temperature effect

8/12/2019 Temperature Effect

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Effect Of Temperature & Strain Rate On

Flow Properties


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The stress-strain curve and the flow and fracture properties of a material are strongly dependent on:- strain rate- temperature at which the test was conducted.

In general strength decreases and ductility increases as:- strain rate is decreased, or- the test temperature is increased.


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Figure 2-1. Yield strength changes as a function of (a) temperatureand (b) strain


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Figure 2-2. Effect of strain rate and temperature on stress-

strain curves.


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Figure 2-3. Changes in engineering stress-strain curve of mild steelwith temperature.


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This general behavior may not take place in certain

temperature ranges if structural changes such asprecipitation , strain aging , or recrystallization occur.

The above thermally activated processes can assist

deformation and reduce or increase strength atelevated temperatures.

When materials are deformed at high temperaturesand/or long exposure, structural changes can occurresulting in time-dependent deformation or creep .


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Figure 2-4. Effect of temperature on the yield strength of body-centered cubic Ta, W, Mo, Fe, and face-centered cubic Ni


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Note For the bcc metals (see Fig. 2.4), the yield stress increases

rapidly with decreasing temperature.

For Ni and most fcc metals, the yield stress is only slightlytemperature dependent.

Fig. 2.4 can also be used to understand why most bcc metalsexhibit brittle fracture at low temperatures.

A comparison of the flow stress of two materials at elevatedtemperature requires a correction for the effect of temperatureon Elastic Modulus.


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The temperature dependence of flow stress at constant strain andstrain rate can be given by:

where Q is the activation energy for plastic flow, C 2 is a constant,T is the testing temperature and R is the universal gas constant

A plot of ln versus 1/T will give a straight line with a slope Q/R

The activation energy Q can be determined by performing twotensile tests at two temperatures, T 1 and T 2 and at a constantstrain rate.

2-1

,2 exp RT QC

12

21

2

1lnT T

T T RQ

2-2


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Equation 2.1 can also be written as:

where H is an activation energy (calorie per mole). It is related

to the activation energy of Eq. 2.1 by Q = m H, where m is thestrain rate sensitivity.

Z is the Zener-Hollomon parameter or temperature-modified

strain rate.

)exp( RT H f Z f 2-3

RT H Z

exp 2-4


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The above equation can be written in a different form for hot-working conditions:

where A, , and n are experimentally determined constants

At low stresses ( < 1.0), Eq. 2.5 reduces to:

The power law equation (Eq. 2.6) can be used to describecreep, and superplasticity to some extent.

RT Q A n exp)(sinh ' 2-5

RT Q A n exp'1 2-6


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At high stresses ( > 1.2), Eq. 2.5 reduces to:

The constants and n can be determined from tests at highand low stresses.

RT Qn A exp)'exp(2 2-7


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Strain Rate Effects

Lowest range of strain rates Creep and Stress Relaxation Intermediate range 10 -4 < < 10 -2 Hot working/Tensile test Highest range shock wave or explosive test

Stress-strain curves can be sensitive to strain rate flow stress increases with strain rate work hardening rate may also increase with strain rate


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Two parameters used to describe the above effects are:- Strain rate sensitivity (m), and this is given as:

and

where

T m

,ln

ln

(2.8)

T

w s

,ln

ln

T d d

w,

(2.9)


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Equations 2.8 and 2.9 can be expressed as

It is possible to determine m from tensile tests by changing the

strain rate suddenly and by measuring the instantaneouschange in stress. This technique is illustrated in Fig. 2.5.

(2.10)m

K

s K d d

' (2.11)


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Figure 2-5. Strain-rate changes during tensile test. Four strainrates are shown: 10 -1, 10 -2, 10 -3, and 10 -4s-1.


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Applying Equation 2.10 and 2.11 to two strain rates andeliminating K, we have:

One can easily obtain m from the strain rate changes in Figure 2-5

The parameter m is important in accessing the superplasticity ofmaterials

(2.12)

12

12

/ln

/ln

m


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Constitutive Equations

Describe the relations between stress and strain in terms of thevariables of strain rate and temperature

Early concept: f( , , ,T) = 0 Analogous to equilibrium in thermodynamics system which

states that:f(P, V, T) = 0

There are several forms of constitutive relations, including thesimple power law relation (Hollomon equation) and itsvariants.


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= f(Z) = f( e H/RT )

where Z is called the Zener-Hollomon parameter, H is anactivation energy (calorie per mole), of which Q = m H

= A(sinh )n` e -Q/RT

where A, , and n` are experimentally determined constants

Other Examples of Constitutive Relations

(2.3)

(2.5)


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At low stresses ( < 1.0) :

where A, , and n` are experimentally determined constants. At high stresses ( > 1.2), and the equation reduces to:

The constants and n` are related by = n`

Constitutive Relations (cont)

(2.6)

(2.7) RT Q

e A /

2 )exp(

RT Qn e A /'1


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Figure 2-6. Stress-strain curves for AISI 1040 steel subjected todifferent heat treatments; curves obtained from tensile test.

temperature effect

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