FE Post Processing

• Plotting• Campbell Diagram• Goodman Diagram• Fracture• Yield• Principal Stress

POST PROCESSING PLOTS

Deformed Shape Plot

Contour Plots

History Plot

Invert Colors for Hard CopiesInvert Colors for Hard Copies

CAMPBELL DIAGRAMS

Campbell Diagram

0

500

1000

1500

2000

2500

3000

3500

0 2000 4000 6000 8000 10000 12000 14000

Fre

qu

en

cy -

Hz

Rotation Rate - RPM

Mode 1

Mode 2

Mode 3

EO: 1

EO: 3

EO: 6

EO: 10

EO: 11

EO: 12

EO: 15

Idle

Red Line

Probabilistic Campbell Diagram

0

500

1000

1500

2000

2500

3000

3500

0 2000 4000 6000 8000 10000 12000 14000

Fre

qu

en

cy -

Hz

Rotation Rate - RPM

Mode 1

Mode 2

Mode 3

EO: 1

EO: 3

EO: 6

EO: 10

EO: 11

EO: 12

EO: 15

Idle

Red Line

GOODMAN DIAGRAMS

Inputs Include

• Material:– Ultimate tensile strength, – Yield stress – 0.2%,– High cycle fatigue strength,

• Loads– Steady stress,– Vibratory,

• Half amplitude, zero-peak, • Full amplitude, peak-peak,

UTS

Y

1R

0

pp

Load Inputs

max

min

R

HCF Test Data

• Fit R=-1 data– For example:

• Pick number of cycles to failure: Nf

• Solve for corresponding half-amplitude stress:

110 /log Rf BAN

1R

Goodman DiagramMaterial Inputs

110 /log Rf BAN

My Choice

FRACTURE MECHANICS

Fracture Modes

Stress Intensity FactorMode I

Stresses near crack tip are singular and vary as the inverse square root of distance from crack tipKI is the stress intensity factor

Fracture – ¼ Points

Modeling Cracks

VON MISES STRESS&

PLASTIC YIELDING

Von Mises Stress

zzyzxz

yzyyxy

xzxyxx

is the stress tensor

3zzyyxxp

is the equivalent hydrostatic pressure

p

p

p

sss

sss

sss

s

zzyzxz

yzyyxy

xzxyxx

zzyzxz

yzyyxy

xzxyxx

is the deviatoric stress

Invariants of Stress

• Invariants do not change values when coordinate system is rotated.

• The first invariant of the stress is

• The second invariant of the deviatoric stress is

• The third invariant of the deviatoric stress is the determinant.

.31 pI zzyyxx

.2

1 2222222222 zzyzxzyzyyxyxzxyxx sssssssssJ

Uniaxial Tension

000

000

00y

33yzzyyxxp

y

y

yp

zzyzxz

yzyyxy

xzxyxx

p

p

p

s

3

100

03

10

003

2

22222 3

1

9

1

9

1

9

4

2

1yyyyJ

:yield stressy

Equivalent Mises Stress

• Yielding occurs when

• Or when equivalent stress

• When yielding occurs

• Stress ratio is

03

1 22 yJ

23JvM

yvM

yvM /

PRINCIPAL STRESSES

Principal Stresses

• Eigenvalues of stress tensor (matrix) are principal stresses– All values are real– Order is 1:maximum, 2: intermediate, 3:minimum

• Associated eigenvectors are normal to face• Use maximum principal stress for fracture

1

2

3

x

y

z

STRESS CONTOURS

Ansys Stress Contour Plots

FE Post Processing• Plotting

– Includes displaced, contour, and scatter plots• Campbell Diagram

– Finds important resonances• Goodman Diagram

– Predicts high cycle fatigue life• Fracture

– Indicates failure due to crack propagation• Yield

– Establishes yield through the use of equivalent (Mises) stress• Principal Stress

– Aids in determining failure due to presence of flaws