Effect of Impact Velocity on Dynamic Crack Growth Across an Interface in Transparent Bilayers: An Experimental Study

Abstract

The effect of impact velocity on the dynamic crack growth across a weak interface, oriented perpendicular to a mode-I crack path was studied using experiments on PMMA bilayers. This is a follow-on study of previous reports by the authors (Sundaram and Tippur in Exp Mech 56:37–57, 2016; Sundaram and Tippur in J Mech Phys Solids 96:312–332, 2016) wherein direct crack penetration or branching events were observed at a weak interface in an elastically homogeneous PMMA bilayer with different interface locations relative to the initial notch tip. The focus of this work is on the effect of impact velocity on crack growth morphology. A modified Hopkinson pressure bar was used to dynamically impact pre-cracked samples in a wedge loading configuration. Three different striker impact velocities were used and subsequent crack growth behaviors were studied with the location of the interface fixed within the bilayer. Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories was performed using transmission-mode Digital Gradient Sensing (DGS) technique in conjunction with ultrahigh-speed photography. The results show that the increase in impact velocity of the striker bar promoted crack branch formation at the interface. The crack branching and penetration mechanics hypothesized by the authors in the previous report (Sundaram and Tippur in J Mech Phys Solids 96:312–332, 2016) supports this observation namely the higher stress intensity factor of the mode-I crack-tip due to increased impact velocity leads to interface debonding before the crack-tip arrival at the interface causing the crack to branch. A higher spatio-temporal resolution experiment was also carried out to obtain visual evidence to support this hypothesized mechanism. Finally, higher impact velocity promoting crack branching was evaluated for an increased interface strength and different interface location as well.

Appendix 

Quasi-static Interface Fracture Toughness

The bilayer interface was initially characterized using mode-I crack initiation toughness under quasi-static loading conditions. Symmetric 3-point bend tests on edge cracked geometries were used for this purpose. It consisted of two rectangular PMMA strips of 70 × 30 mm and thickness of 8.6 mm joined together as shown in Fig. 16. The bonded surfaces (8.6 × 30 mm) were prepared similar to the one used for making dynamic fracture specimens. The bilayer sheets with various bond layer thicknesses from 25 µm to 1.3 mm were fabricated and subsequently machined to make multiple fracture specimens from each sheet. A 3 mm long edge-disbond was introduced along the interface of each sample during preparation. The specimen was left in the vise for 24 h before performing the fracture tests.

Fig. 16

Photograph of the experimental setup used to characterize interface fracture toughness

An Instron 4465 loading machine was used to carryout symmetric 3-point bend tests. The specimen was loaded in displacement control mode with a crosshead speed of 0.005 mm/sec. The load was applied on the interface of the edge cracked beam samples (span = 120 mm) as shown in Fig. 16. The applied load history was recorded up to fracture. Representative load deflection plots for two select interface thicknesses are shown in Fig. 17. The samples fractured in a brittle fashion as evident from the abrupt drop in load at fracture. Using the measured peak load and the specimen geometry, the crack initiation toughness was evaluated using [4],

Fig. 17

a Measured load–deflection response for fracture specimens with 25 μm and 100 μm interface thicknesses. b Variation of crack initiation toughness with interface thickness. (Note that all interfaces have lower crack initiation toughness than virgin PMMA)

$$K_{I} = \frac{F\,S}{{Bw^{3/2} }}\frac{{3\left( \xi \right)^{1/2} \left[ {1.99 - \xi \left( {1 - \xi } \right)\left\{ {2.15 - 3.93\left( \xi \right) + 2.7\left( \xi \right)^{2} } \right\}} \right]}}{{2\left( {1 + 2\xi } \right)\left( {1 - \xi } \right)^{3/2} }},\,\xi = \frac{a}{w}$$

The tests were repeated for various interface thicknesses to quantify the dependence of crack initiation toughness on adhesive layer thickness. The results thus obtained are plotted in Fig. 17b. It can be seen that the crack initiation toughness generally decreases with the interface thickness. Based on these results, two cases, one with an interface thickness of 25 μm and another with 100 μm were identified as ‘strong’ and ‘weak’ interfaces, respectively. The critical static mode-I SIF for neat (virgin) PMMA was also measured using symmetric 3-point bend tests and was recorded as 1.31 ± 0.07 MPa√m (dotted line in Fig. 17b) which is much higher than the crack initiation toughness of both interface thicknesses studied. That is, the ‘weak’ and ‘strong’ interface crack initiation toughness were ~ 52% and ~ 77%, respectively, of that of virgin PMMA.

Dynamic Interface Fracture Toughness

The dynamic interface fracture toughness was evaluated for the interface using a Hopkinson pressure loading and DGS in conjunction with high-speed photography similar to the experimental setup discussed earlier and employed to perform full-field measurements. Two interface thicknesses of 25 µm and 100 µm (‘strong’ and ‘weak’ interfaces, respectively) were studied. The specimen geometry and loading configuration is shown in Fig. 18. The specimen preparation, experimental procedure, image analysis and evaluation of fracture parameters are identical to the ones described earlier. The in-plane orthogonal angular deflection fields at two different time instants for a ‘strong’ interface are shown in Fig. 19. The velocity and SIF histories for both the interface thicknesses are plotted in Fig.  20a and b, respectively. The crack speeds reached approx. 800 and 600 m/s in the ‘weak’ and ‘strong’ interface cases, respectively. These are substantially higher than the corresponding ones in a monolithic sheet, typically in the 250–300 m/s range [4]. The measured fracture toughness of the ‘strong’ interface (0.94 MPa√m) is higher than that of the ‘weak’ interface (0.72 MPa√m). When compared with the dynamic fracture toughness of PMMA (1.12 MPa√m) [28], the fracture toughness of ‘weak’ and ‘strong’ interfaces were 64% and 84%, respectively.

Fig. 18

Specimen geometry and loading configuration used for measuring dynamic fracture toughness of the interface by growing a crack along the interface

Fig. 19

Angular deflection contour plots (contour interval = 2 × 10^–4 rad) proportional to stress gradients of $(\upsigma _{xx} +\upsigma _{yy} )$ in the x- and y-directions for a 25 µm interface. (t = 0 corresponds to crack initiation)

 

Fig. 20

Dynamic fracture parameter histories for 25 μm (‘strong’) and 100 μm (‘weak’) interfaces: a Crack-tip velocity histories, and b SIF histories