Damage tolerance and fracture mechanics

By :-
Patel Dixi
IIEAM, Jain university
16MT1AS005

• Fracture mechanics is where in the a materials resistance to fracture is characterized. In
other words the ‘tolerance’ of a material to crack propagation is analyzed.
• Fracture mechanics is a field of solid mechanics that deals with the mechanical behavior of
cracked bodies.
• Fracture mechanics pose and finds answers to questions related to designing components
and processes against fracture
• Crack propagation can be steady (i.e. slowly increasing crack length with time or load) or
can be catastrophic (unsteady crack propagation, leading to sudden failure of the material.
• Fracture can broadly be classified into Brittle and Ductile fracture. This is usually done
using the macroscopic ductility observed and usually not taking into account the micro
scale plasticity, which could be significant. A ductile material is one, which yields before
fracture . A brittle fracture the crack may grow unstably, without much predictability.
Fracture mechanics

Moderately Ductile
fracture in Impure
Material
Highly Ductile Fracture
in Pure Material
• In Very high purity materials, Tensile Specimen may neck down to a sharp
point, resulting in extremely large plastic strains and nearly 100% reduction in
area
• Materials that contain impurities, however fail at much lower strains
• Example: Steels at High Transition Temperature demonstrate Ductile mode of
Fracture
Ductile Fracture:
Ductile Fracture is a high-energy process in
which a large amount of energy dissipation is
associated with a large plastic deformation
before crack instability occurs.

(a) Necking, (b) Cavity Formation, (c) Cavities coalesce (Crack grows 90 degree
to applied stress )form crack (d) Crack propagation (45 degree - maximum
shear Stress), (e) Fracture
Example on Cup-and-cone fracture in Al

Brittle Fracture is a low-energy process (low energy dissipation), which may
lead to catastrophic failure since the crack velocity is normally high.
• Crack propagation is fast
• Propagates nearly perpendicular to direction of applied stress
• Often propagates by cleavage - breaking of atomic bonds along specific crystallographic
planes
• Little or no appreciable plastic deformation
Brittle Fracture
Brittle fracture in a mild steel

• Three factors have a profound influence on the nature of fracture:
(i) temperature, (ii) strain rate, (iii) the state of stress.
• Materials which behave in a brittle fashion at low temperature may become ductile at
high temperatures. When strain rate is increased (by a few orders of magnitude) a
ductile material may start to behave in a brittle fashion.
.
Factors affecting
fracture
Strain rate
State of
stress
Temperature

Why do high strain rate, low temperature and triaxial state of stress promote brittle
fracture?
• High strain rate (by not giving sufficient time) and low temperature essentially have a
similar effect of not allowing thermally activated motion of dislocations (i.e. ‘not
helping’ plastic deformation by slip).
• In specific cases some of the slip systems being active at high temperatures may
become inactive at low temperatures.
• By triaxial state of stress we mean tensile stresses of same sign along ‘y’ and ‘z’ also.
• Triaxial does not promote crack propagation, but suppresses plastic deformation
(click on link below to know more). Since plastic deformation is suppressed the crack
tip remains sharp, thus promoting brittle fracture.
• So for plastic deformation the following order is better: tri-axial < bi-axial < uni-axial.

Method of Crack/Crack Like Defect Analysis
A. Linear Elastic Fracture Mechanics(LEFM)
In linear and elastic , the elastic energy release rate, G, and the stress intensity
factor K can be used
B. Elastic Plastic Fracture Mechanics (EPFM)
In the elastic-plastic region or yielding fracture mechanics(YFM), the fracture
characterizing parameters are the J integral and the crack-tip-opening displacement,
CTOD
C. Fatigue fracture on a component subjected to fluctuating stresses fail at stress
levels much lower than its monotonic fracture strength.
• Fatigue is an dangerous time-dependent type of failure which can occur without any
obvious warning.
• Three distinct stages in the fatigue failure of a component: Crack Initiation,
Incremental Crack Growth, and the Final Fracture.

D. Creep can be defined as a time-dependent deformation of materials under constant
load (stress).
• The resulting progressive deformation and the final rupture, can be considered as
two distinct, yet related, modes of failure.
• For metals, creep becomes important at relatively high temperatures, i.e., above 0.3 of
their melting point in Kelvin scale.

Types of failure in an uniaxial tension test

Early Days’ of the Study of Fracture
 C.E. Inglis .stress based criterion for crack growth (local)
→ C.E. Inglis (seminal paper in 1913)[1]
 Energy based criterion for crack growth (global)
→ A.A. Griffith (seminal paper in 1920)[2]
 Initially we try to understand crack propagation in brittle materials (wherein the
cracks are sharp and there is very little crack-tip plasticity). The is the domain of
Linear Elastic Fracture Mechanics (LEFM).
 For crack to propagate the necessary global criterion (due to Griffith) and the
sufficient local criterion (due to Inglis) have to be satisfied (as in figure below).
 The kind of loading/stresses also matters. Tensile stresses tend to open up cracks, while
compressive stresses tend to close cracks.
 crack growth and failure

Stress based criterion for crack propagation (Inglis criterion)
• In 1913 Inglis observed that the
stress concentration around a hole (or
a ‘notch’) depended on the radius of
curvature of the notch. I.e. the far
field stress (0) is amplified near the
hole. [[(max / 0) ) is the stress
concentration factor ()].
• A ‘flattened’ (elliptical) hole can be
thought of as a crack.
0 → applied “far field” stress
 max → stress at hole/crack tip
  → hole/crack tip radius
 c → length of the hole/crack

• Sharper the crack (smaller the  ) more the stress amplification (higher value of  max). A
circular hole has a stress concentration factor of 3 [ = 3].
• From Inglis’s formula it is seen that the ratio of crack length to crack tip radius is
important and not just the length of the crack.

Griffith’s criterion for brittle crack propagation
• We have noted that the crack length does not appear ‘independently’ (of the crack tip
radius) in Inglis’s formula. Intuitively we can feel that longer crack must be more
deleterious.
• Another point noteworthy in Inglis’s approach is the implicit assumption that sufficient
energy is available in the elastic body to do work to propagate the crack. (‘What if there is
insufficient energy?’)(‘What if there is no crack in the body?’). Also, intuitively we can
understand that the energy (which is the elastic energy stored in the body) should be
available in the proximity of the crack tip (i.e. energy available far away from the crack tip
is of no use!).
• Keeping some of these factors in view, Griffith proposed conditions for crack propagation:
(i) bonds at the crack tip must be stressed to the point of failure (as in Inglis’s criterion),
(ii) the amount of strain energy released (by the ‘slight’ unloading of the body due to
crack extension) must be greater than or equal to the surface energy of the crack faces
created.
• The second condition can be written as:
Us → strain energy
U→ surface energy
(Energy per unit area: [J/m2])
dc → (‘infinitesimal’) increase in the
length of the crack (‘c’ is the crack
length

 Damage tolerance is a property of a structure relating to its ability to sustain
defects safely until repair can be affected. The approach to engineering design to
account for damage tolerance is based on the assumption that flaws can exist in
any structure and such flaws propagate with usage.
o Slow Crack Growth Design :-structures are designed such that initial damage will grow
at a stable, slow rate under service environment.
o Fail-Safe Design :-structures are designed such that propagating damage is safely
contained after failing a major load path by load shift to adjacent intact elements .
Damage tolerance

• damage tolerance is assured
by the allowance of partial
structural failure
• the ability to detect this
failure prior to total loss of
the structure
• Fail Safe structure is
designed and fabricated
such that unstable rapid
propagation will be stopped
within a continuous area of
the structure prior to
complete failure
• damage tolerance (and thus
safety) is assured only by
the maintenance of a slow
rate of growth of damage, a
residual strength capacity
• sub-critical damage will
either be detected at the
depot or will not reach
unstable dimensions within
several design life times
Slow Crack Growth Design Fail-Safe Design

a wing box is attached to the fuselage carry through structure by multiple
fittings.
A case could be made to qualify this structure as Fail Safe Multiple Load
Path.
if the skin was the major bending member with a design stress of sufficient
magnitude to result in a relatively short critical crack length.
Wing Box Example

• detection of this failure prior to total loss of the structure
• safely within the partial failure prior to inspection
• Residual strength :-
The strength of a structure can be significantly affected by the
presence of a crack
The basic concept in damage tolerance design is to ensure the safety
of the structure throughout the expected service life.
• withstand the maximum working stresses for a certain period of time
even in presence of flaws, cracks, or similar damages of certain
geometry and size

Damage tolerance and fracture mechanics

Single Load Path Residual Strength Diagrams

In built-up structures, due to the complex geometrical configuration, one or more failure
criterion may have to be considered

Widespread Fatigue Damage (WFD)
Presence of cracks in multiple structural details which are of sufficient size
and diversity such that the structure no longer meets the damage tolerance
requirements.
WFD is divided into two types :
• Multiple Site Damage (MSD) :-multiple cracks in a structural element
• Multiple Element Damage (MED):- multiple cracks in adjacent/similar structural
details
Consequence of WFD – Rapid decrease in RESIDUAL STRENGTH
DAMAGE TOLERANCE - ISSUES

Damage tolerance and fracture mechanics

More Related Content

What's hot (20)

Similar to Damage tolerance and fracture mechanics (20)

Recently uploaded (20)

Damage tolerance and fracture mechanics