Analysis of Fatigue Failure in D-shaped Carabiners
Massachusetts Institute of Technology
Center for Sports Innovation
K Blair, D Custer, J Graham, M Okal
April 5, 2002 © MIT Center for Sports Innovation 2
Introduction• Current standard: Single pull to failure test (SPTF)• Climbers need rating reflecting in-field use
– Cyclic & Dynamic loads result from falling, hanging and lowering
– Typical Load Range: 2- 10 kN – Only most severe falls approach minimum SPTF ratings
• Continued cyclic loading can result in fatigue failure of carabiners
• Current carabiner retirement guidelines do not address fatigue life
April 5, 2002 © MIT Center for Sports Innovation 3
Objective
• This study characterizes the lifetime of carabiners under cyclic loads– Loads reflect in-field use– Controlled laboratory environment
April 5, 2002 © MIT Center for Sports Innovation 4
Carabiner Load Analysis
• Worst case scenario is factor 2 fall– Factor = Distance climber
falls/length of belayed rope• Dynamic rope stretches to
absorb 1/3 of the force of the climber’s fall for the belayer
• Top carabiner loaded to 20 kN
Falling Climber
Carabiners
12 kN
8 kN
Dynamic Rope
Belayer
20 kN
April 5, 2002 © MIT Center for Sports Innovation 5
Background: Climbing Loads
• Empirical studies have shown close correlation between in-field loads and those predicted by models
• Single cycle period (0.5 seconds) is in the middle of typical field-load duration
• Forces used in study are in the middle to high range of expected field loading– Low forces unlikely to pose danger to climbers– Testing at low forces prohibitively time consuming
April 5, 2002 © MIT Center for Sports Innovation 6
Carabiners
• All carabiners from same manufacturer• D-Shaped 7075 Aluminum• SPTF rating
– 24 kN Closed gate – 7 kN Open gate
• Each carabiner loaded with 12 kN proof load as part of manufacturing process
April 5, 2002 © MIT Center for Sports Innovation 7
Approach
• Test Design– ASTM Test Set-up:
– Carabiners clipped around 2 steel dowels– Dowels connected to grips
• Testing: Evaluate through cyclic, dynamic loading– Cycles to failure– Carabiner Deformation– Crack Formation (X-ray photography)
April 5, 2002 © MIT Center for Sports Innovation 8
MTS Test System
Carabiner
Machined Steel Grip
Steel Pin
Applied Load
April 5, 2002 © MIT Center for Sports Innovation 9
Equipment Details
• Load and deflection – Measured directly from the MTS machine– LabView computer based data acquisition system– Load error ± 13 N– Displacement error ± 0.01 mm
• Fracture surface observations– X-Ray photos: Torrex 150D X-Ray– Photos: Zeiss Stemi 2000-C microscope
April 5, 2002 © MIT Center for Sports Innovation 10
Test Matrix
Cyclic LoadRange, kN Number Tested
0.5 - 4 30.5 - 5 30.5 - 6 30.5 - 8 3
0.5 - 10 30.5 - 12 40.5 - 14 40.5 - 16 40.5 - 18 40.5 - 20 4
OpenGate
ClosedGate
April 5, 2002 © MIT Center for Sports Innovation 11
Experimental Approach
• Fatigue tests run cyclically from 0.5 kN to indicated maximum load
• Gate gap length measured periodically with micrometer throughout test
• Short exposure X-Ray photographs take periodically in 8, 10 and 12 kN tests– Photos copied to transparencies– Compared to determine deformation as a function of
number of cycles
April 5, 2002 © MIT Center for Sports Innovation 12
Overview of Results
• Determination of Load vs Cycles to failure curve (L-N curve)
• Carabiner deformation apparent only in high load cases– Majority of deformation occurs in first few load cycles
• Post failure analysis of crack surface provides information on critical crack length
• Not able to find evidence of crack formation before failure
April 5, 2002 © MIT Center for Sports Innovation 13
Cycles to Failure vs. Load
0
5
10
15
20
25
0 2000 4000 6000 8000 10000 12000 14000
Cycles to Failure
Max
Loa
d, k
NClosed Gate Open Gate
April 5, 2002 © MIT Center for Sports Innovation 14
Cycles to Failure vs. Load, Log Plot
1
10
100
100 1000 10000 100000
Log (Cycles to Failure)
Log
(Max
Loa
d)Closed Gate Open Gate
April 5, 2002 © MIT Center for Sports Innovation 15
Statistical Data
Cyclic LoadRange, kN
Mean Cyclesto Failure
StandardDeviation % Variation
0.5 - 4 7,849 1,598 20%0.5 - 5 3,350 384 11%0.5 - 6 1,774 413 23%0.5 - 8 10,939 1,657 15%
0.5 - 10 5,533 722 13%0.5 - 12 2,958 439 15%0.5 - 14 1,556 297 19%0.5 - 16 1,451 209 43%0.5 - 18 750 200 24%0.5 - 20 263 51 20%
OpenGate
ClosedGate
April 5, 2002 © MIT Center for Sports Innovation 16
Deformation Observations
• Gate gap measurement and X-Ray photographs failed to detect deformations
• Careful measurement of carabiner length shows small deformation for large load cases (20 kN)
• Majority of carabiner deformation for large loads occurs early in life
April 5, 2002 © MIT Center for Sports Innovation 17
Load vs StrokeFirst Cycle of 0.5-20kN Cyclic Test
0
5
10
15
20
25
0 1 2 3 4 5 6 7
Stroke (mm)
Load
(kN
)
Carabiner plastically deforms 2.7mm along major axis after first cycle
Gate engages (slope increases by factor of ~3)
Plastic deformation begins
April 5, 2002 © MIT Center for Sports Innovation 18
Two Cycles of Loading0.5 -20 kN Case
0
5
10
15
20
25
0 1 2 3 4 5 6 7
Stroke (mm)
Load
(kN
)
Cycle 1Cycle 200
Gate engages
d
April 5, 2002 © MIT Center for Sports Innovation 19
Two Cycles of Loading0.5 - 8 kN Case
-1
0
1
2
3
4
5
6
7
8
9
-33.5 -33 -32.5 -32 -31.5 -31
Stroke [mm]
Load
[kN
]
Cycle 233
Cycle 9291
April 5, 2002 © MIT Center for Sports Innovation 20
Spine Strain for 0.5 – 20 kN Test
0
5
10
15
20
25
0 1000 2000 3000 4000 5000
Strain in Spine (microinches/inch)
Load
(kN
)
Gate engages
April 5, 2002 © MIT Center for Sports Innovation 21
Spine Strain for 0.5 – 8 kN Test
-1
0
1
2
3
4
5
6
7
8
9
-4000 -3500 -3000 -2500 -2000 -1500 -1000 -500 0
Strain [mm/mm]
Load
[kN
]
Cycle 233Cycle 9291
Gate engages
April 5, 2002 © MIT Center for Sports Innovation 22
Surface Crack Formation
• Carabiners cycled at 0.5-8 kN range were X-Rayed to search for surface cracks
• X-Rays take about every 500 cycles• No surface cracks were detected
April 5, 2002 © MIT Center for Sports Innovation 23
• All carabiners break at “elbow”– Fits prediction made by
Finite Element Model– Consistent with in-field
failure characteristics• Observed cross-section
under microscope
Fracture Observations
April 5, 2002 © MIT Center for Sports Innovation 24
Fracture Surface Pictures
0.5 - 8 kN load cycle 0.5 - 14 kN load cycleMagnification = 5x
April 5, 2002 © MIT Center for Sports Innovation 25
Crack Size on Fracture Surface
y = 4.6871x-0.7641
R2 = 0.912
y = 3.1038x-0.3476
R2 = 0.8569
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5Crack Length [cm]
Max
imum
Loa
d [k
N] Closed Gate
Open Gate
[2]
[2]
[3]
April 5, 2002 © MIT Center for Sports Innovation 26
Discussion
• Cyclic Testing– Even at loads representing extreme falls, this specific
carabiner has long life– Result should be encouraging for climbers
• Deformation– Carabiner deformation very small and not detectable,
especially for loads below the manufacturer’s proof test of 50% SPTF
– Any plastic deformation occurs in first few loading cycles
– Data suggests that deformation can be detected using a mold
April 5, 2002 © MIT Center for Sports Innovation 27
Discussion
• Crack Growth– No surface cracks were found during testing– Appears that when the carabiner is un-loaded,
all surface cracks completely close– Crack length vs. cycles to failure trends agree
with theoretical models, but direct comparison cannot be made due to complicated geometry of the carabiner
April 5, 2002 © MIT Center for Sports Innovation 28
Conclusions
• Carabiner failure can be characterized with L-N data
• The carabiner tested exceeds reasonable expectations of carabiner fatigue life
• Decreasing carabiner weight will likely result in decreased life forcing the need for fatigue ratings
• Deformation cannot be used to predict fatigue failure
• Deformation can be used to detect plastic deformation due to excessive loads
April 5, 2002 © MIT Center for Sports Innovation 29
Future Work• Testing other types of carabiners would
allow for more general conclusions• Effect of load history should be studied• Effects of surface damage on the speed of
crack initiation should be investigated• Crack initiation and propagation life should
be characterized– Cycle carabiner at low load levels– Pull carabiner apart on a single load– Measure the length of the crack front
April 5, 2002 © MIT Center for Sports Innovation 30
BACKUPS
April 5, 2002 © MIT Center for Sports Innovation 32
New Testing and Rating Standard• Based on in-field conditions, results, and current
ASTM standard– In-field conditions
• 0.5 sec. average loading period• Dynamic/sinusoidal loading• 20 kN maximum load (worst case scenario)
– Results• Trend line for Cycles to Failure vs. Load
– ASTM standard • Test minimum of 5 for 20 kN test• Factor of Safety = 1.2
• Rate by number of cycles to failure for 20 kN case– Black Diamond Light D Carabiner: ~200 cycles
April 5, 2002 © MIT Center for Sports Innovation 33
Carabiner Fatigue Safety Margin
y = -3.3508Ln(x) + 39.139R2 = 0.9516
5
7
9
11
13
15
17
19
21
0 2000 4000 6000 8000 10000 12000 14000
Cycles to Failure
Max
imum
Loa
d [k
N]
Minimum fatigue failure requirements (based on maximum in-field carabiner use)
Recorded fatigue failure characteristics (standard of 1.2 factor of safety above minimum)
April 5, 2002 © MIT Center for Sports Innovation 34
Introduction
Motivation
Objective
Approach
Results
Conclusions/Future Work
Questions
Outline
April 5, 2002 © MIT Center for Sports Innovation 35
What Is a Carabiner?
• Metal link connecting climber to rope and rope to mountain side via webbing
• Features gate that climber opens to insert/remove rope or webbing under loaded & unloaded conditions
• Most common type – D-shaped– Aluminum
Climber attaching rope to carabiner.
Webbing
Introduction
April 5, 2002 © MIT Center for Sports Innovation 36
Errors
• MTS error load Error: ±13N => = 0.16% error
• Carabiner manufacturing• Negligible errors:
– Strain Gauge– Temperature– Deformation of steel pins (see next slide)
NN
800013100∗
April 5, 2002 © MIT Center for Sports Innovation 37
Pin Error Analysis
lb
mLEIbLPb 6
max 1097.439
)(2/322
−∗==−δ
•From Crandall, Dahl, Lagner:
•Smallest deflection observed: 0.0015 m at 8kN
•This represents a 0.33% error (at most)
=−−
∗35.1697.4100
ee
Carabiner
Grip
Pin
Pin modeled as
April 5, 2002 © MIT Center for Sports Innovation 38
Critical Stress Intensity Factor (Kc)
0
35
70
105
140
175
210
0 5 10 15 20 25 30 35 40Kc [MN/m(3/2)]
Stre
ss [k
Pa]
Closed GateOpen Gate
April 5, 2002 © MIT Center for Sports Innovation 39
Webbing Tests Eliminated
• Too difficult to accurately run tests at desired frequency – Desired test frequency and max. load: 2 Hz, 8 kN– MTS machine capabilities: 1.3 Hz, 7.3 kN
• MTS machine unable to account for stretch in webbing
• 1 test completed at lowest load, results inconclusive
April 5, 2002 © MIT Center for Sports Innovation 40
Plastic Deformation
Motion Resulting from Plastic Deformation
Displacement
Red Paint
Before Plastic Deformation
After Plastic Deformation
Close-up of gate latch on carabiner depicting the resulting displacement due to plastic deformation of the carabiner in an unloaded condition both before
and after the carabiner is cyclically loaded.
Gate Pin
Latch Opening
April 5, 2002 © MIT Center for Sports Innovation 41
• Used to evaluate stress concentrations in carabiner to predict failure area.
• Max Stress at top and bottom of carabiner
• Stress concentrations also evident at bends
PATRAN model
April 5, 2002 © MIT Center for Sports Innovation 42
• MTS Tensile Loading Machine– Program load conditions– Mating of machined grips to vice clamps of MTS– Tare out zero displacement conditions
• Strain Gauges– Attachment to carabiner – Tare out zero load condition
Instrumentation & Calibration