MECHANICAL PROPORTIES OF MATERIALS

ERKİN TAŞ

OVERVIEW• Introduction• Tension and Compression Test• The Stress-Strain Diagram

– Elastic and Plastic Behavior– Yielding & Strain Hardening & Necking

• Stress-Strain Behavior of Ductile and Brittle Materials• Hooke’s Law• Poisson’s Ratio• The Shear Stress-Strain Diagram• Failure of Materials Due to Creep and Fatique• Average Mechanical Proporties of Typical Engineering Materials (SI

Units)

INTRODUCTION Very generally , we can say that stress is the strength of the material from which the body is made and strain is a measure of the deformation of the material. Stress is related to strain.We can determine that by using experimental methods.With the aid of this methods ,we can determine the stress-strain diagram for a specific material.In addition ,mechanical proporties and other test and methods are used for development of the mechanics of the material.

TENSION AND COMPRESSION TEST The strength of a material depends on the ability of the material to deal with the load without any deformation or any failure.This property is inherent in the material itself and can be determine by some experiment.The one of the most significant tests are tension test and compression test.These two test are used primarily to determine the relationship between the normal stress and normal strain in many engineering materials like ceramics ,polymers and composites.As a civil enginner ,we always used the results of these tests.

THE STRESS-STRAIN DIAGRAM The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve. It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress). These curves give us many of the properties of a material.

Stress-Strain diagrams for ductile material (steel).

Elastic and Plastic Behavior Elastic deformations of a material are entirely recoverable once the stress is removed. No part of the object under stress has undergone permanent deformation. Plastic deformation of a material are permanent. One or more parts of the the object under stress has undergone permanent deformation. Elastic deformation on the graph is actually a straight line throughout most of this region is said to be linear elastic.The upper stress limit to this linear relationship is called proportional limit.If the stress slightly exceeds the proportional limit ,the curve tends to bend and flatten out as you can see in the diagram.This continues until the stress reaches the elastic limit.Until reaching that point ,if the load is removed the specimen will still return back to its original shape.But after that point ,if the load is removed the specimen will elongate permanently.

Yielding & Strain Hardening & Necking

Yielding : A slight increase in stress above the elastic limit will result in a breakdown of the material and cause it to deform permanently.The stress that causes the yielding is called yield stress and the deformation that ocurs is called plastic deformation.Strain Hardening : When yielding has ended ,an increase in load can be supported by the specimen ,resulting in a curve that rises contnuously but becomes flatter until it reaches a maximum stress referred to as the ultimate stress in the diagram.The rise in the curve is called strain hardening.Necking : Up to ultimate stress ,the specimen elongates and therefore its cross-srctional area decrease.This decrease is uniform over the specimen’s entire gauge length.Then finaly ,the material fail after necking occurs.

STRESS-STRAIN BEHAVIOR OF DUCTILE AND BRITTLE MATERIALS

Ductile Material : Any material that can be withstand large amount of strain before specimen failing.Engineers often choose ductile materials for design because these materials are capable of absorbing shock and energy ,and if they become overloaded ,they will usually exhibit large deformation before failing.They have small Modulus of Elasticity value and Ultimate Stress value.Steel and aluminum are the best example to ductile materials.Brittle Material : Any material that fracture at lower amount of strain.They exhibit little or no yielding before failure.Therefore they fail suddenly and without any warning.Brittle materials often have large Modulus of Elasticity value and Ultimate Stress value.Glass and Cast Iron are the best example to brittle materials.

HOOKE’S LAWThe stress-strain diagrams for engineering materials ,generally exhibit linear relationship between the stress and strain in the elastic region.If you increase the stress in the diagram ,the strain also increase and there is a direct proportion between stress and strain in the diagram.The slope of the this linear region is give us the Modulus of Elasticity or Young’s Modulus and the proportion between stress ,modulus of elasticity and strain can be expressed mathematically and that is Hooke’s Law which was discovered by Robert Hooke in 1676.

Average Ultimate Strength and Modulus of Elasticity of Engineering Materials

Materials Tensile Ultimate Strength(Mpa)

Modulus of Elasticity (Gpa)

Aluminum (214-T6) 469.0 73.1

Cast Iron (Gray ASTM 20)

179.0 67.0

Red Brass Copper 241.0 101.0

Magnesium Alloy 276.0 44.7

Steel (Str. A-36) 400.0 200.0

Steel (Str. A992) 450.0 200.0

Steel (Stainles 304) 517.0 193.0

Titanium Alloy 1000.0 120.0

Low Str. Concrete None 22.1

High Str. Concrete None 29.0

POISSON’S RATIO When a deformable body is subjected to an axial tensile force ,not only does it elongate but it also contracts laterally.Likewise , a compressive force acting on a body cause it to contract in the direction of the force and yet its sides expand laterally.

In the early 1800s ,the French scientist S.D. Poisson realized that within the elastic range the ratio of these strains is a constant ,since the deformations longitudinal and lateral are proportional for each specific material.This constant is called Poisson’s Ratio which is expressed mathematically as ;

Poisson’s Ratio of Typical Engineering Materials

Materials Poisson’s Ratio

Aluminum (214-T6) 0.35

Cast Iron (Gray ASTM 20) 0.28

Red Brass Copper 0.35

Magnesium Alloy 0.30

Steel (Str. A-36) 0.32

Steel (Str. A992) 0.32

Steel (Stainles 304) 0.27

Titanium Alloy 0.36

Low Str. Concrete 0.15

High Str. Concrete 0.15

THE SHEAR STRESS-STRAIN DIAGRAM The behavior odf a material subjected to pure shear can be studied in a laboratory using specimens in the shape of thin tubes and subjecting them to a torsional loading.If the measurements are made of the applied torque and the resulting angle of twist ,the data can be used to determine the shear stress and the shear strain ,and a shear stress-strain diagram can be plotted.The shear stress-strain diagram is a plot of the shear stress versus shear strain.If the material is homogeneous and isotropic ,and is also linear elastic ,the slope of the straight line within the elastic region is called the Modulus of Rigidity or The Shear Modulus.(G)

FAILURE OF MATERIALS DUE TO CREEP AND FATIQUE

Creep : When a material has to support a load for a long time period ,it may continue to deform until a sudden fracture occurs.So ,it is the time-dependent permanent deformation which stress or temperature play an important role. Fatique : When a metal is subjected to repeated cycles of stress or strain ,it cause ts structure to breakdown ,ultimately leading to fracture.That is fatique and it is usually responsible or causes to a large percent of failures in connecting rods and shafts of engine ,gas turbine blades ,supports of bridge ,railroad wheels etc…

Average Mechanical Proporties of Typical Engineering Materials

Materials Density (Mg/ m3) Modulus of Elasticity,E (Gpa)

Modulus of Rigidity,G (Gpa)

Tensile Yield Strength (Mpa)

Tensile Ultimate Strength(Mpa)

Poisson’s Ratio,v

Aluminum(2014-6) 2.79 73.1 27 414 469 0.35

Cast Iron(Gray ASTM 20) 7.19 67 27 None 179 0.28

Red Brass Copper 8.74 101 37 70 241 0.35

Magnesium Alloy 1.83 44.7 18 152 276 0.30

Structural Steel A-36 7.85 200 75 250 400 0.32

Structural Steel A992 7.85 200 75 345 450 0.32

Stainless Steel 304 7.86 193 75 207 517 0.27

Titanium Alloy 4.43 120 44 924 1,000 0.36

Low Strength Concrete 2.38 22.1 None None None 0.15

High Strength Concrete 2.37 29 None None None 0.15

Wood (Dauglas Fir) 0.47 13.1 None None

REFERENCES1. Mechanics of Material 9th Edition / R.C. Hibbeler2. Materials for Civil and Construction Engineers 3th Edition / Michael S.

Mamlouk ,John P. Zaniewski3. Beer & Johnston / Mechanics of Materials (5th ed.). McGraw Hill4. Mechanics of Materials, E.J. Hearn

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