Structure and Properties of Materials Part II Structure and Properties of Materials

Mechanical Properties CHAPTER 9 Mechanical Properties Fundamentals

9-I. Introduction Mechanical Properties: the relationship between response or deformation to an applied load or force. Deformation: strain Load: stress Important mechanical properties: strength (強度), hardness (硬度), ductility (延展性), and stiffness (剛性). Standardized testing techniques: American Society for Testing and Materials (ASTM) Understanding the relationships between the microstructure of materials and their mechanical properties.

9-II. General Concepts and Mechanical Properties of Metals A. Concepts of Stress (應力) and Strain (應變) Four principal ways in which a load (stress) may be applied： tension (張力，拉力) compression (壓力) shear (剪力) torsional shear (扭力) F 6.1 A-1. TENSION TESTS1 standard tensile specimen The measurement data are dependent on the shape and size of the specimen. Gauge length is used in ductility computations. A stress-strain test is destructive. F 6.2 F 6.3

◎ Engineering stress (for both tension and compression test) F：the instantaneous load applied in newtons (N) or pounds force (lbf) ； A0：original cross-sectional area (m2 or in.2)； : engineering stress, MPa (SI) (where 1 MPa = 106 N/m2), and pounds force per square inch, psi (Customary U.S.).2 (6.1)

(for both tension and compression test) l0：the original length； ◎ Engineering strain (fractional elongation) (for both tension and compression test) l0：the original length； li ：the instantaneous length； Δl＝ li - l0 ： Engineering strain, unitless (meters per meter or inches per inch ; or a percentage) (6.2)

A-2. Compression Tests conducted in a manner similar to the tensile test. Equations 6.1 and 6.2 are utilized to compute compressive stress and strain. Tensile tests are more common because they are easier to perform.

A-3. Shear and Torsional Tests Shear stress F : the load or force imposed parallel to the upper and lower faces, of A0 ; Shear strain, : the tangent of the strain angle . ＝ tanθ Performed on cylindrical solid shafts or tubes. (6.3) A-4. Geometric Considerations Of The Stress State F 6.4 normal stress (6.4a) shear stress (6.4b)

A ＝ A‘ cosθ F ＝ σA σ’ ＝ F cosθ/A’ ＝ ＝ σcos2θ τ＝ ＝ σsinθcosθ

B. ELASTIC DEFORMATION (彈性變形) B-1. Stress-Strain Behavior (A) Tension ◎ For most metals at relatively low levels, stress and strain are proportional to each other Hooke’s law; the constant of proportionality E (GPa or psi): Modulus of elasticity or Young’s modulus. For most typical metals, E=45 GPa (6.5 x 106 psi) for Mg to 407 MPa (59 x 106 psi) for W. (6.5) F 6.11 T 6.1

◎ Deformation in which stress and strain are proportional (a linear relationship) is called elastic deformation; The slope: modulus of elasticity E. ◎ Stiffness: material’s resistance to elastic deformation. The greater the modulus, the stiffer the material. ◎ Elastic deformation is nonpermanent : when the applied load is released, the piece returns to its original shape. ◎ For some materials (e.g., gray cast iron, concrete, and many polymers), initial elastic portion of the stress-strain curve is not linear either tangent or secant modulus is normally used. F 6.5 F 6.13 F 6.6

On an atomic scale (using a bond force curve): (6.6) (B) Compression The stress-strain characteristics at low stress levels are virtually the same for both tensile and compressive situations, (C) Shear (6.7) τ = F/A0 ; ＝ tanθ G is the shear modulus, F 2.8 F 6.7 YM F 6.1

B-3. Elastic Properties of Materials B-2. Anelasticity In most engineering materials, elastic deformation will continue after the stress application, and upon load release some finite time is required for complete recovery. This time-dependent elastic behavior is known as anelasticity, This is significant for some polymeric materials: viscoelastic behavior, If the material is isotopic, then Poisson’s ratio v (6.8) B-3. Elastic Properties of Materials

For isotopic materials, E = 2G(1+v) (6.9) Theoretically, Poisson’s ratio for isotopic materials should be ; the maximum value for v is 0.50. For isotopic materials, E = 2G(1+v) (6.9) In most metals G is about 0.4E; F 6.9 T 6.1

C. PLASTIC DEFORMATION ◎ elastic deformation: recoverable strains ˙for most metallic materials: 0.005 ˙from an atomic perspective：bonds are stretched but not broken. ◎ plastic deformation: permanent or nonrecoverable. ˙from an atomic perspective, breaking of bonds with original atom neighbors and then reforming bonds with new neighbors ˙For crystalline solids: slip noncrystalline solids: viscous flow

C-1. Tensile Properties (A) Yielding (降伏) and Yield Strength F 6.11 F 6.10 (A) Yielding (降伏) and Yield Strength ◎ yield point：the point of initial departure from linearity of the stress-strain curve (proportional limit). ◎ yield strength (σy) ：the stress at yield point. ◎ determination of yield point and yield strength. straight line: parallel at 0.002. nonlinear: the stress at some amount of strain (e.g., = 0.005). F 6.6

◎ yield point phenomenon upper yield point, the lower yield point (≡yield strength); The magnitude of the yield strength for a metal is a measure of its resistance to plastic deformation. Yield strengths may range from 35 MPa (5000 psi) for a low- strength aluminum to over 1400 MPa (200,000 psi) for high-strength steels. F 6.10

(B) tensile strength TS (MPa or psi) ： The maximum stress that can be sustained by a structure in tension (if this stress is applied and maintained fracture will result.). (C) necking (D) fracture strength : the stress at fracture Tensile strengths : 50 MPa (7000 psi) for an aluminum to as high as 3000 MPa (450,000 psi) for the high-strength steels. Ordinarily, when the strength of a metal is cited for design purposes, the yield strength is used. F 6.11

C-2. Ductility degree of plastic deformation that has been sustained at fracture： Brittle and ductile ◎ Ductility may be expressed as percent elongation or percent reduction in area (1) percent elongation (fracture strain) (6.11) lf , fracture length ; lo , original gauge length (plastic deformation at fracture is confined to the neck region, lo should be specified, commonly, lo =50mm) F 6.13

(2) Percent reduction in area (6.12) A0 , original cross-sectional area Af , cross-sectional area at the point of fracture. ◎ Brittle materials : a fracture strain of less than about 5% ◎ Yield strength, tensile strength, and ductility : sensitive to any prior deformation, the presence of impurities, and/or any heat treatment. (Measurement data: more scattering, large uncertainty.) Modulus of elasticity is insensitive to these treatments. (Data: less scattering, smaller uncertainty.) ◎ Yield and tensile strengths decline with increasing temperature; ductility increases with temperature. T 6.2 F 6.14

C-3. RESILIENCE F 6.15 capacity of a material to absorb energy when it is deformed elastically modulus of resilience : the area under the engineering stress-strain curve taken to yielding (6.13a)

Assuming a linear clastic region, is: the strain at yielding units of resilience (J/m3, Pa, in.-1bf/in.3, psi) energy absorption per unit volume. (6.13b) (6-5) (6.14) resilient materials: high yield strengths and low moduli of elasticity (spring).

ability of a material to absorb energy up to fracture D. TOUGHNESS F 8.12 ability of a material to absorb energy up to fracture ◎ Measurement of toughness For dynamic (high strain rate) loading conditions notch toughness : using an impact test (Section 8.6) fracture toughness : a material’s resistance to fracture when a crack is present (Sections 8.5 and 8.5W) (2) For the static (low strain rate) situation the area under the curve up to the point of fracture. ◎ For a material to be tough, it must display both strength and ductility; ductile materials are tougher than brittle ones. F 6.13

E. True Stress And Strain True stress : the load F divided by the instantaneous cross-sectional area Ai (6.15) true strain (6.16) If no volume change (6.17) True and engineering stress and strain (6.18a) (6.18b) F 6.16

F. Elastic Recovery After Plastic Deformation Formation of a neck : introduction of a complex stress state within the neck region the correct stress (axial) within the neck is slightly lower than the true stress. For some metals and alloys form the onset of plastic deformation to the point at which necking begins K and n : constants; n is often termed the strain-hardening exponent and has a value less than unity. (6.19) F 6.17 F. Elastic Recovery After Plastic Deformation G. Compressive, Shear, And Torsional Deformation similar to the tensile counterpart

a measure of a material’s resistance to localized plastic deformation. H. Hardness F 6.2 F 6.3 F 6.11 a measure of a material’s resistance to localized plastic deformation. ◎ Measurement of hardness (A) qualitative : Mohs scale, ranged from 1 on the soft end for talc to 10 for diamond. (B) quantitative : a small indenter is forced into the surface of a material depth or size of the resulting indentation is measured, which is related to a hardness number; (the softer the material, the larger and deeper is the indentation, and the lower the hardness index number) F 6.18 T 6.5

1. They are simple and inexpensive 2. The test is nondestructive ◎ Hardness tests are performed more frequently than any other mechanical test for several reasons: 1. They are simple and inexpensive 2. The test is nondestructive 3. Other mechanical properties often may be estimated from hardness data such as tensile strength ◎ Quantitative measurement (1) ROCKWELL HARDNESS TESTS Rockwell : minor load, 10 kg; major loads, 60, 100, and 150 kg. superficial Rockwell : 3 kg, minor load; 15, 30 and 45 kg, major load. F 6.19

(2) Brinell Hardness Tests (3) Knoop And Vickers (diamond pyramid) Microhardness Tests Applied loads : between 1 and 1000 g. Careful specimen surface preparation (grinding and polishing) Designated by HK and HV, suited for small, selected specimen regions; Knoop is used for testing brittle materials such as ceramics. (4) Other hardness-testing techniques ultrasonic microhardness, dynamic (Scleroscope), durometer (for plastic and elastomeric materials), scratch hardness tests.

Superficial tests are frequently performed on thin specimens. designated by HR, e.g., 80 HRB : Rockwell hardness of 80 on the B scale; 60 HR30W : superficial hardness of 60 on the 30W scale. For each scale, hardness may range up to 130; above 100 or drop below 20 : inaccurate, should utilize the next harder or softer scale. Specimen thickness should be at least ten times the indentation depth, at least three indentation diameters between the center of one indentation and the specimen edge, or to the center of a second indentation smooth flat surface T 6.4 T 6.5

◎ Hardness Conversion a comprehensive conversion scheme has not been devised. Hardness conversion data have been determined experimentally and found to be independent on material type and characteristics. F 6.18 ◎ Correlation Between Hardness And Tensile Strength Both tensile strength and hardness are indicators of a metals’s resistance to plastic deformation. Consequently, they are roughly proportional, (6.20a) (6.20b) F 6.19

◎ Elastic (young’s) Modulus As discussed previously U  F and 2U 2  F  (2.5-2) U   a (2.5-3)