Materials Science

Tensile, Compressive, Shear, and Flexural Stresses

Materials are subject to several types of stresses depending on the way the forces are applied: tensile, compressive, shear, and flexural.

Tensile Stresses

Tensile stresses directly pull apart an object or cause it to be in tension. Tensile stresses occur parallel to the line of force but perpendicular to the area in question ( Fig. 2.5 ). If an object is pulled at both ends, it is in tension, and sufficient force will pull it apart. Two children fighting over a fish scale and exerting opposing forces put it in tension, as shown by the indicator on the scale ( Fig. 2.6 ). Strings are a good example of objects that typically can only have tension applied.

Compressive Stresses

Compressive stresses act to squeeze or compress objects. They also occur parallel to the line of force and perpendicular to the cross-sectional area ( Fig. 2.7 ).

A blacksmith shapes metal by hitting the material with a hammer to squeeze or compress the metal into the desired shape. In the same manner, clay yields to low compressive stress. Clay is distorted and squeezed out of shape by comparatively small forces. Many materials may be strong in compression and relatively weak in tension. The opposite can also be true.

Shear Stresses

Shear stresses act to scissor or shear the object, causing the planes of the material to slide over each other. Shear stresses occur parallel to the applied forces. Consider two blocks ( Fig. 2.8A ) with their surfaces bonded together. If forces acting in opposite directions are applied to these blocks, they tend to slide over each other. If these forces are great enough, the bond between the blocks will break ( Fig. 2.8B ). If the area of the bonded surfaces were increased, however, the effect of the forces would be distributed over a greater area. The average stress would be decreased, and there would be increased resistance to shear stress.

A common lap joint and clevis joint are examples of a shear pin used as the axis of the joint ( Fig. 2.9 ). The lap joint has one shear area of the rivet resisting the forces applied to the lap joint (see Fig. 2.9A ), and the rivet in the box joint (clevis) has an area resisting the applied forces that is twice as great as the area in the lap joint (assuming that the rivets in both joints are the same size; see Fig. 2.9B ). Consequently the clevis joint will withstand twice as much shear force as the lap joint. The lap joint also has less resistance to fatigue (fluctuating stress of relatively low magnitude, which results in failure), because it is more susceptible to flexing stresses.

Flexural Stress

Flexural stress (bending) is a combination of tension and compression stresses. Beams are subject to flexural stresses. When a beam is loaded transversely, it will sag. The top fibers of a beam are in maximum compression while the bottom side is in maximum tension ( Fig. 2.10 ). The term fiber, as used here, means the geometric lines that compose the prismatic beam. The exact nature of these compressive and tensile stresses is discussed later.

Yield Stress

The yield stress or yield point is the point at which the material begins to maintain a deformational change because of the load and therefore the internal stresses under which it has been exposed. Before this point the material is behaving in its elastic zone—that is, any deformation moves back to its original position.

Ultimate Stress

Ultimate stress is the stress at which a material ruptures. The strength of the material before it ruptures also depends on the type of stress to which it is subjected. For example, ultimate shear stresses usually are lower than ultimate tensile stresses (i.e., less shear stress must be applied before the material ruptures than in the case of tensile or compressive stress).

Strain

Materials subjected to any stress will deform or change their shape, even at very small levels of stress. If a material lengthens or shortens in response to stress, it is said to experience strain. Strain is denoted by ε and can be found by dividing the total elongation (or contraction) Δ L by the original length L _O of the structure being loaded:

Consider a change in length Δ L of a wire or rod caused by a change in stretching force F ( Fig. 2.11 ). The amount of stretch is proportional to the original length of wire.

Stress–Strain Curve

The most widely used means of determining the mechanical properties of materials is the tension test. Much can be learned from observing the data collected from such a test. In the tension test, the shape (dimensions) of the test specimen are fixed by standardization so that the results can be universally understood, no matter where or by whom the test is conducted. The test specimen is mounted between the jaws of a tensile testing machine, which is simply a device for stretching the specimen at a controlled rate. As defined by standards, the cross-sectional area of the test specimen is smaller in the center to prevent failures where the test specimen is gripped. The specimen's resistance to being stretched and the linear deformations are measured by sensitive instrumentation ( Fig. 2.12 ).

The force of resistance divided by the cross-sectional area of the specimen is the stress in the specimen ( Eq. 2.1 ). The strain is the total deformation divided by the original length ( Eq. 2.2 ). If the stresses in the specimen are plotted as ordinates of a graph, with the accompanying strains as abscissae, a number of mechanical properties are graphically revealed. Fig. 2.13 shows such a typical stress–strain diagram for a mild steel specimen.

The shape and magnitude of the stress–strain curve of a metal depend on its composition; heat treatment; history of plastic deformation; and strain rate, temperature, and state of stress imposed during testing. The parameters used to describe the stress–strain curve of a metal are tensile strength, yield strength or yield point, percent elongation, and reduction in area. The first two are strength parameters; the last two indicate ductility, or the material's ability to be stretched (and remain stretched) under tension.

The general shape of the stress–strain curve (see Fig. 2.13 ) requires further explanation. In the region from a to b, the stress is linearly proportional to strain, and the strain is elastic (i.e., the stressed part returns to its original shape when the load is removed). When the applied stress exceeds the yield strength, b, the specimen undergoes plastic deformation. If the load is subsequently reduced to zero, the part remains permanently deformed. The stress required to produce continued plastic deformation increases with increasing plastic strain (points c, d, and e on Fig. 2.13 )—that is, the metal strain hardens. The volume of the part remains constant during plastic deformation, and as the part elongates, its cross-sectional area decreases uniformly along its length until point e is reached. The ordinate of point e is the tensile strength of the material. After point e, further elongation requires less applied stress until the part ruptures at point f (breaking or fracture strength). Although this seems counterintuitive, it actually occurs and is best sensed when bolts are overtorqued. Correct torque settings should always be complied with, but practitioners commonly torque bolts using the “as hard as possible” technique, assuming that this method somehow secures the bolt more appropriately than the correct torque and a thread-locking solution. When excessive torque has been applied, the bolt first feels like it has loosened before failing. This simply reflects the fact that the yield point of the material has been surpassed and the bolt is plastically deforming under a decreasing load to failure.

Stress–strain diagrams assume widely differing forms for various materials. Fig. 2.14A shows the stress–strain diagram for a medium-carbon structural steel. The ordinates of points p, u, and b are the yield point, tensile strength, and breaking strength, respectively. The lower curve of Fig. 2.14B is for an alloy steel, and the higher curve is for hard steels. Nonferrous alloys and cast iron have the form shown in Fig. 2.14C . The plot shown in Fig. 2.14D is typical for rubber. Note that these are representative graphs only. The dimensions (and scale) vary greatly for the materials mentioned here.

For any material with a stress–strain curve of the form shown in Figs. 2.14 , it is evident that the relationship between stress and strain is linear for comparatively small values of the strain. This linear relationship between elongation and the axial force causing it was first reported by Sir Robert Hooke in 1678 and is called Hooke 's law. Expressed as an equation, Hooke's law becomes:

where σ = stress (psi), ε = strain (inch/inch), and E = constant of proportionality between stress and strain. This constant is also called Young 's modulus or the modulus of elasticity.

The slope of the stress–strain curve from the origin to point p (see Figs. 2.14A and 2.14B ) is the modulus of elasticity of that particular material E. The region where the slope is a straight line is called the elastic region, where the material behaves in what we typically associate as an elastic manner; that is, it is loaded and stretched, and upon releasing the load the material returns to its original position. The ordinate of a point coincident with p is known as the elastic limit (i.e., the maximum stress that may develop during a simple tension test such that no permanent or residual deformation occurs when the load is entirely removed). Values for E are given in Table 2.1 . Devices and materials are designed to perform in the elastic region (with very few exceptions).

In a routine tension test ( Fig. 2.15 ), which illustrates Hooke's law, a bar of area A is placed between two jaws of a vise, and a force F is applied to compress the bar. Combining Eqs. 2.1, 2.2, and 2.3 and solving for the shortening Δ L gives:

Because the original length L _O , cross-sectional area A, and modulus of elasticity E are constants, the shortening Δ L depends solely on F. As F doubles, so does Δ L.

The operation of a steel spring scale is another practical illustration of Hooke's law ( Fig. 2.16 ). The amount of deflection of the spring for every unit of force of the load remains constant. In Fig. 2.16A the scale indicates three units (pounds, ounces, or grams). With one weight added (see Fig. 2.16B ), the scale indicates 5, or two additional units. A second weight added (see Fig. 2.16C ) causes the scale to indicate 7, or a total of four additional units, and a third weight stretches the spring two more units (see Fig. 2.16D ). Therefore it is possible to make uniform gradations for every unit of force to the point beyond the range of elasticity where the spring would distort or break. Scales are manufactured with springs strong enough to bear predetermined maximum loads. A compression spring scale designed to remain within the elastic range, recording weights to about 250 lb (100 kg) and then returning back to 0, is the common type used for weighing people.

Plastic Range

Plastic range is beyond the elastic range ( b to past e on the stress–strain diagram of Fig. 2.13 ), and the material behaves plastically. That is, the material has a set or permanent deformation when externally applied loads are removed—it has “flowed” or become plastic. In the case of the steel spring scale, if the weight did not actually break the spring, it would stretch it permanently so that the readings on the scale would be no longer accurate.

When forming orthotic bars, the practitioner must bend the bar beyond the elastic limit and into a range of plastic deformation with some associated elastic return. With experience and some basic experiments, the practitioner will be able to accurately predict the range of deformation and return for particular bends. An advisable strategy is to chart this elastic return for the regular bends and commonly used sidebars.

For most materials, the stress–strain curve has an initial linear elastic region in which deformation is reversible. Note the load σ ₂ in Fig. 2.17 . This load will cause strain ε _E . When the load is removed, the strain disappears, that is, point X (σ ₂ , ε _E ) moves linearly down the proportional portion of the curve to the origin. Similarly, when load σ ₁ is applied, strain ε _T results. However, when load σ ₁ is removed, point Y does not move back along the original curve to the origin but moves to the strain axis along a line parallel to the original linear region intersecting the strain axis at ε _P . Therefore with no load, the material has a residual or permanent strain of ε _P . Plastic deformation is difficult to judge because of elastic and plastic deformation but can be predicted for sidebars and charted as previously mentioned. The quantity of permanent strain ε _P is the plastic strain, and (ε _T − ε _P ) is the elastic strain ε _E or:

${\epsilon }_T-{\epsilon }_p={\epsilon }_E$

where ε _T = total strain under load, ε _P = plastic (or permanent) strain, and ε _E = elastic strain.

Thermal Stress

When a material is subjected to a change in temperature, its dimensions increase or decrease as the temperature rises or falls. If the material is constrained by neighboring structures, stress is produced.

The influence of temperature change is noted through the medium of the coefficient of thermal expansion α, which is defined as the unit strain produced by a temperature change of 1 degree. This physical constant is a mechanical property of each material. Values of α for several materials are given in Table 2.2 .

TABLE 2.2

Geometric Factors for Common Shapes

	Rectangle	Triangle	Circle	Semicircle
y − c	h /2	h /3	r	0.425 r
I cc	bh 3 /12	bh 3 /36	0.785 r 4	0.11 r 4
I xx	bh 3 /3	bh 3 /12	3.93 r 4	0.393 r 4
Z	bh 2 /6	bh 3 /24	0.785 r 3	0.19 r 3
C	h /2	2 h /3 (top)	r	0.575 r (top)
		h /3 (bottom)		0.425 r (bottom)

If the temperature of a bar of length L _O inches is increased Δ T F (or C; note : α indicates which measure of temperature it relates to), the elongation Δ L in any units of the unrestrained bar is given by:

If the heated rod is compressed back to its original length, then it will experience compression as given by Eq. 2.4 :

Combining Eqs. 2.6 and 2.7 and solving for stress, σ = F/A, gives:

Eq. 2.8 allows the calculation of stress in a rod as a function of the increase in temperature Δ T, the modulus of elasticity E (see Table 2.1 ), and the coefficient of thermal expansion α ( Table 2.3 ).

Centroids and Center of Gravity

The centroid and center of gravity of objects play important roles in their mechanical properties. The center of gravity and centroid of two identically shaped objects are the same if the density is uniform in each object. The centroid is a geometric factor, and center of gravity depends on mass.

For an object of uniform density, the term center of gravity is replaced by the centroid of the area. The centroid of an area is defined as the point of application of the result of a uniformly distributed force acting on the area. An irregularly shaped plate of material of uniform thickness t is shown in Fig. 2.18 . Two elemental areas ( a and b ) are shown with centroids ( x ₁ , y ₁ ) and ( x ₂ , y ₂ ), respectively. If the large, irregularly shaped plate is divided into small elemental areas, each having its own centroid, then the centroid for the irregularly shaped plate is ( x,y ), where:

and

The y -centroids for several common geometric shapes are given in Table 2.2 .

Stresses in Beams

If forces are applied to a beam as shown in Fig. 2.20 , downward bending of the beam occurs. It is helpful to imagine a beam is composed of an infinite number of thin longitudinal rods or fibers. Each longitudinal fiber is assumed to act independently of every other fiber (i.e., there are no lateral stresses [shear] between fibers). The beam of Fig. 2.20 will deflect downward and the fibers in the lower part of the beam undergo extension, whereas those in the upper part shorten. The changes in the lengths of the fibers set up stresses in the fibers. Those that are extended have tensile stresses acting on the fibers in the direction of the longitudinal axis of the beam, whereas those that are shortened are subject to compression stresses.

One surface in the beams always contains fibers that do not undergo any extension or compression and thus are not subject to any tensile or compressive stress. This surface is called the neutral surface of the beam. The intersection of the neutral surface with any cross-section of the beam perpendicular to its longitudinal axis is called the neutral axis. All fibers on one side of the neutral axis are in a state of tension, whereas those on the opposite side are in compression.

For any beam having a longitudinal plane of symmetry and subject to a bending torque T at a certain cross-section, the normal stress σ, acting on a longitudinal fiber at a distance y from the neutral axis of the beam ( Fig. 2.21 ), is given by:

where I = moment of inertia of the cross-sectional area about the neutral or centroidal axis in in ⁴ , or (m ⁴ ).

These stresses vary from zero at the neutral axis of the beam ( y = 0) to a maximum at the outer fibers ( Fig. 2.21 ). These stresses are called bending, flexure, or fiber stresses.

Beam Torque

Most structural elements in orthoses can be represented by either a cantilever beam loaded transversely with a perpendicular force at the end (e.g., a stirrup in terminal stance; Fig. 2.22 ) or a beam freely supported at the ends and centrally loaded (e.g., KAFO prescribed to control valgum; Fig. 2.23 ).

The maximum torque in cantilevered (see Fig. 2.22 ) and freely supported (see Fig. 2.23 ) beams is given by:

$T_{\max }=\text{FL}$

$T_{\max }=\frac{\text{FL}}{4}$

Fig. 2.24 gives the maximum torque for a few simple beams. If more than one external force acts on a beam, the bending torque is the sum of the torques caused by all the external forces acting on either side of the beam. Subsequently and not surprisingly, device failures commonly occur at the corresponding point of maximum torque (bending moment).

Beam Deflection

The maximum deflection of beams (sidebars, stirrups) is important to practitioners, because the biomechanical objective of a prescribed device commonly depends on the ability of the device either to not deflect or to deflect a given amount. Excessive deflection (bending) of a device may either disturb alignment or prevent successful operation.

Deflection theory provides a technique of analysis for evaluating the nature and magnitude of deformations in beams. The cantilevered beam ( Fig. 2.25 ) carries a concentrated downward load F at the free end. A cantilevered beam is, by definition, rigidly supported at the other end. The general expression for the downward deflection y, anywhere along the length ( x -axis) of the beam, is given by:

$y\left(x\right)=\frac{F{x}^3}{-6EI}+\frac{Fx{L}^2}{2EI}-\frac{F{L}^3}{3EI}$

The maximum deflection of the cantilevered beam ( y _max ) occurs at the free end when x = 0:

$y_{\max }=-\frac{F{L}^3}{3EI}$

The general expression for the deflection of the freely supported beam with the midspan load ( Fig. 2.26 ) is given by:

$y\left(x\right)=\frac{F{x}^3}{12EI}-\frac{Fx{L}^2}{16EI}$

The maximum deflection of the freely supported beam ( y _max ) occurs at the midspan when x = L/2:

$y_{\max }=\frac{F{L}^3}{-48EI}$

The negative sign in Eqs. 2.19 and 2.21 indicates that the maximum deflection is downward from the unloaded position.

Crystallinity

One of the important characteristics of all metals is their crystallinity. A crystalline substance is one in which the atoms are arranged in a definite and repeating order in a three-dimensional pattern. This regular arrangement of atoms is called a space lattice. Space lattices are characteristic of all crystalline materials. Most metals crystallize in one of three types of space lattices:

• Cubic system: Three contiguous edges of equal length and at right angles—simple lattice, body-centered lattice, and face-centered lattice ( Fig. 2.27 )

  

• Tetragonal system: Three contiguous edges, two of equal length, all at right angles—simple lattice and body-centered lattice ( Fig. 2.28 )

  

• Hexagonal system: Three parallel sets of equal-length horizontal axes at 120 degrees and a vertical axis—close-packed hexagonal ( Fig. 2.29 )

  

This orderly state also is described as balanced, unstrained, or annealed. Some metals can exist in several lattice forms, depending on the temperature. Examples of metals that normally exist in only one form are as follows:

• Face-centered cubic: Ca, Ni, Cu, Ag, Au, Pb, Al

• Body-centered cubic: Li, Na, K, V, W

• Face-centered tetragonal: In

• Close-packed hexagonal: Be, Mg, Zn, Cd

Common iron is an example of one of many metals that may exist in more than one lattice form:

• Body-centered cubic: Below 1663°F (906°C)

• Face-centered cubic: 1663°F to 2557°F (906–1403°C)

• Body-centered cubic: 2557°F to 2795°F (1403–1535°C)

A metal in the liquid state is noncrystalline, and the atoms move freely among one another without regard to interspatial distances. The internal energy possessed by these atoms prevents them from approaching one another closely enough to come under the control of their attractive electrostatic fields. However, as the liquid cools and loses energy, the atoms move more sluggishly. At a certain temperature, for a particular pure metal, certain atoms are arranged in the proper position to form a single lattice typical of metal. The temperature at which atoms begin to arrange themselves in a regular geometric pattern (lattice) is called the freezing point. As heat is removed from metal, crystallization continues, and the lattices grow around each center. This growth continues at the expense of the liquid, with the lattice structure expanding in all directions until development is stopped by interference with other space lattices or with the walls of the container. If a space lattice is permitted to grow freely without interference, a single crystal is produced that has an external shape typical of the system in which it crystallizes.

Crystallization centers form at random throughout the liquid mass by the aggregation of a proper number of atoms to form a space lattice. Each of these centers of crystallization enlarges as more atoms are added, until interference is encountered. A diagrammatic representation of the process of solidification is shown in Fig. 2.30 . In this diagram, the squares represent space lattices. In Fig. 2.30A , crystallization has begun at four centers.

As crystallization continues, more centers appear and develop with space lattices of random orientation. Successive stages in the crystallization are shown by Fig. 2.30B–F . Small crystals join large ones, provided they have about the same orientation (i.e., their axes are nearly aligned). During the last stages of formation, crystals meet, but there are places at the surface of intersections where development of other space lattices is impossible. Such interference accounts for the irregular appearance of crystals in a piece of metal that is polished and etched ( Fig. 2.31 ).

Grain Structure

During the growth process, the development of external features, such as regular faces, may be prevented by interference from the growth of other centers. In this case each unit is called a grain rather than a crystal. The term crystal usually is applied to a group of space lattices of the same orientation that show symmetry by the development of regular faces. Each grain is essentially a single crystal. The size of the grain depends on the temperature from which the metal is cast, the cooling rate, and the nature of the metal. In general, slow cooling leads to coarse grain and rapid cooling to fine grain metals.

Slip Planes

When a force is applied to a crystal, the space lattice is distorted, as evidenced by a change in the crystal's dimensions. This distortion causes some atoms in the lattice to be closer together and others to be farther apart. The magnitude of the applied force necessary to cause the distortion depends on the forces that act between the atoms in the lattice and tends to restore it to its normal configuration. If the applied force is removed, the atomic forces return the atoms to their normal positions in the lattice. Cubic patterns (lattices) characterize the more ductile or workable materials. Hexagonal and more complex patterns tend to be more brittle or more rigid. The force required to bring about the first permanent displacement corresponds to the elastic limit. This permanent displacement, or slip, occurs in the lattice on specified planes called slip planes. The ability of a crystal to slip in this manner without separation is the criterion of plasticity. Practically all metals are plastic to a certain degree. During plastic deformations, the lattice undergoes distortion, thus becoming highly stressed and hardened.

Slip, or plastic deformation, can occur more easily along certain planes with a space lattice than along other planes. The planes that have the greatest population of atoms and, likewise, the greatest separation of atoms on each side of the planes under consideration are usually the planes of easiest slip. Therefore slip takes place along these planes first when the elastic limit is exceeded. Sliding movements tend to take place at 45-degree angles to the direction of the applied load, because much higher stresses are required to pull atoms directly apart or to push them straight together.

A particular characteristic of crystalline materials is that slip is not necessarily confined to one set of planes during the process of deformation. Some common planes of slip in the simple cubic system are shown in Fig. 2.32 .

Mechanical Properties

The mechanical properties of metals depend on their lattice structures. In general, metals that exist with the face-centered cubic structure are ductile throughout a wide range of temperatures. Metals with the close-packed hexagonal type of lattice (see Fig. 2.29 ) are appreciably hardened by cold working, and plastic deformation takes place most easily on planes parallel to the base of the lattice.

Of the many qualities of metals, the most significant are the related properties of elasticity and plasticity. Plasticity depends on the ability to shape and contour aluminum and stainless steel to match body contours; elasticity governs their safe and economical use as load-bearing members. The demand on the material used is often compromised, depending on the consideration and prioritization of the manufacturing requirement or the clinical application. A simple example of this is, again, the AFO. The plastics typically used to manufacture an AFO device are chosen for their moldability rather than the forces that will have to be accommodated. The orthosis therefore will perform well for a short time (potentially a year or two) but then will succumb to issues such as the aforementioned creep or even operating past its ultimate strength (especially in areas around the ankle). Choosing a “stronger” material would involve a design of varying thickness (at least) throughout different sections of the orthosis to provide the clinical support and motion required. In most circumstances, this can be a very complex design to manufacture.

As discussed in the section Strength and Stress , a body is said to be elastic if it returns to its original shape upon removal of an external load. The elastic limit is the maximum stress at which the body behaves elastically. The proportional limit is the stress at which strain ceases to be proportional to applied stress; it is practically equal to the elastic limit.

Plasticity

Plasticity is the term used to express a metal's ability to be deformed beyond the range of elasticity without fracture, resulting in permanent change in shape. Characteristically the ratio of plastic-to-elastic deformation in metals is high, on the order of 100 : 1 or 1000 : 1. Although this is rarely a consideration for commercially designed structural components because they are designed to behave within the elastic range, it is crucial to components such as sidebars, which must be plastically deformed (bent) before they are used clinically.

A simple two-dimensional representation of a cubic crystal lattice in an unstrained condition is represented in Fig. 2.33A . If a shearing force within the elastic range is applied, the lattice is uniformly distorted, as in Fig. 2.33B , with the extent of distortion proportional to the applied force.

When the force is removed, the lattice springs back to its original shape (see Fig. 2.33A ). However, when the force exceeds the elastic (or proportional) limit, a sudden change in the mode of deformation occurs. Without further increase in the amount of elastic strain, the lattice shears along a crystallographic plane (or slip plane). One block of the lattice makes a long glide past the other and stops ( Fig. 2.33C ). On release of the load, the lattice in the two displaced blocks resumes its original shape ( Fig. 2.33D ). If the applied force is continued, slip does not continue indefinitely along the original slip plane, which on the contrary appears to acquire resistance to further motion; however, some parallel plane comes into action. Both the extent of slip per plane and the distance between active slip planes are large compared with the unit lattice dimensions. As slip shifts from one slip plane to another, progressively higher forces are required to accomplish it (i.e., the metal has been work hardened). At some stage, resistance to further slip along the primitive set of planes exceeds the resistance offered by some other set of differently directed slip planes, which then come into action. This process elaborates as plastic deformation progresses.

The actual strength of metals as ordinarily measured is only a small fraction of theoretical strength. Some significant comparisons for pure copper are as follows:

• Calculated (theoretical) tensile strength = 1,300,000 psi (or 8900 MPa)

• Measured breaking strength = 62,000 psi (or 427 MPa)

Similar relations exist for other pure metals.

Imperfections of many kinds, such as flaws in the regularity of the crystal lattice, microcracks within a grain, shrinkage voids, nonmetallic inclusions, rough surfaces, and notches of all kinds, may localize and intensify stresses. Many impurities owe their potency to a high degree of insolubility in the solid matrix coupled with high solubility in the fusion. This permits their freezing out relatively late in the solidification process, as concentrates or films between the grains, thus serving as effective internal notches. The greatly weakening effect of graphite flakes in cast iron is an example.

Notches act not only as stress raisers (or stress concentrators) but also as stress complicators, commonly inducing stress in many directions. The deeper the notch and the sharper its root, the more effective it is in this respect. Notches are great weakeners, and practitioners must recognize their prevalence in many situations (e.g., from contouring instruments or grain boundaries). Most importantly, the practitioner must avoid contributing to this weakening by not adding further notches, cracks, scratches, or rough surfaces.

Commercial Name for Metals

Before the stress–strain diagram can be used to compare the properties of various metals, it is necessary to discuss the types of steel and aluminum (aluminium) commercially available and used in orthoses and prostheses and other assistive devices, including wheelchair frames.

The terms surgical steel, stainless steel, tool steel, and heat-treated, along with other general designations, are freely used by manufacturers of orthotic and prosthetic components. The chemical content of these products is not identical from vendor to vendor. For example, the term spring steel, used by many manufacturers, refers to a group of steels ranging in chemical composition from medium- to high-carbon steel and is used to designate some alloy steels. The term tool steel also covers a wide variety of steels that are capable of attaining a high degree of hardness after heat treatment. More care is exercised in manufacturing tool steel to ensure maximum uniformity of desirable properties.

These general designations do not ensure the practitioner is obtaining the exact material that is needed. Because the mechanical properties of a material and subsequent fabrication procedures depend on the material's chemical analysis and subsequent heat treatment or working, the practice of using general descriptions for metals is seriously inadequate. In addition, reliance on these categories is not necessary, because specific designations already exist for each type of steel and processing treatment.

The following sections give a clearer picture of the available steel and aluminum alloys and their specific properties. Practitioners should always clarify the appropriate heat treatment, welding, and work hardening (including bending) for any given material that the supplier is providing. The variation of material properties is enormous, and general “rules of thumb” should be avoided.

Carbon Steel

Iron as a pure metal does not possess sufficient strength or hardness to be useful for many applications. By adding as little as a fraction of 1% carbon by weight, however, the properties of the base metal are significantly altered. Iron with added carbon is called carbon steel. Within certain limits, the strength and hardness of carbon steel are directly proportionate to the amount of carbon added. In addition to carbon, carbon steel also contains manganese and traces of sulfur and phosphorus.

Alloy Steel

To achieve desirable physical or chemical properties, other chemicals are added to carbon steel. The resultant product is known as alloy steel. In presenting some general characteristics distinguishing these alloys, it is necessary to define some terms commonly used to express them:

• Toughness: Ability to withstand shock force

• Hardness: Resistance to penetration and abrasion

• Ductility: Ability to undergo permanent changes of shape without rupturing

• Corrosion resistance: Resistance to chemical attack of a metal under the influence of a moist atmosphere

The addition of other elements can increase elasticity and tensile strength as well as improve surface finish and machinability.

SAE Number and Other Steel Number Grading Systems

The Society of Automotive Engineers (SAE) has assigned a specific number, known as an SAE number, to identify each steel according to its chemical analysis. There is an equivalent AISI number, but for simplicity one means of identification is sufficient. Four digits are used in the SAE description as follows.

The first digit refers to the type of steel. The second digit refers to the approximate percentage of the predominating alloy element in a simple alloy steel. The third and fourth digits refer to the approximate percentage of carbon by weight in of 1%.

The types of steel denoted by the first digit are as follows:

• 1XXX = Carbon steel

• 2XXX = Nickel steel

• 3XXX = Nickel chromium

• 4XXX = Chromium molybdenum (cro-moly)

• 5XXX = Chromium

• 6XXX = Chromium vanadium

• 7XXX = Heat-resistant alloy steel castings

• 8XXX = Nickel cro-moly

• 9XXX = Silicon manganese

For example, SAE 1020 is carbon steel (first digit 1) with no added element (second digit 0) and 0.20% carbon (third and fourth digits 20). Using the same method, SAE 4012 is chromium molybdenum steel with 0.12% carbon content. SAE 4130 is cro-moly steel with 1% chromium and 0.30% carbon. SAE 4130 is an airplane-grade alloy used in orthoses.

There are, of course, other steel grading systems (including British and European systems). Comparisons of the various grading systems are available online. However, practitioners should always obtain information regarding the properties, fabrication, or handling requirements from the supplier of each material.

Comparison of Steel and Aluminum (Aluminium)

Stress–Strain Diagram

Fig. 2.34 is a comparative stress–stain diagram plotting one type of steel and one type of soft aluminum. The straight-line portion of both curves on the diagram indicates the elastic range and stiffness of the material. The dotted lines on the diagram indicate the increased stresses that the material can tolerate before it reaches the yield and ultimate stress phase as the strength of the material is increased. In the case of steel, the modulus of elasticity is 30 million psi (200 GPa). For aluminum the modulus of elasticity is 10 million psi (70 GPa), one third that of steel.