-1-2 -3-4 ( ) -5 ( ) -6-7 -8-9 -10-11 -12 ( ) Chapter 7: Mechanical Properties 1- Load 2- Deformation 3- Stress 4- Strain 5- Elastic behavior 6- Plastic behavior 7- Uniaxial tensile load 8- Bi-axial tensile load 9- Hydrostatic compression 10- Tension test 11- Fracture 12- Modulus of elasticity (Young's modulus) Chapter 7-1 Chapter 7: Mechanical Properties -13-14 -15-16 -17-18 -19-20 -21-22 -23 13- Stiffness 14- Hooke's law 15-Shear modulus 16- Poisson's ratio 17- Yield Strength (YS) 18- Tensile Strength (TS) 19- Ultimate Tensile Strength (UTS) 20- Ductility 21-Toughness 22- Hardness 23- Safety factor Chapter 7-2 1
Common States of Stress Chapter 7-5 Common States of Stress Cable Simple tension Pressurized tank Bi-axial tension Ski lift Drive shaft Torsion (a form of shear) Chapter 7-6 2
Simple compression: Common States of Stress Canyon Bridge, Los Alamos, NM Balanced Rock, Arches National Park Hydrostatic compression Fish under water Chapter 7-7 Mechanical Properties Mechanical behavior: Response of a material to an applied force, e.g. deformation, Structural engineer: Determine stresses and stress distributions within members that are subjected to loads Materials and metallurgical engineer: Produce and fabricate materials to meet service requirements as predicted by these stress analyses Factors to be considered: Nature of the applied load: tensile, compressive, shear, constant with time or may fluctuate continuously Duration: a fraction of a second to many years Environmental conditions Service temperature Chapter 7-8 3
Mechanical Properties Concern to consumers, producers, research organizations, government agencies, Need to have consistency in testing and interpretation of their results Standardized testing techniques Professional societies such as ASTM (American Society for Testing and Materials-www.ASTM.org) in the US Need carefully designed laboratory experiments that replicate as nearly as possible the service conditions. Chapter 7-9 Tension Test Typical tensile specimen extensometer specimen Circular or rectangular cross section specimens Uniaxial tensile load along the long axis of a specimen Typical tensile test machine Gradual increasing of the load until fracture Chapter 7-10 4
Chapter 7-11 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch δ F Elastic means reversible! F δ return to initial Linearelastic Non-Linearelastic Chapter 7-12 5
Plastic Deformation (Metals) 1. Initial 2. Small load 3. Larger load bonds bonds stretch stretch & planes shear 4. Unload planes still sheared F δ F δ F Elastic + Plastic δ plastic linear elastic δ Plastic linear elastic δ Plastic = Permanent! Chapter 7-13 Engineering Stress and Strain Output: a force (F) versus elongation (δ) curve F required for a given δ depends on the cross section area (A 0 ) of the specimen Load and elongation are normalized to engineering stress and engineering strain F linear elastic linear elastic δ Plastic F = the instantaneous load applied perpendicular to the specimen cross section (N, lbf, ) A 0 = the original cross-sectional area before any load is applied (m 2, in. 2, ) l 0 = the original length before any load is applied l i = the instantaneous length δ Chapter 7-14 6
Tensile stress, σ: Engineering Stress and Strain F Area, A o Stress has units: N/m 2 or lb f /in 2 F Strain is unitless: m/m or in/in and sometimes as % σ = F = A o m 2 original area before loading N lb or f in 2 Chapter 7-15 Compression Test Is less common than tension test Is conducted in a similar manner to the tensile test The force is compressive The specimen contracts along the direction of the stress A compressive stress is taken to be negative by convention Compressive strains computed are also negative. Chapter 7-16 7
Chapter 7-17 Shear Test τ = Shear stress F = the force imposed parallel to the upper and lower faces Shear strain (γ)= the tangent of the strain angle θ θ x y 90º Shear strain: γ = x/y = tan θ Chapter 7-18 8
Linear Elastic Properties Hooke's Law: σ = E ε E : Slope of the linear segment : Modulus of Elasticity, Young's Modulus E = Stiffness: Material s resistance to elastic deformation The greater the E, the smaller the elastic strain that results from the application of a given stress. E is important in computing elastic deflections Compression F F _ σ _ Linear/ Elastic + E Tension + ε F F Chapter 7-21 Linear Elastic Properties E depends on bond strength of metal Chapter 7-22 9
Linear Elastic Properties The elastic strain = stretching of interatomic bonds E = a measure of interatomic bonding forces E for Polymers = about 0.007 to 4 Gpa E for metals = 45 GPa (for Mg) and 407 Gpa (for W) E for ceramics = about 70 and 500 GPa G = the shear modulus G = the slope of the linear elastic region of the shear stress strain curve Chapter 7-23 Elastic Properties Chapter 7-24 10
Elastic Properties E decreases with increasing the temperature Chapter 7-25 Chapter 7-27 11
Poisson's ratio, ν Ratio of lateral and axial strains Uniaxial stress + isotropic material: 1- ε x = ε y 2- In most metals G 0.4E If E is known, G and ν may be approximated. Chapter 7-28 Elastic Properties Chapter 7-31 12
Chapter 7-32 Chapter 7-33 13
Plastic (Permanent) Deformation (at lower temperatures, i.e. T < Tmelt /3). Simple tension test: engineering stress, σ Elastic+Plastic at larger stress Elastic initially permanent (plastic) after load is removed ε p engineering strain, ε plastic strain Chapter 7-36 Yielding and Yield Strength Sometimes P is difficult to locate precisely Chapter 7-38 14
Yield Strength, σ y Stress at which noticeable plastic deformation has occurred. when ε p = 0.002 tensile stress, σ σ y = yield strength σ y Note: for 5 Cm sample ε = 0.002 = z/z z = 0.1 mm εp= 0.002 engineering strain, ε σ y : 35 MPa for a low-strength aluminum to over 1400 MPa for high-strength steels Chapter 7-40 2000 Yield Strength : Comparison Metals/ Alloys Steel (4140) qt Graphite/ Ceramics/ Semicond Polymers Composites/ fibers Yield strength, σ y (MPa) 1000 700 600 500 400 300 200 100 70 60 50 40 30 20 Ti (5Al-2.5Sn) W (pure) a Cu (71500) Mo (pure) cw Steel (4140) a Steel (1020) cd Al (6061) ag Steel (1020) hr Ti (pure) Ta (pure) a Cu (71500) hr Al (6061) a Hard to measure, since in tension, fracture usually occurs before yield. dry PC Nylon 6,6 PET humid PVC PP HDPE Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. Room temp. values a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 10 Tin (pure) LDPE Chapter 7-41 15
Elastic Strain Recovery σ yi D σ yo Stress 2. Unload 1. Load Elastic strain recovery 3. Reapply load Strain Chapter 7-43 Tensile Strength, TS Maximum stress on engineering stress-strain curve. TS (Tensile strength) σ y Engineering stress Typical response of a metal strain Engineering strain Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break. UTS (Ultimate Tensile Strength, Fracture strength) Neck acts as stress concentrator TS: 50 MPa for aluminum to 3000 MPa for highstrength steels Chapter 7-45 16
Tensile strength, TS (MPa) 5000 3000 2000 1000 300 200 100 Tensile Strength: Comparison 40 30 20 10 1 Metals/ Alloys Steel (4140) qt W (pure) Ti (5Al-2.5Sn) Steel (4140) a a Cu (71500) Cu (71500) hr cw Steel (1020) Al (6061) Ti (pure) ag a Ta (pure) Al (6061) a Graphite/ Ceramics/ Semicond Diamond Si nitride Al oxide Si crystal <100> Glass-soda Concrete Graphite Polymers Nylon 6,6 PC PET PVC PP LDPE HDPE Composites/ fibers C fibers Aramid fib E-glass fib AFRE( fiber) GFRE( fiber) CFRE( fiber) wood( fiber) GFRE( fiber) CFRE( fiber) AFRE( fiber) wood ( fiber) Room temp. values a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers. Chapter 7-46 Chapter 7-47 17
Chapter 7-48 Chapter 7-49 18
Ductility Plastic tensile strain at failure smaller %EL Engineering tensile stress, σ larger %EL L L %EL = L f o o x 100 L o L f Engineering tensile strain, ε %EL will depend on L 0! (A significant proportion of plastic deformation at fracture is confined to the neck region). The shorter L 0, the higher the value of %EL. L 0 should be specified when %EL are cited (commonly 50 mm)! Chapter 7-50 Ductility RA (Reduction in Area): Another ductility measure A L o o L f A f %RA is independent of both L 0 and A 0. For a given material the magnitudes of %EL and %RA will, in general, be different. Importance of ductility? How much a structure will deform plastically before fracture? How much deformation is allowed during fabrication operations? Chapter 7-51 19
Chapter 7-52 Chapter 7-53 20
Energy to break a unit volume of material Approximated by the area under the stress-strain curve (For the static (low-strain-rate) situation.) Engineering tensile stress, σ Toughness Small toughness (ceramics) Large toughness (metals) Small toughness (unreinforced polymers) Engineering tensile strain, ε Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy Chapter 7-54 Effect of Temperature on Mechanical Properties Chapter 7-55 21
Figure 7.14 Engineering stress strain behavior for iron at two temperatures. Chapter 7-56 True Stress and Strain σ T : True stress ε T : True strain A i = instantaneous cross section area over which deformation is occurring (i.e., the neck, past the tensile point). l i = instantaneous length Chapter 7-62 22
TRUE STRESS AND STRAIN If no volume change during deformation ( ): Necking introduces other stress components in addition to the axial stress The correct stress (axial) within the neck is slightly lower than the stress computed from the applied load and neck cross-sectional area (Fig. 7.16). Chapter 7-63 Chapter 7-65 23
Chapter 7-66 Hardness A measure of a material s resistance to localized plastic deformation (permanently denting or scratching) Qualitative test: The Mohs scale, ranged from 1 for talc to 10 for diamond. Quantitative tests: a small indenter is forced into the surface under controlled conditions and the depth or size of the resulting indentation is measured D apply a known force d measure size of indent after removing load Smaller indents mean larger hardness. Chapter 7-74 24
Chapter 7-75 Hardness: Measurement Table 7.5 Chapter 7-76 25
Hardness Most popular mechanical test Simple and inexpensive Nondestructive Other mechanical properties such as tensile strength, often may be estimated from hardness data Large hardness means: resistance to plastic deformation or cracking in compression better wear properties Chapter 7-77 Design or Safety Factors Design uncertainties mean we do not push the limit. Factor of safety, N Often N is σy between 1.2 and 4 σ working = N Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 3. d σy σworking = 1045 plain carbon steel: N σy = 310 MPa Lo 220,000N ( ) π d 2 / 4 3 d = 0.052 m = 52 mm TS = 565 MPa F = 220,000N Chapter 7-82 26
Chapter 7-83 Chapter 7-84 27
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 σ y. Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Chapter 7-85 28