Article

Surface Irregularity Factor as a Parameter to Evaluate the Fatigue Damage State of CFRP Pablo Zuluaga-Ramírez 1,2, *, Malte Frövel 1 , Tomás Belenguer 1 and Félix Salazar 2 Received: 18 September 2015 ; Accepted: 30 October 2015 ; Published: 11 November 2015 Academic Editor: Robert Lancaster 1 2

*

Instituto Nacional de Técnica Aeroespacial (INTA), Carretera de Ajalvir Km 4, Torrejón de Ardoz 28850, Spain; [email protected] (M.F.); [email protected] (T.B.) Department of Applied Physics, Escuela Técnica Superior de Ingenieros de Minas y Energía, Universidad Politécnica de Madrid, C/ Ríos Rosas 21, Madrid 28003, Spain; [email protected] Correspondence: [email protected] or [email protected]; Tel.: +34-915-201-913

Abstract: This work presents an optical non-contact technique to evaluate the fatigue damage state of CFRP structures measuring the irregularity factor of the surface. This factor includes information about surface topology and can be measured easily on field, by techniques such as optical perfilometers. The surface irregularity factor has been correlated with stiffness degradation, which is a well-accepted parameter for the evaluation of the fatigue damage state of composite materials. Constant amplitude fatigue loads (CAL) and realistic variable amplitude loads (VAL), representative of real in- flight conditions, have been applied to “dog bone” shaped tensile specimens. It has been shown that the measurement of the surface irregularity parameters can be applied to evaluate the damage state of a structure, and that it is independent of the type of fatigue load that has caused the damage. As a result, this measurement technique is applicable for a wide range of inspections of composite material structures, from pressurized tanks with constant amplitude loads, to variable amplitude loaded aeronautical structures such as wings and empennages, up to automotive and other industrial applications. Keywords: fatigue damage; composites materials; CFRP; non-destructive test; non-contact inspection; optical inspection; spectrum fatigue loads; irregularity factor

1. Introduction The knowledge of the fatigue damage state of structures made of composite material such as carbon fiber reinforced polymer (CFRP) is essential to make the next step in the optimization of composite structures in the aeronautic industry and in general industrial applications. Nowadays, fatigue damage is not an essential point in maintenance of aeronautic CFRP structures because these are normally loaded far below their fatigue resistance. However, but for future highly optimized structures, estimating the fatigue damage will become an important issue. Conventional techniques to evaluate the fatigue state of an aircraft structure are based on measurements of structural loads throughout the service life by electric strain gauge sensors, which present some difficulties. One of them is that these sensors are affected by the extreme environmental flight conditions and by the fatigue loads, in such a way that they have an elevated probability to fail and require an exhaustive maintenance program. A second disadvantage is that the stiffness degradation of the composite materials due to the accumulated damage could lead to non-realistic stress-strain relation of the strain gauge sensors. A third disadvantage is that the accumulated fatigue damage determined by a load history is conventionally calculated by linear damage accumulation models (such as Palmgren-Miner) [1]. Experimental studies show that this rule

Materials 2015, 8, 7524–7535; doi:10.3390/ma8115407

www.mdpi.com/journal/materials

Materials 2015, 8, 7524–7535

leads to inaccurate and non-conservative predictions for composite materials under realistic variable amplitude loads [2–4]. There are models developed for fatigue damage accumulation of composite materials, including strength and stiffness degradation. These models are based on fitting experimental values [2], but, due to the complexity of the damage mechanisms, they are only applicable for explicit conditions of loads and materials. The most classic fatigue damage metric is the strength degradation of the material, commonly known as residual strength [2]. When the residual strength becomes equal or lower than the maximum stress applied during cycling, the structure is prone to fail. Although the residual strength is the best metric to determine the damage state of a structure, in actual structures it cannot be measured by non-destructive evaluations. Other classic fatigue damage metric of CFRP, and an alternative to the residual strength, is the stiffness degradation. Several authors have studied stiffness degradation and its relation with residual strength [5–7]. The advantage is that the stiffness can be measured with non-destructive methods, but in general it requires the application of a specific load to the structure with a dedicated test setup that is complicated to achieve in aircraft structures. These difficulties have created the need to assess phenomenological methods [1] such as acoustic emissions [8], digital image correlation [9,10], thermography [10,11], X ray tomography [12], electrical resistance [13], and analysis of the surface [14–16], among others. Previous studies by the authors have shown that changes in the surface topography of CFRP, quantified by the roughness magnitude, could be an indicator of the accumulated fatigue damage [14–16]. Other authors have studied techniques for evaluating the fatigue damage by means of the surface assessment in metal structures, which undergo a surface transition related to metallurgical effects of their crystal structure [17,18]. For CFRP, the change of the surface starts at the beginning of the life of the structure with matrix micro-cracks parallel to the reinforcing carbon fibers. With increasing fatigue cycles, the cracks become bigger and tend to produce local delaminations in sub-surface layers changing the surface topography significantly. Results of previous works by the authors with specimens cycled with constant amplitude loads (CAL) show that the changes of the surface roughness are correlated with the stiffness degradation [14,15], which is a classical metric of fatigue damage. A further study by the authors, which was focused on the evaluation of the methodology with realistic variable amplitude loads (VAL), shows that the agreement between surface roughness magnitude and stiffness degradation is independent of the type of load applied [16]. As mentioned by Sonsino [19], due to the absence of effective cumulative damage, models that predict the life of components under VAL using CAL test data or variable amplitude load tests (VAL) are useful and necessary to understand the behavior of the material under real in-service conditions. The present work evaluates a different approach to assess the changes on the surface topography as a consequence of fatigue damage. The assessment is done in the frequency domain by determining the Power Spectral Density (PSD) of the topography profile, by evaluating the Irregularity Factor (I). This factor was first introduced by Rice [20,21] and is commonly employed to estimate the fatigue life of structures taking into account the PSD of the load history [19,22]. Surface Irregularity Factor The irregularity factor estimates statistically the relation between the numbers of peaks in the profile and the number of upward zero-crossings (see Figure 1a). The I-Factor provides information of the shape of the surface. The mathematical procedure to determine the I-Factor starts with the fast Fourier transform algorithm (FFT). The topographic profile is defined by the discrete function Z(x j )

7525

Materials 2015, 8, 7524–7535

that defines the height of the point x j respect to the mean line. The discrete function of the profile into the frequency domain is Z(ξk ), which is given by the Equation (1): Zpξk q “ ∆x

Pÿ ´1

Zpx j qe´

2πi jk P

(1)

j “0

Materials 2015, 8, page–page 

where L is the length of the topographic profile, P is the number of pixels, ∆x= L/P is the spatial where  L  is  the  length  of  the  topographic  profile,  P  is  the  number  of  pixels,  Δx=  L/P  is  the  spatial  resolution, i is the complex number and j and k are the discrete indices. The spectral density function resolution, i is the complex number and j and k are the discrete indices. The spectral density function  S(ξk ) is computed by the Equation (2): S(ξk) is computed by the Equation (2):  1 Spξk qξ “ 1|Zpξ q|2 (2) (2)  L | kξ |   The factor is is  calculated from thethe  area moments of of  S(ξS(ξ ξk ξ>k  >  0. 0. The The irregularity irregularity  factor  calculated  from  area  moments  k)  when  The area area  k ) when moments are obtained by the Equation (3), where ∆ξ = L´1−1is the spatial frequency resolution. Finally, moments are obtained by the Equation (3), where Δξ = L  is the spatial frequency resolution. Finally,  the Irregularity Factor (I) is determined by the Equation (4): the Irregularity Factor (I) is determined by the Equation (4):  P ÿ Mn “ ∆ξ ξ ξnkξ Spξkξq  

(3)  (3)

k“0

I“?

M2 M0 M4

(4) (4)

AA surface with an I‐Factor close to one has a shape similar to the profile depicted in Figure 1b.  surface with an I-Factor close to one has a shape similar to the profile depicted in Figure 1b. The perturbations of the surface are within a narrow frequency band and oscillate respect to the mean The perturbations of the surface are within a narrow frequency band and oscillate respect to the mean  plane of the surface. A surface with an I-Factor close to zero has a shape similar to the profile shown plane of the surface. A surface with an I‐Factor close to zero has a shape similar to the profile shown  inin  Figure 1c. low spatial Figure  1c. The The frequency frequency band band isis broad, broad, and and the the amplitude amplitude ofof the the perturbations perturbations ofof  low  spatial  frequency is much larger than the perturbations of high spatial frequency. frequency is much larger than the perturbations of high spatial frequency.  1

Mean Line

0 -1

I = 0.97

(b)

1 2

26 L Upward zero-crossing

(a)

50 Peaks

0 -1

I = 0.22

(c)

Figure  Topographic  profile  with  theoretical  points  for  calculating  the  irregularity  factor;   Figure 1. 1.  (a)(a)  Topographic profile with the the  theoretical points for calculating the irregularity factor; (b) (b) Surface with a narrow band, I = 0.97; (c) Surface with a broad band, I = 0.22.  Surface with a narrow band, I = 0.97; (c) Surface with a broad band, I = 0.22.

2.2. Methodology  Methodology 2.1. Materials and Equipment 2.1. Materials and Equipment  The used composite material is a CFRP type MTM-45-1/IM7 from Cytec Industries Inc. (Heanor, The used composite material is a CFRP type MTM‐45‐1/IM7 from Cytec Industries Inc. (Heanor,  UK), which is a relatively new composite material used for aeronautic structures with the ability UK), which is a relatively new composite material used for aeronautic structures with the ability to  tobe processed in and out of autoclave. Panels of 2 mm thickness in a quasi‐isotropic stacking sequence  be processed in and out of autoclave. Panels of 2 mm thickness in a quasi-isotropic stacking sequence of ((45,90,´45,0) )2 , have been autoclave atand  6 bars and C for The ultimate of  ((45,90,−45,0) s)2,  have sbeen  autoclave  cured  at cured 6  bars  130  °C 130 for ˝2.5  h.  2.5 The h.ultimate  tensile  tensile strength (Sut ) of the material is 938 MPa and was determined statistically in a previous strength (S ut) of the material is 938 MPa and was determined statistically in a previous study [14].  Coupons with “dog bone” design, shown in Figure 2, were cut from the panels in order to guarantee  the highest level of stress at the inspected zone. In order to obtain a better load introduction and to  7526 protect  the  coupons  against  the  gripping  forces  of  the  test  machine  clamps,  glass  fibre  reinforced  polymer  (GFRP)  tabs  were  bonded  at  both  extremes  with  film  adhesive  MTA240  from  Cytec  Industries Inc. 

 

Materials 2015, 8, 7524–7535

study [14]. Coupons with “dog bone” design, shown in Figure 2, were cut from the panels in order to guarantee the highest level of stress at the inspected zone. In order to obtain a better load introduction and to protect the coupons against the gripping forces of the test machine clamps, glass fibre reinforced polymer (GFRP) tabs were bonded at both extremes with film adhesive MTA240 from Cytec Industries Inc. The fatigue tests were performed with a MTS 810 hydraulic test machine (MTS Systems Co., Materials 2015, 8, page–page  Eden Prairie, MN, USA) from MTS operated at room temperature under load controlled condition. The stiffness of the specimen was extracted from the test machine during the fatigue cycles. The The surface topography was measured by a confocal microscope (PLμ 2300 Confocal Imaging Profiler,  surface topography was measured by a confocal microscope (PLµ 2300 Confocal Imaging Profiler, from Sensofar (Barcelona, Spain), with an objective zoom of 50×, and a resolution of 5 nm.   from Sensofar (Barcelona, Spain), with an objective zoom of 50ˆ, and a resolution of 5 nm.

2.2. Fatigue Tests and Stiffness Measurements  2.2. Fatigue Tests and Stiffness Measurements In this work, to study the proposed methodology under different load conditions, three types of  In this work, to study the proposed methodology under different load conditions, three types fatigue  loads  were  R == 0.1 0.1 which which  of fatigue loads wereapplied.  applied.Cycling  Cyclingloads  loadswith  withconstant  constantamplitude  amplitude (CAL),  (CAL), with  with an  an R means that the maximum stress (S ) is 10 times the minimum stress (S ). Variable amplitude loads  means that the maximum stress (Smax ) is 10 times the minimum stressmin(S max min ). Variable amplitude (VAL),  representative  of  fighter  aircrafts  using  the  standard  of  loads (VAL), representative of fighter aircrafts using the standardFalstaff,  Falstaff,and  andVAL  VAL representative  representative of transport aircraft using the standard MiniTwist were applied. The quantity of coupons for each type  transport aircraft using the standard MiniTwist were applied. The quantity of coupons for each type of load and their identification number are summarized in Table 1.  of load and their identification number are summarized in Table 1.

  Figure 2. (a) Coupon geometry and principal dimensions (mm); (b) Normalized strain distribution in  Figure 2. (a) Coupon geometry and principal dimensions (mm); (b) Normalized strain distribution in the direction of the tensile load by finite element analysis, showing less than 5% of strain gradient in  the direction of the tensile load by finite element analysis, showing less than 5% of strain gradient in the optical measurement zone; (c) Typical failure of a coupon under tensile fatigue loads.  the optical measurement zone; (c) Typical failure of a coupon under tensile fatigue loads. Table 1. Quantity of specimens and type of load used for the fatigue test.   Table 1. Quantity of specimens and type of load used for the fatigue test.

Type of Sequence 

Number of Coupons

Type of Sequence Number of Coupons Constant Amplitude Load  13 

Coupons Id

Coupons Id C01 to C13 

Tensile Load Ratio R Tensile Load 0.1 Ratio R

9  F01 to F09  Spectrum *  Constant Falstaff  Amplitude 13 C01 to C13 0.1 Load MiniTwist  5  T01 to T05  Spectrum *  Falstaff 9 F01 to F09 Spectrum * * With a relation of R = 0.1 between the maximum peak and minimum valley load.  MiniTwist 5 T01 to T05 Spectrum * * With a relation of R = 0.1 between the maximum peak and minimum valley load. The Falstaff sequence is a standardized representation of the loads supported in the wing roots  of  fighter  aircrafts,  under  the  combinations  of  different  types  of  missions  and  maneuvers  [23,24].   The complete Falstaff consists of approximately 106 cycles of 32 different load levels which represents  7527 200 flights (one year of typical usage). Figure 3a shows a fraction of the load sequence.  The  MiniTwist  is  a  shortened  version  of  the  standard  Twist  (Transport  Wing  Standard),   where  minor  gust loads were  omitted  to shorten  the  tests  whilst  maintaining  the  reliability  of  the  results [23,24]. The MiniTwist represents the entire life time fatigue loads in the wing root of transport 

Materials 2015, 8, 7524–7535

28 24 32 20 28 16 24 12 20 8 16 4 12 0 8 0 4 0 0

Fraction of FALSTAFF

200

400

600

800

Load Levels Load Levels

Load Levels Load Levels

The Falstaff sequence is a standardized representation of the loads supported in the wing roots of fighter aircrafts, under the combinations of different types of missions and maneuvers [23,24]. The complete Falstaff consists of approximately 106 cycles of 32 different load levels which represents 200 flights (one year of typical usage). Figure 3a shows a fraction of the load sequence. The MiniTwist is a shortened version of the standard Twist (Transport Wing Standard), where minor gust loads were omitted to shorten the tests whilst maintaining the reliability of the results [23,24]. The MiniTwist represents the entire life time fatigue loads in the wing root of transport aircrafts of about 4000 flights and is composed of 580 ˆ 103 cycles discretized in 20 load levels. Figure 3b shows a fraction of the load sequence. In order to evaluate the proposed methodology with fatigue cycles of different severity, CALs Materials 2015, 8, page–page  and VALs with different levels of maximum load have been applied. In the case of Falstaff and MiniTwist, the maximum load is the highest peak in the whole sequence and the minimum load is MiniTwist, the maximum load is the highest peak in the whole sequence and the minimum load is  Materials 2015, 8, page–page  the lowest valley (in the present study the ratio between the minimum valley and the maximum peak the lowest valley (in the present study the ratio between the minimum valley and the maximum peak  is With the  the aim  aim of  of obtaining is 0.1). 0.1).  With  obtaining  VALs VALs of of different different severities, severities, the the sequences sequences have have been been scaled scaled to to  MiniTwist, the maximum load is the highest peak in the whole sequence and the minimum load is  several levels of maximum peak load, as shown in Figure 4. several levels of maximum peak load, as shown in Figure 4.  the lowest valley (in the present study the ratio between the minimum valley and the maximum peak  is  0.1).  With  the  aim  of  obtaining  VALs  of  different  severities,  the  sequences  have  been  scaled  to  Fraction of MiniTWIST Fraction of FALSTAFF several levels of maximum peak load, as shown in Figure 4.  10 32

1000

Cycles (n) 200

400 (a) 600

800

1000

8 6 104 82 60 -2 4 -4 2 -6 0 -8 -2 -10 -4 -614000 -8 -10 14000

Fraction of MiniTWIST

14200

14400

14600

14800

15000

14800

15000  

Cycles (n) 14200

14400 (b)14600

Cycles (n)

Cycles (n)

Figure 3. Fraction of the load sequences; (a) Fighter Aircraft—Falstaff; (b) Transport Aircraft—MiniTwist.  Figure 3. Fraction of the load sequences; (a) Fighter Aircraft—Falstaff; (b) Transport (a) (b) Aircraft—MiniTwist. 0.8 Figure 3. Fraction of the load sequences; (a) Fighter Aircraft—Falstaff; (b) Transport Aircraft—MiniTwist.  0.7

 

0.6 0.8

Smax = 0.8Sut

0.5 0.7

% Sut 0.6 0.4

Smax = 0.6Sut Smax = 0.8Sut

0.3 0.5

% Sut 0.4 0.2

Smax = 0.6Sut

0.1 0.3 0.20 0.1

Cycles (n)

 

0 Figure 4. Fraction of Falstaff showing load sequences of different severity, with maximum peak loads  Cycles (n) of 0.8Sut and 0.6Sut.   

Figure 4. Fraction of Falstaff showing load sequences of different severity, with maximum peak loads  Figure 4. Fraction of Falstaff showing load sequences of different severity, with maximum peak loads If  a  coupon  did  not  fail  in  whiting  one  pass  of  the  standard  sequences,  the  load  history  was  of 0.8S ut and 0.6S of 0.8Sut and 0.6Sutut. . 7

repeated until failure with a limit of 10  cycles. In all the cases, the fatigue tests have been interrupted  periodically before failure in order to perform the measurements of the surface topography.  If  a  coupon  did  not  fail  in  whiting  one  pass  of  the  standard  sequences,  the  load  history  was  IfThe  a coupon did not fail in has  whiting one pass ofduring  the standard sequences, load history was stiffness  degradation  been  measured  the  fatigue  cycles the using  the  cross  head  7 cycles. In all the cases, the fatigue tests have been interrupted  repeated until failure with a limit of 10 7 repeated until failure with a limit of 10 cycles. In all the cases, the fatigue tests have been interrupted extension and load data from the testing machine. The stiffness measurements have been normalized  periodically before failure in order to perform the measurements of the surface topography.  periodically before failure in order to perform the measurements of the surface topography. to enable them to be quantified in terms of percentage of the initial stiffness.  The  stiffness  degradation  has  been  measured  during  the  fatigue  cycles  using  the  cross  head  extension and load data from the testing machine. The stiffness measurements have been normalized  2.3. Measurement of the Surface Irregularity Factor 7528 to enable them to be quantified in terms of percentage of the initial stiffness. 

Measurements  of  the  surface  topography  have  been  performed  during  tests  on  both  coupon  2.3. Measurement of the Surface Irregularity Factor  sides  at  an  arbitrary  location  within  the  center  zone  of  the  specimen.  Each  measurement  area  is   1.55 × 1.49 mm2 with a resolution of the confocal microscope of about 21 megapixels. One value per 

Materials 2015, 8, 7524–7535

The stiffness degradation has been measured during the fatigue cycles using the cross head extension and load data from the testing machine. The stiffness measurements have been normalized to enable them to be quantified in terms of percentage of the initial stiffness. 2.3. Measurement of the Surface Irregularity Factor Measurements of the surface topography have been performed during tests on both coupon sides at an arbitrary location within the center zone of the specimen. Each measurement area is 1.55 ˆ 1.49 mm2 with a resolution of the confocal microscope of about 21 megapixels. One value per coupon and per life stage has been obtained by averaging the results of the measured points. Initial reference topographies were taken previous to the fatigue cycling for each area of measurement, just after the specimen manufacturing. Afterwards, the surface degradation is measured after each fatigue cycling block. Cycling blocks are of arbitrary length and depend on the expected fatigue life of the specimen. The PSD of each measurement is calculated from a profile extracted from the confocal Materials 2015, 8, page–page  topography, by sectioning the surface in a plane perpendicular to the reinforcing carbon fibers of the composite material, as shown in Figure 5. The PSD and the surface irregularity factor for each composite material, as shown in Figure 5. The PSD and the surface irregularity factor for each point  point of measurement are calculated by the Equations (1)–(4). of measurement are calculated by the Equations (1)–(4).  The evolution of the irregularity factor is evaluated and analyzed in relation to the number The evolution of the irregularity factor is evaluated and analyzed in relation to the number of  of cycles appliedand  andis isfinally  finallycompared  comparedwith  with a a classical  classical metric  metric of  of fatigue cycles  applied  fatigue  damage damage for for composite composite  materials, which is the stiffness degradation [5]. materials, which is the stiffness degradation [5]. 

  Figure 5. Surface topography in one of the measurement areas and the section profile used to calculate  Figure 5. Surface topography in one of the measurement areas and the section profile used to calculate the irregularity factor.  the irregularity factor.

3. Results and Discussion  3. Results and Discussion 3.1. Stiffness Degradation  3.1. Stiffness Degradation The stiffness stiffness degradation degradation isis aa measure measure of of the the damage damage state state of of the the composite composite material material due due to to  The fatigue loads. In this work, it has been studied in relation to the changes of the I‐factor.   fatigue loads. In this work, it has been studied in relation to the changes of the I-factor. The stiffness degradation as a result of the accumulated damage of the coupons for the CAL tests  The stiffness degradation as a result of the accumulated damage of the coupons for the CAL is  shown  in  Figure  6,  and  the the results  for for the  are  shown shown in in   tests is shown in Figure 6, and results theFalstaff  Falstaffand  andMiniTwist  MiniTwist VAL  VAL tests  tests are Figure 7a,b, respectively. All the data of stiffness evolution are presented in semi‐log scale. The three  Figure 7a,b, respectively. All the data of stiffness evolution are presented in semi-log scale. The three graphics show that the coupons cycled with higher severity loads present faster stiffness degradation,  graphics show that the coupons cycled with higher severity loads present faster stiffness degradation, because higher loads produce earlier damage in the composite material. This behavior was expected  because higher loads produce earlier damage in the composite material. This behavior was expected and is in accordance with earlier studies [15,16], and confirms that the stiffness degradation can be  and is in accordance with earlier studies [15,16], and confirms that the stiffness degradation can be employed to determine the damage state due to fatigue loads.  employed to determine the damage state due to fatigue loads. C01 = 47% SSuC ut

1.0

C02 = 47% SSuC ut 0.9

7529

C03 = 49% SSuC ut C04 = 51% SSuC ut

o

0.8

C05 = 53% SSuC ut C06 = 53% SSuC

is  shown  in  Figure  6,  and  the  results  for  the  Falstaff  and  MiniTwist  VAL  tests  are  shown  in   Figure 7a,b, respectively. All the data of stiffness evolution are presented in semi‐log scale. The three  graphics show that the coupons cycled with higher severity loads present faster stiffness degradation,  because higher loads produce earlier damage in the composite material. This behavior was expected  and is in accordance with earlier studies [15,16], and confirms that the stiffness degradation can be  Materials 2015, 8, 7524–7535 employed to determine the damage state due to fatigue loads.  C01 = 47% SSuC ut

1.0

C02 = 47% SSuC ut C03 = 49% SSuC ut

0.9

C04 = 51% SSuC ut

En /Eo

0.8

C05 = 53% SSuC ut C06 = 53% SSuC ut

0.7

C07 = 55% SSuC ut C08 = 56% SSuC ut

0.6

C09 = 57% SSuC ut C10 = 57% SSuC ut

0.5 0.4 1.E+02

C11 = 62% SSuC ut C12 = 62% SSuC ut 1.E+04

1.E+06

C13 = 66% SSuC ut

Cycles (n)

 

Figure 6.6.  Stiffness  of  coupons coupons  under under  constant constant  amplitude amplitude  fatigue fatigue loads loads (CAL) (CAL) with with  Figure Stiffness degradation  degradation of different maximum load.  different maximum load.

Materials 2015, 8, page–page 

As expected, CAL coupons have failed much6 earlier at the same maximum load than the VAL As expected, CAL coupons have failed much earlier at the same maximum load than the VAL  coupons, because the maximum loads are only punctually applied in the VAL tests and the majority of coupons, because the maximum loads are only punctually applied in the VAL tests and the majority  the loads are of lower magnitude, whilst in the CAL tests the maximum load is applied cycle by cycle. of the loads are of lower magnitude, whilst in the CAL tests the maximum load is applied cycle by cycle.  Figure 7 also confirms that the Falstaff sequence is more severe than the MiniTwist, because the Figure 7 also confirms that the Falstaff sequence is more severe than the MiniTwist, because the  coupons cycled at the same maximum load failed earlier for Falstaff. coupons cycled at the same maximum load failed earlier for Falstaff. 

0.90

F03 =65%SSut ut

0.85

F04 =70% SSut ut

0.80

F05 =70% SSut ut

En /Eo

0.75

F06 =75% SSut ut

0.70

F07 =75% SSut ut

0.65 0.60 1.E+04

1.00 T01 =77.5% SSut ut

0.95

En /Eo

0.95

F01 =60% SSut ut (Run-out) F02 =65% SSut ut

1.00

T02 =80% SSut ut

0.90

T03 =80% SSut ut 0.85

T04 =85% SSut ut

0.80

T05 =85% SSut ut

F08 =80% SSut ut 1.E+05

1.E+06

F09 =80% SSut ut

0.75 1.E+04

1.E+05

1.E+06

Cycles (n)

Cycles (n)

(a)

(b)

 

Figure  Figure 7.  7. Stiffness  Stiffness degradation  degradation of  of coupons  coupons under  under variable  variable amplitude  amplitude loads  loads (VAL)  (VAL) with  with different  different maximum load; (a) Falstaff; (b) MiniTwist.  maximum load; (a) Falstaff; (b) MiniTwist.

3.2. Evolution of the Surface Irregularity Factor (I) through Cycles.  3.2. Evolution of the Surface Irregularity Factor (I) through Cycles The topographic profile and its correspondent spatial spectral density of two measurements and  The topographic profile and its correspondent spatial spectral density of two measurements two  specimens,  are  presented  to  show  the  phenomena  investigated  in  the  present  work.  The  and two specimens, are presented to show the phenomena investigated in the present mentioned specimens are cycled with CAL at different maximum loads. Figures 8 and 9 show the  work. The mentioned specimens are cycled with CAL at different maximum loads. topographic  profile  and  the  PSD  for  the  coupon  C01  cycled  at  Smax  =  47%  Sut  and  C12  cycled  at   Figures 8 and 9 show the topographic profile and the PSD for the coupon C01 cycled at Smax = 62% Sut, respectively.  Smax = 47% Sut and C12 cycled at Smax = 62% Sut , respectively. Figures 8a and 9a show the evolution of the topographic profile during the cycles. In both cases  Figures 8a and 9a show the evolution of the topographic profile during the cycles. In both cases a component of low frequency is generated as a consequence of the cracks and delaminations. This  a component of low frequency is generated as a consequence of the cracks and delaminations. This low frequency component makes the surface more irregular. With increasing cycles, the amplitude  low frequency component makes the surface more irregular. With increasing cycles, the amplitude of the low frequency component increases due to an increment in the delamination, and the surface  irregularity factor is closer to zero.  7530

Topographic profile 5.0

Power Spectral Density

1.E+4

Cycles (n) = 0

two  specimens,  are  presented  to  show  the  phenomena  investigated  in  the  present  work.  The  mentioned specimens are cycled with CAL at different maximum loads. Figures 8 and 9 show the  topographic  profile  and  the  PSD  for  the  coupon  C01  cycled  at  Smax  =  47%  Sut  and  C12  cycled  at   Smax = 62% Sut, respectively.  Materials Figures 8a and 9a show the evolution of the topographic profile during the cycles. In both cases  2015, 8, 7524–7535 a component of low frequency is generated as a consequence of the cracks and delaminations. This  low frequency component makes the surface more irregular. With increasing cycles, the amplitude  of the low frequency component increases due to an increment in the delamination, and the surface of the low frequency component increases due to an increment in the delamination, and the surface  irregularity factor is closer to zero. irregularity factor is closer to zero.  Topographic profile

Power Spectral Density

5.0

2.5

Spectral density

Height z (µm)

1.E+4

0.0

-2.5

Cycles (n) = 0 I = 0.34

1.E+2 1.E+0

Cycles (n) = 120E3 I = 0.18

1.E-2

Cycles (n) = 250E3 I = 0.12

1.E-4 -5.0 0

0.5

1

1.5

1.E-6 5.E-4

2

Profile (mm)

(a)

5.E-3

5.E-2

5.E-1

Spatial Frequency (µm-1)

(b)

 

Figure 8. One area of inspection of the coupon C01 cycled at Smax = 0.47Sut; (a) Topographic profile;   Figure 8. One area of inspection of the coupon C01 cycled at Smax = 0.47Sut ; (a) Topographic profile; (b) Power spectral density of the profile in log‐log scale.  (b) Power spectral density of the profile in log-log scale.

Figures 8b and 9b show the evolution of the surface spectral density function. The PSD results  Figures 8b and 9b show the evolution of the surface spectral density function. The PSD results are are presented in log‐log scale. The low frequencies increase due to the aforementioned increment of  Materials 2015, 8, page–page  presented in log-log scale. The low frequencies increase due to the aforementioned increment of the delamination and cracks. Also, a variation is shown 7  in the high frequency range where the spectral the  delamination  and  cracks.  Also,  a  variation  is  shown  in  the  high  frequency  range  where  the  density increases through the cycles. This variation could be explained by the creation of micro-cracks spectral  density  increases through  the  cycles.  This  variation  could be  explained by  the  creation  of  in the matrix during the fatigue process. These micro-cracks are unrevealed if the topography is micro‐cracks  in  the  matrix  during  the  fatigue  process.  These  micro‐cracks  are  unrevealed  if  the  analyzed only in the spatial domain. topography is analyzed only in the spatial domain.  Power Spectral Density

Topographic profile 5

2.5

Spectral density

Height z (µm)

1.E+4

0

-2.5

Cycles (n) = 0 I = 0.36

1.E+2

Cycles (n) = 10E3 I = 0.17

1.E+0 1.E-2

Cycles (n) = 15E3 I = 0.09

1.E-4

-5 0

0.5

1

1.5

2

1.E-6 5.E-4

5.E-3

5.E-2

5.E-1

Spatial Frequency (µm-1)

Profile (mm)

(a)

(b)

 

Figure 9. One area of inspection of the coupon C12 cycled at Smax = 0.62Sut (a) Topographic profile;   Figure 9. One area of inspection of the coupon C12 cycled at Smax = 0.62Sut (a) Topographic profile; (b) Power spectral density of the profile.  (b) Power spectral density of the profile.

The  evolution  of  the  I‐Factor  versus  the  fatigue  cycles  of  all  the  coupons  cycled  at  CAL  is  The evolution of 10a.  the I-Factor versus the fatigue cyclesmore  of all the coupons cycled atfatigue  CAL is presented  in  Figure  The  specimens’  surfaces  become  irregular  with  increasing  presented in Figure 10a. The specimens’ surfaces become more irregular with increasing fatigue cycles and the slope of the graphs is more pronounced when the fatigue load is higher. The same  cycles and the slope of the graphs is more pronounced when the fatigue load is higher. The same tendencies can be observed when the coupons are cycled with realistic load sequences. The evolution  tendencies canis bepresented  observedin  when the11a  coupons are cycled with realistic load Thethe  evolution for  Falstaff  Figure  and  for  MiniTwist  in  Figure  12a.  In sequences. general,  when  load  forhistory is of higher severity, a faster change in the irregularity factor is produced. That conclusion is  Falstaff is presented in Figure 11a and for MiniTwist in Figure 12a. In general, when the load directly  related  to severity, the  evolution  of  the fatigue  damage  that  higher  loads  produce  more and  faster  history is of higher a faster change in the irregularity factor is produced. That conclusion damage than lower loads.  is directly related to the evolution of the fatigue damage that higher loads produce more and faster damage than lower loads. 0.5

7531

0.4

C01 = 47% SSut ut C02 = 47% SSut ut C03 = 49% SSut ut C04 = 51% SSut ut

0.3

0.9 o

rity Factor

1.0

C05 = 53% SSut ut C06 = 53% SSut

presented  in  Figure  10a.  The  specimens’  surfaces  become  more  irregular  with  increasing  fatigue  cycles and the slope of the graphs is more pronounced when the fatigue load is higher. The same  tendencies can be observed when the coupons are cycled with realistic load sequences. The evolution  for  Falstaff  is  presented  in  Figure  11a  and  for  MiniTwist  in  Figure  12a.  In  general,  when  the  load  history is of higher severity, a faster change in the irregularity factor is produced. That conclusion is  Materialsdirectly  2015, 8, 7524–7535 related  to  the  evolution  of  the fatigue  damage  that  higher  loads  produce  more and  faster  damage than lower loads.  0.5

C01 = 47% SSut ut C02 = 47% SSut ut

0.4

C03 = 49% SSut ut C04 = 51% SSut ut C05 = 53% SSut ut

0.9

0.3

C06 = 53% SSut ut

En/Eo

Irregularity Factor

1.0

C07 = 55%SSut ut

0.2

C08 = 56% SSut ut 0.8

C09 = 57% SSut ut C10 = 57% SSut ut

0.1

C11 = 62% SSut ut 0.0

Sut C12= 62% Sut

0.7 0

50000 100000 150000 200000 250000

0.0

Cycles (n)

0.1

0.2

0.3

0.4

0.5

C13 = 66% SSut ut

Irregularity Factor

(a)

(b)

 

Figure 10. Evolution of the I‐Factor of all the coupons cycled with CAL. The shown I‐Factor for each 

Figure 10. Evolution of the I-Factor of all the coupons cycled with CAL. The shown I-Factor for coupon  is  the  mean  value  of  the  areas  of  inspection;  (a)  Evolution  through  the  fatigue  cycles;   each coupon is the mean value of the areas of inspection; (a) Evolution through the fatigue cycles; (b) Relation between the evolution of the stiffness degradation and the evolution of I‐Factor.  (b)Materials 2015, 8, page–page  Relation between the evolution of the stiffness degradation and the evolution of I-Factor. Materials 2015, 8, page–page  0.5

1

F01 =60% Sut Sut (Run-out) F01 SSSut F02=60% =65%Sut ut (Run-out) ut F02 =65% Sut S F03 =65% SSut ut

1

0.4

0.95

0.4

8 

ut

En /EEon /Eo

Irregularity Factor Irregularity Factor

0.5

0.3 0.3 0.2

0.95

F03 SSut utut F04=65% =70%SSut

0.9

F04 Sutut F05=70% =70%SSut Sut

0.9

SSSut F05 utut F06=70% =75%Sut

0.85

F06 Sutut F07=75% =75%SSut Sut

0.85

SSut F07 Sutut F08=75% =80%Sut

0.2 0.1 0.1 0 0.E+00 0 0.E+00

SSut F08 Sutut F09=80% =80%Sut

0.8 2.E+06

4.E+06

6.E+06

2.E+06

Cycles4.E+06 (n)

6.E+06

(a) (n) Cycles

0.8

0 0

0.2

0.4

Irregularity Factor 0.2 0.4

0.6

Sut F09 =80% Sut

0.6

(b)Factor   Irregularity (a) (b)   Figure 11. Evolution of the I‐Factor of all the coupons cycled with Falstaff. The shown I‐Factor for  Figure each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles;  11. Evolution of the I-Factor of all the coupons cycled with Falstaff. The shown I-Factor for Figure 11. Evolution of the I‐Factor of all the coupons cycled with Falstaff. The shown I‐Factor for  each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles; (b) Relation between the evolution of the stiffness degradation and the evolution of the I‐Factor.  each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles; 

(b) Relation between the evolution of the stiffness degradation and the evolution of the I-Factor. (b) Relation between the evolution of the stiffness degradation and the evolution of the I‐Factor.  0.5

1 1

0.4

T01 =77.5% SSu ut

0.95

0.4

0.95

T01 =77.5% SSu ut T02 =80% SSut ut

0.9

T02 =80% SSut ut T03 =80% SSut ut

0.9

T03 =80% SSut ut T04 =85% SSut ut

En /EEon /Eo

Irregularity Factor Irregularity Factor

0.5

0.3 0.3 0.2 0.2

0.85

0.1 0.1 0 0.E+00 0 0.E+00

T04 =85% SSut ut T05 =85% SSut ut

0.85

T05 =85% SSut ut

0.8 2.E+06

Cycles 2.E+06

4.E+06

(n)

(a) Cycles (n)

4.E+06

0.8

0

0.2

0.4

0

Irregularity 0.4 Factor 0.2

(b)

0.6 0.6

Irregularity Factor

 

(a) (b)   Figure 12. Evolution of the I‐Factor of all the coupons cycled with MiniTwist. The shown I‐Factor for  each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles;  Figure 12. Evolution of the I‐Factor of all the coupons cycled with MiniTwist. The shown I‐Factor for 

Figure (b) Relation between the evolution of the stiffness degradation and the evolution of the I‐Factor.  12. Evolution of the I-Factor of all the coupons cycled with MiniTwist. The shown I-Factor for each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles;  each coupon is the mean value of all the areas of inspection; (a) Evolution through the fatigue cycles; (b) Relation between the evolution of the stiffness degradation and the evolution of the I‐Factor.  (b)3.3. Relation between the Surface Irregularity Factor (I) and the Stiffness Degradation.  Relation between the evolution of the stiffness degradation and the evolution of the I-Factor. 3.3. Relation between the Surface Irregularity Factor (I) and the Stiffness Degradation.  The  stiffness  degradation  is  used  in  order  to  establish  a  direct  relation  between  the  surface  irregularity factor and the damage of the material due to fatigue.  The  stiffness  degradation  is  used  in  order  to  establish  a  direct  relation  between  the  surface  7532 The relation of the stiffness degradation and the I‐Factor for CAL tests is depicted in Figure 10b,  irregularity factor and the damage of the material due to fatigue.  where  the  irregularity  factor  is  lower  when  the  stiffness  of  the  material  is  more  degraded.  The  The relation of the stiffness degradation and the I‐Factor for CAL tests is depicted in Figure 10b,  corresponding  Pearson factor  correlation  coefficient  that  indicates  the  material  strength  is  of more  a  linear  relationship  where  the  irregularity  is  lower  when  the  stiffness  of  the  degraded.  The  between two variables is 0.84, which confirms the direct relation between the I‐Factor and the stiffness 

Materials 2015, 8, 7524–7535

3.3. Relation between the Surface Irregularity Factor (I) and the Stiffness Degradation The stiffness degradation is used in order to establish a direct relation between the surface irregularity factor and the damage of the material due to fatigue. The relation of the stiffness degradation and the I-Factor for CAL tests is depicted in Figure 10b, where the irregularity factor is lower when the stiffness of the material is more degraded. The corresponding Pearson correlation coefficient that indicates the strength of a linear relationship between two variables is 0.84, which confirms the direct relation between the I-Factor and the stiffness degradation. The significant dispersion in the results is expected due to the stochastic nature of the fatigue process. However, a clear tendency can be appreciated in the graphic. Regarding the coupons cycled at realistic load sequences, the same tendency is observed. The linear relation between the I-Factor and the stiffness degradation is similar to the CAL tests. The results for Falstaff are shown in Figure 11b with a Pearson correlation of 0.84. The results for MiniTwist are shown in Figure 12b with a Pearson correlation of 0.79. The lower Pearson correlation of the MiniTwist results can be explained by the lower quantity of tested specimens. Materials 2015, 8, page–page  The relation between the stiffness degradation and the surface irregularity factor for all the load cases studied in the present work (CAL and realistic VAL loads) are presented superimposed in The relation between the stiffness degradation and the surface irregularity factor for all the load  Figure 13. The graph shows that the results present similar tendencies and scattering, which suggest cases studied in the present work (CAL and realistic VAL loads) are presented superimposed in Figure  that the present methodology of damage evaluation is independent of the load history that causes 13. The graph shows that the results present similar tendencies and scattering, which suggest that the  the fatigue. present methodology of damage evaluation is independent of the load history that causes the fatigue.   Regarding the initial value it can be seen in the graph that the CAL and the VAL coupons have Regarding the initial value it can be seen in the graph that the CAL and the VAL coupons have  different I-Factor previous to the fatigue process. That is because both groups of coupons are extracted different I‐Factor previous to the fatigue process. That is because both groups of coupons are extracted  from different panels, and the initial value depends on the manufacturing process of these panels. from different panels, and the initial value depends on the manufacturing process of these panels.  From the results presented in Figure 13, we can conclude that the studied methodology can From the results presented in Figure 13, we can conclude that the studied methodology can be  be applied to evaluate the damage state of a structure without knowing the load cases that have applied to evaluate the damage state of a structure without knowing the load cases that have caused  caused the surface changes. This makes this technique applicable for a wide range of inspections the surface changes. This makes this technique applicable for a wide range of inspections of composite  of composite materials structures from pressurized tanks with CAL fatigue cycles, to variable materials  loaded structures  from  pressurized  tanks  fatigue  cycles,  to automotive variable  amplitude   amplitude aeronautical structures such as with  wingsCAL  and empennages, up to and other loaded  aeronautical  structures  such  as  wings  and  empennages,  up  to  automotive  and  other   industrial applications. industrial applications.  1.00 0.95

CAL

En /Eo

0.90

Falstaff 0.85

MiniTwist

0.80

Trend Line

0.75 0.70 0

0.2

Irregularity Factor

0.4

0.6

 

Figure 13. Relation between the stiffness degradation and the I‐Factor, for the different type of fatigue  Figure 13. Relation between the stiffness degradation and the I-Factor, for the different type of fatigue loads applied.  loads applied.

4. Conclusions   4. Conclusions A  new new  inspection inspection  technique technique  for for  the the  evaluation evaluation  of of  the the  damage damage  state state  of of  composite composite  material material  A structures  has  been  presented.  It  has  been  demonstrated  that  the  method  is  applicable  for  wide  structures has been presented. It has been demonstrated that the method is applicablea for a range of fatigue loads, from constant amplitude load cases to complex spectrum loads of fighter and  wide range of fatigue loads, from constant amplitude load cases to complex spectrum loads of transport  normalized  in  Falstaff inand  MiniTwist  standards,  respectively.  The  stiffness  fighter andaircraft,  transport aircraft, normalized Falstaff and MiniTwist standards, respectively. The degradation and with it, the internal structural damage provoked by fatigue cycles, can be estimated  by  analyzing  and  measuring  the  surface  topography  using  confocal  microscopy.  Hand  held  7533 equipment for structural inspections of this type is already on the market. Examples of commercial  portable perfilometers from the same manufacturer, and with the same technology and precision as  the confocal microscope employed to obtain the results of the present work, are the models PLμ 1300 

Materials 2015, 8, 7524–7535

stiffness degradation and with it, the internal structural damage provoked by fatigue cycles, can be estimated by analyzing and measuring the surface topography using confocal microscopy. Hand held equipment for structural inspections of this type is already on the market. Examples of commercial portable perfilometers from the same manufacturer, and with the same technology and precision as the confocal microscope employed to obtain the results of the present work, are the models PLµ 1300 and Smart, both from Sensofar. The surface irregularity factor, as a parameter to measure the damage state of a carbon fiber component, shows a good agreement with a classical damage metric such as the stiffness degradation. To consider the Pearson correlation of 0.84 as good, we should take into account that fatigue processes are a stochastic phenomenon with high variability. Analysis in the spatial frequency domain could reveal surface changes due to fatigue damage that are hidden in an analysis of the surface roughness magnitude [15,16]. Internal delaminations are revealed by low spatial frequency components and cracks and micro-cracks increase the high spatial frequency content. The results obtained with the present methodology are independent of the load type applied and can be used for a wide range of applications where the in-service loads are known and controlled (such as pressure vessels) and where the loads are of random or variable nature (wings, automotive components, etc.). Acknowledgments: We would like to thank the Instituto Nacional de Técnica Aeroespacial (INTA) Metallic Test Laboratory, the INTA Composite Materials Area and the INTA Space Optics Area for their support during the test campaign and the inspections. This article was funded by the Spanish Ministry of Economy and Competitivity as part of the MINECO ESP2014-56138-C3-3-R. Author Contributions: Pablo Zuluaga-Ramírez and Malte Frövel designed the fatigue tests and coupons, performed the experiments and wrote the paper; Pablo Zuluaga-Ramírez, Tomás Belenguer and Félix Salazar designed the optical measurement setup and methodology; all the authors contributed to analyze the experimental results. Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4.

5.

6. 7. 8.

9.

Boller, C.; Staszewski, W. Aircraft Structural Health and Usage Monitoring. In Health Monitoring of Aerospace Structures: Smart Sensors Technologies and Signal Processing; Staszewski, W., Boller, C., Tomlinson, G., Eds.; John Wiley & Sons Ltd.: West Sussex, UK, 2004; pp. 29–74. Post, N.L.; Case, S.W.; Lesko, J.J. Modeling the variable amplitude fatigue of composite materials: A review and evaluation of the state of the art for spectrum loading. Int. J. Fatigue 2008, 30, 2064–2086. [CrossRef] Epaarachchi, J.A. A study on estimation of damage accumulation of glass fibre reinforce plastic (GFRP) composites under a block loading situation. Compos. Struct. 2006, 75, 88–92. [CrossRef] Zuluaga-Ramírez, P.; Frövel, M.; Arconada, Á.; Belenguer, T.; Salazar, F. Evaluation of the fatigue linear damage accumulation rule for aeronautical CFRP using artificial neural networks. Adv. Mater. Res. 2014, 1016, 8–13. [CrossRef] Highsmith, A.L.; Reifsnider, K.L. Stiffness Reduction Mechanisms in Composite Laminates. In Damage of Composite Materials; ASTM STP 775; Reifsnider, K.L., Ed.; American Society for Testing and Materials: Conshohocken, PA, USA, 1982; pp. 103–117. Whitworth, H.A. A stiffness degradation model for composite laminates under fatigue loading. Compos. Struct. 1997, 40, 95–101. [CrossRef] Van Paepegem, W.; Degrieck, J. Coupled residual stiffness and strength model for fatigue of fibre-reinforced composite materials. Compos. Sci. Technol. 2002, 62, 687–696. [CrossRef] Dzenis, Y.A. Cycle-based analysis of damage and failure in advanced composites under fatigue: 1. Experimental observation of damage development within loading cycles. Int. J. Fatigue 2003, 25, 499–510. [CrossRef] Giancane, S.; Panella, F.W.; Nobile, R.; Dattoma, V. Fatigue damage evolution of fiber reinforced composites with digital image correlation analysis. Proced. Eng. 2010, 2, 1307–1315. [CrossRef]

7534

Materials 2015, 8, 7524–7535

10. 11. 12. 13. 14.

15.

16.

17.

18. 19. 20. 21. 22. 23. 24.

Dattoma, V.; Giancane, S. Evaluation of energy of fatigue damage into GFRC through digital image correlation and thermography. Compos. B Eng. 2013, 47, 283–289. [CrossRef] Ahsan, M.; Han, X.; Islam, S.; Newaz, G. Fatigue damage detection in graphite/epoxy composites using sonic infrared imaging technique. Compos. Sci. Technol. 2004, 64, 657–666. Withers, P.J.; Preuss, M. Fatigue and damage in structural materials studied by X-ray tomography. Annu. Rev. Mater. Res. 2012, 42, 81–103. [CrossRef] Wang, X.; Chung, D.D.L. Self-monitoring of fatigue damage and dynamic strain in carbon fiber polymer-matrix composite. Compos. B Eng. 1998, 29, 63–73. [CrossRef] Zuluaga, P.; Frövel, M.; Restrepo, R.; Trallero, R.; Atienza, R.; Pintado, J.M.; Belenguer, T.; Salazar, F. Consumed fatigue life assessment of composite material structures by optical surface roughness inspection. Key Eng. Mater. 2013, 569–570, 88–95. [CrossRef] Zuluaga-Ramírez, P.; Frövel, M.; Belenguer, T.; Salazar, F. Non-contact inspection of the fatigue damage state of carbon fiber reinforced polymer by optical surface roughness measurements. NDT E Int. 2015, 70, 22–28. [CrossRef] Zuluaga-Ramírez, P.; Arconada, Á.; Frövel, M.; Belenguer, T.; Salazar, F. Optical sensing of the fatigue damage state of CFRP under realistic aeronautical load sequences. Sensors 2015, 15, 5710–5721. [CrossRef] [PubMed] Gordienko, Y.G.; Zasimchuk, E.E.; Gontareva, R.G. Unconventional deformation modes and surface roughness evolution in Al single crystals under restricted cyclic tension conditions. J. Mater. Sci. Lett. 2002, 21, 1713–1716. [CrossRef] Wang, L.; Wang, Z.; Xie, W.; Song, X. Fractal study on collective evolution of short fatigue cracks under complex stress conditions. Int. J. Fatigue 2012, 45, 1–7. [CrossRef] Sonsino, C.M. Fatigue testing under variable amplitude loading. Int. J. Fatigue 2007, 29, 1080–1089. [CrossRef] Rice, S.O. Mathematical Analysis of Random Noise. Bell Syst. Tech. J. 1944, 23, 282–332. [CrossRef] Rice, S.O. Mathematical Analysis of Random Noise. Bell Syst. Tech. J. 1945, 24, 46–156. [CrossRef] Petrucci, G.; Zuccarello, B. Fatigue life prediction under wide band random loading. Fatigue Fract. Eng. Mater. Struct. 2004, 27, 1183–1195. [CrossRef] Engineering Sciences Data Unit (ESDU). IHS ESDU 97018, Standard Fatigue Loading Sequences; ESDU: London, UK, 1999; pp. 5–13. Heuler, P.; Klätschke, H. Generation and use of standardised load spectra and load-time histories. Int. J. Fatigue 2005, 27, 974–990. © 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

7535