Tensile test and Stress-Strain Diagram Stress-Strain Diagram expresses a relationship between a load applied to a material and the deformation of the material, caused by the load . Stress-Strain Diagram is determined by tensile test. Tensile tests are conducted in tensile test machines, providing controlled uniformly increasing tension force, applied to the specimen. The specimen’s ends are gripped and fixed in the machine and its gauge length L 0 (a calibrated distance between two marks on the specimen surface) is continuously measured until the rupture. Test specimen may be round or flat in the cross-section. In the round specimens it is accepted, that L 0 = 5 * diameter. The specimen deformation (strain) is the ratio of the increase of the specimen gauge length to its original gauge length: δ = (L – L 0 ) / L 0 Tensile stress is the ratio of the tensile load F applied to the specimen to its original cross- sectional area S 0 : σ = F / S 0 The initial straight line (0P)of the curve characterizes proportional relationship between the stress and the deformation (strain). The stress value at the point P is called the limit of proportionality: σ p = F P / S 0 This behavior conforms to the Hook’s Law: σ = E*δ Where E is a constant, known as Young’s Modulus or Modulus of Elasticity.
Transcript
Tensile test and Stress-Strain Diagram Stress-Strain Diagram expresses a relationship between a load applied to a material and the deformation of the material, caused by the load . Stress-Strain Diagram is determined by tensile test. Tensile tests are conducted in tensile test machines, providing controlled uniformly increasing tension force, applied to the specimen. The specimen’s ends are gripped and fixed in the machine and its gauge length L0 (a calibrated distance between two marks on the specimen surface) is continuously measured until the rupture. Test specimen may be round or flat in the cross-section.
In the round specimens it is accepted, that L0 = 5 * diameter. The specimen deformation (strain) is the ratio of the increase of the specimen gauge length to its original gauge length: δ = (L – L0) / L0 Tensile stress is the ratio of the tensile load F applied to the specimen to its original cross-sectional area S0: σ = F / S0
The initial straight line (0P)of the curve characterizes proportional relationship between the stress and the deformation (strain). The stress value at the point P is called the limit of proportionality: σp= FP / S0 This behavior conforms to the Hook’s Law:
σ = E*δ Where E is a constant, known as Young’s Modulus or Modulus of Elasticity.
The value of Young’s Modulus is determined mainly by the nature of the material and is nearly insensitive to the heat treatment and composition. Modulus of elasticity determines stiffness - resistance of a body to elastic deformation caused by an applied force. The line 0E in the Stress-Strain curve indicates the range of elastic deformation – removal of the load at any point of this part of the curve results in return of the specimen length to its original value. The elastic behavior is characterized by the elasticity limit (stress value at the point E): σel= FE / S0 For the most materials the points P and E coincide and therefore σel=σp.
A point where the stress causes sudden deformation without any increase in the force is called yield limit (yield stress, yield strength): σy= FY / S0 The highest stress (point YU) , occurring before the sudden deformation is called upper yield limit . The lower stress value, causing the sudden deformation (point YL) is called lower yield limit. The commonly used parameter of yield limit is actually lower yield limit.
If the load reaches the yield point the specimen undergoes plastic deformation – it does not return to its original length after removal of the load.
Hard steels and non-ferrous metals do not have defined yield limit, therefore a stress, corresponding to a definite deformation (0.1% or 0.2%) is commonly used instead of yield limit. This stress is called proof stress or offset yield limit (offset yield strength): σ0.2%= F0.2% / S0 The method of obtaining the proof stress is shown in the picture.
As the load increase, the specimen continues to undergo plastic deformation and at a certain stress value its cross-section decreases due to “necking” (point S in the Stress-Strain Diagram). At this point the stress reaches the maximum value, which is called ultimate tensile strength (tensile strength): σt= FS / S0 Continuation of the deformation results in breaking the specimen - the point B in the diagram.
The actual Stress-Strain curve is obtained by taking into account the true specimen cross-section instead of the original value.
Other important characteristic of metals is ductility - ability of a material to deform under tension without rupture. Two ductility parameters may be obtain from the tensile test:
Relative elongation - ratio between the increase of the specimen length before its rupture and its original length: δ = (Lm– L0) / L0 Where Lm– maximum specimen length. Relative reduction of area - ratio between the decrease of the specimen cross-section area before its rupture and its original cross-section area: ψ= (S0– Smin) / S0 Where Smin– minimum specimen cross-section area.
Physical properties of metals Optical properties Metals reflect equally nearly all visible electro-magnetic waves. Therefore the color of the most of the metals is white or silvery-white (except copper and gold).
Metals are lustrous due to the metallic bonding, contributing free electrons to the metal crystal structure and providing an ability of metals to reflect light when polished. Physical state Metals are solid at normal temperatures (except mercury).
Metals transform to liquid from solid and to gas from liquid at definite temperatures(melting and boiling points), which are high for most of metals (except mercury, sodium and potassium).
Most of metals have relatively high densities (except sodium and potassium with densities lower, than density of water).
Electrical properties Metals have high electrical conductivity, provided by free electrons available in the metal crystal structure.
Peltier effect: When there is an electric current, passing through a junction of two different metals, one of them evolves heat and another absorbs heat.
Thomson effect: A current is produced in a metal conductor when there is a temperature gradient along its length.
The Peltier and Thomson effects are widely used in thermocouples.
Thermal properties Thermal Conductivity Thermal Conductivity (λ) is amount of heat passing in unit time through unit surface in a direction normal to this surface when this transfer is driven by unite temperature gradient under steady state conditions. Thermal conductivity may be expressed and calculated from the Fourier’s law: ΔQ/ Δt = λ*S *ΔT/ Δx Where
Q -heat, passing through the surface S; Δt - change in time; λ - thermal conductivity; S - surface area, normal to the heat transfer direction; ΔT/Δx-temperature gradient along x – direction of the heat transfer. Fourier’s law is analogue of the First Fick’s law, describing diffusion in steady state.
Metals have high thermal conductivity. Heat is transferred through the metal crystal by free electrons. Compare: λ of alumina = 47 BTU/(lb*ºF) (6.3 W/(m*K)). λ of Al = 1600 BTU/(lb*ºF) (231 W/(m*K)). Coefficient of Thermal Expansion Thermal Expansion (Coefficient of Thermal Expansion) is relative increase in length per unite temperature rise: α= ΔL/ (LoΔT) Where
α -coefficient of thermal expansion (CTE); ΔL – length increase; Lo – initial length; ΔT – temperature rise. Thermal expansion of metals is generally higher, than that of ceramics. Compare:
CTE of SiC = 2.3 ºFˉ¹ (4.0 ºCˉ¹). CTE of Al = 13 ºFˉ¹ (23 ºCˉ¹).
Specific Heat Capacity Heat Capacity is amount of heat required to raise material temperature by one unit. Specific Heat Capacity is amount of heat required to raise temperature of unit mass of material by one unit: c= ΔQ/(mΔT) Where
c -specific heat capacity; ΔQ – amount of heat; m – material mass; ΔT – temperature rise. Specific Heat Capacity of metals is lower, than that of ceramics.
“c” of alumina = 0.203 BTU/(lb*ºF) (850 J/(kg*K)). “c” of steel = 0.115 BTU/(lb*ºF) (481 J/(kg*K)). Magnetic properties Most of metals are slightly magnetic, but only few of them (iron, nickel, cobalt and their alloys) display pronounced magnetic properties, calledferromagnetism. Magnetically soft metals – metals, which are demagnetized after the magnetic field is
removed. Magnetically soft metals are used in electric motors and transformers. Magnetically hard metals – metals, retaining their magnetization after the magnetic
field is removed.Magnetically hard metals are used for permanent magnets. Magnetostriction – effect of changing dimensions of a ferromagnetic metal when its
magnetization is changed.
Hardness test methods Hardness is resistance of material to plastic deformation caused by indentation. Sometimes hardness refers to resistance of material to scratching or abrasion.
In some cases relatively quick and simple hardness test may substitute tensile test. Hardness may be measured from a small sample of material without destroying it.
There are hardness methods, allowing to measure hardness onsite.
Principle of any hardness test method is forcing an indenter into the sample surface followed by measuring dimensions of the indentation (depth or actual surface area of the indentation). Hardness is not fundamental property and its value depends on the combination of yield strength, tensile strength and modulus of elasticity. Benefits of hardness test:
Easy
Inexpensive
Quick
Non-destructive
May be applied to the samples of various dimensions and shapes
Depending on the loading force value and the indentation dimensions, hardness is defined as a macro- , micro- or nano-hardness.
Macro-hardness tests (Rockwell, Brinell, Vickers) are the most widely used methods for rapid routine hardness measurements. The indenting forces in macro-hardness tests are in the range of 50N to 30000N. Micro-hardness tests (micro-Vickers, Knoop) is applicable when hardness of coatings, surface hardness, or hardness of different phases in the multi-phase material is measured. Small diamond pyramid is used as indenter loaded with a small force of 10 to 1000gf. Nano-hardness test uses minor loads of about 1 nano-Newton followed by precise measuring depth of indentation.
Brinell Hardness Test
Rockwell Hardness Test
Rockwell Superficial Hardness Test
Vickers Hardness Test
Knoop Hardness Test
Shore Scleroscope Hardness Test Brinell Hardness Test
In this test a hardened steel ball of 2.5, 5 or 10 mm in diameter is used as indenter.
The loading force is in the range of 300N to 30000N (300N for testing lead alloys, 5000N for testing aluminum alloys, 10000N for copper alloys, 30000N for testing steels). The Brinell Hardness Number (HB) is calculated by the formula: HB = 2F/ (3.14D*(D-(D² - Di²)½))
F- applied load, kg D – indenter diameter, mm Di – indentation diameter, mm. In order to eliminate an influence of the specimen supporting base, the specimen should be seven times (as minimum) thicker than indentation depth for hard alloys and fifteen times thicker than indentation depth for soft alloys.
In the Rockwell test the depth of the indenter penetration into the specimen surface is measured. The indenter may be either a hardened steel ball with diameter 1/16”, 1/8” or a spherical diamond cone of 120º angle (Brale). Loading procedure starts from applying a minor load of 10 kgf (3kgf in Rockwell Superficial Test) and then the indicator, measuring the penetration depth, is set to zero. After that the major load (60, 100 or 150 kgf)is applied. The penetration depth is measured after removal of the major load.
Hardness is measured in different scales (A, B, C, D, E, F, G, H, K) and in numbers, having no units (in contrast to Brinell and Vickers methods).
Aluminum alloys, copper alloys and soft steels are tested with 1/16” diameter steel ball at 100 kgf load (Rockwell hardness scale B). Harder alloys and hard cast iron are tested with the diamond cone at 150 kgf (Rockwell hardness scale C). An example of Rockwell test result: 53 HRC. It means 53 units, measured in the scale C by the method HR (Hardness Rockwell).
Rockwell Superficial Hardness Test Rockwell Superficial Test is applied for thin strips, coatings, carburized surfaces. Reduced loads (15 kgf, 30 kgf, and 30 kgf) as a major load and deduced preload (3kgf) are used in the superficial test.
Depending on the indenter, two scales of Rockwell Superficial method may be used: T (1/16” steel ball) or N (diamond cone).
62 R30T means 62 units, measured in the scale 30T (30 kgf, 1/16” steel ball indenter) by the Rockwell Superficial method (R).
Vickers Hardness Test The principle of the Vickers Hardness method is similar to the Brinell method.
The Vickers indenter is a 136 degrees square-based diamond pyramid.
The impression, produced by the Vickers indenter is clearer, than the impression of Brinell indenter, therefore this method is more accurate.
The load, varying from 1kgf to 120 kgf, is usually applied for 30 seconds. The Vickers number (HV) is calculated by the formula: HV = 1.854*F/ D² Where
F-applied load, kg D – length of the impression diagonal, mm
A diamond pyramid indenter with angles 130º and 170º30’ is used in this method. The Knoop Hardness Test is applied for testing soft material and thin coating, since the penetration depth is very small (about 1/30 of the impression length).
The loading force in the Knoop method are usually in the range of 10 gf to 1000gf (micro-hardness range).
The Knoop number (HK) is calculated by the formula:
HK = 14.229*F/L² Where
F-applied load, kg L – long diagonal of the impression, mm
Shore Scleroscope Hardness Test The Shore Scleroscope hardness is associated with the elasticity of the material. The appliance consists of a diamond-tipped hammer, falling in a graduated glass tube from a definite height. The tube is divided into 140 equal parts.
The height of the first rebound is the hardness index of the material.
The harder the material, the higher the rebound.
The Shore method is widely used for measuring hardness of large machine components like rolls, gears, dies, etc.
The Shore scleroscope is not only small and mobile, it also leaves no impressions on the tested surface.
Fracture Toughness Fracture is a process of breaking a solid into pieces as a result of stress. There are two principal stages of the fracture process:
Crack formation
Crack propagation Ductile fracture Ductile materials undergo observable plastic deformation and absorb significant energy before fracture. A crack, formed as a result of the ductile fracture, propagates slowly and when the stress is increased.
Plastic deformation of a multi-phase material causes formation and coalescence of voids on the phase and inclusions boundaries. These voids are responsible for the specific appearance of the ductile fracture surface, consisting of numerous spherical micro-cavities (dimples), initiating formation of the crack. Tensile specimen fractured by the ductile mechanism is characterized by the cap and cone appearance of the fracture. Single-phase alloys and pure metals are more ductile, than metals, containing second phases or inclusions.
Brittle fracture is characterized by very low plastic deformation and low energy absorption prior to breaking.
A crack, formed as a result of the brittle fracture, propagates fast and without increase of the stress applied to the material.
The brittle crack is perpendicular to the stress direction.
There are two possible mechanisms of the brittle fracture: transcrystalline (transgranular, cleavage) or intercrystalline (intergranular). Cleavage cracks pass along crystallographic planes through the grains. Intercrystalline fracture occurs through the grain boundaries, embrittled by segregated impurities, second phase inclusions and other defects. The brittle fractures usually possess bright granular appearance.
Toughness Toughness is ability of material to resist fracture. The general factors, affecting the toughness of a material are: temperature, strain rate, relationship between the strength and ductility of the material and presence of stress concentration (notch) on the specimen surface. Fracture toughness is indicated by the area below the curve on strain-stress diagram (see the figure):
As seen from the diagram toughness of the ductile materials is higher than toughness of brittle materials.
Stress-intensity Factor (K) is a quantitative parameter of fracture toughness determining a maximum value of stress which may be applied to a specimen containing a crack (notch) of a certain length.
Depending on the direction of the specimen loading and the specimen thickness, four types of stress-intensity factors are used: KC, KIC KIIC KIIIC. KC – stress-intensity factor of a specimen, thickness of which is less than a critical value. KC depends on the specimen thickness. This condition is called plane stress. KIC,KIIC, KIIIC – stress-intensity factors, relating to the specimens, thickness of which is above the critical value therefore the values of KIC KIICKIIIC do not depend on the specimen thickness. This condition is called plane strain. KIIC and KIIIC – stress-intensity factors relating to the fracture modes in which the loading direction is parallel to the crack plane. These factors are rarely used for metals and are not used for ceramics; KIC – plane strain stress-intensity factor relating to the fracture modes in which the loading direction is normal to the crack plane. This factor is widely used for both metallic and ceramic materials. KIC is used for estimation critical stress applied to a specimen with a given crack length: σC ≤KIC /(Y(π a)½) Where
KIC – stress-intensity factor, measured in MPa*m½; σC– the critical stress applied to the specimen; a – the crack length for edge crack or half crack length for internal crack; Y – geometry factor. Impact test
Impact test is used for measuring toughness of materials and their capacity of resisting shock.
In this test the pendulum is swing up to its starting position (height H ) and then it is allowed to strike the notched specimen, fixed in a vice. The pendulum fractures the specimen, spending a part of its energy. After the fracture the pendulum swings up to a height H. The impact toughness of the specimen is calculated by the formula: a = A/ S Where
a-impact toughness, A – the work, required for breaking the specimen ( A = M*g*H0–M*g*H), M - the pendulum mass, S - cross-section area of the specimen at the notch. One of the most popular impact tests is the Charpy Test, schematically presented in the figure below:
The hammer striking energy in the Charpy test is 220 ft*lbf (300 J).
Fatigue Fatigue is a type of failure of a material, occurring under alternating loads. Most of the failures of machine details are caused by fatigue.
Fatigue life is the number of cycling stresses, causing failure of the material. Frequency of these stresses is not important.
Fatigue limit is the maximum value of repeatedly applied stress that the material can withstand after an infinite number of cycles (10-20 mln. Cycles in practice).
Fatigue strength at N cycles is the load, producing the material fracture after N cycling applications of the load. Fatigue limit of a material is much lower, than its ultimate tensile strength.
Fatigue tests are carried out in the Wöhler-type machine, schematically shown in the picture.
The rotating specimen in form of a cantilever is driven by an electric motor. The specimen is loaded by the force F, applied to the ball bearing, mounted on the end of the specimen.
Since the force direction does not change, the direction of the stress applied to the specimen will be reversed each 180º of the shaft rotation.
This scheme provides cycling loading of the specimen, presented in the equivalent scheme.
To find the fatigue limit the fatigue test is repeated at different loads.
The tests results are presented in form of S-N curve (stress vs. number of cycles): Fatigue fracture is characterized by presence of two different types of the surface:
One part is smooth and discolored with ripple-like marks, indicating slow crack growth from the center of the crack formation. Another part of the surface has coarse crystalline appearance resulted from the final catastrophic crack propagation.
The following factors affect fatigue fracture:
Surface factor Fatigue cracks form and initiate on the specimen surface therefore hardened and smooth surface (without stress concentrations - notch, flaw) will increase the fatigue limit.
Compressive stress Compressive stresses, produced in the specimen surface by Shot peening, cold work or heat treatment result in considerable increase of fatigue limit.
Micro-structure defects Non-metallic inclusions and other micro-defects may initiate formation of fatigue cracks.
Environmental factor Fatigue in the presence of corrosive environment (Corrosion fatigue) occurs at lower cycling stresses and after lower number of cycles.
Creep Creep is a phenomenon of slow plastic deformation (elongation) of a metal at high temperature under a constant load. The creep mechanism: At low stresses the creep is controlled by the diffusion of atoms through the grain boundaries. At higher stresses the creep strain proceeds due to the dislocations movement. The rate of creep is a function of the material, the applied stress value, the temperature, and the time exposure. Considerable creep deformation, causing damage of machines and structures occur at high temperatures (about a half of the melting point measured in the absolute temperature scale). Therefore this phenomenon is taken into account in design and operation of heat exchangers, steam boilers and pipes, jet engines and other loaded equipment, working at high temperatures.
Soft metals (lead, tin) may experience creep at room temperature.
A typical creep behavior is presented in the diagram:
The initial strain is not time dependent and it is caused mainly by elastic deformation. The first stage creep is characterized by relatively fast plastic deformation occurring at decreasing rate. During this stage resistance creep increases causing decrease the deformation rate. The second stage creep occurs at a constant and relatively low deformation rate. This rate is used in the engineering design.
The rate of creep at the second stage depends on both the load (stress) and the temperature.
The third stage creep is associated with accelerated strain rate caused by decrease of the cross sectional area of the specimen (necking). This stage is finalized by the specimen fracture. At room temperature creep is negligible at any stress below the yield point.
The quantity, which is used in precise design of machines and structures working at elevated temperatures, is creep strength.
Creep strength is a stress which causes a definite creep strain after a specified period of time at a given temperature. Creep strength of a material is much lower, than its tensile strength.
If a large amount of deformation is tolerated rupture strength is used in design.
Rupture strength is a stress which causes a fracture of a metal after a specified period of time at a given temperature. Creep strength and rupture strength are determined in stress-rupture tests conducted in [Tensile test and Stress-Strain Diagram|tensile test]] machines equipped with a furnace providing uniform heating of the tested specimens.
This machine records amount of strain at every moment after the test has started and until the specimen failure.
Plastic deformation Plastic deformation is a change of the material dimensions remaining after removal of the load caused the deformation. Plastic deformations in metals occurs by “slip” mechanism, illustrated in the picture:
When the yield stress is achieved one plane of atoms in crystal lattice glides over another. Few parallel slip planes form a block, neighboring with another block. Thus movement of the crystal planes is resulted in a series of steps, forming slip bands – black lines viewed under optical microscope. Slip occurs when the share resolved stress along the gliding planes reaches a critical value. This critical resolved shear stress is a characteristic of the material. Certain metals (Zn and Sn) deform by a process of twinning, differing from the normal slip mechanism, where all atoms in a block move the same distance. In the deformation by twinning atoms of each slip plane in a block move different distance, causing half of the crystal lattice to become a mirror image of another half. In polycrystalline material directions of slips are different in different crystals. If a grain is oriented unfavorably to the stress direction its deformation is impeded. In addition to thisgrain boundaries are obstacles for the slip movement as the slip direction should be changed when it crosses the boundary. As a result of the above strength of polycrystalline materials is higher, than that of mono-crystals. Slip and twinning processes, occurring during plastic deformation result in formation of preferred orientation of the grains.
If the stress value required for a slip is higher than cohesion strength, metal fracture occurs. Stress-strain relations are considered in the article Tensile test and Stress-Strain Diagram.
