In view of Fatigue & Fracture Mechanics, the slides give a insight off the effects of the Creep and Fatigue Crack growth. As both the fatigue and creep phenomenon is dynamic in nature due to the involvement of parameter w.r.t time. Thereby the J contour Integral parameter is replaced by C-Integral by adopting Hoff's Analogy and Power's Law.

1. TIGUE & FRACTURE MECHANICS
TOPIC: EFFECTS OF FATIGUE AND CREEP
CRACK GROWTH
SIVA S
R19MMD07
M.Tech Machine Design
REVA University

2. • FATIGUE: Phenomenon where
structures fail when subjected to a
cyclic load.
• Alternate Compressive and Expansion load.

3. Creep is stable extension of macroscopic crack.
Unlike brittle fracture, creep deformation does not occur suddenly upon the application of
stress

4. “Both Creep and Fatigue phenomenon are dynamic
behavior i.e., time-dependent deformation”
CREEP CRACK GROWTH
• Traditional approaches to design for creep regime the creep and
material damage were considered to be uniformly distributed.
• Now, approaches are required when creep failure is controlled by a
dominant crack in the structures.

5. Deformation at high temperatures can be divided into
four regimes:
1. Instantaneous(elastic) Strain
2. Primary Creep
3. Secondary Creep
4. Tertiary Creep
These can be plotted from Creep Strain vs log(Time )

6. • Elastic strain: occurs immediately upon
application of the load.
• Primary creep: dominates at short times after
application of the load; the strain rate decreases
with time, as the material strain hardens.
• Secondary creep stage: the deformation
reaches a steady state, where strain hardening
and strain softening are balanced.
• Tertiary stage: Microscopic failure
mechanisms, such as grain boundary cavitation,
nucleate in this final stage of creep

7. • In macroscopic crack at high temperatures all 4 types of creep
response can occur simultaneously.
• The material may be elastic remote from the crack tip, and in
the primary and secondary stages of creep at moderate
distances from the tip.

8. The C* Integral:
• The C* integral is to characterize crack growth in a material undergoing steady
state creep.
• Hoff’s analogy can be applied to steady state creep, since the creep rate is a
function only of the applied stress.
• Hutchinson, Rice, Rosengren (HRR) singular crack tip fields for elastoplastic
material response.

9. C* is intensity of stress singularity @ Crack Tip
The C* integral is defined by replacing strains with strain rates, and displacements
with displacement rates in the /contour integral:

10. “A” and “n”  Material constant from Powers Law
The stress & strain rate field @ crack tip are characterized by C* as:
θ= radius of crap tip during deformation
n= strain hardening exponent factor
Hoff s analogy implies that the C* integral is path-independent, because J is path-independent.
Also, if secondary creep follows a Power Law:

11. J = elastic/non-elastic linear materials
C*= for Viscous material (dashpot)
B = Plate thickness
b = Uncracked ligament length.
η = Dimensionless constant
Crack growth rate follows a power law:
For a material that creeps according to a power law ,the
displacement rate is proportional to ‘P’ and ‘n’.

12. The geometry factor η has been determined for a variety of
test specimens.
The approximate size of the creep zone is given by:
When the load is considered for Long Time Period Condition
At θ = 90°, rc is a maximum and ranges
from 0.2 to 0.5, depending on n. As rc
increases in size, C(t) approaches the
steady state value C*
C(t) = Crack tip at Localized stress

13. The Ct Parameter:
• Initiated by Saxena
• Considered :
Global Displacement =
• Using Irwin’s correction factor we arrive
INSTANTANEOUS
ELASTIC
Time displacement
creep
SSC = Small Scale
Creep