stress concentration

VIT University

Semester:- Fall, 2010-2011

Unit-I

Presented by

Prof.E.RAJ KUMAR

Prof.E.Raj kumar, Design Division, SMBS

Design of Machine Element (MEE302)

Prof.E.Raj kumar, Design division, SMBS 2


WHY STUDY Failure?

The engineer has to minimize the possibility of failure since the design step.

Understand the mechanics of the various failure modes

fracture, fatigue, and creep

Be familiar with appropriate design principles to prevent in-service failures.


Fracture

In response to an imposed stress, any fracture process involves two steps:

crack formation

and propagation.

The mechanism of crack propagation determine the mode of fracture.


Ductile Fracture

Ductile fracture: extensive plastic deformation in the vicinity of an

advancing crack.

proceeds relatively slowly as the crack length is extended.

often said as stable crack. it resists any further extension unless there is an increase in

the applied stress.

Normally there will be evidence of appreciable gross deformation at the fracture surfaces (e.g., twisting and tearing).


Ductile Fracture

Highly ductile fracture in

which the specimen necks down to a point.

Moderately ductile

fracture after some necking.

Brittle fracture

without any plastic deformation.


Ductile Fracture

Normal fracture process stages: necking

formation of small cavities (microvoids) in the interior of the cross section,

as deformation continues, these microvoids enlarge, come together, and to form an elliptical crack,

which has its long axis perpendicular to the stress direction.

The crack continues to grow in a direction parallel to its major axis by this microvoid coalescence process.

Finally, fracture occurs by the rapid propagation of a crack around the outer perimeter of the neck, by shear deformation at an angle of about 45

with the tensile axis

this is the angle at which the shear stress is a maximum.


(a) Initial necking.

(b) Small cavity formation.

(c) Coalescence of cavities to form a crack.

(d) Crack propagation.

(e) Final shear fracture at a 45

angle relative to the tensile direction.


The magnitude of the localized stress diminishes with distance away from the crack tip.

At positions far removed, the stress is just the nominal stress.

Due to their ability to amplify an applied stress in their locale, these flaws are sometimes called stress raisers.


Concept of Stress Concentration

Theoretical stress

concentration factor, Kt

Maximum stress at the discontinuity

Nominal stress, max stress

with no discontinuity

Kt is used for normal

stresses and Kts for

shear stresses.

In a machine element, if there is a discontinuity such as sudden change in cross

section, a fillet Hole,groove or notch;highly localised stresses are induced at such

places. Such discontinuities are called stress raisers and the localised stress

effect they produce is termed as stress concentration.


Concept of Stress Concentration

Consider an elliptical hole in an infinitely large plate loaded in uniform

tension. Using the theory of elasticity the theoretical stress concentration

factor is given by the equation below.

Elliptical hole

2b

2a

For a circular hole Kt = 3

The equation can be applied to a longitudinal crack where b


Stress Concentration Factor

Stress concentration factor is found using experimental methods.

Photoelasticity a plane polarized light is passed thru a photelastic material (all transparent plastics) resulting in a

colorful fringe pattern indicating the intensity of the stress.



Brittle Coating a specially prepared lacquers are usually

applied by spraying on the actual

part. After air drying, the part is

subjected to stress. A pattern of

small cracks appear on the surface.

Data could be used to locate strain

gages for precise measurement of

the stress. The method is sensitive

to temperature and humidity.



Electrical strain gauges

The method is the most popular and widely accepted for strain measurements and

stress analysis. The strain gauge consists of a grid of strain-sensitive metal foil

bonded to a plastic backing material. When the gauge is subjected to a mechanical

deformation, its electrical resistance changes proportionally. The change in voltage

is converted to strain and the stress is calculated from the strain.



Finite Element method

The CAD model is subdivided into many small pieces of simple

shapes called elements.

FEA program writes the equations governing the behavior of each

element taking into consideration its connectivity to other elements.

These equations relate the unknowns, for example displacements in

stress analysis, to known material properties, restraints and loads.

The program assembles the

equations into a large set of

simultaneous algebraic

equations (thousands or even

millions).

These equations are then

solved by the program to

obtain the stress distribution

for the entire model.



Round section

with a fillet



Flat plate

with a hole


IMPACT FRACTURE TESTING

Two standardized tests were designed to measure the impact energy (notch toughness): Charpy (commonly used in the USA)

Izod.

One of the primary functions is to determine whether or not a material experiences a ductile-to-brittle transition with decreasing temperature. If so, what is the range of temperatures over which it

occurs.


, =Impact stress induced

l E

l s

x d

= =

Fl h W 2

1 ) ( = + d

l

AE F

d =

A F s =


Temperature dependence of the Charpy V-notch impact energy (curve A) and percent shear fracture (curve B) for an A283 steel.

AL

UE 2 = s

Al

EG 4 = t

Impact Tension

Impact Torsion


IMPACT FRACTURE TESTING

stress concentration

Documents

design division

raj kumar

kumar prof

stress direction

stress raisers

applied stress

max stress

imposed stress