Creep, Elastic Strain

# Creep, Elastic Strain | Strength of Materials (SOM) - Mechanical Engineering PDF Download

 Table of contents Creep Tension Test Elastic strain and Plastic strain Elasticity Plasticity Strain hardening

## Creep

When a member is subjected to a constant load over a long period of time it undergoes a slow permanent deformation and this is termed as “creep”. This is dependent on temperature. Usually at elevated temperatures creep is high.

• The materials have its own different melting point; each will creep when the homologous temperature > 0.5.

Homologous temp = Testing temperature / Melting temperature > 0.5

A typical creep curve shows three distinct stages with different creep rates. After an initial rapid elongation εο, the creep rate decrease with time until reaching the steady state.

creep curve

• Primary creep is a period of transient creep. The creep resistance of the material increases due to material deformation.
• Secondary creep provides a nearly constant creep rate. The average value of the creep rate during this period is called the minimum creep rate. A stage of balance between competing. Strain hardening and recovery (softening) of the material.
• Tertiary creep shows a rapid increase in the creep rate due to effectively reduced cross-sectional area of the specimen leading to creep rupture or failure. In this stage intergranular cracking and/or formation of voids and cavities occur.

Creep rate = c1 σc2

Creep strain at any time = zero time strain intercept + creep rate ×Time

= εo + c1  σc2 ∗ t

Where, c1, c2 are constants σ = stress

• If a load P is applied suddenly to a bar then the stress & strain induced will be double than those obtained by an equal load applied gradually.
• Stress produced by a load P in falling from height 'h'

I

• Loads shared by the materials of a compound bar made of bars x & y due to load W,

Formula

• Elongation of a compound bar

Elongation

## Tension Test

Graphical representation

• True elastic limit: based on micro-strain measurement at strains on order of 2 ×10-6. Very low value and is related to the motion of a few hundred dislocations.
• Proportional limit: the highest stress at which stress is directly proportional to strain.
• Elastic limit: is the greatest stress the material can withstand without any measurable permanent strain after unloading. Elastic limit > proportional limit.
• Yield strength is the stress required to produce a small specific amount of deformation. The offset yield strength can be determined by the stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic line offset by a strain of 0.2 or 0.1% (ε = 0.002 or 0.001).
• The offset yield stress is referred to proof stress either at 0.1 or 0.5% strain used for design and specification purposes to avoid the practical difficulties of measuring the elastic limit or proportional limit
• Tensile strength or ultimate tensile strength (UTS) σis the maximum load Pmax divided by the original cross-sectional area Ao of the specimen.
• % Elongation, = L- Lo / Lo , is chiefly influenced by uniform elongation, which is dependent on the strain-hardening capacity of the material.
• Reduction of Area: q = A- A/ Ao
1. Reduction of area is more a measure of the deformation required to produce failure and its chief contribution results from the necking process.
2. Because of the complicated state of stress state in the neck, values of reduction of area are dependent on specimen geometry, and deformation behaviour, and they should not be taken as true material properties.
3. RA is the most structure-sensitive ductility parameter and is useful in detecting quality changes in the materials.
• Stress-strain response

Stress-strain response

## Elastic strain and Plastic strain

The strain present in the material after unloading is called the residual strain or plastic strain and the strain disappears during unloading is termed as recoverable or elastic strain. Equation of the straight line CB is given by

σ = εtotal * E - εplastic * E = εplastic * E

Carefully observe the following figures and understand which one is Elastic strain and which one is Plastic strain.

Graphical representation

## Elasticity

This is the property of a material to regain its original shape after deformation when the external forces are removed. When the material is in elastic region the strain disappears completely after removal of the load, The stress-strain relationship in elastic region need not be linear and can be non-linear (example rubber). The maximum stress value below which the strain is fully recoverable is called the elastic limit. It is represented by point A in figure. All materials are elastic to some extent but the degree varies, for example, both mild steel and rubber are elastic materials but steel is more elastic than rubber.

Graph

## Plasticity

When the stress in the material exceeds the elastic limit, the material enters into plastic phase where the strain can no longer be completely removed. Under plastic conditions materials ideally deform without any increase in stress. A typical stress strain diagram for an elastic-perfectly plastic material is shown in the figure. Mises-Henky criterion gives a good starting point for plasticity analysis.

Graph

## Strain hardening

If the material is reloaded from point C, it will follow the previous unloading path and line CB becomes its new elastic region with elastic limit defined by point B. Though the new elastic region CB resembles that of the initial elastic region OA, the internal structure of the material in the new state has changed. The change in the microstructure of the material is clear from the fact that the ductility of the material has come down due to strain hardening. When the material is reloaded, it follows the same path as that of a virgin material and fails on reaching the ultimate strength which remains unaltered due to the intermediate loading and unloading process.

Graph

### Stress reversal and stress-strain hysteresis loop

We know that fatigue failure begins at a local discontinuity and when the stress at the discontinuity exceeds elastic limit there is plastic strain. The cyclic plastic strain results crack propagation and fracture.

When we plot the experimental data with reversed loading and the true stress strain hysteresis loops is found as shown below.

True stress-strain plot with a number of stress reversals

Due to cyclic strain the elastic limit increases for annealed steel and decreases for cold drawn steel.

Here the stress range is Δσ. Δεp and Δεo are the plastic and elastic strain ranges, the total strain range being Δε. Considering that the total strain amplitude can be given as

Δε = Δε+ Δεe

The document Creep, Elastic Strain | Strength of Materials (SOM) - Mechanical Engineering is a part of the Mechanical Engineering Course Strength of Materials (SOM).
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## FAQs on Creep, Elastic Strain - Strength of Materials (SOM) - Mechanical Engineering

 1. What is creep and how does it relate to mechanical engineering?
Ans. Creep is the gradual deformation of a material under constant stress over time. In mechanical engineering, creep is important as it can lead to the failure of components that are subjected to long-term stress, such as turbine blades in power plants or pipelines. Understanding creep behavior is crucial for designing materials and structures that can withstand prolonged stress without significant deformation.
 2. How is tension testing used to determine elastic and plastic strain?
Ans. Tension testing is a common method used in mechanical engineering to determine the mechanical properties of materials, including elastic and plastic strain. During a tension test, a sample of the material is subjected to an increasing load until it eventually fractures. By measuring the resulting strain and stress, engineers can determine the material's elastic strain, which is the reversible deformation that occurs under small stresses, and plastic strain, which is the permanent deformation that occurs after the elastic limit is exceeded.
 3. What is the difference between elasticity and plasticity in mechanical engineering?
Ans. Elasticity refers to the property of a material that allows it to return to its original shape and size after being deformed by an external force. When a material is subjected to stress within its elastic limit, it experiences elastic deformation, which is reversible. Plasticity, on the other hand, refers to the property of a material that allows it to undergo permanent deformation, even after the stress is removed. Plastic deformation occurs when the stress exceeds the elastic limit of the material.
 4. How does strain hardening affect the mechanical properties of a material?
Ans. Strain hardening, also known as work hardening, occurs when a material becomes stronger and more resistant to deformation as it is plastically deformed. This is typically achieved by cold working or deforming the material at temperatures below its recrystallization temperature. Strain hardening increases the yield strength and tensile strength of the material, making it more suitable for applications requiring high strength and resistance to deformation.
 5. What are some common elastic constants used in mechanical engineering?
Ans. Elastic constants are parameters that describe the elastic behavior of a material. Some common elastic constants used in mechanical engineering include: - Young's modulus (E): Measures the stiffness of a material in tension or compression. - Shear modulus (G): Measures the stiffness of a material in shear. - Bulk modulus (K): Measures the material's resistance to uniform compression. - Poisson's ratio (ν): Describes the ratio of lateral strain to axial strain when a material is subjected to stress. - Lame's constants (λ and μ): Used in the theory of elasticity to describe the relationship between stress and strain in a material.

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