Stress-Strain Diagram MCQ Quiz in मराठी - Objective Question with Answer for Stress-Strain Diagram - मोफत PDF डाउनलोड करा

Proof resilience is defined as the maximum energy that can be absorbed within the elastic limit, without creating a permanent distortion.

Explanation:

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).

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

Limit of proportionality

• 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 behaviour of elastic bodies is based on the stress-strain proportionality.

Elastic limit

• 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 the case where the elastic limit and proportional limit are different, the elastic limit is always greater than the proportional limit.

Yield point: 

• Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. There will be thus permanent deformation or permanent set when the load is removed. These two points are termed as upper and lower yield points respectively. The stress at the yield point is called the yield strength.

Fracture: 

• Beyond point E, the bar begins to form the neck. The load falling from the maximum until a fracture occurs at F.

Explanation:

True stress-strain and Engineering Stress-strain Curve:

Engineering stress-strain is lower than true stress-strain because we consider initial area only throughout the process while in true stress-strain curve we consider the deformed area and which is deformed drastically, therefore stress will increase.

Mathematically

\(Engineering~Stress(\sigma_E)={Applied~Force\over Initial~Area}\) and \(True~Stress(\sigma_T)={Applied~Force\over Deforming~Area}\)

As the deformed area will be less than the initial area of the specimen hence, the True stress will always be greater than Engineering stress for the same load.

Also, the curved traced by True stress will be above the Engineering stress and moves left with increases in load and corresponding strain.

But we cannot measure the change in cross-section area during the process in the universal testing machine(UTM), therefore engineering stress we study.

Mathematically, true stress(σT) and engineering stress(σE) relation is represented as

σT = σE(1 + ϵ)

where ϵ is engineering strain. 

Additional Information

Stress-strain Curve 

According to Hooke’s law if a load is applied to the wire in steps until the wire breaks. And because of this, the elongation in the wire is measured as shown in fig. below in this the graph of stress is along Y-axis and strain along X-axis is plotted. The curve obtained is termed as a stress-strain curve.

• From this, we can see that the initial part OE of the graph is a straight line, which shows that stress is directly proportional to strain. Hooke’s law is obeyed up to point E. The value of stress corresponding to point E is called the elastic limit of the material of the wire.
• If the load applied to the wire is removed, the wire completely regains its original length. The point E represents the limit of proportionality between stress and strain.
• If the stress is increased beyond point E, the graph no longer remains a straight line and Hooke’s law is not obeyed.
• In this case, for a small increase in stress, the strain increases faster and a graph bends towards strain axis.
• If the wire is strained up to E’ beyond point E and then if the load is removed, the wire is unable to cover its original length.
• However, the wire retains its elastic properties as soon as the load is removed. The strain OS remains permanently in the wire. If the wire is loaded again, a straight-line graph SE’ is obtained. The strain OS is called a set.
• If the load is increased further, a point Yp is reached, at which the tangent to a curve becomes parallel to strain axis. This means that the extension of wire increases without any increase in stress or load, the wire is said to ‘flow’. The point Yp is called ‘Yield Point’. The value of stress corresponding to the yield point is called yield stress.
• Beyond the yield point, the curve begins to bend upwards and the portion Yp and N graph is obtained.
• At this stage, when wire begins to flow, the cross-section of wire decreases uniformly up to N.
• ‘Neck’ or constriction begins to form at a weak point. The point N represents the maximum stress which the wire can bear and is called ultimate stress/breaking stress.
• Once the neck is formed, the wire begins to thin out locally, where the strain increases faster even though stress is decreased and the wire finally breaks at point B and is called breaking point.

The graph shown above is the stress strain curve of mild steel.

Observations

• It can be clearly seen that before reaching its breaking stress the material has deformed significantly. Hence we can say that material is having good ductility.
• When subjected to metallurgical and mechanical conditions for example, If we increase the carbon percentage the material will become brittle and and the graph will change drastically.

Hence it is more sensitive to metallurgical and mechanical changes.

• The above two observations were done for ductility test but similarly we can do for torsion, impact and combined stresses etc.

Hence the correct answer is, it does not exist because it do exist and we can use it to find various results through various tests.

Explanation:

As per the stress-strain curve,

The occurrence of the following points are given below:

• Proportional limit: It is the highest stress at which stress and strain are directly proportional so that the stress-strain graph is a straight line and follows the Hooke's law.
• Elastic limit: It is the greatest stress that can be applied to it without causing plastic (permanent) deformation. When a material is stressed to a point below its elastic limit, it will return to its original length once the stress is removed.
• Yield point: It is the stress at which the material will retain a 0.2% permanent elongation after the stress or force is removed.
• Ultimate strength: It is the maximum amount of stress the material can withstand. Due to strain hardening material can withstand additional stress beyond the elastic limit. At this point continued static stress will lead to further deformation and fracture.
• Point of rupture/fracture: It is the point at which a material will fail catastrophically through fracturing.

Explanation

Modulus of toughness: It is the total strain energy per unit volume which can be stored in metal without fracture. It is equal to the total area under the stress-strain curve up to fracture point.

Proof resilience: It represents elastic strain energy per unit volume of metal. It is defined for those ductile metals which don't show clear yield point.

Tenacity: It refers to the ultimate tensile strength of the metal. A metal having high tenacity means it has high ultimate tensile strength.

Modulus of resilience: It is the elastic strain energy per unit volume, It is equal to the area under Stress-strain curve within an elastic limit.

Explanation:

Elasticity is the property of a material to regain its original shape after deformation when the external forces are removed. 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.

Modulus of elasticity or Young’s modulus is the slope of the stress-strain curve in the elastic region.

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

Steel is more elastic than rubber.

We know that Young’s modulus is the ratio of stress to the strain.

If the same force is applied to the wire of steel and rubber thread, which are of equal length and cross-section area, we will find that the extension in the rubber thread is much greater than extension in steel wire.

Therefore, for a given stress, the strain produced in steel is much smaller than that produced in the rubber. This implies that Young’s modulus for steel is greater than that for rubber. Therefore, steel is more elastic than rubber.

Concept:

Proportional limit, Elastic limit and yield point are points before the failure of metal, but fracture point is a point of failure where metal fractures.

• So it is evident from the graph that the strain is proportional to stress or elongation is proportional to the load giving a straight line relationship. This law of proportionality is valid up to a point A. Point A is known as the limit of proportionality or the proportionality limit.
• For a short period beyond point A, the material may still be elastic in the sense that the deformations are completely recovered when the load is removed. The limiting point B is termed as Elastic Limit.
• Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. There will be thus permanent deformation or permanent set when the load is removed. These two points are termed as upper and lower yield points respectively. The stress at the yield point is called the yield strength.
• A further increase in the load will cause marked deformation in the whole volume of the metal. The maximum load which the specimen can withstand without failure is called the load at the ultimate strength. The highest point ‘E' of the diagram corresponds to the ultimate strength of a material.
• Beyond point E, the bar begins to form the neck. The load falling from the maximum until a fracture occurs at F.

Explanation:

Creep:

Creep is the property by virtue of which a material undergoes additional deformation over and above that due to applied load with the passage of time under sustained loading.

The ratio of ultimate creep strain to elastic strain is known as the Creep coefficient.

Additional Information Creep modulus:

• The creep modulus is defined as the instantaneous elastic modulus of the material that varies with time.
• The ratio of creep stress over creep strain computes the creep modulus of the material.
• Since the creep stress is maintained constant, the creep modulus is inversely proportional to the creep strain.
• The creep modulus is dependent on the applied stress, where an increase of compressive load amplifies the loss in the creep modulus of the material.

Tertiary creep:

• Tertiary creep has an accelerated creep rate and terminates when the material breaks or ruptures.
• It is associated with both necking and the formation of grain boundary voids.

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.

Additional Information

Elastic and plastic zones can be understood from the stress-strain curve.

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Important Points

Many materials, particularly, Annealed hot rolled mild steel, show a localized, heterogeneous type of transition from elastic to plastic deformation that produces a yield point in the stress-strain curve.

Soft brass produces annealing but after alloying.