MIL-HDBK-17-3F Volume 3,Chapter 7-Damage Resistance,Durability,and Damage Tolerance 4.Perform residual static tests for checking the assumed strength of the damaged structures. General Method The first step of a probabilistic damage tolerance evaluation is the identification of each critical part of the structure with respect to low-velocity,impact damage tolerance.External skins of the aircraft,sub- jected to high compression stresses,which are exposed to in-service accidental impacts,are of prime concern.The following steps are applied to each critical zone: 1.Derive the entire residual static strength versus impact energy curve from analysis supported by test. 2.Determine accidental impact threats in terms of energy versus probability curves. 3.Calculate,within each scheduled inspection interval,the probability to have such accidental dam- ages on the structure. 4. Determine load (or stress,or strain)occurrences versus probability curves. 5.Check that the scheduled inspection program will make damage detection highly probable before the probability target is exceeded. Such probabilistic or more exactly semi-probabilistic approaches are detailed in References 7.2.2.3(e),7.2.2.4(a)and(b).Since not all of the input parameters used in these referenced methods are expressed through a probability law,for instance the residual static strength versus impact energy,the methods are semi-probabilistic. The input parameters for the method are defined as follows(Reference 7.2.2.3(e)): The Impact Threat.The method takes into account a complex threat consisting of miscellaneous damage sources,including occasional sources that may occur only during maintenance operations be- tween two scheduled detailed inspections,and continuous sources for which damage may occur at each flight.Each source of damage is described by a probability function to model the impact energies in- volved (log-normal law). The typical impact sources,which are taken into account in the analysis,are: Continuous impact sources:Tool drop,foot traffic,collision with service vehicles,projection of runway debris. Occasional impact sources:Fall of a removable component during a maintenance operation. The Inspection Program.The method takes into account a complex maintenance program composed of several types of inspections(see Section 7.4)with a different periodicity.The efficiency of each type of inspection is described by a probability distribution to model the detection probability as a function of the damage dent depth.This means that damages that have to be taken into consideration are not only those naturally omitted by the inspection level(damages up to"visible"impact damage(VID)are to be assumed between two detailed inspections),but also those existing and not noticed by the inspector dur- ing the procedure.The latter still have to be accounted for during the next inspection intervals. For commercial aircraft composite structures,complex non-destructive methods are typically not used to find damage.Once the damage is found,other methods (e.g.,ultrasonic)may be used to better char- acterize its extent.The three methods of inspection considered to initially find damage include general visual inspection,external detailed visual inspection and internal detailed visual inspection.The mathe- matical modeling of the detection probability is based on statistical studies,which allow for each type of inspection to derive a probability distribution(log-normal law). The Occurrence of Static Loads.The probability of occurrence of static loads(between limit and ulti- mate Load)is described by a log-linear probability distribution.The probability of occurrence of static loads varies uniformly(on a log-linear basis)from the range of 10per flight hour for a static load equal to Limit Load up to 10 per flight hour for a static load equal to Ultimate Load. 7-21
MIL-HDBK-17-3F Volume 3, Chapter 7 - Damage Resistance, Durability, and Damage Tolerance 7-21 4. Perform residual static tests for checking the assumed strength of the damaged structures. General Method The first step of a probabilistic damage tolerance evaluation is the identification of each critical part of the structure with respect to low-velocity, impact damage tolerance. External skins of the aircraft, subjected to high compression stresses, which are exposed to in-service accidental impacts, are of prime concern. The following steps are applied to each critical zone: 1. Derive the entire residual static strength versus impact energy curve from analysis supported by test. 2. Determine accidental impact threats in terms of energy versus probability curves. 3. Calculate, within each scheduled inspection interval, the probability to have such accidental damages on the structure. 4. Determine load (or stress, or strain) occurrences versus probability curves. 5. Check that the scheduled inspection program will make damage detection highly probable before the probability target is exceeded. Such probabilistic or more exactly semi-probabilistic approaches are detailed in References 7.2.2.3(e), 7.2.2.4(a) and (b). Since not all of the input parameters used in these referenced methods are expressed through a probability law, for instance the residual static strength versus impact energy, the methods are semi-probabilistic. The input parameters for the method are defined as follows (Reference 7.2.2.3(e)): The Impact Threat. The method takes into account a complex threat consisting of miscellaneous damage sources, including occasional sources that may occur only during maintenance operations between two scheduled detailed inspections, and continuous sources for which damage may occur at each flight. Each source of damage is described by a probability function to model the impact energies involved (log-normal law). The typical impact sources, which are taken into account in the analysis, are: • Continuous impact sources: Tool drop, foot traffic, collision with service vehicles, projection of runway debris. • Occasional impact sources: Fall of a removable component during a maintenance operation. The Inspection Program. The method takes into account a complex maintenance program composed of several types of inspections (see Section 7.4) with a different periodicity. The efficiency of each type of inspection is described by a probability distribution to model the detection probability as a function of the damage dent depth. This means that damages that have to be taken into consideration are not only those naturally omitted by the inspection level (damages up to "visible" impact damage (VID) are to be assumed between two detailed inspections), but also those existing and not noticed by the inspector during the procedure. The latter still have to be accounted for during the next inspection intervals. For commercial aircraft composite structures, complex non-destructive methods are typically not used to find damage. Once the damage is found, other methods (e.g., ultrasonic) may be used to better characterize its extent. The three methods of inspection considered to initially find damage include general visual inspection, external detailed visual inspection and internal detailed visual inspection. The mathematical modeling of the detection probability is based on statistical studies, which allow for each type of inspection to derive a probability distribution (log-normal law). The Occurrence of Static Loads. The probability of occurrence of static loads (between limit and ultimate Load) is described by a log-linear probability distribution. The probability of occurrence of static loads varies uniformly (on a log-linear basis) from the range of 10-5 per flight hour for a static load equal to Limit Load up to 10-9 per flight hour for a static load equal to Ultimate Load
MIL-HDBK-17-3F Volume 3,Chapter 7-Damage Resistance,Durability,and Damage Tolerance The Residual Strength of the Impacted Structure.A B-basis curve is assumed for the residual static strength versus impact energy.The effects of environment are taken into account by the use of residual strength values obtained under worst environmental conditions. The Relationships Between Energy.Damage Size.and Indentation.Two empirical deterministic rela- tionships are taken into account in the analysis.The first one links impact energy to the associated dam- age size(delaminated area),and the second one relates the damage size(and thus the impact energy)to an associated indentation parameter(this latter being the relevant parameter for the visual detectability of the damage). The analysis enabling the assessment of the probability of failure(calculated at its maximum,i.e., during the last flight hour of the aircraft's life)is then based on a partition of the energy range involved in the description of the impact sources. The two main steps of the method are: 1.The calculation of the probability of existence of a damage of a given size at the beginning of the last hour of the aircraft life.This calculation takes into account the different damage sources (continuous and occasional in-service sources)as well as the complex maintenance program (date and type of each inspection). 2. The cacution of the probability of falureduring the lastfghhour.which must be lss than10 per flight hour(see Figure 7.2.2.4(b)). A special use of this probabilistic method also enables the determination of the load level kxLL to be sustained by a structure damaged by a VID,in such a way that the static test at kxLL implies an accept- able in-service risk level for the structure with its inspection program. PEILOSOPEY: STATISTICAL ANALYSIS EASED ON TRE ESTIMATION OF TEE RISK OF FAILURE OF ACOHPONENT DAMAGED BY AN IMPACT. TBE INTERVAL INSPECTION AND CEECK METHODS SHOULD BE DEFINED SUCE TRAT TEIS CUHOLATED FAILORE RISK BE LOHER THAN 10-9 /FLIGET BOUR HETHQD:A.S.PROGRAN INCLODES THE FOLLOHING PARAMETRES RISK OF FAILORE E(PAt*PRAt*(1-PdAt)) CALCULATION SELECTED IHPACTS ASSOCLATED ENERGY peinseeatonse nd Indentation 交AOBABILIT￥OR due to lool lall FOR EACH TYPE OF dus lo run sways SELECTED IMPACT: sd=l(E.a.b.l] SAFETY FACTOR OF2 OCCURENCE OF mean energy APPUED ON THE DAMAGE PAt A DEFIHED 2boe or (PAL=0.5]and Sdev let(E.o.b.t) OCCURENCE PROBABILITY DAHAGE SIZE AE cornor Impaet LAW OF PROBABILITY (maintenance tools] OF OCCURENCE OF E --V-a/a下 DAHAGE SIER (felta)Cen X2.1 /RESIDUAL PRAt ST上NGTH OBTAIN2DB￥TESTS sd .LIHLOXD 2 105 /F.MOOR OCCURENCE OF e /light and ita sdev A LOAD LEVEL ULTEKATE LOAD 109/F.WOUR (probablilty 0.5) TXPES OF IHSPECTION INDENTAZION 世rGM3 afety Lactor PRDBABILITY OF DETECTION WALK AROUND AND GENERAL VISUAL mean detected value on the Indentatloa size (that could be A DAHAGE At A walue for EXTERNAL DETAILED VISUAL INSPECTION type of【aspectlon detected】 FIGURE 7.2.2.4(b)Probabilistic methodology for determining inspection intervals. 7-22
MIL-HDBK-17-3F Volume 3, Chapter 7 - Damage Resistance, Durability, and Damage Tolerance 7-22 The Residual Strength of the Impacted Structure. A B-basis curve is assumed for the residual static strength versus impact energy. The effects of environment are taken into account by the use of residual strength values obtained under worst environmental conditions. The Relationships Between Energy, Damage Size, and Indentation. Two empirical deterministic relationships are taken into account in the analysis. The first one links impact energy to the associated damage size (delaminated area), and the second one relates the damage size (and thus the impact energy) to an associated indentation parameter (this latter being the relevant parameter for the visual detectability of the damage). The analysis enabling the assessment of the probability of failure (calculated at its maximum, i.e., during the last flight hour of the aircraft’s life) is then based on a partition of the energy range involved in the description of the impact sources. The two main steps of the method are: 1. The calculation of the probability of existence of a damage of a given size at the beginning of the last hour of the aircraft life. This calculation takes into account the different damage sources (continuous and occasional in-service sources) as well as the complex maintenance program (date and type of each inspection). 2. The calculation of the probability of failure during the last flight hour, which must be less than 10-9 per flight hour (see Figure 7.2.2.4(b)). A special use of this probabilistic method also enables the determination of the load level k×LL to be sustained by a structure damaged by a VID, in such a way that the static test at k×LL implies an acceptable in-service risk level for the structure with its inspection program. FIGURE 7.2.2.4(b) Probabilistic methodology for determining inspection intervals
MIL-HDBK-17-3F Volume 3,Chapter 7-Damage Resistance,Durability,and Damage Tolerance Simplified Method In References 7.2.2.4(a)and (b)there is,first,no differentiation between discrete and continuous damage sources.Therefore,all damage threats are equally shared throughout the inspection interval. Secondly,this method does not include any probability law for detecting the dent-the BVID energy or dent depth must be selected high enough to prevent any oversight. Both assumptions allow calculations to be simplified in the following way: Let pa probability of accidental damage at the end of unit aircraft utilization (e.g.,one flight hour,one flight....). n inspection interval expressed in terms of unit aircraft utilization(n flights.n hours) Pr probability of occurrence of the flight load (e.g.,gust).the intensity of which com- bined with the accidental damage of probability pa would lead to a catastrophic fail- ure. The probability to have at least one accidental damage at the last flight preceding the inspection(where the likelihood of a damaged structure is higher)is then equal to: 1-(1-pa)”≡(n)pa 7.2.2.4(b) The relationship 7.2.2.4(a)then takes the following simple formulation: (Pr(n)pa)<109 7.2.2.4(c) The following steps of the damage tolerance evaluation are illustrated in Figure 7.2.2.4(c)taken from Ref- erence 7.2.2.4(b): 1.The residual static strength versus energy curve is evident as the first quadrant of the diagram.A "B"basis value curve is recommended. 2.The damaged state of the structure after n flights is represented in the fourth quadrant.This is a probability law assumed here to be log-linear in order to simplify the sketch.Actually this law is close to log-linear.From equation 7.2.2.4(b)this curve can be easily obtained through a simple translation of the damage threat per flight.For this illustration,"n"has been assumed to be a thousand flights. 3.The probability law for load (or stresses,or strain)occurrences is represented in the second quadrant.This law is assumed to be log-linear in the interval between limit and Ultimate Loads. Figures reported on the horizontal axis are typical of a commercial aircraft. 4.Each point on the strength versus energy curve(quadrant 1)corresponds to: a. One energy level with its associated probability to have at least one damage of such severity (or higher)on the structure at the last flight before inspection. b. One residual static strength with the associated probability to encounter a load of the same magnitude per flight. 5.The product of these two probabilities is plotted in the third quadrant where a picture of the whole first quadrant curve can be drawn.In the same quadrant,a line representative of equation 7.2.2.4(c)splits the diagram into two domains: 7-23
MIL-HDBK-17-3F Volume 3, Chapter 7 - Damage Resistance, Durability, and Damage Tolerance 7-23 Simplified Method In References 7.2.2.4(a) and (b) there is, first, no differentiation between discrete and continuous damage sources. Therefore, all damage threats are equally shared throughout the inspection interval. Secondly, this method does not include any probability law for detecting the dent - the BVID energy or dent depth must be selected high enough to prevent any oversight. Both assumptions allow calculations to be simplified in the following way: Let pa = probability of accidental damage at the end of unit aircraft utilization (e.g., one flight hour, one flight ....). n = inspection interval expressed in terms of unit aircraft utilization (n flights, n hours) Pr = probability of occurrence of the flight load (e.g., gust), the intensity of which combined with the accidental damage of probability pa would lead to a catastrophic failure. The probability to have at least one accidental damage at the last flight preceding the inspection (where the likelihood of a damaged structure is higher) is then equal to: n 1-(1-pa) (n)(pa) ≅ 7.2.2.4(b) The relationship 7.2.2.4(a) then takes the following simple formulation: -9 (Pr)(n)(pa) < 10 7.2.2.4(c) The following steps of the damage tolerance evaluation are illustrated in Figure 7.2.2.4(c) taken from Reference 7.2.2.4(b): 1. The residual static strength versus energy curve is evident as the first quadrant of the diagram. A “B” basis value curve is recommended. 2. The damaged state of the structure after n flights is represented in the fourth quadrant. This is a probability law assumed here to be log-linear in order to simplify the sketch. Actually this law is close to log-linear. From equation 7.2.2.4(b) this curve can be easily obtained through a simple translation of the damage threat per flight. For this illustration, “n” has been assumed to be a thousand flights. 3. The probability law for load (or stresses, or strain) occurrences is represented in the second quadrant. This law is assumed to be log-linear in the interval between limit and Ultimate Loads. Figures reported on the horizontal axis are typical of a commercial aircraft. 4. Each point on the strength versus energy curve (quadrant 1) corresponds to: a. One energy level with its associated probability to have at least one damage of such severity (or higher) on the structure at the last flight before inspection. b. One residual static strength with the associated probability to encounter a load of the same magnitude per flight. 5. The product of these two probabilities is plotted in the third quadrant where a picture of the whole first quadrant curve can be drawn. In the same quadrant, a line representative of equation 7.2.2.4(c) splits the diagram into two domains:
MIL-HDBK-17-3F Volume 3,Chapter 7-Damage Resistance,Durability,and Damage Tolerance a.Acceptable values(probabilities lower than 10),top right b.Not acceptable values(probabilities higher than 10),bottom left Quadrant 2 Load Residual strength Quadrant 1 Allowable damage size UL Critical damage size LL Load irtensity probability/flight:P 二二 Energy 105 106 107 108 109 109 Assumed impact thet/flight Picture of the Strength/Energy curve i the reliability quadrant 108 log n 107 1000 flights F106 10 Rights Quadrant 3 t105 n=1000 flights Quadrant 4 Equation of the lines:P.nPa=109 Probability of damage existing at the last flight before inspection (with n=inspection interval) FIGURE 7.2.2.4(c)Simplified probabilistic methodology for determining inspection intervals. Acceptable damage tolerance is demonstrated for an inspection interval equal to n if the whole curve is located above the border line.This illustration shows that when the inspection interval(n)increases, the strength-energy picture curve moves downward while the straight line delimiting the 10,probability target moves upward.Acceptable damage tolerance is not achieved when both curves cross. For very thick laminates where VID is extremely improbable,the calculation is performed with n equal to the whole aircraft lifetime.For thinner laminates where VID can be expected,the maximum acceptable inspection interval is the highest one,among those of the scheduled inspection program,containing the whole strength-energy picture curve above it. 7.2.2.5 Comparison of deterministic and probabilistic methods The following paragraphs briefly summarize the major differences between the deterministic compli- ance method and the semi-probabilistic method given in the previous two sections.Both of these meth- ods have been used to successfully certify composite primary structure on commercial transport aircraft. Other probabilistic approaches,covering various aspects of composite design and certification,are re- viewed (Reference 7.2.2.5).In the same reference,Northrop Grumman Commercial Aircraft Division (NGCAD)proposes a quite comprehensive method covering both static and damage tolerance require- 7-24
MIL-HDBK-17-3F Volume 3, Chapter 7 - Damage Resistance, Durability, and Damage Tolerance 7-24 a. Acceptable values (probabilities lower than 10-9 ), top right b. Not acceptable values (probabilities higher than 10-9 ), bottom left Equation of the lines : Pr . n . Pa = 10 -9 (with n = inspection interval) Load intensity probability / flight : P Energy r Load Residual strength Probability of damage existing at the last flight before inspection 10-9 UL LL 10 flights Assumed impact threat / flight Picture of the Strength/Energy curve in the reliability quadrant Allowable damage size Critical damage size 10-8 10-6 10-5 10-7 10-9 10-8 10-7 10-6 10-5 1000 flights log n n = 1000 flights Quadrant 2 Quadrant 1 Quadrant 3 Quadrant 4 FIGURE 7.2.2.4(c) Simplified probabilistic methodology for determining inspection intervals. Acceptable damage tolerance is demonstrated for an inspection interval equal to n if the whole curve is located above the border line. This illustration shows that when the inspection interval (n) increases, the strength-energy picture curve moves downward while the straight line delimiting the 10-9, probability target moves upward. Acceptable damage tolerance is not achieved when both curves cross. For very thick laminates where VID is extremely improbable, the calculation is performed with n equal to the whole aircraft lifetime. For thinner laminates where VID can be expected, the maximum acceptable inspection interval is the highest one, among those of the scheduled inspection program, containing the whole strength-energy picture curve above it. 7.2.2.5 Comparison of deterministic and probabilistic methods The following paragraphs briefly summarize the major differences between the deterministic compliance method and the semi-probabilistic method given in the previous two sections. Both of these methods have been used to successfully certify composite primary structure on commercial transport aircraft. Other probabilistic approaches, covering various aspects of composite design and certification, are reviewed (Reference 7.2.2.5). In the same reference, Northrop Grumman Commercial Aircraft Division (NGCAD) proposes a quite comprehensive method covering both static and damage tolerance require-
MIL-HDBK-17-3F Volume 3,Chapter 7-Damage Resistance,Durability,and Damage Tolerance ments,with an application exercise to the Lear Fan.Nevertheless,none of these methods have so far been implemented in an aircraft certification program. In the deterministic method,an upper limit of 100 ft-lb(140 Joules)is used for ultimate strength im- pact damage,whereas in the probabilistic method,lower levels have been used based on the assess- ments discussed in Section 7.3.3. In the deterministic method there is no upper limit on the energy level for impact damages to be con- sidered for Limit Load analyses;damage is considered up to the point of being readily detectable.In the probabilistic method,the upper limit on impact energy for Limit Load analyses is set at a probability of 10 In the deterministic method,inspection intervals have been set based on a qualitative rating system. which is derived based on structural capability and aircraft service experience for the effects of accidental damage and environmental degradation.In the probabilistic method,the maximum inspection intervals are derived using the probabilities of damage and load occurrence,with a reliability of at least 109. 7.2.2.6 Full-scale tests for proof of structure(civil aviation) Compliance with the requirements is built,step by step,through what is usually called a "building block approach"(see Volume 3.Chapter 4).Tests carried out to support the analysis are arranged like a pyramid,where a full-scale test culminates at the top,the bottom referring to generic tests dedicated to the derivation of a statistical basis for allowable values.Low velocity impacts,with their relevant thresh- olds,should be addressed throughout this pyramid of tests,from the "allowable"level to the full-scale demonstration. When introducing a low velocity impact damage in a test article,it is important that the selected de- tectability threshold captures the worst possible situation in terms of internal damage,hence the need to use blunt impactors.Hemispherical impactor geometry,with the smallest size at least 0.5 inch(12.5 mm) diameter,are recommended. Due to the absence of interaction between high static stresses and fatigue behavior,it is current prac- tice of transport aircraft manufacturers to conduct tests on only one full-scale test article,for both static and fatigue/damage tolerance demonstration.A typical arrangement of tests for this purpose(from vari- ous Airbus applications),is illustrated Figure 7.2.2.6. Limit load Ultimate load tests k x limit load application tests Compliance with 25 305 &307 compliance with 25 571 one lifetime half a lifetime (1.15 load enhancement factor) (1.15 load enhancement factor) Degradation Fatigue safe-life demo. DT demo.for in-service damage for initial flaws (no-growth concept) Start with a structure representative of Introduce detectable accidental the minimum quality damage with increased energies FIGURE 7.2.2.6 Test sequence for the full-scale aircraft,proof of structure test. 7-25
MIL-HDBK-17-3F Volume 3, Chapter 7 - Damage Resistance, Durability, and Damage Tolerance 7-25 ments, with an application exercise to the Lear Fan. Nevertheless, none of these methods have so far been implemented in an aircraft certification program. In the deterministic method, an upper limit of 100 ft-lb (140 Joules) is used for ultimate strength impact damage, whereas in the probabilistic method, lower levels have been used based on the assessments discussed in Section 7.3.3. In the deterministic method there is no upper limit on the energy level for impact damages to be considered for Limit Load analyses; damage is considered up to the point of being readily detectable. In the probabilistic method, the upper limit on impact energy for Limit Load analyses is set at a probability of 10- 9 . In the deterministic method, inspection intervals have been set based on a qualitative rating system, which is derived based on structural capability and aircraft service experience for the effects of accidental damage and environmental degradation. In the probabilistic method, the maximum inspection intervals are derived using the probabilities of damage and load occurrence, with a reliability of at least 10-9. 7.2.2.6 Full-scale tests for proof of structure (civil aviation) Compliance with the requirements is built, step by step, through what is usually called a “building block approach” (see Volume 3, Chapter 4). Tests carried out to support the analysis are arranged like a pyramid, where a full-scale test culminates at the top, the bottom referring to generic tests dedicated to the derivation of a statistical basis for allowable values. Low velocity impacts, with their relevant thresholds, should be addressed throughout this pyramid of tests, from the “allowable” level to the full-scale demonstration. When introducing a low velocity impact damage in a test article, it is important that the selected detectability threshold captures the worst possible situation in terms of internal damage, hence the need to use blunt impactors. Hemispherical impactor geometry, with the smallest size at least 0.5 inch (12.5 mm) diameter, are recommended. Due to the absence of interaction between high static stresses and fatigue behavior, it is current practice of transport aircraft manufacturers to conduct tests on only one full-scale test article, for both static and fatigue/damage tolerance demonstration. A typical arrangement of tests for this purpose (from various Airbus applications), is illustrated Figure 7.2.2.6. k x limit load application compliance with 25 571 Limit load tests Ultimate load tests Compliance with 25 305 & 307 one lifetime (1.15 load enhancement factor) Degradation + Fatigue safe-life demo. for initial flaws DT demo. for in-service damage (no-growth concept) Start with a structure representative of the minimum quality Introduce detectable accidental damage with increased energies half a lifetime (1.15 load enhancement factor) FIGURE 7.2.2.6 Test sequence for the full-scale aircraft, proof of structure test