# Creep in Materials

The permanent deformation (strain) of a material under steady load as a function of time is called creep.

A very common observation, in which length of our waist belt increases after some duration, is due to creep effect. It is thermally actuated process, and hence is influenced by temperature. It is, however, appreciable at temperatures above 0.4 Tm where Tm is melting point of material in degree Kelvin.

Creep occurs at room temperature in many materials such as lead, zinc, solder wire (an alloy of Pb and Sn), white metals, rubber, plastics and leather etc. For an insight, consider zinc whose melting point is 420°C (693 K). Its creep rate is considerable above a temperature of (0.4 x 693 K = 277 K) i.e. at about 4°C only.

## Critical Applications for Creep Consideration

Consideration of creep is very important in applications such as given below.

• Industrial belts,
• Pistons of I.C. engines,
• Rockets and missiles,
• Nuclear reactors,
• Tubes of heat exchangers etc.
• Polymeric and elastomeric constructions.

Creep is sometimes desirable also as in metal forming operations such as hot rolling, extrusion, forging etc. These processes are carried-out at high temperatures where deformation follows power creep law. The forces required in operations are reduced due to raised temperatures.

## Creep Curves

Consider a bar, Figure 1(a), subjected to a steady axial load P at certain temperature T. If this arrangement is kept undisturbed, we shall find the progressive stages of deformation as shown in Figures. 1(b) to 1(d) with lapse of time t. Figure 1(d) indicates creep fracture.

Creep Fracture: The total time of creep fracture (t3 — to) is different for different cases. It depends on the following factors.

1. Magnitude of applied load P and hence the stress a developed in the material,
2. Temperature of the working situation, and
3. Characteristics of the material.

If the elongation δl1, δl2, … are recorded at time intervals t1, t2, … etc. in a creep experimental specimen of length l, the strain e = δl/l can be calculated. The creep curve, then, can be plotted between strain e and time t. We are likely to get this curve as shown in Figure 2. It can be studied in three different stages.

Just at the moment when the load is applied, an instantaneous strain eo  = OA develops at t = 0. This is also known as mechanical strain. It is independent of time.

With the lapse of time, creep takes place in different stages marked stage I, II and III and are called primary creep, secondary creep and tertiary creep respectively. Point D is creep fracture point. It may not be possible in many materials to obtain stage III beyond C as time required may be many tens of years.

In such cases, the experiment is conducted in hours, days, weeks, months or few years and then extrapolation is done to plot the curve. The dotted lines have been used to indicate this extrapolation. The total strain etotal is obtained by summing the instantaneous strain and the creep strain ecr. So

etotal = eo + ecr

## Different Stages of Creep Curves

Three stages of the creep curve are as follows.

1. Transient or cold creep extends from A to B. It is nonlinear. The rate of creep is initially fast but slows down later-on. This part of creep occurs even at very low temperatures hence, it is called cold creep. This is also known as I stage or primary creep.

2. Viscous or hot creep is from B to C, and is almost linear. This part of curve dominates at high temperatures, so is also known as hot creep. Viscous creep is more important to design engineers. This is also known as II stage or secondary creep.

3. Tertiary Creep is the last stage before creep fracture. The curve CD rises upward as rate of straining is too fast due to neck formation in the material. This is also known as III stage.

## Creep Laws

Primary, secondary and tertiary creep curves follow different creep laws for various materials. The variation of creep strain ecr with time t may be expressed as under:

Andrade’s law of transient creep for metals and some plastics expresses creep strain as:

ecr = Ctn

Where, C is a constant, and n is power index constant whose value is 1/3.

Logarithmic law of transient creep for glass and rubber expresses creep strain as,

ecr = K loge(1 + t/t1)

Where, K is a constant and t1 is any arbitrary chosen time.

Hyperbolic law of transient creep for concrete expresses creep strain as,

ecr = λt/(n + t)

Where, λ is a constant, and n is creep-time constant.

Secondary creep law may be stated by

ecr = ecr  + vcrt

Where, e1 is creep-intercept (see Figure 2) and vcr is viscous or minimum creep rate. Minimum creep rate increases with increasing stress and is given by:

vcr = Aσn   (n > 1)

Where A and n are the constants.

## Factors Affecting Creep

It has already been pointed-out that the load (hence stress) and temperature influence the creep behavior of a material. So we obtain different curve profiles as shown in Figure 3.

Three separate curves marked A, B and C for the same material are shown. If the temperature is constant, the curves A, B and C are obtained at stresses σ1, σ2 and σ33 > σ2 > σ1) respectively. Similarly if the stress is kept constant, the curves A, B and C are noticed at temperatures T1, T2 and T3 (T3 > T2 > T1).

Although a single diagram is shown to explain two effects, but it does not mean that the same curves are inter-replaceable in the two cases of σ = constant and T= constant. It may be concluded that

• The effect of increasing stress and temperature is to speed-up the rate of creep.
• At higher stress or at higher temperature, the total strain is large and creep fracture occurs in lesser time.
• The duration of three creep stages also vary. Consequently viscous stage II is prolonged in curve A, reduced in curve B and missing in curve C.

## Mechanism of Creep

Occurrence of creep in materials is supposed to be the effect of following phenomena.

1. Vacancy diffusion.
2. Edge dislocation climb-up or climb-down.
3. Grain boundary sliding.
4. Screw dislocation’s cross-slip
5. Elastic after effect.

Vacancy diffusion mechanism involves inter-transfer of vacancies and atoms. When a stress σ is applied to the material, the vacancies flow from longitudinal to transverse direction. At the same time, the atoms fill-in the vacancies by moving from transverse to longitudinal directions. Correspondingly, there is an increase in longitudinal direction and decrease in transverse direction of the material.

Edge dislocation climb-up occurs at high temperature when the rate of vacancy diffusion is high. When vacancies diffuse into or from the edge dislocations, these climb-up or down. They continue their motion under the influence of applied stress.

Grain boundary sliding: The grain boundaries behave as non-crystalline bodies. At high temperature, they lose their viscosity much faster than the grains. Above 0.5Tm the grains slide with respect to each other, and almost float in less viscous grain boundaries. Such inter-grain sliding is responsible for creep in the materials.

## Creep Resistant Materials

Machine and structural parts functioning at higher temperatures must be creep resistant. Pressure vessels and heat exchangers in oil refinery and chemical industries operate at elevated temperatures. Heat engines need to operate at higher operating temperatures to achieve enhanced thermal efficiency. This necessitates the creep resistant materials to have high melting points. Some of the probable materials may be as follows:

1. Refractories,
2. Tungsten based alloys,
3. Nickel based alloys and nickel super-alloys,
4. Cobalt based alloys,
5. Steel based alloys,
6. Mono-crystal titanium, and
7. Thoria (Th02) dispersed nickel.

Of these the refractories are brittle and cannot take purposeful tensile load. Tungsten and titanium are costly metals. Tungsten is also heavy. Nickel based alloys, cobalt based alloys and steel based alloys are suitable for use from different view-points.

Nickel using thoria by dispersion hardening method is a very good creep resistant material. It can maintain its strength up to a temperature of about 0.9Tm. Some of the latest materials as given below are also useful.

1. Silicon nitride (Si3N4) for piston rings and cylinder heads.
2. Sialons (alloys of Si3N4 and Al203) for gas turbine blades up to 1300°C. Finer grained materials having small crystals are undesirable for use as creep resistant materials.

## Creep Test

Now we shall study as how to experimentally determine the creep limit of a material. The most important creep properties widely used in design of components are the following.

1. Creep deformation strength or creep limit, and

2. Creep rupture strength.

Creep deformation strength is defined as the highest stress that a material can withstand for a specified duration at a certain temperature without excessive deformation which is pre-decided.

Creep rupture strength is defined as the highest stress that a material can withstand for a specified duration at certain temperatures without rupture.

Expected life of machines and equipment: The above strengths are generally obtained for the expected life of the equipments at their operating temperatures. The life may be taken as 2000 hours for gas turbine and 40 years for steam turbine. The allowable deformations, as a fraction of deformation at creep fracture, are

• 0.01% at 1000 K in 2000 hours for gas turbines.
• 0.20% at 1000 K in 100 000 hours for steam turbines.
• 1.00% at 1000 K in 1000 hours for stainless steel.
• 2.00% at 1000 K in 2000 hours for pressure vessels.
• 4.00% at 300 K in 8500 hours for plastic bottles.

## Experimental Set-up of Creep Testing Machine

A creep testing machine is shown in Figure. It is used to conduct creep test at a predetermined temperature. The stepwise procedure is as follows.

1. The specimen is placed inside the furnace and heated for 4 to 5 hours so that its temperature becomes uniform throughout.
2. It is then subjected to a constant load by a lever and a dead weight system.
3. In due course of time, creep deformation (strain) starts in the specimen which is recorded at certain interval of time.
4. Marten’s optical extensometer records the strain in the specimen to an accuracy of 0.001 mm.

The observations may be taken for few hours, few days, few months, few years or full life according to the importance and need. Hence the tests are known as

• Short duration test,
• Medium duration test,
• Long duration test, and
• Life duration test.

Result of the experiment: The recorded strain e and time t curve is plotted for a constant stress σ at a uniform temperature T.

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