شامل شرح الدكتور وأسئلة سنوات لماده كامله ملخص الب مقاومه سابقه والمانيوال

ال تنسوني من صالح الدعاء

سيفلتيي_لجنة المدني

7-Hardness Test .8-THIN WALL CYLINDER .9-Creep Test of Metallic Materials .10-Strain Measurement with Strain Gauges .11-Impact Test .

Experiments :

1- Tensile Test .2-Compression test .3-Deflection of Beams.4-Stability Of Columns .5- Torsion test6-Fatigue Test .

•Tensile TestThe Tensile test is used to :

1-Observe the behavior of materials under tensile load.

2-Determine the strength and other several elastic and plastic .

3-Properties of various materials .

4-Study the fracture of metallic material.

Universal Testing Machine (UTM) : The machine is digital type Tensile Strength Test Machine, Capable doing the following tests:

1. Tensile test 2. Compression test

3- 3 Points bending test 4. Direct shear test

P

P

يتأثر بوجود الشوائب

Li Lf

S=Lf -Li

Df

Deformation = S=Lf -LiStress=𝜎= 𝑃

𝐴الوحده باسكال

Strain= 𝜖 = 𝑺

Li= Lf−LiLi

من دون وحده

Deformation = S= 𝑃𝐿

𝐸𝐴

OR

Stress =𝜎= E* 𝜖 E: how much something will stretch elastically (Young’s modulus of Elasticity )معامل المرونه

P

P

A

عليها يُحدد نوع عالماده بناء

Materials

Brittle Ductile

Happen because normal stress Happen because Shear stress

Fracture at angle 𝟒𝟓°

Shape: Flat

Ductility < 5% Ductility > 5%

Only Elastic Yield=Ultimate=fracture

Hold tension more than

Slope

Fracture at angle 𝟗𝟎°

Low carbonic steelHight carbonic steel

هي مواد مرنه لكنها تتشوه بشكل سريع هي مواد هشة تنكسر بسرعه

Shape : Cup and Cone

Ex: Steel Ex: concreteBrass

Stage Definition Symbol

Proportional limit

من محور اإلجهاد وقيمتهانهايه الخط المستقيم OA

Yield stress(𝜎y)

بين المنطقتين تفصل النقطة الي B

Ultimate stress

المنحنى أعلىالنقطة التي تكون في D

Ruptureor fracture stress

نقطة في المنحنى أخر E

Necking المنقطة الي تقع بين FElastic (A1)

Plastic(A2)

Elastic ,Plastic

Ultimate , Rupture

F

Elastic : إلى شكله الطبيعي سيرجعلو عرضت عليها أكبر قوى ثم أزلتها

Plastic : ولن يرجع إلى شكله الطبيعيتشوه دائم لو عرضت عليه قوى ثم أزلتها سيتشوه

The Modulus of Elasticity (E) : Shows the Elastic resistance to an applied load that causes deformation. It is a measure of the stiffness of materials .

E= 𝜎

𝜖so 𝜎= E* 𝜖 just in Elastic and called Hock’s Law

للمعادن الطرية قليلهقيمتها

The Modulus of Resilience (UR) : Amount of energy stored in stressing the material to the elastic limit This quantity is important in selecting materials for energy storage such as springs .

UR=A1= 1

2𝜎𝑦 𝜖𝑦 (

𝐽

𝑚3)

The modulus of Toughness (UT): Total energy absorption capabilities of the materials to failure this quantity is important in selecting materials for applications where high overloads are likely to occur and large amounts of energy must be absorbed

UT=A1+A2 = 2

3𝜎𝑢 𝜖𝑀𝑎𝑥

Shear modulus of elasticity (G) : 𝐸

2(1−𝑉)

Bulk Modulus(K) :𝐸

3(1−2𝑉)

𝜎𝑇 = 𝜎(1 + 𝜖)

𝜖𝑇 = Ln(1+ 𝜖)

True or Actual Values

V= Poisson’s Ratio=−𝜖

𝐿𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝜖𝐴𝑥𝑖𝑎𝑙

Reduction in Area = 𝐴𝑖−𝐴𝑓

𝐴𝑓*100% Elongation percentage =

𝐿𝑓−𝐿𝑖

𝐿𝑖*100%

Vi=Vf

Ai * Li = Af * Lf

Af = 𝑨𝒊∗𝑳𝒊

𝑳𝒇

Ductility

Then :

مرنه تكون المادهكبير إذا الرقم كان

• The compression test is used to:

1-Observe the stress - strain behavior of some metals under compression load.

2-Determine the strength and other properties of various materials .

• There are special limitations on the compression test:

1- Appling a truly axial load is difficult.

2- There is always a tendency for bending stresses to be set up.

3- Friction between the heads of the testing machine or bearing plates and the end surfaces of the sample

• Universal Testing Machine (UTM) we use it again in this test .

Why we do this test ?

في الضغط أكثر من الشد أكثرتتأكثر المواد الهشة ألن

Compression test P

P

الضغط

الضغط

ال يتأثر بوجود الشوائب

Li

Lf

S=Li-Lf

Notes : . من النهائي أكبراإلبتدائي الطول

.من النهائيه أقلاإلبتدائيه المساحه. حجم العينه النهائي نفسالعينه اإلبتدائيه حجم

Di

Df

P

P

How we can Avoid it ?

Put oil

The friction between sample and the testing machine .

Compressed the sample its begins to bulge outward on the sides

Happen because

𝝐 =𝐿𝑖−𝐿𝑓

𝐿𝑖Shortening =

∆𝐿

𝐿*100%

Increasing in Area= ∆𝐴

𝐴*100%Vi =Vf

Ai Li= Af Lf

L > D Why ?Avoid Buckling

Materials DuctileBrittle

No Fracture Fracture at angle 𝟒𝟓°

شكل الكسر

Caused by : Normal stress

Compression higher than tension ?

Atoms and cracks will be close to each other

Hold compressive load less than Ductile

يحدث فقط تشوهات

Yield=Ultimate=fracture

• Deflection of Beams at Elastic zone

• Objective: Investigate the support reaction forces and deflection of a simply supported beam and a cantilever beam .

• Beam : Structural element that primarily resists loads applied laterally to the beam's axis

Simply supported beam Cantilever beam

𝟎 ≤ 𝒙 ≤𝒍

𝟐

• Simply supported beam

w(x)= 𝐹𝐿3

48𝐸𝐼(3

𝑋

𝐿- 4

𝑋3

𝐿3)

∑𝑀𝐴 = 0

The maximum deflection Where x = 𝒍

𝟐

w(x)= 𝐹𝐿3

48𝐸𝐼

By= F * 𝑋

𝐿

Ay=F * (1-𝑋

𝐿)

∑𝐹𝑦 = 0

b

h

𝐼 =Moment of Inertia= 𝑏ℎ3

12

Or∑𝑀𝐵 = 0

X: A المسافه ما بين القوة و النقطة

b: الطول الكبير

Deflection(Y max) = 𝐹𝐿3

3𝐸𝐼

S or Deformation at point A = Zero

S or Deformation at point B = Max

L : موقع القوه وليس طول البيم

𝐼 =Moment of Inertia= 𝑏ℎ3

12

• Cantilever beam

Deflection Proportional to F and 𝐿3

Deflection Inversely to E and 𝐼

• Sources or error :

1- Error in reading of Dynamometer because the difference in the angle of view .

2- Non-Zeroed Dynamometer .

3- The beam is not straight 100% .

4 - Already Plastic deformation before the experiment in the beam .

5-The dynamometers experience spring excursion under load , in order to prevent measurements errors as a result of additional deflection , the result should be returned to their original position .

E= ቚ ቚ𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙−𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙* 100%

الناتج العملي

الناتج النظري

Measurement of the Deflection : By Dial gauge and the units in (mm) .

Measurement of the Reaction : By Dynamometer and the units in (N) .

• Devices

1 Round= 360∘ = 1mm1 Round = 100 part

Reading

• Notes : Mass of the beam is negligible .Force should be constant .Cross-section of b x h mm .Experimental bar is made of steel .

Stability Of Columns

• Objective: Study the behavior of axially loaded columns,

Determine experimentally the critical buckling load, and to compare results with Euler’s formula .

P

P

P

P

P

P

Column (Compression Load) , (Axial load)

Shaft(Torque)

Beam(Normal Load)

L

D

𝑙 > 𝐷

D

• Pcr = Critical Load “Theoretical value ” : The Load at which the buckling( lateral deflection) will occur .

Pcr = 𝑛2𝜋2𝐸𝐼

(𝐿𝑒𝑓𝑓)2

n=1 , Always in this course L eff = KL

E: Modulus of elasticity

𝐼: Moment of inertiaL eff : Length of column affected by axial load

K : Depends on type End conditionL: Length

𝐼 =𝑏ℎ3

12

P≥ Pcr so buckling happenedUnstable , fail

P < Pcr No failureStable

b: الطول االكبر

• End condition of columns :

1- Pin-Pin

Max Deflection in the middle of column .

2-Fixed-Free

Max Deflection in the top of column .

3- Max Fixed-Fixed Deflection in the middle of column .

4-Fixed-Pinned

Fixed Support تأثر المنطقه القريبه منها تبقى ثابته وال ت

E= ቚ ቚ𝑃𝑐𝑟−𝑃

𝑃𝑐𝑟

* 100%

Torsion test

Objective :

Determine the behavior of materials when subjected to torsion, and to obtain some of their Mechanical Properties.

𝝓 = Angle of twist

نتجت الزاويه عندما تحركت من نقطة إلى نقطه

Fixed 𝛄: Shear strain angle

𝛾=𝑟𝜙

𝐿𝜏𝑚𝑎𝑥 = 𝑇𝑟

𝐽

𝜏 : Shear stressT: Torque (N.m) r: Radius of shaft (m)J: Polar moment of inertia

𝛾: Shear strain angle (Rad)𝑟 : Radius of shaft (m) 𝜙: Angle of twist (Rad)𝐿: length of shaft (m)

𝜙:للخارج : (+)

للداخل : (-)

Elastic and PlasticElastic only

كلما ابتعدنا عن المركز زاد اإلجهاد

𝜙=𝑇𝐿

𝐺𝐽𝛾=

𝑇𝑟

𝐺𝐽

𝜏 =𝑃𝐶 + 3𝐴𝑃

2𝜋𝑟3

Plastic only

Slope at Proportional limit = G modulus of elasticity or rigidityD

L

D= RuptureL= Yield

Or كما هو موضوح في الرسمه خط عامودي ثم خط أفقي وارسم مماسخذ

dT=PC

d𝜙 = 𝜙 = BC

T=AP𝜏 =

1

2𝜋𝑟3(𝜙

𝑑𝑇

𝑑𝜙+3T)

• The Modulus of Rigidity(G) :

Slope of the 𝜏 –𝛾 curve in the elastic range 𝜏 =G*𝛾 𝛾(Rad)

• The Modulus of Resilience : Area under the elastic portion represents

the energy absorbed by the material in the elastic region = 1

2𝜏𝑦𝛾𝑦

• The Modulus of Rupture (Toughness) : Total area represents the total

energy absorbed by the material before fracture = 2

3𝜏𝑢𝛾𝑀𝑎𝑥 .

𝜙 and G : inverse Relation

Flat

Fracture at angle 𝟒𝟓°Fracture at angle 𝟗𝟎°

Caused by : Shear stress

Brittle (Pure) Ductile

Note : Not pure Brittle it’s the same Ductile

Shape : Shape :

Caused by : Normal stress

• Fatigue Test

Compression then Tension then Compression ….

So , Fracture happen at a stress less than yield stress or Ultimate stress

For this reason Oscillating stresses more dangerous .

𝝈 < 𝝈𝒖𝒍𝒕

𝝈 < 𝝈𝒚Or

Form of Fracture at angle 𝟗𝟎° :

P1

P2

T

C

C

T

From P1 From P2

Zero- Nothing

One cycle = Tension and compression

𝟏

𝟐cycle = Tension turn compression

Or compression turn tension

Apply Tension then nothing then compression so every point on the surface goes from max compression then to nothing then to max tension .

C is always negative ? ألن القوه بتكون داخله في الجسم

Fatigue Life: It is the number of cycles to cause failure at a specific stress taken from S-N curve

Fatigue strength: It is the stress at which failure will occur for a specified number of cycles.

S: stress

N: # of cycles

𝝈𝒎 > 𝝈a 𝝈𝒎 < −𝝈aȁ ȁ𝝈𝒎 > 𝝈a

𝝈𝒎: Mean stress 𝝈a :Alternating stress

One cycle consist from 𝝈𝒎and 𝝈a

C

T𝝈𝒎𝒂𝒙 = 𝜎𝑚+ 𝜎𝑎𝝈𝒎𝒊𝒏 = 𝜎𝑚 − 𝜎𝑎

𝜎= 𝑀𝑐

𝐼

M: Bending Moment = F*L

I: Moment of Inertia= 𝜋𝑑4

64

c = Centroid = 𝑑

2, r=

𝑑

2 #of cycles = ∞ then No failure#of cycles = Zero then 𝜎 = 𝜎𝑢𝑙𝑡

Endurance : the number N of load cycles until rupture at a certain load.

Relation between Stress and #of cycles is inverse

Fatigue Endurance Limit: It is the stress level at which fatigue will never occur, that is the largest value of fluctuating stress that will not cause failure for infinite number of cycles.

• Hardness Test (مقاومه الماده للخدش)• Hardness of any metal is : Its resistance to surface indentation under standard

test conditions and its Non-Destructive test.

• Uses : 1- for Comparison between the metals and the value is not important in design , useful in Comparison .

2- check on heat treatment to a metal and checking the tensile strength of ferrous materials . • Device : Universal Hardness Tester .

• Three main test methods are used: 1-Brinell (HB)2-Vickers (HC)3-Rockwell (HRC/HRB)

• Components :1- Specimenالعينه الذي أريد ان أخدشها

2- Indenterالماده الذي أريد الخدش بها

3- Indentationاألثر الذي تتركه القوه

F

Specimen

Indenter diameter D

Indentation diameter d

d ≤ D

We measure the diameter by microscope

Indenter

Indentation

1-The Brinell test : Indenter : Steel ball (2.5mm)

BHN=Brinell harness number = 𝐿𝑜𝑎𝑑

Area of curved surface of indentation=

𝑃(𝑘𝑔𝑓)1

2𝜋𝐷 𝐷− 𝐷2−𝑑2 (𝑚𝑚2)

kgf=kgP: Force applied (kg) D: Diameter of indenter (mm) d: Diameter indentation(mm)

Tensile strength (𝝈𝒖𝒍𝒕)(MPa) = 3.45(BHN).

Steel only

• Notes :

• Don’t use Brinell tests if BHN ≥ 450 why ?

ball maybe easily deformed and this will introduce errors .

• The test maybe unreliable for hard or very soft materials .

• If several readings must be taken on the same specimen, they should be spaced away from each other and away from the edges of the work piece ≥ 4𝐷 .

• Distance from edge and specimen should be ≥3D .

• Hardness ball ≥ 1.7 Hardness of specimen .

Thickness of the test piece T

Values of 𝑇

𝑡:

For soft materials ≥ 15

For hard materials = ≥ 7

• Depth of indentation independent with BHN .

2-Vickers (HC)

Vickers Hardness number (VHN) = 𝑃

𝐷2

2∗sin

1

2(136°)

= 1.854𝑃

𝐷2

Square based diamond pyramid indenter

Types of Load : 1- Pre-Load 2-Main Load

Pre-Load: 1- Make contact between the specimen and the indentor 2- Overcome the roughness on the surface of specimen

Main Load : After pre-Load

• Requires a smoother finish on the test material

Notes :

• Provides a suitable hardness scale ranging from the very soft to very hard material.

P : LoadD: diameter

• Depth of indentation independent with VHN .

• Hardness number of ≥ 300 the Brinell and Vickers Hardness values are same

• More suitable than the Brinell test for testing finished components.

3-Rockwell (HRC/HRB)

HRC :Rockwell test Type C HRB :Rockwell test Type B

Indentor : Diamond Indentor : Steel bar

Main Load = 100N Main Load = 150N

Cant be used for soft material

ونخدشها باأللماس لضمان حدوث التشوه ل العينه للمواد الصلبه جدا يستخدم

Diamond :Very hard it will scratch

Cone : Hight stress concentration

• Nine scales of the hardness are available (A to K inclusive) but the most commonly used are the B & C scale .

• THIN WALL CYLINDER

𝑡

𝐷≤

1

20

Thickness (t)

Diameter (D) لكي تكون الشرطيجب تحقق هذا

THIN WALL CYLINDER

• We put water , oil in the cylinder so we get stress and strain .

𝝈H ∶ Hoop Stress = 𝑃𝐷

2𝑡

موجوده دائما 𝝈L ∶

Longitudinal stress = 𝑃𝐷

4𝑡

اإلسطوانه إذا كانت مفتوحه أم مغلقه نوعتعتمد على

Pressing in the Ends of the cylinder

Pressing in the Inner wall of the cylinder

Open cylinder : Zero

Closed cylinder : = 𝑃𝐷

4𝑡

𝝈H > 𝝈L

𝝈H = 2𝝈L

• Stress Types : 1- Hoop Stress (𝝈L) 2- Longitudinal stress (𝝈H )

P: Pressure D: Diameter t: Thickness

𝝈L and𝝈H= عالقه طرديه

Slope= E E: modulus of elasticity

𝝈L =0 When its Spherical

Fail because 𝝈H

• Strain Types : 1- Hoop Strain (𝜖H ) 2- Longitudinal Strain (𝜖L)

𝜖L = 𝝈L

𝐸− 𝑉

𝝈H

𝐸𝜖H =

𝝈L

𝐸− 𝑉

𝝈L

𝐸

V: Poison's ratio

E: Modulus of Elasticity

𝜖 ≠ 0

𝝐𝐋and 𝝐𝐋= عالقه طرديه Slope= V

.الفشل ولكي نتجنب حدوث اإلجهاد االقل بهذا اإلتجاه ويكون مع خط اللحام نضع

Depends on end Condition

• Creep Test of Metallic Materials

Creep : A consequence of this is that steel under a constant stress at an elevated temperature will continuously deform with time .

Annealing : Treatment of metal by heating for a certain time and then cooling to room temperature to improve ductility , reduce hardness and its causes creep .

Work hardening(cold working ) : Strengthening of a metal and more difficult to deform and needs more stress to produce deformation , more stronger and harder so the strain increases .

• Annealing opposite Work hardening

• Rate of Strain (Creep ) depends on : 1- Temperature 2- Stress

Ductility: Ability of material which allows them to deform plastically under tension

• Application of creep test : 1- Tungsten lamps 2- The blades of an electric generators

• Strengthening occursbecause of dislocation movements .

• Deform depends on the ability of dislocation

Creep occurs if :

• Ts ≥ 0.4 Tm

Tm: Absolute melting Temperature Ts : Surrounding Temperature

• 𝝈 ≥ 𝝈𝒚

𝝈 = 𝑃

𝐴𝝈 < 𝟓𝐌𝐏𝐚 : 𝜀 = A𝝈𝑛𝑒

−𝐸

𝑅𝑇

𝝈 > 𝟓𝑴𝑷𝒂: 𝜀 = B𝑒𝝈𝛼𝑒−𝐸

𝑅𝑇

T: Temperature (kelvin)

1 to 2 Primary (Transient) Creep : Diminishing rate due to work hardening of the metal Work hardening > AnnealingRate of strain decreases

2 to 3 Secondary Creep(Quasi-viscous) : Constant rate because a balance is achieved between the work Hardening and annealing (thermal softening) processes.Work hardening = AnnealingRate of strain constantDetermines the life of a given componentNeeds more time , Most important stage Prime importance as a design criterion

3 to 4 Tertiary Creep :The creep rate increases due to necking of the specimen and the associated increase in local stress. Failure occurs at point 4. Work hardening < annealing Rate of strain increases

Slope= Rate of strain

Unit : 1

𝑠𝑒𝑐

The weight hanger has two pinning positions: 1. The uppermost is used to pin the hanger in the rest position.2. The lower hole is used to pin the hanger in the loaded position .

F=(2.84+8m)*gUnit : N

F: Tensile pull on the specimen g = Acceleration due to gravity

Ln 𝜺

𝝈

Slope= Ln𝜷-𝑬

𝑹𝑻= 𝜶

• Strain Measurement with Strain Gauges

• Give accurate measurements of strain .

When External forces are applied to a stationary object, stress and strain are the result.

The strains measured with strain gauges are normally very small also the changes of resistance are also very small cannot be measured by ohmmeter .

Strain Gauges : Sensor whose resistance varies with

applied force; It converts force, into a change in electrical resistance which can then be measured .

External forces : 1- Normal force 2- Axial force

. نضع المقاومه في داره كهربائيه لذلك

Stress : Object's internal resisting forces

Strain: Displacement and deformation that occur.

Two types of strain : 1- Axial : Install the strain gauge Parallel2- lateral : Install the strain gauge Perpendicular

• A strain gage’s sensitivity is expressed by the ratio of the relative change of resistance to the strain and it is represented by the symbol k .

K= ∆𝑅

𝑅𝑜∆𝐿

𝐿𝑜

= ∆𝑅

𝑅𝑜

𝜖

so K∗ 𝜖 = ∆𝑅

𝑅𝑜

Unit less

• Piezoelectric materials : الماده التي يتم صنع االسالك بها ألنها حساسيتها عاليه جدا للمقاومه

∆𝑅

𝑅𝑜:

ك قيمتها قليله جدا وال يمكن حسابها بالجهاز لذلنضعها في الداره الكهربائيه

• Normal force

𝜎 = 𝑃

𝐴

𝜎= 𝑀𝑐

𝐼

𝜖=∆𝐿

𝐿

P: Load A: Area = 𝑟2 ∗ 𝜋L: Length ∆𝐿= Deformation

M: Max moment I: Moment of inertia Y: Distance y from the neutral axis c = Y max

• Axial force

a) Quarter Bridgeيوجد مقاومه وحده

c) Diagonal Bridgeاإلشارهنفسمقاومتين فوق بعضهم و لهم

b) Half Bridgeمقاومتين بجانب بعضهم ولهم إشارات معاكسه

d) Full bridge.جميع المقاومات

Wheatstone Bridge

𝑉𝑜

𝑉𝑠=𝑘

4(𝜖1)

𝑉𝑜

𝑉𝑠=𝑘

4(𝜖1−𝜖2 + 𝜖3 - 𝜖4)

Actual Strain = القراءة

1

Actual Strain = القراءة

4Actual Strain =

القراءة2

Actual Strain = القراءة

2

𝑉𝑜

𝑉𝑠=𝑘

4(𝜖1 + 𝜖3)

𝑉𝑜

𝑉𝑠=𝑘

4(𝜖1 − 𝜖2)

• There are two conditions where Vo = 0:

1-When all bridge resistors are equal value . 2-Ratios in the two halves of the bridge are the same.

Slope= K

𝜖𝑙𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝜖𝑎𝑥𝑖𝑎𝑙

𝝈

𝜖𝑎𝑥𝑖𝑎𝑙

Slope= E

Slope= V= −𝝐𝒂𝒙𝒊𝒂𝒍𝝐𝒍𝒂𝒕𝒆𝒓𝒊𝒂𝒍

∆𝑅

𝑅𝑜

𝜖

R= 𝜌𝐿

𝐴

R: resistance𝜌 : ResistivityL: length A: area

∆𝑅 and ∆L عالقه طرديه

• Impact Test

• Toughness : The energy required to fracture a material and it

depends on geometry (strength) and ductility or

Total strain energy per unit volume of a metal .

• Purpose : Evaluating the relative toughness of engineering

materials.

• Uses : Impact test is used to compare results for different types of materials

And its not important in design because there is Notch .

• Definition : Impact is a shock load which is applied for a very short time

under consideration.

• Consideration : t<1

3Wn

t: time of application of load on specimenWn : natural period of vibration of structure(natural frequency)

Toughness and ductility

عالقه طرديه

Toughness and Temperature

عالقه طرديه

There is a notch in the specimen why ?

1- There will be no extra energy consumed in plastic deformation of the specimen.

2- Concentrate the stress

3- Facilitate the breakage

Types of Notch : 1- V 2- U

Type V U

Toughness Low Hight

Stress concentration Hight Low

Same geometry

Types of impact tests

1. Charpy test 2. Izod test

• Notch in the side of tension .

1-Notch opposes the hammer2-Specimen is simply supported3-Simple and fast 4- Low Toughness

(Brittle example : steel)

5- Two shearing Area

6- E Charpy =2 E Izod

7- التدريج الخارجي

1-Notch faces the hammer2-Cantilever type specimen (clamped)3-More complicated and slower4- Hight Toughness

(Ductile example : Aluminum)

5- One shear Area

6- E Izod =1

2E Charpy

7- التدريج الداخلي

Charpy test Izod test أوسع انتشارا

Ep= potential energy= mghEk=kinetic energy = 1

2𝑚𝑣2

Mechanical energy = Potential Energy + Kinetic Energy

Ep= Max

Ep= Ek=Zero

m: Mass g: Acceleration due to gravityH: Hight

The hammer is released from a

90 degree angle (point A) and

the maximum angle it swings

to (point B) .

Pendulum swings to a maximum

height (point C) which is lower

than point B above.

• The energy loss due to air resistance will be equal to the

difference in potential energy between points A and B .

• we calculate the energy needed to break a metallic test piece (specimen)

Max velocity so h1= zero then h2=𝑣2

2𝑔

U= mg(h1-h2)- friction

U= P1-P2- friction

U= mgL(cos 𝜃1-cos 𝜃2) - friction

• Toughness = Frication( بدون العينه) – Reading( العينه)

• The results obtained for a material from an impact

test are sensitive to the following :

1. Heat treatment

2. Compositions.

3. Sulfur and phosphorous content.