Materials science

Chapter 3 Materials science




Key Points








Metals and plastics are the basic principal materials used in orthotics and prosthetics. To understand recommended design and fabrication procedures, a basic knowledge of the properties of the various available materials is necessary. The practitioner must be familiar with these materials in order to cope with both standard and difficult designs and fabrication problems and have the ability to prevent structural or functional failures of device due to the material.


Selection of the correct material for a given design depends partially on understanding the elementary principles of mechanics and materials, concepts of forces, deformation and failure of structures under load, improvement in mechanical properties by heat treatment, work (strain) hardening or other means, and design of structures. For example, the choices for a knee–ankle–foot orthosis (KAFO) may include several types of steels, numerous alloys of aluminium, and titanium and its alloys. Important but minor uses of other metals include copper or brass rivets and successive platings of copper, nickel, and chromium. Plastics, fabrics, rubbers, and leathers have wide indications, and composite structures (plastic matrix with reinforcing fibers) are beginning to be used. Often complex combinations of materials are used in manners that are not appropriate from the material point of view but are appropriate for the particular clinical application. Understanding these properties not only assists with the selection, manufacture, and management of the device but extends to the management of the patient and the information that the practitioner will instill into patients. A simple example is the combination of flexible materials such as a strap and thermoplastic, using an alloy rivet.


Despite publicity for exotic materials, no single material is a panacea. One reason is that a single design frequently requires divergent mechanical properties (e.g., stiffness and flexibility required in an ankle–foot orthosis [AFO] for dorsiflexion restraint and free plantar flexion). In addition, practitioners rarely are presented with situations where they will use only one material or with single-design situations that will not require modification, customization, or variation over time.


In general, understanding by the practitioner of the mechanics and strength of materials, even if intuitive, is important during the design stage. A general understanding of stresses arising from loading of structures, particularly from the bending of beams, is needed. The practitioner then can appreciate the importance of simple methods that allow controlled deformation during fitting, provide stiffness or resiliency as prescribed, and reduce breakage whether from impact or repeated loading. A general discussion of materials and specific theory related to design, fabrication, riveting guidelines, troubleshooting, and failure considerations follows.


Consideration should be given to the international standards of terminology that are used to describe orthotics, prosthetics, properties of materials, and units of measure (whether imperial or metric) as well as the engineering principles for describing the various effects of loading upon these materials. Unless they are familiar with the particular definitions of the terms used, practitioners should generally avoid using specific terminology in favor of more objective descriptive language.



Strength and stress


One of the practitioner’s main considerations is the strength of the material selected for fabrication of orthoses or prostheses. Strength is defined as the ability of a material to resist forces. When comparative studies are made of the strength of materials, the concept of stress must be introduced.


Stress relates to both the magnitude of the applied forces and the amount of the material’s internal resistance to the forces. Stress is defined as force per unit cross-sectional area of material and usually is expressed in pounds per square inch (psi, imperial) or megapascals (MPa, Newtons per square meter, metric). The amount of stress (σ) is computed using the equation:



image   (3-1)



Where F = applied force (pounds or Newtons), and A = cross-sectional area (square inches or square meters).


The same amount of force applied over different areas causes radically different stresses. For example, a 1-lb weight is placed on a cylindrical test bar having a cross-sectional area of 1 in2. According to Equation 3-1, the compressive stress σc in the cylindrical test bar is 1 lb/in2 (Fig. 3-1). When the same 1-lb weight is placed on a needle having a cross-sectional area of 0.001 in2, the compressive stress σc in the needle is 1000 psi (Fig. 3-2).




A force exerted on a small area always causes more stress than the same force acting on a larger area. When a woman wears high-heeled shoes, her weight is supported by the narrow heels, which have an area of only a fraction of a square inch. With flat shoes, the same weight or force is spread over a heel having a larger cross-sectional area. The stress in the heel of the shoe is much greater when high-heeled shoes are worn because less material is resisting the applied forces.


Similar problems are encountered in orthoses and prostheses. A child weighing 100 lb and wearing a weight-bearing orthosis with a 90-degree posterior stop (Fig. 3-3) can exert forces at initial contact that create stresses of thousands of pounds per square inch. If the child jumps, the force would increase with the height of the jump. The stress at the stop or on the rivet could be great enough to cause failure.




Tensile, compressive, shear, and flexural stresses


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





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. 3-7, A) 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. 3-7, B). 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. 3-8). The lap joint has one shear area of the rivet resisting the forces applied to the lap joint (Fig. 3-8, A), 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; Fig. 3-8, B). 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.








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 dimensions of the specimen coupon are fixed by standardization so that the results can be universally understood, no matter where or by whom the test is conducted. The specimen coupon 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 coupon is smaller in the center to prevent failures where the coupon is gripped. The specimen’s resistance to being stretched and the linear deformations are measured by sensitive instrumentation (Fig. 3-11).



The force of resistance divided by the cross-sectional area of the specimen is the stress in the specimen (Equation 3-1). The strain is the total deformation divided by the original length (Equation 3-2). 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. Figure 3-12 shows such a 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.


The general shape of the stress–strain curve (Fig. 3-12) 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. 3-12), 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 prior to 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. Figure 3-13, A 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. 3-13, B is for an alloy steel and the higher curve is for hard steels. Nonferrous alloys and cast iron have the form shown in Fig. 3-13, C. The plot shown in Fig. 3-13, D is typical for rubber.



For any material having a stress–strain curve of the form shown in Figs. 3-13, A–D, it is evident that the relation 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 Hookes law. Expressed as an equation, Hooke‘s law becomes:



image   (3-3)



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


The slope of the stress–strain curve from the origin to point p (Figs. 3-13, A and B) 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 3-1.



In a routine tension test (Fig. 3-14), 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 Equations 3-1, 3-2, and 3-3 and solving for the shortening ΔL gives:




image   (3-4)



Because the original length L0, cross-sectional area A, and modulus of elasticity E are constants, the shortening ΔL depends solely on F. As F doubles, so does ΔL.


The operation of a steel spring scale is another practical illustration of Hooke’s law (Fig. 3-15). The amount of deflection of the spring for every pound of force of the load remains constant. In Fig. 3-15, A, the scale indicates three units (pounds, ounces, grams). With one weight added (Fig. 3-15, B), the scale indicates 5, or two additional units. A second weight added (Fig. 3-15, C) causes the scale to indicate 7, or a total of four additional units, and a third weight stretches the spring two more units (Fig. 3-15, D). 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. 3-12), 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 σ2 in Fig. 3-16. This load will cause strain εE. When the load is removed, the strain disappears, that is, point X2, εE) moves linearly down the proportional portion of the curve to the origin. Similarly, when load σ1 is applied, strain εT results. However, when load σ1 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 εP. Therefore, with no load, the material has a residual or permanent strain of εP. 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 εP is the plastic strain, and (εT – εP) is the elastic strain εE or:




image   (3-5)



where εT = total strain under load, εP = plastic (or permanent) strain, and εE = elastic strain.



Yield point


Yield point (point b on the stress–strain diagram of Fig. 3-12) refers to that point at which a marked increase in strain occurs without a corresponding increase in stress. The horizontal portion of the stress–strain curve (b-c-d in Fig. 3-12) indicates the yield stress corresponding to this yield point. The yield point is the “knee” in the stress–strain curve for a material and separates the elastic from the plastic portions of the curve.







Moment of inertia


The moment of inertia of a finite area about an axis in the plane of the area is given by the summation of the moments of inertia about the same axis of all elements of the area contained in the finite area. In general, the moment of inertia is defined as the product of the area and the square of the distance between the area and the given axis. The moments of inertia about the centroidal axes Icc of a few simple but important geometric shapes are determined by integral calculus and are given in Table 3-3. Although Young’s modulus is an indication of the strength of the material, the moment of inertia is an indicator of the strength of a particular shape about the aspect in which it will be loaded. This is a highly important parameter for the practitioner to know because he or she often will be able to influence the shape.




Stresses in beams


If forces are applied to a beam as shown in Fig. 3-19, downward bending of the beam occurs. 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. 3-19 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. 3-20), is given by:




image   (3-10)



where I = moment of inertia of the cross-sectional area about the neutral or centroidal axis in inches4.


These stresses vary from zero at the neutral axis of the beam (y = 0) to a maximum at the outer fibers (Fig. 3-20). These stresses are called bending, flexure, or fiber stresses.







Metals


A metal is defined as a chemical element that is lustrous, hard, malleable, heavy, ductile, and tenacious and usually is a good conductor of heat and electricity. Of the 93 elements, 73 are classified as metals. The elements oxygen, chlorine, iodine, bromine, and hydrogen and the inert gases helium, neon, argon, krypton, xenon, and radon are considered nonmetallic. There is, however, a group of elements, such as carbon, sulfur, silicon, and phosphorus, that is intermediate between the metals and nonmetals. These elements portray the characteristics of metals under certain circumstances and the characteristics of nonmetals under other circumstances. They are referred to as metalloids.


The most widely used metallic elements include iron, copper, lead, zinc, aluminum (or aluminium), tin, nickel, and magnesium. Some of these elements are used extensively in the pure state, but by far the largest amount is used in the form of alloys. An alloy is a combination of elements that exhibits the properties of a metal. The properties of alloys differ appreciably from those of the constituent elements. Improvement of strength, ductility, hardness, wear resistance, and corrosion resistance may be obtained in an alloy by combinations of various elements. Orthotics and prosthetics typically contain alloys of aluminum and carbon steels, particularly stainless steel. Titanium also is frequently used, and, despite references to “pure titanium” (particularly in applications such as osseointegration), it is the alloy that is being referenced. Although these alloys (steel, aluminum, titanium) can be categorized as similar depending on the base metal and some of the contributing alloy metal, they are potentially infinitely variable.



Crystallinity


One of the important characteristics of all metals is their crystallinity. A crystalline substance is one in which the atoms are arranged in 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:








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:






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





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 about 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. 3-29. In this diagram, the squares represent space lattices. In A, 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 B, C, D, E, and 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. 3-30).





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. 3-31.





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 by A in Fig. 3-32. If a shearing force within the elastic range is applied, the lattice is uniformly distorted as in B, with the extent of distortion proportional to the applied force.



When the force is removed, the lattice springs back to its original shape (A). 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 (C). On release of load, the lattice in the two displaced blocks resumes its original shape (D). 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 in comparison to 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 but a small fraction of theoretical strength. Some significant comparisons for pure copper are as follows:




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 great weakening effect of graphite flakes in cast iron is an example.


Notches act not only as stress raisers but also as stress complicators, frequently 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 do well to recognize their prevalence under many disguises (i.e., from either contouring instruments or grain boundaries). Most importantly, every care should be taken to minimize the contribution to these weakeners by not adding further notches, cracks, scratches, or rough surfaces.



Steel and aluminum alloys



Commercial name for metals


Before the stress–strain diagram is used as a basis for comparing the properties of various metals, it is necessary to discuss the types of steel and aluminum commercially available and used in orthotic and prosthetic applications.


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 assure the orthotist or prosthetist of 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.



Jul 12, 2016 | Posted by in ORTHOPEDIC | Comments Off on Materials science
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