Mechanical Properties of Materials - 3 - GATE ME Strength Free MCQ Test

• Toughness is a material's ability to absorb energy and plastically deform without fracturing.


• It is a crucial property for materials used in structural applications to prevent sudden failure under impact or dynamic loading.

• Strength is the ability of a material to resist deformation or fracture under an applied load.


• Toughness, on the other hand, measures the amount of energy a material can absorb before fracturing.

• Microstructure: Fine-grained materials tend to exhibit higher toughness due to more obstacles for crack propagation.


• Temperature: Toughness decreases at lower temperatures due to reduced atomic mobility and increased brittleness.


• Material composition: Certain alloying elements can enhance toughness by promoting dislocation movement and preventing crack propagation.

• Tough materials are used in aerospace, automotive, and construction industries to ensure structural integrity and safety.


• Examples of tough materials include steel, titanium, and some polymers with high impact resistance.

• Toughness is a critical property for materials to withstand impact and dynamic loading without catastrophic failure.


• Materials with high toughness can absorb large amounts of energy before fracturing, making them suitable for various engineering applications.

• Definition: Coaxing is the method of increasing the fatigue resistance of a metal by over-stressing it through successively increasing loadings.



• Process:




• Initially, the metal is subjected to a load that is below its fatigue limit.


• After a certain number of cycles, the load is increased slightly to induce microstructural changes in the metal.


• This process is repeated multiple times, each time increasing the load slightly higher than the previous cycle.





• Objective: The main goal of coaxing is to enhance the fatigue resistance of the metal by inducing compressive residual stresses in the surface layers of the material.



• Benefits:




• Improves the fatigue life of the metal component.


• Enhances the performance of the material under cyclic loading conditions.


• Allows the metal to withstand higher stress levels without failure.

In the stress-strain curve for a mild steel specimen, the upper yield point is the maximum stress at which the material begins to deform plastically and is characterized by a sudden drop in stress with increasing strain.

On the graph, the upper yield point is represented by point B, which is the highest point on the initial yield plateau. This point marks the transition from elastic deformation (where stress and strain are proportional) to plastic deformation (where permanent deformation begins).

To summarize:

• A to B: Elastic range, stress increases linearly with strain.
• B: Upper yield point – maximum stress before yielding starts.
• C to D: Yield plateau with lower yield point at D.
• E to F: Plastic range with strain hardening and eventual failure.

Therefore, the correct answer is B.

A: Proportional limit
B : Elastic limit
C : UYP
D: LYP
E: UTS
F: Rupture point

Glass is a brittle material and it can’t withstand tension.

• Definition: The impact strength of a material is a measure of its ability to withstand sudden applied forces or shocks without breaking or fracturing.


• Importance: It is an important property to consider in applications where the material will be subjected to dynamic loads or impact forces.

• Definition: Toughness is the ability of a material to absorb energy and plastically deform without fracturing.


• Relationship: Impact strength is closely related to toughness, as materials with high toughness tend to have high impact strength.

• Hardness: Hardness is the resistance of a material to indentation or scratching, while toughness is the resistance to fracture.


• Impact Strength: While hardness may contribute to impact strength to some extent, it is primarily toughness that determines how well a material can withstand impact forces.

• Correct Answer: The impact strength of a material is best characterized by its toughness, as this property directly relates to the material's ability to withstand sudden shocks or forces without failure.

Except endurance limit all are elastic properties of the material in tension. Endurance limit is the fatigue property and found out by reversible cyclic loading.

• Anisotropic materials have unique properties depending on the direction of measurement.
• Examples include wood, which is stronger along the grain than across it.
• These materials exhibit varying stiffness, thermal conductivity, and strength based on orientation.
• This contrasts with isotropic materials, which have uniform properties in all directions.
• Understanding anisotropy is crucial in fields like engineering and materials science for effective design and application.

Isotropy is the property in which material posses same properties any where within it.

Creep is that property by virtue of which a metal specimen undergoes additional deformation with the passage of time under sustained loading within elastic limit. It is permanent in nature and cannot be recovered after removal of load, hence is plastic in nature.

Resilience is the total strain energy stored in a given volume of a material within elastic limit. On removal of load this energy is released. In other words, it is the area under load deflection curve within elastic limit.

Ductility is defined as the ability of the material to deform to a greater extent before the sign of crack, when it is subjected to tensile force. Ductile materials are those materials which deform plastically to a greater extent prior to fracture e.g. mild steel, copper and aluminium.

When metals are subjected to constant loads, metals tends to deform continuously. This continuous deformation of metals under constant loads is called as creep.

The stress which can be withstand for some specified number of cycles is the fatigue strength of material. The stress level which can be withstand for an infinite number of cycles, without failure is called endurance limit.

Strain energy is the energy stored by a system undergoing deformation.

Toughness is the ability of material to absorb the energy upto fracture point, i.e. toughness of material is the total area under stress-strain curve.

• Bulk modulus: The unit of bulk modulus is Pascal (Pa) which is a measure of a substance's resistance to compression.


• Kinematic viscosity: The unit of kinematic viscosity is square meters per second (m^2/s) which represents the fluid's resistance to flow.


• Surface tension: The unit of surface tension is Newton per meter (N/m) which is the force acting on the surface of a liquid.


• Strain: Strain is a dimensionless quantity as it is the ratio of the change in dimension to the original dimension of a material. It has no unit.

Explanation:

• Visco-elastic material : Small plastic zone - This is not correctly matched because visco-elastic materials do not exhibit a small plastic zone. Visco-elastic materials exhibit time-dependent behavior and show both viscous and elastic properties.


• Strain hardening material : Stiffening effect felt at some stage - This is a correct match. Strain hardening materials undergo a stiffening effect as deformation increases.


• Orthotropic material : Different properties in three perpendicular directions - This is a correct match. Orthotropic materials have different mechanical properties in three mutually perpendicular directions.


• Isotropic material : Same physical properties in all directions at a point - This is a correct match. Isotropic materials have the same physical properties in all directions at a point.

Therefore, the correct answer is option A, as visco-elastic materials do not have a small plastic zone.

Hooke’s law holds up to the proportional limit.

Hooke’s law in terms of stress and strain is Stress∝Strain→σ∝ε→σ=Eε

The constant of proportionality is called the elastic modulus or Young’s modulus, E. It has the same units as stress. E is a property of the material used. 

When a specimen is loaded beyond proportional limit, it has tendency to regain its initial size and shape when the load is removed, this shows elastic stage. The point up to which material shows this tendency is called elastic limit.

The material and its properties. Different materials have different limits of proportionality, which is the maximum stress a material can withstand before it no longer behaves in a linearly elastic manner. It also depends on the temperature and the strain rate.

In plastic design the stress-strain curve is bilinear as shown in figure (a). However, the stress-strain curve for ideal plastic materials is as shown in figure (c). Figure (b) shows stress-strain curve for brittle materials. Figure (d) shows stress-strain curve for ductile materials.

ESteel = 210 GPa
EAluminium = 70 GPa
ECopper = 130 GPa

• Cast iron, being a brittle material, does not show any elongation, but ductile materials like mild steel, aluminium and copper elongate due to the application of tensile force.
• Both steel and copper are ductile, but copper is more ductile because it can withstand a greater strain than steel before breaking.

Ductility is the ability of a material to withstand tensile force when it is applied upon it as it undergoes plastic deformation whereas Brittleness is the opposite of ductility as it refers to the ability of materials to break into pieces upon application of tensile force without any elongation or plastic deformation.

Tenacity is the property of a metal to resist the fracture when under the action of tensile load. it refers to the ultimate tensile strength of the material, a metal having high tenacity means it has high tensile strength.

Toughness is the ability to absorb mechanical energy up to failure.

Malleability is that property by which a metal can be drawn into a thin sheet of negligible thickness.

Plasticity is an ability of material to deform without any rupture by non-returnable way. After removing the load there are staying permanent deformations.

• Shear Strength: Shear strength is the maximum resistance of a material to shear stress. This property cannot be evaluated by a static tension test, as tension tests are specifically designed to measure the material's response to tensile forces, not shear forces.


• Modulus of Elasticity: The modulus of elasticity, also known as Young's modulus, can be determined from a static tension test. It measures the stiffness of a material.


• Ductility: Ductility is the ability of a material to undergo significant plastic deformation before rupture. This property can be evaluated by a static tension test by observing the material's elongation and reduction in cross-sectional area before failure.


• Poisson's Ratio: Poisson's ratio is the ratio of transverse strain to axial strain when a material is under tension or compression. It can also be determined from a static tension test.

Percentage elongation

where
L_o = original gauge length
L_f = final length between the gauge mark measured after fracture
since local yielding occurs before the fracture of the specimen, the percentage elongation depends upon the gauge length of the specimen.

• Definition: Modulus of resilience is a material property that measures its ability to store energy without undergoing significant deformation.


• Property to Store Energy: It is a measure of how much energy a material can absorb without undergoing permanent damage or deformation.


• Resistance to Deformation: Materials with a high modulus of resilience can withstand a significant amount of energy before any permanent changes occur.


• Relation to Elasticity: While modulus of resilience is related to elasticity, it specifically focuses on the ability of a material to store energy rather than just return to its original shape.


• Importance: Understanding the modulus of resilience is crucial in designing materials for applications where energy absorption is critical, such as in impact-resistant materials.

• Definition: Modular ratio of two materials is the ratio of their modulus of elasticities.


• Explanation: The modulus of elasticity is a measure of a material's stiffness or resistance to deformation when subjected to an external force. It is also known as Young's modulus. The ratio of the moduli of elasticity of two materials is known as the modular ratio.


• Significance: The modular ratio is important in structural engineering and material selection, as it helps in determining how two materials will behave when combined in a structure or component.


• Calculation: The modular ratio is calculated by dividing the modulus of elasticity of one material by the modulus of elasticity of the other material. For example, if material A has a modulus of elasticity of 200 GPa and material B has a modulus of elasticity of 100 GPa, the modular ratio of A to B would be 2:1.


• Application: Engineers use the modular ratio to design structures that require different materials with specific properties, such as strength, stiffness, and flexibility. By understanding the modular ratio, they can ensure that the materials work together effectively to meet the structural requirements.

• Proof resilience per unit volume: Proof resilience is the maximum energy that can be absorbed per unit volume without causing permanent deformation. It is a measure of a material's ability to absorb energy when deformed elastically.


• Definition of modulus of resilience: Modulus of resilience is defined as the proof resilience per unit volume of a material. It is a material property that quantifies the amount of energy that can be absorbed per unit volume without causing permanent deformation.


• Calculation: Modulus of resilience is calculated by dividing the proof resilience by the volume of the material. It provides a measure of how much energy a material can absorb per unit volume before it permanently deforms.


• Importance: Modulus of resilience is an important material property as it indicates the ability of a material to withstand impact or shock loading without permanent deformation. Materials with high modulus of resilience are preferred in applications where impact resistance is crucial.

• Residual Compressive Stress: The presence of residual compressive stress on the outer surface of the rotating shaft helps to counteract the tensile stress induced by the external bending load.


• Effect on Fatigue Life: The axial residual compressive stress reduces the overall tensile stress experienced by the shaft during bending. This reduction in stress helps to increase the fatigue life of the shaft.


• Increased Fatigue Life: Due to the presence of the residual compressive stress, the shaft is less likely to experience fatigue failure, leading to an increased fatigue life.


• Beneficial Effect: The beneficial effect of the residual compressive stress on the fatigue life of the shaft is more pronounced under higher bending loads, where the reduction in tensile stress plays a significant role in preventing fatigue failure.