Design and Sizing of Structure for Safe Service Life under Fatigue Loading. Fatigue from a structural mechanics point of view

Transcription

1 Design and Sizing of Structure for Safe Service Life under Fatigue Loading Fatigue from a structural mechanics point of view TMMI09 Vibrations and Fatigue, December 15, 2015

2 Life Design Principles Static Safety-by-margin Safe-life Safety-by-retirement Fail-safe Safety-by-design Damage tolerance Safety-by-inspection

3 Safe-Life Safety-by-Retirement No defects are considered to exist in new constructions. Establish an allowable usage time so that all structures will be removed from service before the worst one suffer fatigue failure. No inspections necessary.

4 Durability Analysis

5 Design for inspectability and redundancy (multiple load paths) or crack arrestors so that structure can tolerate large damages. Inspections shall be performed frequently enough to ensure the detection of cracks prior to strength to fall below the lowest acceptable limit = residual strength requirement No requirement limits the period of use Fail-safe Safety-by-Design

6 Fail-Safe designs

7 The wing s bending material is mainly concentrated the flanges of the beams. The beam alone is the primary load carrier. Rough sections of the beams leads to high fracture growth rate for any fatigue crack and short critical crack lengths. If one tries to maintain security using inspections, it would require unrealistically short inspection intervals. It is better to replace the lower flange after a usage corresponding safe life. i.e. Not Fail-safe, classify the structure as Safe-Life structure

8 Three beams with divided flanges (two L- profiles for each beam) gives improved failsafe characteristics. Although fatigue crack would grow relatively quickly and result in complete failure of an L profile, the beam retains the wing s main load carrying capacity.

9 Further distribution of the wing s bending material on both beam flanges and stringers, besides the load carrying wing skin, brings improvements in two respects : 1. When the number of parallel collaborating elements increase, any loss of an element due to fatigue failure will result in a relatively mild impact on the residual strength. 2. Closely spaced stringers reduces the growth rate of any skin cracks, and will also increase the critical crack length for any skin cracks, i.e. makes the skin more damage tolerant.

10 By dividing the skin in several "planks" it is even possible to allow a skin plate crack to grow beyond critical length with a possibility of unstable growth. At any unstable crack growth, it is possible to tolerate a complete plank to get lost and still maintain a satisfactory residual strength of the complete wing section.

11 Comparison between beam flange and stringer reinforced panel: Although the difference in the damage tolerance is large, there exists no distinct difference between safe-life behavior and fail-safe behavior. It is only a question of degree difference, which, however, has great practical significance in the determination of the inspection procedures

12 Damage Tolerance Safety-by-Inspection Crack like defects of the specified size are considered to exist already in new constructions Slow Crack Growth - Non inspectable Determine an allowed usage time < half the time needed for the strength, due to crack growth, to be reduced below the residual strength requirement. Slow Crack Growth - inspectable Establish a safe inspection interval < half the time needed for the strength, due to crack growth, to be reduced below the residual strength requirement. No limitations of the period of use. Fail Safe After the total failure of a load path, or for unstable fracture growth with following crack arrest, shall the remaining life be at least two inspection intervals before strength reduced down to residual strength requirement. No limitations of the period of use

13 Damage Tolerance Analysis critical crack length (a c ) CRACK LENGTH max allowable crack length (a f ) a d Slow crack growth Non-inspectable life visually detectable crack length (a d-v ) safe inspection inteval - visual detectable crack length (a d-ndi ) needs special NDI Initial flaw quality (a i ) safe inspection inteval - NDI LIFE

14 Fatigue prone components Attachments - bolted joints - lugs - bolts Stress concentrations - holes - thickness steps - radii - stiffener run-out - eccentricity

15 Fatigue analysis task Test specimen Manufacturing and surface treatment effects Structural configuration Test loading Constant amplitude Operational loading Variable amplitude Environmental effects

16 Fatigue and Damage Tolerance Management Mission Analysis Service Loads Monitoring Loads Analysis Flight Testing Regulations & Specifications Structural Analysis Local Analysis Product Model Structural Testing Details Complete A/C Manufacturing Service

17 Operational Analysis Mission Types basic training air-to-air air-to-surface reconnaissance Example: Combat Air Patrol CRUISE RETURN Mission Segments safety and function tests ground manoeuvring combat manoeuvring store separation gun firing landing CLIMB AIR COMBAT Mission Parameters accelerations angular velocities speed altitude control surface deflections thrust fuel consumption store configurations INTERCEPT DESCENT CRUISE LANDING

18 Operational profile influence on loads

19 Principles of loads model CFD analysis wind tunnel measurements configuration data flight parameters Solution of unit load cases pressure distributions unit load cases Pressure distribution M=0.9, a=6 o Pressure distribution M=1.2, b=6 o calculation of balanced loading of airframe flight control system aeroelasticity acceleration distributions Selection and extraction of local load sequences for any structural part of the model internal pressures temperatures point loads

20 Fatigue life calculation under safe life principles Loading Structural configuration Failure criterion Effective stress Damage accumulation Calculated Fatigue life Material properties Safety factor Allowed service life

21 Fatigue Strength data Basic

22 Adjustment factors (examples) SD : κ- Factors for Aluminium, Surface Treatments Surface Treatments Machining Operations Temperature Exposure SD : κ- Factors for Aluminium, Combined Operations and Corrosion Protection

23 LUG Life Enhancement by CX & RB AA7010-T3651 Fatigue Test Results: The points of crack initiation are located to the hole surface A ratio of is obtained when the fatigue life of the basic lug and the expanded lug are compared

24 Local stress analysis example of a bolted joint

25 Load sequence M max Left inner elevon torque M M min Time step

26 The Rain Flow Count Algorithm STRESS cycle: cycle: cycle: cycle: -3-1

27 Rain flow count and the materials stress-strain hysteresis loop A C B G H E F D B D F C H A G E

28 Fatigue Damage Model Palmgren Miners cumulative damage law DD = 1 N i j i D DD = = = å å i= 1 n N i D o During timet 0 n Fatigue life ended when D Reach the value 1 = å N S Reference period T n n Value D = å = 1 Is reached at time T = T 0 D 0 N T = Fatigue life is calculated æ ç è T0 n ö N ø å T 0 25 S a n = N S m = (40+(-10))/2 S a = (40-(-10))/2 S m = N

29 Fatigue Damage Model Example Max Load Truncation n z s = 24 x nz Truncation Level

30 PAGE 30 Fatigue Damage Model Example Max Load Truncation

31 PAGE 31 Fatigue Damage Model Example Max Load Truncation

32 Fatigue Damage Model Insufficiency A moderate number cycles to high maximum tensile stresses are promoting fatigue life because they leave local residual compressive stresses at stress concentrations. According to cumulative damage hypothesis all cycles that exceed the fatigue limit are damaging. The beneficial effect is enhanced if the high stress cycles are spread throughout the loading block compared to occur close together in time (sequence effect). The cumulative damage hypothesis is not able to take into account the order of loads. Stress variations with low compressive stresses are more harmful than what corresponds to partial damage since such variations after leave unfavorable tensile residual stresses. The unfavorable effect is enhanced if the compressive stresses are scattered throughout the sequence. PAGE 32

33 Fatigue Damage Model A Reflection Stress cycles less than the fatigue limit gives no contribution to partial damage at N =. In reality, these small stress cycles reduce figigue life by accelerating the growth of previously formed cracks, promote fretting corrosion or help to extinguish favorable residual stress state

34 Log(Ds) N N 2 1 æ s = ç è s 1 2 ö ø k 1 k 4 < k < 8 Log(N) Increase of stress with 20% reduce life to 1/3 6 ( 1 1.2) N 2 N1 = = = Decrease of stress with 10% doubles the life N N = ( 1 0.9) 1. 9

35 Safety against fatigue Margins using safety factors on: Loads Usage period Fatigue strength - design for larger loads than expected to occur - design for a larger number of loads than expected - design using materials data which is worse than available test data. Apply combinations of these factors in order to obtain a probability of failure which is in acceptable levels

36 A probability of failure in the range of 10-3 means that one construction out of 1000 is expected to fail. To determine the safety factor required to achieve this failure probability or less with testing is not feasible Collection of operating experience get usually only failure data for the extremely worst specimens. To gain insight into these low probabilities must extrapolations be used i.e. to choose a probability model and a probability distribution. Prerequisites for loads what is the expected scatter? What are the design load cases? Median values or do they represent severe conditions which only a few structures are exposed to? Prerequisites for material strength What kind of materials data is available? Is it average data or reduced data? Uncertainties Are there any uncertainties in the calculations? Is there sufficient support for adjustments of test data (surface treatment, etc.) Target What is acceptable failure probability

37 Sizing with requirements that no stresses may exceed the fatigue limit Choice of safety factor f s Assuming that the stress is normally distributed, the required reduction factor fs for a failure probability of 10-3 can be determined f s = s max50 s s max Material s max 50 s s s s / s max 50 f s s SAE T s max 50 f s

38 Severe design spectra and reduced materials data Design spectrum (2.3% exceedings) 2 s n = log f n Level of severity corresponds to z standard deviations and can be expressed as a factor f n n dim z n = = 10 s n Average spectrum (50% exceedings) 1 Dx ³ 0 Equivalent to a total factor on life f = f f T n N log f n Dx log f N f N Reduction factor on materials data log f T

39 Sequences for test verification addition of overloads for test verification of composite structures peak loads truncation for test verification of metallic structures elimination of insignificant cycles for composite structures elimination of insignificant cycles for metallic structures

40 Full-scale test programme - Airframe (examples) Test # Wing to fuselage attachment Test # Rear fuselage with fin and rudder Test # Canard wing and pivot

41 Mechanical systems - test overview SL = Safe Life DT = Damage Tolerance Flight control system servo actuators (SL+DT) pedal housing (SL+DT) control stick assembly (SL+DT) leading edge flap control system Landing gear system nose and main landing gear (SL) actuators (SL) wheels and brakes (SL) Escape and oxygen system pressure vessel (SL) Hydraulic system tubes and fittings (SL) pumps (SL) valve units (SL) accumulators (SL) Secondary power systems auxiliary power unit (SL) air turbine starter (SL) aircraft gear box (SL) power transmission shaft (SL) Environmental system reduce and shut off valve (SL) heat exchangers (SL) engine bleed systems (SL) Gun and armament install. gun deflector (SL+DT) gun fwd attachment (SL+DT) weapon pylons (SL) Fuel system engine feed pipe (SL+DT) refuelling transfer units (SL) cooling and transfer pipe (SL)

42 Damage tolerance test verification of servo actuators Two test articles 40 artificial defects inserted Fatigue crack growth from 33 defects

43 Case Studies Evolution of Requirements Fail of Fail-Safe

44 Lusaka - Boeing C May 14, hours & flights Take-off Nairobi: Approach Lusaka: 09.28

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46 Failed Tailplane Spar

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