The history of orthoses and their use is long and hono rable. No doubt, the first application occurred in the fi eld of fracture splinting. Skeletons of the earliest kno wn humans show evidence of fractures that healed in r elatively good alignment. One example of such early evidence is an origi- na l Neanderthal skeleton that has an ulna with a well -aligned healed fracture. Until recently it was not unreasonable to suppose that splinting of some typ e had been performed, but perhaps this was evi- d ence only of an isolated ulnar fracture. In the excavation of the Nubian Desert, the first di rect evidence of fracture bracing was found. There mummies of the fifth dynasty (2750 to 2625 B.C.) still had splints intact and wrapped within the buri al clothes. These splints appeared to have been ad equate and relatively effective by current standard s. Closed reduction and splinting were described in g reat detail by Hippocrates prior to his death in 370 B.C. He stressed that for complete immobilization of the femur, the splint had to include the hip and knee. In addition, he specified that the pressure po ints of the splints should not be over bony protube rances. Galen (131-201 A.D.) may have been the first to u se dynamic bracing for scoliosis and kyphosis. In addition to his devices, he employed breathing exe rcises, loud singing, and voluntary expansion of th e concavity to treat these conditions. He also used a type of chest jacket to control the direction of ch est expansion. This would seem to be the prototyp e of the Correl casts, which utilize chest expansio n in the treatment of scoliosis. The splints and braces of the next 1000 years were probably heavy, clumsy, and of marginal efficienc y. The standards of European medicine in general were well below those of the Greeks and early Ro mans, and there is little reason to assume that the orthoses used were any different. In the twelfth ce ntury the medical school at Bologna became a wor ld leader, and the application of braces was consid ered an important part of medical knowledge. Adv ances made by the medical school consisted of sta ndardizing, simplifying, and lightening the existin g models. Applicances of wood and metal were us ed for the back and extremities. Ambroise Pare (1510-1590), the predominant surg eon of the sixteenth century, devoted an entire boo k to orthoses, prostheses, and other assistive devic es. In it he described spinal corsets, fracture brace s, and weight-relieving appliances for hip disease. He also described special shoe modifications for c lubfoot. From the seventeenth century on, alteration of pre existing devices was associated with nearly every famous surgeon and many famous physicians. Gel sson (1597-1677), professor at Cambridge, wrote about rickets and used orthoses to straighten the b owleg deformities. Venel of Geneva established th e first hospital for musculoskeletal disease in 179 0, and in his writings scoliosis and clubfoot braces received particular emphasis. About the same time Levacher and Portal, independently, developed spi nal defices with head suspension systems, the fore runner of the present halo casts and braces.

mid-1700s. He was unconcerned with fractures but devoted his energies instead to the preventio n of de- For deformities of all types, he used ort hoses. His dictum: "If the spine be crooked in th e form of an S, the best method you can take to mend it is to have recourse to the whale bone bo dice, stuffed parts shall exactly answer to those protuberances which ought to be repressed, and t hese bodices must be renewed every three mont hs, at least." What a job for the orthotist in a bus y clinic! Andry also used dynamic devices for lordosis.You must give the child a pair of stitched stays contrived in such a manner that if the belly advances forward they may push it bac k, and if the back side sticks out too much they may push it inwar ds. There are a few stay makers but can easily contrive them so a s to answer these purposes.

No brief history of bracing would be complete w ithout special mention of Nicholas Andry, Profe ssor of Medicine at the University of Paris in the

Would that we could be so optimistic about the valu e of most of the present orthoses to control lordosis! In the nineteenth century the relationship betwe en bonesetters and bracemakers became increasi ngly close, and a personal bracemaker was a part of every "orthopaedic office." This closeness led to use of the term mechanosurgery to describe or thopaedists. Hugh Owen Thomas, who is best k nown for his fracture splint, exemplified this rela tionship. He and his orthotist designed orthoses t o control almost every joint. His long hip splint i s not unlike the ischial weightbearing orthoses o f today. After World War II, advances in prosthetics wer e remarkable. New fitting techniques, new mater ials, and new concepts of design all aided the am putee. There was no similar technologic progres s in orthotics, however. As recently as the early 1970s it seemed appropriate to describe the field of orthotics as the most personal, parochial, and provincial portion of orthopaedics and rehabilita tion. Of the hundreds of devices that were availa ble for most conditions only a few were used in any one community. These were known by local names, and two orthoses with striking resemblan ce might be differently named. The rationale for the selection was poorly understood by the presc ribers. Consequently, residents and students wer e totally unaware of any reasoning behind the ch oice. Their role, then, was to learn by rote which orthosis to prescribe so as not to offend their eld ers. If they moved to a new region of the countr y, the entire learning process had to be repeated. The significant advance in orthotic thinking cam e as a result of the close cooperation between me dicine and engineering. From this developed the idea that the attention of both the physician and t he orthotist should be focused on the biomechan ical deficits of the patient, not the specific diseas e process. This application of biomechanics to th e handicapped person gave the orthopaedic surg eon a rational and generic basis for the prescripti on of an orthosis best suited to a particular patie nt's need. As a means of emphasizing this conce

pt, the biomechanical analysis system was devel oped. Although such a form is intuitively used b y the knowledgeable practitioner, the explicit for m provides a model that is helpful to the young physician in developing the concepts of biomech anics and patient needs. All orthoses are force systems that act on the bo dy segments. This is true whether the orthosis is used for support, correction of a deformity, or st abilization of a joint or limb, and the implication is that the forces which an orthosis may generate are limited by the tolerance of the skin and subc utaneous tissue. In many applications of orthoses this is not a pro blemparticularly when devices are designed to st abilize a joint in one plane while allowing motio n in another. In other conditions the corrective f orce applied by an orthosis may be of such magn itude as to place the skin at risk. This is particula rly true when compression forces alternate with sheer forces. Forces of large magnitude are gene rated when an orthosis is used to overcome sever ely spastic muscles or the ground reaction force i n a large heavy person. This leads to the realization that there are times when an orthosis cannot fulfill the expectations placed on it. If a large disparity exists between t he expectations and the actual result, the orthosis is usually blamed rather than the recognition ma de that the indications were exceeded. This tend ency to fail to recognize the limitations and then decry the results infests the entire orthotic field, from cerebral vascular accidents to scoliosis, fro m fractures to deformities in children. The authors in the present volume do not agree with those who propose that orthoses are the defi nitive treatment for most conditions. Rather they have carefully attempted to delineate the particul ar conditions for which orthoses are appropriate, those for which surgery is more appropriate, and the interaction betweeen the two. A few words about words. The names of correc tive devices and their makers have been in a stat e of flux since the time of Nicholas Andry. His c orrective devices were called "stays" and the peo ple who made them "stay makers." In the ninete enth century, particularly in England, the correct ive devices were called "irons," as a brief survey of their appearance will demonstrate was approp riate. The makers of these then were called "iron mongers." In the United States in the twentieth c entury, corrective appliances came to be calle d "braces" and "brace makers" people who prod uced them. In today's terminology orthosis is fre quently chosen to refer to an apparatus that provi des support or improves function of the movable parts of the body. These are designed -and produ ced by orthotists. As with other words, however, this one has also led to some confusion. In the current volume, produced by the America n Academy of Orthopaedic Surgeons Committee

on Prosthetics and Orthotics, the word ORTHOTICS is a noun referring to the field of knowledge abo ut such devices and their use. The device itself (also a noun) is an ORTHOSIS. A room full of these devices would contain many "orthoses." If we ar e thinking or speaking about a device, the word ORTHOTIC is the adjective of the family. This cust om does not seem to be honored by an increasin g number of publications, however, for the adjec tive often is used as a noun. It is hoped that this Atlas will set the example in correct usage of the se words, despite the slipups that may occasional ly get by. SELECTED READINGSAndry, N.: Orthopaedia. Book II (translation), London, 17 43. Bick, E.M. Source book of orthopaedics, New York, 196 8, Hafner Publishing Co., Inc. Garrison, F.H.: History of medicine, Philadelphia, 1929, W.B. Saunders Co. Rang, M.: Anthology of orthopaedics, Baltimore, 1968, T he Williams & Wilkins Co.

2PHYSICAL PROPERTIES O F MATERIALS, INCLUDIN G SOLID MECHANICSEugene F. Murphy Albert H. Burstein Availability and choice of materials The increasing availability of a wide variety of materials for orthotic appliances-some with cent uries of use, others with a background of decade s, and a growing number from the space age-imp oses greater responsibility for wise selection. In addition, new materials open possibilities for no vel designs and offer opportunities for solutions to perennial problems such as breakage, bulkine ss, clothing damage, poor hygiene, or inadequate support. Selection of the correct material in the right plac e for each appliance depends on understanding t he elementary principles of mechanics of materi als, concepts of forces, deformations and failure of structures under load, improvements in mecha nical properties by heat treatments or other mean s, and design of structures. The choice, today, a mong materials is already extensive. Metals traditionally were used for structures and are still needed in some applications, although th eir share of the total market has decreased in rec ent years. Useful metals include several types of steels, numerous alloys of aluminum, and (to a li mited extent) titanium and its alloys. Plastics, fa brics, rubbers, and leathers have wide indication s; and composite structures (of epoxy or plastic matrix plus reinforcing metal "whiskers" or boro n or graphite fibers) are being studied. In the fiel

d of plastics the laminates of knitted or woven fa brics (often themselves synthetics) with thermos etting plastics like polyesters and epoxies are in competition with thermoplastics such as polyeth ylene, polypropylene, polycarbonate, ionomer, a nd acrylonitrile-butadiene-styrene (ABS). Despite publicity for exotic new materials, and a ccelerating research, there is no single magic ma terial that will serve as a panacea for all orthotic problems. One reason is that different and even diametrically opposite properties are needed for special clinical situations or even parts of the sa me device. Elastic properties are an example. Sti ffness of the structure may be desirable for a kne e-ankle-foot orthosis (KAFO) intended to suppo rt body weight. By contrast, considerable flexibil ity and range of motion are necessary if an ankle orthosis is to allow plantar flexion in response to heel strike. Static strength and resistance to deformation are needed by heavy patients. At the same time duct ility is essential during the process of fitting a m etal bar to the contours of the individual person. These rigid members are permanently deformed by the very high local stresses that the orthotist d eliberately applies with the bending irons. Becau se of the need for a permanent set, the orthotist d islikes excessive elasticity, which would require overbending to allow for springback; and it is ce rtainly hoped that the patient's weight will not ca use further plastic deformation or breakage. So that widely divergent mechanical demands ca n be met, combinations of material are commonl y used to construct an orthosis. The cuffs of conventio nal metal orthoses generally are made of steel or alu minum. These are then fitted with felt pads and leat her covers held in place with rivets of copper or a so fter grade of cuff metal. Springs, dampers, or locks often involve combinatio ns of materials. A spring, typically formed from a st rip of high-strength wire, is often inserted in a struct ure of another material. In recent years flexible plast ics, such as polypropylene, capable of indefinitely la rge numbers of repeated bends, have been used as hi nges with or without significant spring-return effect. Sometimes these hinges are attached to plastic lami nates or other structures, such as body jackets. In so me cases they serve as an integral joint (e.g., an ankl e joint) in an orthotic structure that is stiffened in ot her portions by inherent shape or the deliberate addi tion of corrugations. 19 Another example of combinations of materials occu rs in many efforts to protect against corrosion. A ste el frame, if not made of stainless steel, may be coate d with plastisol and heated or cured. or it may be pla ted with a combination of materials, such as copper first, then nickel. and perhaps chromium. Aluminum orthoses may be given an electrochemical anodizing treatment to form a tough relatively .hick film of alu

minum oxide on the surface, a special case of the co mbining of materials. Color added in the anodizing bath may be used to simulate costume jewelry, just as eyeglass frames are sometimes designed as "fashi on eyewear" instead of camouflaged. Composite materials are still not widely used despit e the fact that availability is improving, working tec hniques are better understood, and costs are decreasi ng as uses are found for these materials. Most comp osites were developed for extremely demanding app lications in aerospace or in high-performance aircraf t. Graphite fibers laminated with epoxy or acrylic ha ve extreme stiffness, although brittle failure with lo w energy absorption is a severe imitation They are l ess expensive than boron composites. They may be combined with thermoplastics, often transparent, tra nslucent, or flesh colored, that are heated until softe ned and then draped, stretched, and usually vacuumformed 56,62,64 over plaster models. The orthotist can now purchase prefabricated. persh aped, but moldable composites of glass and carbon f abrics in acrylic thermoplastic resin that can be inco rporated in the molding of thermoplastic orthoses. F or example, crescent-shaped portions with chamfere d edges can be heated, molded, and adhered behind and below the malleoli on a plaster model and firml y trapped during vacuum forming to stiffen and rein force a foot-ankle orthosis designed to prevent ankle motion. 21 The unit cost of material used in orthotic devices is a relatively insignificant part of the total investment. A far greater sum has been spent in assuring the ade quacy of fabrication and assembly and the professio nal services of fitting and aligning to the individual. Hence even large variations in unit prices of compet itive materials are not of great importance. More important than unit price of materials are facto rs like physical properties, stability during use over a substantial range of temperatures, endurance unde r repeated loading, resistance to wear and corrosion, and ease of working in the shop and adjusting in the fitting room. The economic choice among suitable materials may also depend on the number of steps a nd time required for initial processing, adjustments, and maintenance. When compared with the additional steps and delay s in delivery that can occur in the plating of ordinar y steels, the direct use of expensive stainless steel is often economically justified. Similarly, the speed an d simplicity of molding thermoplastic synthetic bala ta directly on the body without discomfort is very at tractive, particularly for temporary orthoses, when c ompared with the additional cost and delays involve d in preparing a plaster cast and then a plaster mode l before using other thermosetting plastic laminate. Nevertheless, vacuum forming of a hot sheet of ther moplastic material against a plaster model appears t

o have advantages. To test materials and to specify reproducible recipes once proved successful in clinical application, we n eed detailed standards and specifications for raw ma terials, treatments, and methods of construction. For tunately, many exist already and more are being dev eloped by professional societies, trade associations, and commercial companies. Both individual laborat ories and the postgraduate prosthetics-orthotics educ ation schools are writing manuals detailing step by s tep which construction methods have proved most s uccessful*, and federal, state, and local government s have a variety of procurement specifications. The American Society for Test*References 3. 19. 20. 29. 36-38. 43-47. 39. 63.

When a force is applied to an object, either some type of motion is created or, when this cannot oc cur. the energy is absorbed within the structure t o cause a change in shape. This static situation is significant to decisions relating to orthotic desig n. Stress and strain are the terms employed to de fine the acting forces and their effects.Definitions

ing and Materials, in its multivolume Annual Book of ASTM Standards,2 includes a number of specifica tions, test methods, and recommended practices app licable to orthotics and to surgical implants. Reasons for engineering mechanics and solid me chanics For a number of reasons, a general (even if intuit ive) understanding of engineering mechanics, so lid mechanics, and strength of materials is impor tant to the members of the orthotics clinic team a nd especially to the orthotist. A general understa nding of stresses, strains, and total deflections ar ising from loading of structures, particularly fro m the bending of beams, is needed. The physicia n and the orthotist can then appreciate the import ance of simple methods to allow controlled defo rmation during fitting, to provide stiffness or resi liency as prescribed, and to reduce breakage whe ther from impact or from repeated loading. Certain problems can be solved by a branch of st udy called engineering mechanics, usually subdi vided into statics (analysis of constant forces on an orthosis when it is stationary) and dynamics (analysis of moving or changing forces). From k nowledge of external gross forces on a structure, whether animate or inanimate, it is often possibl e to calculate the major internal forces at joints or within beams, bones, etc. The basic concepts of solid mechanics applicable to orthotics will b e presented in a relatively nonmathematical fashi on. Much also can be learned from kinematics, "the mathematics of motion," the science that describ es motion without immediate regard to the force s involved. The complex motions of the human knee, for example, have been described by use o f kinematic techniques. This chapter does not attempt to cover the engin eering mechanics of structure or the kinematics of the body or the experimental and analytical m ethods of analysis. Some sources, however, are s uggested in the reading list.7,22,23,28,48,58SOLID MECHANICS

Strain. The term strain refers to the change in sh ape within a material whether it is visible or mic roscopic. There are two basic types of changelen gth and angular. Length change, or normal strain. When an ext ernal load is applied to the ends of a bar, a chang e in length occurs. This type of deformation is ca lled normal strain, because the force is perpendic ular (or normal) to the cross section studied. Nor mal strain is designated by the Greek letter epsil on (e). It is the change in length as a proportion of the original length. With change being design ated by the Greek letter delta (), this relationshi p is expressed as L/L (Fig. 2-1). Normal strain is therefore a practically dimensio nless quantity. Since most of the normal strains with which we deal in using metals are very sma ll (on the order of several millionths or 10-6), we often talk in terms of microstrain. One microstra in represents a change in length of one part in on e million (e.g., 0.000,001 cm/cm or inch/inch). Two types of normal strain can occur-lengthenin g and shortening. When the length of the structu re increases, it is called a tensile strain and recor ded as a positive number. Shortening is a compr essive strain and is expressed as a negative num ber. Normal strain is easily measured by a variety of techniques. One common strain-measuring devic e is a strain gauge, which translates the length ch ange into an electrical signal. Constructed of a s mall coil of wire (Fig. 2-2), it is glued onto the s urface of the object to be measured. The electric al resistance of the wire alters as the material to which it is fastened receives strain. The change i n electrical resistance is proportional to the norm al strain. Such instrumentation is capable of mea suring strains as small as one one-hundredth of a microstrain. The distribution of strains on the surface of an o bject can be described by applying a brittle coati ng and then studying the pattern of cracks that re sult from loading. Mechanical devices that magn ify small motions and display the results opticall y are also used. Angular change, or shear strain. When the ext ernal load is applied obliquely in the cross sectio n studied, the change in the object is an angular deformity. This is called a shear strain. It can be readily demonstrated by drawing two lines on th e object's surface at right angles to each other an d

nothing their change (Fig. 2-3). After the material o n which the lines are scribed is subjected to an exter ~al load, the lines will no longer be perpendicular b ut will be deformed by the angle gamma (). Aeme shear is an angular deformity from the origina1 nor mal (perpendicular) state. Shear strain is defined as t he tangent of . For most materials the magnitude of shear is sufficiently small to allow the approximatio n tan where is measured in radians. (A complete circle [360 degrees] equals 2p radians; so 1 radian is appo ximately 57.3 degrees, and 90 degrees equals 2p ra dians. ) Cambimed normal and shear strain. The exisc of st rain in a material is not a simple onedemensional co ndition. Tension and compression strains are always associated with shear strains. this can he demonstrat ed by drawing a square and its diagonals on the obje cts's surface (Fig. 2-4). Application of equal and op posite forces compressing the faces parallel to lines b and d would cause shortening (compressive strain) of lines a and c but a smaller lengthening (tensile str ain) of b and d. For convenience, we can apply diag onal forces just sufficient to cause shortening of the horizontal top and bottom but to create no net chang e or strain in the vertical lines. At the same time the diagonals, which initially intersected at right angles, assume a different angle. They have suffered shear s train. A similar pattern of deformity occurs with ten sile strain of the horizontal lines (Fig. 2-5). We have chosen to examine only a limited number of lines of the infinite number that could be drawn on the squar e. It is easily demonstrated that only lines b and d re main strain free. All others undergo either tension or compression whereas any line pair not parallel to th e edges suffers shear strain as well. The reciprocal behavior occurs if the sample of material is deformed by an oblique load (Fig. 26). In this case the square deforms into a parallel ogram. Line pairs a-b, b-c, c-d, and d-a undergo shear strain but not normal strain. The diagonal l ines, e and f, however, do undergo tension and c ompressive strains respectively but do not suffer shear strain; they remain perpendicular to each o ther. This inherent interaction between induced strain s is vital to an understanding of material behavio r. The general principles are valid for all solid m aterials.28 Stress. When an object is stationary, it is said to he in equilibrium. This is the case when the net f orce acting on the object is zero. At the same tim e each portion of the structure also is in equilibri um and all the forces acting on any portion shoul d sum to zero. In response to externally applied l oads, new internal (intermolecular) forces are ge nerated. These may he imagined as "glue" holdin g the structure together. They may also be consi dered as existing at every point on any cross sect

ion. Their distribution over the particular areas o f concern is described as stress. Stress is generally defined as the load per unit cr oss-sectional area of a material. Because the con cern usually relates to internal changes, it may al so be defined as the ratio of the force applied on an internal surface to the area of this surface (Fi g. 2-7). For analysis we can imagine that the orig inal body is divided at a designated plane; the int ernal forces on this area are now "external." This area represents an internal surface with a unifor m distribution gion. of forces acting on it exactly equal to and opposite the forces on t he formerly contiguous wall of the other portion, which has been removed. When the internal force distribution is not of uni form intensity, the determination of the magnitu de of the stress on any portion of the surface req uires that the total area be subdivided into suffici ently small portions to allow the force to be cons idered uniformly distributed over each small regi on. Normal stress. When the forces are perpendicula r to the surface on which they act, the ratio of for ce to area is called normal stress. This is designa ted by the Greek letter sigma (s). If the force acting on a particular area is directed outward from the surface, it is said to be tensile s tress (Fig. 2-8). Conversely, when the force is di rected perpendicularly into the surface in questio n compressive stress exists (Fig. 2-9). The distri bution of normal stress acting on a plane may in clude both tensile and compressive stresses. 28,58 Shear stress. When, instead of acting perpendicio t he internal surface, a distributed force is parallel to t he surface, the ratio of the force to the surface on w hich it is acting is called shear stress (Fig. 2-10) Combined normal and shear stress. It is import ant that shear stress and normal tensile or compr essive stress may exist simultaneously on any int ernal surface. Actually coexistence is the far mor e usual situation. An example would be the anal ysis of a section from the bar of an orthosis subj ected to a compressive load (Fig. 2-11). It is reas onable to expect that the small element selected for analysis will also be subjected to compressiv e forces on its transverse planes (planes a and b). The combined stress can be demonstrated by slic ing the cube on a diagonal and examining the lo wer portion (Fig. 2-11). A force (F) is required on a diagonal plane (c) to keep the small element from moving upward in r esponse to the force on the lower face. It is the st resses acting on surface c that produce this net d ownward force, thus maintaining equilibrium. S uch a force (F) can be considered to have two co mponents, F. perpendicular (normal) to plane c a nd F, parallel. Each of these components of force

F is related to a stress on surface c. The con dition of stress on surface c thus consists of compression stress attributable to F. and shear stress attributable to F, In an analogous manner, if the s

trut were subjected to a pulling or tensile load, th e diagonal plane would have tension and shear st resses imposed on it. In general, when a member has normal stresses on transverse planes, all othe r internal planes except longitudinal planes have stresses on them. Each plane has normal and she ar stresses in a proportion dependent on its angle relative to the longitudinal axis. On planes locate d at 45 degrees there is a tension (compression) s tress equal to half the tension (compression) stre ss on the transverse planes. Twisting or loading a structure in torsion induce s shear stress. Fig. 2-12 shows a small piece of material in a tubular strut that is being twisted. T he shear stress created on each longitudinal (a) a nd transverse (b) face is the same as the other she ar stresses. The small cube is in equilibrium. sin ce the forces and moments produced by the shea r stresses sum to zero. If we examine half the cu be after slicing along one 45-degree diagonal (Fi g. 212), we see that with forces produced by the shear stresses on only two surfaces (a and b) the piece of material would not be in equilibrium. W hat is needed for equilibrium is a force acting on surface d. This required force (D) is perpendicul ar to surface d and therefore produces a tension s tress. A similar argument would show that the ot her 45 degree diagonal plane (e) would be subje ct to a compressive stress (E) (Fig. 2-12). In gen eral. then. if a material is directly subjected to sh ear stress (e.g., that caused by torsional loading). there are shear stresses of equal intensity on the t ransverse and longitudinal planes. On the 45-deg ree diagonal planes there are only tension or co mpression stresses. The magnitude of these stres ses on the 45 degree planes is equal to the magnitude of the shear stresses on the transverse and longitudinal planes. H owever, on diagonal planes not at 45 degrees to the axis there are both normal (tension or compression) and shear stresses. Note that the concept of stress involves a force d istributed over an internal surface in a material. Because this internal force distribution is inacces sible, it is not possible to measure stresses direct ly in solids. We can only calculate stresses by kn owing the shape of the structure, the nature of th e loading, and the properties of the material. Experimental relationship between stress and s train. Many times it is desirable to know the ulti mate loading condition that a material can tolerat e in terms of stress. For instance, some forms of aluminum are classed as capable of resisting 414 meganewtons per square meter (MN/m2) of tens ion or 60,000 psi (lb/in2) before deforming perm anently. Although stress is not directly measurab le, the levels of stress in a complex shape can be determined by measuring the strain exhibited in response to controlled loading and applying kno wn stress-strain relationships. To determine the relationship between stress and strain for a particular material, several standard t

ests have been established. The most common of these is the tension test. This procedure requires the gradual elongation of a carefully prepared sa mple of material along with simultaneous measu rement of the induced load and the elongation of a section of uniform cross-sectional area. The no rmal tensile stress can be calculated by dividing the load by this area. The specimen is designed t o provide uniform stress distribution across the a rea of the gauge section. The strain is calculated as the ratio of the change in length of the gauge s ection to its original length. Stress is then plotted against strain (Fig. 2-13). In this schematic diagr am, for clarity the strain during the initial straigh t~line elastic portion is exaggerated compared to the remaining plastic strain to breakage at x. stress-strain curve for a mild steel depicts the mo st important parameters of the usual structural materials: elastic range, yield point, plastic range, a nd fracture point. The initial portion of the curve is virtually linear. If the material is loaded up to point a within this linear region and then unloaded, both s tress and strain will return to 0. This type of behavio r is termed elastic and the linear portion of the curve (0-b) is called the elastic region. Springs, for instanc e, are designed to operate within this region elastic deformation is reversible on removal of the stress. T he slope of this region is known as the modulus of e lasticity, elastic modulus, or Young's modulus (E) a nd is a measure of the stiffness of the material. If the stress is increased significantly beyond the linear region, say, to point c, then permanent stra in is produced. If the induced load is allowed to return to 0, the decreasing curve will be parallel to the elastic region but will intersect the horiz ontal axis (with a residual strain e). There will re main a plastic deformation equal to 0-e. This con cept is used in forming orthotic components wit h bending irons. Although the "snapback" strain that occurs elastically is reversible, that which o ccurs plastically is permanent. To distinguish more clearly between these two b ehavioral regions, one must define a measurable point (d in Fig. 2-13). A sample loaded to this va lue and then unloaded will retain a deformation of 0.2%. The stress at d is called the yield stress. The highest point on the stress-strain curve (0 re presents maximum nominal stress calculated fro m the original cross-sectional area of the test spe cimen. The stress at this condition is called the u ltimate stress. Further loading at this point cause s the material to reduce its cross-sectional area at some point. This necking is caused by shear strai n on the 45-degree planes and can be easily seen in a steel or aluminurn tensile specimen. The amount of permanent or plastic deformation that a material will undergo before failure is call ed its ductility. To varying degrees, most steels a nd surgical metals are ductile materials. Materials that do not plastically deform before fr acture are called brittle materials. Glass at ordina

ry temperatures is a brittle material. The stress-st rain curve for it shows no flattening to the right of the elastic curve (Fig. 2-14), that is, no plastic deformation before fracture. The strain is compl etely reversible in this material for any loading c ycle before failure. By contrast, at elevated temp eratures the glass softens, allowing large perman ent strains at very low stresses. For many materials, on release of the load, the c urve does not retrace itself as the specimen regai ns its original shape. The closed loop formed by the loading and unloading cycle is called the hys teresis curve. It is a measure of the amount of en ergy the material absorbs each loading cycle. Brittle materials, though sometimes attractive be cause of their high ultimate strength, may be uns uitable for shock loading under impact because t hey cannot absorb much energy before fracturin g. For example, a hard brittle steel with an ultim ate stress of 975 MN/m2 (141,000 psi) and a 5% ultimate strain (Fig. 2-15) can absorb, before bre aking, only about one third the energy of a mild steel 'th a yield stress of 325 MN/m 2 (47,000 ps i), an ultimate tensile strength of 490 MN/m 2 (7 1,000 psi), and about 25% ultimate strain at brea kage. One may best visualize this behavior by o bserving the area under the stress-strain curve, a direct measure of the energy required for failure. This comparison, however, is based on the total energy required for failure, not the amount of en ergy required to deform the material permanentl y. In certain cases permanent deformation is tant amount to failure. For an elastic material the am ount of energy required to deform it permanentl y is dependent on the yield stress and the elastic modulus. Actually, the energy required to defor m a volume of metal permanently is given by th e equation

where is the yield stress and E the elastic modulus. The higher the yield stress for a given modulus (Fig. 2-16, A) or the lower the elastic modulus for a given yield stress (Fig. 2-16, B), the greater will be the en ergy required before plastic deformation occurs. Un der shock loading, then, a material of high yield stre ss but relatively low modulus -a "resilient" materialmay be desirable. Failure of materials. There are two general type s of elastic materials, brittle and ductile. These te rms actually describe failure modes under custo mary loading conditions. Unusual conditions suc h as sharp notches, extreme stiffening, or other u nusual configurations may so alter the customary behavior of many ductile materials as to cause br ittle fracture. For most applications, though, the ductility of a material (expressed as percent elon gation to failure) will indicate the mechanism of probable failure under a single overload. Most e ngineering metals have a ductility falling betwee n 10% and 40%. The general tendency within a f

amily of materials is for decreasing yield strengt h to correspond to increasing ductility. Thus stru ctural steel has lower yield stress but much great er ductility than does the hardened toof steel in a chisel; a softer aluminum alloy, such as 2024, lik ewise has lower yield stress but higher ductility t han does hardened tool 7075-T6 aluminum alloy. A ductile failure is indicative of simple onecycle overload generally arising from an emergency. I n an orthotic device, permanent deformation-or e ven rupture after extensive distortion-may indica te desirable energy absorption, protecting the pat ient during an accidental fall. Such failures are id entified by distortion of the structure in the regio n of the fracture. The pieces when reassembled d o not reproduce the shape of the original structur e. The fracture area will usually be reduced in cr oss section. Such failures suggest a need to reeva luate the design because of functional overload e ven if this is under emergency conditions. Decisi ons must be made as to the probability of future similar loads as well as the safest course of event s. There is little value in protecting an external o rthotic device against failure but ensuring that th e patient will fracture a bone! Fractures of brittle orthotic materials can be caus ed by discontinuities in structural members. In a structure under load, any notch or geometric disc ontinuity is most serious because it tends to incre ase the local risk of failure above that which wou ld otherwise be present. The sharp bottom of the notch so concentrates the forces that load per uni t area (stress) can be doubled or trebled. This ma y initiate a crack, which raises the stress even fur ther and creates a self-propagating situation until the entire structure is fatally weakened and fails under an ordinary load. Obviously, the goal must be to avoid the "sharp-blade" effect of a narrow crack and to blunt the "cutting edge" of any notc h or reentrant corner by making it as shallow and rounded as feasible. 42 In this direction, paradoxi cally, a part may be strengthened greatly by havi ng a hole drilled to blunt the leading edge of a cr ack or by removing material on either side of a Vshaped notch to create a smoother broader Ush aped trough. Similarly paradoxically, a stronger, stiffer, but more brittle material may embody gre ater risk of breakage during clinical use with rep eated loads and occasional impacts and accident al scratches than a seemingly lower-strength but more flexible, tougher, and more ductile material (which absorbs blows and stretches slightly with out breakage to blunt the leading edge of a crac k). Fatigue fracture. Multiple loadings, producing s tresses of insufficient intensity to cause yielding, may cause a structure to fail by a process known as metal fatigue. This rather complex process ent ails the initiation and slow propagation of cracks through the material. The cracks, which usually s tart at the surface or at an internal flaw, effective ly reduce the cross-sectional area. One final loa d, nominally as safe as similar earlier loads, caus

es a stress at the ultimate strength and a brittlelik e failure results. 6,52 Fatigue failure depends on the establishment and growth of crack planes through the material. An ything that aids either the initiation or the propag ation of these crack planes enhances fatigue. Fac tors that stimulate the formation of surface crack s are stress concentrations, surface imperfections attributable to material or finish, corrosion, and gross intensity of stress. The growth rate of a cra ck is a function of both the number and the inten sity of the loading cycles in a given period. It is i mportant to note that the effect of loading is cum ulative. Resting periods do not allow the metal t o regain strength or repair cracks. 6,52 Mechanical structures, unlike bones, lack physiologic system s, which respond to stress levels; thus there is no remodeling or hypertrophy to meet the new dem ands.40 Nor is there a means to conserve and ref orm available raw materials by selective atrophy of structures when they are no longer needed. The ability of a material to resist fatigue failure i s demonstrated by the relation of allowable stres s to the number of cycles of that stress that can b e tolerated. Curves for a particular steel and a pa rticular aluminum are shown in Fig. 2-17. Altho ugh they represent the most likely lifetime of a material, usually a considerable scatter of actual data is found. Endurance limit. Ferrous alloys typically can wi thstand some level of stress for an unlimited nu mber of cycles. The greatest repetitive stress for which the material does not fail is called the end urance limit. This is reached where the curve of stress versus cycles becomes horizontal. If a ferr ous alloy can withstand 106 cycles, it will probabl y withstand an indefinitely larger number of simi lar cycles. This indefinite "life" is not true for other metals, especially aluminum alloys. In these the nominal tensile endurance limit is defined as the greatest tensile stress that would allow 5 X 108 (or 500 m illion) cycles. Actually, it is possible to cause fat igue failure in aluminum alloys at the nominal e ndurance limit simply by increasing the number of cycles. Because the curve of tolerable stress v ersus number of cycles is so nearly horizontal at a large number of cycles, only a small reduction in stress will prolong the probable useful life by 10, 100, or even 1000 times. Generally the endurance limit of a metal is betw een 30% and 50% of its yield stress. Any tensile stress of higher value repeatedly applied will ind uce fatigue failure. Because notches, roughness, or c r rosion are such serious sources of increase d stressaccelerated fatigue failure, much attentio n should be given to their prevention in orthoses and other str uctures that experience critical loading under constr aints of weight and bulk; such attention is more effe ctive than searching for nominally stronger material

s. Stress in complex loading situations Bending. The most common and crucial comple x stress condition existing in orthotic devices is bending. The stresses associated with bending lo ads are combinations of shear, compression, and tension. To understand the stress condition caused by ben ding, we can examine a beam of uniform cross s ection subjected to bending forces on each end (Fig. 2-18). By isolating a portion of the structur e (a "free body" in engineering terms) and analys ing the external forces and moments acting on o ne surface (A), we can discern the resultant inter nal reaction on it. If a condition of equilibrium e xists, the resultant of the internal reaction must b e equal to the moment applied to the beam. If thi s were not true, the body would not be in equilib rium and would tend to spin. This internal reacti on moment achieved by a stress distribution co nsisting of noth tension and compression (Fig. 219). The creater the internal reaction moment (b ending monent), the greater are these stresses. M aximum compression occurs on the cross section near the surface on the concave side of the curv e. Maxittum tension occurs opposite this, on the convex surface. The normal stress distribution in bending of any beam varies evenly from maximum tension at on e surface to maximum compression at the opposi te. The stresses are 0 (changing from tension to c ompression) at the neutral axis. The amount of st ress in a beam depends on the amount and distri bution of material in the cross-sectional area. Th e parameter that measures this is called the secti on modulus (z). For instance, a three-flanged nai l has a much lower section modulus than does an 1 beam of similar size (Fig. 2-20). The 1 shape p laces more material farther from the neutral axis and as a result the material can sustain a higher b ending moment perpendicular to that plane. The 1 beam has a lower modulus, however, for bendi ng across its face than does the nail. The use of s uch special shapes requires knowledge as to the direction of the load and the magnitude. The greater the section modulus, the lower will b e the stress. The stress for a bending load is alwa ys maximum at the outermost point on the cross section. Usually, a beam breaks because of failur e of the outermost fiber with subsequent progres sive ruptures of the succeeding fibers. For an asy mmetric cross section like the tibia, the maximu m compressive stress may be less than the maxi mum tensile stress because the distance to the ou termost fibers in compression is less (Fig. 2-21). Since a knowledge of bending stresses is useful in understan ding the mechanics of orthoses, this concept will be further examined by separate study of the variables of bending moment and section modulus. The value of the internal bending moment (M) ii4

n any section of a cantilever beam or a beam sup ported at the ends and bearing a single concentra ted load is the product of a force and a distance. This means that given the same transverse force acting on one end of the beam, the internal mom ent and thus the stress at any section distal to the force will vary with the length of the beam. For equal sections, a simple beam that is twice as lon g will have twice,the maximum resulting stress s ince its maximum moment at its center is twice t he value of the shorter beam (Fig. 2-22). The section modulus is an important parameter i n consideration of the strength of beams. The se ction modulus is a property of the cross-sectiona l area that takes into account not only the total a mount of area but also the disposition of the area with respect to the neutral axis. Beams may possess the same area but have wide ly differing sectional moduli. Three beams with t he same area, 4 cm2 , but with various distributio ns of material demonstrate different sectional m oduli. For a beam positioned as a plank (Fig. 2-2 3, A) the section modulus is 0.667 cm3. When th e same area is formed into a square shape (Fig. 2 -23, B), the section modulus will be 1.333 cm 3. I f the beam is turned up on edge as a joist (Fig. 223, C), the section modulus increases to 2.667 c m3 . There is a factor of 4 between the first and l ast illustration. The value of the section modulus (calculated as the base multiplied by the square of the height divided by 6 for rectangular cross s ections) is a measure of the strength of the beam. In other words, for a given bending moment the beam with a maximum-value section modulus w ill have the minimum bending stress and thus the least tendency to fail. A beam on edge will supp ort a larger bending moment than can be support ed by the same beam oriented flat. Normal stress is not the only type of stress produ ced in a beam under bending. For a section of a centrally loaded beam, near the center force (Fi g. 2-24) there is both a moment and a shear forc e. Both the moment and the shear force are need ed to enable the beam to remain in equilibrium. The shear force (F) produces stresses whose dist ribution depends on the shape of the cross sectio n. For most applications, the bending shear stress is not critical; its magnitude is usually much lower than that of the bending tension and the bending co mpression stresses. Nevertheless the compromises b etween tension, compression, and shear illustrate th e problems facing a designer. For a given weight of beam the designer, confident of the direction of load ing, may attempt to move material outward from the neutral axis (e.g., as in a joist or an I beam) to mini mize tension and compression stresses. If material is moved too far, however, a deep narrow joist likely t o buckle or wrinkle in the center may result. The tw o planks, flanges of an exaggerated I beam, are conn ected by a thin membranelike web so overstressed i

n shear as to be nearly useless in connecting the two flanges for mutual support. The real orthosis may w ell have practical limitations of cosmesis, clothing d amage, or difficult fitting to the particular patient. T hus, in efforts to reduce stress, there are realistic lim its to changes in cross section. Torsional loading. When a body is subjected to a moment or torque tending to twist about its axi s, it is said to be subjected to torsion. As a result it undergoes a complex state of deformation and etress. An example is the solid cylinder subjecte d to torque (Fig. 2-25). For the portion of the cyl inder to the left of section A (isolated as a free b ody), the stress distribution must produce a resul tant moment equal to and opposite the net torque imposed on the left end of the cylinder. This mus t be true if this element of the body is to remain i n equilibrium. In addition, there can be no resulti ng axial or radial force since there are no compar able applied loads. The stress distribution that sa tisfies these criteria is thown in Fig. 2-25, B. It c an be seen that all the stresses on the cross sectio n are shear stresses. The shear stress is distribute d over the entire cross section A. The magnitude of the stress is proportional to the distance from t he center of the bar (with the maximum at the ou ter edge) and inversely proportional to the area moment of inertia (a measure of the distribution of the section area relative to the center point). In the human tibia subjected to torsional loading (Fig. 2-26), the shear stress generally increases li nearly with distance from the neutral axis along a given radius. However, a point on the surface f ar from the neutral axis of a triangular or other n oncircular shaft (and somewhat like the apex of t he triangular tibial section) has a lower shear stre ss from torsion than does a surface point near th e axis (like the flat portion of the triangle). The l ocal shear stress is analogous to the correspondin g slope of a soap bubble blown on a hole of the s ame section. The uniform slope of the bubble ed ge around the circumference of the round hole (li ke the uniform shear around the circumference o f Fig. 2-25) is obvious and can be used for calibr ation. Conversely, the irregular bubble on a squa re or triangular hole displays both gentle and ste ep slopes. 28 This paradoxical stress distribution leads to high shear stresses at the roots of keywa ys in shafts, at graft sites, or near other irregulari ties in the shafts, bones, or any structures subject to torsion. Because of changes in the shape of the bone and the distribution of bony material, the values of m aximum shear stress vary throughout the length of the bone. At the junction of the proximal three fourths and distal one fourth (section B in Fig. 226), the cross-sectional distribution produces a st ress approximately twice that at the proximal sec tion (A) even though the cortical bone is thicker at the distal section. The torsional fracture of the tibia would be expected to occur at the distal sect ion, as is commonly observed.

If a ferrous alloy rod is twisted until it breaks, th e failure plane will be noted to lie perpendicular to the axis of loading, in the plane of maximal sh ear stress. Objects such as cylinders, cylindrical and square tubes, and tibias have closed cross sections. 1 be ams, channels, and C sections all have open secti ons. Opening a closed section (e.g., cutting a slot in a tibia) drastically decreases the ability of the structure to carry torsional loads by altering the s tress distribution and hence reducing the strength of the section. This can be seen by comparing th e stress distributions in closed and open sections subjected to torsion (Fig. 2-27). In the closed sec tion the stress distribution is such that all stresses have counterclockwise moments about the centr al axis. Thus they all effectively contribute to the equalization of the applied torque. In the open se ction, however, the shear stresses are not all simi larly directed. The moment produced by the mor e central shear stresses is in the same direction a s the applied torque and is additive. Since the ap plied torque must be resisted by the net moment of the induced stresses, the stresses along the ext erior are greater than those inside. Thus, in resist ing the same torque, much larger stresses are pro duced in the open than in the closed section. She ar stresses under torsional loading are associated with equivalent tensile and compressive stresses on diagonal planes, leading to spiral failures of b rittle materials, particularly under shock loading. In the case of the open section under torsion, lar ge shear, tensile, and compressive stresses are de veloped in response to the torque. Such clinical problems as fractures of donor tibias or of other bones opened by cysts and tumors illustrate failu res of open sections subjected to torsion. Concepts of rigidity, including elastic materia l properties and section and length considerat ions. The section modulus of a structure relates i ts strength to the distribution of material through out its cross section. In addition to a considerati on f strength, which is a measure of load-carryin g capacity, we are also interested in the rigidity of a structure. Rigidity is a measure of the amou nt of load needed to produce deformation and is related to the area moment of inertia. The rigidit y of a beam is the ratio of the applied load to the deflection. Thus the rigidity of a beam might be 5000 N/cm, meaning that 5000 newtons are requ ired to produce 1 cm of deformation at the cente r. It might be that the beam would fail at 1000 N of load and 0.2 cm deflection, but this would not alter our statement of rigidity. The more rigid th e structure, the greater must be the load to produ ce a given deformation. Several factors influence the rigidity of beams: e lastic modulus of the material, area moment of i nertia of the cross section. and length of the bea m. The area moment of inertia is another measur e of the distribution and amount of cross-section

al area. For rectangles it is the base multiplied b y the cube of the height divided by 12. Thus a st eel orthosis (E = 207,000 MN/m2) is more rigid t han an aluminum one (E = 70,000 MN/m2) of th e same size and shape. In the same material, dou bling the thickness of vertical strut (Fig. 2-28) w ill increase its anteroposterior bending rigidity b y a factor of 2 and in its mediolateral by a factor of 8 (because the moment of inertia depends on the cube of the he ight). If the length of the beam is halved, its rigi dity will increase by a factor of 8. Maximum rigidity is not necessarily a desirable goal particulariv if shock loading must be resiste d. If a structure is too rigid, it will not deflect mu ch and therefore will not absorb much energy be fore it Energy concepts in loading Elastic and plastic strain energy. If a beam is a i ductile material and a sufficient load is made of ductile material and a sufficient load is placed o n it. the load deformation curve obtained will be as shown in Fig. 2-29. The left-hand portion of the curve (O-Q) represe nt the familiar reversible linear elastic deflection induced in the material by the bending stresses. Eventually the outermost fiber yields at the secti on with maximum moment; that is, it continues t o deform without any increase in stress and per manent dislocation occurs in the crystalline struc ture. As the loading is continued, the fibers belo w the outermost one also yield. If the load is no w removed, a permanent change in shape will be noted. This is the mechanism used by the orthoti st to deform a component with bending irons. If the load is increased, eventually a point is reache d at which all fibers at this critical section yield and, under constant load, the beam continues to deform. Such deformation may continue until ru pture occurs (point S). The amount of elongation that a simple tension specimen of any material can undergo before ruptur e is often used as a measure of the ductility of the m aterial. For example, 316 stainless steel elongates 2 7% whereas chemically pure titanium elongates as much as 36%. Influences of energy of failure in columns. En ergy concepts are also useful for understanding f ailures in columnar structures. A column is a lon g slender structure loaded axially. When an ident ical structure is loaded as a beam (transverse loa d), the amount of energy that can be absorbed is proportional to the deflection (as long as no per manent [plastic] deformation occurs). Columns behave in a nonlinear way. Fig. 2-30, A, illustrates the deformation produce d by an axial load on a column. The amount of e nergy absorbed in this manner is also the area un der the load-deformation curve. If the column co uld remain straight, the energy would increase w

ith the load in a linear manner (O-Q in Fig. 2-30, C). There are other shapes, however, that the col umn will assume if the load continues to increas e. One is illustrated in Fig. 2-30, B. The load def ormation characteristics for this configuration ar e reflected in 0S-T. The initial straight-line porti on (O-R) represents the erect column, which is b eing loaded axially while remaining in a linear c onfiguration. In region R-S the column suddenly bows. At point S the total energy is less than at R. Energy is lost in the damping of vibration whe n the column snaps from one position to another. Actually, in practical cases, if the column reache s the energy storage level indicated at point R, an y small disturbance will drastically change its co nfiguration (to that at 1), a state of pronounced b owing. MATERIALS Steel Steel is the general term used to describe a famil y of alloys produced by removal of impurities fr om pig iron. It is abundant, relatively cheap, and avail able in various alloyed and heat-treated stat es. The basic advantages that can be incorporated in to steel are high strength, high rigidity, consider able ductility, long fatigue life, and ease of fabri cation and availability. Among its disadvantages are high density, need for expensive alloying to prevent corrosion, and poor surface wear charact eristics in bearings. Steels may be divided into three classes: carbon, low-alloy, and high-alloy. The carbon steels hav e a variety of uses, ranging from structural parts to cutting tools. Low-alloy steels are used when higher strength is required together with moderat e ductility. High-alloy steels are used for high-st rength applications and are the most corrosion re sistant. Mechanical characteristics Carbon steel. At low concentrations of carbon (0.05% to 0.10%), steel is very ductile but has a low yield strength. As the percentage of carbon increase s, the ductility decreases and the yield strength incre ases. At any particular level of carbon content, appr opriate heat treatment can also increase strength at t he cost of reducing ductility. The actual yield strength of carbon steel may var y from 207 MN/m 2 (30,000 psi) to 860 MN/M2 (125,000 psi) depending on carbon content and h eat treatment. The corresponding range in ductili ty is from approximately 40% to less than 10%, Low-alloy steels. Low-alloy steels have mechani cal properties that fall between those of the carb on steels and the high-alloy steels. Their tensile yields are between 345 and 380 MN/m 2 (50,000 to 55,000 psi), with ductility of approximately 2 5%. They thus are not often used for medical pro ducts. High-alloy steels. When corrosion resistance is not a requirement, high-alloy steels can be obtai

ned with extremely high strength-to-weight ratio s. These steels are well suited for structures subj ected to large repetitive loads. They are more ex pensive than low-carbon steels and also more dif ficult to fabricate. They can be heat treated or co ld worked to improve their strength levels even f urther. If corrosion resistance is also a requirement for a particular application, there are three types of .St ainless steel" of increasing corrosion resistance f rom which to choose: series 400 iron-chromium stainless steels (hardenable only by cold-workin g), series 400 iron-chromium stainless steels (of slightly different composition that can be harden ed by heat treatment), and series 300 iron-chrom ium-nickel stainless steels. Cold-worked iron-ehromium alloys. Used mai nly in industrial applications requiring moderate corrosion resistance without electroplating, these materials might be suitable for such medical app lications as deep-drawn instrument trays. Heat-treatable iron-chromium alloys. Containi ng up to 16% chromium, possessing considerabl y greater corrosion resistance, and capable of har dening by heat treatment, these alloys are widely used in forceps, suture needles, and other surgica l instruments. Iron-chromium-nickel alloys. The addition of n ickel provides even greater corrosion resistance i n all temperature ranges. These alloys cannot be heat treated to increase hardness or strength, but coldworking can be used to improve these prope rties. An early alloy of 18% chromium and 8% n ickel is widely known for many industrial and so me medical applications. Surgical implants are t ypically 17% to 19% chromium, 12% to 14% ni ckel, and 2% to 3% molybdenum. When such ste els are made with less than 0.03% carbon (c. g., 316L), they are even more resistant to corrosion. Aluminum In both its pure and its alloyed forms aluminum i s a useful metal because of its low density, mode rate corrosion resistance, and relatively high stre ngth. Unfortunately, the last two properties are u sually optimized at the expense of each other: in creased strength often results in decreased corros ion resistance. Pure aluminum is a very ductile low-strength ma terial (34.5 MN/m 2 , 5000 psi yield) with unlim ited uses. Because of the oxide that rapidly form s on its surface, progressive oxidation cannot tak e place. For practical purposes, the pure aluminu m is "corrosion resistant." This resistance is ofte n obtained in alloys by covering with pure alumi num (Alclad). However, hydrochloric acid and a lkalis dissolve the oxide film on aluminum surfa ces and allow rapid material degradation. Theref ore the corrosion resistance of pure aluminum ap plies only to atmospheric conditions. Aluminum is high reactive in physiologic solutions. Aluminum alloys may be divided into two classe s: those used for casting and those that are wrou ght.

Casting aluminum. Casting aluminum may be a lloyed with copper, silicon, and/or magnesium. These have low to moderate strengths (131 to 16 5 MN/m 2, 19,000 to 24,000 psi yield) and low d uctilities (0.5% to 1.3%). Wrought aluminum. Wrought aluminum may e xist in sheet, bar, tube, or extruded form. Some members of this class can be hardened, and their mechanical properties improved, by precipitatio n of copper at slippage planes, often by heat treat ment. Such precipitation takes place spontaneous ly at room temperature for certain alloys and at moderate temperatures for others. In the case of 2024-T3 alloy, often used in ortho ses, moderate temperature (1750 to 2050 C, 350 0 to 400' F) causes the previously precipitated co pper to be dissolved and allows the crystal plane s to slide over each other relatively easily, even f or a short time after the aluminum alloy is rapidl y quenched. The alloy can be conveniently shape d and then rehardened by the work-hardening du ring shaping as well as by aging within a few (12 to 24) hours at room temperature and more rapidly at moderately el evated temperatures. The copper is again precipitate d to "key" the crystal planes, restoring the yield stre ngth and resistance to further deformation. This beh avior seems paradoxical to persons familiar only wit h carbon steels, for which heating to high temperatu res and then rapidly quenching in water will cause s ubstantial permanent increases in strength and hardn ess (e.g., heat-treating a chisel blade). Heating well beyond 200C will cause permanent annealing with low strength but high ductility (e.g., at 365C, 600 F, about 10% of the tensile and yield strengths but more than triple the elongation noted in material kep t at room temperature or heated to only 175C). Cold-working can also be used to improve the m echanical properties of wrought aluminum alloy s. There are two groups of these alloys: the MnMg and the Cu-Si-Mn-Mg. Heat treatment and c oldworking can produce moderate yield strength s (up to 483 MN/m2 , 70,000 psi) but will result i n low ductilities at these levels. Comparisons. There are several similarities and dissimilarities between aluminum and steel alloy s. The elastic modulus of aluminum alloys is 69,00 0 MN/m2 whereas that of steel alloys is 207,000 MN/m2 . This means that for the same shape and loading, aluminum structures will elastically defl ect three times more than steel structures. Another basic difference is that steel has an endu rance limit under repeated or fatigue loading wh ereas aluminum does not. This means that if the l oading conditions are known a steel structure ca n be designed to allow for infinite life. An alumi num structure, however, is eventually subject to fatigue failure as long as it continues to be loade d. Fortunately, as noted earlier, at a practical hig h number of load cycles a small decrease in stres s will allow a tenfold increase in life. Finally, it can be said that "high-strength" alumi

num alloys generally demonstrate much greater i ncreases in static strength than in fatigue loading strength at 1 million to 500 million cycles. Furth ermore, these alloys often are heat treated or wor khardened to greater hardness but lower ductility and typically are much more sensitive to notche s; thus they are not as useful in practical orthotic s applications as their static strengths might indi cate. Titanium and magnesium Titanium. Titanium has been commercially avai lable for about 35 years, yet already it is an extre mely important metal. Its alloys are stronger tha n those of aluminum and are comparable in stren gth to many steels, it demonstrates more corrosio n resistance than aluminum alloys and steel do, a nd (as an added benefit) it is only 60% as dense as steel. However, it is more difficult to machine than aluminum or steel although assembly of pre fabricated components may reduce or eliminate t his disadvantage for small facilities. The elastic modulus of titanium (116,200 MN/m 2 ) is higher than that of aluminum but only slight ly more than half that of steel. Titanium will abs orb about twice as much energy before yielding as a comparable strength of steel will. Unlike other metals, titanium is structurally usef ul in its commercially pure form. Depending on heat treatment and working, it is available with y ield strengths of 210 to 490 MN/m2 (30,000 to 7 0,000 psi), with correspondingly inverse ductiliti es of 25% to 15%. As with steel and aluminum a lloys, titanium is weldable. Although some steels can he welded in an air atmosphere, both titaniu m and aluminum alloys must be welded with eit her a tungsten are and inert gas (TIG) or a metal are and inert gas (MIG). In either system the iner t gas is usually argon or helium. Titanium alloys contain a variety of elements: F e, N, Pd, AI, Mn, Sn, Mo, Zr, and V. Alloying el ements are used to increase workability, machin ability, strength, and biocompatibility. A titaniu m alloy containing 6% AI and 4% V is used as a surgical implant. In most cases, however, titaniu m and its alloys can be formed and fabricated by the same processes as used for aluminum alloys and for steel. The major exception is casting. Tit anium is a difficult material to cast. Magnesium. Magnesium is considerably lighter than titanium and somewhat lighter than aluminu m, and its modulus of elasticity is even lower tha n that of aluminum. However, screw threads are likely to be stripped unless special precautions ar e taken. Magnesium bars or castings are used for some special cases in a variety of industries, but magnesium has had relatively little application i n orthotics. Plastics There are two major categories of plastics-therm osetting, which require application of heat to cur

e or harden but which do not soften upon further heating, and thermoplastic, which will soften eac h time the temperature is raised but harden upon lowering of the temperature. Thermosetting plastics. Thermosetting plastics are production-molded from phenol, urea, or mel amine and are widely used in industry. In prosth etics, however, and to a lesser extent in orthotic s, custom-molded low-pressure laminates are ma de from polyester or epoxy resins (or, increasing ly, from thermoplastic acrylic resins). The original and still widely used variety is base d on phenol-formaldehyde, which is supplied as a powder and is formed at high temperature (149 C, 300F) and pressure (13.8 MN/m2 , 2000 ps i). The resulting tensile properties will vary with the filler material but range from 27.6 to 82.7 M N/m2 (4000 to 12,000 psi). For improved structur al properties the phenol-formaldehyde may be "f illed" with chopped fibers or may be used as a re sin to bind materials like paper or cloth into stru ctural shapes. Such laminates have improved me chanical properties but are also more hygroscopi c. Because of the expensive mold needed, pheno l-formaldehyde plastics are better suited for mas s production. The second important class of thermosetting plas tics, urea-formaldehyde resins, do not differ in th eir fabrication and properties significantly from t he phenol-formaldehyde plastics except that they are less expensive, may be colored, and are mod erately resistant to water. These materials are av ailable in sheet and bar form, but more complex structural shapes must be fabricated by means of expensive dies and complex molding machinery. For decades (since World War II) polyester resin s have been used to form low-pressure thermoset ting laminated prostheses and, to a lesser extent, orthoses. Epoxy resins, introduced about 1948, were used particularly in Europe. Because little or no pressure is required to cure these materials (typically as laminates), larger sections can be fa bricated and with less expensive Tools. They are suitable for custom molding over a plaster model and are used as the binding resin in a two-phase l aminate material (e.g., woven sheets or strips of glass fiber, bundles of parallel glass fibers [term ed roving]. and knitted Dacron polyester stockin et). Epoxy is also used as a very strong glue. Exothermic reactions after mixing of resin comp onents and catalysts or promoters permit "bench Curing" of individual laminated sockets, orthose s, etc. Complete polymerization, however, is nee ded to assure strength and to avoid dermatitis fro m contact with uncured resin. Thermoplastics. The thermoplastics can be sub divided into (1) polyvinyl resins, (2) polyethylen e and polypropylene, and (3) polycarbonate. The major composition used commercially in the rmoplastics, the polyvinyl resins, includes polyvi nyl chloride (PVC), polyvinyl chloride acetate, p olyvinyl alcohol (PVA), and polyvinyl acetate. T he PVC group consists of tough, hard materials t

hat usually require a plasticizer or softener. Amo ng the uses for these materials are leather substit utes, piping and tubing, and small complex struc tural components. All structural fabrications req uire special tooling and injection -molding equip ment. Tubelike shapes may be extruded, but the t ooling is expensive. Commercial PVC tubing (lo w cost in stock sizes) can be cut for specific requ irements and, if necessary, heated and bent for ra pid assembly of endoskeletal prostheses. PVC an d PVA sheets and bags are widely used for plasti c laminating in prosthetics and orthotics. Becaus e PVA can be softened by dampening, a conical sleeve may be stretched over a relatively comple x plaster model of a residual or paralyzed limb. Other important thermoplastic composit ions are polyethylene and polypropylene. Both t hese material are highly stable and resistant to w ater and solvents. They are easily formed and ha ve many medical uses, including (for polyethyle ne) internal prostheses and for polypropylene, be cause of its in definitely long fatigue life under r epeated loading) orthotic hings joints. Polyethyle ne, polypropylene, and (more recently) polycarb onate and ionomer are being used increasingly f or orthotic structures of new design and for prost hetic sockets. A heated and softened sheet is sha ped on a plaster model by vacuum molding, with the thicknesses skillfully controlled and the edge s trimmed and polished. Although polyethylene and polypropylene are semicrystalline materials at body temperature and not transparent, the thic knesses and grades used in orthotics are transluc ent. By contrast, polycarbonate, ionomer, and po lymethyl methacrylate are transparent. allowing better detection of pressure spots and a less cons picuous appearance. Special care must be taken to dry polycarbonate before molding, to prevent crazing, with reductio n of its transparency and exceptional strength. P olycarbonate is very stiff. Recently ionomer, a th ermoplastic that does not need to be dried before molding, has been used increasingly for orthoses despite its lower ultimate tensile strength. It is re asonably transparent but much more flexible. As we have seen, yielding is sometimes equated wit h failure, but in many cases the yielding of plasti c under emergency circumstances will minimize other dama ge, particularly if the ultimate strength is not reache d and if, as with some metals and thermoplastics, th e device can be restored to its original shape. Table 2-1559 compares physical properties of selected ther moplastics used in orthoses. Polymethyl methacrylate has long been available and occasionally used for upper-limb splints, but it is relatively weak. Acrylonitrile-butadiene-styr ene (ABS) combines high rigidity with high tens ile and flexural yield strengths and high impact s trength. It is available in many colors and is wid ely used commercially for casings and housings. In orthotics it is used for spinal orthoses and cust om-molded wheelchair seats.

Nylon is a strong, tough, abrasion-resistant ther moplastic but has the disadvantage of absorbing water. In addition, it is relatively expensive com pared to some materials with similar properties. Low-cost nylon washers, however, have been us ed without lubrication in orthotic joints, particul arly with aluminum bars.57 The ability to form an orthosis or a prosthetic so cket safely, comfortably, and rapidly directly on the body of the patient has long been a goal. It is also desirable to be able to modify the device in certain areas to relieve pressure spots, to change alignment slightly, or to accommodate small am ounts of growth or atrophy. By contrast, the devi ce should not be affected by accidental contact with a steam radiator, storage in the trunk of an a utomobile on a hot day, or exposure to various c hemicals in the environment. Synthetic balata (P olysar)61 and a perforated version (Orthoplast)36,3 7 have undergone considerable development. Th ey can be heated in boiling water until soft and t hen molded on the body, either directly on the sk in or over thin stockinet. Rapid evaporation of th e film of water and radiation during transfer to th e body apparently cool the surface to a tolerable level. The very low thermal diffusivity of the ma terial (related to its low density and low thermal conductivity) prevents rapid heat transfer from d eeper inner layers to the interior and exterior sur faces, avoiding pain to the patient and allowing t he orthotist to continue brief molding of the soft ened thermoplastic with the hands followed by st eady support during several minutes of hardenin g. While wet and heated, the material sticks to it self, which is desirable for seams. Surfaces that s hould not adhere can he sprayed with separating fluid. Temporary prosthetic sockets and fracture braces have been made from Polysar, and Orthoplast is used extensively for temp orary upper-limb splints. Although some process si milar to vulcanization would seem desirable to incre ase strength and retain shape after forming, another worthwhile objective is retaining the ability to make repeated small additional adjustments. Rubbers. The term rubber is used to denote the family of natural and artificial elastomers that in cludes, along with natural rubber, butyl rubber, p olysulfide rubbers, neoprene, nitrile rubbers, and GR-S butadiene-styrene copolymer. Rubber is used whenever large elastic deformati on (up to 3000% of the original length of the ma terial) is required with relatively low force level s. Because most rubbers are almost perfectly ela stic, there is only limited energy loss by hysteres is or internal friction. The nonlinear stress-strain characteristics of rubber can provide in a finishe d structure a large excursion at relative low force s, then more rapidly increasing forces, and finall y such large forces as to block further motion. R ubber is a much better elastic energy absorber, o n a weight or volume basis, than any metal. Thus

it can be effective in bumpers, elastic straps, etc. The skid resistance of cane or crutch tips on wet pavements or ice depends on high flexibility and hysteresis. 32 Natural rubber and some styrene-b utadiene compounds, preferably with oil extensi on of either, would be most suitable around the f reezing temperature of water. Besides being resistant to wear, natural rubber h as excellent tensile properties. Its resistance to c old, flexing, and aging is also excellent. Howeve r, it is not impervious to sunlight or to most oils or solvents. Butyl rubber offers improved resista nce to ~unlight and solvents but lacks the high te nsile ~strength or wear resistance of natural rubb er. Because of the wide variety of properties that ca n be produced in rubber by compounding, it is of ten possible to produce a material that is well sui ted for a particular application. Cellular rubbers and plastics. Numerous cellula r rubbers and plastics (e.g., polyurethane, polyst yrene, polyethylene, polypropylene some capabl e of custom molding while comfortably hot) are used in prosthetics and orthotics. The softer grad es are best for padding, but firmer and more den se varieties are also being used increasingly for c osmetic covers of endoskeletal prostheses or eve n as structural elements. Some types have interc onnecting pores, allowing absorption and passag e of fluids, gases, or vapors. These open-cell mat erials, however, can create hygienic problems if perspiration or debris accumulates in the pores. Other types, closed-cell forms, have individual g as-filled cells or "bubbles" that do not interconne ct. When cellular plastic is molded, a smooth and re latively tough skin typically is formed against th e wall of the mold that is often an advantage. Bl ocks cut from cellular material, and perhaps furt her sanded to desired shape, have rough surfaces with randomly distributed cavities of remaining pores. In some cases these surfaces can be sealed and smoothed by painting with latex. For structu ral uses one or more layers of plastic laminate m ay be added. DESIGN CONSIDERATIONS Practical and economic considerations In selecting specific materials and components f or the various portions of an orthosis, it is necess ary to consider practical and economic factors. S afety, case of working, compatibility of prefabri cated components, ease of adjustment during fitt ing or subsequent use, and feasibility of attachm ent are aspects. In any portion that comes in contact with the bod y, safety is essential. There must be no toxicity, allergenic tendency, or mechanical irritation. A material such as fiberglass may be used for reinf orcement of a laminate if it is buried in the matri x, but special care must be taken to reseal the fib er ends exposed by grinding during trimming an d fitting. To avoid toxic or allergic reactions to u ncured components of the resin, curing of plastic

s must be complete. During the initial use of plas tic laminates in prosthetics, it was reported by a few facilities that skin irritation resulted from fre e monomers left after incomplete curing. The ch aracteristic odor of the monomer was readily det ected near the supposedly cured laminate. With adequate care, however, these difficulties were o vercome, If any doubt remains, heating the finis hed laminate briefly with a heat lamp is effectiv e. With tile current interest in forming prosthetic sockets and orthotic devices directly on the patie nt's body, not only the toxicity of base materials, plasticizers, or solvents but also their workabilit y at tolerable temperatures are factors. Ease of working with available facilities is' an i mportant practical consideration. The necessity of forming orthotic structures to fit each patient i mposes unusual requirements not typically foun d in many industrial operations. Conventional molds, dies, and punches used in mass production of identical parts are sometimes ap propriate for prefabricated components of orthotic d evices. These devices are typically produced in a fe w stock sizes, perhaps capable of being cut to length or of being slightly adjusted further to shape; but an y part that fits the body must be formed to the indivi dual. A wide variety of straps, buckle attachments, a nd similar parts is available from a few central man ufacturers as inexpensive prefabricated elements. Prefabricated ankle or knee joints have been avai lable for decades and increasingly widely used a fter the mid-1950s, partly because of improved c ontrol of tolerances and quality. Probably the gre atest incentives were the economic savings from the reduction in time required of skilled labor an d the possibility of more rapid delivery to the pat ient.'s' In some designs the "joint head" is a sepa rate element adapted for attachment to a bar or o ther structural element by screws or rivets. Quite commonly the joint head is delivered by the man ufacturer as an integral piece with a relatively lo ng straight bar that can be formed to shape and c ut to the appropriate length for the individual pat ient by the local orthotics facility. Metal bars or similar structures typically are adjusted by using bending irons to strain the metal into the plastic r egion, leaving a permanent set when this load is removed. By contrast with practice common prio r to 1950, forging of metal bars at high temperat ure now seldom occurs in local orthotics facilitie s. With the proliferation of new designs of orthose s, the conventional prefabricated components of the 1960s will probably continue to decrease in usefulness. Some joints will be replaced entirely by the bending of selected portions of the structu re. Other prefabricated components, redesigned t o attach readily and securely to plastic laminate, thermoplastic, or composite structures, will conti nue to cut labor costs and improve service. Some of the cuffs, shells, or other portions in co

ntact with the patient's body are now prefabricat ed in a few sizes and shapes. They can then be sl ightly distorted by straps or laces or more extens ively modified (as with a heat gun in the case of thermoplastics or postforming thermosetting pla stic laminates). Simple adjustments during daily wear should be possible and are provided preferably by Velcro s traps. 36 Small adjustments can then be easily m ade, as opposed to the substantial amount of man ipulation needed to move a conventional buckle between successive holes in a belt. Preferably a s trap should be "snubbed," or passed through a lo op fastened by another strap or a billet to the opp osite structure and then laid back on itself and th e loose end attached to the original portion by m ating Velcro elements. Just as in a rope-and-pull ey system, the load on each end and thus the she ar load on the Velcro are cut in half, compared w ith the situation that exists when mating straps o verlap from opposite sides of the structure. Buckles with tongues and perforated straps are a lso widely used and are adequate for adjustments requiring substantial steps, but they are especiall y appropriate for repeated attachment (by a dextr ous patient) or for opening and closing at a relati vely fixed position. Buckles capable of sliding a djustment along a fabric strap are frequently use d to modify the length of a harness or suspension. Traditionally the longitudinal bars or uprights of lower-limb orthoses for children have consisted of two portions fastened together by several scre ws. The length could be incrementally modified to accommodate growth by use of the uniform di stance between screw holes in one of the bars. A few of the newer orthoses lack this adjustability. Thermoplastic materials may allow for slight mo dification of diameter or shape to fit a changing body portion, but they do not seem appropriate f or accommodating to longitudinal growth. Some sort of telescoping construction may be needed. Attachments of orthotic components may be ma de in a variety of ways. As we have seen, an occ asional material like synthetic balata (Orthoplast or Polysar 36,61) may stick to itself under certai n conditions, such as when it is hot and wet. Ind eed, release agents must be applied to areas that are not supposed to adhere when they come into contact during the construction or fitting process es. Some resins, particularly the epoxies, can be used effectively not only for laminating but also as cements. Metal joint heads may be welded by electric arc or gas flame to given an integral met al bond to adjoining upright bars. Brazing or sol dering provides a weaker metal-to-metal connect ion by a bond that melts at a much lower temper ature than the major structural metal. Some thermoplastic sheet materials can be weld ed with a slender rod of the same material. 17 Th e abutting edges are beveled to leave a V-shaped groove to be filled with the heated end of the ro d. Skill is needed to fuse edges and rod into a sin gle strong sheet.

Frequently parts are attached temporarily by a fe w light screws or rivets before the fitting proces s. Then more secure connection in the desired ali gnment is made by additional heavier screws or rivets or by brazing or welding. Composite structures are considerably more com plex than those of a single material. It can be de monstrated that there will necessarily be loading directly proportional to the respective moduli of elasticity if two or more different materials are u sed in parallel with equal deflections. Suppose, f or example, that a rigid frame supports a relative ly rigid loading bar (constrained to remain parall el) by a stiff high-modulus steel wire and a relati vely flexible low-modulus rubber band. The stee l wire (with but microscopic deflection) will carr y almost all the load whereas the rubber band (st retching the same slight amount) supports only a trivial share of the total load. Conversely, of cou rse, if the bar is free to change angular position a nd the flexible and stiff supports carry equal loa ds the flexible support will deform much more a nd the bar will no longer be parallel to the frame. In an important but less dramatic case, a strip of laminate or composite structure under tension ca rries most of the load on rather stiff fabric, stiffe r fiberglass, or much stiffer boron or graphite fib ers whereas the low-modulus resin matrix carrie s relatively little load. The transfer of load, even between two components respectively stiff and f lexible, in a single composite material or especia lly in a more complex structure forced to deform as a whole, may he complicated and involves sh earing stresses at the interfaces. Such transfer ca n be visualized by imagining structures of chains and springs connected by bars or beams. There are also stresses within structures subject t o external loading near sudden changes of stiffne ss. It is well known that these can concen