Thermal conductivity (λ) is the intrinsic property of a material which relates its ability to conduct heat. Heat transfer by conduction involves transfer of energy within a material without any motion of the material as a whole. Conduction takes place when a temperature gradient exists in a solid (or stationary fluid) medium. Conductive heat flow occurs in the direction of decreasing temperature because higher temperature equates to higher molecular energy or more molecular movement. Energy is transferred from the more energetic to the less energetic molecules when neighboring molecules collide.
Thermal conductivity is defined as the quantity of heat (Q) transmitted through a unit thickness (L) in a direction normal to a surface of unit area (A) due to a unit temperature gradient (ΔT)under steady state conditions and when the heat transfer is dependent only on the temperature gradient. In equation form this becomes the following:Thermal Conductivity = heat × distance / (area × temperature gradient)
Magnetic permeability or simply permeability is the ease with which a material can be magnetized. It is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 Henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µ0.
Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic. Materials that concentrate magnetic flux by a factor of more than one but less than or equal to ten are called paramagnetic; materials that concentrate the flux by a factor of more than ten are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.
In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µ o represents the permeability of free space (that is, 4p X10-7H/m or 1.257 x 10-6H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by:
µr = µ / µ0
For non-ferrous metals such as copper, brass, aluminum etc., the permeability is the same as that of "free space", i.e. the relative permeability is one. For ferrous metals however the value of µ r may be several hundred. Certain ferromagnetic materials, especially powdered or laminated iron, steel, or nickel alloys, have µr that can range up to about 1,000,000. Diamagnetic materials have µr less than one, but no known substance has relative permeability much less than one. In addition, permeability can vary greatly within a metal part due to localized stresses, heating effects, etc.
When a paramagnetic or ferromagnetic core is inserted into a coil, the inductance is multiplied by µr compared with the inductance of the same coil with an air core. This effect is useful in the design of transformers and eddy current probes
λ = Q × L / (A × ΔT)Approximate values of thermal conductivity for some common materials are presented in the table below.
Material | Thermal Conductivity W/m, oK | Thermal Conductivity (cal/sec)/(cm2, oC/cm) |
| Air at 0 C | 0.024 | 0.000057 |
| Aluminum | 205.0 | 0.50 |
| Brass | 109.0 | - |
| Concrete | 0.8 | 0.002 |
| Copper | 385.0 | 0.99 |
| Glass, ordinary | 0.8 | 0.0025 |
| Gold | 310 | - |
| Ice | 1.6 | 0.005 |
| Iron | - | 0.163 |
| Lead | 34.7 | 0.083 |
| Polyethylene HD | 0.5 | - |
| Polystyrene expanded | 0.03 | - |
| Silver | 406.0 | 1.01 |
| Styrofoam | 0.01 | - |
| Steel | 50.2 | - |
| Water at 20 C | - | 0.0014 |
| Wood | 0.12-0.04 | 0.0001 |
Electrical Conductivity and Resistivity
It is well known that one of the subatomic particles of an atom is the electron. The electrons carry a negative electrostatic charge and under certain conditions can move from atom to atom. The direction of movement between atoms is random unless a force causes the electrons to move in one direction. This directional movement of electrons due to an electromotive force is what is known as electricity.Electrical Conductivity
Electrical conductivity is a measure of how well a material accommodates the movement of an electric charge. It is the ratio of the current density to the electric field strength. Its SI derived unit is the Siemens per meter, but conductivity values are often reported as percent IACS. IACS is an acronym for International Annealed Copper Standard or the material that was used to make traditional copper-wire . The conductivity of the annealed copper (5.8108 x 107S/m) is defined to be 100% IACS at 20°C. All other conductivity values are related back to this conductivity of annealed copper. Therefore, iron with a conductivity value of 1.044 x 107 S/m, has a conductivity of approximately 18% of that of annealed copper and this is reported as 18% IACS. An interesting side note is that commercially pure copper products now often have IACS conductivity values greater than 100% because processing techniques have improved since the adoption of the standard in 1913 and more impurities can now be removed from the metal.
Conductivity values in Siemens/meter can be converted to % IACS by multiplying the conductivity value by 1.7241 x10-6. When conductivity values are reported in microSiemens/centimeter, the conductivity value is multiplied by 172.41 to convert to the % IACS value.
Electrical conductivity is a very useful property since values are affected by such things as a substances chemical composition and the stress state of crystalline structures. Therefore, electrical conductivity information can be used for measuring the purity of water, sorting materials, checking for proper heat treatment of metals, and inspecting for heat damage in some materials.
Electrical Resistivity
Electrical resistivity is the reciprocal of conductivity. It is the is the opposition of a body or substance to the flow of electrical current through it, resulting in a change of electrical energy into heat, light, or other forms of energy. The amount of resistance depends on the type of material. Materials with low resistivity are good conductors of electricity and materials with high resistivity are good insulators.
The SI unit for electrical resistivity is the ohm meter. Resistivity values are more commonly reported in micro ohm centimeters units. As mentioned above resistivity values are simply the reciprocal of conductivity so conversion between the two is straightforward. For example, a material with two micro ohm centimeter of resistivity will have ½ microSiemens/centimeter of conductivity. Resistivity values in microhm centimeters units can be converted to % IACS conductivity values with the following formula:
172.41 / resistivity = % IACS
Temperature Coefficient of ResistivityAs noted above, electrical conductivity values (and resistivity values) are typically reported at 20 oC. This is done because the conductivity and resistivity of material is temperature dependant. The conductivity of most materials decreases as temperature increases. Alternately, the resistivity of most material increases with increasing temperature. The amount of change is material dependant but has been established for many elements and engineering materials.The reason that resistivity increases with increasing temperature is that the number of imperfection in the atomic lattice structure increases with temperature and this hampers electron movement. These imperfections include dislocations, vacancies, interstitial defects and impurity atoms. Additionally, above absolute zero, even the lattice atoms participate in the interference of directional electron movement as they are not always found at their ideal lattice sites. Thermal energy causes the atoms to vibrate about their equilibrium positions. At any moment in time many individual lattice atoms will be away from their perfect lattice sites and this interferes with electron movement.
When the temperature coefficient is known, an adjusted resistivity value can be computed using the following formula:
R1 = R2 * [1 + a * (T1–T2)]
Where: R1 = resistivity value adjusted to T1
R2 = resistivity value known or measured at temperature T2
a = Temperature Coefficient
T1 = Temperature at which resistivity value needs to be known
T2 = Temperature at which known or measured value was obtained
For example, suppose that resistivity measurements were being made on a hot piece of aluminum. Normally when measuring resistivity or conductivity, the instrument is calibrated using standards that are at the same temperature as the material being measured, and then no correction for temperature will be required. However, if the calibration standard and the test material are at different temperatures, a correction to the measured value must be made. Presume that the instrument was calibrated at 20oC (68oF) but the measurement was made at 25oC (77oF) and the resistivity value obtained was 2.706 x 10-8 ohm meters. Using the above equation and the following temperature coefficient value, the resistivity value corrected for temperature can be calculated.
R1 = R2 * [1 + a * (T1–T2)]
Where: R1 = ?
R2 = 2.706 x 10-8 ohm meters (measured resistivity at 25 oC)
a = 0.0043/ oC
T1 = 20 oC
T2 = 25 oC
R1 = 2.706 x 10-8ohm meters * [1 + 0.0043/ oC * (20 oC – 25 oC)]
R1 = 2.648 x 10-8ohm meters
Note that the resistivity value was adjusted downward since this example involved calculating the resistivity for a lower temperature.
Since conductivity is simply the inverse of resistivity, the temperature coefficient is the same for conductivity and the equation requires only slight modification. The equation becomes:
s1 = s2 / [1 + a * (T1–T2)]
Where: s1 = conductivity value adjusted to T1
s2 = conductivity value known or measured at temperature T2
a = Temperature Coefficient
T1 = Temperature at which conductivity value needs to be known
T2 = Temperature at which known or measured value was obtained
In this example let’s consider the same aluminum alloy with a temperature coefficient of 0.0043 per degree centigrade and a conductivity of 63.6% IACS at 25 oC. What will the conductivity be when adjusted to 20 oC?
s1= 63.6% IACS / [1 + 0.0043 * (20 oC – 25 oC)]
s1= 65.0% IASC
The temperature coefficient for a few metallic elements is shown below.
| Material | Temperature Coefficient (/ oC) |
| Nickel | 0.0059 |
| Iron | 0.0060 |
| Molybdenum | 0.0046 |
| Tungsten | 0.0044 |
| Aluminum | 0.0043 |
| Copper | 0.0040 |
| Silver | 0.0038 |
| Platinum | 0.0038 |
| Gold | 0.0037 |
| Zinc | 0.0038 |
Magnetic permeability or simply permeability is the ease with which a material can be magnetized. It is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 Henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µ0.
Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic. Materials that concentrate magnetic flux by a factor of more than one but less than or equal to ten are called paramagnetic; materials that concentrate the flux by a factor of more than ten are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.
In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µ o represents the permeability of free space (that is, 4p X10-7H/m or 1.257 x 10-6H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by:µr = µ / µ0
For non-ferrous metals such as copper, brass, aluminum etc., the permeability is the same as that of "free space", i.e. the relative permeability is one. For ferrous metals however the value of µ r may be several hundred. Certain ferromagnetic materials, especially powdered or laminated iron, steel, or nickel alloys, have µr that can range up to about 1,000,000. Diamagnetic materials have µr less than one, but no known substance has relative permeability much less than one. In addition, permeability can vary greatly within a metal part due to localized stresses, heating effects, etc.
When a paramagnetic or ferromagnetic core is inserted into a coil, the inductance is multiplied by µr compared with the inductance of the same coil with an air core. This effect is useful in the design of transformers and eddy current probes.
Corrosion
Corrosion involves the deterioration of a material as it reacts with its environment. Corrosion is the primary means by which metals deteriorate. Corrosion literally consumes the material reducing load carrying capability and causing stress concentrations. Corrosion is often a major part of maintenance cost and corrosion prevention is vital in many designs. Corrosion is not expressed in terms of a design property value like other properties but rather in more qualitative terms such as a material is immune, resistant, susceptible or very susceptible to corrosion.The corrosion process is usually electrochemical in nature, having the essential features of a battery. Corrosion is a natural process that commonly occurs because unstable materials, such as refined metals want to return to a more stable compound. For example, some metals, such as gold and silver, can be found in the earth in their natural, metallic state and they have little tendency to corrode. Iron is a moderately active metal and corrodes readily in the presence of water. The natural state of iron is iron oxide and the most common iron ore is Hematite with a chemical composition of Fe203. Rust, the most common corrosion product of iron, also has a chemical composition of Fe2O3.
The difficulty in terms of energy required to extract metals from their ores is directly related to the ensuing tendency to corrode and release this energy. The electromotive force series (See table) is a ranking of metals with respect to their inherent reactivity. The most noble metal is at the top and has the highest positive electrochemical potential. The most active metal is at the bottom and has the most negative electrochemical potential.
Corrosion involve two chemical processes…oxidation and reduction. Oxidation is the process of stripping electrons from an atom and reduction occurs when an electron is added to an atom. The oxidation process takes place at an area known as the anode. At the anode, positively charged atoms leave the solid surface and enter into an electrolyte as ions. The ions leave their corresponding negative charge in the form of electrons in the metal which travel to the location of the cathode through a conductive path. At the cathode, the corresponding reduction reaction takes place and consumes the free electrons. The electrical balance of the circuit is restored at the cathode when the electrons react with neutralizing positive ions, such as hydrogen ions, in the electrolyte. From this description, it can be seen that there are four essential components that are needed for a corrosion reaction to proceed. These components are an anode, a cathode, an electrolyte with oxidizing species, and some direct electrical connection between the anode and cathode. Although atmospheric air is the most common environmental electrolyte, natural waters, such as seawater rain, as well as man-made solutions, are the environments most frequently associated with corrosion problems.
A typical situation might involve a piece of metal that has anodic and cathodic regions on the same surface. If the surface becomes wet, corrosion may take place through ionic exchange in the surface water layer between the anode and cathode. Electron exchange will take place through the bulk metal. Corrosion will proceed at the anodic site according to a reaction such as
M → M++ + 2e-
where M is a metal atom. The resulting metal cations (M++) are available at the metal surface to become corrosion products such as oxides, hydroxides, etc. The liberated electrons travel through the bulk metal (or another low resistance electrical connection) to the cathode, where they are consumed by cathodic reactions such as
2H+ + 2e- → H 2
The basic principles of corrosion that were just covered, generally apply to all corrosion situation except certain types of high temperature corrosion. However, the process of corrosion can be very straightforward but is often very complex due to variety of variable that can contribute to the process. A few of these variable are the composition of the material acting in the corrosion cell, the heat treatment and stress state of the materials, the composition of the electrolyte, the distance between the anode and the cathode, temperature, protective oxides and coating, etc.
Types of Corrosion
Corrosion is commonly classified based on the appearance of the corroded material. The classifications used vary slightly from reference to reference but there is generally considered to be eight different forms of corrosion. There forms are:
Uniform or general – corrosion that is distributed more or less uniformly over a surface.
Localized – corrosion that is confined to small area. Localized corrosion often occurs due to a concentrated cell. A concentrated cell is an electrolytic cell in which the electromotive force is caused by a concentration of some components in the electrolyte. This difference leads to the formation of distinct anode and cathode regions.
- Pitting – corrosion that is confined to small areas and take the form of cavities on a surface.
- Crevice – corrosion occurring at locations where easy access to the bulk environment is prevented, such as the mating surfaces of two components.
- Filiform – Corrosion that occurs under some coatings in the form of randomly distributed threadlike filaments.
Intergranular – preferential corrosion at or along the grain boundaries of a metal.
- Exfoliation – a specific form of corrosion that travels along grain boundaries parallel to the surface of the part causing lifting and flaking at the surface. The corrosion products expand between the uncorroded layers of metal to produce a look that resembles pages of a book. Exfoliation corrosion is associated with sheet, plate and extruded products and usually initiates at unpainted or unsealed edges or holes of susceptible metals.
Galvanic – corrosion associated primarily with the electrical coupling of materials with significantly different electrochemical potentials.
Environmental Cracking – brittle fracture of a normally ductile material that occurs partially due to the corrosive effect of an environment.
- Corrosion fatigue – fatigue cracking that is characterized by uncharacteristically short initiation time and/or growth rate due to the damage of corrosion or buildup of corrosion products.
- High temperature hydrogen attack – the loss of strength and ductility of steel due to a high temperature reaction of absorbed hydrogen with carbides. The result of the reaction is decarburization and internal fissuring.
- Hydrogen Embrittlement – the loss of ductility of a metal resulting from absorption of hydrogen.
- Liquid metal cracking – cracking caused by contact with a liquid metal.
- Stress corrosion – cracking of a metal due to the combined action of corrosion and a residual or applied tensile stress.
Erosion corrosion – a corrosion reaction accelerated by the relative movement of a corrosive fluid and a metal surface.
Fretting corrosion – damage at the interface of two contacting surfaces under load but capable of some relative motion. The damage is accelerated by movement at the interface that mechanically abraded the surface and exposes fresh material to corrosive attack.
Dealloying – the selective corrosion of one or more components of a solid solution alloy.
- Dezincification – corrosion resulting in the selective removal of zinc from copper-zinc alloys.
The mechanical properties of a material are those properties that involve a reaction to an applied load. The mechanical properties of metals determine the range of usefulness of a material and establish the service life that can be expected. Mechanical properties are also used to help classify and identify material. The most common properties considered are strength, ductility, hardness, impact resistance, and fracture toughness.
Most structural materials are anisotropic, which means that their material properties vary with orientation. The variation in properties can be due to directionality in the microstructure (texture) from forming or cold working operation, the controlled alignment of fiber reinforcement and a variety of other causes. Mechanical properties are generally specific to product form such as sheet, plate, extrusion, casting, forging, and etc. Additionally, it is common to see mechanical property listed by the directional grain structure of the material. In products such as sheet and plate, the rolling direction is called the longitudinal direction, the width of the product is called the transverse direction, and the thickness is called the short transverse direction. The grain orientations in standard wrought forms of metallic products are shown the image.
The mechanical properties of a material are not constants and often change as a function of temperature, rate of loading, and other conditions. For example, temperatures below room temperature generally cause an increase in strength properties of metallic alloys; while ductility, fracture toughness, and elongation usually decrease. Temperatures above room temperature usually cause a decrease in the strength properties of metallic alloys. Ductility may increase or decrease with increasing temperature depending on the same variablesIt should also be noted that there is often significant variability in the values obtained when measuring mechanical properties. Seemingly identical test specimen from the same lot of material will often produce considerable different results. Therefore, multiple tests are commonly conducted to determine mechanical properties and values reported can be an average value or calculated statistical minimum value. Also, a range of values are sometimes reported in order to show variability.
Loading
The application of a force to an object is known as loading. Materials can be subjected to many different loading scenarios and a material’s performance is dependant on the loading conditions. There are five fundamental loading conditions; tension, compression, bending, shear, and torsion. Tension is the type of loading in which the two sections of material on either side of a plane tend to be pulled apart or elongated. Compression is the reverse of tensile loading and involves pressing the material together. Loading by bending involves applying a load in a manner that causes a material to curve and results in compressing the material on one side and stretching it on the other. Shear involves applying a load parallel to a plane which caused the material on one side of the plane to want to slide across the material on the other side of the plane. Torsion is the application of a force that causes twisting in a material.
Stress and Strain
StressThe term stress (s) is used to express the loading in terms of force applied to a certain cross-sectional area of an object. From the perspective of loading, stress is the applied force or system of forces that tends to deform a body. From the perspective of what is happening within a material, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. The stress distribution may or may not be uniform, depending on the nature of the loading condition. For example, a bar loaded in pure tension will essentially have a uniform tensile stress distribution. However, a bar loaded in bending will have a stress distribution that changes with distance perpendicular to the normal axis.
Simplifying assumptions are often used to represent stress as a vector quantity for many engineering calculations and for material property determination. The word "vector" typically refers to a quantity that has a "magnitude" and a "direction". For example, the stress in an axially loaded bar is simply equal to the applied force divided by the bar's cross-sectional area.
Psi = lbs/in2 (pounds per square inch)
ksi or kpsi = kilopounds/in2 (one thousand or 103 pounds per square inch)
Pa = N/m 2 (Pascals or Newtons per square meter)
kPa = Kilopascals (one thousand or 103 Newtons per square meter)
GPa = Gigapascals (one million or 106 Newtons per square meter)
*Any metric prefix can be added in front of psi or Pa to indicate the multiplication factor
It must be noted that the stresses in most 2-D or 3-D solids are actually more complex and need be defined more methodically. The internal force acting on a small area of a plane can be resolved into three components: one normal to the plane and two parallel to the plane. The normal force component divided by the area gives the normal stress (s), and parallel force components divided by the area give the shear stress (t). These stresses are average stresses as the area is finite, but when the area is allowed to approach zero, the stresses become stresses at a point. Since stresses are defined in relation to the plane that passes through the point under consideration, and the number of such planes is infinite, there appear an infinite set of stresses at a point. Fortunately, it can be proven that the stresses on any plane can be computed from the stresses on three orthogonal planes passing through the point. As each plane has three stresses, the stress tensor has nine stress components, which completely describe the state of stress at a point.Strain Strain is the response of a system to an applied stress. When a material is loaded with a force, it produces a stress, which then causes a material to deform. Engineering strain is defined as the amount of deformation in the direction of the applied force divided by the initial length of the material. This results in a unitless number, although it is often left in the unsimplified form, such as inches per inch or meters per meter. For example, the strain in a bar that is being stretched in tension is the amount of elongation or change in length divided by its original length. As in the case of stress, the strain distribution may or may not be uniform in a complex structural element, depending on the nature of the loading condition.
If the stress is small, the material may only strain a small amount and the material will return to its original size after the stress is released. This is called elastic deformation, because like elastic it returns to its unstressed state. Elastic deformation only occurs in a material when stresses are lower than a critical stress called the yield strength. If a material is loaded beyond it elastic limit, the material will remain in a deformed condition after the load is removed. This is called plastic deformation.
Engineering and True Stress and Strain The discussion above focused on engineering stress and strain, which use the fixed, undeformed cross-sectional area in the calculations. True stress and strain measures account for changes in cross-sectional area by using the instantaneous values for the area. The engineering stress-strain curve does not give a true indication of the deformation characteristics of a metal because it is based entirely on the original dimensions of the specimen, and these dimensions change continuously during the testing used to generate the data.Engineering stress and strain data is commonly used because it is easier to generate the data and the tensile properties are adequate for engineering calculations. When considering the stress-strain curves in the next section, however, it should be understood that metals and other materials continues to strain-harden until they fracture and the stress required to produce further deformation also increase.
Stress ConcentrationWhen an axial load is applied to a piece of material with a uniform cross-section, the norm al stress will be uniformly distributed over the cross-section. However, if a hole is drilled in the material, the stress distribution will no longer be uniform. Since the material that has been removed from the hole is no longer available to carry any load, the load must be redistributed over the remaining material. It is not redistributed evenly over the entire remaining cross-sectional area but instead will be redistributed in an uneven pattern that is highest at the edges of the hole as shown in the image. This phenomenon is known as stress concentration.Tensile Properties
Tensile properties indicate how the material will react to forces being applied in tension. A tensile test is a fundamental mechanical test where a carefully prepared specimen is loaded in a very controlled manner while measuring the applied load and the elongation of the specimen over some distance. Tensile tests are used to determine the modulus of elasticity, elastic limit, elongation, proportional limit, reduction in area, tensile strength, yield point, yield strength and other tensile properties.The main product of a tensile test is a load versus elongation curve which is then converted into a stress versus strain curve. Since both the engineering stress and the engineering strain are obtained by dividing the load and elongation by constant values (specimen geometry information), the load-elongation curve will have the same shape as the engineering stress-strain curve. The stress-strain curve relates the applied stress to the resulting strain and each material has its own unique stress-strain curve. A typical engineering stress-strain curve is shown below. If the true stress, based on the actual cross-sectional area of the specimen, is used, it is found that the stress-strain curve increases continuously up to fracture.
The slope of the line in this region where stress is proportional to strain and is called themodulus of elasticity or Young's modulus. The modulus of elasticity (E) defines the properties of a material as it undergoes stress, deforms, and then returns to its original shape after the stress is removed. It is a measure of the stiffness of a given material. To compute the modulus of elastic , simply divide the stress by the strain in the material. Since strain is unitless, the modulus will have the same units as the stress, such as kpi or MPa. The modulus of elasticity applies specifically to the situation of a component being stretched with a tensile force. This modulus is of interest when it is necessary to compute how much a rod or wire stretches under a tensile load.
There are several different kinds of moduli depending on the way the material is being stretched, bent, or otherwise distorted. When a component is subjected to pure shear, for instance, a cylindrical bar under torsion, the shear modulus describes the linear-elastic stress-strain relationship.
Axial strain is always accompanied by lateral strains of opposite sign in the two directions mutually perpendicular to the axial strain. Strains that result from an increase in length are designated as positive (+) and those that result in a decrease in length are designated as negative (-). Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state.
Only two of the elastic constants are independent so if two constants are known, the third can be calculated using the following formula:
E = 2 (1 + n) G.
| Where: | E | = | modulus of elasticity (Young's modulus) |
| n | = | Poisson's ratio | |
| G | = | modulus of rigidity (shear modulus). |
Yield PointIn ductile materials, at some point, the stress-strain curve deviates from the straight-line relationship and Law no longer applies as the strain increases faster than the stress. From this point on in the tensile test, some permanent deformation occurs in the specimen and the material is said to react plastically to any further increase in load or stress. The material will not return to its original, unstressed condition when the load is removed. In brittle materials, little or no plastic deformation occurs and the material fractures near the end of the linear-elastic portion of the curve.
With most materials there is a gradual transition from elastic to plastic behavior, and the exact point at which plastic deformation begins to occur is hard to determine. Therefore, various criteria for the initiation of yielding are used depending on the sensitivity of the strain measurements and the intended use of the data. (See Table) For most engineering design and specification applications, the yield strength is used. The yield strength is defined as the stress required to produce a small, amount of plastic deformation. The offset yield strength is the stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic part of the curve offset by a specified strain (in the US the offset is typically 0.2% for metals and 2% for plastics).
| In Great Britain, the yield strength is often referred to as the proof stress. The offset value is either 0.1% or 0.5% |
Some materials such as gray cast iron or soft copper exhibit essentially no linear-elastic behavior. For these materials the usual practice is to define the yield strength as the stress required to produce some total amount of strain.
- True elastic limit is a very low value and is related to the motion of a few hundred dislocations. Micro strain measurements are required to detect strain on order of 2 x 10 -6 in/in.
- Proportional limit is the highest stress at which stress is directly proportional to strain. It is obtained by observing the deviation from the straight-line portion of the stress-strain curve.
- Elastic limit is the greatest stress the material can withstand without any measurable permanent strain remaining on the complete release of load. It is determined using a tedious incremental loading-unloading test procedure. With the sensitivity of strain measurements usually employed in engineering studies (10 -4in/in), the elastic limit is greater than the proportional limit. With increasing sensitivity of strain measurement, the value of the elastic limit decreases until it eventually equals the true elastic limit determined from micro strain measurements.
- Yield strength is the stress required to produce a small-specified amount of plastic deformation. The yield strength obtained by an offset method is commonly used for engineering purposes because it avoids the practical difficulties of measuring the elastic limit or proportional limit.
On the stress-strain curve above, the UTS is the highest point where the line is momentarily flat. Since the UTS is based on the engineering stress, it is often not the same as the breaking strength. In ductile materials strain hardening occurs and the stress will continue to increase until fracture occurs, but the engineering stress-strain curve may show a decline in the stress level before fracture occurs. This is the result of engineering stress being based on the original cross-section area and not accounting for the necking that commonly occurs in the test specimen. The UTS may not be completely representative of the highest level of stress that a material can support, but the value is not typically used in the design of components anyway. For ductile metals the current design practice is to use the yield strength for sizing static components. However, since the UTS is easy to determine and quite reproducible, it is useful for the purposes of specifying a material and for quality control purposes. On the other hand, for brittle materials the design of a component may be based on the tensile strength of the material.
Measures of Ductility (Elongation and Reduction of Area)
The ductility of a material is a measure of the extent to which a material will deform before fracture. The amount of ductility is an important factor when considering forming operations such as rolling and extrusion. It also provides an indication of how visible overload damage to a component might become before the component fractures. Ductility is also used a quality control measure to assess the level of impurities and proper processing of a material.
The conventional measures of ductility are the engineering strain at fracture (usually called the elongation ) and the reduction of area at fracture. Both of these properties are obtained by fitting the specimen back together after fracture and measuring the change in length and cross-sectional area. Elongation is the change in axial length divided by the original length of the specimen or portion of the specimen. It is expressed as a percentage. Because an appreciable fraction of the plastic deformation will be concentrated in the necked region of the tensile specimen, the value of elongation will depend on the gage length over which the measurement is taken. The smaller the gage length the greater the large localized strain in the necked region will factor into the calculation. Therefore, when reporting values of elongation , the gage length should be given.One way to avoid the complication from necking is to base the elongation measurement on the uniform strain out to the point at which necking begins. This works well at times but some engineering stress-strain curve are often quite flat in the vicinity of maximum loading and it is difficult to precisely establish the strain when necking starts to occur.
Reduction of area is the change in cross-sectional area divided by the original cross-sectional area. This change is measured in the necked down region of the specimen. Like elongation, it is usually expressed as a percentage.
As previously discussed, tension is just one of the way that a material can be loaded. Other ways of loading a material include compression, bending, shear and torsion, and there are a number of standard tests that have been established to characterize how a material performs under these other loading conditions. A very cursory introduction to some of these other material properties will be provided on the next page.
Compressive, Bearing, & Shear Properties
Compressive Properties 
In theory, the compression test is simply the opposite of the tension test with respect to the direction of loading. In compression testing the sample is squeezed while the load and the displacement are recorded. Compression tests result in mechanical properties that include the compressive yield stress, compressive ultimate stress, and compressive modulus of elasticity.Compressive yield stress is measured in a manner identical to that done for tensile yield strength. When testing metals, it is defined as the stress corresponding to 0.002 in./in. plastic strain. For plastics, the compressive yield stress is measured at the point of permanent yield on the stress-strain curve. Moduli are generally greater in compression for most of the commonly used structural materials.
Ultimate compressive strength is the stress required to rupture a specimen. This value is much harder to determine for a compression test than it is for a tensile test since many material do not exhibit rapid fracture in compression. Materials such as most plastics that do not rupture can have their results reported as the compressive strength at a specific deformation such as 1%, 5%, or 10% of the sample's original height.
For some materials, such as concrete, the compressive strength is the most important material property that engineers use when designing and building a structure. Compressive strength is also commonly used to determine whether a concrete mixture meets the requirements of the job specifications.
Bearing Properties Bearing properties are used when designing mechanically fastened joints. The purpose of a bearing test is to determine the the deformation of a hole as a function of the applied bearing stress. The test specimen is basically a piece of sheet or plate with a carefully prepared hole some standard distance from the edge. Edge-to-hole diameter ratios of 1.5 and 2.0 are common. A hardened pin is inserted through the hole and an axial load applied to the specimen and the pin. The bearing stress is computed by dividing the load applied to the pin, which bears against the edge of the hole, by the bearing area (the product of the pin diameter and the sheet or plate thickness). Bearing yield and ultimate stresses are obtained from bearing tests. BYS is computed from a bearing stress deformation curve by drawing a line parallel to the initial slope at an offset of 0.02 times the pin diameter. BUS is the maximum stress withstood by a bearing specimen.
Shear Properties A shearing stress acts parallel to the stress plane, whereas a tensile or compressive stress acts normal to the stress plane. Shear properties are primarily used in the design of mechanically fastened components, webs, and torsion members, and other components subject to parallel, opposing loads. Shear properties are dependant on the type of shear test and their is a variety of different standard shear tests that can be performed including the single-shear test, double-shear test, blanking-shear test, torsion-shear test and others. The shear modulus of elasticity is considered a basic shear property. Other properties, such as the proportional limit stress and shear ultimate stress, cannot be treated as basic shear properties because of “form factor” effects.
Hardness
Hardness is the resistance of a material to localized deformation. The term can apply to deformation from indentation, scratching, cutting or bending. In metals, ceramics and most polymers, the deformation considered is plastic deformation of the surface. For elastomers and some polymers, hardness is defined at the resistance to elastic deformation of the surface. The lack of a fundamental definition indicates that hardness is not be a basic property of a material, but rather a composite one with contributions from the yield strength, work hardening, true tensile strength, modulus, and others factors. Hardness measurements are widely used for the quality control of materials because they are quick and considered to be nondestructive tests when the marks or indentations produced by the test are in low stress areas.Toughness
The ability of a metal to deform plastically and to absorb energy in the process before fracture is termed toughness. The emphasis of this definition should be placed on the ability to absorb energy before fracture. Recall that ductility is a measure of how much something deforms plastically before fracture, but just because a material is ductile does not make it tough. The key to toughness is a good combination of strength and ductility. A material with high strength and high ductility will have more toughness than a material with low strength and high ductility. Therefore, one way to measure toughness is by calculating the area under the stress strain curve from a tensile test. This value is simply called “material toughness” and it has units of energy per volume. Material toughness equates to a slow absorption of energy by the material.
- Strain rate (rate of loading)
- Temperature
- Notch effect
There are several standard types of toughness test that generate data for specific loading conditions and/or component design approaches. Three of the toughness properties that will be discussed in more detail are 1) impact toughness, 2) notch toughness and 3) fracture toughness.
Fatigue Properties
Fatigue cracking is one of the primary damage mechanisms of structural components. Fatigue cracking results from cyclic stresses that are below the ultimate tensile stress, or even the yield stress of the material. The name “fatigue” is based on the concept that a material becomes “tired” and fails at a stress level below the nominal strength of the material. The facts that the original bulk design strengths are not exceeded and the only warning sign of an impending fracture is an often hard to see crack, makes fatigue damage especially dangerous.The fatigue life of a component can be expressed as the number of loading cycles required to initiate a fatigue crack and to propagate the crack to critical size. Therefore, it can be said that fatigue failure occurs in three stages – crack initiation; slow, stable crack growth; and rapid fracture.
As discussed previously, dislocations play a major role in the fatigue crack initiation phase. In the first stage, dislocations accumulate near surface stress concentrations and form structures called persistent slip bands (PSB) after a large number of loading cycles. PSBs are areas that rise above (extrusion) or fall below (intrusion) the surface of the component due to movement of material along slip planes. This leaves tiny steps in the surface that serve as stress risers where tiny cracks can initiate. These tiny crack (called microcracks) nucleate along planes of high shear stress which is often 45o to the loading direction.In the second stage of fatigue, some of the tiny microcracks join together and begin to propagate through the material in a direction that is perpendicular to the maximum tensile stress. Eventually, the growth of one or a few crack of the larger cracks will dominate over the rest of the cracks. With continued cyclic loading, the growth of the dominate crack or cracks will continue until the remaining uncracked section of the component can no longer support the load. At this point, the fracture toughness is exceeded and the remaining cross-section of the material experiences rapid fracture. This rapid overload fracture is the third stage of fatigue failure.
Factors Affecting Fatigue Life
In order for fatigue cracks to initiate, three basic factors are necessary. First, the loading pattern must contain minimum and maximum peak values with large enough variation or fluctuation. The peak values may be in tension or compression and may change over time but the reverse loading cycle must be sufficiently great for fatigue crack initiation. Secondly, the peak stress levels must be of sufficiently high value. If the peak stresses are too low, no crack initiation will occur. Thirdly, the material must experience a sufficiently large number of cycles of the applied stress. The number of cycles required to initiate and grow a crack is largely dependant on the first to factors.
In addition to these three basic factors, there are a host of other variables, such as stress concentration, corrosion, temperature, overload, metallurgical structure, and residual stresses which can affect the propensity for fatigue. Since fatigue cracks generally initiate at a surface, the surface condition of the component being loaded will have an effect on its fatigue life. Surface roughness is important because it is directly related to the level and number of stress concentrations on the surface. The higher the stress concentration the more likely a crack is to nucleate. Smooth surfaces increase the time to nucleation. Notches, scratches, and other stress risers decrease fatigue life. Surface residual stress will also have a significant effect on fatigue life. Compressive residual stresses from machining, cold working, heat treating will oppose a tensile load and thus lower the amplitude of cyclic loading
The figure shows several types of loading that could initiate a fatigue crack. The upper left figure shows sinusoidal loading going from a tensile stress to a compressive stress. For this type of stress cycle the maximum and minimum stresses are equal. Tensile stress is considered positive, and compressive stress is negative. The figure in the upper right shows sinusoidal loading with the minimum and maximum stresses both in the tensile realm. Cyclic compression loading can also cause fatigue. The lower figure shows variable-amplitude loading, which might be experienced by a bridge or airplane wing or any other component that experiences changing loading patterns. In variable-amplitude loading, only those cycles exceeding some peak threshold will contribute to fatigue cracking.
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