Spall Characterization in Epoxy Via Laser Spallation

Abstract

Background: The strength of materials under extreme dynamic loading conditions, such as in the case of shock wave loading, is assessed from their spallation characteristics. Under laboratory conditions, flyer plate impact, or sometimes laser-induced stress waves, is employed to instigate spall in a material. These methods are often combined with velocity interferometer system for any reflector (VISAR) technique for performing transient measurements. Although the VISAR can record the velocity of extremely fast-moving surfaces, it requires a complex optical setup and a specialized data reduction technique. Objective: In this study, a simpler approach is adopted by extending laser spallation method to determine the spall strength of epoxy, while performing in situ interferometric measurements, directly on top of thick epoxy films. Methods: The glass/epoxy test samples are prepared by transferring an aluminum coating on top of epoxy layers with different thicknesses. Laser-induced stress waves transmit across the substrate/film interface and induce subsurface failure in the epoxy at sufficiently high incident laser energy. The nature and magnitude of the waves are deciphered from the out-of-plane displacement histories of the top reflective sample surfaces, which are recorded by using a Michelson interferometer. Results: The interferometric data reveal the development of two (temporally) well-separated stress waves: an ablation-induced high-amplitude short-duration longitudinal pulse, which is referred to as the primary wave, and a secondary wave, which travels at a comparatively slower speed. The complex constructive interaction of the two waves develops a high-magnitude tensile stress region in the epoxy layer. The spall strength is quantified by superimposing the two stress wave histories associated with the critical energy fluence. Conclusions: The spall depths predicted from spatiotemporal wave travel analyses are in excellent agreement with the experimental observations. The newly adopted methodology estimates the spall strength of epoxy as 260 ± 20 MPa.

Appendices

Appendix A: Laser-induced failure at the glass/epoxy interface

The development of primary and secondary waves in glass/epoxy samples upon the incidence of laser energy is discussed in Sect. ‘Interferometric Measurements’. To exclude the influence of secondary waves on the stress field, the experiments are performed on a sample prepared by depositing a 4-μm-thick epoxy layer on a glass substrate. This thin epoxy layer will experience at least five back-and-forth reflections of the longitudinal wave before the secondary wave appears at the glass/epoxy interface (in 8 ns). The failure initiation micrograph included in Fig. 14a corresponds to a YAG energy incidence of 65 mJ/mm². The spallation image at 120 mJ/mm² and its associated surface profile (illustrated in (b) and (c)) suggest glass/epoxy interfacial failure.

Fig. 14

a The glass/epoxy interfacial failure initiation and b complete spallation, observed in a 4-μm-thick epoxy film. c Profilometric scan across the spalled region, shown in (b)

Representative fringes obtained by conducting experiments on a glass/Al calibration sample at 60 mJ/mm² (just before failure initiation) are shown in Fig. 15a. The data are analyzed by following steps, as discussed in Sect. ‘Experimental Details’, and the longitudinal pulse history in the substrate is plotted in Fig. 15b. The interfacial stress history shown in Fig. 15c is obtained by performing computations on a sample with a 4-μm-thick epoxy layer. The modeling details are discussed in Sect. ‘Evaluating Stress Field in Epoxy’. The glass/epoxy interfacial strength is inferred to be ~200 MPa from the peak value of the interfacial stress.

Fig. 15

a The representative interferometric data obtained by conducting laser spallation experiments on the glass/aluminum calibration sample at 60 mJ/mm² laser fluence. b The substrate stress history associated to the primary wave. c Computationally obtained glass/epoxy interface stress history (with 4-μm-thick epoxy layer) corresponding to the transient loading shown in (b)

Stress history in epoxy prior to interfacial failure

The computationally obtained stress field in the epoxy layer is analyzed next to estimate the maximum tensile stress in the epoxy film prior to failure initiation at the substrate/film interface. The substrate stress corresponding to a laser energy of 50 mJ/mm², as shown in Fig. 16a, is employed as the loading pulse in the 4-μm-thick epoxy layer model.

Fig. 16

a The stress history in a glass substrate obtained by performing interferometric measurements at 50 mJ/mm² laser fluence, b Computationally obtained stress field in a 4-μm-thick epoxy layer at various times. A zero ns refers to the time when the stress wave begins to transmit into the epoxy layer

The stress histories in epoxy at various times are illustrated in Fig. 16b. The labeled times are measured with respect to when the longitudinal pulse begins to transmit into the epoxy layer. The values of 0 and 4 μm on the x-axis correspond to the glass/epoxy interface and the free surface of the epoxy layer, respectively. After ~4 ns, a tensile region started to develop in the epoxy film. The figure clearly shows that by 4.75 ns, the entire epoxy layer is subjected to tensile stress. At 5.75 ns, the maximum tensile stress is noted to be ~175 MPa. Further continuing the simulations reveals a drop in the magnitude of the stress field (not included in the plot for clarity).

Appendix B: Post-spallation interferometric measurements

All measurements and analyses reported in Sect. ‘Interferometric Measurements’ were performed for the laser fluence, which was marginally lower than those required for failure initiation. The interferometric data exhibited distinct primary and secondary fringes (see Figs. 8, 9 and 10). Had the spallation initiated because of the primary compressive wave, the optical signal would have contained only the primary fringes, as shown in Fig. 17. The typical wave reflections and mode conversions following spallation are sketched in Fig. 18. The illustrated x-t diagram is the same as shown in Fig. 11, except that the spall plane introduces additional mode-conversions. Primary (p with a numeral subscript) and secondary (s with a numeral subscript) waves are illustrated by the solid and dashed lines, in which the compressive and tensile waves are shown in blue and red, respectively. As shown in the figure, p₃ and s₂ develop due to the wave reflections from the spall plane. The sketch indicates that the interferometric data recorded at the free surface should contain the signatures of the p₁, p₃ and s₁ waves. By considering the spall depths shown in Table 1 and using 2675 m/s and 2375 m/s as the primary and secondary wave speeds, respectively, the time difference between the arrival of the p₃ and s₁ waves to the free epoxy surface is calculated to be less than 2 ns. Clearly, it will be difficult to distinguish the signature of the two waves within such a short duration. In addition, the two waves reaching the free surface are of opposite sign (see Fig. 18). Since the primary and secondary waves have comparable magnitudes, their destructive interaction would not allow secondary fringes to develop. Another reason for the diminished interferometric signal is the scattering of the probe beam from the spallation-induced crumbled (and uneven) surface of epoxy.

Fig. 17

a–d The representative interferometric fringes correspond to the laser fluneces at which the spall had been detected. The data illustrated in (a) to (d) are for 78 μm, 165 μm, 197 μm and 410 μm epoxy film cases, respectively. The associated primary compressive pulses are shown in (a1–d1).

Fig. 18

The travel and mode conversions of the primary (p) and secondary (s) waves following the development of a spall plane in the epoxy. The red and blue lines indicate tensile and compressive waves, respectively