Session Title

Presented by: (First and Last name of presenter(s)

H O S T E D B Y :

Evaluation of Stress Concentrators and Their Effect on Fatigue Life

Evaluation of Stress Concentrators and Their Effect on Fatigue Life

Thursday, Oct. 3 2019

8 a.m – 8:50 a.m.

Jason Sicotte

NPD Engineering Manager

Associated Spring

Outline

• Four Factors of fatigue approach to evaluation of stress concentrators

• Visual examination

• Real-world examples

• Questions

Four Factors of Fatigue

Full

evaluation

of stress concentration

1. Applied Stress

2. Residual Stress

3. Material Fatigue

Strength

4. Geometric Stress

Concentrators

• Load applied to the spring during use

• Is different depending on location on the spring and wire cross-section– The highest operating stresses in springs are at the wire

surface

1. Applied Stress

Spring ID Spring OD

Compression Spring

Example

• The stress present in the spring in the free state (absence of any external load or force)

• Stress relieving lowers the residual tension on the spring ID

• Shot peening creates residual compression at and just below the wire surface

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Depth below ID (µm)

Resid

ual

Str

ess (

MP

a)

Resid

ual

Str

ess (

ks

i)

Depth below ID (0.001")

Residual Stress

Coil + Stress Relieve

Shot Peened + Heat Set

2. Residual Stress

• Compressive residual stress from shot peening helps minimize the effect of stress concentrators

– But, it does not “heal” defects in the material!

– It does reduce the likelihood that defects within the compressive residual stress zone will induce failure

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Depth below ID (µm)

Resid

ual

Str

ess (

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a)

Resid

ual

Str

ess (

ksi)

Depth below ID (0.001")

Residual Stress

Shot Peened + Heat Set

Defects within compressiveresidual stress zone less likely to induce failure

2. Residual Stress

“Net” Stress Concept• Net Stress = Summation of applied and residual stresses

• Coil + stress relieve only spring

1. Applied Stress 2. Residual Stress

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sid

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l S

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ss

(M

Pa

)

Depth below ID (µm)

Re

sid

ua

l S

tre

ss

(k

si)

Depth below ID (0.001") Coil + SR Residual Stress

Moderate Applied Stress

Net Stress

“Net” Stress Concept• Net Stress = Summation of applied and residual stresses

• Shot peened and heat set spring

1. Applied Stress 2. Residual Stress

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sid

ua

l S

tre

ss

(M

Pa

)

Depth below ID (µm)

Re

sid

ua

l S

tre

ss

(k

si)

Depth below ID (0.001")

SP + HS Residual Stress

Higher Applied Stress

Net Stress

• The maximum stress amplitude, S, level that a material can withstand for a specified of cycles without failure

Callister, William D. Materials Science and Engineering: An Introduction. New York: John Wiley & Sons, 2000.

3. Material Fatigue Strength

Example: S/N curve for music wire helical compression spring

3. Material Fatigue Strength

Design Handbook: Engineering Guide to Spring Design. Connecticut: Barnes Group Inc., 1987.

4. Geometric Stress Concentrators

• Stress concentrator, definition: a small flaw (internal or surface) or structural discontinuity at which applied stress will be amplified and from which a crack may initiate

• Geometric stress concentrators include any feature which may locally increase the stress, examples include – Raw material surface defects– Non-metallic inclusions– Spring manufacturing induced defects– Rust/corrosion pits– Contact wear in the application

• Evaluation– Must consider size, shape, and location

Stress Concentration• Surface or internal flaws are a detriment to the fracture strength because

the applied stress is amplified or concentrated at the tip. The magnitude of the amplification depends on the flaw orientation and geometry

Callister, W. D. (2000). Materials Science and Engineering: An introduction. New York: John Wiley & Sons.

Nominal applied tensile stress

Maximum stress at the flaw tip

Stress Concentration

𝜎𝑚 = 𝜎0[1 + 2 𝑎/ρ𝑡]

• 𝜎𝑚 – maximum stress at flaw tip

• 𝜎0 – nominal applied stress

• 𝑎 – length of surface flaw or ½ length of internal flaw

• 𝜌𝑡 – radius of flaw tip

•𝜎𝑚

𝜎0

is denoted as 𝐾𝑡 – stress concentration factor

Kt= 1 + 2 𝑎/ρ𝑡

One estimation calculation,

there are many!

Callister, W. D. (2000). Materials Science and Engineering: An introduction. New York: John Wiley & Sons.

Stress ConcentrationExample

Sharp DefectCorrosion pit

SeamDie Mark

Wide DefectPressure Mark from Tooling

Stress Concentration• The sharper the discontinuity, the more severe the stress

concentration:

Sharp defect (small 𝜌𝑡 ) vs. Wide defect (large 𝜌𝑡 )

𝜎𝑚 = 𝜎0[1 + 2 𝑎/ρ𝑡]

𝑎 = 10 µm 𝑎 = 10 µm

𝜌𝑡 = 5 µm 𝜌𝑡 = 2000 µm

𝜎𝑚 = 3.8𝜎0 𝜎𝑚 = 1.1𝜎0

Stress concentration is over 3 times greater for the sharp defect!

Four Factors of Fatigue

Applied

Stress

Residual Stress

Stress Concentrator

Factor

Material Fatigue

Strength+ x>or<

𝐼𝑓 𝜎𝑚 ≥ 𝑆, 𝑡ℎ𝑒𝑛 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒𝐼𝑓 𝜎𝑚 < 𝑆, 𝑡ℎ𝑒𝑛 𝑁𝑂 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒

𝜎𝑚 = 𝜎𝑛𝑒𝑡 𝑥 𝐾𝑡

compare to S

Visual Examination of Stress Concentrators

• Use of progressively higher magnification instruments to find and study the stress concentrator

• Naked eye observation

• Stereo microscope or digital microscope analysis

• Scanning electron microscope (SEM)

Visual Examination of Stress Concentrators

• Cell phone camera!

• Even better with inexpensive clip on lens

• Find correct lighting to highlight feature

– good use of shadows

Real-World Examples

Example 1: ID Coiling Tool MarkNon-Shot Peened Compression Spring• Visual examination using a stereomicroscope

Tool Mark• Visual examination using SEM

Tool Mark

• Visual examination using your phone

1. Applied Stress 2. Residual Stress

Tool Mark

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0 1 2 3 4 5 6 7 8 9 10

Resid

ual

Str

ess (

MP

a)

Depth below ID (µm)

Resid

ual

Str

ess (

ksi)

Depth below ID (0.001")

Residual Stress

Coil + SRResidualStress

ID Surface Residual Stress = +40 ksi

ID Surface Applied Stress = +87 ksi

ID OD

3. Stress Concentration 4. Material Strength

Tool Mark

𝐾𝑡 = 1 + 2 𝑎/ρ𝑡𝑎 = 20 µm

𝜌𝑡 = 2112 µm𝐾𝑡 = 1.19

ASTM A401 CrSi alloy Material strength at 107

cycles, S = 114 ksi

Assuming 38% UTS max allowable stress for a non-peened and non-set out

compression spring 0.062” wire diameter, UTS = 300 ksi

𝑎 = 20 µm𝜌𝑡 = 2110 µm

Cross-sectional metallographic mount

Tool Mark

AppliedStress87 ksi

ResidualStress40 ksi

Stress Concentration

Factor1.19

Material Fatigue Strength

114 ksi

151 ksi > 114 ksi∴ 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒

𝜎𝑚 = 𝜎𝑛𝑒𝑡 𝑥 𝐾𝑡, compare to S𝜎𝑚 = 127 𝑘𝑠𝑖 𝑥 1.19

1. Applied Stress 2. Residual Stress

Move the same Tool Mark to the OD

OD Surface Residual Stress = -40 ksi

ID

OD Surface Applied Stress = +60 ksi

OD

While a helical compression spring ID surface is in residual

tension after spring coiling, the OD surface is in residual

compression

AppliedStress60 ksi

ResidualStress-40 ksi

Stress Concentration

Factor1.19

Material Fatigue Strength

114 ksi

24 ksi < 114 ksi∴ 𝑁𝑂 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒

𝜎𝑚 = 𝜎𝑛𝑒𝑡 𝑥 𝐾𝑡, compare to S𝜎𝑚 = 20 𝑘𝑠𝑖 𝑥 1.19

Move the same tool mark to the OD

Where are Stress Concentrators a Problem on a Compression Spring?

Example 2: Non-Metallic Inclusion

Init

iati

on

Init

iati

on

• Visual examination using a stereomicroscope

Non-Metallic Inclusion• Visual examination using your phone

Inclusion• Visual examination using SEM

277 µm (0.0109”)

Inclusion• Visual examination using SEM

32.0 µm25.0 µm

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Str

ess (

MP

a)

Depth below ID (µm)

Resid

ual

Str

ess (

ksi)

Depth below ID (0.001")

Residual Stress

SP + HS ResidualStress

1. Applied Stress 2. Residual Stress

Inclusion

Applied Stress at sub-surface initiation depth = +182 ksi

Residual Stress at sub-surface initiation depth = +50 ksi

3. Stress Concentration 4. Material Strength

Inclusion

𝐾𝑡 = 1 + 2 𝑎/ρ𝑡𝑎 = 16 µm𝜌𝑡 = 11 µm𝐾𝑡 = 3.42

ASTM A877 Grade A – Valve spring quality CrSi alloy Material strength at 107

cycles, S = 143 ksi

Assuming 55% UTS max allowable stress for a shot peened and set

removed spring 0.225” wire diameter, UTS = 260 ksi

𝜌𝑡 = 11 µm

2𝑎 = 32 µm

Inclusion

AppliedStress182 ksi

ResidualStress50 ksi

Stress Concentration

Factor3.42

Material Fatigue Strength

143 ksi

793 ksi > 143 ksi∴ 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒

𝜎𝑚 = 𝜎𝑛𝑒𝑡 𝑥 𝐾𝑡, compare to S𝜎𝑚 = 232 𝑘𝑠𝑖 𝑥 3.42

Inclusion

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Depth below ID (µm)

Resid

ual S

tress (

MP

a)

Resid

ual S

tress (

KS

I)

Depth below ID (0.001")

Shot Peened Helical Compression Spring Fatigue Test Results

1.8M

cycles

190ksi

60.4M

cycles

150ksi

3.8M

cycles

170ksi

65.8M

cycles

150ksi

Red circles correspond to

inclusion size & depth

1.6M

cycles

200ksi

InclusionLarge Inclusion (31.6 X 34.2 µm)

3.76M cycles to failure at 170ksi

Small Inclusion (12.6 X 12.9 µm)

60.4M cycles to failure at 150 ksi

Questions?

Raw Material Surface Defects

Wire Drawing Defect

Wire Drawing Defect

Defect Depth

Check Streak Wire Drawing Defect

Check Streak Wire Drawing Defect

Check Streak Wire Drawing Defect

Crack Depth

Wire Surface Defect

Wire Surface Defect

Raw Wire Quench Crack

Wire Drawing Defect / Scab

Wire Drawing Defect / Scab

Non-Metallic InclusionsSteel Mill Imperfection

Flapper Valve InclusionInitiation

Flapper Valve Inclusion

Flapper Valve Inclusion

Spring Manufacturing Induced Defects

Coiling Crack

Post-Spring Manufacturing Defects

Flapper Valve Edge Abrasion

Flapper Valve Edge Abrasion

Flapper Valve Edge Abrasion

Spring Abrasion1.29M cycles to failure at 200ksi

Flapper Valve Corrosion

Flapper Valve Corrosion

Flapper Valve Corrosion

Thursday Reminders

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