Theory of Critical Distances

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Theory of Critical Distances Giovanni de Morais R&D SIMULIA, Durability Technology Senior Manager


What are we talking about Today?

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•

The Critical Distance Concept

•

Notch Sensitivity

•

The Fracture Mechanics Link

•

Applications for the TCD

•

Fatigue Methods available at the critical distance


What is the Question?

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The need for predicting failures that occur at notches.

What is the Issue? Fatigue predictions are too conservative when based on stress histories (evaluated by FEM) on the stress concentration areas.


Supposed Inconsistencies SIZE effect:

LOAD effect:

Smax Smax

longer life to failure

Smax bending

But isn’t fatigue driven by stress and strain amplitudes? Same Amplitudes but Distinct Fatigue Lives? 4

Shorter life to failure

Smax axial


Defining Notch Sensitivity

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Kf 1 q Kt  1

Peterson 1959

q

It is a measure of how sensitive a material is to notches or geometric discontinuities. q  0  Kf  1

no notch sensitivity

q  1  K f  Kt

notch sensitivity

1 1

cP



Neuber 1955

1

q 1

cN



Heywood 1962

1

q

12

cH



CP, CN, CH = material constants

 = notch tip radius Peterson was interested in evaluating the fatigue limit at a given distance from the apex of the notch.


Connecting Fatigue and Fracture Mechanics Critical Distance 1  Kth  a0      0 

 Notch Sensitivity

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Threshold range of the stress intensity factor for long cracks under Mode I Loading. Plain Fatigue limit range (i.e. twice the fatigue limit amplitude).

Note: in fe-safe the critical distance is named L rather than a0 6

This stress determines if the crack will initiate This stress determines if the crack will propagate to failure

a0

Whether a crack will propagate or not is defined by the stress some distance below the surface. This “critical distance” is a material property obtained from Kth.


Why is this formula important? El Haddad, Topper, Smith. Prediction of Non Propagating Cracks. Engineering Fracture Mechanics, vol. 11, pp 573-584 (1979).

Kitagawa-Takahashi Diagram  (log)

   0

1  K  a0   th     0 

Short cracks

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2

 

Kth

a

Long Cracks a (log) LEFM

To describe the short to long cracks transition the intrinsic crack model is used:

Kth   g ,th   a  a0  Threshold value of the gross nominal stress range Threshold value of the stress intensity factor range

  a / a0  0    0

  a / a0     Kth /  a


Typical Critical Distance Values

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The Different Methods

Point Line

 

 eff      0, r 

 eff

1  2a0

a0     0 2

Point

2 a0

    0,r  dr  

0

0

Line

Area

 eff

1  2  a0

 2 a0

    ,r   r  dr   0

0

0

Area 9


What is the TCD good for? • Materials where the Critical Distance is reasonably large Low Carbon Steels, Grey Cast Irons, Ceramics, Concrete, Polymers

• Notched components (steep stress gradients) • Welded joints Supported by Professors Taylor, Tovo, Susmel

• Fretting Fatigue • High Cycle Fatigue Problems

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What are the requirements?

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• Recommended Mesh Refinement Two elements within the critical distance (L for the Point Method) or four elements for the Line Method.

• Critical distance Specify directly the critical distance L or the cyclic stress intensity threshold Kth and the fatigue limit  0 .

• Shear Parameter The shear parameter K should be determined (by fatigue testing) for shear sensitive materials.

How can it be verified? 3DS.COM © Dassault Systèmes | Confidential Information | 03-Nov-17 | ref.: 3DS_Document_2015

Stress Field around the Crack Tip

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Stress Intensity Factors along the Crack Path

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Critical Plane Invariant


Multiaxial Fatigue Methods Susmel-Lazzarin

Max Normal Stress

 0   n ,max   SL   a   0   0 2    a Axial fatigue limit Torsional fatigue limit Shear Stress Amplitude

Matake

Prismatic Hull

 2 0

Applicability

 n ,max   Lim a lim 

  1   n ,max   0  0 

 Mtk   a  

 PH 

Max Hydrostatic Stress

     3 0  3   H ,max   0 2  0 

a

0

2 0   0


Solving Real World Problems Which notch should be taken seriously? 265MPa

Fully Reversed Torsion

177MPa

380MPa (highest stresses)

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Methods and Materials

15

Fatigue Method Material Definition

Fatigue SN Curve

Taylor L


Enabling the TCD

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When to evaluate the TCD Fatigue Methods Criteria for determining the critical plane Interpolation


Fatigue Results

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The TCD as implemented in fe-safe is an Infinite Life Method. Meaning that the results are Fatigue Reserve Factors (aka safety factors)

The Critical Notch

Critical Distance


Surface FRF=0.61

FRF=1.06

FRF=0.7

It is not evident which notches (1,2,3) are the critical ones when the Prismatic Hull Method is evaluated at the surface (Figure 1). It becomes clear that notch #3 is the worse by evaluating the PH Method at the critical distance (Figure 2).

FRF=1.5

3 1

Figure 1 18

FRF=1.02

2

Figure 2

FRF=0.87

Understanding Stress Gradients 3DS.COM © Dassault Systèmes | Confidential Information | 03-Nov-17 | ref.: 3DS_Document_2015

Von Mises Stresses

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Highest stresses

Fatigue Reserve Factors

Highest damage


Summary

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• The TCD can easily expose those cases where the maximum stresses location is not the critical in terms of damage. • Susmel-Lazzarin, Matake and Prismatic Hull fatigue methods are now available at the critical distance in the fe-safe 2018 FD02 release. • The TCD may open opportunities for addressing fretting fatigue and fatigue of welds (Tovo, Susmel, Araujo, Taylor). • Is the TCD more related to where (critical distance) fatigue should be evaluated rather than how (fatigue method)? Food for thought!

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3DS.COM/SIMULIA © Dassault Systèmes | Confidential Information | 03-Nov-17 | ref.: 3DS_Document_2015