SIFAT MEKANIS 1

Materi kuliah : Konsep tegangan dan regangan. Sifat elastis dan sifat plastis material. Uji tarik. Kurva tegangan regangan dan intepretasinya.

DEFORMASI ELASTIS Elastic means reversible! 1. Kondisi awal 2. Beban kecil 3. Beban dilepas Elastic means reversible! 2

DEFORMASI ELASTIS Deformasi elastis bersifat reversibel

DEFORMASI PLASTIS (LOGAM) Deformasi plastis bersifat tetap (permanen)

KONSEP TEGANGAN • Tegangan tarik, s: • Tegangan geser, t: Satuan tegangan : N/m2 atau lb/in2 4

KONDISI PEMBEBANAN • Tegangan tarik (kabel) • Tegangan geser (poros) Ski lift (photo courtesy P.M. Anderson) • Tegangan geser (poros) Note: t = M/AcR here. 5

KONDISI PEMBEBANAN • Beban tekan : Note: compressive structure member (photo courtesy P.M. Anderson) Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson) 6

KONDISI PEMBEBANAN s < 0 • Tegangan tarik 2 sumbu: • Tekan Hidrostatik: Pressurized tank (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) s < 0 h 7

KONSEP REGANGAN • Regangan tarik : • Regangan lateral: • Regangan geser : Regangan merupakan besaran tanpa satuan. 8

CONTOH SOAL 1 Sebatang tembaga dengan panjang 305 mm ditarik dengan tegangan sebesar 276 MPa, jika deformasi yang terjadi adalah deformasi elastis, hitung resultan elongasinya. JAWAB : Pada deformasi elastis, hubungan antara tegangan dan regangan adalah : Elongasi (∆l) dapat dihitung dengan persamaan :

CONTOH SOAL 1 Harga ∆l dapat dicari....... Gabungan dari kedua persamaan tersebut, didapat : Dengan memasukkan harga – harga : σ = 276 MPa l0= 305 mm E properti tembaga = 110 x 103 MPa Harga ∆l dapat dicari.......

CONTOH SOAL 2 Sebuah tegangan tarik diberikan pada sebuah batang kuningan yang berdiameter 10 mm. Hitung beban yang diperlukan untuk menghasilkan perubahan diameter 2,5 x 10-3 mm, jika deformasi yang terjadi adalah deformasi elastis : JAWAB :

Ketika gaya F diberikan, spesimen akan mengalami perpanjangan arah z dan mengakibatkan pengecilan diameter, Δd = 2,5 x 10 -3 mm dalam arah x. Regangan arah z dapat dihitung dengan persamaan:

Tegangan yang diberikan dapat dihitung dengan Hukum Hooke : Gaya yang harus diberikan :

UJI TEGANGAN DAN REGANGAN • Contoh spesimen uji tarik • Skema uji tarik Adapted from Fig. 6.2, Callister 6e. Adapted from Fig. 6.3, Callister 6e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.) • Tipe uji lain : -- tekan : bahan getas (misal : beton) -- torsi : poros, tabung silinder 9

Tensile Test Machine (Instron)

Extensometer Grip Specimen Grip

TENSILE STRENGTH, TS • Maximum possible engineering stress in tension. Adapted from Fig. 6.11, Callister 6e. • Metals: occurs when noticeable necking starts. • Ceramics: occurs when crack propagation starts. • Polymers: occurs when polymer backbones are aligned and about to break. 17

Terms Necking: The localized decrease in diameter in a specimen near the rupture point. Elastic Deformation Region: The area of a stress - strain curve where the specimen will deform under load, yet return to its original shape when the load is removed. Plastic Deformation: Deformation that occurs once the object has been stressed past its elastic limit. The deformation is no longer reversible.

Grip Tensile Test Specimen Grip

Necking Starts Necking Starts

Necking “Necking” occurs as the sample leaves the elastic deformation region and begins to deform plastically.

Fracture Initiates at Necking Area

Fracture is Complete at Necking Area

The classic cup & cone shape of a fairly ductile tensile fracture is visible here.

DUCTILE VS BRITTLE FAILURE • Classification: Adapted from Fig. 8.1, Callister 6e. • Ductile fracture is desirable! Ductile: warning before fracture Brittle: No warning 2

Compare the material properties of these three metal samples. All three failed under tension

Tensile Test Stress Strain Diagram The applied stress versus the strain or elongation of the specimen shows the initial elastic response of the material, followed by yielding, plastic deformation and finally necking and failure. Several measurements are taken from the plot, called the Engineering Stress-Strain Diagram. These include: Modulus of elasticity Yield strength Tensile strength Modulus of resilience Failure stress Ductility Toughness

Modulus of elasticity - the initial slope of the curve, related directly to the strength of the atomic bonds.

Menghitung modulus elastisitas Modulus elastisitas (E) ε0 ε1 σ1 σ0 Daerah elastis

Yield strength, usually defined as the point at which a consistent and measureable amount of permanent strain remains in the specimen.

0.2 % Offset Yield StrengthOffset Yield Strength Defining the yield stress as the point separating elastic from plastic deformation is easier than determining that point. The elastic portion of the curve is not perfectly linear, and microscopic amounts of deformation can occur. As a matter of practical convenience, the yield strength is determined by constructing a line parallel to the initial portion of the stress-strain curve but offset by 0.2% from the origin. The intersection of this line and the measured stress-strain line is used as an approximation of the material's yield strength, called the 0.2% offset yield.

0.2 % Offset Yield Strength

Tensile strength - the maximum stress applied to the specimen.

Failure stress - the stress applied to the specimen at failure (usually less than the maximum tensile strength because necking reduces the cross-sectional area)

DUCTILITY, %EL • Plastic tensile strain at failure: Adapted from Fig. 6.13, Callister 6e. • Another ductility measure: • Note: %AR and %EL are often comparable. --Reason: crystal slip does not change material volume. --%AR > %EL possible if internal voids form in neck. 19

Ductility - the total elongation of the specimen due to plastic deformation, neglecting the elastic stretching (the broken ends snap back and separate after failure).

% elongation =100 * (Lf - Lo)/ Lo Ductility % Elongation: % elongation is a measure of ductility, which is given by: % elongation =100 * (Lf - Lo)/ Lo where, Lo = Initial length Lf = Final Length

% reduction in area =100 * (Ao - Af)/ Ao Ductility % Reduction in Area: % reduction in area is a measure of ductility, which is given by: % reduction in area =100 * (Ao - Af)/ Ao where, Ao = Initial arae Af = Final area

Modulus of resilience - the area under the linear part of the curve, measuring the stored elastic energy.

Toughness - the total area under the curve, which measures the energy absorbed by the specimen in the process of breaking.

TOUGHNESS • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. 20

PLASTIC (PERMANENT) DEFORMATION (at lower temperatures, T < Tmelt/3) • Simple tension test: 14

YIELD STRENGTH, sy • Stress at which noticeable plastic deformation has occurred. when ep = 0.002 15

 = (applied force)/(area) =P/A True Stress and Engineering Stress: True stress is calculated by :  = (applied force)/(area) =P/A where A=Actual area (actual area constantly decreases from its initial value) Substitution of the actual area into the equation gives a larger stress (true stress) than the engineering stress. Note that engineering stress uses the initial area, regardless of the change in diameter during the tensile test. TRUE STRESS STRESS ENGINEERING STRESS STRAIN

STRAIN HARDENING EXPONENT • An increase in sy due to plastic deformation. • Curve fit to the stress-strain response: 22

SUMMARY • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure. 24