K. L. E. SOCIETY’SCOLLEGE OF ENGINEERING AND TECHNOLOGY

BELGAUM - 590 008

Design Data Handbook for FRACTURE MECHANICS

III Semester M-Tech (Design Engineering)

DEPARTMENT OF MECHANICAL ENGINEERING

2009-2010

Approvals

Prof. HG Patil(Teaching faculty)

Prof. SR Basavaraddi(Head of the Dept)

I-In plane crack tip stresses:

Stress intensity factor(K):

Condition for crack growth:

Griffith Criterion:

; Stress intensity factor:

Crack growth propagation:

II-Airy’s stress function:- Airy’s Stress function(ψ):

Equilibrium equations (plane case):

Stress-strain relations:

Complex functions:

Cauchy-Reimann conditions:

Westergaard function:

C-R equation:

Stresses at crack tip:

Stress function for Mode-I crack under biaxial stress:

and Stresses at crack tip;

Modified stress function:

Displacements:

Stresses:

Or , Mode-III

General Solution:

Weastergaard, Irwin,Koiter (infinte plate):

Fig 3.4 Stresses on the edges of strip cut from infinite plate with collinear cracks.

Fedderson, Isida, Irwin finite width corrections: SIF for small edge crack:

Special Cases:

SIF for internal pressure:

For central located wedge force(x=0):

Modified SIF :

General soln for eccentrical point force(Green’s soln): Reduced SIF:

Elliptical Cracks(from table 3.1):

Plastic Zone Correction Factor:

Max SIF:

Flaw shape parameter:

Max SIF for surface flaw: Fig 3.13- Kobayashi correction (Mk) for proximity of front free-surface

3.14 Stress intensity for surface flaws tension & bending

Mode-I Stresses:

Stresses (polar co-ordinates): Principal stress:

Mode-II Crack opening displacement:

III-Crack Tip Plastic Zone:Irwin plastic zone Correction:

Area A=B:

Crack tip opening Displacement:

Dugdale Approach: SIF for S distributed force:

s=a to a+ρThe value ρ is:

Shape of Plastic zone:

By Von-Mises criterion

Crack tip Stress field Equations:

Tresca Criterion:

Plastic constraint factor: Plastic zone correction:

COD(x=0):

Thickness Effect:

V-Energy Principle:Condition for crack growth (plate with unit thickness)

Elastic Energy(cracked plate):

Energy release rate:

Energy released as work:

Energies from different mode:

Criterion for crack growth:

Critical stress:

,

for plane strain case

R-CURVE:

From graph:

Irwin correction: Alternative R- curves:

COMLIANCE: Relation b/w G & K:

where Relative Displacement:

Compliance of specimen:

Energy release rate interms of compliance:

SIF:

Fig 5.20 Load displacement diagram for cracked body of nonlinear elastic material

J-INTEGRAL:

J-integral around crack tip contour:for linear elastic case

For non-linear elastic

Fig 5.22 constant Jic for centre cracked specimens [23] (courtesy ASTM)

Tearing modulus: For Stable crack growth:

fracture instablity occursParis Dimensionless form;

Stability:

Fig 6.5 Tensile stress & shear stress as fun of θ, as affected by crack speed

`VII- Dynamics & Crack Arrest:Crack tip subjected to displacements u & v :

Speed of displacement:

Resulting Kinetic enrgy:

Crack growth rate:

Crack Branching The Principle of crack arrest:

IV- Chapter1. Analytical solution:i. Using Airy’s stress function:

ii. Method of Conformal Mapping

2. Numerical Method [fem]:a. Direct Method:

b. Indirect method: Compliance

3. Experimental method:i. Based on photo elasticity:

ii. Strain Gauge method:

iii. Compliance Method:

ASTM Test Standard:Bend Specimen: B = 0.25 W to W; Span (S) = 4WFor 0.45 < (a/w) < 0.55

For 0.2 < (a/w) < 1

Tension Specimen: a = 0.45-0.55W ; B = 0.25W to 0.5W

For 0.45 < (a/w) < 0.55

For 0.2 < (a/w) < 1

II Estimation of stress intensity factor:

Size Requirement:Bmin = 2.5 (KIC/δy)2

W= 2a, 2B= WL = 1.2W Compact tensionL = 4W Bend Specimen

Non-Linearity:

and

VI- Chapter

Crack tip opening displacement:

Experimental CTOD:

Experimental CTOD:

Veerman & Muller equation

Parameters Affecting Critical CTOD:

Relation b/w J-integral & CTOD: