Fracture Mechanics Handbook

K. L. E. SOCIETY’S COLLEGE 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:

C-R equation:

Stresses at crack tip:

Westergaard function: Stress function for Mode-I crack under biaxial stress:

and Stresses at crack tip;

Modified stress function:

Stresses:

Displacements:

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):

Elliptical Cracks(from table 3.1):

Reduced SIF:

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:

Crack tip opening Displacement:

Area A=B:

Dugdale Approach:

SIF for S distributed force:

s=a to a+ρ The value ρ is:

Shape of Plastic zone:

By Von-Mises criterion Crack tip Stress field Equations:

Tresca Criterion:

Plastic constraint factor:

COD(x=0):

Thickness Effect:

Plastic zone correction:

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

Elastic Energy(cracked plate):

Energy release rate:

Energy released as work:

Criterion for crack growth:

Energies from different mode:

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 occurs Paris Dimensionless form;

Stability:

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

Speed of displacement: Resulting Kinetic enrgy:

Crack growth rate:

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

Crack Branching

The Principle of crack arrest:

IV- Chapter 1. Analytical solution: i. Using Airy’s stress function:

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

ii. Method of Conformal Mapping

b. Indirect method: Compliance

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

iii. Compliance Method:

ii. Strain Gauge method:

ASTM Test Standard: Bend Specimen: B = 0.25 W to W; Span (S) = 4W For 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, L = 1.2W L = 4W

Non-Linearity:

2B= W Compact tension Bend Specimen

and VI- Chapter

Crack tip opening displacement:

Experimental CTOD:

Experimental CTOD:

Veerman & Muller equation

Parameters Affecting Critical CTOD:

Relation b/w J-integral & CTOD: