) _app and (K _II ) _app values plotted as a function of the radial distance r to the crack tip, the true K _I and K _II were determined.

Fig. 21

Details of the numerical simulations; finite element model showing the discretization and the boundary conditions used

Appendix 2

Experimental Repeatability

Multiple experiments were conducted for monolithic and bi-layered configurations (both weak and strong interface cases) to ensure repeatability in terms of dynamic fracture behavior as well as fracture parameters. Fig. 22(a) shows photographs of two fractured samples of monolithic specimen whereas Fig. 22(b) and (c) show two fractured samples of specimens with strong and weak interface, respectively. A high degree of reproducibility in crack paths throughout the fracture event (well past the interface) is clearly evident in Figs. 22(b) and (c). Figure 23(a) and (b) show SIF histories for two different samples with a weak and a strong interface, respectively. Again, repeatability can be readily seen in the measured values of SIF histories too. That is, the SIF histories of multiple samples closely agree with each other before the crack reaches the interface. After the crack penetrates the second layer there are only marginal differences between the two SIF histories. Despite the highly transient nature of the problem, and the possibility of potential variations in material and interface characteristics, a rather high degree of reproducibility is evident.

Fig. 22

Multiple fractured samples of each configuration

Fig. 23

SIF histories for multiple fractured samples of each configuration. The vertical broken lines denote the crack tip vicinity