Owing to their unique physical and mechanical properties, carbon fiber reinforced plastics (CFRPs) are finding wide applications in a variety of industries. This broad application necessitates a consideration of the material response in nontraditional environments to evaluate their overall reliability. In the current study, we investigate the time-dependent behavior of unidirectional [0°]6 CFRPs irradiated by a short pulse Nd:YVO4 near-infrared laser for durations ranging between 100 and 500 ms. Post irradiation, the damage on the surface was characterized using optical and electron microscopy as well as optical surface profilometry. Qualitatively, the heat-affected zone (HAZ) was found to primarily consist of an out-of-plane expansion and anisotropic matrix removal with no structural damage to the fibers. The growth in HAZ size is conduction dependent and has a rapid trajectory along the fiber direction and a subdued trajectory along the transverse direction. Further evaluation of the subsurface via x-ray micro-CT showed the HAZ to be surface localized. An analytical heat conduction approach was also used to understand the evolution of surface HAZ with exposure time. This simplified approach was found to adequately capture the shape and growth of the HAZ.

Efficiency driven lightweighting has largely been, and continues to be, met by structures made from polymer matrix composites (PMCs). A PMC system that has demonstrated the greatest potential is carbon fiber reinforced plastic (CFRP). CFRPs retain high specific strength and stiffness relative to standard structural metals (aluminum, steel, magnesium, etc.).1–3 They also show an equivalent or better response under cyclic loading and corrosion environments.3,4 As a result, CFRPs have become a bill of material for frames of air, space, marine, and ground vehicles. With such extensive application, it also becomes necessary to consider their performance in more nonconventional environments.

One atypical environment that merits attention is that facilitated by light-based directed energy sources. This environment is encountered during laser machining processes and exposure to high energy laser (HEL) weapons. Laser machining of PMCs is desired over conventional machining approaches because it eliminates tool wear, reduces delamination, and prevents contamination.5–10 Beyond machining, advances in optics technology are enabling compact designs with higher power capacities (1–100 kW) suitable for HELs.11–13 Thus, HEL impact of PMC structures on military vehicles is a plausible concern from a survivability perspective.14 

Much of our understating on laser-PMC interactions is based on the numerous investigations that have been conducted on machining approaches. The earliest of these works was performed by Tagliaferri et al. where a continuous wave (CW) infrared (IR) laser was evaluated for sectioning PMCs reinforced by different fiber materials.5 It was shown that a greater difference in thermal properties (heat capacity, thermal conductivity, fusion and vaporization temperatures, etc.) between the reinforcing fibers and polymer matrix greatly influences the heat-affected zone (HAZ). Typically, the HAZ is characterized by a region outside the beam boundary where matrix damage (recession) occurs due to heat conduction. CFRPs, which retain high conductivity fibers in polymer matrix, have been critical in illustrating this damage mode under various conditions.5–7,15–19 Absorptivity and layup anisotropy are two additional material properties that have also been identified as critical for managing material removal depth and size of the HAZ.20,21 Moreover, the beam characteristics (emission wavelength, intensity, and duration) must be taken into consideration for a holistic assessment of damage. With respect to beam duration and intensity effects, Herzog et al. was able to show that machining by a pulsed near-infrared (NIR) laser (0.02–0.1 S/pulse, 57 MW/cm2) produces a smaller HAZ and a lower reduction in static strength of CFRP samples relative to disk NIR (30 MW/cm2) and CW IR sources (2 MW/cm2).22 Pulses of short duration are noted to reduce the interaction time (conduction) and deliver higher intensity bursts, which result in vaporization/plasma formation.20,22 Irradiation of composites containing multiwalled carbon nanotubes has been shown to also result in increased electrical conductivity while maintaining overall mechanical strength.23–25 This application has potential for CFRPs where electrical properties are critical and conductive paths are needed. The majority of machining studies, including those mentioned here, are concerned with the efficacy of the process. To the best of the authors’ knowledge, there is little-to-no work that explores the progressive damage mechanisms at very short intervals of exposure. It is important to establish this understanding since it will enable the development of suitable strategies for both machining and HEL survivability of CFRPs.

The current study presents an experimental evaluation of the time-dependent response of CFRP targets irradiated by a short pulsed NIR laser source. Operating parameters that yield maximum average power at nanosecond pulse duration are applied throughout the experiments. At each increment in exposure time, the corresponding damage region is examined both qualitatively and quantitatively using a variety of surface characterization methods. Information gathered from the microstructural assessments is used to render a detailed description of the resulting damage progression with emphasis on the underlying mechanisms. Finally, a simplified approach to understand the evolution of HAZ on the composite surface is advanced using the fundamental heat conduction equation.

The base material for the CFRP panel was a unidirectional prepreg carbon fiber fabric (#2114, Fiberglast Developments Co., Brookville, OH, USA) with an areal weight of 139 g/m2 and resin content of 38 ± 3%. Initially, six rectangular prepreg layers (or lamina) were extracted from the fabric with dimensions of 317.5 × 165.1 mm2. The prepreg lamina were then stacked on an aluminum mold with the fibers oriented in the same direction to form the [0°]6 composite laminate and vacuum bagged. Per the suppler specifications, a curing temperature of 132 °C and a dwell time of 4 h were applied to fully harden the epoxy matrix. After manufacturing, the panel length and width were trimmed to yield final dimensions of 304.8 × 152.4 × ∼1.0 mm3. Water jet cutting was then used to extract smaller samples (15 × 3 × ∼1 mm3) for laser irradiation experiments. These samples retained fibers oriented in the short transverse direction as illustrated in Fig. 1(a). One of the samples was mounted in epoxy and polished to a 1 μ finish along the cross section to examine the CFRP microstructure using a scanning electron microscope (SEM) (Quanta 650 FEG, FEI Technologies Inc., Hillsboro, OR, USA). As shown in the electron micrographs of Fig. 1(b), the composite consists of a thin (<50 μm) epoxy rich layer on the top surface as well as observable matrix rich pockets and voids in the subsurface laminates. A matrix coverage of 36.3 ± 3.2% was determined for the CFRP by thresholding the SEM micrographs using an image analysis freeware (fiji, ImageJ). The latter is noted to be in good agreement with the resin content of the starting prepreg fabric.

FIG. 1.

(a) Diagram depicting the stacking sequence and fiber orientation of the CFRP sample. The letter designations L, W, and t correspond to the length, width, and thickness of the CFRP, respectively. (b) Electron micrographs of the polished CFRP cross section.

FIG. 1.

(a) Diagram depicting the stacking sequence and fiber orientation of the CFRP sample. The letter designations L, W, and t correspond to the length, width, and thickness of the CFRP, respectively. (b) Electron micrographs of the polished CFRP cross section.

Close modal

An Nd:YVO4 laser (BL6S 106Q, Spectra-Physics Co., Santa Clara, CA, USA) operating at a wavelength of 1064 nm was used to irradiate the CFRP samples. The output beam is specified to retain a Gaussian (TEM00) distribution with an M2 value <1.2 and a divergence of 3 mrad. For the irradiation experiments, the laser was operated in a Q-switched mode at a repetition rate of 35 kHz. The latter setting ideally produces a pulse that is 7.9 ns in duration. The manufacturer calibration for the latter settings also suggest a slightly elliptical beam (M2 > 1) with a major waist radius, wx, of 268 μm and a minor waist radius, wy, of 255.5 μm. [The beam waist is taken as the radius at which the beam intensity falls to a value that is (1/e2) of the maximum.] Considering that the average power at a frequency of 35 kHz is 5.94 W, each pulse is estimated to deliver a peak power of ∼21 kW. Single pulse or CW exposure is not used due to the limitation in power output from the laser for these settings. The beam profile was visually inspected using a monochrome CCD camera (Chameleon3, FLIR Systems Inc., Santa Barbara, CA, USA). The beam was expanded to more than ten times its initial output size using a diverging lens with a focal length of 50 mm. The latter setup reduced the intensity down to acceptable thresholds for safe operation of the optics and sensors in the profilometer. Figure 2 shows the resulting surface profile of the beam with an overlay plot of the one-dimensional color intensity variation at the center in both the vertical and horizontal directions. The plotted curves are bell shaped (i.e. Gaussian) and a three-dimensional translation of the surface also shows this same Gaussian nature of the beam.

FIG. 2.

Visual-based profilometry of the output beam from the Nd:YVO4 laser operating at 35 kHz. The plot in the right shows a three-dimensional rendering of the surface beam profile.

FIG. 2.

Visual-based profilometry of the output beam from the Nd:YVO4 laser operating at 35 kHz. The plot in the right shows a three-dimensional rendering of the surface beam profile.

Close modal

A schematic depicting the complete laser irradiation experimental setup is provided in Fig. 3. Initially, the composite sample is secured onto a metal fixture and mounted inside a vacuum chamber with the irradiation surface perpendicular to the incident beam. The chamber pressure is then reduced from ambient (∼760 Torr) to ∼70 Torr using a Venturi pump. A chamber with a vacuum environment reduces scattering of the beam and limits outgassing of vaporization products. After establishing rough vacuum, a pneumatic actuator is used to move the laser head toward the chamber until it is 10 cm away from the sample surface. This is the closest possible separation between the beam and sample based on allowable equipment clearances. The chamber retains a port that is covered with a magnesium fluorite (MgF2) window. MgF2 windows transmit ∼96% of incident light at 1064 nm wavelength. A computer interfacing with the laser control/power supply unit is then used to input the repetition rate and turn-on the laser head. The beam remains suppressed by the Q-switch gate, which is controlled externally by a function generator (33220A, Agilent Technologies Inc., Santa Clara, CA, USA). The signal generator is programed to respond to an external/manual trigger upon which it sends a single square pulse with a 5 ns edge time and a duration that is equivalent to the desired exposure time. In the current study, five evenly spaced exposure times ranging between 100 and 500 ms were examined with five samples being used for each time step.

FIG. 3.

Schematic and photographs of the laser irradiation setup.

FIG. 3.

Schematic and photographs of the laser irradiation setup.

Close modal

After laser irradiation, the surface of each sample and the subsurface of the selected samples were assessed using various characterization methods. Initial characterization efforts were focused on understanding the in-plane damage morphology. These were accomplished using both optical (Olympus SZX7, Olympus Co., Center Valley, PA, USA) and electron microscopes. While optical imaging provides information on the overall damage boundary, high resolution imaging via SEM yields greater details on the extent of damage by the individual phases (matrix and fiber). After in-plane analysis, the out-of-plane damage was determined using a 3D optical profilometer (NewView 8300, Zygo Co., Middlefield, CT, USA). Finally, x-ray microcomputed tomography (micro-CT) (SkyScan 1272, Bruker Co., Billerica, MA, USA) was used to investigate the subsurface damage on a sample irradiated for a duration of 500 ms. The scan was performed at 40 kV (166 A) through 180° rotation with a step size of 0.2°. The resolution of the two-dimensional slices was 2.5 μm/pixel. An in-depth micro-CT investigation of samples from all exposure times was not practical due to the long scan times needed to obtain high resolution radiographs capable of discerning the ∼5 μm fibers in the CFRP.

Optical microscopy images of the laser irradiated CFRP surface are shown in Fig. 4. There are three distinct regions in the HAZ that are observed from these images. The first region is located at the center of the exposed area, and it has a nearly circular boundary highlighted in dark as well as an interior that is reflective (silverlike). This region also appears to be protruding from the surface. Further out from the center is the outer HAZ region where the colorization is again reflective. The boundary of this region is more easily noticeable since it extends very near to the unirradiated surface. A third region, identified by a darker discoloration, is situated between the outer HAZ and the unirradiated surface. This edge HAZ is more pronounced for exposure times, te, greater than 200 ms. As the exposure time increases, the diffusion of heat along the fiber axis leads to greater level of damage to the composite (i.e., greater HAZ size). Moreover, we observe an asymmetry in the overall HAZ shape where a greater coverage results along the fiber direction relative to the transverse direction. This response is attributed to the anisotropic thermal properties of the composite.4,8 Higher resolution imaging reveals more details on the nature of the HAZ and the findings are presented next.

FIG. 4.

Optical microscope images of the laser irradiation damage on the CFRP surface for each exposure time interval. In the image for te= 300 ms, indicators are used to highlight the center HAZ (first region), outer HAZ (second region), and edge HAZ (third region).

FIG. 4.

Optical microscope images of the laser irradiation damage on the CFRP surface for each exposure time interval. In the image for te= 300 ms, indicators are used to highlight the center HAZ (first region), outer HAZ (second region), and edge HAZ (third region).

Close modal

The SEM images in Fig. 5 provide an overall and close-up view of the laser irradiation damage on the surface of the CFRP. Relative to the optical images, these electron micrographs provide enhanced details of the damage features. For instance, the reflective damage regions observed in Fig. 4 are clearly identified here as exposed (or matrix-free) fibers. From a mechanism aspect, this observation suggests that the laser irradiation primarily works to ablate the epoxy layer on the surface. The remnant epoxy that is not fully ablated is observed to retain a weblike porous texture. The porous microstructure may result from greater decomposition in areas where the epoxy content is thinner. Beyond the ablation of the surface epoxy, the laser irradiation does not appear to have physically degraded the carbon fibers. We can thus infer that the maximum temperature attained during laser irradiation is lower relative to the sublimation temperature for carbon fiber (∼3900 °C). Still, there are randomly located areas within the damage region where adjacent fibers are splayed. This splaying may have resulted from pressure generated by evaporation by-products (gases) escaping from the subsurface as the radial heat conduction by the fibers decomposes the underlying epoxy matrix.26 Similar to the optical images, the SEM images also show a discoloration of material around the primary damage. This discoloration is determined to manifest from a light ablation of the surface epoxy layer. The light ablation is also associated with conduction-based heating. One missing feature that is not evident in the electron micrographs is the central region in the HAZ, which was highlighted in the optical images. The reflection properties in optical microscopy are thus more potent in defining critical topology features relative to electron microscopy in secondary-electron imaging mode. This notion is explored further in the follow-on section where optical surface mapping is used to examine both surface and out-of-plane damage.

FIG. 5.

SEM micrographs of the HAZ for individual exposure times. The images were retrieved using the secondary-electron detector.

FIG. 5.

SEM micrographs of the HAZ for individual exposure times. The images were retrieved using the secondary-electron detector.

Close modal

Optical surface profiles of the damage from the five distinct exposure times are presented in Fig. 6. These profiles show that the maximum out-of-plane displacement (i.e. relative change in the Z dimension) of the damage surface occurs at the center. This is very similar to the observation of a central HAZ from the optical microscopy images (see Fig. 4). It clearly supports the earlier assertion that this region protrudes outward from the surface. This behavior likely results from the buildup of subsurface pressure as the epoxy matrix below the topmost fiber layer is evaporated and the by-product gases escape to the surface. It is important to note that this surface protrusion is a critical feature of the HAZ from laser irradiation of the CFRP, in addition to the removal of the topmost epoxy layer. Furthermore, the region beyond the damage boundary, which was observed as a discoloration in both optical and SEM images appears as a gradual increase in the epoxy content in the surface profiles. Specifically, as we traverse the matrix-depleted zone in the damage region to the unirradiated CFRP surface, we encounter a gradual rise in height indicative of a partial removal of the epoxy layer on the surface. This was similarly identified as a light ablation region in the electron micrographs (see Fig. 5).

FIG. 6.

Optical surface profiles of the irradiated surface highlighting the HAZ for each exposure time interval. The red lines in each image are locations where a line profile was extracted [see Fig. 7(d)].

FIG. 6.

Optical surface profiles of the irradiated surface highlighting the HAZ for each exposure time interval. The red lines in each image are locations where a line profile was extracted [see Fig. 7(d)].

Close modal

Each of the characterization approaches covered above (optical microscopy, electron microscopy, and surface profilometry) yield measurable damage features, which can be assessed as a function of exposure time. The results for the in-plane feature measurements are presented in Figs. 7(a)7(c). All three plots show the variation in the HAZ size parallel and perpendicular (or transverse) to the fiber orientation. As shown in these plots, the measurements from the three distinct characterization sources are in good agreement. Relative to the damage in the transverse direction, the damage along the fiber direction is observed to be twice as large at the lowest exposure time (te=100ms) and grow by more than three times at the highest exposure time (te=500ms). As noted above, this behavior is directly linked to the higher thermal conductivity of carbon fiber. It is further observed that for all exposure times, the HAZ size in all directions is greater than the nominal beam waist diameter, [Here, the nominal beam waist diameter is taken as the average of the beam waist in the x (2wx) and y (2wy) directions (∼523.5 μm).] This suggests that a greater portion of the observed damage is associated with conduction and that this effect increases drastically with exposure time. The local damage by the beam is most closely represented by the central damage zone in the optical microscopy images (see Fig. 4). As shown in Fig. 7(a), this damage feature is found to be equivalent to the nominal beam diameter for te=100ms, and it increases slightly by a factor of one-half for te=500ms. This slight increase with exposure time is again attributed to the greater degree of influence by the conductivity effect as the exposure time by the heat source increases. Line profiles along the center of the HAZ are obtained from the surface profiles presented in Fig. 5 (red lines). The five profiles obtained for the five irradiation conations are averaged and presented in a stacked order in Fig. 7(d). [Note that five irradiation conditions (i.e. exposure times) were investigated and five samples were used for each condition to yield a total of 25 line profiles.] It is observed from this figure that the protrusion height and width grow with increase in exposure time. Additionally, the growth in height stagnates after 400 ms exposure, while the growth in width stagnates after 200 ms exposure. The stagnation in damage along the width is expected based on the 2D transverse damage measurements presented in Figs. 7(a)7(c). Further assessment of the damage height was performed by determining the variation in maximum value of each line profiles. A plot of the average value for the five measurements for each of the five conditions is presented in Fig. 7(e). It is found that at te=100ms, the surface protrusion is very limited with an average maximum height of 10.27 ± 5.0 μm, and it grows by a factor of three (31.24 ± 9.71 μm) for te=500ms. Between these two extremes, there is a variation in the growth rate where the average out-of-plane damage rapidly increase in size from 14.20 ± 6.73 to 29.58 ± 9.58 μm followed by a drastic decrease in height change to a near plateau. This would suggest that there is a limit to the penetration depth of the laser beam energy (heat) and hence a limitation on the extent of matrix evaporation below the topmost surface.21,26 This behavior may arise from the limited thermal conductivity due to loss of contact between underlying fibers (air gaps) and/or competing effects of conduction along fibers versus conduction around the epoxy matrix connecting fibers.

FIG. 7.

Plots of the in-plane HAZ features as a function of exposure time with emphasis on the damage parallel and transverse to the carbon fiber direction. Measurements taken from (a) an optical microscope, (b) a scanning electron microscope, and (c) an optical surface profiler. (d) Out-of-plane damage profiles for each exposure time. (e) Plot of the variation in the maximum height of the out-of-plane damage as a function of exposure time.

FIG. 7.

Plots of the in-plane HAZ features as a function of exposure time with emphasis on the damage parallel and transverse to the carbon fiber direction. Measurements taken from (a) an optical microscope, (b) a scanning electron microscope, and (c) an optical surface profiler. (d) Out-of-plane damage profiles for each exposure time. (e) Plot of the variation in the maximum height of the out-of-plane damage as a function of exposure time.

Close modal

A well-rounded understanding of the laser irradiation response requires that we consider the subsurface damage in addition to the surface damage. In this study, x-ray micro-CT, a nondestructive method, was used to assess the subsurface damage of a single sample irradiated at te=500ms. As alluded to in the experimental section, micro-CT is both time and cost intensive. Hence, only the extreme damage case was chosen for analysis. Figures 8(a) and 8(b), respectively, show the reconstructed volume of the sample with the HAZ fully contained and a cross-sectional view at the center. The full volume [Fig. 8(a)] shows the HAZ, which retains very similar features as the electron micrographs and surface profiles. By contrast, the cross-sectional view [Fig. 8(b)] yields very valuable information on the morphology and size of the subsurface HAZ. First, we find that the subsurface HAZ is hemispherical in shape, with the highest depth resulting at the center (much like the surface extrusion profile) of the irradiated area. This shape is mostly attributed to the Gaussian intensity profile of the laser beam (see Fig. 2). For this particular sample, the damage depth is ∼240 μm. This size encompasses nearly two of the six layers, which makeup the composite. This finding suggests that for the exposure times applied in this study, the maximum damage is limited to two plies. Additionally, the lower x-ray attenuation of the damage region yields a distinct color scheme (dark gray) relative to the surrounding (light gray). (In postprocess visualization, the color scheme is inverted from the scan settings. Lighter regions are more attenuating than darker regions.) The latter confirms that a loss of matrix material occurs in the subsurface. This realization supports our earlier assertions that the out-of-plane surface extrusion results from a pressure buildup by evaporation gas entrapped beneath the topmost layer. Given these findings, additional micro-CT examination is warranted in future efforts, so that we may understand the specific evolution of the subsurface damage with time. Still, the current characterization allows us to reach the conclusion that the laser irradiation time scales applied in this work lead primarily to near-surface absorption/damage.

FIG. 8.

X-ray micro-CT reconstructions of a CFRP sample irradiated for 500 ms showing the (a) HAZ volume and (b) cross section.

FIG. 8.

X-ray micro-CT reconstructions of a CFRP sample irradiated for 500 ms showing the (a) HAZ volume and (b) cross section.

Close modal

Each of the characterizations presented above provide critical information, which enables us to understand the progressive damage during laser irradiation. Initially, the mechanism of damage is evaporation of the matrix layer on the surface. Owing to the excellent conduction of heat by the carbon fibers, there is a slight extension of the ablation zone beyond the beam diameter, even in this early stage of irradiation. Still, the beam intensity (and energy) is not sufficient to break down the fibers, so they remain intact with minor damage. Prior to 100 ms of exposure, a very small portion of the subsurface epoxy surrounding the fibers is evaporated. The evaporated gases are trapped below the fiber layer and pressure builds. As the gases escape to the atmosphere, they lead to splaying and out-of-plane extrusion of the surface fiber layer. The extrusion is very minimal for exposures ≤100 ms, since the heat source is not maintained long enough. Increasing the exposure time from 100 to 400 ms leads to a significant increase in the HAZ size especially along the fiber direction. Additionally, there is an increase in subsurface evaporation and subsequent surface extrusion. However, this extrusion and subsurface HAZ become sluggish with further increase in exposure time (i.e. te>400ms). Specifically, the evaporated subsurface matrix leaves behind air pockets between fibers, which in turn impede heat conduction needed for further evaporation. The exposed surface fibers are also highly absorptive of radiation at 1064 nm, and this would significantly limit penetration of the beam. Hence, continued evaporation would likely occur through convection where the surface fibers heat up the surrounding air and the fibers that are further below conduct the heat to the surrounding matrix. Evaporation of the subsurface matrix all the way through the thickness would require much longer and lead to physical degradation of the fibers as well as ignition of the CFRP (if conducted in air). Although these time interval studies of the irradiation reported in this paper provide the basis for constructing the damage progression and associated mechanisms, further investigation is needed with respect to longer exposure times (>1 s) and in situ monitoring (i.e. visualization and/or sensing of damage).

Fundamental heat conduction has the potential to determine the observed surface profiles of HAZ on the composite. This same approach cannot be implemented to determine subsurface HAZ since it does not fully capture the influence of matrix rich regions (interface) between plies and defects (pores and delaminations). Still, this exercise is useful for showing the relative importance of heat conduction as a damage mechanism for high intensity laser irradiation on CFRPs.

Numerical, empirical, and analytical approaches have been utilized in previous efforts to simulate pulsed laser heating of various materials.15,16,26–30 In the current work, the analytical approach is implemented to determine the heat accumulation on the CFRP surface. We start the analytical exercise by considering the heat developed by a laser source on an absorptive body, which is typically described by the beam intensity. For a source emitting a Gaussian beam, the distribution of the unattenuated intensity in Cartesian coordinates, I(x,y), is determined by the following equation:

I(x,y)=I0exp(((xwx)2+(ywy)2)),
(1)

where I0=(2Ppk/πwxwy) is the maximum intensity (∼0.2 GW/cm−2 for this work) and Ppk is the peak power. Following the work of Yakovlev et al., the corresponding initial temperature profile, T(x,y), is assumed to be normally distributed and directly related to the intensity given by Eq. (1),31 

T(x,y)=Tmax[I(x,y)/I0],
(2)

where Tmax=(αAI0τ/cρ) is the maximum temperature, α is the optical absorption coefficient, A is the absorptivity, τ is the pulse duration, c is the specific heat capacity, and ρ is the density. The fundamental heat conduction equation, which describes the distribution of the temperature field over time is given by the following expression:

KxT(x,y)x+KyT(x,y)y=cρT(x,y)t,
(3)

where Kx and Ky are the respective thermal conductivities for an anisotropic system. Equation (3) is directly solved by transforming the partial differential equation into Fourier integrals for a semi-infinite body and applying Eq. (2) as the initial temperature profile when t=0 [i.e. T(x,y,0)],27,29,31

T(x,y,t)T0=Tmaxwxwy(wx2+4axt)(wy2+4ayt)×exp[(x2wx2+4axt+y2wy2+4ayt)].
(4)

In Eq. (4), T0 is the temperature at infinite distance from the source (i.e. room temperature ∼273 K) and ax and ay are the anisotropic thermal diffusivities. [The thermal diffusivities are assumed to be constant and they are determined using the respective thermal conductivity values by the following relation, ai=Ki/cρ (i=x,y).] This solution only accounts for the incidence of a single pulse, while heat accumulation requires the consideration of each pulse for the duration of the irradiation. Following previous derivations with similar conditions, a summation of Np total pulses prior to the incidence of the Np+1 pulse is advanced in order to determine the overall temperature field.27,31 The resulting equation for the heat accumulation is as follows:

T(x,y,t=Nf)T0=N=1NpTmaxwxwy(wx2+4axNf)(wy2+4ayNf)×exp[(x2wx2+4axNf+y2wy2+4ayNf)],
(5)

where f is the controlled pulse frequency (i.e. repetition rate, 35 kHz) of the beam. We note that Eq. (5) does not consider the cooling per pulse and only presents the cumulative temperature profile (pure pulse) over time.

The required material properties needed to determine the laser induced temperature field via Eq. (5) are provided in Table I. In constructing this table, the properties of the epoxy matrix and carbon fiber were independently collected, and a rule of mixtures strategy was applied to obtain the property of the unidirectional CFRP. Also highlighted in Table I is the directionality aspect of Eq. (5), where the conductivity and diffusivity are determined parallel (x axis) and transverse (y axis) to the fiber direction. The predicted temperature profiles for the low and high exposure times applied in this work are shown in Figs. 9(a1) and 9(b1), respectively. The profile temperature is shown to increase from a base temperature of 200 K to the maximum attainable temperature. The relative change in temperature is predicted to rise by ∼440 K as the exposure time is increased from 100 ms (Np=3500) to 500 ms (Np=17500). The gradual temperature change with time may be associated with a greater preference for conduction away from the center of the irradiated zone by the carbon fibers. In observing the distribution of the temperature profile, we find that, in general, it closely resembles the elliptical geometry of the observed surface HAZ profiles. In the characterizations (optical and SEM), we clearly identify damage as the removal of the matrix layer on the topmost surface. It is thus desirable to identify the region of the temperature profile for a given exposure time, which is greater than or equal to the epoxy evaporation temperature (i.e., T800K). This was performed by limiting the output temperature profile of Eq. (5) between 200 and 800 K. The results are displayed adjacent to the corresponding unbounded profiles in Figs. 9(a2)9(b2) for 100 and 500 ms exposures, respectively. These profiles clearly highlight the hotspot region where matrix evaporation likely to occurs. Furthermore, there is a qualitative agreement in the evolution of the surface damage morphology with direct observations in Figs. 4 and 5. This finding supports our previous assertion that conduction plays a critical role in determining the extent of laser irradiation damage of the CFRP.

FIG. 9.

Heat conductivity-based predictions of the temperature profiles arising due to accumulation of laser pulses (i.e. exposure times on the CFRP surface). Unbounded temperature profiles [(a1) and b1)] and temperature profiles bounded between 200 and 800 K [(a2) and b2)] to highlight the region of matrix evaporation on the surface (i.e., HAZ).

FIG. 9.

Heat conductivity-based predictions of the temperature profiles arising due to accumulation of laser pulses (i.e. exposure times on the CFRP surface). Unbounded temperature profiles [(a1) and b1)] and temperature profiles bounded between 200 and 800 K [(a2) and b2)] to highlight the region of matrix evaporation on the surface (i.e., HAZ).

Close modal
TABLE I.

Thermal, physical, and optical properties of CFRP constituents and composite bulk.

Density, ρ
(g cm−3)
Thermal conductivity, K
(W m−1 K−1)
Specific heat capacity, c
(J kg−1 K−1)
Thermal diffusivity, a
(cm2 s−1)a
Evaporation temperature, Tev
(K)b
Absorptivity, AAbsorption coefficient, α
(cm−1)
Epoxy 1.26 ± 0.06a 0.15c 1200d 9.92 × 10−4 700–800 0.034e 0.9e 
Carbon fiber 1.83 ± 0.04a 50c/5d 710d 0.38/0.038 3900–4000 0.72f 90g 
CFRPh 1.61 ± 0.04 31.06/3.16 896 0.22/0.022 — 0.46 56.1 
Density, ρ
(g cm−3)
Thermal conductivity, K
(W m−1 K−1)
Specific heat capacity, c
(J kg−1 K−1)
Thermal diffusivity, a
(cm2 s−1)a
Evaporation temperature, Tev
(K)b
Absorptivity, AAbsorption coefficient, α
(cm−1)
Epoxy 1.26 ± 0.06a 0.15c 1200d 9.92 × 10−4 700–800 0.034e 0.9e 
Carbon fiber 1.83 ± 0.04a 50c/5d 710d 0.38/0.038 3900–4000 0.72f 90g 
CFRPh 1.61 ± 0.04 31.06/3.16 896 0.22/0.022 — 0.46 56.1 
a

Calculated based on thermal conductivity.

b

Values obtained from Refs. 18, 27, and 28.

c

Average value determined from values provided in Refs. 15, 18, 21, and 26–28.

d

Values for transverse fiber thermal conductivity as well as matrix and fiber heat capacities obtained from Ref. 17.

e

Values obtained from Ref. 32.

f

Value obtained from Ref. 33.

g

Value estimated to be two orders of magnitude higher than the absorption coefficient for the matrix.

h

Calculated based on volumetric rule of mixtures of the components.

A quantitative comparison of the predicted damage geometries is given in Fig. 10. SEM-based measurements were chosen as baselines due to their clear feature outlines and reliability. In assessing the plot, there is good agreement for HAZ size prediction along the fiber for exposure times >200 ms. There is, however, a slight underestimation at 100 ms. This may be due to the greater effect of loss mechanisms such as convection and reradiation by vapor particles at lower exposure times where the temperature is much closer to the matrix decomposition temperature. In comparison, the predicted HAZ size in the direction transverse to the fibers is slightly lower for exposures <300 ms and slightly higher for exposures >300 ms. The overall discrepancy in the transverse damage prediction is very likely due to the difficulty in properly representing the manner of conduction where the matrix is more critical and the assumed rule of mixtures strategy fails to suffice. Despite these shortcomings, it is still the case that the conduction-based damage analysis is a physics-based approach for predicting the irradiation response of the CFRP. However, a more rigorous prediction is needed. As perceived from the current exercise, future efforts will necessitate the availability of more reliable thermal and optical properties for the CFRP constituents as well as analytically driven numerical approaches, which take into consideration heat loss mechanisms during irradiation.

FIG. 10.

Plot of the predicted and baseline HAZ sizes parallel and transverse to the fiber direction as a function of exposure time. The baseline is taken as the electron micrograph-based measurements from Fig. 5.

FIG. 10.

Plot of the predicted and baseline HAZ sizes parallel and transverse to the fiber direction as a function of exposure time. The baseline is taken as the electron micrograph-based measurements from Fig. 5.

Close modal

The time-dependent behavior of CFRPs irradiated by a pulsed laser source was determined using surface and subsurface characterization approaches. Irrespective of the irradiation time, an HAZ develops from the irradiation process with matrix recession and no visible damage to the fibers. This HAZ becomes more pronounced along the fiber direction with time due to the high conductivity of carbon fibers. Out-of-plane extrusion of the composite surface occurred due to the expansion of matrix vapor (gases).

Prediction of the surface HAZ via simple heat conduction approach was also performed. The results showed that the geometry and growth of the HAZ is predicted well with conduction. However, there were limitations in matching the predicted HAZ boundary with measurements obtained from experiments, especially in the direction transverse to the fibers. It is noted that this discrepancy arises from loss mechanisms that are not considered (convection and radiation), as well as overestimation of the optical and thermal properties of the CFRP by the rule of mixtures.

Fundamental understanding of the response of CFRPs to repeated laser pulse irradiation is especially important for processing purposes. The findings from this study show the need to consider simple composite layups as a starting point for developing an understanding of HAZ formation. Unlike woven fabric-based CFRPs, unidirectional fabric arrangements show the importance of anisotropic thermal properties in driving the damage morphology. Therefore, it is possible to reduce pulsed laser induced HAZ by tailoring the thermal properties of the composite constituents.

The study also identifies thermal conduction as a key parameter for approximating the size of the damage zone. This implies that pulsed laser irradiation conditions relate to cumulate heating events. However, more robust analytical/numerical approaches are still needed to address intermittent cooling during pulses and subsurface heating with the inclusion of defects and interfaces.

The authors would like to thank Srinavasen Chandrasekar, Director of Purdue’s Center for Materials Processing and Tribology, for providing the means to perform the surface profile measurements and Mojib Saei for providing hands on assistance in the process. We would also like to thank Purdue’s Center for Particulate Products and Processes (CP3) for providing the tools to run and analyze the X-ray micro-CT scans. The author(s) declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The authors acknowledge financial support from the Office of Naval Research (ONR) under Grant No. N00014-17-1-2711 (Program Manager: David Shifler) for the research, authorship, and/or publication of this article.

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