the other theory stress strain curve

7/25/2019 The Other Theory Stress Strain Curve

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The Stress - Strain Curve

Ductile Material Materials that are capable of undergoing large strains

(at normal temperature) before failure. Ductile materials are also capable

of absorbing large amounts of energy prior to failure. Ductile materials

include mild steel, aluminum and some of its alloys, copper, magnesium,nickel, brass, bronze and many others.

Brittle Material Materials that exhibit very little inelastic deformation.

In other words, materials that fail in tension at relatively low values of

strain are considered brittle. rittle materials include concrete, stone, cast

iron, glass and plaster.

Failure Modes:

rittle materials fail due to tensile (normal) stresses and rupture occurs

along a surface perpendicular to the load.

Ductile materials usually fail on planes that correspond to the maximum

shear stresses (!"#). $ cup and cone failure is typical for ductile materials

with the sides of cup and cone inclined at approximately !"# to the

specimen axis.

%lastic & 'lastic Deformation

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The Stress Strain Curve for a ductile material.

In the early (low strain) portion of the curve, the materials obey 3ooe4s

law to a reasonable approximation, so that stress is proportional to strain

with the constant of proportionality being the modulus of elasticity or

5oung4s modulus, denoted by %.

6e7 %8e

In this region, during elastic deformation the atom4s bonding stretch a

little, and when the tension is removed, all get bac to the original

position. 9his is supported by the fact that the %lastic Modulus dependsmostly on the chemical bonding a.

$s strain is increased, many materials eventually deviate from this linear

proportionality, the point of departure being termed the proportional limit.

3owever, if we continue to apply the stress and the crystal is ductile, it

will have to deform plastically, in which it will have a permanent

deformation. 9he tension at which this deformation starts is the 5ield

-trength, (9he yield stress, denoted 65, is the stress needed to induce

plastic deformation in the specimen)

$fter the upper yield point is reached there is a mared fall in stress to the

lower yield point. This is because this is the frst instance when the

dislocations move and acilitate plastic deormation.

$fter the lower yield point, there is a stress:induced ;plastic< =ow with in

the specimen. 3ere the material is undergoing a rearrangement of its

internal molecular or microscopic structure, in which atoms are beinga *ompounds with stronger bonds have a higher elastic modulus (sti+ness)than wea bonded compounds.-ee this lin http//bit.ly/0rM1r2x


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moved to new e>uilibrium positions. This plasticity requires a

mechanism for molecular moility! "hich in crystalline materials

can arise from dislocation motion. 9he 'ortevin?e *hatelier e+ect

('?*) describes the serrated stress:strain curveor @ery =ow, which some

materials exhibit as they undergo plastic deformation. In materials, the

motion of dislocations is a discontinuous process. 1hen dislocation meets

obstacles (lie forest dislocations) they are temporary arrested for a

certain time. During this time solutes (such as interstitial particles) di+use

around the dislocations further strengthening the obstacles held on the

dislocations. %ventually these dislocations will overcome these obstacles

with suAcient stress and will >uicly move to the next obstacle where

they are stopped and the process can repeat again.

Materials lac#in$ this option of moility! y havin$ internal

microstructures that loc# dislocation motion! are usually rittle

rather than ductile. 9he stress:strain curve for brittle materials aretypically linear over their full range of strain, eventually terminating in

fracture without appreciable plastic =ow.

Bote that the stress needed to increase the strain beyond the proportional

limit in a ductile material continues to rise beyond the proportional limitC

the material re>uires an ever:increasing stress to continue straining, a

mechanism termed strain hardenin$.

It appears that the rate of strain hardening diminishes up to a point

labeled 9-, for ltimate 9ensile -trength. eyond that point, the material

Eappears4 to strain soften, so that each increment of additional strain

re>uires a smaller stress.

The apparent chan$e from strain hardenin$ to strain softenin$ is

an artifact of the plottin$ procedure, however, as is the maximum

observed in the curve at the 9-. eyond the yield point, molecular =ow

causes a substantial reduction in the specimen cross:sectional area $, so

the true stress 6t7 '/$ actually borne by the material is larger than the

engineering stress computed from the original cross:sectional area (6e7

'/$F). 9he load must e>ual the true stress times the actual area (' 7 6t$),

and as long as strain hardening can increase t enough to compensate forthe reduced area A, the load and therefore the engineering stress will

continue to rise as the strain increases.9herefore the stress or the true

stress never actually decreases as shown in the engineering stress strain

diagram.

%ventually, however, the decrease in area due to =ow becomes larger

than the increase in true stress due to strain hardening, and the load

begins to fall.

https://en.wikipedia.org/wiki/Stress-strain_curvehttps://en.wikipedia.org/wiki/Plastic_deformationhttps://en.wikipedia.org/wiki/Plastic_deformationhttps://en.wikipedia.org/wiki/Stress-strain_curve


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%ven though the 9- is perhaps the materials property most commonly

reported in tensile tests, it is not a direct measure of the material due to

the in=uence of geometry as discussed above, and should be used with

caution. 9he yield stress 65 is usually preferred to the 9- in designing

with ductile metals, although the 9- is a valid design criterion for brittle

materials that do not exhibit these =ow:induced reductions in cross:

sectional area.

9he true stress is not >uite uniform throughout the specimen, and there

will always be some location : perhaps a nic or some other defect at the

surface : where the local stress is maximum. Gnce the maximum in the

engineering curve has been reached, the localiHed =ow at this site cannot

be compensated by further strain hardening, so the area there is reduced

further.

9his increases the local stress even more, which accelerates the =owfurther. 9his localiHed and increasing =ow soon leads to a ;nec< in the

gage length of the specimen such as that seen below.

ntil the nec forms, the deformation is essentially uniform throughout

the specimen, but after necing all subse>uent deformation taes place in

the nec. 9he nec becomes smaller and smaller, local true stress

increasing all the time, until the specimen fails. 9his will be the failure

mode for most ductile metals. %s the nec# shrin#s! the non-uniform

$eometry there alters the unia&ial stress state to a comple& one

involvin$ shear components as "ell as normal stresses. 9he

specimen often fails nally with a ;cup and cone< geometry, as seen

below, in which the outer regions fail in shear and the interior in tension.



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Strain 'ardenin$

It is observed in a variety of FCC and CC substitutional and interstitial

alloys. FCC has more slip planes and conse!uently more ductile than CC.

?attice structure has imperfections called dislocations or line defects. 9heyprovide a mechanism for the material to deform and undergo plastic

deformation. 9he dislocation moves along slip directions and slip planes.

If dislocation motion is favored, plastic deformation becomes easier. Gn

the other hand if these motions are bloced/ hindered the material

becomes harder to deform and thus strengthens.

1hen is the movement hinderedJ

0 1hen there are a large no. of dislocations & the dislocations have

already moved as much as they can and further movement re>uires more

force. %.g. 1hen 9wo lie dislocations come close to each other they will

repel each other. $nd therefore it will diAcult for movement of planes to

occur and thus strengthening the material.

2 1hen a lot of interstitial atoms are present that hinder the movement

of dislocations.

(here do "e "ant plastic deformation)%.g. for easier *old Kolling of

sheets.

Ductile materials are easy to roll as they have dislocations presents that

facilitate plastic deformation. $lso after rolling the rolled sheet will havehigher strength on account of strain hardening.

(here do "e "ant stren$thenin$) %.g.for strengthening a cran shaft

by*old Lorging.

1hen we wor harden the material, what we gain in strength we lose in

ductility. -o no doubt cold forged cranshafts will be stronger but they will

have limited scope for further ductility. 9here are many times more

dislocations per mm2 in cold wored metals than otherwise but they are all

hindered or entangled.



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Stress Strain Behaviors of di*erent materials

Stress Strain Behaviors of +olymers

Ligure above shows the characteristic stress:strain behavior for an

amorphous polymer. It is characteriHed by a linear elastic region, a

yielding followed by a drop in stress, a formation of a nec, a drawing of

the nec, an increase in stress due to straightening of polymer chain, and

nally fracture.

9he elastic deformation in amorphous , and semi-crystalline

(polymers is the result of two mechanisms.

-ome examples of Semi-crystalline +olymers are linear polyethylene

('%), polyethylene terephthalate ('%9), polytetra=uoroethylene ('9L%) or

isotactic polypropylene (''))



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0 $n applied stress causes the covalent bonds within the amorphous

polymer chain to stretch and distort, allowing the chains to elongateelastically. 1hen the stress is removed, recovery from this distortion is

almost instantaneous. In addition, entire segments of the polymer chains

may be distorted. In this case when a stress is applied and removed, the

chains moves bac to their original position but over a period of time.

(9his time can range from a few seconds to a few months.)

Gnce the yield strength is exceeded the polymer deforms plastically.

'lastic deformation is the result of chains sliding, stretching, rotating, and

disentangling under load.

$s seen in Ligure, there is a drop in stress beyond the yield point. 9his is

because the initially tangled and intertwined chains become straight and

untangled. Gnce the chains are straighten, additional stress causes

necing, in which there is the continued sliding and deformation of the

chains.

$morphous

In amorphous polymers continued necing causes the chains to become

closer together and almost parallel. $t this point strong an der 1aals

bonding between the more closely aligned chains re>uires higher stress inorder to complete the deformation and fracture.



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Gn the basis of experimental investigations, the ultimate tensile strength

and yield strength are said to decrease with an increase in temperature,

except at a temperature of 2"F #* where these properties increase a little.



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9he modulus of elasticity continuously decreases with an increase in

temperature. $lso, from the engineering stress:strain diagram, it is visible

that strains at NFF #*, !FF #*, and "FF #* are somewhat reduced in

comparison with the ones at higher temperatures.

nterstitial Free Steels ,F Steels

9he term EInterstitial Lree steel or IL steel4 refers to the fact, that there are

no interstitial solute atoms to strain the solid iron lattice, resulting in very

soft steel. IL steels have interstitial free body centered cubic (bcc) ferrite

matrix. 9hese steels normally have low yield strength, high plastic strain

ratio (r:value), high strain rate sensitivity and good formability. In these

-teels, normally, the content of interstitial elements (*, B) is ept below

NF ppm.

9he lac of interstitial atoms in the atomic structure enables IL steel to

have extremely high ductility, ideal for deep:drawn products. In fact, ILsteels are sometimes called extra deep drawing steels (%DD-). 9hey have

relatively low strength (although they are sometimes strengthened by the

reintroduction of nitrogen or other elements), but high wor hardening

rates and excellent formability.

9hese steels have high strain hardening potential during forming, lending

deep:drawn parts (lie truns, tailgates, doors, linings, wheel arches, etc.)

good dent resistance.

$ wor hardened material has lower ductility and higher resistance to

deformation. (9ae a forged cranshaft for example.)


the other theory stress strain curve

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