MECHANICAL PROPERTIES AND TESTS Materials Science
Stress Stress is a measure of the intensity of the internal forces acting within a deformable body. Mathematically, it is a measure of the average force per unit area of a surface within a the body on which internal forces act The SI unit for stress is Pascal (symbol Pa), which is equivalent to one Newton (force) per square meter (unit area). Three types of stresses -> Tensile; Compressive; Shear
Mechanism of Stress (Tensile)
Tensile, Compressive and Shear Stresses A1 Stress???
Strain Strain is deformation of a physical body under the action of applied forces It is the geometrical measure of deformation representing the relative displacement between particles in the material body Strain is a dimensionless quantity Strain accounts for elongation, shortening, or volume changes, or angular distortion Normal stress causes normal strain (tensile or compressive) Shear strain is defined as the change in right angle ( or angle change between two originally orthogonal material lines)
Types of Strains tensile load produces an elongation and positive linear strain. compressive load produces contraction and a negative linear strain. torsional deformation
Tensile Test and Stress-strain relationship
Tensile Test Used for determining UTS, yield strength, %age elongation, and Young s Modulus of Elasticity The ends of a test piece are fixed into grips. The specimen is elongated by the moving crosshead; load cell and extensometer measure, respectively, the magnitude of the applied load and the elongation
Stress-Strain Relationship
For structural applications, the yield stress is usually a more important property than the tensile strength, since once the yield stress has passed, the structure has deformed beyond acceptable limits.
Important Terms (Stress-Strain Rel.) Elastic Limit -> Maximum amount of stress up to which the deformation is absolutely temporary Proportionality Limit -> Maximum stress up to which the relationship between stress & strain is linear. Hooke s Law -> Within elastic limit, the strain produced in a body is directly proportional to the stress applied. ζ = E ε
Important Terms (Stress-Strain Rel.) Young s Modulus of elasticity - > the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds Elasticity -> the tendency of a body to return to its original shape after it has been stretched or compressed Yield Point -> the stress at which a material begins to deform plastically
Important Terms (Stress-Strain Rel.) Plasticity -> the deformation of a material undergoing non-reversible changes of shape in response to applied forces Ultimate Strength -> It is the maxima of the stress-strain curve. It is the point at which necking will start. Necking -> When tensile deformation becomes localized in a small region of the material, the deformation mode is called necking
Important Terms (Stress-Strain Rel.) Fracture Point -> The stress calculated immediately before the fracture. Ductility -> The amount of strain a material can endure before failure. Ductility is measured by percentage elongation or area reduction
Important Terms (Stress-Strain Rel.) A knowledge of ductility is important for two reasons: 1. It indicates to a designer the degree to which a structure will deform plastically before fracture. 2. It specifies the degree of allowable deformation during fabrication
Engineering stress strain behavior for Iron at three temperatures
Resilience 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 (U r ) is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding.
Resilience Assuming a linear elastic region For SI units, this is joules per cubic meter (J/m 3, equivalent to Pa) Thus, resilient materials are those having high yield strengths and low moduli of elasticity; such alloys would be used in spring applications
EXAMPLE PROBLEM A piece of copper originally 305mm (12 in.) long is pulled in tension with a stress of 276MPa (40,000psi). If the deformation is entirely elastic, what will be the resultant elongation? Magnitude of E for copper from Table 6.1 is 110GPa
Poisson s Ratio Poisson s ratio is defined as the ratio of the lateral and axial strains Theoretically, Poisson s ratio for isotropic materials should be 1/4; furthermore, the maximum value for ν is 0.50 For isotropic materials, shear and elastic moduli are related G=0.4E
EXAMPLE PROBLEM 6.2 A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10mm. Determine the magnitude of the load required to produce a 0.0025mm change in diameter if the deformation is entirely elastic. For the strain in the x direction:
EXAMPLE PROBLEM 6.2
True stress = load/ actual area in the necked-down region, continues to rise to the point of fracture, in contrast to the engineering stress. σ = F/A o ε = (l i -l o /l o ) σt = F/A i ε T = ln(l i /l o )
True Stress and Strain The decline in the stress necessary to continue deformation past the point M, indicates that the metal is becoming weaker. Material is increasing in strength.
True Stress and Strain True stress ζ T is defined as the load F divided by the instantaneous cross-sectional area A i over which deformation is occurring True strain Є T is defined as: n= slope of True Stress-strain curve
True Stress and Strain If no volume change occurs during deformation that is, if A i l i = A 0 l 0 Then true and engineering stress and strain are related according to The equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, crosssectional area, and gauge length measurements
EXAMPLE PROBLEM 6.4 A cylindrical specimen of steel having an original diameter of 12.8mm is tensile tested to fracture and found to have an engineering fracture strength σ f of 460MPa. If its cross-sectional diameter at fracture is 10.7mm, determine: (a) The ductility in terms of percent reduction in area (b) The true stress at fracture Ductility is computed as
EXAMPLE PROBLEM 6.4 True stress is defined by Equation where the area is taken as the fracture area A f However, the load at fracture must first be computed from the fracture strength as And the true stress is calculated as:
TOUGHNESS It is a property of material by virtue of which it resists against fracture under impact loads. Toughness is the resistance to fracture of a material when stressed Mathematically, it is defined as the amount of energy per volume that a material can absorb before rupturing Toughness can be determined by measuring the area (i.e., by taking the integral) underneath the stress-strain curve
Toughness (contd ) Toughness = Where ε is strain ε f is the strain upon failure ζ is stress The Area covered under stress strain curve is called toughness
Toughness (contd ) Toughness is measured in units of joules per cubic meter (J/m 3 ) in the SI system Toughness and Strength -> A material may be strong and tough if it ruptures under high forces, exhibiting high strains Brittle materials may be strong but with limited strain values, so that they are not tough Generally, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupture
Ductile Material Uniform deformation Neck begins to form max. load Deformation concentrated in neck Fracture
Ductile Failure Copper Duralumin Ductile materials exhibit significant permanent deformation after yielding before fracture.
Brittle Materials Exhibit very little deformation after yielding and fracture immediately
As temperature increases: Ductility and toughness increase. Yield stress and the modulus of elasticity decrease. Temperature also affects the strain-hardening exponent of most metals, in that n decreases as temperature increases. Temperature Effects
HARDENING An increase in s y due to plastic deformation. s s y 1 s y 0 large hardening small hardening Curve fit to the stress-strain response: e s = K ( e ) n T T hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers) true stress (F/A) true strain: ln(l/l o ) 44
Design or Safety Factors Design uncertainties mean we do not push the limit. Factor of safety, N s working = s y N Often N is between 1.2 and 4 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 5. s 220,000N ( ) d 2 / 4 working 5 = s y N d = 0.067 m = 6.7 cm 1045 plain carbon steel: s y = 310 MPa TS = 565 MPa F = 220,000N 45 d L o
Hardness Hardness is the property of material by virtue of which it resists against surface indentation and scratches. Macroscopic hardness is generally characterized by strong intermolecular bonds Hardness is dependent upon strength and ductility Common examples of hard matter are diamond, ceramics, concrete, certain metals, and superhard materials (PcBN, PcD, etc)
Hardness Tests (BRINELL HARDNESS TEST) Used for testing metals and nonmetals of low to medium hardness The Brinell scale characterizes the indentation hardness of materials through the scale of penetration of an indenter, loaded on a material test-piece A hardened steel (or cemented carbide) ball of 10mm diameter is pressed into the surface of a specimen using load of 500, 1500, or 3000 kg.
BRINELL HARDNESS TEST P where: P = applied force (kgf) D = diameter of indenter (mm) d = diameter of indentation (mm) The resulting BHN has units of kg/mm 2, but the units are usually omitted in expressing the numbers
Rockwell Hardness Test A cone shaped indenter or small diameter ball (D = 1.6 or 3.2mm) is pressed into a specimen using a minor load of 10kg Then, a major load of 150kg (at max) is applied The additional penetration distance d is converted to a Rockwell hardness reading by the testing machine. This is an advantage as we don t need to make calculations.
Rockwell Hardness Test The differences in load and indenter geometry provide various Rockwell scales for different materials. The most common scales are listed in table below: Diamond Steel Diamond
Vickers Hardness Test Uses a pyramid shaped indenter made of diamond. It is based on the principle that impressions made by this indenter are geometrically similar regardless of load. The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the indenter, and the indenter can be used for all materials irrespective of hardness Indenter= diamond Accordingly, loads of various sizes are applied, depending on the hardness of the material to be measured
Vickers Hardness Test Where: F = applied load (kg) D = Diagonal of the impression made the indenter (mm) The hardness number is determined by the load over the surface area of the indentation and not the area normal to the force
Vickers Hardness Test
Vickers Hardness Test
Knoop Hardness Test It is a microhardness test - a test for mechanical hardness used particularly for very brittle materials or thin sheets A pyramidal diamond point is pressed into the polished surface of the test material with a known force, for a specified dwell time, and the resulting indentation is measured using a microscope Length-to-width ratio of the pyramid is 7:1
Knoop Hardness Test (contd ) The indenter shape facilitates reading the impressions at lighter loads HK = Knoop hardness value; F = load (kg); D = long diagonal of the impression (mm)
Hardness of Metals and Ceramics
Hardness of Polymers
Conversion of Hardness on Scales
IMPACT TEST
Impact Fracture Testing Fracture behavior depends on many external factors: Strain rate Temperature Stress rate Impact testing is used to ascertain the fracture characteristics of materials at a high strain rate and a triaxial stress state. In an impact test, a notched specimen is fractured by an impact blow, and the energy absorbed during the fracture is measured. There are two types of tests Charpy impact test and Izod impact test.
Impact Test: The Charpy Test The ability of a material to withstand an impact blow is referred to as notch toughness. The energy absorbed is the difference in height between initial and final position of the hammer. The material fractures at the notch and the structure of the cracked surface will help indicate whether it was a brittle or ductile fracture.
Impact Test (Charpy) Data for some of the Alloys In effect, the Charpy test takes the tensile test to completion very rapidly. The impact energy from the Charpy test correlates with the area under the total stress-strain curve (toughness)
Impact Test: The Izod Test Generally used for polymers. Izod test is different from the Charpy test in terms of the configuration of the notched test specimen
Impact Test (Izod) Data for various polymers
Impact Tests: Test conditions The impact data are sensitive to test conditions. Increasingly sharp notches can give lower impact-energy values due to the stress concentration effect at the notch tip The FCC alloys generally ductile fracture mode The HCP alloys generally brittle fracture mode Temperature is important The BCC alloys brittle modes at relatively low temperatures and ductile mode at relatively high temperature
Transition Temperatures As temperature decreases a ductile material can become brittle - ductile-to-brittle transition The transition temperature is the temp at which a material changes from ductile-to-brittle behavior Alloying usually increases the ductile-to-brittle transition temperature. FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals.
Ductile to Brittle Transition The results of impact tests are absorbed energy, usually as a function of temperature. The ABSORBED ENERGY vs. TEMPERATURE curves for many materials will show a sharp decrease when the temperature is lowered to some point. This point is called the ductile to brittle transition temperature (relatively narrow temperature range). A typical ductile to brittle transition as a function of temperature. The properties of BCC carbon steel and FCC stainless steel, where the FCC crystal structure typically leads to higher absorbed energies and no transition temperature.
Transition Temperatures BCC metals have transition temperatures FCC metals do not Can use FCC metals at low temperatures (eg Austenitic Stainless Steel)
Effect of Temperature on Properties Generally speaking, materials are lower in strength and higher in ductility, at elevated temperatures
Hot Hardness A property used to characterize strength and hardness at elevated temperatures is Hot Hardness It is the ability of a material to retain its hardness at elevated temperatures
Numerical Problems Problems 6.3 to 6.9; 6.14 to 6.23; 6.25 to 6.33; 6.46 to 6.48
Self Study
COMPRESSION Compression test is where specimen is subjected to a compressive load Carried out by compressing a solid cylindrical specimen between two well-lubricated flat dies Slender specimens can buckle during this test Cross-sectional area of the specimen will change along its height and obtaining the stress strain curves in compression is difficult When results of compression and tension tests on ductile metals are compared, true stress true strain curves coincide
COMPRESSION Behavior is not true for brittle materials as they are stronger and more ductile in compression than in tension When a metal is subjected to tension into the plastic range, the yield stress in compression is lower than that in tension Phenomenon known as Bauschinger effect
COMPRESSION Disk Test Disk test is where a disk is subjected to compression between two hardened flat plates Tensile stresses develop perpendicular to the vertical centerline along the disk Fracture begins and the disk splits in half vertically Tensile stress in the disk is P = load at fracture d = diameter of the disk t = thickness
TORSION
TORSION A workpiece may be subjected to shear strains Torsion test can be used to determine properties of materials in shear Performed on a thin tubular specimen The shear stress can be calculated from the formula T = torque r = average radius of the tube t = thickness of the tube at its narrow section
TORSION Shear strain can be calculated from l = length of tube subjected to torsion Φ = angle of twist in radians Ratio of shear stress to the shear strain in the elastic range is called shear modulus, or modulus of rigidity, G G is a quantity related to the modulus of elasticity E
BENDING
Bending Preparing specimens from brittle materials, such as ceramics and carbides, is difficult because of problems in shaping and machining them to certain dimensions. The most common test for brittle materials is the bend or flexure test.
Bend / Flexure Test Rectangular specimen supported at its ends. Load is applied vertically at 1 or 2 pts. The stress at fracture in bending is known as the modulus of rupture, flexural strength, or transverse rupture strength.
Section 6.6 The Bend Test for Brittle Materials Bend 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.
The stress-strain behavior of brittle materials compared with that of more ductile materials
(a) The bend test often used for measuring the strength of brittle materials, and (b) the deflection δ obtained by bending