CHE 333 Class 11

Mechanical Behavior of Materials

Elastic Deformation.Consider a metal rod fixed at one end.

At the other end a load can be applied

by some manner. When a small amount

of load is applied, if the length of the metal

rod was measured it would be longer. If the

load is removed, and the rod measured

again, it would return to the original

length. It is said that the deformation

was recovered. This type of deformation

is ELASTIC, that is all recovered on load removal.

It was also found that the extension of the rod

was directly proportional to the load applied.

Load extension data would be as shown

in the diagram.

Service loads should be ELASTIC

Load

Extension

Plastic DeformationFollowing elastic deformation, the load

extension curve is no longer linear,

as shown in the diagram. After the linear

elastic portion, a non linear region starts

which indicates the start of PLASTIC

deformation. If the load is removed at

a point after plastic deformation is initiated

the metal rod will not return to the same

length as the initial length. It will be longer

by the amount of plastic deformation. The

new increase length is the plastic

deformation. In this case all the deformation

was not recovered. The elastic portion is

recovered but not the plastic deformation.

The load removal curve decreases parallel

to the elastic deformation line.

Load

Extension

Load Removal

Final lengthafter load removal

Stress Strain Curves

The load extension data can be transformedinto Stress Strain data by normalisingwith respect to material dimensions.The stress is the load divided by the original cross sectional area.

= L/As – stress , units MPa, or psi or ksiL – load appliedA – original cross sectional area

The strain is the increase in length normalised by the original length.

e = l/le – strain – dimensionless (in/in)l – increase in lengthl – original lengthStrain is often given in percent so x100As the normalisations are by constantsthe shapes of the curves stays the same.

Strain rate is e/t. Most materials are strainrate sensitive that is their mechanical behavior depends on the rate of deformation.

Stress

Strain

Hooke’s Law and Young’s Modulus

Stress

Strain

Yield Stress

Hooke’s Law is concerned withElasticity.

= EeStress is proportional to strain,But only in the elastic region.This is the “elasticity” or elasticModulus of materials, sometimesCalled “Young’s Modulus”.Metal Youngs Mod

106psiAluminum 11Gold 16Copper 28Iron (BCC) 41

Yield Stress Ultimate Tensile Stress

Stress

Strain

Yield Stress

Ultimate Tensile Stress

The Yield Stress is at the onset of plastic deformation.The Ultimate Tensile Stress is the maximum stress duringthe stress strain test.Manufacturing between YS and UTSThe strain to failure can bemeasured from the stress straindata,

The 0.2% yield stress is used formaterials such as steel as the yield point is sometimes difficult to determine. At 0.2% strain a lineis drawn parallel to the elasticportion of the data until it intersectsthe plastic portion of the data. Thestress level at this point is the 0.2%yield stress. (0.002 strain)

Strain at Failure

0.2% YS

Brittle Behavior

Stress

Strain

Brittle materials exhibit little onno plastic deformation region.Only elastic deformation is found.The energy of failure is then the area under the stress stain curve,which for a brittle material is the area of a right angel triangle,or half base multiplied by the height.Or half the strain at failure multipliedby the stress at failure. Plastic deformation adds a considerableamount of energy to the failure process.Ceramics and martensitic steels showthis behavior.Energy of failure is the area under the stress strain curve. For brittle materialsit is half the strain multiplied by the failure stress.

Failure at this stress

Reduction of Area

At the UTS, for metals local deformation starts, and thereafter the deformation is concentratedlocally. This causes a “NECK” to occur shown above along with the crack at failure.Thecross section is reduced at the failure point compared to the region outside the neck. One measure of “DUCTILITY” besides elongation at failure is “reduction of area”

ROA = final cross sectional area/ original cross sectional area

Cup and Cone Failure

Final failure in round bar is oftencharacterized for a ductile materialas a “Cup and Cone” failure. Anexample is shown. The fracture startsin the interior of the material and spreadsinternally until only a small annulus of materialremains. This then shears at 45o to the applied stress. The more ductile the materialthe larger the shear lip.

Sheet Tensile Sample

A sheet material tensile sample is shown above. ASTM has standard dimensions. At eitherend is a grip area, and in the center is the gauge length which is a narrower section to ensurefailure outside the grip area effects. The thickness and width of the sample need to be known to calculate the stress data and the original length to calculate the strain at failure.

Failed Sample Metal

A failed sample is compared to a new untested sample. Note the failure is at 45o to the applied stress. The local deformation in this case is very near the failure point. ROAData would be very difficult in this case. Elongation at failure would be more useful

Failed Sample - Polymer

A failed polymer sample has a large elongation at failure in comparison to the metal sample.Sample is 0.5 in wide to provide a scale.

Polymer Stress Strain Curve

Stress

StrainPolymers generally have low elastic modulus and long elongations to failure compared toMetals.

Homework

• Draw a stress strain curve for a ductile material indicating yield stress, UTS, strain to failure.

• Draw the stress strain curve for a brittle material.

• Briefly describe strain rate sensitivity.