Observed fracture strength is always lower than theoretical cohesive strength .

Griffith explained that the discrepancy is due to the inherent defects in brittle

materials leading to stress concentration implies lower the fracture strength of the materials.

Crack propagation criterion: Consider a through thickness crack of length 2a, subjected to a uniform tensile stress σ, at infinity.

Crack propagation occurs when the released elastic strain energy is at least equal to the energy required to generate new crack surface.

Griffith theory of brittle fracture:

The stress required to create the new crack surface is given as follows :

In plane strain condition, the equation becomes :

The Griffith equation is strongly dependent on the crack size a,and satisfies only ideally brittle materials like glass.

However, metals are not ideally brittle and normally fail with certain amounts of plastic deformation, the fracture stress is increased due to blunting of the crack tip.

Irwin and Orowan suggested Griffith’s equation can be applied to brittle materials undergone plastic deformation before fracture by including the plastic work, γp, into the total elastic surface energy required to extend the crack wall, giving the modified Griffith’s equation as follows :

Modified Griffith equation

In mode I failure and plane-strain condition, the relationship between GIC an KIC can be shown by an expression as

follows :

Where KIC is the critical stress intensity factor ilure

Stress intensity factor

Crack deformation mode.

Fracture modes

Stress intensity factor KIC can be described as fracture toughnessof materials (material resistance to crack propagation) under

conditions of : 1) brittle fracture 2) in the presence of a sharp crack 3) under critical tensile loading

Where KIC is the critical stress intensity factor for plane strain condition

in mode failure. ac is the critical crack length in an infinite plate σ app is the applied stress α is a parameter dependent on specimen and crack geometry

K values of various crack geometries:

Fracture toughness of material can be determined according to LEFM analysis

1) KIC fracture toughness : works well for very high strength materials. exhibiting brittle fracture 2) Crack tip opening displacement CTOD : Used for lower strength materials (σo < 1400 MPa),

exhibiting small amount of plastic deformation before failure. 3) J-integral (JIC) : Used for lower strength materials, exhibiting small

amount of plastic deformation before failure. 4) R-curve : The resistance to fracture of a material during slow and

stable crack propagation

Determination of fracture toughness

KIC fracture toughness of material is obtained by determining the ability of material to withstand the load in the presence of a sharp crack before failure.

Fracture toughness is required in the system of high strength and light weight, i.e., high strength steels, titanium and aluminium alloys.

KIC fracture toughness

Fracture toughness How long the existing crack will grow until the specimen fails

Flaw geometry and design of cylindrical pressure vessel

BCC structure metals experience ductile-to-brittle transition behaviour when subjected to decreasing temperature, resulting from a strong yield stress dependent on temperature.

Ductile to brittle transition behaviour

BCC metals possess limited slip systems available at low temperature, minimising the plastic deformation during the fracture process.

Increasing temperature allows more slip systems to operate, yielding general plastic deformation to occur prior to failure .

Theory of the ductile to brittle transition :

The criterion for a material to change its fracture behaviour from ductile to brittle mode is when the yield stress at the observed temperature is larger than the stress necessary for the growth of the microcrack indicated in the Griffith theory.

Cottrell studied the role of parameters, which influence the ductile to-

brittle transition as follows;

τ i is the lattice resistance to dislocation movement k’ is a parameter related to the release of dislocation into a

pile-up D is the grain diameter (associated with slip length). G is the shear modulus β is a constant depending on the stress system.

Creep and stress rupture

Subjects of interest

• Objectives / Introduction• The high temperature materials problem• Temperature dependent mechanical behaviour• Creep test• Stress rupture test• Structural change during creep• Mechanisms of creep deformation• Fracture at elevated temperature• High temperature alloys

INTRODUCTIONHigh temperature applications

Subjected to high stress at high temperature

Steam Power Plants

Steam Turbine Used in Power Plants

Oil Refineries

High temperature materials problem

Atoms move faster diffusion controlled process.

This affects mechanical properties of materials.

Greater mobility of dislocations (climb).

Increased amount of vacancies. Deformation at grain boundaries. Metallurgical changes, i.e., phase

transformation,precipitation, oxidation, recrystallisation.

TEMP

What is creep? Creep occurs when a metal is subjected to a constant tensile load at an elevated

temperature. In materials science, creep is the tendency of a solid material to slowly move or deform permanently under the influence of stresses.

At which temperature will material will creep?  Since materials have its own different melting point, each will creep when the homologous

temperature > 0.5.

The creep test measure the dimensional changes which occur when subjected to high temperature.

The rupture test measures the effect of temperature on the long-time load bearing characteristics.

Creep Test The creep test is carried out by applying a constant load to a

tensile specimen maintained at a constant temperature

Schematic creep testing machine

fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading.

The nominal maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material.

The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets are therefore important to increase the fatigue strength of the structure.

FATIGUE

Fatigue failure is characterized into 3 - steps Crack initiation Crack propagation Final facture

Jack hammer before fatigue

Jack hammer after fatigue

Characteristics of fatigue In metals and alloys, the process starts with

dislocation movements, eventually forming persistent slip bands that nucleate short cracks.

The greater the applied stress range, the shorter the life.

Damage is cumulative.Materials do not recover when rested.

Fatigue life is influenced by a variety of factors, such as temperature, surface finish, microstructure, presence of oxidizing or inert chemicals, residual stresses, contact (fretting), etc.

Some materials (e.g., some steel and titanium alloys) exhibit a theoretical fatigue limit below which continued loading does not lead to structural failure

In recent years, researchers have found that failures occur below the theoretical fatigue limit at very high fatigue lives (109 to 1010 cycles). An ultrasonic resonance technique is used in these experiments with frequencies around 10–20 kHz.

High cycle fatigue strength (about 103 to 108 cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, achieving frequencies up to 250 Hz.

Some examples for fatigue

The S-N curve In high-cycle fatigue situations, materials

performance is commonly characterized by an S-N curve, also known as a Wöhler curve . This is a graph of the magnitude of a cyclic stress (S) against the logarithmic scale of cycles to failure (N).

S-N curves are derived from tests on samples of the material to be characterized (often called coupons) where a regular sinusoidal stress is applied by a testing machine which also counts the number of cycles to failure. This process is sometimes known as coupon testing.

Factors that affect fatigue-life Cyclic stress state: Depending on the complexity of the

geometry and the loading, one or more properties of the stress state need to be considered, such as stress amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load sequence,

Geometry: Notches and variation in cross section throughout a part lead to stress concentrations where fatigue cracks initiate.

Surface quality. Surface roughness cause microscopic stress concentrations that lower the fatigue strength. Compressive residual stresses can be introduced in the surface by e.g. shot peening to increase fatigue life. Such techniques for producing surface stress are often referred to as peening, whatever the mechanism used to produce the stress. Low Plasticity Burnishing, Laser peening, and ultrasonic impact treatment can also produce this surface compressive stress and can increase the fatigue life of the component. This improvement is normally observed only for high-cycle fatigue.

Material Type: Fatigue life, as well as the behavior during cyclic loading, varies widely for different materials, e.g. composites and polymers differ markedly from metals.

Residual stresses: Welding, cutting, casting, and other manufacturing processes involving heat or deformation can produce high levels of tensile residual stress, which decreases the fatigue strength.

Size and distribution of internal defects: Casting defects such as gas porosity, non-metallic inclusions and shrinkage voids can significantly reduce fatigue strength.

Direction of loading: For non-isotropic materials, fatigue strength depends on the direction of the principal stress.

Grain size: For most metals, smaller grains yield longer fatigue lives, however, the presence of surface defects or scratches will have a greater influence than in a coarse grained alloy.

Environment: Environmental conditions can cause erosion, corrosion, or gas-phase embrittlement, which all affect fatigue life. Corrosion fatigue is a problem encountered in many aggressive environments.