fracture mechanics handbook
TRANSCRIPT
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: