Unfolding the early fatigue damage process for CFRP cross-ply laminates

This study investigates the early fatigue damage of cross-ply carbon/epoxy laminates. The aim is to unfold the damage accumulation process, understand the interaction between different damage mechanisms, and quantify their contribution to stiffness degradation. Tension-tension fatigue tests were performed, while edge observation and DIC technique monitored the damage evolution. It was found that different accumulation process and interactive levels between transverse matrix cracks and delamination exist for specimens with similar stiffness degradation. A linear increase of stiffness degradation was observed with the increase of matrix crack density, while the growing trend of stiffness degradation converged with the increase of delamination.


Introduction
During in-service life, composite laminates are subjected to a variety of loads over time that induce fatigue damage and as a consequence degrade the mechanical properties of the structure. The fatigue damage levels and corresponding loading capacities are generally represented by degradation of stiffness [1][2][3] and variation of self-generated temperature [4][5][6] from the macroscopic perspective. In view that stacking sequences and material properties of laminates determine if thermomechanical effects are detectable, measuring of temperature variation is less universal than that of stiffness variation. A three-stage process in a rapid-slow-rapid manner has been reported as the representative stiffness degradation for laminates under fatigue loading, as illustrated in Fig. 1 [1][2][3]. Considering that the stiffness degrades significantly in early fatigue life, it would be of great interest to firstly put emphasis on early fatigue damage, uncovering which damage mechanisms accumulate, how they interact and affect the stiffness degradation. This may also help gain a better insight of the significant scatter phenomenon about failure life for composites and further pave the way to probabilistic predictions of fatigue life with physics of damage involved.
Early fatigue damage usually refers to damage within the first 10% of the fatigue life that distributes throughout the entire laminate leading to stiffness degradation and specimen heating [7,8]. As is matrix-dominant, it contains two kinds of mechanisms: off-axis matrix cracks and delamination.
For coupon-level laminates, off-axis matrix cracks usually generate from free edges due to stress concentration which then propagate through the fibre direction [9,10]. Their initiation, driven by local maximum principal stress and local hydrostatic stress in the matrix [11], appears at the first few cycles when the maximum stress under fatigue loading is higher than the threshold stress to induce off-axis matrix cracks under quasi-static loading, otherwise the initiation delays [9]. Considering randomly-distributed micro-defects, such as voids, inclusion of foreign particles and local fibre-matrix debonding, which usually occurs during the manufacturing process [12], the resistance to off-axis matrix cracks under fatigue loading varies among local regions of a laminate [13]. As a result, the fatigue life, when the first off-axis matrix crack occurs, usually presents a significant scatter band, especially for low stress levels [10,11,14,15]. During the subsequent fatigue cycles, the number of off-axis matrix cracks gradually increases up to a saturation state, which is also termed as Characteristic Damage State (CDS) [1,2,16]. It has been proposed that the CDS is independent to loading conditions and only depends on laminate layups, geometries and material properties [1,2], while experimental evidences [16][17][18] showed that both fatigue life and matrix crack density at CDS depend on stress levels and loading control modes, and they can be even different among specimens under the same loading condition [15].
Delamination is another damage mechanism that appears at the early fatigue life of a laminate and it usually originates from the tips of off-axis matrix cracks or free edges due to the high inter-laminar stress concentrations [1,5]. Initially, it was hypothesized that, delamination initiate after CDS [1], however, experimental observations [2] showed that before reaching CDS, delamination may appear specifically at regions with high density of off-axis matrix cracks. Furthermore, Hosoi et al. [19] reported that edge delamination initiates and propagates before or simultaneously with the initiation of off-axis matrix crack under low stress level. Xu et al. [20] proposed that the constraining determine whether off-axis matrix cracks would initiate before or after the onset of delamination. Pakdel and Mohammadi [2] and Shen et al. [17] concluded that delamination could postpone or prevent further generation of off-axis matrix cracks at neighbouring regions. Further, based on the stress state analysis of co-existing off-axis cracks and delamination, Talreja [21] found that the maximum axial stress in the middle of adjacent cracks at the off-axis plies decreases with the increase of delamination length, causing the reduction of driving force for producing new off-axis matrix cracks. These different occurring sequences of the off-axis matrix crack initiation, saturation and delamination initiation reflect multiple levels of interaction behaviours between both damage mechanisms.
The accumulation and interaction of fatigue damage produce cyclicdependent deformation, accompanied with time-dependent deformation (i.e. creep) induced by the viscoelasticity of matrix [22]. Both types of deformation contributes to significant stiffness degradation and it appears within a short duration of fatigue life at Stage I, followed by Stage II that occupies most of the fatigue life where the stiffness almost remains constant and Stage III with sudden drop of stiffness, as presented in Fig. 1. Different phenomenological models have been established to describe the degradation process [23], and they were also implemented afterwards into fatigue progressive damage frameworks for fatigue life prediction [24,25]. In some prior studies [1,5], off-axis matrix cracks were founded to be the only damage mechanism at Stage I, after which delamination occur at Stage II followed by fibre breakage at Stage III. As the non-interactive scheme about fatigue damage accumulation, the transition point of stiffness degradation from Stage I to Stage II is ideally at CDS (see Fig. 1). For this case, off-axis matrix cracks are the only contributor to stiffness degradation within Stage I [16,17,26]. Accordingly, in the progressive fatigue damage model proposed by Shokrieh    laminates within Stage I, which is then terminated by a sudden 90-ply discount when reaching CDS [27,28]. Wharmby et al. observed a linear relationship between the normalized stiffness and matrix crack density [29]. However, in case that both damage mechanisms interact within Stage I, at which moment CDS occurs: within Stage I, at the transition point of the first two stages or within the Stage II, as marked in Fig. 1, and how off-axis matrix cracks and delamination contribute to stiffness degradation individually have not been studied yet. A fundamental understanding towards this direction could be achieved by performing experimental campaigns aiming to isolate each damage mechanism and identify the moments of interaction. So far, different damage monitoring techniques have been involved to investigate the progressive damage behaviour of composites under fatigue loading. For Glass Fibre Reinforced Polymer, due to their high transparency, in-situ monitoring of matrix crack density and delamination area has been successfully achieved by transmitted light photography combining with post image processing [17,26,[29][30][31]. However, this technique is not applicable for non-transparent composites like Carbon Fibre Reinforced Polymer (CFRP), and a challenge still remains for the detection of delamination. A common practice is to perform multiple interruptions of the fatigue testing for in-situ/ex-situ crack replica or microscopy inspections on edges [2,3,32,33], and exsitu examination of internal damage (i.e. off-axis matrix cracks towards the width direction and delamination) using X-radiography [18,19,33,34], which actually affects both fatigue life and damage accumulation process of composites [35,36]. Therefore, experimental improvements towards in-situ damage monitoring, especially for delamination, are needed for CFRP composites.
In the present study, edge observation and Digital Image Correlation  (DIC) techniques were used under tensile-tensile fatigue loading to achieve in-situ damage monitoring of cross-ply CFPR laminates. Stiffness degradation and accumulation of both damage mechanisms (i.e. transverse matrix cracks and delamination) were characterized and quantified in the early fatigue life. The objectives are to explore the accumulation and interaction of early fatigue damage occurred at Stage I, and to further understand the contribution of each damage mechanism to stiffness degradation.

Material and specimens
The specimens used in the present work were fabricated using unidirectional (UD) Prepreg named Hexply® F6376C-HTS(12 K)-5-35% with high tenacity carbon fibres (Tenax®-E-HTS45) and a tough epoxy matrix (Hexply® 6376) involved. This UD Prepreg system has a nominal ply thickness of 0.125 mm and a nominal fibre volume content of 58%. The laminated panels of 300 mm × 300 mm size and stacking sequence of [0 2 /90 4 ] S were cured inside an autoclave according to recommendation from Hexcel [37], and the material properties of UD lamina in cured condition is listed in Table 1 [38]. Based on ASTM D3479/D3479M-19 standard [39], the cured panels were cut into rectangular shape with 250 mm × 25 mm size using a water-cooled diamond saw and both ends of specimens with 50 mm length were glued with thick paper tabs using cyanoacrylate adhesive to increase clamping grip (see Fig. 2(a)).

Test set-up
Seven specimens were tested under tension-tension fatigue loading on a 60 kN hydraulic fatigue machine at room temperature. The test setup and a schematic representation of applied loading profile, containing the repetitive cyclic loading blocks and the tensile loading-unloading ramps, are shown in Fig. 2(b) and (c), respectively. Constant amplitude of sinusoidal waves, with maximum stress of 507 MPa (70% of UTS), stress ratio 0.1 and frequency 5 Hz were applied, while the tensile loading and unloading ramps were applied before and after every 500 cycles with the rate of 19 kN/s. The maximum stress was determined based on the results of static tensile and preliminary fatigue tests. During tests, two 9 Megapixel cameras with 50 mm-focal-length lens were placed at left and right sides of the clamped specimens to monitor the damage on both edges. The edge surfaces of each specimen were covered with thin white paint in order to enhance the white-black contrast of cracked and uncracked regions. Furthermore, the exterior 0ply was painted with a white base coat and printed with black dots using a speckle roller with the dot size of 0.18 mm. A second pair of 5 Megapixel cameras with 23 mm-focal-length lens was placed in the front of specimens to measure the in-plane strain field. All cameras were triggered simultaneously during the tensile loading-unloading ramps to capture images every 50 ms. Tests stopped when reaching 10 5 cycles, which guarantees that the stiffness degradation develops through the Stage I and approaches to the stable phase of Stage II. Two specimens were scanned by an ultrasonic C scanner to detect the delamination area after test.
A user-defined MATLAB image-analysis code was developed to count the number of transverse cracks at 90 plies and measure the length of inter-laminar cracks at 0/90 interface. As for the DIC

Table 2
The value of crack growth factor a and related R-square.

Specimen
Group 1 Group 2  calculations, a subset size of 29 pixels and step size of 7 pixels were fixed for all specimens. The interest area was fixed at gauge region with~80 mm length for both edge damage and DIC (see Fig. 2(a)).

Longitudinal stiffness
Stress/strain hysteresis loops are usually used to obtain secant stiffness and dynamic stiffness (also termed as fatigue stiffness [40]) with and without considering the creep effect respectively [41]. In the present study, dynamic stiffness along the axial direction was calculated every 500 cycles, based on the slope of σ xx and ε xx for each tensile loading ramp (see Fig. 2(c)), where σ xx is the axial stress and ε xx is the average axial strain as calculated by the DIC. Fig. 3 plots normalized longitudinal stiffness E N /E 0 in function of number of cycles N. E 0 is the initial axial stiffness obtained from the first tensile loading ramp (see Fig. 2(c)) and E N is the degraded axial stiffness at cycle N. Furthermore, the transition points from Stage I to Stage II, quantified as the moment when E N /E 0 decreases less than 0.001 every 5 data points, are also marked in the pentagon shape (see Fig. 3) Until the end of Stage I, stiffness degraded about 8% to 11% and a slower decreasing rate was shown for specimens of Group 2 than that of Group 1 (see Fig. 3). In a linear-elastic material system, energy dissipation can be derived from stiffness degradation under constant load or displacement [42]. Based on this, a slower increasing rate of dissipated energy can be inferred for specimens of Group 2 than Group1. The reason for different rates of stiffness degradation and dissipated energy between both groups is the damage accumulation process which should be further explored.

Accumulation process of early fatigue damage
In the present study, early fatigue damage is focused at Stage I, which contains off-axis matrix cracks, also named as transverse matrix cracks for cross-ply laminates, and delamination.

Transverse matrix cracks
Transverse matrix cracks initiated within the first 500 cycles for most of specimens, except specimen #2-2 and #2-3 which delayed to the third and fifth 500 cycles respectively. During the tests, most of transverse matrix cracks were extended throughout the entire width immediately due to the thick 90-ply block in the middle of laminates. To further quantify the accumulation process, matrix crack density ρ was introduced, which was calculated by the average number of transverse matrix cracks at both edges divided by the gauge length (~80 mm). Fig. 4 presents the matrix crack density ρ as a function of number of cycles N until CDS for two groups of specimens. Compared with Group 1, ρ at Group 2 started with a particularly slow increase up to certain cycles (i.e. N c1 , N c2 and N c3 for specimen #2-1, #2-2 and #2-3 respectively, as marked in Fig. 4(b)), after which the growing trends were suddenly accelerated and then the similar increasing trends as Group 1 was observed. This difference is caused by the generally higher fatigue resistance of specimens in Group 2 than that in Group 1. To establish a phenomenological relation between ρ and N, one fitting function was selected as follows: where a, b and N c are model parameters. Here, N c is used to eliminate the initial section where slow crack generation appeared at the beginning of tests and b is regarded as constant among specimens of each group. For Group 1, N c = 0 and b = 7 × 10 −5 ; for Group 2, N c = min{ N c1 , N c2 , N c3 } = 6500 and b = 5.46 × 10 −5 . The final fitting functions and curves for each group are shown in Fig. 4. Obviously, only a determines the growing trend of ρ(N) and is defined as a crack growth factor in the present study. Table 2 listed the value of a and related Rsquare. Despite similar stiffness degradation within each group, the accumulation process of transverse matrix cracks is different (see Fig. 4), further resulting in the scatter of saturated matrix crack density ρ s and fatigue life N s at CDS. Fig. 5 shows linear relationships between ρ s and N s . For both groups, the higher the ρ s was, a smaller number of fatigue cycles were needed to reach CDS. The decreasing trends of N s with ρ s were similar among both groups. In addition, ρ s ranged from around 0.21 to 0.35 mm −1 while the difference of N s was about 10,000 cycles among specimens of each group. Fig. 6 presents number of cycles N and normalized longitudinal stiffness E N /E 0 at CDS and at the end of Stage I. For most specimens, accumulation of transverse matrix cracks consumed 56%-75% of fatigue life within Stage I, while 73-89% of stiffness degradation was occurred until CDS, except specimen #1-3 for which the accumulation of matrix crack consumed 27% and 43% of the fatigue life and stiffness up to the end of Stage I. The results indicate that a different damage mechanism, e.g. delamination, occurred within Stage I and contributed to stiffness degradation. Therefore, it would be of great interest to investigate when delamination initiates and understand how it interacts with transverse matrix cracks and degrades stiffness.

Delamination
Oz et al. observed Poisson contraction and transverse strain concentrations through DIC at the exterior surface of quasi-isotropic CFRP laminates when delamination was generated at interfaces [43]. Following this observation and aiming at developing a DIC-based parameter to describe the delamination accumulation inside the CFRP laminates, the relations among transverse strain concentrations, Poisson contraction and delamination are further explored hereafter. Fig. 7(a) shows a linear growth of in-situ Poisson's ratio νwith the normalized area of transverse strain concentration A C at the DIC interest area for all specimens. Here, ν is calculated by − ε ε¯y y xx , where ε yy and ε xx are the average transverse and axial strains of the exterior 0-ply respectively. A C is obtained by the total area of transverse strain concentration divided by the DIC measurement area. The threshold of transverse strain at the concentration region is quantified as the minimum value of transverse strain when ν starts to increase. Moreover, Fig. 7(b) correlates the delamination area from C-scanning with transverse strain concentration area from DIC at numbered local regions for specimen #1-1 and #1-2 after tests stopped at 10 5 cycles, which indicates that transverse strain concentration area can represent the delamination area. Based on all-mentioned above, in-situ Poisson's ratioν can be used to describe the accumulation process of delamination.
Inter-laminar cracks originated at tips of transverse matrix cracks, and then they propagated along 0/90 interfaces with the increase of displacement at the transverse matrix crack surfaces, which also affected the stiffness degradation process as Qi et al. mentioned [13]. Here, inter-laminar cracks ratio I r , obtained by the average of max{ L r1 , L r2 } and max{ L l1 , L l2 } and divided by the gauge length (~80 mm), was used to express the accumulation of inter-laminar cracks. L r1 , L r2 are the total length of inter-laminar cracks located at each interface of the right edge and similarly L l1 , L l2 were for the left edge. Fig. 8(a)-(b) present the evolution of ν and I r as a function of number of cycles while the stars pinpoint the CDS. The in-situ Poisson ratio ν remained stable at the beginning and then continuously increased due to the expansion of transverse strain concentration region, while I r experienced a slowrapid-slow growing trend. For most of specimens, ν ranged from around 0.025 to 0.05 until the saturation of transverse matrix cracks (see Fig. 8(a)) and the corresponding maximum A C was around 0.05 (see Fig. 7(a)) meaning that only 5% of gauge region delaminated. On the contrary, except specimen #1-3, inter-laminar cracks at edges propagated more than~35% of gauge length until CDS (see Fig. 8(b)). These phenomena indicate that delamination propagated faster along the length than within the width of the specimens, as reported by O'Brien [44]. In view that delamination is more likely to concentrate near the edges rather than propagate inside the specimens before CDS, in-situ Poisson's ratio ν is not capable to reflect the delamination propagation during this period.
As a result, the delamination ratio d r , calculated by × ν I r , is proposed hereafter to represent the accumulation process of delamination along both length and width directions, as presented in Fig. 8(c). Compared with Group 2, an earlier increase of d r was observed at Group 1, which indicates specimens with faster stiffness degradation at Stage I accompanied with earlier accumulation of delamination.

Interaction between transverse matrix cracks and delamination
For all specimens at CDS, the inter-laminar cracks occupied around 15%-80% of the gauge length (see Fig. 8(b)), while the delaminated  area fluctuated within 15% according to the range of Poisson's ratio, i.e. 0.023-0.1 (see Fig. 7(a) and Fig. 8(a)). The co-existing of both transverse matrix cracks and delamination indicates the existence of interactive periods between both damage mechanisms, which might cause the differences of damage accumulation process for specimens with similar stiffness degradation and thus need to be further explored. Fig. 9 plots the growing trend of delamination ratio d r with matrix crack density ρ. For both groups, most of specimens experienced an exponential increase of d r when ρ was larger than a certain threshold, approximately 0.1 mm −1 for specimen #1-1/#1-2/#2-1, 0.15 mm −1 for specimen #1-4/#2-3 and 0.25 mm −1 for specimen #1-3/#2-2. The lower this threshold was, the higher the d r was for the same matrix crack density within each group. This fact triggered different levels of    Table 3 The fatigue life at the start and end of interaction for all specimens.

Specimen
Group 1 Group 2 interactions between transverse matrix cracks and delamination, leading to different accumulation of both damage mechanisms for each group. As a result, specimens with larger d rs (i.e. delamination ratio at CDS) showed lower ρ s . The results reflect the constraining effect of delamination on the generation of new transverse matrix crack as reported in literature [2,17,21], which then postpones the occurrence of CDS.
In the same range of ρ s , wider scatter band of d rs was presented for the specimens at Group 1 (see Fig. 9), which indicates the severer interactive levels between both damage mechanisms for specimens with lower initial fatigue resistance. Besides, the lowest level of interaction can be regarded as specimen #1-3 due to the negligible d rs . To quantify the severity of interactive levels between both damage mechanisms, the proposed crack growth factor a was related to matrix crack density and delamination ratio at CDS. In Fig. 10, a linear increase of ρ s as a function of a is presented for both groups, while d rs shows a non-linear decreasing trend with the increase of a. For both groups, lower a corresponds to more significant interaction between transverse matrix cracks and delamination as a result of lower matrix crack density and higher delamination ratio, and vice versa.
In order to explore further the interaction between both damage mechanisms, the growth rates of matrix crack density ρ N Δ /Δ and delamination ratio d N Δ /Δ r with increase of N are presented in Fig. 11. ρ N Δ /Δ was obtained from the fitting function ρ(N) (see Fig. 4). Considering the remarkably slow accumulation process of transverse matrix cracks during the first 6500 cycles for specimens of Group 2 (see Fig. 4(b)), the corresponding ρ N Δ /Δ was zero here. A decreasing trend is showed for ρ N Δ /Δ , and the larger the a (see Table 2) is, the accumulation of transverse matrix cracks happens faster. This fact highlights that a represents the growing trend of matrix crack density. Different from ρ N Δ /Δ , d N Δ /Δ r experienced an increasing trend followed by a gradual decrease till the end of Stage I for most of specimens. The highest d N Δ /Δ r appearred around CDS (marked as stars in Fig. 11(b)) except specimen #1-3 which had a continuously linear increase as a consequence of low-level interaction between both damage mechanisms. A relatively slow growth rate for both matrix crack density and delamination ratio were observed for specimen of Group 2, presenting the consistency of accumulation rate of both damage mechanisms with the degradation rate of stiffness. Within each group, specimens with high ρ N Δ /Δ usually accompanied with low d N Δ /Δ r , which reflects the constraints between both damage mechanisms.

Decoupling of stiffness degradation related to individual damage mechanics
Seeking to understand the accumulation and interaction of transverse matrix cracks and delamination, the contribution of each damage mechanism on stiffness degradation during Stage I should be decoupled. Fig. 12 shows the increase of matrix crack density ρ and delamination ratio d r as a function of stiffness degradation D for specimen #1-2. D is calculated by (E 0 -E N )/(E 0 -E I ) where E I is the dynamic stiffness at the end of Stage I. To decouple D, the first step is to quantify the interaction period at Stage I, where it is assumed that one damage mechanism played the dominant role to degrade stiffness at each moment. Delamination controlled D at the flat section of ρ (see the grey region in Fig. 12), while transverse matrix cracks were the dominant contributor to D at the section where ρ increased rapidly and the effect of delamination on D is ignored in view that d r had a slight increase (see the white region in Fig. 12). As a result, the start of interaction is defined at the moment when ρ remains constant and d r is larger than zero, while the end of interaction is exactly at CDS, as marked in Fig. 12. After CDS,  delamination, as the only active damage mechanism, continued to affect D. Table 3 lists the fatigue life at the start and end of interaction period for all specimens.
Based on what is proposed above, the growing trend of decoupled stiffness degradation, D TC and D del for transverse matrix cracks and delamination respectively, is shown in Fig. 13. A linear increase of D TC is obtained with the increase of ρ, which is also reported by Wharmby et al. [29] As for D del , a non-linear increase with d r is presented for all specimens and the growing trend of D del converges, indicating the existence of a threshold for which further growing of delamination does not affect the stiffness.
In addition, the contributions of transverse matrix cracks and delamination on the stiffness degradation at CDS and from CDS to Stage I are quantified in Fig. 14. For all specimens, the majority of stiffness within Stage I was degraded because of the delamination (see the shadow region) rather than the transverse matrix cracks (see the nonshadow region). Although this observation contradicts part of the literature, which reports that transverse matrix cracks are the dominant damage mechanism for the stiffness degradation during the fatigue life [16,17,26], the delamination's dominance can be attributed to the plyblock of the 90°plies. Until CDS, larger portion of stiffness degradation was produced by transverse matrix cracks (see Region ①), accompanying with less amount induced by delamination (see Region ②) for specimens with higher saturated matrix crack density ρ s . This result reflects the competitive relation between the two damage mechanisms to degrade stiffness. From CDS to the end of Stage I, the stiffness degradation, caused by delamination, was lower at Region ③ than that at Region ②. Only specimen #1-3 showed the opposite phenomenon due to the less significant interaction between both damage mechanisms compared with other specimens. Fig. 15 shows the non-linear growing trends of D TC and D del as a function of N. Compared with Group 1, a slower increase of both D TC and D del with number of cycles was observed for specimens of Group 2 with the slower accumulation process of both damage mechanisms and higher fatigue resistance. As D del increased, the growing rate of D TC decreased due to the restriction from delamination and this fact is evident for the specimens of Group 2 than that of Group 1. After CDS, as a result of the shielding effect between delamination tips propagating towards each other [26], D del was constant within 20,000 cycles for most of specimens with significant interaction between both damage mechanisms.

Conclusions
The accumulation and interaction of transverse matrix cracks and delamination in early fatigue life are characterized and quantified for CFRP cross-ply laminates. The contribution of each damage mechanism on stiffness degradation is also analysed. The main conclusions are listed as follows: (1) Until the end of Stage I, stiffness degrades about 8% to 11% and two groups of decreasing trends are obtained among specimens. (2) In-situ Poisson's ratio at the exterior 0-ply and delamination obtained from C-scanning are correlated with each other through the DIC-based transverse strain concentrations, but the former cannot fully represent the early propagation of delamination concentrated near the edges. The inter-laminar crack ratio I r is introduced, measured by the edge cameras, in order to calculate the delamination near the edges. (3) For specimens where stiffness degrades slower, both damage mechanisms also show relatively slower growth rates and longer fatigue life is consumed to reach CDS. (4) Among specimens with similar stiffness degradation, different accumulation process and interactive levels of transverse matrix cracks and delamination are presented. Lower saturated matrix crack density coexists with larger delamination ratio at CDS, and it takes longer fatigue life to reach CDS. (5) The crack growth factor a can be used to quantify the growth rate of matrix crack density and the interactive levels between both damage mechanisms. Low a corresponds to slow accumulation of transverse matrix cracks and significant interaction between both damage mechanisms. (6) Delamination is responsible for larger stiffness degradation than transverse matrix cracks at Stage I. This observation is attributed to the ply-block of 90°plies. A linear increase of stiffness degradation is obtained with the increase of matrix crack density, while the growing trend of stiffness degradation due to delamination converges with the increase of delamination ratio.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.