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1. 1. TOUGHNESS
 “The energy per unit volume that can be absorbed by a material up to
the point of fracture is called toughness”.
 Toughness of a material may be measured by calculating the area
under the stress-strain diagram and impact test indicates the relative
toughness energy.
2. IMPACT TESTING TECHNIQUES
 ASTM Standard E 23, ‘‘Standard Test Methods for Notched Bar Impact
Testing of Metallic Materials.’’
 Various types of notched-bar impact tests are used to determine the
tendency of a material to behave in a brittle manner.
 Two standardized tests, the Charpy and Izod, were designed and are
still used to measure the impact energy, sometimes also termed notch
toughness.
 The primary difference between the Charpy and Izod techniques lies in
the manner of specimen support, as illustrated
 The Charpy V-notch (CVN) technique is most commonly used in the
United States.

2.  For both Charpy and Izod, the specimen is in the shape of a bar of
square cross section, into which a V-notch is machined as shown in
figure.
Figure: Specimen used for charpy and izod impact test
 The apparatus for making V-notch impact tests is illustrated
schematically in Figure 9.19b.

3.  The load is applied as an impact blow from a weighted pendulum
hammer that is released from a cocked (tilt) position at a fixed height
h.
 The specimen is positioned at the base as shown. Upon release, a knife
edge mounted on the pendulum strikes and fractures the specimen at
the notch, which acts as a point of stress concentration for this high
velocity impact blow.
 The pendulum continues its swing, rising to a maximum height h’,
which is lower than h. The energy absorption, computed from the
difference between h and h’, is a measure of the impact energy.

4.  Furthermore, these are termed impact tests in light of the manner of
load application. Variables including specimen size and shape as well
as notch configuration and depth influence the test results.
v- notch test:( calculate energy by using formula)
There is a formula which is used to measure the toughness if the equipment
is not computerized.
E = Pl (COSα2 - COSα1)
Where
E = Energy absorbed by a material, joules
P = Weight of the pendulum, Kg
l = length of the pendulum, m
α2 = lift angle, degree
α1 = Breaking angle, degree
Example: A MS sample is subjected to impact test, calculate the absorbed
energy of the specimen if the breaking angle is 100o.
The configuration of the impact tester is: Weight of the pendulum 26.72Kg,
Length of the pendulum 0.750m and lift angle 140.5o.

5. 3. SIGNIFICANCE OF FRACTURE TOUGHNESS:
 Impact test gives quantitative comparative useful data with relative
simple test specimens and equipment. However this test does not
provide property data for design purpose for material selection
containing cracks and flaws. Or
 The chief difficulty is that the result of the charpy test are difficult to
use in design, since there is no measurement in terms of stress level,
moreover there is no correlation of charpy data with flaw size.
 Fracture toughness values can be used in mechanical design to predict
the allowable flaw size in alloy with limited ductility when acted upon
by specific stresses.

6. 4. INTRODUCTION TO FRACTURE TOUGHNESS
 Fracture toughness is a quantitative way of expressing a material's
resistance to brittle fracture when a crack is present. If a material has
much fracture toughness it will probably undergo ductile fracture.
Brittle fracture is very characteristic of materials with less fracture
toughness
Definition:
 A property that is a measure of a material’s resistance to brittle
fracture when a crack is present.
Or
Fracture toughness is a property which describes the ability of a
material containing a crack to resist fracture, and is one of the most
important properties of any material for virtually all design
applications.
Or
Fracture toughness is an indication of the amount of stress required to
propagate a preexisting flaw. It is a very important material property
since the occurrence of flaws is not completely avoidable in the
processing, fabrication, or service of a material/component
Or
 Flaws may appear as cracks, voids, metallurgical inclusions, weld
defects, design discontinuities, or some combination thereof.
 Since engineers can never be totally sure that a material is flaw free, it
is common practice to assume that a flaw of some chosen size will be
present in some number of components and use the linear elastic
fracture mechanics (LEFM) approach to design critical components.

7.  This approach uses the flaw size and features, component geometry,
loading conditions and the material property called fracture toughness
to evaluate the ability of a component containing a flaw to resist
fracture.
 A parameter called the stress-intensity factor (K) is used to determine
the fracture toughness of most materials
STRESS INTENSITY FACTOR K:
 The stress intensity factor, , is used in fracture mechanics to predict
the stress state ("stress intensity") near the tip of a crack caused by a
remote load or residual stresses
 The stress-distribution at the crack tip in a thin plate for an elastic solid
in terms of the coordinate shown in figure11-2

8.  In dealing with the stress intensity factor there are several mode of
deformation that could be applied to a crack.
These have been standardized as shown in figure11-3(dieter) or figure
9.9(calister).

9. Mode I: the crack opening mode, refer to a tensile stress applied in the y-
direction normal to the faces of the crack. This is the usual mode for
fracture-toughness test and the critical value of stress-intensity determined
for this mode would be designated KIC.
Mode II: the forward shear mode, refer to s shear stress applied normal to
the leading edge of the crack but in the plane of the crack.
Mode III: theparallel shear mode is for shearing stresses applied parallel to
the leading edge of the crack.
 The stress intensity factor is a function of loading, crack size, and
structural geometry. The stress intensity factor may be represented by
the following equation:
Where: KI is the fracture toughnessin
σ is the applied stress in MPa or psi
a is the crack length in meters or inches
β
is a crack length and component geometry factor that is different for each specimen
and is dimensionless.
 The critical value of the stress-intensity factor (KI) that cause failure of
the plate is called the fracture toughness (KIC) of the material
KIC = Y σ√πa
Or
 Fracture toughness KIC has the unusual units MPa√m and ksi√in or
psi√in

10.  Y or f is a dimensionless parameter or function that depends on both
crack and specimen sizes and geometries, as well as the manner of load
application.
 Relative to this Y parameter, for planar specimens containing cracks
that are much shorter than the specimen width, Y has a value of
approximately unity.
 For example, for a plate of infinite width having a through-thickness
crack (Figure 9.11a), Y = 1.0; whereas for a plate of semi-infinite width
containing an edge crack of length a (Figure 9.11b), Y ≈ 1.12.
Mathematical expressions for Y have been determined for a variety of
crack-specimen geometries; these expressions are often relatively
complex.
 For relatively thin specimens, the value of Kc will depend on specimen
thickness. However, when specimen thickness is much greater than the
crack dimensions, Kc becomes independent of thickness; under these
conditions a condition of plane strain exists.

11.  By plane strain we mean that when a load operates on a crack in the
manner represented in Figure 9.11a, there is no strain component
perpendicular to the front and back faces. The Kc value for this thick-
specimen situation is known as the plane strain fracture toughness KIc
; {the crack-extension resistance under conditions of crack-tip plane
strain(Mode I)}.
 furthermore, it is also defined by
KIC = Y σ√πa
5. Problems related to Fracture toughness:
Example 1
A structural plate component of an engineering design must support
207MPa in tension. If aluminum alloy 2024-T851 is used for this application
what is the largest internal flaw size that this material can support? Use Y=1
and KIC of that alloy is 26.4Mpa√m.
Formula: KIC = Y σ√πa
Ans: the largest internal crack size that plate can support = 10.36mm

12. Example 2
The critical stress intensity for a material for a component of a design is
22.5Ksi√in. What is the applied stress that will cause fracture if the
component contains an internal crack 0.12in long? Assume Y=1.
Ans: 51.8Ksi
Example 3
What is the largest size (inches) internal crack that a thick plate of
aluminum alloy 7178-T651 can support at an applied stress of (a) ¾ of the
yield strength and (b) 1/2 of the yield strength? Assume Y=1.
Hint:
Material KIC σ, Yield strength
MPa√m Ksi√in MPa Ksi
Aluminum Alloy”
2024-T851 26.4 24 455 66
7075-T651 24.2 22 495 72
7178-T651 23.1 21 570 83
Ans: (a) 0.072in (b) 0.163in

13. 6. Stress intensity factors for fracture toughness tests
I. Compact tension specimen

14. II. Single edge notch bending specimen

15. 7. Standards
1. ASTM E399-09: 'Standard Test Method for Plane Strain Fracture
Toughness of Metallic Materials'. American Society of Testing and
Materials, Philadelphia, 2009.
2. ASTM E1290-09: 'Standard Test Method for Crack-Tip Opening
Displacement (CTOD) Fracture Toughness Measurement'. American
Society of Testing and Materials, Philadelphia, 2009
3. ASTM E1820-09: 'Standard Test Method for Measurement for Fracture
Toughness'. American Society of Testing and Materials, Philadelphia,
2009.
4. ASTM E1823-09: 'Technology Relating to Fatigue and Fracture Testing'.
American Society for Testing and Materials, Philadelphia, 2009.
5. ASTM E1921-09 'Standard Test Method for Determination of Reference
Temperature, T0, for Ferritic Steels in the Transition Range'. American
Society of Testing and Materials, Philadelphia, 2009
6. ESIS P1-92: 'ESIS Recommendation for Determining the Fracture
Resistance of Ductile Materials' European Structural Integrity Society,
1992.
7. ESIS P2-92: 'ESIS Procedure for Determining the Fracture Behaviour of
Materials'. European Structural Integrity Society, 1992.
8. DNV-RP-F108: 'Fracture control for pipeline installation methods
introducing cyclic plastic strain'. Det Norske Veritas, January 2006.
9. DNV-OS-F101: 'Submarine pipeline systems'. Det Norske Veritas,
October 2007

16. 8. Orientation
 The fracture toughness of a material commonly varies with grain
direction. Therefore, it is customary to specify specimen and crack
orientations by an ordered pair of grain direction symbols.
 The first letter designates the grain direction normal to the crack plane.
The second letter designates the grain direction parallel to the fracture
plane.
 For flat sections of various products, e.g., plate, extrusions, forgings, etc.,
in which the three grain directions are designated (L) longitudinal, (T)
transverse, and (S) short transverse, the six principal fracture path
directions are: L-T, L-S, T-L, T-S, S-L and S-T.

17. 9. Role of Material Thickness
Specimens having standard proportions but different absolute
size produce different values for KI. This results because the
stress states adjacent to the flaw changes with the specimen
thickness (B) until the thickness exceeds some critical dimension.
Once the thickness exceeds the critical dimension, the value of KI
becomes relatively constant and this value, KIC , is a true material
property which is called the plane-strain fracture toughness. The
relationship between stress intensity, KI, and fracture toughness,
KIC, is similar to the relationship between stress and tensile stress.
The stress intensity, KI, represents the level of “stress” at the tip of
the crack and the fracture toughness, KIC, is the highest value of
stress intensity that a material under very specific (plane-strain)
conditions that a material can withstand without fracture. As the
stress intensity factor reaches the KIC value, unstable fracture
occurs. As with a material’s other mechanical properties, KIC is
commonly reported in reference books and other sources.

18. i. Plane Strain - a condition of a body in which the displacements of
all points in the body are parallel to a given plane, and the values of
theses displacements do not depend on the distance perpendicular
to the plane
ii. Plane Stress – a condition of a body in which the state of stress is
such that two of the principal stresses are always parallel to a
given plane and are constant in the normal direction
10. Plane-Strain and Plane-Stress
When a material with a crack is loaded in tension, the materials
develop plastic strains as the yield stress is exceeded in the region near
the crack tip. Material within the crack tip stress field, situated close to
a free surface, can deform laterally (in the z-direction of the image)
because there can be no stresses normal to the free surface. The state
of stress tends to biaxial and the material fractures in a characteristic
ductile manner, with a 45o shear lip being formed at each free surface.
This condition is called “plane-stress" and it occurs in relatively thin
bodies where the stress through the thickness cannot vary appreciably
due to the thin section.
However, material away from the free
surfaces of a relatively thick component is not
free to deform laterally as it is constrained by
the surrounding material. The stress state
under these conditions tends to triaxial and
there is zero strain perpendicular to both the
stress axis and the direction of crack
propagation when a material is loaded in
tension. This condition is called “plane-strain”

19. and is found in thick plates. Under plane-strain conditions, materials
behave essentially elastic until the fracture stress is reached and then
rapid fracture occurs. Since little or no plastic deformation is noted,
this mode fracture is termed brittle fracture.