---
title: "Testing of Materials"
tags : "SEM3, MME"
---

Structure and Properties of Material are corelated

Property - A material trait (characteristic) in terms of kind and magnitude of response to a specific imposed stimulus.

Stimulus :arrow_right: Response :arrow_right: Properties
>Applied Load :arrow_right: Mechanical :arrow_right:


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Testing - Quantifying quality to assess a particular behaviour requires TESTING for determination of properties

Polymer (PMMA)
- Low modulus - but not too low as rubber
- PMMA (Polymethyl methacrylate) - ease of fabrication
- Appeareance/ feel/ texture -Low density - light

Testing Levels
- Speciman Level
- Atomic Level
- Structural Level

Available Material -> Testing -> Properties to be known
Properties required -> Testing -> Materials required

Selection of Material
- Design and Fabrication
- Mass Production
- Purchase as per specification
- Failure Disputes

Composition Control -> Chemical Testing
Microstructural contol -> Mechanical Testing

---
### Test Significance

- Commercial ad Routine Testing
1.Checking Acceptability of materials
2.Control of properties during maunfacture
- Scientific Testing
Accumulation of data on fundamental behaviour of materials (performing multiple test)

### Mechanical tests

1. Hardness: Rockwell, Brinell, Vikers, Shore, Knoop tests
- Dropping a weight on the material from a height
2. Tension: Simple Tension, Notch Tensile
3. Compression
4. Bend
5. Torsion
6. Impact: Charpy, Izod
7. Fatigue: Bend, Axial, Low Cycle, High cycle, thermal corrosion
8. Creep: High Temperature, Stress rupture
9. Fatigue: Creep Interaction Tests


### Ideal Material

- High Strength
- High Ductility
- High Toughness
- Good Fabricability
- Machinability
- Weldability
- Formability
- Impervious to Environmental Attack
- Elevated/Cryogenic Temperature Stability

### Basic Considerations

- Types of stresses
- Tensile
- Compressive
- Normal/ Shear
- Types of loads
- Steady
- Fluctuation
- Cyclic Dynamic
- Impact
- Shock
- Environmental Conditions

# Hardness

- Flow Curve - Plastic Deformation
- Resistance to Permanent Plastic Defromation
- Metallurgist - Resistance to indention
- Design Engineer - Measure of flow stress
- Lubrication Engineer - Resistance to wear
- Mineralogist - Resisteance to scratch
- Machinist - Resistance to cutting

## Hardness Test Classification

- Type of measurement - indentation, rebound, scratch
- Magnitude of indentaion load - macro, micro and nanohardness (< 1gm)
- Nature of test - Static, dynamic or scratch

### Type of hardness

Nature of test

- Static - Indentation Hardness
- Rockwell - Depth of penetration
- Brinell - Area of indentation
- Knoop - Area
- Vickers - Area
- Dynamic - Rebound
- Shore scheleroscope
- Scratch
- Moh's Scale

### Magnitude of Indentation

1. Macrohardness
- Identation loads are 1kgf or greater
- Vickers testing may use loads from 1 to 120 kgf
- Rockwell test loads vary from 15 to 120kgf, depending on the trype od indenter and the Rockwell scale of measurement
- Brinell tests involve 500 and 3000 kgf loads though intermeditae loads
2. Microhardness 1gf to 1kgf
- Use smaller loads - 1gf to 1kgf
- common - 100 to 500gf - thicker than 3mm
3. Nanohardness
- Instrumented Indentation test
- Depends on the simlutaneous measurement of the load and depth of indentation produced by loads that may be as small as 0.1mN, with depth measurement in the 20nm range

## Hardness testers

- Rockwell
- Diamond Indenter - A, C, D
- Ball Indenter (1/16, 1/8, 1/4, 1/2 inch diameter) - B
- Load - 60, 100, 150 kgf
- Various combination of load and indenter we have different scales - Common Scales C, A, B, D - upto V
- Depth of peneteration
$HR_C = 100 - \displaystyle\left(\frac d{0.002}\right)$

- Brinell
- Ball Indenter (2.5, 5, 10mm diameter)
- Load - Upto 3000 kgf - 500 - 3000 kgf
- Indentation - Area
- Brinell Hardness Number

- Vickers
- Load
- Macro - 1 to 120 kgf
- Micro - 1gmf to 1kgf
- Vickers Pyramid Number

### Rockwell Hardness test

- Specimen placed on anvil, dial attached to indenter
- Ball - curvature
- Diamond - sphero conical diamon 0.2mm diameter
- Minor load of 10kgf - set
- Ball Indentor - Red Scale - 130 Divisions
- Diamond Indentor - Black Scale - 100 Divisions - Superficial scale
- Least count 0.002
- Less Depth - More hardness


- Minor load - Zero datum
- increases accuracy
- Avoids blacklash due to surface break through by indenter
- Avoids errors
- Sinking - Edges sink in - Area measured more
- Ridging - Edges Buldge out - Area measured less
- Thickness of the Specimen - Mark or bulge is not produced on the reverse side of piece
- Thicknes of sample should be 10 times the depth of indentation


- Sensitivity
- Change of HRc - 5 division
- 20 to 25 - Small change in hardness condition
- 50 to 55 - Large change in hardness condition

- Choice of Scale
- Type of Material
- Refer Standard table of scales
- Hard material - Diamond Indentor - 6 options
- Specimen Thickness
- Cold working - Room Temperature
- Work
- The Rockwell N scales of a superficial hardness tester are used for materials similar to those testes on the Rockwell C, A, and D scales. but of thinner gage or case depth
- Test Location
- Scale Limitation
- Anvils
- Spot
- Flat
- Black Scale - 20-70 Valid range
- Red Scale - 0 to 130 values - 0 to 100 valid values

### Brinell Hardness Test

- Ball Indenter - Hard steel ball - 2.5, 5 or 10mm diameter
- Load - 500 to 3000 kgf - 250kgf increments
- Long time period to ensure that plastic flow has begun
- Low-power microscope is used to measure the diameter

$\quad HB = \frac {P}{\pi D (\text{depth})} \\ = \frac{2P}{\pi D (D - \sqrt {D^2 - d^2})}$

- If we want to maintain the same HB (which it should be), independent of the size of the sphere, the load has to varied according to the relationship

$\frac {P}{D^2} = \text {constant}$

If these ratios are fixed the indentations produced or the value of 'd' will be in a particular range
d = 0.5D - Largest indentation
d = 0.25D - Smallest indentation

P/D^2^
= 30 for steel
= 10 for non-ferrous metals
= 2 for soft metals like lead

- Hardened steel balls - hardness only upto 350HB is reliable
- Tungsten carbide balls - 627HB
<br>
- Indentation produced - different surfave characteristic
- Cold-worked metals - Room Temp deformation - Ridging
- Fully annealed metals and light case-hardened steels more often show sinking aroung the indentation - heat treatment
<br>
- Thickness of sample should be 10 times depth of indentation
$\quad \text{Depth (mm)} = \frac P{\pi D (HB)}$

Brinell number is roughly related to the tensile strength

### Vickers Hardness Test

- Pyramidal Indenter with square base and of $136^\circ$
Edge angle - 148° 06' 43''

$HV = \displaystyle\frac{2P sin(\alpha / 2)}{d^2} = \frac {1.8544P}{d^2}$

#### Types
- Macroindentation ASTM E92-72
- Microindentation ASTM E384

Microindentation - 1 to 1000 gf
Macroindentation - 1 to 120 kgf

Vicker's testing requires a much better preparation of the material's surface than does Rockwell testing

Grind - Polish - Alumina - Etching

Material gets deformed easily at begining but then it becomes tougher - work-hardening

Ridging and Sinking is an issue

For a curvature, a correction factor must be introduced

Distance from edge or other indentation - 2.5 times the diagonal length

Thickness - 1.5 times length of diagonal

Advantages
- Indepented of the force when determined on homogeneous material, except possibly at forces below 5kgf
- The edges are well defined
- Geometrically similar indentations irrespective of size
- One continous scale is used for a given force from lowest to highest values
- Indenter deforamtion is negligible on hard material

Disadvantage
- Test is slow - preparation
- Measurement of diagonals is operator dependent

Brinell vs Vicker
- Load independent
- Indenter size

Micro Vickers Test
- 1gmf to 1000gmf

Ridging during Vicker - metarial extrudes upwards along the face of the diamond - Convexity - cold worked

### Micro Indentation

- Vickers
- Diamond Indenter - 136°
- Square pyramid Indenter
- HV = 1.857P/d^2^
- P - load in gf
- d - mean diagonal in µm
- Knoop
- Longitudinal agnle - 172°30'
- Transverse angle - 130°
- Rhombo pyramid
- KHN/HL = PC~p~L^2^
- P - load in kgf
- C~p~ - Constant supplied by the manufacturer of the machines - 0.070208

Knoop is used in the same machine as Vickers and conducted in the same manner - just the long diagonal is used to calculate the projected area of indent rather than the surface area of the indient

- The narrowness - ideal for steep hardness gradient
- Vickers - the two halves of indent parallel to the hardness gradient may have a substantial difference in length
- Knoop is better choice for hard brittle materials where indentaion cracking would be more extensive using Vickers indenter at the same load
- Knoop indent is shallower than the Vickers indent
- Knoop is better suited for testing thin coatings
- Knoop hardness varies with test load and conversion is difficult

### Scratch Hardness

- Consists of 10 minerals arranged in increasing order of their hardness

Mohs scale of hardness
1. Talc
2. Gypsum
3. Calcite
4. Fluorite
5. Apatite
6. Orthoclase(or feldspar)
7. Quartz
8. Topaz
9. Corundum
10. Diamond

Tall Girls Can Flirt And Only Quit To Chase Dwarves

### Rebound Hardness

- Shore's Scheleroscope
- Diamond tipped Hammer is dropped
- Great Instantaneous force
- Hard Material - Small Indentation - More rebound height
- Soft Material - Large Indentation - Less rebound height
- Scleroscope scale consists of units determined by dividing into 100 units the avergae rebound of a hammer from a quenched and untempered water-hardened tool steel

Types of Scleroscope hardness testers
- Model C
- Vertically disposed barrel containing a precision-bore glass tube
- Scale graduated - 0 to 140 - set behind the tube
- Hardness is read from the vertical scale
- Model D
- Analog or Digital readouts
- Vertically disposed barrel that contains a clutch to arrest the hammer at the maximum height of rebound
- Short rebound height
- Hammer is longer and heavier - even though dropped from a shorter distance

ASTM E448 - Standard Practise for Scleroscope Hardness Testing of Metallic Materials
ASTM A427 - Standard Specification for Wrough Alloy Steel Rolls for Cold and Hot Reduction

HFRSc or HFRSd

ASTM C886 - Standard Test Method for Scleroscope Hardness Testing of Fine-Grained Carbon and Graphite Materials - Model C carbon Calibration

Model C - commonly unmounted - Minimum weight of 2.3kg

Model D - Due to its critical vertical alignment - Should not be unmounted - erroneous reading

Workpiece Finish
- Workpiece finsh requirements shouldbe met to obtain accurate, consistent readings
- Filed, machined, ground or polished - avoid overheating or excessively cold working the surface
- Soft metals to hardened steel - surface finish ranges from a minimum finish as produced by a No.2 file
- Case-hardened steel with cases as thin as 0.25mm can be accurately tested - core hardness is not less than 30 Scleroscope

### Uncommon Hardness Testing methods

#### Durometer Harndess

The durometer is a hand-sized instrument that measures the indentation hardness of rubber and plastic products

Durometer hardness is the resistance of the material being tested to the penetration of the indenter as the result of a variable force applied to the indenter by a spring.

ASTM D2240 - Standard Test Method for Rubber Property-Durometer Hardness

#### Monotron Hardness Tester

Indenter - 0.75mm hemispherical diamond indenter

For soft materials - tungsten carbide indenters of 1.53 or 2.5mm are used and hardness is referred as M~3~ and M~4~

Indenter is forced into the metal upto a standard depth of 0.05mm

The load required to force the indenter to this depth is measured to find hardness

Machine - Two circular scales

Top dial indicates load
Bottom dial is used for reading depth of penetrarion

Hardness number is read directly on top scales

Use - hardness of thin layers - carburized, nitride layers, thin strips

#### Hot Hardness

At higher temperature the hardness decreases

Hardness of metal is related to strength at room temperature similarly can be related to high temp

Prediction of creep strength may be possible to a certain extent with the knowledge of high temperature hardness

Vicker's machine with sapphire indenter in vacuum is used

Linear relationship between hot hardness and strength of metal - both varying (decreasing) parallely with increasing temperature

#### Meyer's Hardness

Instead of surface area projected area is used for calculation

As per Meyer
Empirical relationship exists between applied load and size of indentation

$P = Kd^{n_1}$

P - load in kg
n~1~ - Material constant based upon strain hardening of metal
K - A material constant based upon the resistance of metal
d - Diameter of indentation in mm

log p vs log d - Straight line - slope - n~1~

The plastic zone beneath ahardness indentation is surrounded with elastic material which acts to hidner plastic flow in a manner similar to the die constraint forces in a closed die forging

Mean compressve stress required to cause plastic flow - exceeds that in simple compression

##### Relationship between Hardness and the flow curve

Determining plastic region of True stress - strain curve form indentation hardness measurement

- There is similarity in the shapw of flow cukrve and the curve obtained when Meyers hardness is measured on a number of specimens subjected to increasing amounts of plastic strain

$P_m = C \sigma_0$

$\sigma_0$ - considered the flow stress at a given value of true strain

True stain is proportional to the ratio of d/D and can be give as

$\epsilon = 0.2\displaystyle \frac dD$

#### Ultrasonic Microhardness Testing

- Max indentation load - 800gf
- Depth of indentation - 4 to 18 $\mu$m
- The workpiece surface is unharmed, thus classifying this test as undestructive
- Automated on-line testing up to 1200 parts/h can be tested
- Vickers Diamond is attached to one end of a magnetostrictive metal rod
- Diamond-tipped rod is excited to its natural frequency by a piezoelectric converter
- Resonant frequency of the rod changes as the free aend of the rod is brought into contact with the surface of a solid body
- Once device is calibrated for the known modulus of elasticity of the tested material, the area of contact between the diamond tip and the tested surface can be derived from the measured resonant frequency
- The area of contact is inversely proportional to the hardness of the tested material, provided the force pressing the surface is constant
- The Scale should not onlybe considered as ranging from 0-100
- When major load is applied poionter moves from setposition of 100 to 90,80...
- If the pointer crosses 0 it is read as -5 instead of 95 on rockwell scale

Why B scale is upton 130 and not 100?

- The red scale is numbered from 0-130
- There is overlapping of 30 rockwell units
- Set position 130 and down the scale 120,110,...
- Negative hardness value is never accepted

# Tensile Testing

Maximum Load bearing capacity of the material

## Introduction

Mechanical properties that are important to a design engineer differ from those that are of interest to the manufactureing engineer

- In design - properties such as elastic modulus and yield strength are important to resist permanent deformation under applied stress - Elastic
- In Manufacturing - the goal is to apply stresses that exceed the yield strength of the material so as to deform it to the required shape - Plastic

Tensile Test - Basic Principle
- An axial force applied to a specimen of original lenth (l~0~) elongates it, resulting in reduction in cross-section area

## Stress-Strain

Engineering Stress Strain Curve - Original Dimensions are used to calculate the Stress and Strain

True Stress Strain Curve - Using instantaneous change in Area and Length


Hooke's Law
$\sigma_e = Ee

E - Modulus of Elasticity - Measure of the inherent stiffness of a material

The two regions of Stress-Strain curve

1 - Elastic Region - prior to yielding of the material
2 - Plastic Region - after yielding of the material

### Yeild Point in Stress-Strain Curve

As Stress increases - a point is reached - material begins to yield
aka yield strength, yield stress, elastic limit

Yield Point - Y - Strength property

### Plastic Region

Yield point marks the beginning of plastic deformation

Hooke's Law is no longer obeyed

As load is increased beyond Y, elongation proceeds at a much faster rate than before, causing teh slope of the curve to change dramatically

### Categories of Stress-Strain Relationship

- Perfectly Elastic
- Elastic and perfectly plastic
- Elastic and strain hardening

## Terminology

### True Stress

- Uses the instantaneous or actual area of the specimen at any given point, as opposed to the original are used

True Stress-Strain will be higher than the Engineering Stress-Strain Curve

### Modulus of Elasticity

The modulus of elasticity (E) is a measure of the stiffness of the material

Greater modulus - smaller elastic strain resulting from the application of a given stress

The modulus of elasticity is determined by the binding
forces between atoms

Structure-insensitive mechanical property

Affected by alloying, heat treatment, or cold work

Increasing the temperature decreases the modulus of elasticity - elevated temperature - dynamic methods

### Resilience

The ability of material to absorb energy whwn deformed elastically and tp return it when unloaded is called resilience

This property usually is measured by the modulus of resilience, which is the strain energy per unit volume required to stress the material from zero stress to the yield stress (σ~0~)

Strain energy per unit volume for uniaxial tension

$U_0=\displaystyle\frac12\sigma_xe_x$

Ideal material for resisting energy loads in applications - must not undergo permanent distortion - high yield stress and low modulus of elasticity

### Toughness

Ability to absorb energy in plastic range

Toughness may be considered to be the total area under the stress-strain curve

### Yield Point

- Some metals show heterogeneous type of transition from elastic to plastic deformation taht produces a yield point in the stress-strain curve
- Load increases steadily with t=elastic strain, then it drops suddenly and fluctuates about some approximately constant value of load and then rises with further strain
- The load at which the sudden drop occurs is called the upper yield point
- The constant load is called the lower yield point and the elongation that occurs at constant load is called the yield-point elongation
- At the upper yield point a discrete band of deformed metal - often readily visble - appears at astress concentration such as a filet
- With the formation of the band, the load drops to the lower yield point - the band then propagates along the length of the specimen causing yield-point elongation
- 45° to tensile axis
- Luder bands, stretcher strains, Piobert effect
- After Luder bands have propagated to cover the entire length of the specimen test section, the flow will increase eith strain in the typical manner

### Flow Curve

- Uniform plastic deformation

σ = Kε^n^

n - strain-hardening exponent
K - strength coefficient

Log-log plot of true stress and ture strain up to maximum load will result in a stright line if above equation is satisfied

n = 0 - Perfectly plastic solid
n = 1 - elastic solid

## Effect of Strain Rate and Temperature on FLow properties

Strain rate - $\displaystyle \frac{d\epsilon}{dt}$ - s^-1^

Increaseing Strain rate - Increases the flow stress

Strain-rate dependence of strength increases with increasing temperature

If the crosshead velocity of a testing machine is v = dL/dt then train rate in conventional engineering strain is -

$ė = \displaystyle\frac{de}{dt} = \frac{d(L-L_0)/L_0}{dt} = \frac{1\cdot dL}{dt} = \frac{v}{L_0}$

True strain rate is given by

$\displaystyle\frac{d\epsilon}{dt} = \frac vL$

$\displaystyle\frac{d\epsilon}{dt} = \frac vL = \frac{L_0}{L}\frac{de}{dt} = \frac{1}{1+e}\frac{de}{dt} = \frac {ė}{1+e}$

## Measure of Ductility

Ductility - qualitative, subjective property of a material

- To indicate extento which a metal can be deforemed without fracture in metal working operations, such as rolling and extrusion
- To indicate to the designer the ability of the metal to flow plastically before fracture
- an indicator of changes in impurity level or processing conditions

Current measure of ductility are -
- Eng. strain at fracture
- reduction in area at fracture

## Instability in Tension

Necking generally begins at maximum load during the tensile deformation of a ductile metal

An ideal plastic material in which no strain hardening occurs would become unstable in tension and begin to neck as soon as yielding occurred

At necking

dP = 0
$P = σA$
$dP = σdA + Adσ$

Volume is contant

$\displaystyle\frac{dL}{L} = -\frac{dA}{A} = dε$

$\displaystyle\frac{dσ}{dε} = σ$

$\displaystyle\frac{dσ}{de} = \frac{σ}{1+e}$

# Fatigue

Fatigue is the progressive, localized, and permanenet structural damage that occurs when a materis is subjected to cyclic or fluctuating strains at nominal stresses that have maximum values less than (and often much less than) the static yield strength of the material

Process of Fatigue can be divided into different stages -
1. Cyclic plastic deformation prior to fatigue crack initiation
2. Initiation of one or more microcracks
3. Propagation or coalescence of microcracks to form one or more macrocracks
4. Propagation of one or more macro cracks
5. Final Failure

A Fatigue failure is particularly dangerous because it occurs without any obvious warning

Fatigue occurs with brittle appearing fracture with no gross deformationation the fracture

On macroscopic scale fracture surface is usually normal to the direction of the principal tensile stresses

A Fatigue failure - recognized fromt he appreance of the fracture surface - due to rubbing action as the crack propagaes and rough region where the component fails in a ductile manner - cross section can no longer carry load

Progress of the fracture is indicated by series of rings known as beach marks - progressing inwards from the point of failure


Basic Factors necessary to cause fatigue -
1. A maximum tensile stress of sufficiently high value
2. A large enough variation or fluctuation in the applied stress
3. Sufficiently large number of cycles of applied stress

## Stress Cycles

$\displaystyle\sigma_{mean} = \frac{\sigma_{max} + \sigma_{min}}{2}$
$\displaystyle\sigma_{amp} = \frac{\sigma_{max} - \sigma_{min}}{2}$

$\displaystyle\text{Stress Ratio, R } = \frac {\sigma_{min}} {\sigma_{max}}$

Amplitude Ratio

$\displaystyle A = \frac{σ_{amp}}{σ_{mean}} = \frac{1-R}{1+R}$

If the Mean Stress is Zero - Completely reverse cycle (R = -1)

Constant Amplitude Loading - Constant parameters - laboratory

Variable Amplitude Loading - Spectrum Loading

Study of the cyclic behaviour of materials can be divided into -
- Stress Based Approach
- Strain Based Approach
- Fracture Mechanics

Low Cycle Fatigue - Strain Based Approach
N~f~ $\leq$ 10^4^

1. Completely Reverse Cycle of stress
- Mean stress = 0
- Max Stress = -Min Stress
2. Repeated Stress Cycle
- Max and Minimum stresses are not equal
- Both the stresses could be either tension or compression or tension - compression
3. Complicated Stress Cycle
- Spectrum Lading
- Variable Amplitude Loading


### S-N Curce

Plot of stress S against number of cucles to failure N

Endurance Limit - Load below which the material can be said to have infinte life

## Effect of Mean Stress on Fatigue Life

The mean stress σ~m~ affects - fatigue strength

The Fatigue life decreases as the mean stress increases


for σ~a~ = σ~f~, the fatigue life is simply 1/4th of a cycle

σ~a~ + σ~m~ ≤ σ~f~

Various empirical expressions have been propsed which take into account the effect of mean stress on fatigue life

Goodman's Relationship, which assumes a linear effect of mean stress between σ~m~ = 0 and σ~UTS~

$\displaystyleσ_a = σ_0\left[1-\frac{σ_{mean}}{σ_{UTS}}\right]$

Gerber's relationship
Assumes a parabolic effect of mean stress between σ~m~ = 0 and σ~UTS~

$σ_a = σ_0\left[1-\frac{σ_{mean}}{σ_{UTS}}^2\right]$

Experimentally - Data falls between Gerber nad Goodman lines - Goodman is consevative estimate of mean stress effect

### Effect of Frequency

Fatigue life decreases at higher frequencies - attributed to temperature increase that results in the higher-frequency

## Cumulative Damage and Life Exhaustion

Basquin's Equation
$\sigma_{max} = \sigma_{f'}(N_f)^b$

$\sigma_{f'}$ - Fatigue Strength Coefficient
b - Strength Exponent

Coffinmanson Relationship
$\epsilon_{max} = \epsilon_{f'}(N_f)^c$

$\epsilon_f$ - Fatigue Ductility Coefficient
c - Fatigue Ductility Exponent

Palmgren Miner's Rule, Cummulative Linear Damage

$\displaystyle\underset {i=1}{\overset {k}{\sum}}\frac{n_i}{N_i} = 1$

k - No of stress levels
N - Fatigue lives corresponding to stress level
n - No of cycles carried out at that stress level

Damage is accumulative

#### Fatigue Life Diagram

Hagg's Life Diagram
Constant Amplitude Fatigue Diagra

If for some R we do not have S-N curve
- Find Cycle Parameters
- Use the S-N curve values for other known R and plot a graph of σ~amp~ and σ~mean~
- Which will have boundary as σ~UTS~ and σ~UCS~
- Join the points which have failed after same number of cycles

# Impact

Sudden Load

### Why test?

- To compare and select the toughest for service conditions
- To compare a particular material's fracture against a specified standard

Ductile Failure - Fiberous Texture (Dimpled Structure)
Brittle Failure - Granular Texture
- To predict the effects of service conditions (e.g., corrosion, fatigue, stress corrosion) on the material toughness
- To study the effects of microstructural changes on material toughness

Qualitative Text - Charpy impact test

### Factors which cause Brittle-Cleavage type of fracture

- A triaxial state of stress
- A low temperature
- A high strain rate or rapid rate of loading

Any 2 are enough to cause a brittle failure

A triaxial state of stress, which exists at a notch and low temperature are responsible for most service failures of britle type

## Impact Testing

### Types of Notch-Toughness Tests

- A notch is made - to cause fracturing in one attempt
- Change in Potential energy of the impacting head is determined with a calibrated dial that measure the total energy absorbed

Other quantitative Parameters, such as fracture appearance and degree of ductility/deformation (Lateral expansion or notch root contraction) are also measured

Categories of impact tests can be classified in terms of loading method (pendulum or dropweight) and the typr of notch speciment (Charpy V, Charpy U, Izod V)

Charpy - three point loading

Izod - specimen is set up as a cantilever beam

Charpy perpendicular - opposite side of notch

Charypy is more often used because
Impact strength,

Test may not reveal exact ductile to brittle transition temperatures for large full-size part

We can get a range from this test

Charpy - $140^\circ$
Izod - $90^\circ$

At lower temp - Brittle - Less energy

Annealing - Heat till austenitizing temperature and slow cooling
Quenched - Heat and cool immediately - induces stresses -
Temperered -

The temperature at which a change occurs from a high-energy fracture to a low-energy one is called the ductile-brittle transition temperture (DBTT)

Greater fraction of Fibrous fracture - greater energy absorbed by the specimen

Lateral contration that occurs at the notch root, or lateral expansion of the specimen

ASTM E23 - notch bar
BS121-2 - Charpy V
BS131-3 - Charpy U

ASTM E23, ISO148, ISO83 - Specimen standards

Charpy - No separation of initiation and propagation components of energy

Under current testing procedures, the Charpy Vnotch test is reproducible and produces close approximations of transition temperatures found in full-size parts.

### Test Temperature

Specimen temperature can drastically affect the results of impact testing

If not stated otherwise - 21 to 32°C

Charpy - RT to -46°C

A certain amount of testing is also done down to -196°C - Cryogenic service

At liquid helium and liquid hydrogen temperature - Researching purposes

### Test Results

Results of impact testing are determined in three ways

In the first method, already discussed, they can be read directly from the testing machine - common

It is desirable to test three specimen at each test temperature

If a minimum test value is specified for material acceptance, not more thatn one test result of the three should fall below that value

If the Values differs by 6J, the specimens should be retested

### Fracture Appreance Method

Ductile Fracture - Shear Fracture - Fiberous Fracture

Charpy V- notch - impact strengths of 14J and lower are likely to initiate fractures

Impact strength of 27J is likely to propagate brittle fracture

### Drop Weight Testing

On Larger specimen

Drop-Weight Test and Drop-Weight Tear Test

Transition temperature that nearly coincides with that of full sized path

Nil-Ductulity temperature

Smallest specimen size - 16x51x127mm

DWT - 9.5mm
DWTT - 74mmx305mm

Initial test of a with a given strength level should be conducted with a given strength level should be conducted with the drop-weight

A cleavage crack form in the bad as soon as incipient yield occurs (at about 3°)

The specimen is allowed to deflect slightly under the impact load, controlled by deflection stops

The specimen is then examines to see whether or not it has fractured

A specimen is considered to be broken if the crack extends to one or both sides

No break

### Drop weight Tear Test

V-Notch

ASTM E436

0.5mm Notch

Test Procedure
- Tested at various temperature
- Brought to desired temperature by immersing in cooled solution - 15min
- The Bath is agitated
- The specimen should be broken within 10s
- Colled specimen is insertes in the anvil
- If the specimen buckles under the test load, the thes is considered to be invalid
- Otherwise, the specimen fractures and separates

Principal Short coming - plate material - 3 to 19 mm

Only concerned with transition temperature
300 140
2700J energy may be imparted

Anvil
- The holder for the test specimen must support the specimen on edge (305mm) in such a manner that rotaion will not occur when the specimen is struck

Speciman Preparation

- Sawing, shearing or flame cutting
- 305 mm notch is impresses

The specimen is brought to a desired temperature by immersing them in a cooled solution and holding for at least 15 min at temperature

The Bath should be agitated and if several specimens are cooled simultaneously

# Creep

Creep deformation - any permanent inelastic strain that occurs when a material is subjected to a sustained stress

The rate of deformation - depends on magnitude of applied stress, time and temperature

Above a critical stress, both elastic and plastic strains exists, and that part remaining after unloading represents plastic deformation called inelastic strains

Temperature is relative queantity for any material

When service temperature is greater than or equal to approximately 0.5T~m~ - T~m~ is the absolute melting temperature (Kelvin)

T/T~m~ - Homologous Temperature

## Creep Mechanism:
1. Dislocation Motion:
(i) Edge Climb
(ii) Cross Slip
2. Diffusion Creep.
Here the atoms (at higher temperature) diffuse axial to the stress.(Stress assisted diffusion + substitutional diffusion viz vacancy assisted viz available at higher temp)
3. Grain Boundary Sliding.
Here the grain boundary can be said to act like liquid! The grains 'slip' with respect to each other.

## Stages of Creep

In the inital stage, or primary creep, the strain rate is relatively high, but slows with increasing time

This is due to work hardening

The strain rate eventually reaches a minimum and becomes near constant

This is due to the balance between

Creep test - minimum creep rate
Stress Rupture Test - Mechanism of deformation, time to cause failure at a given nominal stress for a constant temperature
### Deformation Map

### Stress Concentration and Griffith Criterion of Fracture

The most fundamental requisite for the porpagation of a crack is that the stress at the tip of the crack must exceed the theoretical cohessive strength of the material

This is indeed the fundamental criterion, but it is not very useflu; - tough to measure stress on the crack

Griffith Criterion - energy balance

#### Stress Concentration

The lines of force, acting as elastic strings, tend to minimize their lengths and thus group together near the ends of the elliptic hole

Essentially the stress near cracks are higher


as can be seem the stress at the tip of the crack is much higher. and from the formula we can see having a smaller tip radius can increase the stress. Hence the windows in an airplane is rounded. Since the corners of square windows have very small radius the stress concentrate and hence can lead to breaking of the glass. Thus rounded/ circular windows are used. which causes the stress to be eqaully distributed

#### Griffith Criterion

Thermodynamic Energy Balance
- Elastic strain energy is released

Thin - Along the plane
Thick - ε = 0 -

As the crack grows, strain energy is released but additional surfaces are created

The crack becomes stabble when these energy components balance each other

$2\gamma s = \pi \sigma^2 a/e$

Plane stress
$\sigma_c = \displaystyle\sqrt\frac{2E\gamma_s}{\pi a}$

Rearranging this equation
$\sigma\sqrt{\pi a} = \sqrt{2E\gamma_s}$

LHS - Critical stress and square root of crack length

Plane strain
$\sigma_c = \displaystyle\sqrt\frac{2E\gamma_s}{\pi a (1-\nu^2)}$

$\nu$ - Poisson's Ratio

Plane stress
-

Normal and shear stress at

The critical stress corresponding to fracture in the plane-strain situation

Strain energy release rate and fracture toughness

Plastic deformation occurs in engineering metal, alloys, and some polymers

Orowan modified Griffith's elastic surface energy expression, by adding a plastic deformation enrgy or plastic strain work $\gamma_P$

### Measure of strain energy release rate/ fracture toughness

A single-edge notch specimen is loaded axially

### Stress Intensity Factor

- Local stresses near a crack depend on the product of nominal stress σ

K - Stress intensity value

Plain Stress
$K^2 = GE$ - Plain Stress
$K^2 = GE/(1-\nu^2)$ - Plain Strain

LEFM -

## Elastic-Plastic Fracture Mechanics (EPFM)

if the material is very ductile it is difficult to measure the stress at the crack tip

$G = \frac {\tau}{\gamma}$

$G = \frac{M_TL}{J\theta}$

Torsional stresses for large plastic strains

# Torsion Test

A torsion test measures the strength of any material against maximum twisting force

How much twist can a material withstand before cracking

Applied pressure - Torque

## Types of Torsion Tests

- Failure testing
- Twisting the material unit it breaks
- Proof testing
- Can bear a certain amount of torque load over a given period of time
- Operational Test
- Test specific products to confirm their elastic limit before going on the market

Stress-Strain
Y - Torque - Stress
X - Angle of Twist - Strain

Quater degree

- Torsion test is not widelt accepted
- Determine elasticity in shear, the torsion yield strength and the modulus of rupture
- Often used for testing Brittle materials

## Torsion-Testing equipment

- A twisting head with a chuck for gripping the specimen and for applying the twisting moment to the specimen
- A weight head which grips the other end of the specimen and measures the twisting moment of Torque

Specimen
- Usually Tubular
- Circular cross section specimen is normally used since in the elastic range, shear stress varies linearly from a value zero at the centre of the bar to a maximum value at the surface

Performing the test
- Applying twisting moment to the specimen and measure the troque
- Determination of angular displacement is made by a Troptometer

Shear Strain
$\gamma = \displaystyle\text{tan}\phi = \frac{r\theta}{L}$

$\theta$ - Angle of twist
L - Length of the specimen

Equating Twisting movement to internal resisting momeny

$\tau$ - Shear Stress, Pa
M~T~ - Torsional Moment, Nm
r - Radial Distance measured from the center of the bar
J - Polar moment of intertia

$M_T = \frac{\tau J}{r}$

Polar moment of Area - quantity used to predict an object's ability to resist torsion in objects

Larger Polar moment of area - lesser angle of twist for a given torque

Shear Stress

## Elastic Properties and Yield Strength

0.04 radian m^-1^

Tubular Specimen - Precision measurement of the torsional elastic limit

Solid - Stress gradient across the diameter

Wall thickness should not be reduced too greatly - fail due to buckling rather than torsion

$\frac{\text{Length of reduced section}}{\text{Outside diameter}} = 10$

$\frac{\text{Diameter}}{\text{Thickness}} = 8-10$

Modulus of Rupture
Ultimate torsional shearing stress

$G = \displaystyle\frac\tau\gamma$

$G = \frac{M_TL}{J\theta}$

# Non-Destructive Tests

- Manufacturing
- Servicing
- Failure Analysis

## Visual Inspection

Using normal Sensory Organs
Dimensional defects

## Leakage Test

Pressure Vessels
Pipelines

## Dye/Liquid Penetrant

Surface/Sub-surface defects

## Magnetic Particle Inspection

Magnetised Sample
Magnetic powder slurry

## Replica Microscopy

## Thermal Methods

Colour Changing dye
Infrared technique

## Radiography

## Acoustic Methods

## Eddy Current Method

## How to decide what test

1) Material
2) Service Conditions
3) Process of Manufacture
4) Cost
5) Availability of NDT
6)