Mechanical Properties of Materials

1. Mechanical Properties of Materials Chapter 7 and 8 ari.cankaya.edu.tr/~ebiber/ie114/week-8.ppt, 13 dec 2010

2. Stress and Strain: If a load applied to the material is static or changing slowly with time and it is applied uniformly on the surface of interest, then we can test the behavior of the material under applied load by a test called “stress-strain” test. The ways of applying load are summarized in the figure below:

3. Tension test is the most common. A typical specimen is: Typically L=4 x d (diameter) L=2 in (50 mm) Test continues usually till the specimen is permanantly deformed or fractured.

4. The load and deformation relationship depends on the geometrical factors of the specimen; therefore, normalization of them to geometric dimensions are helpful in comparing the materials. Engineering stress: where F= perpendicular force applied to the surface uniformly. A0= the original cross sectional area before loading unit of σ is N/m2 or lbf/in2 (psi). Engineering strain: where li =instantaneous length l0=initial length strain is unitless and it is sometimes expressed in percentage by multiplying the value with 100.

5. Compression test is not very common. It is usually used if the material application consists of compressive force system or if the material is brittle under tensile force. Compressive force is negative by convention yielding negative stress and strain. Shear and torsional tests: Shear stress: where F=force parallel to the surface shear stress shear strain is γ, calculated by tangent of strain angle θshown in the figure.

6. Torsion is a variation of pure shear, wherein a structural member is twisted like in machine axles and drive shafts. • is the angle of twist. • is a function of torque T while  is a function of . This test is usually performed on cylindrical shafts or tubes.

7. Stress state is a function of the orientations of the planes. For example; pp’ plane is oriented at an angle of ө. The stress on this plane is not a pure tensile stress anymore.

8. Hooke’s Law: Elastic Deformation: is observed when stress and strain are proportional. E=modulus of elasticity or Young’s modulus (GPa or psi) for metals E=45-407 GPa. for polymers E=0.007-4 GPa E is a measure of material’s stiffness or materials 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. Elastic deformation is nonpermanent.

9. There are materials (gray cast iron, concrete, and many polymers) for which this initial elastic portion of the stress-strain curve is not linear. In this case either tangent or secant modulus is normally used (shown in the figure above).

10. Elastic strain is due to small changes in interatomic spacing and streching the interatomic bonds. Therefore the magnitude of E is a measure of the resistance to separation of adjacent atoms/ions/molecules. This modulus is proportional to the slope of the F versus r curve:

11. The imposition of compressive, shear or torsional stresses evokes elastic behavior as well. For low shear stress levels: G= shear modulus We assume that the elastic deformation is time independent. However, there is a time-dependent elastic strain component. Elastic deformation will continue after the stress application and during the complete recovery. This time-dependent elastic behavior is known as anelasticity. For metals anelastic component is normally small and is usually neglected. For polymers, its magnitude may be significant (viscoelastic behavior).

12. If the material is isotropic and applied stress is uniaxial (only in z diraction): • = Poisson’s ratio (theoretical value =0.25; for many metals b/w 0.25-0.35.) x = y

13. Many materials are elastically anisotropic. This means the elastic behavior changes with crystallographic direction. Therefore to characterize the elastic properties of the material, several E values should be reported for specific directions. In fact even for isotropic materials, at least two constants should be given. Mechanical Behavior of Materials Metals: Elastic deformation of metallic materials is usually upto strains of about 0.005. Beyond this point, the stress and strain are no longer proportional and deformation of the material becomes permanent and nonrecoverable. This is called plastic deformation. Plastic deformation corresponds to the breaking of bonds with original atom neighbors and reforming bonds with new neighbors. This permanent deformation for metals is accomplished by means of a process called slip, which involves the motion of dislocations. For isotropic materials:

14. Tensile properties of Metals: • Yielding and yield strength Most structures are designed to ensure that only elastic deformation will result when a stress is applied. Therefore it is useful to know the stress level at which plastic deformation begins or where the yielding occurs.

15. If the transition from elastic to plastic behavior is gradual, the point of yielding may be determined as the initial departure from linearity (P=proportional limit). In cases where it is difficult to determine this point (P point) precisely, a conventional approach is used. A straight line is constructed parallel to the elastic deformation line at a strain offset usually 0.002. The stress correspoding to this point is yield strength (y). For the materials having nonlinear elastic region, yield strength is defined as the stress required to produce some amount of strain (=0.005). For the materials showing a behavior like in Figure 7.10b, the yield strength is the average of the upper and lower limits. The magnitude of yield strength is a measure of material’s resistance to plastic deformation. Yield strength may range from 35 MPa to 1400 MPa.

16. 2) Tensile strength: M is the stress at the maximum point of the stress-strain curve. F is the fracture point. necking Tensile strength may vary between 50 MPa to as high as 3000 MPa.

17. 3) Ductility: It is a measure of the degree of plastic deformation that has been sustained at fracture. A material that experiences very little or no plastic deformation upon fracture is termed brittle. Quantitatively: lf and Af are length and area at the fracture. Ductility of materials is important for at least two reasons: (i) it indicates the degree to which a structure will deform plastically, (ii) it specifies the degree of allowable deformation during fabrication. Fracture strain of brittle materials is about 5%.

19. The mechanical properties of the materials are sensitive to any prior deformation, presence of impurities, heat treatment. The modulus of elasticity is one mechanical parameter that is insensitive to these treatments. Similar to modulus of elasticity, the magnitudes of both yield and tensile strengths decline with increasing temperature.

20. 4) Resilience: is the capacity of a material to absorb energy when it is deformed elastically and then upon unloading to have this energy recovered. Modulus of resilience (Ur) = strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding. assuming a linear elastic region:

21. 5) Toughness: is a mechanical term. It is a measure of the ability of a material to absorb energy up to fracture. For dynamic loading conditions and when a notch is present, notch toughness is assessed. Fracture toughness is material’s resistance to fracture when a crack is present. For low strain rate situation, the area under - curve up to the point of fracture corresponds to toughness. For a material to be tough, it must display both strength and ductility and often ductile materials are tougher than brittle ones.

22. This decrease is not because of reducing strength, it is because of changing geometric properties. True stress and strain: Sometimes it is more meaningful to use a true stress-true strain curve.

23. True stress: True strain: If there is no change in volume: these equations are valid up to the onset of necking, beyond necking actual stress or strain has to be calculated using actual load and area/length.

24. With the formation of necking, axial stress is no longer axial instead we observe a complex stress state within the neck region. As a result the correct stress (axial) within the neck is slightly lower than the stress computed from the applied load and neck X-sectional area. for some metals and alloys, the region of true stress and ture strain curve from the onset of plastic deformation to the beginning of necking: K and n are constants (Table 7.3).

25. Elastic strain recovery: parallel to elastic deformation line For compression loadings, there will be no maximum since no necking occurs. The mode of fracture is different for this case.

26. Hardness: is a measure of a material’s resistance to localized plastic deformation. Measured hardnesses are relative (not absolute). Hardness tests are; • simple and inexpensive • test is nondestructive • other mechanical properties can be estimated from hardness data. Rockwell Hardness tests: (ASTM standard E 18) Several different scales can be used from possible combinations of various indenters and different loads. Indenters: spherical and hardened steel balls (1/16, 1/8, ¼, ½ in. diameter) and a conical diamond (Brale) intender. Hardness number is determined by the difference in depth of penetration resulting from the application of an initial minor load followed by a larger load. On the basis of minor and major loads there are two tests: Rockwell and superficial Rockwell tests.

27. 80 HRB = Rockwell hardness of 80 on b scale 60 HR30W= superficial hardness of 60 on 30W scale. For Rockwell: minor load is 10 kg and major loads are 60, 100, and 150 kg. For superficial Rockwell: minor load is 3 kg and 15, 30, and 45 kg are major loads. For each scale, hardness may range up to 130, however, as hardness number rise above 100 or drop below 20 on any scale, the accuracy of test decreases.

28. Knoop and Vickers test: A very small diamond indenter having pyramidal geometry is forced into the surface of the specimen.Applied loads=1-1000 g. the impression is analyzed by microscope and measured. The measurement is then converted to hardness number. Brinell hardness tests: The diameter of the hardened steel or tungsten carbide indenter is 10 mm. Applied Loads= 500-3000 kg.The diameter of resulting indentation on the surface is measured using a special low power microscope. the measurement is converted to hardness number.

30. Hardness Conversion:

31. For most steels: Correlations between hardness and tensile strength: Hardness and tensile strength are indicators of a metal’s resistance to plastic deformation.

32. Variability of material properties: There are numbers of factors causing uncertainities in the measured data: • measurement method • variations in the specimen fabrication procedures • operator • calibration of the apparatus. These variabilites affect the masurements accuracy and consistency.

33. Design and Safety Factors: In addition to variabilities of the material properties, the applications on the material also have many uncertanities. As a result, design allowances must be made to protect against unanticipated failure. Design stress: is calculated by multiplying calculated stress (using the maximum load) by a design factor N’. N’>1 Select a material with a yield strength at least as high as d. Safe stress or working stress can be used as an alternative to design stress. N=1.2-4.0