CE205 MATERIALS SCIENCE PART_6 MECHANICAL PROPERTIES

Transcription

1 CE205 MATERIALS SCIENCE PART_6 MECHANICAL PROPERTIES Dr. Mert Yücel YARDIMCI Istanbul Okan University Deparment of Civil Engineering

2 Chapter Outline Terminology for Mechanical Properties The Tensile Test: Stress-Strain Diagram Properties Obtained from a Tensile Test True Stress and True Strain The Bend Test for Brittle MaterialS 2

3 Questions to Think About Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point do dislocations cause permanent deformation? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them? Ceramic Materials: What special provisions/tests are made for ceramic materials? 3

4 BASIC TYPES OF LOADING Tensile Compressive Shear Torsion 4

5 STRESS AND STRAIN CONCEPTS (For Compression and Tension) 5

6 STRESS AND STRAIN CONCEPTS (For Shear and torsion) 6

7 The role of structural engineers is to determine stresses and stress distributions within members that are subjected to well-defined loads If a load is static or changes relatively slowly with time and is applied uniformly over a cross section or surface of a member, the mechanical behavior may be ascertained by a simple stress strain test; these are most commonly conducted for metals at room temperature. 7

8 Stress-Strain Test Tensile test specimen d=12.8mm Tensile testing machine One of the most common mechanical stress strain tests is performed in tension. The tension test can be used to ascertain several mechanical properties of materials that are important in design A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of a specimen 8

9 The tensile testing machine is designed to elongate the specimen at a constant rate, and to continuously and simultaneously measure the instantaneous applied load (with a load cell) and the resulting elongations (using an extensometer). A stress strain test typically takes several minutes to perform and is destructive; that is, the test specimen is permanently deformed and usually fractured. 9

10 The output of such a tensile test is recorded (usually on a computer) as load or force versus elongation. These load deformation characteristics are dependent on the specimen size. For example, it will require twice the load to produce the same elongation if the cross-sectional area of the specimen is doubled. To minimize these geometrical factors, load and elongation are normalized to the respective parameters of engineering stress and engineering strain. Engineering stress Engineering strain 10

11 Engineering Stress and Strain Cross-sectional area A F F x x Stress σ = F / A L 0 x F L 0 x L 1 F Elongation ΔL = (L 1 L 0 ) Strain ε = ΔL / L 0 F is the instantaneous load applied perpendicular to the specimen cross section (N). A 0 and is the original crosssectional area before any load is applied (mm 2 ) Engineering stress (stress) is in MPa (=1N/mm 2 =10 6 N/m 2 ) L 0 is the original length before any load is applied. L 1 is the instantaneous length.

12 Tensile Test 12

13 Important Mechanical Properties from a Tensile Test Young's Modulus (Modulus of Elasticity): This is the slope of the linear portion of the stress-strain curve, it is usually specific to each material; a constant, known value. Yield Strength: This is the value of stress at the yield point, calculated by plotting young's modulus at a specified percent of offset (usually offset = 0.2%). Ultimate Tensile Strength: This is the highest value of stress on the stress-strain curve. Percent Elongation: This is the change in gauge length divided by the original gauge length. 13

14 Terminology Load - The force applied to a material during testing. Strain gage or Extensometer - A device used for measuring change in length (strain). Engineering stress - The applied load, or force, divided by the original cross-sectional area of the material. Engineering strain - The amount that a material deforms per unit length in a tensile test.

15 Stress (σ) Strain Stress Relation P P Strain (ε)

16 Stress (σ) Strain Stress Relation P P Strain (ε)

17 Stress (σ) Strain Stress Relation P P Strain (ε)

18 Stress (σ) Plastic deformation Strain Stress Relation P Elastic def. P Strain (ε)

19 Stress (σ) Plastic deformation Strain Stress Relation P Elastic def. P Strain (ε)

20 Stress (σ) Plastic deformation Strain Stress Relation P Elastic def. P Strain (ε)

21 Plastic deformation Stress (σ) Modulus of Elasticity or Young Modulus (E) Stress and strain are linearly proportional upto an elastic limit through the relationship Hooke s Law Elastic def. Strain (ε) σ = E ε The constant of proportionality E (GPa) is the modulus of elasticity, or Young s modulus. For most typical metals the magnitude of this modulus ranges between 45 Gpa, for magnesium, and 407 GPa, for tungsten. It is about 200 GPa for structural steel The slope of this linear segment corresponds to the modulus of elasticity E

22 E modulus may be thought of as stiffness, or a material s resistance to elastic deformation. The greater the modulus, the stiffer the material, or the smaller the elastic strain that results from the application of a given stress. The modulus is an important design parameter used for computing elastic deflections. 22

23 Values of the modulus of elasticity for ceramic materials are about the same as for metals; for polymers they are lower. These differences are a direct consequence of the different types of atomic bonding in the three materials types. 23

24 Elastic Deformation σ σ σ ε Lineer elastic ε Non- L i n e e r e l a s t i c ε Deformation in which stress and strain are proportional is called elastic deformation. There is no permanent deformation on the elastic material after unloading!

25 Elastic Deformation Cast iron, concrete, many polymers For this nonlinear behavior, either tangent or secant modulus is normally used. Tangent modulus is taken as the slope of the stress strain curve at some specified level of stress, while secant modulus represents the slope of a secant drawn from the origin to some given point of the s curve 25

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28 Elastic Deformation 1. Initial 2. Small load 3. Unload bonds stretch return to initial F Elastic means reversible. 28

29 Plastic Deformation (Metals) 1. Initial 2. Small load 3. Unload F Plastic means permanent. linear elastic plastic linear elastic 29

30 Typical stress-strain behavior for a metal showing elastic and plastic deformations, the proportional limit P and the yield strength σ y, as determined using the strain offset method (where there is noticeable plastic deformation). P is the gradual elastic to plastic transition. 30

31 Yield Stress & Strain in different metallic materials presenting and not presenting appearent yield point 31

32 Poisson s Ratio Poisson s ratio is defined as the ratio of the lateral and axial strains. metals υ = ~ 0.33 ceramics (concrete) υ = ~ 0.25 Polymers υ = ~ 0.40 Max value is 0.5 (incompressible material; rubber) 32

33 Anelasticity Upto now it has been assumed that; Elastic deformation is time independent that is, that an applied stress produces an instantaneous elastic strain that remains constant over the period of time the stress is maintained. Upon release of the load the strain is totally recovered that is, that the strain immediately returns to zero. In most engineering materials, however, there will also exist a time-dependent elastic strain component. 33

34 Anelasticity In most engineering materials, however, there will also exist a time-dependent elastic strain component. That is, 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. It is due to time-dependent microscopic and atomistic processes that are attendant to the deformation. For metals the anelastic component is normally small and is often neglected. However, for some polymeric materials its magnitude is significant; in this case it is termed viscoelastic behavior, which will be the topic of next lectures. 34

35 Plastic Deformation (Permanent deformation) From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors. After removal of the stress, the large number of atoms that have relocated, do not return to original position. Yield strength is a measure of resistance to plastic deformation. 35

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37 (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Localized deformation of a ductile material during a tensile test produces a necked region. The image shows necked region in a fractured sample

38 Ductile failure (The fracture surface is more tortuous) Brittle failure (Fracture surface is very sharp and smooth) 38

39 Permanent Deformation Permanent deformation for metals is accomplished by means of a process called slip, which involves the motion of dislocations. Most structures are designed to ensure that only elastic deformation results when stress is applied. A structure that has plastically deformed, or experienced a permanent change in shape, may not be capable of functioning as intended. 39

40 Yield Strength, y y tensile stress, p = engineering strain, 40

41 BASIC PROPERTIES of STRESS-STRAIN DIAGRAM of METALS OA Portion: Elastic Region. The stress is linearly proportional to the strain in this region. or σ σ = E ε E = ε σ σ e A B C D O ε e ε 41

42 AB Portion: Non-lineer elastic or σ Elastic-plastic transition region The point A defines the initial σ B y deviation from linearity of the stress-strain curve. This point A sometimes is called as propotional limit of the material. Some materials exhibits non-lineer elastic behavior in between proportional limit (A) and yield limit (Point B). O Yield point can be determined as the intersection of the curve and a straight line drawn as parallel to elastic portion of the curve at a specified strain offset of It is assumed that there is no permanent deformation on the material if the sample is unloaded before reaching the yield point. C D ε 42

43 BC Portion After yielding, the stress necessary to continue plastic deformation in metals increases to a maximum (point C) and then decreases to the eventual fracture (point D). The tensile strength is the stress at the maximum on the engineering stress strain curve. σ A B C D If the material in unloaded in between BC, the curve will follow back with the same E This corresponds to the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, fracture will result. O The maximum stress which the material can support without breaking is called tensile strength. ε 43

44 CD Portion (Necking) All deformation up to point C is uniform throughout the narrow region of the tensile specimen. However, at this maximum stress, a small constriction or neck begins to form at some point, and all subsequent deformation is confined at this neck. This phenomenon is termed necking and fracture ultimately occurs at the neck. The fracture strength corresponds to the stress at fracture (Point D). O A B C D ε 44

45 Stress-strain behavior found for some steels with yield point phenomenon. 45

46 Yield Stress & Strain in different metallic materials 46

47 T E N S I L E P R O P E R T I E S 47

48 Yield Strength: Comparison Room T values a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered 48

49 TENSILE RESPONSE OF POLYMERIC MATERIALS In an undeformed thermoplastic polymer tensile sample, (a) the polymer chains are randomly oriented. (b) When a stress is applied, a neck develops as chains become aligned locally. The neck continues to grow until the chains in the entire gage length have aligned. (c) The strength of the polymer is increased 49

50 Tensile Strength: Comparison Room T values Based on data in Table B4, Callister 6e. 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. 50

51 See tensile responses of various types of metalic and polymeric materials

52 Example 1 Tensile Testing of Magnesium A specimen of magnesium having a rectangular cross section of dimensions 3.2 mm x 19.1 mm is deformed in tension. Using the given load elongation data answer the questions below. a) Plot the data as engineering stress vs. engineering strain. b) Compute the modulus of elasticity. c) Determine the yield strength at a strain offset of d) Determine the tensile strength of this material. 52

53 Example 1 SOLUTION 53

54 Ductility, %EL Ductility is a measure of the plastic deformation that has been sustained at fracture: l f lo % EL = x100 l o A material that suffers very little plastic deformation is brittle. Ao Af Another ductility measure: % AR = x100 A Ductility may be expressed as either percent elongation (% plastic strain at fracture) or percent reduction in area. %AR > %EL is possible if internal voids form in neck. 54 o

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56 Toughness is the ability to absorb energy up to fracture. Toughness Lower toughness: ceramics Higher toughness: metals tough material has strength and ductility. Approximated by the area under the stress-strain curve. 56

57 Toughness Energy to break a unit volume of material Approximate by the area under the stress-strain curve. Engineering tensile stress, smaller toughness (ceramics) larger toughness (metals, PMCs) smaller toughnessunreinforced polymers Engineering tensile strain, 21

58 Hooke's Law: Linear Elastic Properties = E y x Poisson's ratio: metals: n ~ 0.33 ceramics: n ~0.25 polymers: n ~0.40 n = x / y Modulus of Elasticity, E: (Young's modulus) Units: E: [GPa] or [psi] n: dimensionless 58

59 Engineering Strain Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed tensile stress. Strain is dimensionless. 59

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61 Poisson s Ratio If the applied stress is uniaxial (only in the z direction), and the material is isotropic, then A parameter termed Poisson s ratio is defined as the ratio of the lateral and axial strains, or Theoretically, Poisson s ratio for isotropic materials should be ¼. The maximum value is For isotropic materials, shear and elastic moduli are related to each other and to Poisson s ratio according to G is about 0.4E 61

62 Elastic Constants = E t = G avg = g K D V Vo Normal Shear Volumetric Stresses Strains 62

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64 10 cm cm SAMPLE PROBLEM Dimensions of the cube before and after the load application of kgf are given below. Determine modulus of elasticity (E) and the Poisson s ratio (υ) if the material response is entirely elastic and the material is isotropic. P=10000 kgf 10 cm cm Before loading After loading 64

65 P=10000 kgf Δd/2= cm P=10000kgf σ= 10*10 Δl/2=0.002 cm ε long = = 100 kgf/cm 2 Δl l = = cm E= σ ε = 100 = kgf/cm POISSON S RATIO: 10 cm kgf ε lat = Δd d = = ν = =

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68 True Stress and True Strain True stress The load divided by the actual cross-sectional area of the specimen at that load. True strain The strain calculated using actual and not original dimensions, given by ε t ln(l/l 0 ). The relation between the true stresstrue strain diagram and engineering stress-engineering strain diagram. The curves are identical to the yield point.

69 Stress-Strain Results for Steel Sample (1psi= MPa) 69

70 Young s Moduli: Comparison Diamond Si carbide 400 Tungsten Al oxide Carbon fibers only Molybdenum Si nitride E(GPa) Steel, Ni CFRE( fibers)* 200 Tantalum <111> Platinum Si crystal Cu alloys <100> Aramid fibers only 100 Zinc, Ti 80 Silver, Gold Aluminum Glass-soda AFRE( fibers)* 60 Glass fibers only Magnesium, 40 Tin GFRE( fibers)* Concrete 20 GFRE* 10 9 Pa Composite data based on CFRE* Graphite GFRE( fibers)* 10 8 CFRE( fibers)* 6 AFRE( fibers)* Polyester 4 PET PS PC Epoxy only Metals Alloys Graphite Ceramics Semicond Polymers PP HDPE PTFE LDPE Composites /fibers Wood( grain) reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 70

71 Example 3: True Stress and True Strain Calculation

72 Mechanical Behavior of Ceramics The stress-strain behavior of brittle ceramics is not usually obtained by a tensile test. Because; It is difficult to prepare a tensile test specimen with a specific geometry. It is difficult to grip brittle materials without fracturing them. Ceramics fail after roughly 0.1% strain; Therefore the specimen have to be perfectly aligned, it is very difficult... 72

73 For Brittle Materials, Bending test is used in determining tensile strength. Bending test - Application of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load. Flexural strength or modulus of rupture -The stress required to fracture a specimen in a bend test. Flexural modulus - The modulus of elasticity calculated from the results of a bend test, giving the slope of the stress-deflection curve.

74 BENDING TEST (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. (a) The bend test often used for measuring the strength of brittle materials, and (b) the deflection δ obtained by bending

75 (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. The stress-strain behavior of brittle materials compared with that of more ductile materials

76 Flexural Strength Schematic for a 3-point bending test. Able to measure the stress-strain behavior and flexural strength of brittle ceramics. Flexural strength (modulus of rupture or bend strength) is the stress at fracture. 76

77 MEASURING ELASTIC MODULUS FROM BENDING TEST cross section d b rectangular F L/2 L/2 = midpoint deflection Determination of E modulus from bending test is Possible only in the elastic region of the loading. E = F L 3 4bd 3 For rectangular Cross-section 23

78 THREE-POINT BENDING vs. FOUR-POINT BENDING Three-point bending P P/2 P/2 Four-point bending L/2 L/2 L/3 L/3 L/3 L L Three-point bending and four-point bending test on prismatic samples is uased in determining the flexural properties of brittle materials (as concrete) 78

79 THREE-POINT BENDING vs. FOUR-POINT BENDING Three-point bending P P/2 P/2 Four-point bending h L/2 L/2 L/3 L/3 L/3 b [V] [M] + f flex = L P/2 - (P.L/4) -P/2 [V] + P/2 [M] P. L 2. b. h 2 f flex = L P. L b. h 2 - (P.L/6) -P/2 79

80 THREE-POINT BENDING vs. FOUR-POINT BENDING Three-point bending P P/2 P/2 Four-point bending L/2 L/2 L/3 L/3 L/3 L L The peak stress in 3-point bending test is at the specimen midpoint as concentreted stress. The peak stress in 4-point bending test is at an extended region of the specimen in the mid-region. Hence, potantial to encounter a defect or flaw on the maximum stress region is high. Therefore testing the materials with 4-point bending provides more realistic results particularly in heteregeneous materials like concrete. 80

81 Stress-Strain Behavior: Elastomers 3 different responses observed in polymers: A brittle failure B plastic failure C - highly elastic (elastomer) --brittle response (microstructure: aligned chain, cross linked & networked case) --plastic response (microstructure: semi-crystalline case) 81