Chapter 6
Poisson's ratio
For many metals and other alloys, values of ____ range between 0.25 and 0.35
yield strength
For materials having a nonlinear elastic region, use of the strain offset method is not possible, and the usual practice is to define the ____ as the stress required to produce some amount of strain (e.g., ε = 0.005)
yield point phenomenon
For metals that display the ____, the yield strength is taken as the average stress that is associated with the lower yield point because it is well defined and relatively insensitive to the testing procedure. Thus, it is not necessary to employ the strain offset method for these materials.
stress
If the applied ____ is uniaxial (only in the z direction) and the material is isotropic, then εx = εy
elastic deformation
Most structures are designed to ensure that only ____ will result when a stress is applied.
elastic strain
On an atomic scale, macroscopic ____ is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds.
proportional limit
P The position of this point P is difficult to measure precisely As a consequence, a convention has been established by which a straight line is constructed parallel to the elastic portion of the stress-strain curve at some specified strain offset, usually 0.002. The stress corresponding to the intersection of this line and the stress-strain curve as it bends over in the plastic region is defined as the yield strength, σy (MPa or psi)
atomic bonding
The differences in the moduli of elasticity for the different types of materials are a direct consequence of the different types of ____ in the three materials types.
plastic deformation
The magnitude of the yield strength for a metal is a measure of its resistance to ____
plastic deformation
The mechanism of ____ is different for crystalline and amorphous materials.
modulus of elasticity
The stress-strain characteristics at low stress levels are virtually the same for both tensile and compressive situations, to include the magnitude of the ____
stress strain
The tensile strength TS (MPa or psi) is the stress at the maximum on the engineering ____ curve. This corresponds to the maximum stress that can be sustained by a structure in tension; if this stress is applied and maintained, fracture will result.
plastic deformation
The transition from elastic to plastic is a gradual one for most metals; some curvature results at the onset of ____, which increases more rapidly with rising stress.
Poisson's ratio
Theoretically, ____ for isotropic materials should be ¼; furthermore, the maximum value for ν (or the value for which there is no net volume change) is 0.50
stress strain
There are some materials (i.e., gray cast iron, concrete, and many polymers) for which this elastic portion of the ____ curve is not linear; hence, it is not possible to determine a modulus of elasticity with Hooke's law
elastic deformation
deformation in which stress and strain are proportional is called ____ a plot of stress vs strain results in a linear relationship with a slope of E
tension
for most metals that are stressed in ____ and at relatively low levels, stress and strain are proportional to each other through the relationship σ = Eε
anelasticity
for some polymeric materials, the magnitude of the ____ is significant; in this case it is termed viscoelastic behavior
shear stress
for tests performed using a pure shear force, the ____ is computed according to: τ = F/A₀ F = load or force imposed parallel to the upper and lower faces A₀ = area of each face
static
if a load is ____ or changes relatively slowly with time and is applied uniformly over a cross section or surface of a member, the mechanical behavior may be ascertained by a simple stress-strain test; these are most commonly conducted for materials at room temperature
strain
independent of unit system
load
it is possible for the ____ to be tensile, compressive, or shear, and its magnitude may be constant with time or it may fluctuate continuously; application time may be only a fraction of a second, or it may extend over a period of many years; service temperature may be an important factor
load
it requires twice the ____ to produce the same elongation if the cross sectional area of the specimen is doubled
mechanical properties
key ____ are stiffness, strength, hardness, ductility, and toughness
loads
many materials are subjected to forces or ____ when in service; in such situations it is necessary to know the characteristics of the material and to design the member from which it is made such that any resulting deformation will not be excessive and fracture will not occur
strain
sometimes expressed as a percentage, with the value multiplied by 100
dogbone specimen
the ____ is mounted by its ends into the holding grips of the testing apparatus
modulus of elasticity
the ____ is proportional to the slope of the interatomic force-separation curve at the equilibrium spacing E ∝ (dF/dr) at r₀
stress
the ____ state is a function of the orientations of the planes upon which the stresses are taken to act
tension
the ____ test can be used to ascertain several mechanical properties that are important in design
stress
the degree to which a structure deforms or strains depends on the magnitude of an imposed ____
tensile
the output of a ____ test is recorded as load or force vs elongation; these load-deformation characteristics depend on the specimen size
load
there are 3 principle ways in which a ____ may be applied: tension, compression, shear
modulus of elasticity
with increasing temperature, the ____ decreases
Poisson's ratio
For isotropic materials, shear and elastic moduli are related to each other and to ____ according to E=2G(1+ν)
yield point phenomenon
Some steels and other materials exhibit the tensile stress-strain behavior in which the elastic-plastic transition is very well defined and occurs abruptly in what is termed a ____
Knoop and Vickers Microindentation Hardness Tests
Two other hardness-testing techniques are the Knoop (pronounced nūp) and Vickers tests (sometimes also called diamond pyramid).
yield strength
Typically, when the strength of a metal is cited for design purposes, the ____ is used because by the time a stress corresponding to the tensile strength has been applied, often a structure has experienced so much plastic deformation that it is useless
stress strain
Upon release of the load during the course of a ____ test, some fraction of the total deformation is recovered as elastic strain.
modulus of resilience
Ur = ½σy*εy = ½σy*(σy/E) = σ²y/2E
modulus of resilience
Ur, which is the strain energy per unit volume required to stress a material from an unloaded state up to the point of yielding associated with resilience
N
____ values normally range between 1.2 and 4.0.
Percent elongation
(%EL) is the percentage of plastic strain at fracture, or %EL=(lf−l₀ / l₀)×100 lf = fracture length l₀ = original gauge length
percent reduction in area
(%RA) is defined as %RA=(A₀−Af / A₀)×100 A₀ = original cross sectional area Af = cross sectional area at the point of fracture
modulus of elasticity
= E = young's modulus is the constant of proportionality for Hooke's law
standard deviation
A large value of the ____ corresponds to a high degree of scatter.
brittle
A metal that experiences very little or no plastic deformation upon fracture is termed ____
specimen
A number of factors lead to uncertainties in measured data, including the test method, variations in ____ fabrication procedures, operator bias, and apparatus calibration. Furthermore, there might be inhomogeneities within the same lot of material and/or slight compositional and other differences from lot to lot.
Poisson's ratio
A parameter termed ____, ν, is defined as the ratio of the lateral and axial strains, or ν=−εx/εz=−εy/εz
hardness
A qualitative and somewhat arbitrary ____ indexing scheme was devised, termed the Mohs scale, which ranged from 1 on the soft end for talc to 10 for diamond.
permanent
A structure or component that has plastically deformed—or experienced a ____ change in shape—may not be capable of functioning as intended. It is therefore desirable to know the stress level at which plastic deformation begins, or where the phenomenon of yielding occurs.
plastic deformation
After yielding, the stress necessary to continue ____ in metals increases to a maximum, point M, and then decreases to the eventual fracture, point F
tensile
All deformation up to this point of maximum stress is uniform throughout the narrow region of the ____ specimen. However, at this maximum stress, a small constriction or neck begins to form at some point, and all subsequent deformation is confined at this neck
safe stress
Alternatively, a safe stress or working stress, σw, is used instead of design stress.
design safety factor
Although ____ is still an acceptable procedure for some structural applications, it does not provide adequate safety for critical applications such as those found in aircraft and bridge structural components
average
An ____ value is obtained by dividing the sum of all measured values by the number of measurements taken
Knoop and Vickers Microindentation Hardness Tests
Applied loads are much smaller than for the Rockwell and Brinell tests, ranging between 1 and 1000 g. The resulting impression is observed under a microscope and measured; this measurement is then converted into a hardness number
modulus of elasticity
As a consequence, the magnitude of the ____ is a measure of the resistance to separation of adjacent atoms, that is, the interatomic bonding forces.
stress
As a result of elastic elongation, there will be constrictions in the lateral (x and y) directions perpendicular to the applied ____; from these contractions, the compressive strains εx and εy may be determined
tensile
As a rule of thumb, for most steels, the HB and the ____ strength are related according to TS(MPa)=3.45×HB TS(psi)=500×HB
modulus of elasticity
As with modulus of elasticity, the magnitudes of both yield and tensile strengths decline with increasing temperature; just the reverse holds for ductility—it usually increases with temperature
elastic behavior
As would be expected, the imposition of compressive, shear, or torsional stresses also evokes ____
plastic deformation
At the upper yield point, ____ is initiated with an apparent decrease in engineering stress. Continued deformation fluctuates slightly about some constant stress value, termed the lower yield point; stress subsequently rises with increasing strain.
toughness
Because it is nearly impossible (as well as costly) to manufacture materials with zero defects (or to prevent damage during service), fracture ____ is a major consideration for all structural materials.
N
Because large ____ values lead to increased material cost and weight, structural designers are moving toward using tougher materials with redundant (and inspectable) designs, where economically feasible.
grain
Because the ____ orientation is random in most polycrystalline materials, these may be considered to be isotropic; inorganic ceramic glasses are also isotropic.
Knoop and Vickers Microindentation Hardness Tests
Both are well suited for measuring the hardness of small, selected specimen regions
resilience
Both joules and inch-pounds force are units of energy, and thus this area under the stress-strain curve represents energy absorption per unit volume (in cubic meters or cubic inches) of material, which is ____
plastic deformation
Both tensile strength and hardness are indicators of a metal's resistance to ____ and are roughly proportional for tensile strength as a function of the HB for cast iron, steel, and brass The same proportionality relationship does not hold for all metals
Knoop and Vickers Microindentation Hardness Tests
Careful specimen surface preparation (grinding and polishing) may be necessary to ensure a well-defined indentation that may be measured accurately.
neck
Coincident with the formation of a ____ is the introduction of a complex stress state within the ____ region (i.e., the existence of other stress components in addition to the axial stress). As a consequence, the correct stress (axial) within the ____ is slightly lower than the stress computed from the applied load and ____ cross-sectional area. This leads to the "corrected" curve
modulus of resilience
Computationally, the ____ for a specimen subjected to a uniaxial tension test is just the area under the engineering stress-strain curve taken to yielding
design safety factor
During the 20th century, the protocol was to reduce the applied stress by a ____
modulus of elasticity
During the unloading cycle, the curve traces a near straight-line path from the point of unloading (point D), and its slope is virtually identical to the ____, or parallel to the initial elastic portion of the curve. The magnitude of this elastic strain, which is regained during unloading, corresponds to the strain recovery If the load is reapplied, the curve will traverse essentially the same linear portion in the direction opposite to unloading; yielding will again occur at the unloading stress level where the unloading began. There will also be an elastic strain recovery associated with fracture.
hardness
Early ____ tests were based on natural minerals with a scale constructed solely on the ability of one material to scratch another that was softer.
superficial Rockwell
For ____ tests, 3 kg is the minor load; 15, 30, and 45 kg are the possible major load values. These scales are identified by a 15, 30, or 45 (according to load), followed by N, T, W, X, or Y, depending on the indenter.
metals
For ____, the anelastic component is normally small and is often neglected
ductility
For a metal to be tough, it must display both strength and ____
slip
For crystalline solids, plastic deformation is accomplished by means of a process called ____, which involves the motion of dislocations
toughness
For dynamic (high strain rate) loading conditions and when a notch (or point of stress concentration) is present, "notch ____" is assessed by using an impact test
hardness
For each scale, ____ values may range up to 130; however, as ____ values rise above 100 or drop below 20 on any scale, they become inaccurate; because the scales have some overlap, in such a situation it is best to utilize the next-harder or next-softer scale.
Knoop and Vickers Microindentation Hardness Tests
For each test, a very small diamond indenter having pyramidal geometry is forced into the surface of the specimen.
anisotropic
For elastically ____ materials, the elastic properties are completely characterized only by the specification of several elastic constants, their number depending on characteristics of the crystal structure Even for isotropic materials, for complete characterization of the elastic properties, at least two constants must be given
Rockwell
For example, 80 HRB represents a ____ hardness of 80 on the B scale, and 60 HR30W indicates a superficial hardness of 60 on the 30W scale.
stress
For less critical static situations and when tough materials are used, a design ____, σd, is taken as the calculated ____ level σc (on the basis of the estimated maximum load) multiplied by a design factor, N′; that is σd=N′σc N′ is greater than unity Thus, the material to be used for the particular application is chosen so as to have a yield strength at least as high as this value of σd.
stress strain
For metals that experience this gradual elastic-plastic transition, the point of yielding may be determined as the initial departure from linearity of the ____ curve; this is sometimes called the proportional limit and represents the onset of plastic deformation on a microscopic level
elastic deformation
For most metallic materials, ____ persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke's law ceases to be valid), and permanent, nonrecoverable, or plastic deformation occurs.
stress strain
For nonlinear elastic behavior, either the tangent or secant modulus is normally used. The tangent modulus is taken as the slope of the ____ curve at some specified level of stress, whereas the secant modulus represents the slope of a secant drawn from the origin to some given point of the σ-ε curve.
necking
For some metals and alloys the region of the true stress-strain curve from the onset of plastic deformation to the point at which ____ begins may be approximated by σT = K*ε^n∨T K and n are constants; these values vary from alloy to alloy and also depend on the condition of the material (whether it has been plastically deformed, heat-treated, etc.) parameter n is often termed the strain-hardening exponent and has a value less than unity
Rockwell
For the ____ test, the minor load is 10 kg, whereas major loads are 60, 100, and 150 kg. Each scale is represented by a letter of the alphabet
toughness
For the static (low strain rate) situation, a measure of ____ in metals (derived from plastic deformation) may be ascertained from the results of a tensile stress-strain test. It is the area under the σ-ε curve up to the point of fracture. The units are the same as for resilience (i.e., energy per unit volume of material).
structural
For virtually all ____ materials, εx and εz will be of opposite sign; therefore, the negative sign is included in the preceding expression to ensure that ν is positive
plastic deformation
From an atomic perspective, ____ corresponds to the breaking of bonds with original atom neighbors and then the re-forming of bonds with new neighbors as large numbers of atoms or molecules move relative to one another; upon removal of the stress, they do not return to their original positions
specimen
Furthermore, testing of ____s stacked one on top of another is not recommended.
loads
Harder materials require greater applied ____.
true
If no volume change occurs during deformation—that is, if Ai*li=A₀*l₀ then ____ and engineering stress and strain are related according to σT=σ(1+ε) εT=ln(1+ε) valid only to the onset of necking; beyond this point, true stress and strain should be computed from actual load, cross-sectional area, and gauge length measurements
Brinell
In ____ tests, as in Rockwell measurements, a hard, spherical indenter is forced into the surface of the metal to be tested.
Brinell Hardness Tests
In addition, a well-defined indentation is required; this necessitates a smooth, flat surface in which the indentation is made.
metals
In most ____, G is about 0.4E; thus, if the value of one modulus is known, the other may be approximated BUT PROF SAYS v = 0.33 FOR METALS
elastic strain
In most engineering materials, there will exist a time-dependent ____ component—that is, elastic deformation will continue after the stress application, and upon load release, some finite time is required for complete recovery.
specimen
Inaccuracies also result if the test ____ is too thin, if an indentation is made too near a specimen edge, or if two indentations are made too close to one another.
%EL
Inasmuch as a significant proportion of the plastic deformation at fracture is confined to the neck region, the magnitude of ____ will depend on specimen gauge length. The shorter l0, the greater the fraction of total elongation from the neck and, consequently, the higher the value of ____. Therefore, l0 should be specified when ____ values are cited; it is commonly 50 mm (2 in.)
Rockwell Hardness Tests
Indenters include spherical and hardened steel balls having diameters of 116116, 1818, 1414, and 12 in.12 in. (1.588, 3.175, 6.350, and 12.70 mm, respectively), as well as a conical diamond (Brale) indenter, which is used for the hardest materials.
variability
It is important for the design engineer to realize that scatter and ____ of materials properties are inevitable and must be dealt with appropriately. On occasion, data must be subjected to statistical treatments and probabilities determined.
measured
It is often desirable to specify a typical value and degree of dispersion (or scatter) for some ____ property; this is commonly accomplished by taking the average and the standard deviation, respectively
ductility
Knowledge of the ____ of materials is important for at least two reasons. First, it indicates to a designer the degree to which a structure will deform plastically before fracture. Second, it specifies the degree of allowable deformation during fabrication operations.
anisotropic
Many materials are elastically ____; that is, the elastic behavior (the magnitude of E) varies with crystallographic direction
Brinell Hardness Tests
Maximum specimen thickness and indentation position (relative to specimen edges) as well as minimum indentation spacing requirements are the same as for Rockwell tests.
hardness
Measured ____ values are only relative (rather than absolute), and care should be exercised when comparing values determined by different techniques.
brittle
Most metals possess at least a moderate degree of ductility at room temperature; however, some become ____ as the temperature is lowered
factor of safety
N
Rockwell
On the basis of the magnitude of both major and minor loads, there are two types of tests: ____ and superficial ____.
hardness
Other ____-testing techniques frequently employed include ultrasonic microhardness, dynamic (Scleroscope), durometer (for plastic and elastomeric materials), and scratch hardness tests.
hardness
Quantitative ____ techniques have been developed over the years in which a small indenter is forced into the surface of a material to be tested under controlled conditions of load and rate of application. The depth or size of the resulting indentation is measured and related to a ____ number; the softer the material, the larger and deeper the indentation, and the lower the ____ index number.
N
Selection of ____ will depend on a number of factors, including economics, previous experience, the accuracy with which mechanical forces and material properties may be determined, and, most important, the consequences of failure in terms of loss of life and/or property damage.
Brinell
Semiautomatic techniques for measuring ____ hardness are available. These employ optical scanning systems consisting of a digital camera mounted on a flexible probe, which allows positioning of the camera over the indentation. Data from the camera are transferred to a computer that analyzes the indentation, determines its size, and then calculates the ____ hardness number. For this technique, surface finish requirements are normally more stringent than those for manual measurements.
Rockwell Hardness Tests
Several different scales may be used from possible combinations of various indenters and different loads, a process that permits the testing of virtually all metal alloys (as well as some polymers)
Rockwell Hardness Tests
The ____ constitute the most common method used to measure hardness because they are so simple to perform and require no special skills.
Brinell
The ____ hardness number, HB, is a function of both the magnitude of the load and the diameter of the resulting indentation
Knoop and Vickers
The ____ hardness numbers are designated by HK and HV, respectively,18 and hardness scales for both techniques are approximately equivalent.
Knoop and Vickers
The ____ techniques are referred to as microindentation-testing methods on the basis of indenter size.
N
The choice of an appropriate value of ____ is necessary. If ____ is too large, then component overdesign will result; that is, either too much material or an alloy having a higher-than-necessary strength will be used.
structural
The current approach for critical structural applications is to utilize materials that have adequate toughnesses and also offer redundancy in the ____ design (i.e., excess or duplicate structures), provided there are regular inspections to detect the presence of flaws and, when necessary, safely remove or repair components.
Brinell Hardness Tests
The diameter of the hardened steel (or tungsten carbide) indenter is 10.00 mm (0.394 in.). Standard loads range between 500 and 3000 kg in 500-kg increments; during a test, the load is maintained constant for a specified time (between 10 and 30 s).
hardness
The facility to convert the ____ measured on one scale to that of another is most desirable. However, because ____ is not a well-defined material property, and because of the experimental dissimilarities among the various techniques, a comprehensive conversion scheme has not been devised.
Rockwell
The modern apparatus for making ____ hardness measurements is automated and very simple to use; hardness is read directly, and each measurement requires only a few seconds. This apparatus also permits a variation in the time of load application. This variable must also be considered in interpreting hardness data.
hardness
The modern microindentation ____-testing equipment has been automated by coupling the indenter apparatus to an image analyzer that incorporates a computer and software package. The software controls important system functions, including indent location, indent spacing, computation of hardness values, and plotting of data.
necking
The phenomenon of deformation confined at the neck is termed ____, and fracture ultimately occurs at the neck
resilience
The units of ____ are the product of the units from each of the two axes of the stress-strain plot. For SI units, this is joules per cubic meter (J/m3, equivalent to Pa), whereas with customary U.S. units, it is inch-pounds force per cubic inch (in.-lbf/in.3, equivalent to psi)
load
There will always be uncertainties in characterizing the magnitude of applied loads and their associated stress levels for in-service applications; typically, ____ calculations are only approximate
Brinell Hardness Tests
This diameter is measured with a special low-power microscope using a scale that is etched on the eyepiece. The measured diameter is then converted to the appropriate HB number using a chart; only one scale is employed with this technique.
modulus of resilience
Ur=∫ from 0 to εy of σdε Assuming a linear elastic region, we have Ur=½σy*εy in which εy is the strain at yielding
design stress
Utilization of ____ is usually preferred because it is based on the anticipated maximum applied stress instead of the yield strength of the material; normally, there is a greater uncertainty in estimating this stress level than in the specification of the yield strength.
percent reduction in area
Values of ____ are independent of both l0 and A0. Furthermore, for a given material, the magnitudes of %EL and %RA will, in general, be different.
modulus of elasticity
Values of the ____ for ceramic materials are about the same as for metals; for polymers they are lower
ductile
We sometimes refer to relatively ____ materials as being "forgiving," in the sense that they may experience local deformation without fracture, should there be an error in the magnitude of the design stress calculation.
tensile
When a ____ stress is imposed on a metal specimen, an elastic elongation and accompanying strain εz result in the direction of the applied stress (arbitrarily taken to be the z direction)
Rockwell
When specifying ____ and superficial hardnesses, both hardness number and scale symbol must be indicated. The scale is designated by the symbol HR followed by the appropriate scale identification.
Rockwell Hardness Tests
With this system, a hardness number is determined by the difference in depth of penetration resulting from the application of an initial minor load followed by a larger major load; utilization of a minor load enhances test accuracy.
materials and metallurgical engineers
____ are concerned with producing and fabricating materials to meet service requirements as predicted by these stress analyses; this necessarily involves an understanding of the relationships between the microstructure (internal features) of materials and their mechanical properties
fracture strengths
____ are not normally specified for engineering design purposes
mechanical properties
____ are of concern to a variety of parties (producers and consumers of materials, research organizations, government agencies) that have differing interests
hardness
____ conversion data have been determined experimentally and found to be dependent on material type and characteristics. The most reliable conversion data exist for steels for Knoop, Vickers, Brinell, and two Rockwell scales; the Mohs scale is also included.
fracture strength
____ corresponds to the stress at fracture
variability
____ exists for other measured material properties, such as density, electrical conductivity, and coefficient of thermal expansion.
torsional
____ forces produce a rotational motion about the longitudinal axis of one end of the member relative to the other end
plastic deformation
____ in noncrystalline solids (as well as liquids) occurs by a viscous flow mechanism
ductility
____ is a measure of the degree of plastic deformation that has been sustained at fracture
toughness
____ is a property that is indicative of a material's resistance to fracture when a crack (or other stress-concentrating defect) is present
torsion
____ is a variation of pure shear in which a structural member is twisted
safe stress
____ is based on the yield strength of the material and is defined as the yield strength divided by a factor of safety, N, or σw=σyN
elastic deformation
____ is nonpermanent, meaning that when the applied load is released, the piece returns to its original shape
Resilience
____ is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered
measured
____ material properties are not exact quantities
Brittle
____ materials are approximately considered to be those having a fracture strain of less than about 5%
resilient
____ materials are those having high yield strengths and low moduli of elasticity; such alloys are used in spring applications.
ductility
____ may be expressed quantitatively as either percent elongation or percent reduction in area
modulus of elasticity
____ may be thought of as stiffness, or a material's resistance to elastic deformation, and is an important design parameter for computing elastic deflections
mechanical behavior
____ of a material reflects its response or deformation in relation to an applied load or force
mechanical properties
____ of materials are ascertained by performing carefully designed lab experiments that replicate as nearly as possible the service conditions; factors to be considered include the nature of the applied load and its duration, and environmental conditions
standard deviation
____ s is determined using the following expression
Tensile
____ strengths vary from 50 MPa (7000 psi) for an aluminum to as high as 3000 MPa (450,000 psi) for the high-strength steels
Shear
____ stress and strain are proportional to each other through the expression τ=Gγ G = the shear modulus
superficial Rockwell
____ tests are frequently performed on thin specimens
tensile
____ tests are more common because they are easier to perform; for most materials used in structural applications, very little additional information is obtained from compressive tests
torsional
____ tests are normally performed on cylindrical solid shafts or tubes
hardness
____ tests are performed more frequently than any other mechanical test for several reasons: 1) They are simple and inexpensive—typically, no special specimen need be prepared, and the testing apparatus is relatively inexpensive. 2) The test is nondestructive—the specimen is neither fractured nor excessively deformed; a small indentation is the only deformation. 3) Other mechanical properties often may be estimated from ____ data, such as tensile strength
compressive
____ tests are used when a material's behavior under large and permanent (plastic) strains is desired, as in manufacturing applications or when the material is brittle in tension
specimen
____ thickness should be at least 10 times the indentation depth, whereas allowance should be made for at least three indentation diameters between the center of one indentation and the specimen edge, or to the center of a second indentation.
Yield strength
____ values may range from 35 MPa (5000 psi) for a low-strength aluminum to greater than 1400 MPa (200,000 psi) for high-strength steels
average
____ xbar of some parameter x is xbar = n∑i=1 xi / n n = number of observations or measurements xi = value of a discrete measurement
True stress
____, σT, is defined as the load F divided by the instantaneous cross-sectional area Ai over which deformation is occurring (i.e., the neck, past the tensile point) σT=F / Ai
compression
a ____ test is conducted in a manner similar to the tensile test, except that the force is compressive and the specimen contracts along the direction of the stress
stress strain
a ____ test typically takes several minutes to perform and is destructive, meaning that the test specimen is permanently deformed and usually fractured
shear stress
a ____ τ is a function of the applied torque T, whereas shear strain γ is related to the angle of twist φ (phi)
hardness
a measure of a material's resistance to localized plastic deformation (e.g., a small dent or a scratch)
tensile
a specimen is deformed, usually to fracture, with a gradually increasing ____ load that is applied uniaxially along the long axis of a specimen; normally the cross section is circular, but rectangular specimens are also used; this "dogbone" specimen configuration was chosen so that during testing the deformation is confined to the narrow center region (which has a uniform cross section along its length) and also to reduce the likelihood of fracture at the ends of the specimen
variability
appropriate measures should be taken to minimize the possibility of measurement error and mitigate those factors that lead to data ____
compressive
by convention, ____ force is taken to be negative, which yields a negative stress; because l₀ is greater than li, ____ strains are necessarily also negative
stress strain
compression ____ tests may be conducted if in-service forces are of this type
tensile
consider the the cylindrical tensile specimen that is subjected to a ____ stress σ applied parallel to its axis, and the plane p-p' oriented at some arbitrary angle θ to the ends of the specimen upon the plane p-p', the applied stress is no longer a pure ____ one; a more complex stress state is present that consists of a ____ (or normal) stress σ' that acts normal to the plane and a shear stress τ' that acts parallel to the plane σ' = σ*cos²θ = σ[(1+cos(2θ)) / 2] τ' = σ*sinθ*cosθ = σ(sin(2θ) / 2) these same mechanics principles allow the transformation of stress components from one coordinate system to another coordinate system with a different orientation
tensile strength
declines with increasing temperature
failure
design approaches must be employed to protect against unanticipated ____
variability
even if we have a most precise measuring apparatus and a highly controlled test procedure, there will always be some scatter or ____ in the data that are collected from specimens of the same material
Rockwell Hardness Tests
for ____, accuracy is dependent on the indentation being made into a smooth flat surface
necking
for compression, there is no maximum because ____ does not occur; furthermore, the mode of fracture is different from that for tension.
shear
in engineering practice many loads are torsional rather than pure ____
tests
it is imperative that there be some consistency in the manner in which ____ are conducted and in the interpretation of their results, which is accomplished by using standardized testing techniques
structural
materials are frequently chosen for ____ applications because they have desirable combinations of mechanical characteristics
plastic deformation
metals may experience ____ under the influence of applied compressive, shear, and torsional loads. The resulting stress-strain behavior into the plastic region is similar to the tensile counterpart
tension
one of the most common mechanical stress-strain tests is performed in ____
plastic deformation
permanent, nonrecoverable deformation
sperately
polymers and ceramics are treated ____ because they are, to a large degree, mechanically different from metals
modulus of elasticity
range of ____ values for metals is between 45GPa and 407 GPa dependent on temperature
Knoop
the ____ technique is used for testing brittle materials such as ceramics
tensile
the ____ testing machine is designed to elongate the specimen at a constant rate, and to continuously and simultaneously measure the instantaneous applied load with a load cell and the resulting elongations with an extensometer
toughness
the ability of a material to absorb energy and plastically deform before fracturing
modulus of elasticity
the greater the ____, the stiffer the material, and the smaller the elastic strain that results from an applied stress
structural engineers
the role of ____ is to determine stresses and stress distributions within members that are subjected to well-defined loads; this may be accomplished by experimental testing techniques and/or by theoretical and mathematical stress analyses
shear modulus
the slope of the linear elastic region of the shear stress-strain curve
dogbone specimen
the standard diameter is about 12.8mm/0.5in. whereas the reduce section length should be at least 4 times this diameter: 60mm/2.25in. is common; guage length is used in ductility computations with a standard value of 50mm/2.0in.
stress
the true ____ necessary to sustain increasing strain continues to rise past the tensile point M′ The "corrected" true stress-strain curve takes into account the complex stress state within the neck region.
metal
these properties (yield strength, tensile strength, and ductility) are sensitive to any prior deformation, the presence of impurities, and/or any heat treatment to which the ____ has been subjected. The modulus of elasticity is one mechanical parameter that is insensitive to these treatments.
anelasticity
time-dependent elastic behavior is known as ____, and it is due to time-dependent microscopic and atomistic processes that are attendant to the deformation
engineering
to minimize these geometrical factors, load and elongation are normalized to the respective parameters of ____ stress and ____ strain
ductility
usually increases with temperature
variability
virtually all engineering materials exhibit a ____ in their measured mechanical properties, have imperfections that were introduced during manufacture, and, in some instances, will have sustained damage during service
shear strain
γ = tanθ = ∆x/L defined as the tangent of the strain angle θ
engineering strain
ε = (li - l₀)/l₀ = ∆l/l₀ (unitless or m/m or in./in.) l₀ = original length before any load is applied li = instantaneous length
true strain
εT εT=ln( li / l₀ )
Hooke's law
σ = Eε
engineering stress
σ = F/A₀ (in MPa, 1 MPa = 10⁶ N/m², or psi) F = the instantaneous load applied perpendicular to the specimen cross section (N or lb force) A₀ = original cross sectional area before any load is applied (m² or in.²)
