shear properties

7/28/2019 Shear Properties

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SHEAR PROPERTIES

Dr. Ouzhan YILMAZ

ME 215 ENGINEERING MATERIALS-I


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PROPERTIES IN SHEAR

Shear stress plays an important role in the failure ofductile

materials (which resist to normal stress by undergoing largeplastic deformations, but fails by rupturing under shearstress. )

However, the shear tests have not met wide acceptance and

use that have been given to tension test.

This unpopularity may largely be due to the fact that an ideaabout the shear properties of a material can often be obtainedfrom the tensile properties (eg. Ssy=~0.5Sy).

Consequently the shear test are usually conducted to obtain ameasure ofshear strength for specific applications.


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Types of Shear Stresses

There are two main types of shear categorized due to the loadings.

(a)Direct Shear Stress (rivets & beams are examples)

(b)Torsional Shear Stress (Shafts are subjected to pure torsion)


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Differences between shear tests

Direct or transverse shear tests are usuallyemployed to obtain a shear strength (Ssy or

Ssu) for specific applications

Whereas torsion test is usually employed to

evaluate the shear behavior and properties ofa material (similar to the tensile test ofmaterials)


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Properties in direct shear

Direct shear tests is employed in various ways as seen in figure.

The specimen is usually clamped in a fixture and a shearingforce F is applied through a shear tool and the max. load F isdetermined.

3 types of direct sheartests are:Single shear test (a)

Double shear test (b)

Punch shear test (c)


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In direct shear tests, usually the max load F (required to shear

the test specimen) is determined. The same maximum load is then converted to the max. direct

shear stress (ultimate strength in shear ) via suitable equation.

This test however does not provide reliable information for the

properties (such as yield strength, stiffness, resilience etc) ofmaterial in shear.

This testprovides only the ultimate strength of material inshear. Even this property is not always reliable due to factorssuch as:

Hardness, sharpness and correct setting of shearing tools Bending stresses and friction between the parts

Etc.

Properties in direct shear


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Torsion TestTorsion tests are done on special type of machines which have

been developed especially for this purpose.

These tests are carried outapplying a given twisting momentto

one end of a specimen while measuring the deformation as

angular displacementat the other end.


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Torsion Test

The torsion test is not used in material specification to the

same extent as the tension test.

The main reason for lack of popularity of torsion tests arises

from the fact thatno uniform shear stress can be generated

within the material.


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Nevertheless, the torsion test is still useful in determination ofmaterial properties such as;

Shear modulus of elasticity G (*),

torsional yield strength Ssy(**) and

shear modulus of rupture Su(***).

G (Modulus of Rigidity), (Poissons Ratio)

Torsion Test


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Torsion tests can be also carried outon full sized engineeringcomponents themselves such as:

shafts, twist drills etc. in order todetermine their behavior underservice conditions.

Plastic deformation is almost

uniform over the whole length ofspecimen, which makes it possible todetermine deformations and stressmore reliably for highly ductilematerials, especially pure metals.

Crank Shaft

Twist drill Axles Twisted member


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There are two main parts of the Torsion Test Machine;

A- Loading Unit B- Indicating Unit

Torsion Testing Machine


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The test specimens for torsional tests are

cylindrical, usually having square orhexagonal shaped ends to be holdeasily at the chucks, as shown in thefigure.

The two units are seperated from each other by the specimen.

While one unit is fixed to the bed the other is free to move along the bed to

compensate for the variation in the length of the specimen when subjected

to the torsional load.

Otherwise the specimen will be subjected

to axial stresses which will then disturb

the state of pure shear stress


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Elastic Behaviour in Torsion

When the one end of a beam is fixed to the wall and a torque is

applied to the other free end of the beam, gradually the beamwill undergo a rotational deformation as seen in figure.

T is applied load Torque and is output and measurement


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The deformation here is circumferential and equal to s=R on thesurface of the bar.


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Stiffness in Torsion (Modulus of Rigidity)

As in the tension test the slope of the -(tau-gamma)curvein elastic range gives the stiffness value;

This equation is valid only for

materials which behave linearly

in the elastic range.


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Modulus of Rigidity G, can also be determined from a materialsYoungs Modulus, E, provided that the Poissons ratio, , forthat material is known.

As can seen from equation ofG, the higher the E, the higher the Gvalue in torsion.


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Different materials and G values are given in Table 4.5


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Elastic Shear Strength (Ssy)

The elastic shear strength is measured by the maximum stress in thetorsion specimen, corresponding to a torque load representing the

transition from the elastic to plastic range.For solid bars, Tsy point is not generally apparent due to stress gradientacross the diameter (having a non uniform stress distribution over thecross-section of the bar)

Contrary to the solid bars which have a non uniform stress distributionover the cross-section of the bar, the thin walled specimens will have a

uniform stress across the thickness of the wall and allow an accuratedetermination of the Ssy point.


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Because thin walled tubular specimens do not benefit from thestrengthening effect of inner fibers which were at lower shear stress

values than surface.For Ssy& Gdetermination a tubular specimen with;

L10d and d10tis recommended.

Simply, thinner is the wall thickness, more sensitive is the measure of elastic

strength since all fibers are at about the same stress.

However, if a thin walled tube is subjected to torsion, it would first fail bybuckling before the shear strength of material is reached, if the geometry is notin suitable proportion.

IfL/dand d/tratios are not kept within limits, tubular specimens generally

fail by buckling before the Ssypoint is reached.

Failure by buckling, however, happens generally if d > 10t.

For thin walled specimens during torsion tests, the

both end should be plugged, so that the jaws of the

testing machine will not collapse the specimen


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For tubular thin walled specimens the shear stress is derived as:

The general equation of shear stress for solid specimen

is not directly used for tubular specimens and a new

equation is derived

So, Shear Elastic Strength is:

where Tsy is the torque at yield point and has to be measured during test


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The first start point ofyielding is not readily appearentwith most materialsbecause of the stress gradientacross the diameter of a solid bar.

Outer most fibers are restrained from yielding by the less stressed inner fibers.

It is not until considerable yielding has taken place that any noticeable effect isapparent unless the material has very marked upper and lower yield points asshown in figure below.

Where Tsyis the torque atproportional limit or the

torque at specified offset

angle of twist.

Consequently, the off-set-yield is commonly empolyed in torsion testing

(similar to tension test) to provide a common basis for comparison.

The offset angle of twist is generally taken as 4 x 10E-5 radian/mm of gauge

length.The elastic shear strength, Ssy , is thus determined employing;


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Modulus of Resilience

Resilience is the capacity of a material for returningto original dimension after deformation.

More mathematically; modulus of resilience is, theelastic energy per unit volume which can bestored in the material with no plasticdeformation.


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Plastic Behaviour in TorsionAfter torsional yield strength limit the shear stress distribution

over the cross-section of a specimen is no longer linear.

It is, however, customary for comparison purposes with similarmaterials, to employ the previous equation. Though they do notrepresent the actual situation.


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Plastic Shear Strength

Plastic shear strength is the appearent maximum strength intorsion. The special name of Modulus of rupture is given tothis strength and calculated from,

For purposes of comparison only the modulus of rupture gives a

sufficiently accurate index of the ultimate shear strength.


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Toughness (Index No.)

Toughness is the ability of material to absorb energy in theplastic range and is defined as To = Tu x f/Volume,

similar to the case of tension. To = Sutx f


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Types of Torsion Failures Ductile Materials fracture at 90

oto the specimen axis in

maximum shear plane. Brittle materials fracture at 45

oto the specimen axis in maximum

tensile stress plane.

Buckling will happen ifL/d & d/t ration are not in limits.


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Failure of a crankshaft
http://met-tech.com/images/fractured-input-shaft-4.jpg


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http://met-tech.com/images/fractured-input-shaft-3.jpghttp://met-tech.com/images/fractured-input-shaft-4.jpghttp://met-tech.com/images/fractured-input-shaft-6.jpg


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Side View of Sector Shaft

The side view of the broken

shaft, at right, showed twistingdeformation from torsional forces

during fracture. The fracture

showed no indications of fatigue

cracking, which would possibly

point to a defect in the shaft as

the cause for failure

Fracture Surface of Sector Shaft

The fracture surface had

circumferential smearing and a

slightly off-center final fracture zone


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A close-up view of the fracturedretention stud. A brittle torsional

spiral fracture is observed

One of the retention studs was fractured

through the shank in a spiral fashion

from the region of the first thread. A

second stud was intact but cracked in

the same manner.


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Torsion Test ProcedureWe have to follow a procedure during torsion test, and it is as follows:

The specimens should be prepared in compliance with the standarts and ensure auniform stress distribution along the length of the specimen.

The surface of the specimen should be clear/free from scratches and notches

The loading over the specimen have to be pure torsional, and any condition whichmay cause tension/compression or bending must be eliminated.

The torsion load must be applied gradually to give the effect of static loading.

Load must be applied until fracture/failure is observed. During loading, values of torque and corresponding angular deformation should benoted at regular intervals (T and vaues)

After test:

By making use of the measurements (T and vaues), shear stress vs shear

strain (-) graph can be plotted.

Torsional yield strenght, shear modulus of rupture and ultimate shear strengthvalues can be calculated.

Also the ductility or brittleness of the material can be found.

The graph can be plotted whether by hand or by the electrograph of the testmachine.


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