Aircraft materials lecture 3

STRESS-STRAIN CURVESLECTURE 3

By: Kanu Priya JhanjiAsst. Professor

School of Aeronautical SciencesHindustan University

[email protected]

AIRCRAFT MATERIALS

UNIT-1

Introduction

Creep is high temperature progressive deformation at constant stress.

"High temperature" is a relative term dependent upon the materials involved. Creep rates are used in evaluating materials for boilers, gas turbines, jet engines, ovens, or any application that involves high temperatures under load.

Understanding high temperature behavior of metals is useful in designing failure resistant systems.

So, creep test is essential to predict the working life of machine components which are subjected to creep

SCHOOL OF AERONAUTICAL SCIENCESHINDUSTAN UNIVERSITY

Creep test

The test piece of metal is held in a steel structure such that one of its ends is held in a holder and the other end is loaded through a lever.

Surrounding the specimen, there is a temperature controlled chamber by which we can do the creep testing at a constant temperature over a long period of time.

First, the zero reading of the length is noted. Load is then applied and after few minutes

extension(axial deformation) is measured periodically throughout the test.

In this way, a number of readings are taken. The extension is measured either directly by a telescope

or a mirror and scale arrangement.

Creep testing Machine

Fatigue test

The failure of a material under repeated applied stress is called fatigue.

The fatigue strength of a material is increased by the surface compressive residual stress and decrease by stress concentration due to notch or hole.

Fatigue test is conducted on rotary beam fatigue testing machine as shown in figure.

Process

The test piece is loaded in pure bending and rotated about its axis with the help of motor.

With each rotation, the stress at any part of the cross-section of the specimen (except at an axis down the center) varies sinusoidally between maximum tensile and maximum compressive stresses.

Each revolution thus constitutes one cycle of stress reversal. The speed of the motor will indicate the frequency of the stress

reversal and it is indicated by revolution counter. The stress (S) is varied using different loads and the number of

cycles (N) till failure occurs is noted for each load. It is observed that after a sufficient number of stress reversals,

a crack is formed on the outer surface of the specimen, in the form of a ring.

This crack goes on extending towards the center of the test piece till it breaks away

S-N Curve

A curve is plotted as “S” versus logarithm of “N”. From the S-N curve it can be seen that the lower the applied stress, the

greater the number of cycles to failure. The stress value at which the curve flattens out or the curve becomes

parallel to the log N(no. of cycles to failure)axis is called endurance limit or fatigue limit of the given material.

This defines the stress at which the specimen exhibits “infinite life”. Stresses below the fatigue limit can be applied repeatedly an indefinite

number of times without causing failure. The strength of materials under repeated or cyclic stresses is more

commonly defined by the endurance or fatigue strength which is the stress amplitude “S”, that produces failure in 107 cycles

Fractures

A fracture is the separation of an object or material into two or more pieces under the action of stress.

The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid.

If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.

Fracture strength or breaking strength is the stress when a specimen fails or fractures.

Types of fractures

Fatigue fractureCreep fracture

fractures

A brittle fracture may be defined as a fracture which takes place by the rapid propagation of crack with a quite negligible plastic deformation

Ductile fracture may be defined as the fracture which takes place by a slow propagation of crack with appreciable plastic deformation.

Fatigue fracture is defined as fracture which takes place under repeatedly applied fatigue stresses. It occurs at stresses well below the tensile strength of the material. The tendency of fatigue fracture increases with the increase in temperature and higher rate of straining.

Creep fracture is defined as the fracture which takes place due to excessive creeping of materials under steady loading. It occurs in metals like iron, copper and nickel at higher temperatures. The tendency of creep fracture increases with the increase in temperature and high rate of straining.

D/B Brittle and Ductile Fracture

Brittle fracture is the one which has the movement of crack with a negligible plastic deformation adjacent to crack.

Rapid rate of crack propagation.

Failure is on account of direct stress.

Surface obtained at the fracture is dull and accompanied with hills and valleys.

It is characterized by separation of normal to tensile stress.

It occurs when material is in elastic condition.

The tendency of brittle fracture is increased by decreasing temperature, increasing strain rate and work hardening.

Ductile fracture is the one which is accompanied with large plastic deformation and it is result of intense localized plastic deformation adjacent to crack.

Slow rate of crack propagation Failure is on account of shear

stress developed at 45⁰. Surface obtained at the fracture

is shining and accompanied with the formation of slip planes.

It is characterized by the formation of cup and cone.

It occurs when the material is in plastic condition.

The tendency of ductile fracture is increased by dislocations and other defects in metals.

Stress-Strain curve for ductile materials

A ductile material is one having relatively large tensile strains up to the point of rupture like structural steel and aluminum .

The stress-strain diagram for mild steel is shown below.

Proportional Limit (Hooke's Law)

From the origin O to the point A called proportional limit, the stress-strain curve is a straight line.

This linear relation between elongation and the axial force causing was first noticed by Sir Robert Hooke in 1678 and is called Hooke's Law that within the proportional limit, the stress is directly proportional to strain or 

σ∝ε   or   σ=Eε

The constant of proportionality E is called the Modulus of Elasticity  or Young's Modulus and is equal to the slope of the stress-strain diagram from O to A.  

The elastic limit is the limit beyond which the material will no longer go back to its original shape when the load is removed, or it is the maximum stress that may be developed such that there is no permanent or residual deformation when the load is entirely removed.

The region in stress-strain diagram from O to B is called the elastic range.

The region from B to F is called the plastic range.   Yield point is the point at which the material will have an appreciable

elongation or yielding without any increase in load.   The maximum ordinate in the stress-strain diagram is the ultimate

strength or tensile strength. 

Rupture strength is the strength of the material at rupture. This is also known as the breaking strength.

From point B to point E strain hardening will takes place. In this region, while specimen is elongating, its x-sectional area will decrease. Decrease in area is fairly uniform over entire gauge length

At ultimate stress, x-sectional area begins to decrease in a localized region. As a result, a constriction or “neck” tends to form in this region as specimen elongates further. Specimen finally breaks at fracture stress(point F).

Modulus of resilience is the work done on a unit volume of material as the force is gradually increased from O to A, in Nm/m3.

This may be calculated as the area under the stress-strain curve from the origin O to up to the elastic limit E (the shaded area in the figure).

The resilience of the material is its ability to absorb energy without creating a permanent distortion. 

Modulus of toughness is the work done on a unit volume of material as the force is gradually increased from O to F, in Nm/m3.

This may be calculated as the area under the entire stress-strain curve (from O to F).

The toughness of a material is its ability to absorb energy without causing it to break. 

Working stress is defined as the actual stress of a material under a given loading.

The maximum safe stress that a material can carry is termed as the allowable stress.

The allowable stress should be limited to values not exceeding the proportional limit. However, since proportional limit is difficult to determine accurately, the allowable stress is taken as either the yield point or ultimate strength divided by a factor of safety.

The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety.

True stress-strain diagram

Instead of using original cross-sectional area and length, we can use the actual cross-sectional area and length at the instant the load is measured

Values of stress and strain thus calculated are called true stress and true strain, and a plot of their values is the true stress-strain diagram

In strain-hardening range, conventional σ- diagram shows specimen supporting decreasing load

While true σ- diagram shows material to be sustaining increasing stress

Although both diagrams are different, most engineering design is done within elastic range provided

1. Material is “stiff,” like most metals2. Strain to elastic limit remains small3. Error in using engineering values of σ and is very small

(0.1 %) compared to true values