DOKUZ EYLÜL UNIVERSITY

MECHANICAL ENGINEERING DEPARTMENT

INTRODUCTION TO FRACTURE MECHANICS

FRACTURE TOUGHNESS

Prof. Dr. M. Evren Toygar

FRACTURE TOUGHNESS

What is fracture toughness?

Toughness is the resistance of a material to the propagation of crack.

The stress intensity at the crack tip is dependent on both the applied

stress and the length of the crack.

A mechanical variable, Stress Intensity Factor, KI, is used to define

the behavior of the elastic region at the crack tip and NOT a material

property:

where,

f is shape correction factor and it is related to geometry of specimen

and flaw

is the applied stress

a is the half of a crack length or the length of an internal crack

KI has a unit of Mpa(m)½ or psi(in)½ .

afK I

Prof.Dr. M.Evren TOYGAR

Fracture Toughness

When the stress intensity, KI is increased to a critical value,

i.e., the critical stress intensity, KIC , crack propagation will occur,

which will lead to fracture.

It is written as:

where,

KIC is a measure of a materials resistance to crack propagation.

It is a material property.

KIC is dependent on temperature, microstructure, thickness and strain

rate.

KIC usually increases with a reduction in grain size.

afKIC

Prof.Dr. M.Evren TOYGAR

How to use KIC ?

Fracture toughness is most useful in mechanical designs.

The design criterion that should be used is KIC , where

Taking into account KIC , which is a material property, the

allowable stress (s) and/or the allowable flaw size a, half of a

crack length can be determined.

ICI KK

Fracture Toughness

Material Selection:

If the maximum applied stress, σmax , and maximum crack

length acr are specified for a certain application, then only the

materials with KIC greater than KI can be used:

maxmax afK IC

Prof.Dr. M.Evren TOYGAR

Allowable stress design (if amax and KIC are specified, then the allowed

stress is,

1

max

max

f

Ka IC

max

maxaf

K IC

Fracture Toughness

Prof.Dr. M.Evren TOYGAR

Critical Stress Intensity Factor

A crack propagates when KIC is achieved at the tip of a crack.

Variation of K with thickness of the material.

As the thickness increases, the stress intensity becomes the material fracture toughness,

KIC, and independent of thickness.

Thus, objects break independent of their size.

Prof.Dr. M.Evren TOYGAR

Fracture Toughness – Crack Surface Energy

When a material has an applied strain, it undergoes an elastic strain related

to the modulus of elasticity, E, of the material.

When a crack propagates, this strain energy is released, which reduces the

overall energy.

However, two new surfaces are created by the extension of the crack,

which increase the energy associated with the surface.

By balancing the strain energy and the surface energy, g, we find that the

critical stress required to propagate the crack is given by:

a

Ecritical

2

This equation shows that even small cracks can severely limit the

strength of a material.

This equation is particularly applicable to ceramics.

Prof.Dr. M.Evren TOYGAR

Determination of Fracture Toughness

Fracture toughness of material can be determined according to LEFM

analysis:

KIC Fracture Toughness (stress based)

Works well for very high strength materials

Crack Tip Opening Displacement CTOD (displacement based)

Used for lower strength materials (σo < 1400 MPa),

exhibiting small amount of plastic deformation before failure.

J- Integral JIC (energy based)

Used for lower strength materials, exhibiting small amount of plastic

deformation before failure.

R – Curve (energy based)

The resistance to fracture of a material during slow and stable crack

propagation.Prof.Dr. M.Evren TOYGAR

Determination of Fracture Toughness KIC

KIC - the critical stress intensity in mode I fracture

Need to make sure that the specimen is tested under mode I fracture

and in a plane strain condition.

Therefore, brittle condition will be obtained.

Validation of KIC fracture toughness value

Specimen preparation

Testing procedure

Calculation of KIC value

Prof.Dr. M.Evren TOYGAR

Validation of KIC value

Since the stress distribution under the notch varies due to specimen

thickness, which also affect toughness of materials of different test

specimen dimensions.

Due to the criterion for brittle fracture in the presence of the notch,

the plane strain condition, is required for the validation of fracture

toughness KIC values.

2

5.2,,

ys

ICK

aawB

Prof.Dr. M.Evren TOYGAR

Specimen preparation

Select the specimen dimensions.

Select the crack propagation direction.

Fatigue pre-cracking by applying fatigue load at a controlled

condition of small load and amplitude to obtain a sharp fatigue

pre-crack to ensure high stress distribution ahead of the crack

tip.

Prof.Dr. M.Evren TOYGAR

Test procedure for KIC fracture toughness

A pre-cracked specimen (three point bending specimen) is arranged

and monotonically loaded until failure.

Load and clip gauge displacement are recorded during loading to give

a graph, which will be used for calculation.

Prof.Dr. M.Evren TOYGAR

Measuring fracture toughness, K1c. Two test configurations

are shown here. Again, fracture toughness is a material property not to be confused with impact.

How to measure fracture toughness, K1C

Prof.Dr. M.Evren TOYGAR

Calculation of KIC fracture toughness

Fracture toughness KQ is calculated using the following expression

(for a bend specimen).

SENB Specimen C(T) SpecimenProf.Dr. M.Evren TOYGAR

If KQ value obtained from above equation is verified according to

thickness Equation , ,KIC will be obtained.

Calculation of KIC fracture toughness

If the KIC value of material is known and the presence of a crack is

allowed, we can then monitor the crack propagation during service

prior to failure. How long we can use the component before it fails.

Fracture toughness and design

Crack in the component (in service) can be detected by using Non

Destructive Testing (NDT), i.e., ultrasonic, dyepenetrant, X-ray, Eddy

current, ferromagnetic inspection.

2

5.2,,

ys

ICK

aawB

Prof.Dr. M.Evren TOYGAR

A chart of fracture toughness Klc and modulus E.

The contours show the toughness, Gc.Prof.Dr. M.Evren TOYGAR

A chart of fracture toughness K1c and yield strength σy.

The contours show the transition crack size, ccrit.Prof.Dr. M.Evren TOYGAR

Flaw geometry and design of cylindrical pressure vessel

Fracture toughness is required in the system of high strength and light weight, i.e., high

strength steels, titanium and aluminium alloys. The cylindrical pressure vessel can be

given as an example:

Prof.Dr. M.Evren TOYGAR

Problem 1: The dimensions and material properties of the AISI 4340 plate made of

steel and containing a crack in the center are as given below. This plate has a defect of a

1mm as an initial crack. Calculate the stress intensity factor for the plate and the crack

position as the plate is subjected to a tensile load of P = 240 N. (W = width, B =

thickness, H = height) .

Prof.Dr. M.Evren TOYGAR

Problems:

Problem 2: The fracture toughness of a piece of aircraft made of aluminum is 40

MPa(m)1/2. It has been identified that the fracture occurs under 300 MPa stress and

the maximum internal crack length reaches 4.0 mm. For the same part and alloy,

calculate whether the fracture occurs while 260 MPa stress applied and the

maximum internal crack length reaches 6.0mm? Why?or why not? Please explain?

?

Prof.Dr. M.Evren TOYGAR

Problems:

Solution 2: Airplane parts are made of aluminum alloy ...If we look at the

definition of critical fracture toughness, to provide information about the

geometry of. We can use.

(Y) is the shape correction factor and it can be used to calculate KI value and

after second loading the crack dimension is measured, and the resulting value is

compared with fracture toughness value.

In the second case fracture will occur because the value of KI is greater than

the value of KIC.

Problems:

Prof.Dr. M.Evren TOYGAR

Problem 3 : You are asked to confirm that he fracture toughness of a particular steel alloy is

approximately 60 MPa√m. Furthermore the test is the test is to be conducted with the smallest

possible load cell, using either a 1-cm thick, center-cracked panel (CCT) or compact (CT)

specimen. Which specimen would you choose for this property verification? The stress

intensity relations

for CCT (center-cracked tension) panel :

for CT (compact tension) panel :

For the CCT panel, a=2 cm and W=10 cm,

For CT panel, a=3 cm and W=6 cm

Prof.Dr. M.Evren TOYGAR

)/( WafBW

aPK

W

aWaf

sec)/(

)/( WafWB

PK

432

5.1)/(6.5)/(72.14)/(32.13/64.4886.0

/1

/2)/( WaWaWaWa

Wa

WaWaf

Problems:

Problems:

Problem 4:20 inc. in width and 0.050 inc. In thickness of a plate is fixed at one end andpulled from the other end with a force of 36000 lbs. The fracture toughness of this platemade of steel is KIC = 50 ksi(in) ½ . When the plate contains the center crack, calculatethe critical crack length before fracture occurs.

Answer 4 : a=0.60 inc (15.2mm) , 2a=1.20 inc (30.4 mm)

Problem 5: Plates with dimensions of 180-350 mm from two different A and B steels

are subjected to a pull load of P = 45000 N. If the minimum crack size is 2.5 mm with

non-destructive control and the minimum weight in design is taken into consideration,

which steel should be selected?

A steel : yield strength = 91 N/mm2 , fracture toughness = 364 N/mm 3/2

B steel : yield strngth = 103.5 N/mm2 , fracture toughness = 174 N/mm 3/2

Answer 5: A steel must be choosen.

Prof.Dr. M.Evren TOYGAR

Problems:

Problem 6: Bir A tensile sample is 10 mm wide and the half of a crack length is a = 0.3

mm long. When the applied tensile stress reaches 450 MPa on this sample, the crack

propagates suddenly. The elastic modulus is given as 200 GPa

a) when there is a center crack,

b) when there is a edge crack,

Calculate the fracture toughness.

Problem 7: The width of the plate made of low carb is 4 in. And the tensile stress

applied to this plate is 32 ksi. Calculate the value of the minimum fracture toughness to

be tolerated for the plate with a 2 mm crack with edge notch.

Answer 7 : 19.4 MPa(m)1/2

Prof.Dr. M.Evren TOYGAR