Analysis of Fatigue Failure in D-shaped...

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


Objective

• This study characterizes the lifetime of carabiners under cyclic loads– Loads reflect in-field use– Controlled laboratory environment


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


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


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


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)


MTS Test System

Carabiner

Machined Steel Grip

Steel Pin

Applied Load


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


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


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


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


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


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


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


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


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


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


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


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


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


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


• 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


Fracture Surface Pictures

0.5 - 8 kN load cycle 0.5 - 14 kN load cycleMagnification = 5x


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]


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


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


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


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


BACKUPS


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


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)


Introduction

Motivation

Objective

Approach

Results

Conclusions/Future Work

Questions

Outline


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


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∗


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


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


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


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


• 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


• 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

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