Stress-Strain Diagram MCQ Quiz - Objective Question with Answer for Stress-Strain Diagram - Download Free PDF

Explanation:

Creep in Materials

• Creep is the phenomenon of slow and progressive deformation of a material under a constant load or stress, typically occurring over an extended period of time. This process happens when the material is subjected to a constant tensile, compressive, or shear stress, often at elevated temperatures, but it can also occur at room temperature for certain materials.
• During a tensile test or other loading conditions, a material subjected to a constant load may experience deformation that increases gradually over time. This deformation is not recoverable and occurs due to the movement of dislocations, grain boundary sliding, and diffusion processes within the material structure. The creep behavior is typically characterized by three stages:
  • Primary Creep: This is the initial stage where the creep rate decreases over time due to strain hardening.
  • Secondary Creep: In this stage, a constant creep rate is observed, which is the result of a balance between strain hardening and recovery processes.
  • Tertiary Creep: This stage involves an accelerated creep rate leading to material failure due to necking or microstructural damage.

Factors Affecting Creep:

• Stress Level: Higher stress levels lead to increased creep rates.
• Temperature: Elevated temperatures accelerate the creep process, as thermal activation facilitates dislocation movement and grain boundary sliding.
• Material Type: Certain materials, such as metals, polymers, and ceramics, exhibit creep behavior. Metals like aluminum, lead, and nickel-based alloys are more prone to creep at high temperatures.
• Time Duration: Creep deformation increases with the duration of applied stress.

Applications: Understanding creep behavior is essential in industries where materials are exposed to high temperatures and sustained loads, such as:

• Aerospace industry for turbine blades and jet engines.
• Power plants for boiler tubes and heat exchangers.
• Construction industry for bridges and high-rise buildings.
• Automotive industry for engine components.

Explanation:

Creep:

• Materials subjected to constant load at an elevated temperature (> 0.4 - 0.5 times of Melting Temperature) will Creep i.e exhibit time dependant deformation.
• It occurs in three stages.

Stages of Creep:

Primary Creep	Secondary Creep	Tertiary Creep
Creep rate decreases with time (decreasing slope) due to the strain hardening process resulting from deformation.	Creep rate becomes linear (Constant slope) There is a balance between strain hardening  and recovery (softening) of the material because of recrystallization.	Creep rate increases with time (Increasing slope) leading to necking and finally fracture because of the structural changes occurring in the material.

Factor affecting Creep:

• Material Properties (Melting point, Young’s Modulus, Grain size)
• Exposure time
• Exposure temperature
• Structural load

Fatigue strength: 

It is the highest stress that a material can withstand for a given number of cycles without breaking.

Practically, levels of stress are not held constant as in S – N tests, but can vary below or above the designed stress level.

Overstressing: The initial applied stress level is higher than the fatigue limit for a short period of time beyond failure, then cyclic stressing below the fatigue limit. This overstressing reduces the fatigue limit.

Understressing: The initial applied stress level is lower than the fatigue limit for a period of time, then cyclic stressing above the fatigue limit. This under-stressing increases the fatigue limit (might be due to strain hardening on the surface).

Engineered Stress-strain curve:

 It is the graphical representation of stress and corresponding strain in the material.

A typical stress-strain curve looks like this:

The tensile strength, yield strength, or yield point on the stress-strain curve of a material indicates the strength of the material, and the percent of elongation & reduction of the area on the stress-strain curve of a material indicates the ductility.  

 The shape of the stress-strain curve of material depends on its composition, heat treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress imposed during the testing. 

Theory of simple bending or Euler-Bernoulli beam theory assumes that plane sections remain plane and perpendicular to the beam axis after bending. One critical assumption is that the material is homogeneous and isotropic, meaning the material properties (like Young's Modulus) are the same in tension and compression. Another important assumption is that the beam's cross-sectional dimensions are small compared to the radius of curvature of the bent beam, ensuring the bending moment is the dominant force.

Calculation:

The cross-sectional area A of his legs will increase as the square of the linear dimension, so A' = 8²A.

Stress is force (weight) per unit area, so the stress in his legs after the growth is given by:

σ' = W' / A' = (8³W) / (8²A) = 8(W / A)

Therefore, the stress in the man's legs will increase by a factor of 8.

The correct answer is: Option 4 - 8

Explanation:

Perfectly Plastic Material:

For this type of material, there will be only initial stress required and then the material will flow under constant stress.

The chart shows the relation between stress-strain in different materials. 

Stress-Strain Curve	Type of Material or Body	Examples
	Rigidly Perfectly Plastic Material	No material is perfectly plastic
	Ideally plastic material.	Visco-elastic (elasto-plastic) material.
	Perfectly Rigid body	No material or body is perfectly rigid.
	Nearly Rigid body	Diamond, glass, ball bearing made of hardened steel, etc
	Incompressible material	Non-dilatant material, (water) ideal fluid, etc.
	Non-linear elastic material	Natural rubbers, elastomers, and biological gels, etc

Explanation:

Elastic recovery/strain: The strain recovered after the removal of the load is known as elastic strain.

Plastic strain: The permanent changes in dimension after the removal of load is known as plastic strain.

The load is removed when the stress was 200 MPa and the corresponding strain was 0.03

After the removal of load, the body recovered and the final strain found was 0.01.

∴ Elastic strain = 0.03 - 0.01 ⇒ 0.02 and Plastic strain = 0.01 respectively.

Explanation:

The stress-strain diagrams for different type of materials are given below:

Explanation:

In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain.

A rigid, linearly strain hardening material requires an increasing stress level to undergo further strain, thus, its flow stress (the magnitude of the stress required to maintain plastic deformation at a given strain) increases with increasing strain.

Statement 1: True

Hooke’s Law states that the strain in a solid body is directly proportional to the applied stress and this condition is valid upto the limit of proportionality (i.e. point A in the figure).

\(Stress\; \propto Strain \to \;\sigma \propto \varepsilon \; \to \;\sigma = E\varepsilon \)

Statement 4: True

Limit of proportionality is the stress at which the stress-strain curve ceases to be a straight line. It is the stress at which extension ceases to be proportional to strain. The proportional limit is important because all subsequent theory involving the behavior of elastic bodies is based on the stress-strain proportionality.

Elastic limit is is that point in the stress-strain curve up to which the material remains elastic, i.e. the material regains its shape after the removal of the load.

However, for many materials, elastic limit and proportional limit are almost numerically the same and the terms are sometimes used synonymously. In case where the elastic limit and proportional limit are different, the elastic limit is always greater than the proportional limit.

Explanation:

Elastic Modulus(E): Also known as Young's modulus or Modulus of Elasticity is the fundamental property of every material which cannot be changed but depends upon temperature and pressure. It describes the relationship between stress and strain of the material. Young's modulus is the ratio of stress to strain.

\(E\ =\ \frac{\sigma}{\varepsilon}\)

The relationship between stress and strain of different materials are given below:

From the above graph for a perfectly rigid plastic body, the strain is zero even though stress is applied, so from the equation

\(E\ =\ \frac{\sigma}{\varepsilon}\)

If the strain is zero then young's modulus becomes infinity

∴ The elastic modulus for the perfectly rigid plastic body is infinity

Explanation:

Stress-strain diagram:

Yield point:

• The yield point is the point in the stress-strain curve from which transitions from elastic behaviour (where removing the applied load will return the material to its original shape) to plastic behaviour (where deformation is permanent) takes place.  After the yield point material shows permanent deformation on loading.

Plastic deformation:

• As we know plastic deformation is significant in ductile material only, brittle material failed after elastic deformation rather than being deformed permanently. Hence we can observe the yield point on the stress-strain curve for ductile material only. 
• Cast iron and glass are brittle materials, so they do not produce yield point, they just break when stress exceeds a certain limit. Hence we cannot observe any definite yield point in cast iron or brittle materials.

Thus, option(2) is the Correct Answer.

Explanation:

Proof resilience:

The strain energy stored in a body due to external loading, within the elastic limit, is known as resilience and the maximum energy which can be stored in a body up to the elastic limit is called proof resilience.

Modulus of resilience:

Modulus of resilience is defined as proof resilience per unit volume. It is the area under the stress-strain curve up to the elastic limit.

Toughness:

It is defined as the ability of the material to absorb energy before fracture takes place.

• This property is essential for machine components which are required to withstand impact loads.
• Tough materials have the ability to bend, twist or stretch before failure takes place.
• Toughness is measured by a quantity called modulus of toughness. Modulus of toughness is the total area under the stress-strain curve in a tension test.

Flexure rigidity:

• It is a measure of the resistance of a beam to bending, that is, the larger the flexural rigidity, the smaller the curvature for a given bending moment.
• EI = Flexural rigidity

Explanation:

Stress-strain diagram:

It is a tool for understanding material behavior under load. It helps in selecting the right materials for specific loading conditions.

Various points are mentioned in the stress-strain diagram, the details are mentioned below:

Proportion limit (Hooke's Law):

• From the origin up to point 'P' called the Proportional limit, the stress-strain curve is a straight line i.e σ ∝ ε.
• If the stress is increased beyond the point P, the graph no longer remains a straight line and Hooke’s law is not obeyed.

Elastic limit:

• Point 'E' represents the elastic limit, the limit up to which the material will return its original shape and size when the load is removed.
• After point E, a small increase in stress, the strain increases faster and a graph bends towards the strain axis, and then if the load is removed, the material is unable to cover its original size and shape.

Yield point (Y_p):

• It is the point at which the material will have an appreciable elongation OR a slight increase in stress above the elastic limit that results in permanent deformation. This behaviour is called yielding for ductile materials. It is denoted by Y_p.
• Materials which is less ductile do not have a well-defined yield point, which is determined by the offset method- by which a line is drawn parallel to linear portion of the curve and intersecting at some values most commonly 0.2 %. It is denoted by point S.

Breaking stress / Ultimate stress:

• The maximum ordinate (stress) in the stress-strain diagram which represents the maximum load that a material can sustain without failure. It is denoted by point N.
• Necking: After the ultimate stress, the cross-sectional area begins to decrease in a region of the specimen which causes the apparent stress to rapidly decrease. This phenomenon is known as necking.

Breaking point:

Once the neck is formed, the material begins to thin out locally, where the strain increases faster even though stress is decreased and the material finally breaks at point B which is called breaking point.

Explanation:

Stress-Strain curve for some materials: