Temperature-dependent cutting physics in orthogonal cutting of carbon �bre reinforced thermoplastic (CFRTP) composite

The global commitment towards reducing carbon emissions drives the implementation of sustainable carbon-fibre-reinforced-thermoplastic composites (CFRTPs). However, the machining of CFRTPs presents challenges due to the material’s ductile -brittle composition and sensitivity to machining-induced high temperatures. For the first time, we conducted temperature-controlled orthogonal cutting of CFRTP (using CF/PEKK as a demonstrator) to unveil its temperature-dependent cutting physics. Three representative cutting temperatures,


Introduction
Manufacturing industry is one of the most significant industries that contribute towards the global socio-economic growth.As the world seeks to reduce carbon emissions to meet the urgent environmental targets, there has been an unprecedented demand for the deployment of high performance/lightweight materials such as carbon fibre reinforced polymer (CFRP) in various manufacturing sectors, including energy [1], automobile [2] and aerospace [3].
Machining processes, including drilling, milling, turning, etc, are frequently utilized in CFRP manufacturing to precisely cut, shape, and finish parts and structures while minimizing fibre damage and maintaining the material's mechanical properties [4,5].However, due to the ease of damage formation, high cost of specialized cutting tools and the time-consuming / energy intensive nature of the process, machining can account for up to 25% of the total production cost of CFRP components [6].
In recent years, carbon fibre reinforced thermoplastic composites (CFRTPs) are increasingly used in various industry sectors to replace conventional thermoset CFRP (mainly carbon fibre reinforced epoxy (CF/epoxy)), due to their high impact resistance, short cycle time, less critical preservation conditions and high production turnover [7].The thermoplastic nature of CFRTP matrices also significantly enhances the products' recyclability and repairability [8], making them a promising material candidate for next generation sustainable aircraft structures.Although many CFRTP parts can be moulded into net shapes [9], machining still remains an indispensable process in meeting the stringent dimensional accuracy and achieving reliable joining of dissimilar materials (e.g.CFRTP with Ti or Al alloys ) [3].
Several pioneer research on CFRTP machining (e.g.carbon fibre reinforced poly-etherketone-ketone (CF/PEKK) [10,11], carbon fibre reinforced poly-ether-ether-ketone CF/PEEK [12] and carbon fibre reinforced polyurethane (CF/TPU) [13]) reported various machining induced defects (such as delamination [11], burr [14], thermal degradation [10], fibre debonding [12] and surface cavity [11]), which are highly sensitive to the machining induced high temperatures (up to 200 o C [10,15]).These defects not only affect the parts' surface quality/assembly tolerance, but also compromise their reliability and lead to high part rejection rate [16][17][18].The rapid tool wear and severe tool clogging associated with CFRTP machining is another significant challenge, which contribute greatly to the increased manufacturing cost and wasteful power expenditure [19,20].Due to their unique ductilebrittle material composition and the presence of temperature sensitive thermoplastic matrix, the machining behaviour of CFRTP is distinctly different from that of the conventional thermosetting CF/epoxy [10,21].However, despite intensive research and development on CFRTP, the understanding of its cutting physics, especially the associated damage formation under different machining temperatures, is still very limited.
In common composite machining processes such as drilling, milling and turning, the workpiece material is subjected to local transient orthogonal cutting force exerted by the tool cutting edge [22].Recently, Wang et al. [23] and Qin et al. [24] developed macroscale and microscale finite element analysis (FEA) numerical models respectively, to simulate the chip formation of CF/PEEK during orthogonal cutting.Li et al. [22] and Ge et al. [20] utilized the Johnson-Cook (JC) model to simulate the matrix material behaviour in orthogonal cutting of CF/epoxy and CF/PEKK.Nevertheless, a notable constraint of these studies is that they do not incorporate the matrix thermal softening effect into their models.Specifically, these models only considered the room temperature material properties and neglected the temperature change associated with the cutting process.Consequently, they failed to capture the change of matrix stiffness/strength caused by machining induced high temperatures, and hence cannot truly represent the practical machining conditions.While a macroscale model based on Hashin and Puck criterion by Han et al. [25] considered the thermal effect in CF/epoxy orthogonal cutting, this model failed to capture the subsurface microstructural damage (e.g.fibre deflection and interface debonding) under different temperatures, due to the simplification of CF/epoxy composite as an equivalent homogeneous material (EHM).
Another microscale model developed by Xu et al. [26] simulated the subsurface microstructural damage qualitatively.However, the subsurface damage depth has not been quantified due to the lack of robust temperature-dependent material constitutive models for matrix and fibre-matrix interface (i.e.without considering matrix plasticity, the change of interface strength and fracture toughness).Therefore, a high-fidelity microscale numerical model considering the temperature-dependent properties of composite's different constituents (especially the matrix and the interface) is crucial for developing insight into the material removal mechanisms and associated subsurface damage under different temperatures.
Given the mechanical properties of the thermoplastic matrix / fibre-matrix interface can deteriorate drastically as the temperature approaches / exceeds the glass transition temperature (Tg) of the matrix [27,28], we hypothesize that the machining induced high temperatures would have a strong impact on the cutting physics of CFRTP.Despite its significance, this research area remains understudied.CF/PEKK, a high performance CFRTP, has outstanding mechanical properties, wide processing window, and high thermal stability (Tg ~159 ℃) [10].These qualities make it a top choice for aircraft structures.
In this work, temperature-controlled orthogonal cutting experiment was conducted on CF/PEKK as a demonstrator material, to reveal the impact of different temperatures (i.e.ambient temperature, below Tg and above Tg) on its machining behaviour.This is the first study to reveal the impact of temperature on machining of CFRTP.To unveil the complex material removal mechanisms and damage mechanics, we further develop a microscale FEA model to simulate the chip formation and surface/subsurface damage evolution.This model introduces a novel approach by incorporating temperature-dependent materials properties (i.e., the PEKK stiffness / strength, and the fibre-matrix interface strength / fracture toughness) under direct implementation of temperature fields.The simulation results are also well validated by experimental observation.

Temperature-controlled orthogonal cutting
The experiment setup for temperature-controlled orthogonal cutting is shown in Fig. 1 (a).
The experiment was conducted on a Deckle FP3A 3 axis CNC machine (spindle locked).The cutting force was recorded in-situ using a Kistler 9272 4 component dynamometer with a sampling frequency of 18 kHz.The cutting tool (solid carbide with TiAlN coating, Changzhou Aitefasi Tools Co., Ltd.) has a rake angle of 10°, flank angle of 18° and cuttingedge radius of 8 μm.The experiment was conducted at four typical fibre cutting orientations θ (defined in Fig. 1 (b)), namely, 0°, 45°, 90° and 135°, respectively.A depth of cut a p =150 μm and a cutting speed of υ c =500 mm/min were selected following published work [31].Three cuts were performed for each set of parameters to ensure repeatability.To eliminate the effect of tool wear, the cutting tool was replaced after every three cuts and no significant change of edge radius and edge chipping/rounding were observed under Alicona.℃ (ambient temperature), (b) 100 ℃ (below Tg) and (c) 200 ℃ (above Tg) were deployed for the temperature controlled orthogonal cutting to reveal their effects on material's cutting physics.To ensure the temperature uniformity, the testing workpiece were heated on both sides using heating elements (Haljia, 12V 30W) until the temperature reached equilibrium [31].The heating elements were covered by high temperature polyimide tapes (3M 5413) to avoid their adhesion to the workpiece.The temperature of the surface under machining was monitored using a FLIR A6751 infrared thermal camera (125Hz, 640 pixel × 512 pixel) to ensure the temperature control/measurement accuracy.The maximum temperature of CF/PEKK workpiece surface (T max ) during orthogonal cutting was measured in situ.

Post-machining characterisation
The morphology and roughness of the machined surface were analysed by Alicona infinite focus G5 microscope (10× magnification).The chip morphology, machined surface morphology and subsurface damage (side surface image) were observed by SEM.The samples were gold sputtered prior to SEM inspection.

FEA model configuration
To provide further mechanistic insights to the material deformation/fracture during machining, 3D microscale FEA models were developed for UD CF/PEKK orthogonal cutting using ABAQUS/Explicit 2018.Fig. 2 shows a representative configuration of the FEA model (θ=45°).Specifically, the cutting tool was modelled as a rigid body, with its geometries (edge radius, rake angle and flank angle) representing those of the actual cutting tool.The workpiece (2mm × 2mm × 1 μm) consists of three individual constituents (carbon fibre, PEKK matrix and the interface).In accordance with the well-established approach [33], the nominal diameter of the fibres was used as the fibre width in the FEA model and the width of the PEKK matrix was determined from the nominal fibre volume fraction (60%), see Fig. 2.
As suggested in previous studies [33][34][35], such planar microscale model can accurately capture the deformation/damage of each constituent (fibre, matrix and interface) while minimizing the computation time.The carbon fibres and matrix were modelled using solid elements C3D8R with element deletion and enhanced hourglass control and the fibre/matrix interface was modelled as a cohesive contact surface.The workpiece was fully constrained at its bottom and its movement in the y direction was constrained on the left surface [36].The out-of-plane movement of the side surfaces was also constrained in the x direction to avoid potential buckling or bending [34].The interaction between the cutting tool and the workpiece was modelled using ABAQUS penalty contact involving Coulomb friction model (friction coefficient = 0.3) [24].Temperature measured by infrared thermal camera shows that the maximum temperature rise caused by the cutting process is within 10% of the full temperature range (23 ℃ to 200 ℃) under investigation.Based on this, the following assumptions were made for our microscale FEA modelling: (1) The temperature of the machined work piece is close to constant during the machining process and temperature change caused by the cutting process is negligible.
Therefore, the effect of frictional heat generation and transfer is not considered.
(2) Isothermal condition can be adopted by direct implementation of a constant temperature field T c to capture the temperature-dependent properties of each constituent of CF/PEKK composite, while optimizing the computational performance and cost.

Carbon fibre
According to the literature [22,36], carbon fibre can be considered as a typical linear elastic and transversely isotropic material.The constitutive model of carbon fibre is defined by Eq.
(1) based on the elasticity theory [37]: C= where C is the stiffness matrix, σ the stress tensor and ε the strain tensor.1, 2,3 represent the fibre longitudinal and two perpendicular transverse directions, respectively.E ii , ν ij , and G ij (i,j=1, 2, 3) are the Young's modulus, Poisson's ratio and shear modulus, respectively.

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Out-of-plane shear failure: When any of the damage variables reaches 1, the carbon fibre fails and the element will be deleted.The material constitutive model and the damage criterion of carbon fibre are defined by a user subroutine VUMAT in Abaqus/Explicit.As the carbon fibre is thermally stable up to 1000 ℃ [38], their mechanical properties are assumed to be temperature-independent in this study.The mechanical properties of carbon fibres deployed in the simulation are summarized in Appendix B Table B. 1.

PEKK matrix
The PEKK matrix can be modelled as an isotropic and elastoplastic material [27,28] and its constitutive model is highly dependent on temperature.PEKK is expected to transit from glassy to rubbery state as the temperature approaches its Tg, and this will result in a dramatic change of its elastic modulus and strength.The material shows a linear elastic behaviour when the stress is lower than the yield stress σ y0 , which can be defined as: where  ,  and  are the stress, elastic strain and the Young's modulus of the PEKK matrix.
When the applied stress exceeds the PEKK yield strength, the material enters a plastic state, and the Johnson-Cook (JC) constitutive model can be deployed to reflect its temperaturedependency [28]: where  is the flow stress, A is the yield strength at the reference temperature and reference strain rate, B, n and C are the strain hardening coefficient, the strain hardening power coefficient and the rate hardening coefficient, respectively.ε pl is the equivalent plastic strain, ε̇p l the equivalent plastic strain rate and ṙ ef  the reference strain rate.T is the temperature, m the thermal softening power coefficient and T * the homologous temperature defined by: where T ref is the reference temperature, and T mel the melting temperature of PEKK matrix.
Therefore, the effect of thermal softening of the PEKK can be taken into consideration in this model.The failure of PEKK matrix occurs when the equivalent plastic strain reaches the fracture strain ε 0 pl .The plastic and damage behaviour of the PEKK matrix are defined by the built-in JC model and ductile damage in Abaqus/Explicit.The corresponding material properties used for the simulation can be found in Appendix B Table B. 1.

Fibre-matrix interface
The fibre-matrix interface is modelled by the cohesive contact behaviour in Abaqus/Explicit and traction-separation law is deployed to define its deformation behaviour [39], see Under normal/ shear loading.The cohesive damage is defined by the quadratic traction criterion as: where t n 0 , t s 0 and t t 0 represent the maximum strength in normal and two shear directions, respectively.t n , t s and t t are the traction stresses.
The mixed-mode damage evolution is deployed by implementing Benzeggagh-Kenane (BK) fracture criterion: where 09 is the material mix-mode parameter [24].
According to the literature [40], the fibre-matrix interface strength decreases with increasing temperature (similar to the thermoplastic matrix behaviour).Therefore, it is assumed that the interface strength t n 0 , t s 0 and t t 0 decrease proportionally with the matrix strength as temperature increases.The interface strength t i 0 (T) at a specific temperature T can be calculated following: where t i 0 (T r ) is the interface strength at room temperature T r , σ y0 (T r ) and σ y0 (T) are the yield stress of PEKK matrix at room temperature and a specific temperature T, respectively.
According to the modified cohesive zone model developed by Yuan et al. [41] considering thermal effects, the fracture energy of the fibre-matrix interface also reduces with increasing temperature [42,43] and the fracture energy G i C (T) at a specific temperature T can be calculated as [41]: where G i C (T  ) denotes the fracture energy of the fibre-matrix interface at room temperature, and t i 0 (T  ) and t i 0 (T) represent the interface strength at room temperature and a specific temperature T, respectively.
The traction separation law considering thermal softening is depicted in Fig. 3  This is in contrast to machining of CF/epoxy under similar conditions, where powdery chips were produced from cutting [44,45].This is because, epoxy is a typical brittle matrix with low fracture strain (1.5-8.0%[10]), while PEKK matrix has excellent ductility (fracture strain >40% [28]).Fibre-matrix interface separation then occurs along the fibre orientation as a result of the inplane shear stress and fibre extrusion.Consequently, the fibre-matrix interface separation occurs as shown in Fig. 7 (a5) and Fig. 8 (a5) and continuous chips are formed due to ease of chip flowing / evacuation under such condition.The extruded fibres only occurs at regular intervals where the interface shear stress is most concentrated.The larger chip curvature as compared to θ=0° can be attributed to the better alignment of the extruded fibres, which support each other and enhance their resistance against bending [24].
=  ℃: For T c > Tg, the interface separation takes place uniformly across the chips, see    =  ℃: The chips in Fig. 12 (a1) tend to roll up and accumulate in front of the cutting edge.This is attributed to an 85% reduction in the PEKK matrix Young's modulus and a 66% reduction in its yield strength as the temperature increases from 23 ℃ to 200 ℃.The details of the associated subsurface damage will be discussed in Section 4.3.
For θ=135°, the machined surface features severe matrix cracks and torn pits (see Fig. 16 (d1, d2, d3)).The material removal is achieved through bending of fibres (by the tool rake face) rather than shear fracture caused by the cutting edge.The excessive bending of carbon fibres can result in fibre breakage beneath the machined surface as well as matrix crack propagation.With increasing temperature, the mechanical support from the surrounding PEKK matrix deteriorates and consequently more severe bending of carbon fibres occurs to achieve the material removal.This explains the largest cracks present on the machined surface in Fig. 16 (d3).
Fig. 16 (e) depicts the increasing trend of machined surface roughness (Sa) with temperature for all cutting orientations.Sa at θ=135° is the highest and most sensitive to temperature variation (4-fold increase from 23 ℃ to 200 ℃).This shows that temperature is a crucial factor affecting the final machined surface quality, in addition to the previously reported fibre cutting orientation [23] and machining parameters [24].Proper control of the machining temperature is expected to mitigate the machining induced surface damage, which is a potential topic for future research.90°, the cutting tool travels perpendicularly to the fibre longitudinal direction, resulting in severe fibre bending before the ultimate fibre fracture occurs.The PEKK matrix softens and loses its support to carbon fibres under elevated temperature, exacerbating the fibre deflection.Our FEA model again reveals the effect of PEKK thermal softening on the subsurface damage formation (fibre deflection).The finding is in strong contrast to the machining of CF/epoxy under similar condition, where severe fibre fracture was evidenced under the machined surface [5,31].For CF/PEKK, fibre deflects under the machined surface, as the highly ductile PEKK matrix can withstand large extent of plastic deformation.The matrix effectively encapsulates / supports the carbon fibres, therefore suppressing the fibre fracture/crack propagation, and impeding the elastic recovery of the bent carbon fibres.B. 1.The degradation of fibre-matrix interface bonding strength can further contribute to the fibre deflection and subsurface fibre debonding/crack.θ=135° shows the greatest depth of damage amongst all four fibre cutting orientations (from 870 μm to 1766 μm as temperature increases from 23 ℃ to 200 ℃).For θ=135°, the material removal mechanism is dominated by fibre bending fracture, which induces the most severe deflection of carbon fibres.The extent of the subsurface damage reported here is similar to the findings in orthogonal cutting of CF/epoxy [31,46], and our simulation results complied well with the experimental data, with an average prediction error of 11.2%.• For θ = 0°, the material removal mechanism undergoes a transition from fibre bending fracture to a combination of fibre bending fracture and micro-buckling, as the temperature approaches and exceeds Tg.This transition occurs due to the reduced constraint on fibre movement in its transverse direction.Extensive matrix loss and voids tend to form on the machined surface when temperature exceeds Tg, as a result of the severe matrix tearing when removed along with carbon fibres.
• For θ = 45°, the material removal is governed by fibre-matrix interface separation.
With temperature increasing from 23 °C to 200 °C, the chip microstructure evolutes • For θ = 90°, the material removal is dominated by fibre shear/compressive fracture.This causes severe fibre breakage/deflection beneath the machined surface, with maximum subsurface damage extended from 343 μm to 885 μm when temperature increases from 23 °C to 200 °C.The ductile PEKK matrix can withstand large extent of plastic deformation, which impends the elastic recovery of the bent carbon fibres.
• For θ = 135°, the primary mechanism governing the material removal is fibre bending fracture rather than cutting by the cutting edge, which consequently induces severe matrix crack / fibre-matrix interface debonding beneath the machined surface.The maximum subsurface damage depth increases from 870 μm to 1766 μm with temperature rising from 23 ℃ to 200 ℃, due to the 66% reduction in the interface bonding strength.
• The temperature dependency of CF/PEKK cutting physics lies in the deteriorated stiffness and strength of PEKK matrix and loss of fibre/matrix interfacial bonding strength and fracture toughness under elevated temperature (especially when above Tg).This emphasizes the importance of considering high-temperature properties of CFRTP to achieve precise prediction and control of cutting-induced damage.
The findings of this study are expected to have significant implications for the broader composite manufacturing field.The temperature-dependent cutting physics and FEA model developed here can be applied to a wide range of CFRTP composites, including CF/PEEK, CF/ABS, CF/PPS, and others.By providing a fundamental understanding of the material removal and damage formation mechanisms under different temperature conditions, this work opens up new avenues for the development of more sustainable and efficient CFRTP manufacturing processes.The mechanistic insights gained and the methodology established will inform future composite manufacturing research in areas such as cryogenic machining, thermal-assisted machining, vibration-assisted machining, welding, and novel cutting tool design.
It is important to recognize that the current study has certain limitations, primarily in its capacity to capture the intricate interplay of dynamic temperature changes and the associated material deformation processes as observed in real-world machining processes.To address this, future endeavours are encouraged to explore and integrate advanced technologies such as real time Digital Image Correlation (DIC) and micro Computed Tomography (micro CT) to gain deeper insights into deformation behaviour of CFRTPs under dynamic temperature field.It will be of particular interest to explore the cutting behaviour of different CFRTPs around their Tg, to obtain more insights on the effect of CFRTP's unique temperature sensitive mechanical properties.

Fig. 1 (
Fig. 1 (a) Schematic showing the experiment setup for the temperature-controlled orthogonal cutting; (b) Schematic showing orthogonal cutting parameters; (c) IR thermal camera image of heated CF/PEKK composite workpiece ready for cutting PEKK matrix experiences severe loss of stiffness and strength as the temperature approaching its Tg (159 ℃) [32], therefore three typical controlled temperatures (Tc): (a) 23

Fig. A. 1 in
Appendix A shows that the T max under Tc = 23 ℃, 100 ℃ and 200 ℃ during machining are within the ranges of: 42.7 ±5.9 ℃, 101.9 ±1.3 ℃, and 201.7 ±1.3 ℃, respectively.This indicates the cutting process has only induced minor temperature rise of workpiece and negligible influence on the associated material properties under each specific temperature range.

Fig. 2
Fig. 2 Schematic showing a representative setup of the FEA model (θ=45°) 3.2.Material constitutive models and damage criteria Detailed constitutive models and damage criteria for the three different constituents are defined as follows.

4 . Results and discussion 4 . 1 .
Fig. 3 (a) Traction separation law considering thermal softening; (b) Change of interface strength t i 0 and fracture energy G i C against temperature 4. Results and discussion 4.1.Material removal mechanisms based on chip analysis To obtain an in-depth understanding of the material removal mechanisms under different T c , microscopic analysis of chips was carried out.4.1.1.Material removal at θ=0° At θ=0°, continuous chips were produced under all three T c (see Fig. 4 (a2) -Fig.6 (a2)).
The substantial plastic deformation (smearing) of PEKK matrix is well evidenced in Appendix C Fig.C. 1.  =  ℃ and   =  ℃ : The back surface of the chips (chip surface in contact with tool rake face) is smooth and continuous due to matrix smearing (see Fig.4(a2) and Fig.5

Fig. 9 (
Fig. 9 (a3).This can be associated with the 66% reduction of the fibre-matrix interface bonding strength as compared to room temperature (as demonstrated in Appendix B Table B. 1).As a result, interface sliding occurs easily under in-plane shear stress exerted by the cutting tool.The chip is stiffer due to the reduced relative movement between adjacent fibres, hence a chip with larger curvature radius than those of T c = 23 ℃ and T c = 100 ℃ is produced, see Fig. 9 (a1).

Fig. 18
Fig. 18 Subsurface damage at fibre cutting orientation θ=45° under different Tc : (a1-a3): experimental results; (b1-b3) FEA simulation (black dashed lines denote the machined surface, yellow dashed lines denote the depth of the maximum subsurface damage and black arrow denotes the cutting direction) Fig. 19 (a1-a3) shows the subsurface damage at θ=90°, which features fibre deflection along the cutting direction.As Tc increases from 23 ℃ to 200 ℃, more severe fibre deflection occurs, with maximum subsurface damage extended from 343 μm down to 885 μm.At θ =

Fig. 19
Fig. 19 Subsurface damage at fibre cutting orientation θ=90° under different Tc : (a1-a3): experimental results; (b1-b3) FEA simulation (white dashed line denote the deformed fibre profile, black dashed lines denote the machined surface, yellow dashed lines denote the depth of the maximum subsurface damage and black arrow denotes the cutting direction) Subsurface damage at θ=135° features matrix crack/debonding, see Fig. 20 (a1-a3).The cracks and tears caused by severe fibre bending deflection on the machined surface can be easily transmitted along the fibres, leading to subsurface matrix cracks/debonding.With Tc increasing from 23 ℃ to 200 ℃, the maximum subsurface damage depth increases from 870

Fig. 20
Fig. 20 Subsurface damage at fibre cutting orientation θ=135° under different Tc : (a1-a3): experimental results (insets: side surface before polishing); (b1-b3) FEA simulation results of subsurface damage (black dashed lines denote the machined surface, yellow dashed lines denote the depth of the maximum subsurface damage and black arrow denotes the cutting direction) Fig. 21 summarizes the experimental and simulated maximum depth of the subsurface damage for each fibre cutting orientation θ under three Tc.The clear increasing trend of damage with temperature can be related to the degradation of PEKK matrix mechanical properties under elevated temperatures, see Appendix B Table B. 1.The degradation of

Fig. 21
Fig. 21 Experimental and simulation results of the maximum depth of subsurface damage for different fibre cutting orientations 5. Conclusions This is the first study reporting temperature-controlled orthogonal cutting of CFRTP where CF/PEKK was chosen as a demonstrator material.Associated temperature-dependent material removal behaviour and damage formation have been revealed through advanced microscopic analysis of chips and the machined surface.To provide further insights into the cutting physics, a novel high-fidelity microscopic FEA model has been developed by incorporating temperature-dependent constitutive behaviours of PEKK matrix (stiffness and strength change) and fibre-matrix interface (strength and fracture toughness change), to achieve a more realistic representation of the cutting process in the context of CFRTP machining.The main findings and contributions of this work can be summarized as follows: extrusion to individual fibres extrusion along the fibre-matrix interface.The subsurface damage features fibre debonding / breakage and the maximum subsurface damage depth rises from 8.2 μm to 48.1 μm, as the thermal softening of PEKK leads to decreased support of carbon fibres against bending deformation.

Fig. A. 1
Fig. A. 1 Maximum workpiece temperature (Tmax) under different Tc conditions Appendix B. Parameters deployed in FEA simulation

Fig.B. 1 Fig
Fig.B. 1 The traction-separation law for cohesive contact behaviour (a) normal direction; (b) shear direction