Nearly Mode I Fracture Toughness and Fatigue Delamination Propagation in a Multidirectional Laminate Fabricated by a Wet-Layup

Five double cantilever beam specimens were tested quasi-statically to obtain a GIR resistance curve. In addition, nine double cantilever beam specimens were tested in fatigue to obtain a Paris-type relation to describe the delamination propagation rate da/dN where a is delamination length and N is the cycle number. Displacement ratios of Rd = 0.10 and 0.48 were used for five and four specimens, respectively. The specimens were fabricated by means of a wet-layup process from carbon fiber reinforced polymer plies. The interface containing the delamination was between a unidirectional fabric and a woven ply. The fracture toughness and fatigue delamination propagation protocols are outlined. The mechanical and thermal residual stress intensity factors were obtained by means of finite element analyses and the conservative M-integral along the delamination front. They were superposed to determine the total stress intensity factors. It was found that the total mode I stress intensity factor dominates the other two stress intensity factors. Thus, nearly mode I deformation was achieved. Interpolation expressions for the mechanical and thermal residual stress intensity factors were determined using three and two-dimensional fittings, respectively. Results are presented with an expression for GIR determined. Moreover, the fatigue data is described including threshold values and master-curves. These results shed light on the behavior of delamination propagation in multidirectional laminate composites.


INTRODUCTION
Composite materials, in general, and carbon fiber reinforced polymers (C.RP), in particular, have evolved greatly since the 1960s. Currently, composite materials are used in industries, such as automotive manufacturing, air, marine and space structures, civil construction, medical equipment and more. These significant developments, especially in the aerospace industries, stemmed from the fact that polymer composites have low specific weight, with respect to metals. These composites are characterized by high ratios of toughness to weight and strength to weight, which allow them to tolerate defects. These features enable such structures to have longer life cycles and lower fuel consumption, which reduces economic costs [1].
Composite laminates may develop delaminations between plies, as a result of stress raisers, such as cor-ners, free surfaces, an interface between different materials, and more [2]. Quasi-static and cyclic nearly mode I deformation that may cause structural failure are the main focus of this study. .or the first, a IR G resistance curve is determined to characterize the mode I energy release rate I G which leads to catastrophic delamination propagation for a given delamination length a. .or the second, a Paris relation between delamination propagation length per cycle d d a N and a function of I I , ( ), G f G is obtained as each test type is discussed, including a description of the test setup. Obtaining the integrated averaged mode I energy release rate is discussed in Sect. 3 for determining IR , G Imax G and Imin . G .or fatigue, the method of calculating a and d d a N for each cycle is described in Sect. 3, as well. In Sect. 4, the results from fracture toughness and fatigue delamination propagation tests are presented. In addition, a technique for determining I G threshold values and achieving master curves will be described. .inally, a discussion and conclusions of this investigation is presented in Sect. 5. It may be noted that there is a separate section entitled: Supplementary material, where all sections, figures and tables are enumerated with a prefix S.

Specimen and Material
The specimen used in this study is the double cantilever beam (DCB) as presented in .ig. 1. Load blocks were used to apply opening displacements. The specimen length, width and thickness are l, b and h, respectively. The initial delamination length 0 a was measured from the center of a load block hole to the delamination front. All specimens were fabricated by a water jet process from the same plate. The width and thickness ranges, for all specimens, were between 19.74 and 20.08 mm and between 4.75 and 5.01 mm, respectively. The length of all specimens was about 200 mm and 0 a was about 54 mm. The measurements were carried out guided by the standards in [11,12] with some differences as described in Sect. S1 of the Supplementary material. The specimen measurements for the fracture toughness test specimens are presented in Table S1; those for fatigue delamination propagation test specimens may be found in Tables S2 to S4. It should be noted that the standards are for unidirec-tional (UD) material; whereas, the specimens considered here consist of a multidirectional (MD) laminate.
The composite laminate was fabricated from carbon fibers in an epoxy matrix with a small amount of glass fibers in the UD ply. The mechanical properties and coefficients of thermal expansion (CTEs) of those three constituents are presented in Table S5. The laminate consisted of 19 plies of three different types as illustrated in .ig. 2. The first type is a UD-fabric with carbon fibers in the 0°-direction (along the 1 x -axis) which included a small percentage of glass fibers transverse to the carbon fibers. The two other ply types are plain, balanced weaves with tows in the 0°/90° and the +45°/45°-directions, respectively. The upper ply of the interface is the UD-fabric and the lower ply is the weave with tows in the +45°/45°-directions as shown in .ig. 2. The laminate was manufactured by means of a wet-layup and cured in an oven at 85°C.
The weight fraction of each component (carbon and glass fibers, epoxy and voids) in each ply were found by dissolving the matrix in an acid bath. .or the UD fabric, the carbon was burned off to measure the weight fraction of the glass fibers. The equivalent volume fractions are presented in Table S6. The material properties of the constituents, as well as their volume fractions were used as input to the high-fidelity generalized method of cells (H.GMC) micromechanical model [13] to obtain the effective mechanical and thermal properties of the UD-fabric and the weave. These properties are presented in Tables S7 and S9, respectively. The UD-fabric is modeled to be transversely isotropic [14] with five independent effective mechanical properties and two CTEs. The glass fibers were accounted for by increasing the Youngs modulus of the matrix by means of the rule of mixtures. The weave is tetragonal [14] and described by six independent effective mechanical properties and two CTEs.

.racture Toughness Test Protocol
The fracture toughness standards [11,12] make use of a DCB specimen to measure the mode I delamination toughness of UD laminates. These standards were used as guidance in testing the MD laminate composed of a UD-fabric and woven plies. It is emphasized that the delamination is between two plies with fibers in different directions making it an interface crack between two effectively anisotropic (homogeneous) materials. Moveover, the delamination plane is not a symmetry plane. Thus, there are three deformation modes: .ig. 1. DCB specimen with load blocks (color online). 1, 2 and III. The contribution of the shear modes will be discussed in the sequel.
The test protocol used here followed the two standards and that developed in [10]. .racture toughness tests were performed on five DCB specimens denoted as .T-wet-1-0j (j = 4, ..., 8); .T represents fracture toughness; wet indicates that the specimens were fabricated by means of a wet-layup; the first numeral represents the batch number; the second numeral represents the specimen location in the plate, with respect to the other specimens.
The system used in the test is described in Sect. S3 and presented in .ig. S5 in the Supplementary material. As prescribed in the standards, the tests were conducted under displacement control. Automatic test instructions were written using Instron WaveMatrix computer software [15] which interacts with the Instron servohydraulic loading machine (model number 8872; High Wycombe, England) used in the tests. An Instron 250 N Dynacell load cell was used with an accuracy of about ±0.25% of the measured load greater than 2.5 N. In the first test stage, the displacement rate was set to increase at 1 mm/min, until a load drop of at least 2 N occurred or the delamination propagated between 3 and 5 mm, as prescribed in the standards. Then, the specimen was unloaded with a displacement rate of 4 mm/min until the value of the load acting on the specimen was 3 N. A small positive load was chosen so as not to induce compression in the specimen. The standards recommend a displacement rate of between 0.5 and 5 mm/min for loading; for unloading, the displacement rate should be less than 25 mm/min. The rates used in this protocol were in keeping with the standards. In the next step, the displacement rate was again set to 1 mm/min. This displacement rate was used until the delamination propagated by at least 60 mm.
.inally, in the last step of the test, unloading was performed to 3 N with a displacement rate of 8 mm/min. Every 0.5 s during a test, an image was taken using a LaVision digital camera (model Imager Pro SX, Göttingen, Germany). .rom the images and after the test, it was possible to measure the delamination length a as it propagated. Concurrently, values of the load and displacement were also recorded. It may be noted that there was full synchronization between the load, displacement and images. Each test took approximately 60 min. The specimens were stored in an environmental conditioning chamber (M.R.C. BTH80/-20, Holon, Israel) at least one week before a test was performed with a temperature of 23 ± 1°C and a relative humidity (RH) of 50 ± 3%. The ASTM standard requires a temperature of 23 ± 3°C and relative humidity of 50 ± 10%. During each test, the room temperature and RH were measured every five minutes.

.atigue Test Protocol
Tests were performed on five specimens, .TG-wet-1-0j (j = 9, ..., 13) with a cyclic displacement ratio d R = 0.10, and on four, .TG-wet-1-0j (j = 14, ..., 17 cycles N leading to delamination propagation initiation as a function of the mode I maximum energy release rate Imax G in a cycle for a DCB UD laminate specimen. Currently, there is no standard for delamination propagation of MD laminates, and in particular, for woven plies. Since the present study focuses on delamination propagation, the test protocol is different from that described in the standard; rather, it follows that presented in [10]. However, this study is consistent with the spirit of the standard in preparation of the specimens, use of suitable equipment, maintenance of environmental conditions, etc.
The system used for the fatigue tests is the same as that used for the fracture toughness tests. Again, displacement control was applied. Every 10 or 15 min during the tests, measurements of temperature and RH were recorded. These tests lasted up to 9 days running continuously.
Correctly determining the actuator position is an important aspect in the test procedure. The position of the actuator, once connected to the specimen, was recorded as 0 d as shown in .ig. 3. .irst, a quasi-static opening displacement at a rate of 1 mm/min was applied in order to propagate the delamination between 3 and 5 mm, as indicated in the standard. The procedure was carried out as described in Sect. 2.2 for the fracture toughness tests. The maximum actuator displacement * max d was recorded as shown in .ig. 3a. It is used as the maximum displacement in the fatigue tests. Next, unloading was performed at a rate of 8 mm/min until the load P = 3 N was reached. There are two difficulties associated with the test system. The first problem relates to the uncertainty in a load less than 2.5 N as explained in Sect. 2.2. This is especially problematic for d R = 0.10. The second problem results from some freedom in the test system which may be a result of the connections between the specimen and the test machine. It may be observed in .ig. 3b in the load displacement (Pd) curve that the minimum displacement does not return to its initial position 0 .
d The unloading curve was extrapolated linearly as shown by the dotted orange line in .ig. 3b to obtain the expected position 0 m d for P = 0. The maximum actuator displacement in a fatigue cycle relative to its position at were recorded. The number of cycles desired for each specimen was 3 × 10 6 . In Table 1, it is possible to observe that not all specimens experienced the full number of cycles. An explanation is detailed in Sect. 4.

THEORY AND CALCULATIONS
In this section, the process for obtaining various required quantities will be described. In Sect. 3.1, details about the finite element analyses (.EAs) used in this study are discussed. In addition, the integrated average of the mode I energy release rate along the delamination front is presented so that IR , G Imax G and Imin G may be determined. In Sects. 3.2 and 3.3, respectively, the methods for obtaining the delamination length a in each fatigue cycle and the delamination length per cycle d d a N are described. Several choices for

.inite Element Analyses to Obtain I G
.inite element analyses of the DCB specimens were carried out using the program ABAQUS [17]. .our plies directly above the interface and three plies directly below it were modeled using the effective material properties found for each ply. In order to reduce computation time and computer memory required, the six outer upper and outer lower plies were modeled as one effective homogenous, anisotropic material (see .ig. 2). These plies are relatively far from the delamination/interface. The material properties of all plies are presented in Sect. S2. There were four types of materials used in the .EAs including the UD-fabric, the +45°/45° weave, the 0°/90° weave and the outer homogenized, anisotropic material. The effective mechanical properties of the latter are presented in Table S10; whereas, the thermal properties are the same as those for the woven plies given in Table S9. In .ig. 4, the distribution of the plies in the finite element model is illustrated. Since the homogenized outer material is truncated in .ig. 4, its thickness is not to scale relative to the other plies. In Sect. S4, a convergence study to determine an optimal mesh is described.
Next, the stress intensity factors resulting from the mechanical loading (f ) m K (m = 1, 2, III), as well as the thermal residual curing stresses (r) m K (m = 1, 2, III), arising from the curing process, are considered. .or each specimen, seven .EAs were performed to determine the displacement field in the specimen including six mechanical analyses and one thermal analysis. All seven analyses were carried out in the same manner as described in Sect. S4 with a mesh similar to that shown in .ig. S8. The refined region of the mesh remains the same as that shown in .ig. S8. Since it is placed surrounding the delamination front, a change in the delamination length translates the location of the refined region.
.or mechanical analyses, the applied load was taken to be 1 N. Six delamination lengths were used in the fracture toughness and fatigue models. .or fracture toughness: 1 a = 50 mm, 2 a = 65 mm, 3 a = 80 mm, 4 a = 95 mm, 5 a = 110 mm, and 6 a = 120 mm; for fatigue: 1 a = 50 mm, 2 a = 55 mm, 3 a = 60 mm, 4 a = 65 mm, 5 a = 70 mm, and 6 a = 80 mm. These delamination length ranges span the lengths achieved during the tests. Using the conservative mechanical M-integral, which was extended in [18] for the interface shown in .ig. 2, six sets of mechanical stress intensity factors, (f ) m K (m = 1, 2, III) were obtained for each specimen, along the delamination front, for each delamination length n a (n = 1, 2, ..., 6). Of the six sets obtained from the mechanical analyses, it is possible to assemble the data in a three-dimensional space. The data included points K a x for each of the three stress intensity factors (m = 1, 2, III). A three-dimensional surface was fit through the points for each mechanical stress intensity factor as shown in .ig. 5. In addition, a functional relation was obtained relating (f ) m K to a and 3 x which is given by In Eq.  for the fracture toughness specimens may be found in Tables S13 to S17 and for the fatigue specimens in Tables S23 to S31. .or the thermal analysis, a constant temperature change was applied given by 90 .
i ∆ϑ = ϑ −° (8) In Eq. (8), i ϑ was selected as the value of the temperature at the beginning of the test for each specimen. These values are presented in Tables S41 and S45, for fracture toughness and fatigue delamination propagation tests, respectively. In Eq. (8), the value of 90°C is the maximum temperature measured during the curing process at five thermo-couples placed within the composite plate. There was an exothermic reaction. .or the thermal analyses, a delamination length of a = 85 mm for the fracture toughness tests and a = 65 mm for fatigue tests were selected. One analysis, instead of six, was sufficient for each specimen; it was found that the delamination length has a negligible effect on the residual curing stress intensity factors (r) .

m K
Using the thermal M-integral [18], a single set of (r) m K was obtained for each specimen, along the delamination front. .rom the set obtained from the thermal analyses, a mathematical relation between (r) m K and 3 x was found using a 14th-order polynomial defined as where i d are fitting constants. .or the fracture toughness specimens, i d may be found in Tables S18 to S22; for the fatigue specimens, see Tables S32 to S40.
The total stress intensity factors (t) m K may be calculated as a function of 3 x for each cycle in the test as The parameter P in Eq. (10) is the load leading to delamination propagation in a fracture toughness test or max P or min P from the fatigue tests. Through the images, the given load P is associated with the delamination length a and used in Eq. (7). With (t) m K a function of 3 , x for a given value of a and P, it is possible to obtain the interface energy release rate as a function of 3 x as where b is the specimen width. If P in Eq. (10) is the load for delamination propagation in a fracture toughness test, then I G in Eq. (12) is identified as IR G for the corresponding delamination length a. On the other  hand, if P in Eq. (10) is chosen as max P or min , P I G in Eq. (12) would be Imax G and Imin , G respectively, for the appropriate delamination length a. In the sequel, the overbar is omitted and the energy release rates are understood to be averaged through the specimen width.

Delamination Length in Each .atigue Cycle
In this section, the method for determining the delamination length during a particular fatigue cycle is presented. .or each cycle in a fatigue test, the values of the maximum and minimum loads and displacements, max , P min , P max d and min , d respectively, were recorded. .rom these values, the compliance C was calculated in each cycle as max min max min To proceed, the delamination lengths from the specimen images, taken during the test, were measured using ImageJ software [20]. The corresponding compliance values from Eq. (13) were known as a result of the synchronization between load, displacement and image number. Points of compliance versus delamination length were plotted as shown as red × in .ig. 6 for specimen .TG-wet-1-09. .or these points, an expression was found as , where the parameters g and n are power law fitting parameters. .or specimen .TG-wet-1-09, the values of g, n and the coefficient of determination 2 R were found as 98.97, 0.3386, and 0.9949, respectively. Values for all other specimens may be found in Table S43. Using the relationship from Eq. (14) and knowledge of the compliance values in each cycle, it was possible to calculate the approximate delamination length in each cycle which is shown as blue dots in .ig. 6. It may be observed that there is good agreement between the measured and calculated values of a.

Delamination Propagation Rate d d a N in Each Cycle
A method is presented for determining delamination length a as a function of the cycle number N, in each cycle of the test. Differentiating this function with respect to N leads to the relation between d d a N and N, in each cycle. In many studies, a seven (or another number) point incremental fit was used to obtain a relation between a and N, in each cycle of the test. This method is described in [21]. In [10], it was shown that the seven point incremental fit leads to much scatter in the relationship between a and N. Instead, the relation [ B and 2 B varying between 10 000 and 10 000, until the best value of 2 R was obtained. The solver function uses a nonlinear generalized reduced gradient (GRG). The solver increments the values of 1 B and 2 B so that the value of 2 R increases. When the value of 2 R ceases to increase, the solver stops and produces the relevant values of 1 2 , , A A 1 , R This method produces a local maximum for 2 R in a range of 1 B and 2 B and not necessarily the global maximum. Therefore, it is necessary to run the solver multiple times with different initial values for 1 B and 2 . B Moreover, existence of a high value for 2 R was not the final step taken to verify Eq. (15). Equation (15) was compared to the visually obtained measurements of a from the images .ig. 6. Delamination length versus compliance in a fatigue test for specimen .TG-wet-1-09 (color online).    Table S44. In .ig. 7, a plot of delamination length as a function of the cycle number for specimen .TG-wet-1-09 is presented. Points marked with a red × are visually obtained measurements of delamination lengths using the images taken during the test. In addition, the green curve describes Eq. (15). Note that the visual measurements from the test and Eq. (15) are well correlated. Differentiating Eq. (15) by the cycle number N leads to

Relation between d d a N and I G
In [10], normalized functions for and where Imin G is defined similarly to Imax G in Eq. (17). The parameter IR G in Eq. (17) is taken from the IR Gcurve for a specific delamination length; that is, during a fatigue test as a increases, IR G increases until it reaches its steady state value. By substituting Eq. (17) into Eq. (1), it is possible to plot d d a N versus Imax G on a log-log scale for various values of the cycle ratio R as shown schematically in .ig. 8a. .or each R-ratio, the same asymptotic value (at high values of d d ) a N giving the cycle fracture toughness are found for all curves. .or low values of d d , a N each curve approaches a different threshold value which increases with R. Next consider substituting Eq. (18) into Eq. (1); one may obtain the plot shown in .ig. 8b. It may be observed that the same threshold value is obtained for each curve, independent of R. Moreover, each curve approaches a different value (at high values of d d ), a N increasing as R decreases. It may be observed that the slopes of the linear part of the curves are high. In [10], the values of m in Eq. (1) were between 7 and 27 for 0.10 ≤ d R ≤ 0.75. When comparing slopes obtained for metals using stress intensity factors in a Paris relation, the powers for I ( ) f G must be multiplied by a factor of 2. Thus, for a small change or error in the applied load, the delamination growth rate is very high making this approach difficult for use in a damage tolerance paradigm.
Hence, a function used originally for metals [23] was adapted in [4] by defining the function and used in [8,9]. In Eq. (19), Ithr G is the threshold value of Imax G from which there will be no delamination propagation and A is a constant which may be thought of as the cyclic fracture toughness. In [4], the value of m in Eq. (1) was fixed at 2 and various material sets for modes I and II, and mixed mode I/II were examined for UD material. .or each material, a value of D in Eq. (1) was fixed and Ithr G and A were varied. In [8], values of m varied between 2.4 and 7.5. In [ where the hat quantities are as in Eq. (17). In [10], Eq. (20) was substituted into Eq. (1) yielding a master curve which is independent of the cyclic load or displacement ratio for the material system described there. A value for Ithr G was obtained by examining the test data. By fitting Eq. (1) to the test data, a slope of m = 5.2 was found. It would appear that with these lower slopes for both Eqs. (19) and (20) as compared to the functions in Eqs. (17) and (18)

.racture Toughness Test Results
.racture toughness tests were carried out on a set of 5 DCB specimens. Additional information about the tests is presented in Sect. S5 in the Supplementary material.
The specimens were analyzed by means of the finite element method to determine the stress intensity factors as described in Sect. 3.1. The values of 0 i p and 1 j p (i = 0, 1, ..., 5 and j = 0, 1, ..., 4) from Eq. (7), and i d (i = 0, 1, ..., 14) from Eq. (9), are presented for each specimen in Tables S13 through S22. Values of load and displacement were recorded during the test producing loaddisplacement (Pd) curves which are presented in .ig. S9. Since the system compliance was 0.5% less than the compliance of the specimen, the actuator displacement d was used in place of the loadline displacement. Using the appropriate loads and de-lamination lengths, the total stress intensity factors in Eq. (10) were obtained. It was found that the value of (t) 1 K was much greater than the other two stress intensity factors. .urther details are given in Sect. S4. Thus, it may be concluded that the tests produce nearly mode I deformation. .urthermore, from the .EAs, numerically obtained Pd curves for each specimen were determined. Comparison between the tests and the numerical analyses in the linear region of the curves showed good agreement. By this comparison, the effective mechanical and thermal properties found for the plies are validated.
As mentioned previously, the specimens were measured before the tests (see Table S1). After the tests were carried out, the delamination lengths were measured on both sides of each specimen with the optical mode of an Olympus confocal microscope (model no. OLS4100, Tokyo, Japan) and given in Table S42. The difference between these measurements was less than 2 mm conforming to the standards [11,12] for UD material. In addition, during the tests, values of temperature and RH were recorded and may be found in Table S41. The tests conform to the standards.
Using Eqs. (11) and (12), values of I G were calculated for each load and delamination length. Note that i G in Eq. (11) is identified as I G and the overbar is omitted. These values are averaged over the thickness. This data is plotted as points in .ig. 9. An initiation fracture toughness is shown for ∆a = 0 as Ic G = 357.9 N/m. As ∆a increases, the values of IR G increase, as well, reaching a steady state value of ss G = 727.7 N/m for ∆a = 30 mm. .itting the points between 0 ≤ ∆a ≤ 30 mm leads to the power law given by

.atigue Tests Results
In this section, the fatigue tests carried out as described in Sect. 2.3 are presented. Results and additional explanations are given in Sect. S.6. Recall that two cyclic displacement ratios were used: d R = 0.10 and 0.48. The aim was for each specimen to undergo 3 × 10 6 cycles. In Table 1, the number of cycles experienced by each specimen is presented. During the tests on specimens .TG-wet-1-09 and .TG-wet-1-10, there was a power failure. If a test is interrupted, it is not possible to remount the specimen in the same position that it had been before the interruption. Hence, the number of cycles experienced by each of these specimens is less than 3 × 10 6 . Although specimen .TG-wet-1-14 was subjected to all planned cycles, it appears that there was a temperature change which affected the measured compliance values as shown in .ig. 10. It is possible to note that the room temperature for N ≈ 475 000 cycles is about 23.5°C; after that, it decreased suddenly to less than 21.0°C. In addition, the compliance value increased significantly for N = 475 000 cycles. As a result, data from this cycle forwards was not taken into account in calculating the delamination propagation rate. It was found that the specimens tested in this investigation were very sensitive to temperature changes. Another illustration is described in the sequel for specimen .TG-wet-1-15. As a result, data from the first 30 000 cycles of this test was omitted. .or all specimens, the compliance values calculated as a function of N are illustrated in .ig. S10.
As described in Sect. 3.2, the delamination length may be obtained using Eq. (14) with the value of the compliance in each cycle. In Table S43, the fitting constants g and n, together with the coefficient of determination 2 R of Eq. (14) are presented for each specimen with 2 R > 0.97. Moreover, in Sect. 3.3, a method for determining a relation between the delamination length a and the cycle number N in Eq. (15) was described. In Table S44, the fitting constants, 1 2 1 , , A A B and 2 , B and the coefficient of determination 2 R are presented for all specimens with 2 R > 0.97. Next, in a manner similar to that described in Sect. 4.1 for the fracture toughness tests, the stress intensity factors and the maximum and minimum values of the energy release rates Imax G and Imin G were determined. The coefficients 0 from Eqs. (17) and (18), respectively, were also determined in each cycle.
As mentioned earlier, a change in the room temperature affected the behavior of specimen .TG-wet-1-15 during the test. All obtained data for this specimen was used to plot a curve for d d a N as a function of Imax G on a log-log scale. This curve, together with that for specimen .TG-wet-1-14, are shown in .ig. 11a. It may be observed that for low values of d d a N the curves approach one another; whereas, for high values of d d , a N they diverge. It should be noted that for specimen .TG-wet-1-14, data is shown only for N ≤ 475 000. Since the tests of these two specimens were performed with d R = 0.48, it was expected that they would show similar behavior. Next, for specimen .TG-wet-1-15, the temperature is examined in .ig. 11b during the first 100 000 cycles. .or N < 30 000 cycles, the temperature increased from 23.75°C to above 24.5°C. .or N > 30 000 cycles, the temperature decreased to about an average value of 23.3°C until the end of the test. This small change in temperature apparently created a reduction in the delamination propagation rate. There is no discontinuity in the compliance values as in specimen .TG-wet-1-14. But the compliance values differ from those of specimen .TG-wet-1-14 during the first 30 000 cycles of the test. As a result of .ig. 11, going forward, the analysis of specimen .TGwet-1-15 was performed without the data from the first 30 000 cycles. It may be noted that the ASTM standards recommend temperatures of 23 ± 3°C. Clearly, the temperatures for this specimen conform to the standards.
Possible explanations for this behavior are presented next. The plate from which the specimens were taken was manufactured by means of a wet-layup. During the curing stage, the maximum imposed temperature was about 85°C with an exothermic reaction bringing the temperature to 90°C within the composite plate. The data sheet for the epoxy used in these specimens specifies that the maximum curing temperature should be 130°C in order to obtain a glass transition temperature g T = 130°C [24]. Dynamic mechanical analysis (DMA) tests were performed where it was found that g T = 104°C. This lower value of g T may explain the sensitivity of these specimens to small temperature changes.
Recall that for specimen .TG-wet-1-14 in .ig. 10, a temperature decrease of about 3°C significantly af-fected the compliance value. In practice, this change affected the minimum load min P measured in the corresponding cycle which decreased by about 0.4 N. As a result the compliance value increased, as may be seen in Eq. (13).
Moreover, the temperature sensitivity may be related to the load cell sensitivity of the Instron testing machine. To this end, a test was carried out by hanging a mass of 1 kg on the load cell and heating and cooling the room between 25 and 21.5°C. It was seen that the load varied between 9.81 N, at the higher temperature, and 9.56 N, at the lower one. These small changes in the load affect, in particular, min P and hence, the compliance. It is speculated that both the low glass transition temperature, as well as the load cell sensitivity affected the compliance and, hence, the final results.
Some additional data is given in the Supplementary material. In Table S45, the average cyclic load ratio p , R for each specimen in the first 10 000 cycles, is shown. It is somewhat lower than d .
R .or specimen .TG-wet-1-15, p R is an average for the first 30 000 to 40 000 cycles. In addition, the delamination lengths at the end of the tests for each specimen, on both sides, and their differences , f ∆ are given, as well. It was seen that f ∆ < 2 mm, in keeping with the fracture toughness test standards. Initial test temperatures are also shown.
Next, values of d d a N versus Imax G and Ieff , G ∆ from Eqs. (17) and (18), were plotted on a log-log scale as shown in .igs. 12a and 12b, respectively. Generally, linear behavior is observed. Such curves may be used to predict delamination propagation when Imax G or is known for a structure containing the interface studied here. In .ig. 12, the plots include data for all fatigue specimens. It may be observed that the data for high values of d d a N appear to approach an .ig. 12. Plots of d d a N versus Imax G (a) and (1), .TG-wet-1-10 (2), .TG-wet-1-11 (3), .TG-wet-1-12 (4), .TG-wet-1-13 (5), .TG-wet-1-14 (6), .TG-wet-1-15 (7), .TG-wet-1-16 (8), .TG-wet-1-17 (9) (color online). Ignoring the data for large values of d d a N (up to 500 cycles), a mathematical expression in the linear range of the curves on a log-log scale, in .igs. 12a and 12b, are given by where the parameters i D and i m (i = 1, 2) are power law fitting constants. These parameters for each specimen are presented in Table 2, together with 2 R and the number of sampling points. It may be seen that 2 R > 0.9877 for all specimen, which is excellent.
In .igs. 12a and 12b, it may be observed that the specimens separate into two groups according to the cyclic displacement ratio d .
(1 )    free parameter and used in the fitting; whereas, IR G changes as the delamination length increases.
Equation (1) is used with The parameters D and m are found by fitting the fatigue data to a straight line on a log-log scale with A and ( ), f G respectively, the data was plotted and the best fit for the master curve is shown as a continuous black line. The lines are independent of d .
R However, it may be seen that there is some scatter in the test results, as reflected in the coefficient of determination. Recall that the results obtained from each test do not include the first 500 cycles. The value of the slope m for Eq. (1) using 2 K ∆ is lower than the slopes presented in Table 2 for the curves presented in .ig. 12a for Imax . G Recall that for purposes of comparison, the slopes in Eq. (22) require multiplication by a factor of 2. Nevertheless, in [10] for another material system, it was shown that use of does not result in a smaller increase in d d a N as the delamination propagates. The value of the slope in Eq. (1) using 1 , K ∆ is higher than the slope for Eq. (1) using 2 K ∆ with values of 2 R almost identical.

DISCUSSION AND CONCLUSIONS
In this section, a discussion and conclusions are presented. This study focused on nearly mode I fracture toughness and fatigue delamination propagation tests carried out with DCB specimens illustrated in .ig. 1. The specimen plies were composed of carbon fibers in an epoxy matrix. The laminate consisted of 18 multidirectional, plain, woven plies and one UDfabric ply as shown in .ig. 2 which was fabricated by means of a wet-layup process. The woven plies alternated between those with tows in the 0°/90°-directions and +45°/45°-directions. The delamination was between a UD-fabric (upper) ply and a woven (lower) ply with tows in the +45°/45°-directions.
.racture toughness tests on five DCB specimens led to a IR G -curve as shown in .ig. 9. This resistance curve or R-curve is characterized by two values of G. The curve initiates from its fracture toughness value of Ic G = 357.9 N/m at ∆a = 0. .rom this value, an increase may be observed until a steady state value ss G = 727.7 N/m is reached at ∆a = 30 mm. .or the material system discussed in [10], which included only MD woven plies, the values were Ic G = 508.0 N/m and ss G = 711.0 N/m. Moreover, a steady state was reached at ∆a = 10 mm.
.atigue delamination propagation tests on nine DCB specimens for two cyclic displacement ratios d R = 0.10 and 0.48 provided d d a N data. The compliance C in each cycle was obtained using Eq. (13). Measured values of delamination length a were plotted versus matching compliance values as presented as red × in .ig. 6. A relation between a and C was obtained by fitting Eq. (14) to the measured delamination lengths. In this way, values of a in each cycle could be found without additional measurements. These values of a, calculated with Eq. (14), were plotted versus the corresponding values of are nondimensional parameters to be determined in the fitting of Eq. (15). The methods for determining a in each cycle of a test and obtaining a relation between a and N were found to be effective. In .ig. 6, it may be observed that there is good agreement between the measured and calculated values of a. Moreover, in .ig. 7 it is possible to observe that the visual measurements of a from a test and Eq. (15) are well correlated. A relation between d d a N and N in each cycle was determined by differentiating Eq. (15) to obtain Eq. (16).
The curing process may have a significant effect on the results. In this study, the glass transition temperature g T was found to be 104°C which is lower than that specified in the data sheet (130°C) for this epoxy. This lower value of g T may partially explain the sensitivity of the specimens to small temperature changes. Recall that for specimen .TG-wet-1-14 in .ig. 10, a temperature decrease of about 3°C significantly affected the compliance value. Moreover, the temperature sensitivity may be also related to the load cell sensitivity of the Instron testing machine, as described in Sect. 4 different asymptotic values are approached for each value of the cycle ratio R, as described in .ig. 8b. In .igs. 12a and 12b, ideally the curves for each d R should coincide. In practice, this is not the case, and there is variability between the curves. The data from specimen .TG-wet-1-16 for d R = 0.48 deviates from the rest of the specimens in its group. No explanation was found for this behavior except that it is normal scatter in fatigue data. .urthermore, the slopes of the curves for d R = 0.10 are smaller than those for d R = 0.48, as illustrated in .ig. 8. An increase in the slopes, as d R increases was expected and also seen in [

SUPPLEMENTARY MATERIAL
Section, figure, table and equation numbers are preceded with an S; those without an S are in the body of the paper. In Sect. S1, measurements of the fracture toughness and fatigue delamination propagation specimens are given. The mechanical and thermal proper-ties of the plies are described in Sect. S2. In Sect. S3, the test setup is discussed. Details about the finite element analysis and a convergence study are presented in Sect. S4. In Sects. S5 and S6, elaboration of the fracture toughness and fatigue delamination propagation tests, respectively, is discussed. S1. MEASUREMENTS O. DCB SPECIMENS .racture toughness tests were performed on five DCB specimens denoted as .T-wet-1-0j (j = 4, 5, 6, 7, 8); .T represents fracture toughness; wet indicates that the specimens were fabricated by means of a wet-layup; the numeral 1 denotes batch 1; the next number represents the location in the row of the plate from which it was fabricated. .or each specimen, the length, width and thickness were measured; these measurements are presented in Table S1. The width and thickness were measured at five locations along the specimen length as shown in .ig. S1. Average values and standard deviations (SDVs) of these five measurements were calculated and are also presented. Note that the width of the specimen was measured by means of a caliper with a resolution of 0.01 mm and the thickness of the specimen was measured by means of a micrometer with a resolution of 0.001 mm. .or each specimen, the delamination length 0 a was measured from the center of the loading holes to the end of the delamination front on . both sides of the specimen: front and back, and marked with a superscript (f) and (b), respectively. These measurements were made with the optical mode of an Olympus confocal microscope (model number OLS4100; Tokyo, Japan) and given in Table S1; its resolution is 0.001 mm. The difference between them 0 ∆ is also presented. It may be seen that the differences are less than 2 mm which complies with the fracture toughness standards [1,2]. The parameter a in Table S1 is the delamination length from the edge of the specimen to the delamination front. This parameter was also measured on both sides (front and back) of the specimen. The difference between these two measurements is denoted as ∆. In addition, the length of the specimens l was measured with a ruler and complies with the requirement that l be at least 125 mm. .atigue delamination propagation tests were carried out on nine DCB specimens: five with the cyclic displacement ratio d R = 0.1 and four with d R = 0.48 (see Eq. (2) for a definition of d ).
R Specimen width measurements are presented in Table S2 and thickness .ig. S1. Measurement locations of DCB specimens for fracture toughness tests (color online). Table S2. Width measurements and averages as presented in .ig. S2 (mm) .    Table S3. Each specimen is denoted with .TG indicating that it is a specimen tested in fatigue; wet denotes that it is fabricated by means of a wet-layup; the number 1 indicates that this is batch 1; the next number represents the location in the row of the plate from which the specimen was fabricated. It may be noted that all of the specimens tested here, both fracture and fatigue, were fabricated from the same plate. Specimen .T-wet-1-08, from the fracture toughness set, was next to specimen .TG-wet-1-09, from the fatigue delamination propagation set, in the plate. The locations at which measurements were carried out of the width b and thickness h are presented in .ig. S2. The coordinate system in .ig. S2 is positioned at the location where 2 b is indicated with the origin on the edge of the specimen next to 23 .
h It is not located there in the figure so that it will be clearly visible. Two width measurements shown as 1 b and 4 b were made 25 mm from each edge of the specimen (along the 1 x -axis). These two measurements were made as indicated in the ASTM fracture toughness standard [1], while the fatigue standard [3] suggests measurement of 2 b along the delamination front. The last width measurement 3 b was made nearly half-way between 2 b and 4 . b The ASTM standard [1] recommends making only one measurement between 1 b and 4 . b In addition, this standard recommends making only one thickness measurement, along the specimen width, in each location at which a width measurement is made and along the centerline of the specimen. Since the polytetrafluoroethylene (PT.E) film (13µm thick) forming the delamination may have an effect on the thickness measurement, at the location where 1 b was measured, a thickness measurement was not made there. At each of the locations at which 2 , b 3 b and 4 b were measured, three thickness measurements were made along the specimen width and not only at the one prescribed in [1]. The purpose of making three measurements was to account for the change of thickness along the 3 x -axis, which may vary as a result of the wet-layup manufacturing process. In the ISO fracture toughness standard [2], three width measurements at equal distances along the specimen length are recommended. At the location of the middle one, of these three, performance of three thickness measurements is recommended, similar to those shown in .ig. S2. At the locations of the other width measurements, only one thickness measurement is prescribed. In this investigation, a combination of that recommended in both fracture toughness standards was carried out on the fatigue delamination propagation specimen set so that the measurements are ideal for obtaining the width and thickness of the specimen. These measurements were performed using the same instruments, caliper and micrometer, respectively, for the width and thickness, which were used for measurements of fracture toughness specimens. In addition, for the measurements presented in Tables S2 and S3, the SDV is also given.
.or all width and thickness measurements presented in .ig. S2, average values were calculated and are presented in Table S4. The value of the coefficient of variation (CV) given as where X is the average value of a group of measurements was calculated. The largest value of CV for the width measurements was 0.02. In addition, for each specimen, the SDV value for each group of thickness measurements  Table S3. The largest value of CV for the thickness measurements is 0.02, as well. Table S5. Mechanical properties [4] and CTEs [5,6] of carbon fibers, epoxy and glass fibers [7] Material   In addition, the delamination length measurements shown in .ig. S2, at the front and back sides of the specimen, (f ) 0 a and (b) 0 , a respectively, and the difference between them 0 ∆ are also presented in Table S4. The measurements were made from the center of the loading block hole to the delamination front using the optical mode of the confocal microscope. The values of 0 ∆ in Table S4 are less than 2 mm as recommended in both fracture toughness standards. Similarly, after the tests were performed, the delamination length was measured on both sides of the specimen; these measurements will be presented in Sect. S6. The length of each specimen was measured with a ruler and is also presented in Table S4.

S2. MECHANICAL AND THERMAL PROPERTIES O. PLIES IN THE LAMINATE
This investigation deals with carbon fiber reinforced polymer (C.RP) composite laminates. .igure 2 in the body of the paper may be consulted for the laminate layup. The constituents include carbon fibers in an epoxy matrix with a small amount of glass fibers in the UD-fabric ply. The mechanical properties of the carbon fibers were taken from [4]. The coefficients of thermal expansion (CTEs) were taken from [5,6]. Typical properties were taken for the epoxy. .rom [7], the properties of the glass fibers were obtained. The mechanical and thermal properties are presented in Table S5, where A E and T E are the Youngs moduli, .ig. S3. Two-dimensional schematic view of a plain weave with an RUC shown in red (a); three-dimensional schematic view of the RUC (b); image of +45°/45° woven ply (c) (color online).
x 1  α and T α are the CTEs in the axial and transverse directions, respectively. The carbon fibers are transversely isotropic, described by five independent mechanical properties and two independent CTEs. The shear modulus T G is related to T E and T . ν The epoxy and glass are both isotropic materials, described by two independent mechanical properties and one independent CTE.
The volume fraction of each constituent in the UDfabric and woven plies are presented in Table S6. Two samples were provided for each ply and an average value was calculated which was used to obtain the effective material properties by means of the micro-mechanical model, the high-fidelity generalized method of cells (H.GMC) [8]. .or the UD-fabric, these properties are presented in Table S7. It may be noted that the glass fibers which are transverse to the carbon fibers were used to increase the Youngs modulus of the epoxy. Thus, the ply is effectively transversely isotropic.
In order to calculate material properties of the woven ply by means of the H.GMC micromechanical model, a repeating unit cell (RUC) was chosen as shown schematically in two dimensions as the red box in .ig. S3a and in three dimensions in .ig. S3b. The geometric parameters of the RUC are the thickness of the RUC h, the length of the tows a in the 1 x -and 3 xdirections and the length and width of the epoxy pocket g between them. The parameters a and g were measured at 110 random locations of the ply using a Dino Lite digital microscope (model no. AM311ST, AnMo Electronics Corp., Taiwan). The thickness of an entire specimen was measured with a micrometer at 7 locations. The thickness of the UD fabric ply was mea-.ig. S6. Image of DCB specimen taken with LaVision digital camera (color online).

Millimeter paper
Tracking marks Delamination tip  sured to be 0.145 mm. By simple arithmetic, the ply thickness h was obtained and is presented in Table S8 together with the SDV. An additional geometric parameter, which is dependent on two of the previous ones, is the angle of the yarn β with respect to the 1 x -direction as shown schematically in .ig. S4. This angle is given by and is also presented in Table S8.
Using H.GMC with these measurements, together with the constituent properties and volume fractions, the effective mechanical properties and CTEs of the woven ply with tows in the 0°/90°-directions were found; they are presented in Table S9. .urther details my be found in [9]. These properties were rotated [10] by 45° about the 2 x -axis to obtain the effective mechanical properties and CTEs of the ply with tows in the +45°/45°-direction, which are also presented in Table S9 (see .ig. S3c).
Rather than modeling each individual ply, six outer, upper and lower plies of the laminate, as presented in .ig. 2, were modeled in the finite element analyses as an effective material with anisotropic, homogenized properties. In this way, computer time and memory were reduced. The mechanical properties of the effective material were calculated by means of H.GMC and are presented in Table S10. The effective CTEs are the same as for each woven ply and presented in Table S9. All other plies were modeled individually in the analyses.

S3. TEST SETUP
The tests (fracture toughness and fatigue) were performed with an Instron hydraulic tensile testing machine (model number 8872; High Wycombe, UK). It includes a fast track 8800 controller as shown in .ig. S5. The load cell has a capacity of 250 N with an accuracy of ±0.25% of the load measured for a load greater than 2.5 N. To track the delamination front, a digital camera from LaVision (model Imager pro SX, LaVision GmbH, Göttingen, Germany), was used, with the accompanying computer and software. Using an external PTU (programmable timing unit) controlled by DaVis computer software [11], the images taken with the camera were correlated to the load and actuator displacement at the moment of capture. An image of the DCB specimen, taken with the camera of the LaVision system, is shown in .ig. S6. All of the LaVision components were synchronized with a LaVision light source shown in .ig. S5. Each time an image was taken, the light source was turned on. In addition, the LaVision system is synchronized with the Instron; the load value appears on the image of the specimen. Attached to the specimen was millimeter paper used for calibration when the delamination length was determined visually. In .ig. S6, it is possible to see tracking Table S12. Largest relative difference (LRD) between stress intensity factors along the delamination front with 0.0375 ≤ 3 x b ≤ 0.9625, for pairs of meshes and for both problems. The data of the meshes is presented in Table S11 Meshes Very coarse and coarse Coarse and fine .ine and finest In this study, DCB specimens were modeled for finite element analyses (.EAs) [12]. Achieving conver-.ig. S8. .inite element mesh for DCB specimen used in this investigation with mesh data presented in Table S11 (color online).
x 1 gence of the results, requires sufficiently fine meshes. .or the convergence study, a DCB specimen was modeled with dimensions shown in .ig. 1 of l = 200 mm, b = 20 mm, h = 5 mm and 0 a = 50 mm. The loading blocks were not modeled. It was found that the difference in the results with and without loading blocks is negligible. .our different meshes were used in the convergence study. Very coarse, coarse, fine and finest meshes with a description of each presented in Table S11.
Twenty noded, isoparametric brick elements were used in the analyses. Along the delamination front, quarterpoint elements were used to model the dominant square-root singularity. The oscillatory part of the singularity was not modeled.  The laminate layup is presented in .ig. 2. Each of the seven plies, four above and three below the interface, was modeled individually using their effective homogenous, anisotropic material properties given in Tables S7 and S9. The outer six upper and lower plies were modeled as one effective homogenous, anisotropic material with mechanical properties given in Table  S10 and the CTEs in Table S9. These plies are relatively far from the delamination/interface. Therefore, there is no need to model each ply individually. In total, there were four material types used in the finite element analyses: the UD-fabric ply, the +45°/ 45° woven ply, the 0°/90° woven ply and the group of outer plies. In .ig. 4, the distribution of plies in the finite element model, according to the materials which were used, is presented, with the effective outer material truncated. Thus, the thickness of the outer ply groups are not to scale relative to the other plies.  Two different problems were solved in the convergence study. The first problem examined the DCB specimen with an applied load; in the second, a change in temperature was considered. .or the first problem, a line-force perpendicular to the delamination in the 2 x -direction (see .ig. S1) along the specimen width was applied to nodes along the upper surface of the upper arm of the DCB specimen. The force was applied at a distance 0 a from the delamination front. In addition, the opposite nodes on the lower specimen arm were constrained to be stationary in the 1 x -and 2 x -directions. The applied load and displacement boundary conditions cause the specimen arms to separate in the 2 x -direction. .or all four meshes, there were 40 elements along the width of the specimen which is in the 3 x -direction. As a result of this number and the type of element used, the displacement boundary conditions were applied to 81 nodes on the lower specimen arm. The total force applied in the model was where el n is the number of elements across the width  while the force acting on the outer two nodes is el 6.
. As a result, the total force on a shared node from two elements is el 3.
. In the second problem, a temperature difference was imposed with 90 .
i ∆ϑ = ϑ −°(S5) In Eq. (S5), i ϑ was taken to be a typical room temperature value of i ϑ = 25°C. Thus, ∆ϑ = 65°C. In Eq. (S5), the value of 90°C is the maximum temperature which was measured in the laminate during the curing process.
By means of mechanical and thermal M-integrals [9], mechanical and thermal residual stress intensity factors were obtained along the delamination front, for the four meshes. .or 0.0375 ≤ 3 x b ≤ 0.9625, the relative difference between the stress intensity factors, for each pair of meshes and for each problem type, was calculated. In Table S12, the largest relative differences (LRD) calculated between the stress intensity factors are presented. One may observe the convergence of the stress intensity factors as the meshes become finer.  ing on the mechanical properties of the plies on either side of the interface. The phase angle ψ represents the in-plane mode mixity; whereas, the phase angle φ represents the out-of-plane to in-plane mode mixity. It was found that both ψ and φ were less than 0.2 rad along the delamination front, except near the specimen edges. Thus, the shear modes are negligible. As a result, the total energy release rate T G is considered to be the mode I energy release rate I . G Although (t) 1 K was dominant, calculations of I G included all stress intensity factors as given in Eq. (11). .T-wet-1-04 (1), .T-wet-1-05 (2), .T-wet-1-06 (3), .T-wet-1-07 (4), .T-wet-1-08 (5) (color online).   .T-wet-1-07 24.8 24.6 .T-wet-1-08 24.6 24.2 As described in Sect. 3.1, surfaces were fit through the finite element results for each of the five fracture toughness specimens to obtain a relation between (f ) m K (m = 1, 2, III), the normalized delamination length  Tables S13 through S17. .or the residual stress intensity factors arising from the curing process, lines were fit through the finite element results to obtain a relation between (r) m K (m = 1, 2, III) and normalized position along the delamination front 3 .
x b The equation for the lines is given in Eq. (9). The values of i d (i = 0, 1, ..., 14) in this equation are given in Tables S18 through S22. .or the nine fatigue delamination propagation specimens, the values of 0 .racture toughness tests were carried out on five DCB specimens guided by the ASTM [1] and ISO [2] standards. These standards were developed for UD laminates. Values of load and displacement were recorded during the tests to produce load-displacement curves, as presented in .ig. S9 for each specimen. Each precipitous load drop in the curve indicates unstable delamination propagation. When the load decreased in a continuous fashion, the delamination propagated stably. The first delamination propagation (first load drop) occurred for 42 N ≤ P ≤ 45 N, except for specimen .T-wet-1-04. In that case, the load reached 50 N before abruptly decreasing. In addition, the initial de- versus the cycle number N, for all fatigue specimens: .TG-wet-1-09 (1); .TG-wet-1-10 (2); .TG-wet-1-11 (3); .TG-wet-1-12 (4); .TG-wet-1-13 (5); .TG-wet-1-14 (6); .TG-wet-1-15 (7); .TG-wet-1-16 (8); .TG-wet-1-17 (9); fit, R d = 0.10 (10); fit, R d = 0.48 (11) (color online).  , , A A B and 2 B and the coefficient of determination 2 R of Eq. (15) are presented. The number of sampling points is also given in Table S44. It may be observed that 2 R is very high for all specimens; for specimen .TG-wet-1-15, it is slightly lower than the others. Here there is a lower number of sampling points. When data from all cycles for this specimen were used, a higher value of 2 , R like those for other specimens was achieved. Nevertheless, 2 R for this specimen is still excellent. It may be concluded from the high 2 R values that the method for obtaining Eq. (15) is an effective tool for determining a relation between a and N. In addition, from .ig. 7, for specimen .TG-wet-1-09, it may be seen that the visually measured delamination lengths, from the images taken during the test, fit well to the curve described by Eq. (15). Moreover, it may be observed in Table S44 that the values of the fitting constants of Eq. (15) are quite variable. .or each specimen, different fitting constants were obtained which led to the best value of 2 . R In Table S45, the average cyclic loading ratios p R for each specimen during the first 10 000 cycles, are shown. .or specimen .TG-wet-1-15, p R is an average for the first 30 000 to 40 000 cycles. It may be observed that the cyclic load ratios differ somewhat from the cyclic displacement ratios. .or values of N > 10 000, p R does not change significantly. In addition, in Table S45, the delamination length at the end of the tests for all specimens, (f ) f a and (b) f , a at the front and back sides of the specimen, respectively, are shown. The difference between these lengths is denoted as f ∆ and is also presented in Table S45. The values of f , ∆ are less than 2 mm as required by the two fracture toughness test standards [1,2]. In addition, the initial temperature in the tests is also shown in Table S45 and is denoted as .