Materials Selection and Design (2010) Part 13 ppsx

As a consequence, material hardness is generally not a sufficient indicator of wear resistance or wear performance in specific situations.. Table 5 Typical wear applications for selected

Trang 1

Table 2 Operational classification of wear situations

Trends: Wear increases with increasing slip and presence of particles Adhesive and abrasive wear modes can predominate but with pure rolling fatigue modes predominate Mildest wear situation Smooth surfaces preferred

Impact

Dry, without particles Fatigue (elastic or plastic)

Adhesive Dry, with particles Fatigue (elastic or plastic)

Adhesive Abrasive Fluid, without particles Fatigue (elastic or plastic)

Adhesive

With moving body

Fluid, with particles Fatigue (elastic or plastic)

Adhesive Abrasive

Trends: With stationary body, induced vibrations and misalignment can cause fretting, which tends to increase wear Plastic deformation generally unacceptable except in short life applications For lives greater than 10 6 , contact stresses need to be in the elastic range With moving object, wear increases with the amount of sliding and sliding effects can predominate Fluid

lubrication effects can be very significant With particles, wear tends to increase

Adhesive Large amplitude, fluid Fatigue

Adhesive Large amplitude, particles Fatigue

Adhesive Abrasive

Adhesive Small amplitude, fluid Fatigue

Adhesive

Cyclic

Small amplitude, particles Fatigue

Adhesive Abrasive

Trends: More than one type of mechanism involved Fatigue mechanism is mildest and conditions that minimize adhesion and abrasion preferred Low contact stresses preferred Mild to severe wear transitions often associated with the transition from elastic to plastic deformation Predominant mechanisms(s) can change with wear In mild wear situations, terminal mode often fatigue With the presence of particles, abrasion tends to become predominant mode Nature of contact shape, such as large area, conforming, line, and point, can be significant in wear behavior

One-body contact with fluid

Impingement

Low angle

High angle

Abrasive (deformation)

Flow

Trang 2

Without particles None

Streamline

Measurable wear model (a)

Variable energy mode d[Q/ ( maxW)4.5] = Cd (S/W)

Constant energy mode dQ = Cd (S/W)

Impact

Percussive impact model V = kv m N

Zero wear model (condition for zero

wear) (b) N0 = (2000/1 + ) [ R ( / y)]

9

Measurable wear model (c) dV = (V/N) dN + g(9V/ ) d

Rolling

Surface endurance model (condition

for surface cracks) N1 = N2

Load-stress factor model Le = K1 {w/[(1/R1) + (1/R2 )]}

log K1 = [(B - log N)/A]

Abrasion

Erosion

General model (d) e = KAI

Liquid drops model e = K sin n Mv m

d v n cosn sin ( / ) + K b v m sinm ] M

Vibration-induced cavitation model e = K n

Trang 3

Amplitude of vibration Peak contact pressure

C, k, K, Kb, Kd, m, n, R , R Tribosystem empirical coefficients

Source: Ref 8, 9, 10

(a) Zero wear model for sliding can be used to determine C

(c) For constant-energy mode, g = 0 For variable-energy mode, g = 1

(d) Where K is a function of time, A is a function of angle, and I is a function of stream intensity

References cited in this section

2 A.F Bower and K.L Johnson, J Mech Phys Solids, Vol 37 (No 4), 1989, p 471-493

3 K Johnson, Proc 20th Leeds-Lyon Symp Tribology, Elsevier, 1994, p 21

4 F Aleinikov, Soviet Phys.-Tech Phys., Vol 2, 1957, p 505, 2529

5 P Blau, Friction and Wear Transitions of Materials, Noyes Publications, Park Ridge, NJ, 1989

6 N.C Welsh, Proc Royal Society, Vol A257, 1965, p 31

7 S.C Lim and M.F Ashby, Acta Metall., Vol 35, 1987, p 1-24

8 R.G Bayer, Mechanical Wear Prediction and Prevention, Marcel Dekker, 1994

9 P Blau, Ed., Friction, Lubrication, and Wear Technology, Vol 18, ASM Handbook, ASM International,

1992

10 M Peterson and W Winer, Ed., Wear Control Handbook, American Society of Mechanical Engineers,

1980

Design for Wear Resistance

Raymond G Bayer, Tribology Consultant

Lubrication

Friction is the resistance to relative motion between two bodies in contact A lubricant is defined as any substance that reduces the friction between two surfaces The use of these materials is one of the principal ways of reducing wear and extending the life of mechanical equipment Lubricants provide a low shear interface between surfaces by physically separating those surfaces and by allowing the formation or modification of surface films on those surfaces While the principal effect of lubrication on wear behavior is associated with the reduction of adhesive wear, the other types of mechanisms can also be affected by the presence of a lubricant For example, mechanisms that are influenced by shear stresses, such as some deformation and fatigue mechanisms, can be affected by changes in traction caused by the use of a lubricant Oxidation wear mechanisms can be affected by the changes in surface films resulting from the use of a lubricant Lubricants can also inhibit or modify the formation of tribofilms

In general, lubricants tend to reduce wear However, there are some situations in which they can increase wear For example, they may inhibit the formation of a beneficial tribofilm without providing adequate lubrication This is often the case in tribosystems in which self-lubricating materials are used Another example is abrasive wear situations, where abrasive particles tend to agglomerate or where wear debris can clog an abrasive counterface These actions tend to reduce abrasive wear rates, but in these situations, lubricants tend to prevent the agglomeration or clogging, which leads

to a higher wear rate In abrasive wear situations a lubricant can also reduce the critical angle for cutting, which also tends

to increase wear

Trang 4

Lubrication can also affect wear behavior in other ways In circulating systems, lubricants can provide cooling to the interface and remove wear debris In non-circulating systems, oil and grease films tend to hold abrasive particles in dirty environments, which can lead to increased wear

Except for abrasive and erosive wear situations, the effective application of lubrication generally results in mild wear behavior Severe wear behavior in a lubricated situation is often an indication of lubricant breakdown, improper lubricant selection, or an inadequate supply Even though one of the ways a lubricant works is to separate the surfaces, thick lubricant layers are not required to obtain significant improvements in wear performance Thin films, even down to monomolecular layers, can have significant effects provided that they are maintained

Lubrication by thin films is often referred to as boundary lubrication Its effectiveness primarily depends on the ability of the lubricant to coat or react with the surface With fluids it is possible to generate thicker films as a result of squeeze film effects in the fluid As a result of these effects it is sometimes possible to achieve complete separation of the surfaces, which virtually eliminates wear This is referred to as fluid lubrication (Design procedures for lubrication are beyond the scope of this article and can be found in books on bearing design and fluid lubrication.) The state of lubrication between boundary and fluid lubrication is called mixed lubrication Wear rates are lower with mixed lubrication than with boundary lubrication (Ref 11)

By using almost any lubricant, wear rates are generally reduced by one to two orders of magnitude However, there can be significant differences in the lubricating abilities of different lubricants, so it is often possible to obtain larger reductions (e.g., several orders of magnitude) by optimizing the selection Lubricant selection for a wear application often involves two other elements One is supply of the lubricant If there is an inadequate supply, wear rate will increase, as shown in Fig 4 The other is the chemical stability of the lubricant in the application Generally, when a lubricant degrades, its ability to protect the surface is decreased and wear rates increase

Fig 4 Effect of oil supply rate on the wear of a high-speed printer component Wear occurred at the interface

between a pivoting type element and a type carrier backstop The materials were hardened steel The wear resulted from a combination of impact and fretting Source: Ref 12

Types of Lubricants. Lubricants are either fluids or solids The fluid category includes gases, liquids, and greases Common solid lubricants are molybdenum disulfide, polytetrafluoroethylene, graphite, and soft metals Because fluids tend to be displaced easily, other materials are frequently added to enhance their boundary lubrication characteristics Solid lubricants and reactive compounds are often used in greases and oils for this reason These types of additives are generally called extreme pressure (EP) additives Solid lubricants are also used as fillers in plastics to make self-lubricating materials With these materials the solid lubricants provide lubrication by forming tribofilms on the rubbing surfaces While fluid films tend to be more easily displaced than solid lubricant films, they have the ability to self-heal Solid lubricant layers do not However, this limitation of solid lubricants is removed when they are used as additives and fillers (Ref 13)

While lubrication is used to reduce both friction and wear, the effects that a lubricant has on each of these phenomena can

be different As a consequence, the best lubricant for friction reduction is not necessarily the best for wear reduction

Trang 5

Often the coefficients of friction can be similar for different lubricants, while wear rates can differ by orders of magnitude Table 4 contains data that illustrate these two points

Table 4 Effect of different lubricants on friction and wear for reciprocating sliding in a ball-plane

Steel/steel Stainless steel/steel

Oil

Coefficient of

friction

Depth of wear, m

Coefficient of friction

Depth of wear, m

11 E.R Booser, Ed., Handbook of Lubrication, Vol II, CRC Press, 1984

12 R Bayer, Wear, Vol 35, 1975, p 35-40

13 E.R Booser, Ed., Handbook of Lubrication, Vol III, CRC Press, 1994

14 IBM General Products Division Technical Report TR 01.17.142.678, 10 April 1962

Material Selection for Wear Applications

Some fundamental criteria can be applied in the selection of a material for wear applications The primary criterion is that the material remain chemically, mechanically, and thermally stable under the operating conditions A secondary criterion

is that the nominal contact stresses be within the elastic range of the material If either of these criteria is not met, it is likely that severe wear behavior and unacceptably high wear rates will result For long life under sliding it is generally desirable to have a 2-to-1 or larger ratio between yield point and nominal contact stress For impact and rolling this ratio can be smaller, approaching 1, and still be acceptable, In abrasive wear situations, it is generally desirable to have the material harder than the abrasives present, or at least of comparable hardness, to minimize wear and obtain long life A corollary is that if a particular material must be used, the conditions of use need to be changed so that these criteria are satisfied

As stated above, material wear resistance is not an intrinsic property, like elastic modulus or density It tends to vary with the wear situation and is best viewed as a system response While there is a general trend for wear to decrease with increasing hardness, there is considerable scatter about that trend As a consequence, material hardness is generally not a sufficient indicator of wear resistance or wear performance in specific situations It is often necessary to consider other properties of the material as well Basically this is because hardness is not the only material property that is associated with wear behavior, and because the differences between materials are not limited to hardness, particularly in the case of different types or classes of materials Because of the many factors associated with wear behavior, different types of materials tend to be used for different wear situations (Ref 15) Table 5 provides an overview of typical wear applications for different classes of materials

Trang 6

Table 5 Typical wear applications for selected engineering materials

Abrasi

on

Unlubric ated wear

Lubrica ted wear

Abrasi

on

Impa

ct wear

Three -body abrasi

on

Fluid erosi

on

Cavitati

on

Drop erosi

on

Parti cle erosi

on Structural

Because of the system nature of wear, rankings of materials in terms of their wear resistance often change with the nature

of the wear applications or the nature of the wear test used to determine the rankings For example, rankings obtained

Trang 7

from abrasive wear tests are typically not the same as those obtained from nonabrasive wear tests Similarly, different rankings tend to be obtained in lubricated and unlubricated tests or in high- and low-speed tests, among others Because of this, wear tests used to rank or evaluate materials for use in specific situations need to simulate the wear application in all essential details (Ref 8, 16, 17, 18, 19, 20, 21) The basic elements that need to be considered in simulation are loading conditions, contact geometry, motions involved, and environmental conditions

Highly wear-resistant materials are often materials that maintain average wear characteristics under extreme conditions, such as high ambient temperatures or a corrosive environment As a result, these kinds of materials may provide no better and sometimes poorer wear performance than other materials in situations where these extreme conditions do not exist

15 B Bhushan and B.K Gupta, Handbook of Tribology, McGraw-Hill, 1991

16 R.G Bayer, Ed., Selection and Use of Wear Tests for Metals, STP 615, American Society for Testing and

19 C.S Yust and R.G Bayer, Ed., Selection and Use of Wear Tests for Ceramics, STP 1010, American Society

for Testing and Materials, 1988,

20 A.W Ruff and R.G Bayer, Ed., Tribology: Wear Test Selection for Design and Application, STP 1199,

American Society for Testing and Materials, 1993

21 Mechanical Testing, Vol 8, Metals Handbook, 9th ed., American Society for Metals, 1985

Wear Models

Because of the complex nature of wear behavior, there is no universal wear model that is applicable to all situations However, there are wear models that can be used for design for specific situations (Ref 8, 9, 10, 22) There are models for generic wear situations, such as rolling and sliding, as well as models for specific devices, such as journal and roller bearings Table 3 contains a list of models used for sliding, rolling, impact, and erosion Table 6 lists some application models These models provide relationships between wear and design parameters in a number of forms In some cases the relationships are for the amount of wear, others are for wear and erosion rates, and still others are for equivalent wear conditions (i.e., those combinations of load and usage that result in the same amount of wear)

Table 6 Application wear models

• PV model for plastic bearings

• K factor model for journal bearings

bearings

Trang 8

• Type wear in impact printers

AFBMA, Antifriction Bearing Manufacturers' Association Source: Ref 8, 9, 10, 11

All these models involve one or more empirical coefficients, which are material and environment dependent While empirical, they tend to be heuristically related to or based on a variety of general physical concepts and mechanisms These heuristic concepts can often be used as an aid in the application of these models to particular situations For example, they are often of use in estimating the values for the empirical coefficients, in evaluating the applicability of a model to a given situation, or in extending a model In-depth treatment of these models and their use can be found elsewhere (Ref 8, 9, 10)

While there are a number of different models available for design use, most wear situations encountered in design can be adequately covered with the use of relatively few The zero wear model for sliding (Ref 8, 23), the measurable wear model for sliding (Ref 8, 24), the zero wear model for impact (Ref 8, 25), the measurable wear model for impact (Ref 8, 26), and the surface endurance model for rolling (Ref 8, 27), summarized in Table 3, are applicable in most engineering situations where abrasion is not predominant In those situations in which abrasion predominates, the abrasive wear model given in Table 3 provides good correlation with performance

The coefficients of the models are determined from wear tests that match the conditions required by the model In most cases not all of the coefficients of the model can be determined simply by measuring wear after a certain amount of time, sliding distance, or number of operations It is generally necessary to develop a wear curve or series of wear curves that can be analyzed to determine the coefficients for the model A wear curve is a plot of wear versus time, sliding distance,

or number of operations While laboratory tests are often used to determine values for different materials and environmental conditions, it is sometimes possible to analyze existing hardware data to determine the coefficients In situations where there is neither available data for the specific materials or environmental conditions involved in the application nor the ability to perform the appropriate tests, it is generally possible to estimate the values, based on published data regarding these models Such information can be found in Ref 8, 9, 10 and 15

1992

1980

22 K Ludema and R.G Bayer, Ed., Tribological Modeling for Mechanical Designers, STP 1105, American

Society for Testing and Materials, 1991

23 R.G Bayer, W.C Clinton, C.W Nelson, and R.A Schumacher, Wear, Vol 5, 1962, p 378-391

24 R.G Bayer, Wear, Vol 11, 1968, p 319-332

25 P Engel, T Lyons, and J Sirico, Wear, Vol 23, 1973, p 185

26 P Engel and R.G Bayer, J Lubr Technol., Oct 1974, p 595

27 G Talbourdet, Paper 54-Lub-14, American Society of Mechanical Engineers, 1954

Trang 9

Wear Design

Wear design involves four elements (Ref 8): system analysis, modeling, data gathering, and verification

System analysis is the starting point of a wear design It begins with the examination of the design and the

identification of possible wear points or concerns It then involves the characterization of the tribosystem associated with each one Initially this characterization may be very general and more qualitative than quantitative It might simply be the determination of the general nature of the wear situation, such as lubricated sliding at low or moderate temperatures or a particle erosion situation with possible corrosion As the wear design proceeds, system analysis involves such elements as the determination of loads and contact stresses, detailed characterization of the environment, detailed characterization of the motions involved, and determination of the factors that affect these variables System analysis also involves the determination of how much wear can be allowed and the establishment of a failure criterion In general it consists of all those elements needed to implement the modeling and data gathering elements

Modeling. The modeling phase of a wear design approach involves the selection of a model, which provides a basis for the determination of the design Model selection is basically done by matching the characteristics of the tribosystem to the descriptions of the various wear models and selecting the most appropriate one Once this is done, the model is then used

to determine the values of the design parameters necessary to obtain the desired wear life or performance

Data Gathering. In order to use models in the fashion described above, it is generally necessary to determine the values

of one or more empirical coefficients, which generally are material and environment dependent Existing data may be used for this purpose if they were obtained for conditions that match or simulate the conditions of the current application

If not, appropriate wear tests need to be done to determine those coefficients Estimates for these coefficients based on theoretical considerations or extrapolation of existing data can also be used, but these are generally less accurate then those obtained from wear tests that simulate the wear situation

In some situations it may be necessary to consider more than one model This could be because there is inadequate information available to differentiate between models, or because the wear situation is so complex that several different conditions need to be considered In this case the design parameters should be selected so that adequate wear performance

is predicted by all the models Alternatively, this complexity may be eliminated by doing further system analysis, doing some tests to identify the appropriate model, or introducing elements in the design to eliminate some of the possibilities For example, damping may be introduced to eliminate possible fretting motions that may contribute to the wear, or seals may be used to eliminate the possibility of abrasive particles in the contact region

Verification. In addition to the normal verification that the design works, it is necessary to verify the validity of different assumptions made in the other three phases These include examinations to verify that the characteristics of the wear are consistent with the modeling (e.g., correct location and appearance of wear scar)

Theoretical versus Empirical Wear Design Approaches. In practice, wear design approaches can be completely theoretical, semi-empirical, or completely empirical In the completely theoretical approach the basis for selection of a model is a description of the tribosystem Also, existing empirical coefficients or estimates based on them are used to predict wear behavior using those models In the semi-empirical approach, some testing is done to determine values for the coefficients or to verify the applicability of a model that was selected on a theoretical basis In the completely empirical approach the model and coefficients are determined empirically An example of this might be the use of regression analysis to determine a suitable model While the completely theoretical approach is most desirable from a design standpoint, it tends to be the least accurate and to be associated with a higher degree of risk As a result, such approaches should be more conservative and use larger safety factors for establishing designs than those involving some experimental elements

Designing for Preferred Modes of Wear. An important factor in wear design is the recognition that the selection of design parameters and the overall nature of the design affects not only the wear rate but also the wear modes and behavior Preferred modes of wear can be ensured by proper design The primary criterion is that the design be selected to

Trang 10

ensure mild wear behavior In two-body, nonabrasive wear situations this generally means that contact stresses should be

in the elastic range In the case of sliding, contact stresses should be a small fraction of the yield strength, generally less than 0.5 and less than 0.2 for very low wear rates Some form of lubrication should also be used For rolling and impact, the stresses can be significantly higher (i.e., greater than 0.5) for long life, provided that sliding is not involved In abrasive wear situations, materials similar in hardness to the abrasives or, preferably, harder than the abrasives should be used Materials should be compatible with the environment in which they are to be used A list of other rules for wear design is given in Table 7

Table 7 Design rules for wear applications

• Reliance on analytical design procedures increases the degree of conservatism that should be used

• Wear is a system property; utilize all the parameters that influence wear

• Design with the limits and characteristics of the materials in mind

• Design so that a mild wear condition exists

• Minimize exposure to abrasive particles

• Optimize contact to minimize stresses

o Ensure good alignment

o Round corners and edges

• Use a lubricant whenever possible

• Use dissimilar materials

• To increase system life (reduce system wear), it is sometimes necessary to increase hardness of both members

• Rolling is preferred over sliding

• Sliding or fretting motions should be eliminated in impact wear situations

• Impacts should be avoided in sliding contacts

• Elastomers frequently out perform harder materials in impact situations

• Thickness of conventional coatings generally should be greater than 100 m

• Use moderate surface roughness

• Avoid the use of stainless steel shafts with impregnated sintered bronze

• When molded, filled plastics tend to exhibit significant difference between initial and long-term wear behavior

• When glass or other hard fillers are used, the hardness of the counterface should be equal to or greater than that of the filler For glass, this hardness should be >60 HRC

• The tendency for galling can be reduced by using dissimilar and hard materials of low ductility, lubricating, and reducing contact stresses; stress level above threshold levels for galling should be avoided

• Avoid designs in which fretting motions can occur

• When fretting motions are present, design for optimum sliding wear life and to minimize abrasive wear

• Sacrificial wear design should be considered when satisfactory life cannot be achieved by other means

• Conform to vendor recommendations for optimum wear performance

• Changes associated with design modifications or new applications should be reviewed carefully with respect to their affect on potential wear behavior

Bracketing. One technique that is often helpful in wear design is called bracketing, which is illustrated in Fig 5 This involves the development of two theoretical wear projections for a design Different models may be used for each projection For example, in the case of sliding, one projection might be based on the K-factor model and the other on the combination of the sliding zero wear and measurable wear models One projection is an optimistic projection, using the

Trang 11

most favorable values for the coefficients that have been reported for the most favorable model, if two or more models are potentially applicable The other is a pessimistic or worst-case projection, using the least favorable values for the least favorable model If the optimistic projection exceeds the allowable wear, it is generally advisable to change the design concept If the pessimistic projection gives acceptable wear, the proposed design is acceptable If the two curves bracket the required wear behavior, the design is considered to be feasible but further work is required to establish a satisfactory design This further work generally requires the determination of the coefficients for different materials In cases where more than one model was used, this generally requires some testing to determine which model is the correct one

Fig 5 Bracketing analysis (a) The design is satisfactory and no further modifications are required (b) A design

change is needed (c) Further work is needed to identify satisfactory materials and, if applicable, the correct model for the wear situation

Design Modifications. While the focus of the wear design methodology is the avoidance of wear problems in new designs, it can also be applied to the resolution of existing wear problems It provides a methodology for establishing corrective actions when a design modification is required In these situations the existence of wear data and worn

Trang 12

hardware is often valuable The failure analysis and hypothesis development activity that is normally associated with problem-solving efforts provides valuable input to the system analysis and modeling required for wear design

Reference cited in this section

Methods for Wear Design

In most cases a wear design starts out with a general design outline based on function This design outline defines the generic shapes, motions, and environment It may also provide some limits on the type of materials and method of lubrication that can be used Based on this input a wear model is selected, then used to determine the specifics of the design based on wear considerations This may take the form of sequentially evaluating designs, where specific materials, dimensions, tolerances, and roughnesses are assumed, to see if any of the combinations will provide adequate wear behavior It may also take the form of determining what material properties, dimensions, and so on are required in order

to obtain adequate wear performance In practice, the former is often tried first and if a successful design cannot be found, the latter approach is incorporated into the analysis If a successful design cannot be obtained within this framework, it is then usually necessary to see if other general designs for that function can provide adequate wear performance It is in these cases that the bracketing technique is often useful

Example: Design Approach for Low-Wear Computer Peripherals

The details of wear design methods tend to vary not only with the type of wear but also with the needs of the organization However, a design approach used for low-wear applications in computer peripherals can be used to illustrate the general nature of a wear design approach (Ref 28, 29) Other examples of specific approaches can often be found in

wear and design publications, such as Machine Design, Wear, and Tribology International A number of wear design

examples and methods can also be found in Ref 8

The design approach used for computer peripherals is primarily a theoretical approach, which is based on the zero wear model for sliding In this model zero wear is defined as a wear scar whose average depth is the center-line average (CLA) roughness of the surface, as illustrated in Fig 6 This model relates material properties and stress levels so that a zero wear condition will not be exceeded It can be used to determine the maximum load that can be applied to a design for a given lifetime and not have the depth of wear exceed the surface roughness level Expressions for the allowable load were developed for a number of different geometries and motions, as shown and described in Fig 7, 8, 9, and 10 and Tables 8,

9, 10, and 11

Table 8 Key to symbols used in Fig 7, 8, and 9

Symbol Description

a The radius of that circle which best fits the contour of the edge in the region of contact, in

E Young's modulus of elasticity, psi

H m Microhardness, kg/mm2

K Stress-concentration factor used in cases where the contact between bodies terminates abruptly

L Length of contact in cases involving cylinders and planes, in

L' Width of contact in cases of flat-on-flat conforming geometry, in

N Number of passes

no Frequency of oscillation, oscillations/min

nr Angular velocity of a shaft, rpm

P Normal force between two contacting surfaces, lb

Trang 13

PA Allowable normal force for a specific geometry, material, lubrication, and life, lb

R Principal radius of curvature, in

x Operation time, h/month

y Machine life, months

z Total linear travel for one oscillation cycle, in./cycle

Angle of contact in a shaft-in-hole conforming geometry, degree

R Zero-wear factor

Coefficient of friction

v Poisson's ratio

y Tensile yield stress, psi

max Maximum shear stress in contact region, psi

y Shearing yield stress, psi ( y = y /2)

Total angular travel for one oscillation cycle, degree/cycle

Note: Subscripts 1 and 2 of these variables apply to Body 1 and Body 2 as shown in the sketches and equations in Fig 7, 8, and 9

Table 9 Allowable loads for mechanisms shown in Fig 7

Trang 14

Trang 15

Trang 16

Note: The relationship between cos and values for m and n is shown in Fig 10

Trang 17

Fig 6 Illustration of zero wear concept (a) Surface profile when wear is less than the zero wear criterion (b)

Near the zero wear criterion (c) Above the zero wear criterion (d) Definition of the zero wear criterion

Trang 18

Fig 7 Allowable load relationships for area-contact sliding mechanisms (a) Cylinder in hole Rotating cylinder;

fixed partial hole; R1 = R2 = R (b) Cylinder in hole Rotating cylinder; fixed full hole; R1 = R2 = R (c) Cylinder

in hole Fixed cylinder; rotating hole; R1 = R2 = R (d) Cylinder in hole Linear oscillation; either member fixed; travel (z/2) greater than contact length; R1 = R2 = R (e) Cylinder in hole Linear oscillation; either member fixed; travel (z/2) less than contact length; R1 = R2 = R (f) Plane on plane Linear translation; travel (z/2) greater than contact length (g) Plane on plane Linear translation; travel (z/2) less than contact length (h)

Sphere in socket Partial socket (<180°); either member fixed; oscillation in one plane; travel ( /2) greater than contact angle (i) Sphere in socket Partial socket (<180°); either member fixed; oscillation in one plane; travel ( /2) less than contact angle Source: Ref 28

Trang 19

Fig 8 Allowable load relationships for "line"-contact sliding mechanisms (a) Cylinder in hole Rotating cylinder;

fixed hole; R2 < 0.99 R1 (b) Cylinder in hole Rotating hole; fixed cylinder; R2 < 0.99 R1 (c) Cylinder on plane

Rotating cylinder; fixed plane (d) Cylinder on cylinder One cylinder fixed; one rotating (Note: Reverse sign of

R1 in B9 and B10.) (e) Cylinder in hole Linear oscillation; either member fixed; travel (z/2) greater than contact length (f) Cylinder in hole Linear oscillation; either member fixed; travel (z/2) less than contact length (g) Cylinder on plane Linear oscillation parallel to cylinder axis; either member fixed; travel (z/2)

greater than contact length (h) Cylinder on plane Linear oscillation parallel to cylinder axis; either member

fixed; travel (z/2) less than contact length (i) Cylinder on plane Linear oscillation perpendicular to cylinder

axis; either member fixed Source: Ref 28

Trang 20

Fig 9 Allowable load relationships for "point"-contact sliding mechanisms (a) Crossed cylinders Unequal

cylinder diameters; linear oscillation parallel to axis of larger-diameter cylinder (b) Crossed cylinders Unequal cylinder diameters; linear oscillation parallel to axis of smaller-diameter cylinder (c) Sphere on plane Linear oscillation; either member fixed (d) Sphere on cylinder Rotating cylinder; fixed sphere (e) Sphere on cylinder Rotating grooved cylinder; fixed sphere Source: Ref 28

Trang 21

Fig 10 Plot of m and n vs cos Values for m and n appear in the stress-concentration factor (K) expression

in Fig 8 and in some of the allowable-load expressions in Fig 9 Source: Ref 28

The wear design method is to evaluate a proposed design by using the relationships shown in Fig 7, 8, and 9 to determine

an allowable load The allowable load is then compared with an estimate of the actual load If the allowable load is significantly higher than the estimated actual operating load, the design is accepted and is given further consideration only

if problems develop in subsequent functional tests

If the allowable and estimated loads are comparable, changes to the design are considered to improve the safety margin If this cannot be done, the wear of the device is closely monitored in life and functional tests to verify adequate performance

If the allowable load is less than the estimated load, design changes are explored to obtain a condition in which the allowable load exceeded the estimated load Typical changes that are considered in this approach are dimensional and material changes, as well as any changes that would affect the loading situation

This wear design method is a conservative approach, because most applications can tolerate wear depths one to two orders of magnitude above the CLA value In situations where an acceptable "zero wear design" cannot be found because

of cost or technical reasons, a less conservative approach is then used In this situation a more realistic failure criterion is used for the amount of wear that can be tolerated Generally this is the amount of wear that would cause functional problems A combination of the zero wear model for sliding and the measurable wear model for sliding is then used to project wear and evaluate potential designs Examples of this method can be found in Ref 21, 30, 31, and 32

Trang 22

28 R.G Bayer, A.T Shalkey, and A.R Wayson, Mach Des., 9 Jan 1969, p 142-151

29 R.G Bayer and A.R Wayson, Mach Des., 7 Aug 1969, p 118-127

30 R.G Bayer, Proc First European Tribology Congress, The Institution of Mechanical Engineers, 1973, p

79-84

31 R Bayer, Standardization News, American Society for Testing and Materials, 9 Feb 1974, p 29-32, 57

32 P Engel et al., J Lubr Technol., Vol 100, 1978, p 189-195

Trang 23

References

1 ASTM G 40-92, "Standard Terminology Relating to Wear and Erosion"

2 A.F Bower and K.L Johnson, J Mech Phys Solids, Vol 37 (No 4), 1989, p 471-493

3 K Johnson, Proc 20th Leeds-Lyon Symp Tribology, Elsevier, 1994, p 21

4 F Aleinikov, Soviet Phys.-Tech Phys., Vol 2, 1957, p 505, 2529

5 P Blau, Friction and Wear Transitions of Materials, Noyes Publications, Park Ridge, NJ, 1989

6 N.C Welsh, Proc Royal Society, Vol A257, 1965, p 31

7 S.C Lim and M.F Ashby, Acta Metall., Vol 35, 1987, p 1-24

1992

1980

12 R Bayer, Wear, Vol 35, 1975, p 35-40

13 E.R Booser, Ed., Handbook of Lubrication, Vol III, CRC Press, 1994

14 IBM General Products Division Technical Report TR 01.17.142.678, 10 April 1962

16 R.G Bayer, Ed., Selection and Use of Wear Tests for Metals, STP 615, American Society for Testing and

19 C.S Yust and R.G Bayer, Ed., Selection and Use of Wear Tests for Ceramics, STP 1010, American Society

for Testing and Materials, 1988,

20 A.W Ruff and R.G Bayer, Ed., Tribology: Wear Test Selection for Design and Application, STP 1199,

American Society for Testing and Materials, 1993

22 K Ludema and R.G Bayer, Ed., Tribological Modeling for Mechanical Designers, STP 1105, American

Society for Testing and Materials, 1991

23 R.G Bayer, W.C Clinton, C.W Nelson, and R.A Schumacher, Wear, Vol 5, 1962, p 378-391

24 R.G Bayer, Wear, Vol 11, 1968, p 319-332

25 P Engel, T Lyons, and J Sirico, Wear, Vol 23, 1973, p 185

26 P Engel and R.G Bayer, J Lubr Technol., Oct 1974, p 595

27 G Talbourdet, Paper 54-Lub-14, American Society of Mechanical Engineers, 1954

28 R.G Bayer, A.T Shalkey, and A.R Wayson, Mach Des., 9 Jan 1969, p 142-151

29 R.G Bayer and A.R Wayson, Mach Des., 7 Aug 1969, p 118-127

30 R.G Bayer, Proc First European Tribology Congress, The Institution of Mechanical Engineers, 1973, p

79-84

31 R Bayer, Standardization News, American Society for Testing and Materials, 9 Feb 1974, p 29-32, 57

Trang 24

32 P Engel et al., J Lubr Technol., Vol 100, 1978, p 189-195

Properties Needed for Electronic and Magnetic Applications

Eugene J Rymaszewski, Rensselaer Polytechnic Institute

where R is the electrical (Ohmic) resistance of the wire, in ; is the electrical resistivity of the wire material, in · m;

A is the cross-sectional area of the wire, in m2; and l is the wire length, in m Note that A and l are the

dimensions structural parameters of the wire and is the property of the wire material The wire is directly involved in the voltage/current interaction, as opposed to a structure supporting the wire, which may be involved indirectly

The physical dimensions of this structure and its mechanical and thermal properties may also be relevant, albeit indirectly,

to the numerical determination of For example, sufficiently high values of V and I generate enough heat to raise the wire temperature and, consequently, alter the value of R and, therefore, The temperature rise will depend on the

thermal path (cooling) between the wire and its environment determined by the structure The temperature rise causes expansion in most materials that can lead to mechanical stresses in the wire and/or its support structure Thus, there are mechanical and thermal interactions to be considered Such interactions, if not properly considered, may lead to wrong conclusions For example, if one were to measure the voltage or current dependency of and not factor in the temperature rise and its effect, then an excessively high positive value of / V would be "measured." In reality, it may be zero (or

even negative); or the presumed resistor stability, which neglects its thermal coefficient of resistivity (TCR) and temperature rise, will not occur, and the design may fail to perform as expected

The nonelectromagnetic parameters fall into two distinctly different categories: those involved in fabrication (melting solder, making thermocompression bond, sputtering or evaporating film, diffusing impurities into semiconductors, sintering ceramics), and those involved in operation of the equipment, such as the wire example described above This article focuses, as its name indicates, on this second category of properties

Trang 25

Background Information

Classes of Materials. The value of electrical resistivity of materials, , and its inverse, the electrical conductivity, , vary over almost 24 orders of magnitude at or near room temperature Its subranges classify the materials as conductors, semiconductors, and insulators Conductors are typically metals with ranging from 10-8 to 10-4 · m The electrical conductivity results from the presence of "free" electrons, that is, free to move in response to the presence of an electric field

No "free" electrons are present in the insulators, and consequently, their is from 104 to 1016 · m (Ref 1) Insulating materials fall into two major categories, the organic (polymers) pure, as in polymers, or composite, as in epoxy-impregnated fiberglass cloth and inorganic, usually ceramics

The gap in the values of between the conductors and insulators is filled by the semiconductors whose electrical conductivity mechanism is best explained by the band-gap theory (Ref 2) The of semiconductors is in the 10-4 to 104

· m range The semiconductors are either group IV elements, silicon (Si) and germanium (Ge), or composite formed by two or more group III-V or group II-VI materials, such as GaAs (Ref 3)

The magnetic materials can be metals, alloys, and ceramics They all have the ability to carry high magnetic flux in response to applied magnetizing force Their broad classification is based on the atomic structure and values of relative permeability The high-permeability materials fall into two distinct groups, the magnetically hard and magnetically soft The hard materials have high coercivity; once magnetized, they resist demagnetizing forces caused by any applied or stray magnetic fields (Ref 4)

The electronic and magnetic applications cover a very wide span of generating and processing information: from placing

a telephone call (in a house, on the road, in an airplane) to watching TV from the air, cable, or satellite, to using computers of various sizes and performance capabilities, to remotely interacting with a space ship, and so forth Many, probably most, of these applications entail generation, processing, transmission, and storage of information, as well as using information to initiate an action creation of sound, light, or mechanical force, for example All of the above material categories are used in the electronics hardware in various structures, with widely varying structural dimensions and demands on their properties As a rule, mutually compatible sets of materials must be employed, placing further demands on their properties

Small, inexpensive items, such as handheld calculators, are designed for the lowest manufacturing cost, which often precludes repair (a "throwaway" product) The more expensive, and more complex, products usually consist of several subassemblies that are semipermanently joined These joints are either solder or connectors, a technology in itself to provide satisfactory performance and reliability at affordable cost (Ref 5)

Electronic Applications. The semiconductors play a pivotal role in electronics for processing and storing data and in interfacing the electronic circuits with their exterior, for example, fiberoptic interconnections, optical scanners, displays and, ultimately, humans The metals and insulating materials (organic and/or inorganic) are directly involved in electronic circuit embodiments by providing interconnections They also provide mechanical support, environmental protection, and facilitate heat transfer (Ref 5)

Magnetic materials play a key role in permanent storage and retrieval of information Furthermore, their use in transformers enables more than just changing magnitude of the voltage A current transformer reduces high current values

to make them more suitable for an ammeter Transformers (both voltage and current) also isolate the output circuit(s) from the input, which is important for a multitude of reasons, such as keeping away very high powerline voltages from the instrument panel or separating the telephone line from the interior circuitry of a modem

The materials properties, such as , are customarily given for the "bulk" materials those having similar magnitude cross-sectional dimensions, on a macroscopic scale The numerical values of these properties may change

Trang 26

order-of-when the dimensions are reduced to submicron range, as is the case with thin films which see an increasing use in electronic applications (Ref 6) Another factor influencing the numerical values is the microstructure of the material: totally amorphous, crystalline regions within an amorphous matrix, polycrystalline, or monocrystalline Chemical composition of some amorphous structures may deviate from the stoichiometric, with the resultant alterations in their properties Figure 1 shows an example of near-zero dispersion of amorphous BaxTi2-xOy thin films and still very low dispersion of partially and fully crystallized barium-titanate films (Ref 7, 8) Properties of the crystalline materials may be direction dependent As already indicated above, a materials property is often temperature dependent

Fig 1 Frequency dependency of dielectric constant for selected dielectric materials

The Ohm's law equations (Eq 1, 2, 3, 4) indicate that either a voltage V or a current I can be the stimulus that, through the

geometry and resistivity/conductivity of the material will determine the value of the response An underlying assumption

is the independence of = 1/ on either voltage or current This is not always the case, even at a constant temperature

Perhaps the most striking example is the V-I (voltage-current) characteristic (interdependence) of a semiconductor diode,

formed at the junction of two oppositely doped regions In addition to being highly nonlinear, it is very strongly polarity dependent, as shown in Fig 2 (Ref 9) Such nonlinear response is pivotal to the very existence of all digital electronic circuits

Trang 27

Fig 2 Voltage-current characteristic of a semiconductor junction Source: Ref 9

Information-handling applications require periodic or, at least, occasional changes in the values of voltages and currents Consequently, dependency of the materials properties on such changes must be known and considered for a particular application For example, the resistivity equations (Eq 1, 2, 3, 4) imply uniform current density throughout the cross-

sectional area A However, as the frequency of the current increases, the current penetration depth decreases (skin effect),

causing the resistivity to increase In the time domain, the skin effect manifests itself as time-dependent resistance: high shortly after start of the current flow and decreasing to its DC value The time it takes depends on the dimensions of the conductor (Ref 10)

Materials may be stressed beyond their mechanical limits, with the resultant permanent deformation An equivalent situation may occur with the excessive electric stresses that can affect insulators (dielectric breakdown) and conductors (melting, electromigration, void migration) (Ref 11, 12)

Properties of Interest. In this section, an overview of the electric and magnetic parameters is followed by detailed discussion of the significance of these parameters for electronic applications Many applications prescribe particular values and tolerances of such parameters, and significant efforts are still underway to achieve a particular combination of values of several properties in a particular material Increasingly, they have to be engineered because such combinations

of properties are not available in the existing materials

Some of these parameter values or properties are not desired because they have deleterious impacts In such cases they are considered parasitic and, consequently, attempts are made to keep them small, below or within acceptable limits For example, a particular resistor value is required in a circuit By contrast, resistance of an interconnection should be low to avoid excessive values of voltage drop Also, resistance of an insulator, for example, dielectric of a capacitor, must be high enough to prevent excessive leakage currents

As is shown at the end of the section "Power and Energy Conversion, Storage, and Transmission," some sets of values cannot be altered beyond certain limits for a given set of structural dimensions regardless of the materials properties, only appropriate dimensional changes will produce the desired results The most notable example is the product of inductance and capacitance of an interconnection (a pair of electrodes, such as wires) This product reaches a minimum for nonmagnetic materials ( = 1) with low dielectric constants r 1 (e.g., air) Any further reduction is possible only with

a shorter length of the interconnection Such reduction can easily lead to a complete structural redesign

An analogous situation may occur when the heat generated by electronic circuits is within a small area, causing high values of heat flux, often expressed in W/cm2 The heat flowing to its environment encounters thermal resistance, causing

Trang 28

the temperature to rise The thermal conductivity of the materials in the heat-flow path and their structural geometries (cross-sectional area and path length) control the thermal resistance As shown in Fig 3, the power densities on the order

of 100 W/cm2 and higher not unusual in some aggressive initial electronics designs are likely to cause excessively high operating temperatures The limited thermal conductivities of materials used often require close attention to the structural dimensions Some relief may soon be provided from development of affordable exotic materials with high thermal conductivity, for example, diamond films An alternative is the use of Peltier-junction based (Ref 13) thermoelectric coolers

Fig 3 Temperature versus power density Source: Ref 5

Most electronic structures, whether integrated circuit (IC) interconnections or packaging, are multilayer structures, with conducting layers alternating with the insulating layers All layers are appropriately patterned and bonded by a variety of processing techniques The interlayer bonds are part chemical, part mechanical The bond strength is often of concern, as delamination can have disastrous reliability consequences Inadequate bond strength and excessive shear forces (caused, for example, by mismatched thermal coefficients of expansion and large temperature variations) are of prime concern

Important Trends and Considerations Not Addressed in Detail. The trend in electronic applications is toward increasing density more functions per unit area or per unit volume Figure 4 shows dramatic reductions in the volume required for 1 MB (megabyte) of electronic memory storage from 1950 to 2010, a sixty-year interval during which the technology changed from small magnetic (ferrite) cores to IC chips (Ref 13) Packaging had evolved as well and contributed to the volumetric improvements beyond those that would have been possible with just the magnetic core and semiconductor chip technologies which are basically planar, two dimensional

Trang 29

Fig 4 Memory density trends Source: Ref 5

At the same time, the trend is often toward increasing the area of the IC chips, multichip modules (MCMs) and printed wiring boards (PWBs) Thus, the number of pixels per each subassembly is steadily increasing (Ref 14) This trend taxes the capabilities of design support systems and, especially, the defect-free manufacturing processes There is a strong competitive pressure to balance the design of leading-edge products against the expense of establishing, maintaining, and improving defect-free manufacturing environment Consequently, a certain percentage of the product, especially during its early manufacturing phase, is likely to be defective It has to be weeded out prior to the final assembly, or even sooner Sophisticated testing facilitates the weeding out However, nonkiller defects escape detection, are shipped, and contribute

to failures early in the life of the products A prestress process, known as "burn-in," endeavors to enhance the out of defects (Ref 11, 15)

weeding-References cited in this section

1 J.F Shackelford, Introduction to Materials Science for Engineers, 3rd ed., Macmillan, 1992, Fig 11.7.1

2 L Solymar and D Walsh, Lectures on the Electrical Properties of Materials, 3rd ed., Oxford University

Press, 1984

3 S.K Ghandhi, VLSI Fabrication Principles, 2nd ed., John Wiley & Sons, 1994

4 P.S Neelakanta, Handbook of Electromagnetic Materials, CRC Press, 1995

5 R Tummala, E.J Rymaszewski, and A.G Klopfenstein, Ed., Microelectronics Packaging Handbook, Part

1, 2nd ed., Chapman & Hall, 1997

6 S.P Murarka and M.C Peckerar, Electronic Materials Science and Technology, Academic Press, 1989, p

272

7 E.J Rymaszewski, High-Dielectric Constant Thin Films for High-Performance Applications, Proc DARPA

Physical Electronic Packaging Program Review, Washington, DC, March 1993

8 W.-T Liu, S Cochrane, P Beckage, D.B Knorr, T.-M Lu, J.M Borrego, and E.J Rymaszewski,

Trang 30

Deposition, Structural Characterization, and Broadband (1 kHz 40 GHz) Dielectric Behavior of BaxTi2-xOy

Thin Films, Proc Mater Res Soc., Spring, 1993

9 W.D Callister, Jr., Materials Science and Engineering: An Introduction, 3rd ed., John Wiley & Sons, 1994,

Fig 19.20

10 S.O Kasap, Principles of Electrical Engineering Materials and Devices, McGraw-Hill, 1997

2, Semiconductor Packaging, 2nd ed., Chapman & Hall, 1997

12 D.D Pollock, Physical Properties of Materials for Engineers, 2nd ed., CRC Press, 1993

13 E.J Rymaszewski, Revolution in Packaged Electronics, MRS 1996 Fall Meeting Tutorial Program,

Symposium J, 2 Dec 1996

14 E.J Rymaszewski, Dense, Denser, Densest ., J Electron Mater., Vol 18 (No 2), 1989

3, Subsystem Packaging, 2nd ed., Chapman & Hall, 1997

Overview of Electric and Magnetic Parameters and Materials Properties

Electric voltage, current, and power are fundamental electrical units V, I, and P They are measured in volts (V), amperes

(A), and watts (W), respectively A potential difference, or electromotive force, of 1 V exists between two points of a conductor carrying a constant current of 1 A when the power dissipated between these points equals 1 W (Ref 16) Note that implicit to this definition is the electrical resistance of 1 Ohm ( ) present between these points

Power and Energy Conversion, Storage, and Transmission. The very definition of fundamental electrical units invokes power dissipation, that is, the conversion of the electrical energy into thermal The energy can also be temporarily stored, either in the electric field associated with a voltage between two or more conductors, or in the magnetic field caused by and associated with the current flowing through a conductor Changes in the field energies are linked with the corresponding temporary flow of current and appearance/application of voltage Electric permittivity, a materials property, is the proportionality constant that directly relates the voltage and structural geometry to the electrical field energy Magnetic permeability is its magnetic field energy counterpart

The static (constant with time) magnetic and electric fields may and do exist independent of each other The dynamic (changing with time) fields do not: a charge must be transported to alter the electrical potential between any two (or more)

electrodes, such as capacitor plates or electrical connections Note that I(t) = dQ/dt = C(dV/dt) Such current I(t) creates a magnetic field associated with it This current will in turn cause a voltage V = L(dI/dt) Thus, the dynamic voltages and

currents are interdependent and interlinked in space An interconnection consisting of two wires of uniform

cross-sectional geometry has an inductance per unit length, L0, and a capacitance per unit length, C0

The ratio of the above V and I on an infinitely long interconnection (no reflections) with a uniform cross-sectional geometry is referred to as the characteristic impedance Z0:

The value of Z0 and, therefore, the ratio L/C = L0/C0 depend on cross-sectional geometry, magnetic permeability, and electric permittivity of the material(s) surrounding the interconnection conductors The geometry dependence for some selected geometries is shown in Fig 5; this dependency as well as very detailed data are presented in Ref 17 The detailed theory is discussed in many texts, such as Ref 18 and 19

Trang 31

Fig 5 Characteristic impedance versus cross-sectional geometries of two parallel wires and coaxial cable

The velocity of propagation v of the "interlocked" voltage V(t) and current I(t) waves does not depend on the

cross-sectional geometry, only on the permeability and permittivity of the insulating material between the conductors,

where c is the velocity of light in free space Thus, for a given length, the product LC is fixed and reaches a minimum for

= = 1 To reduce the value of LC, the interconnection length must be reduced often a difficult task

Capacitance and Dielectric Materials. An ideal capacitor has no electrical conduction between its plates; it only stores any amount of electrical energy and returns it in full The dielectric material between the capacitor plates largely determines the degree to which these ideal characteristics are met It has four key properties the dielectric constant, the dielectric leakage, the dielectric breakdown, and the dielectric loss which limit the ideal behavior of a capacitor The leakage current drains the charge and may be very detrimental in applications in which the capacitor is expected to separate (block) dc circuits or to maintain its charge, as in dynamic random access memory (DRAM) chips

The dielectric leakage depends on the electric field strength It is commonly normalized to the electrodes area Its metric

is then the current density J, often given in A/cm2 In many applications, it is very important to keep the capacitor area A

to a minimum Two factors determine the capacitance density (for example, expressed in nF/cm2): the dielectric constant

and the thickness of the dielectric, d Thinner dielectric produces higher electric field E = V/d, often measured in MV/cm, for the same applied voltage V Usually, it increases the value of J Figure 6 shows examples of the leakage currents J versus capacitance densities for some recently developed thin films, with the values of d well into the

submicron range (Ref 13)

Trang 32

Fig 6 Leakage current densities versus capacitance densities of new dielectric thin

There is another limitation to the voltage between the capacitor plates the dielectric breakdown, a situation caused by excessive electric field strength and manifested by avalanching current, often producing permanent destruction (Ref 10) The breakdown field strength is inversely dependent on the dielectric constant, as illustrated in Fig 7, breakdown field versus permittivity (Ref 13) It must be noted here that very thin films may well have disproportionately low breakdown voltages (and average fields) because the dielectric will first break down at locations of reduced thickness caused, for example, by microroughness of the metals onto which the dielectric was deposited or by presence of small particles

Fig 7 Breakdown field dependency on the dielectric constant

Trang 33

Unlike the leakage currents and breakdowns that occur at dc, the dielectric losses are an ac phenomenon In an ideal capacitor, there is a 90° phase shift at the angular frequency = 2 f between the applied ac voltage vector V and the vector I of the ac current flowing through the capacitor C; I = V × j2 fC = V × j C, with C = A/d With all real materials, the dielectric constant is a complex number = ' + j '' As a rule ' '' The ratio of '' to ' is often referred to as the "loss-angle tangent," tan For the most insulating materials, it remains relatively constant and small at all frequencies at which ' remains constant A change (reduction) in ' with frequency is known as dispersion and is

associated with rising '' and, therefore, a higher value of tan that fairly accurately tracks d '/df (d '/d ) (Ref 4, 10, 12,

20)

The onset of dispersion occurs at lower frequencies for the higher values of This is another factor to be considered, in addition to the lower breakdown field strength shown in Fig 7 As shown in Fig 1, minimum dispersion, if any, occurs with the amorphous thin films Another property of higher dielectric constant materials to consider is the temperature dependency of

Inductance is conceptually related to the resistance in the sense that a change in the current flowing through it is

resisted by appearance of voltage V = L(dI/dt) or, in case of a steady alternating current of frequency f, V = I × j L The

term L is called reactance, the positive counterpart to reactance of a capacitor 1/j C or -j/ C Again, an ideal inductor

temporarily stores energy in its magnetic field and returns all of it In the real world, this is never fully the case (except in superconductors) because of the Ohmic wire resistance and, if magnetic materials are used, because of their losses caused

by the remanence (area within the hysteresis loop)

Signal Transmission. Unlike water flow from a hose or light emitted by its source, the electric current can flow only

in a circuit (containing resistances and reactances) that forms a closed loop, that is, with connections to both terminals of the source It is common among electronics engineers to imply presence of a "return" current path, without being explicit about it In most situations, it works well and justifies the simplification The return current path is usually formed by the

"ground": the body (chassis) of equipment or planes used to deliver the power (see the next section "Mutual Inductance" ) However, such a design has a poorly controlled return-current path, which can cause performance problems (Ref 5) Characteristic impedance and signal velocity of propagation along such lines are briefly covered in the section "Power and Energy Conversion, Storage, and Transmission." Ideal transmission lines preserve the amplitude and transition time

of the signal The inevitable losses occur due to the interconnection resistance (particularly troublesome in the small cross-section lines of high density ICs and packages) and, to a much lesser degree, in the insulating dielectrics

Mutual Inductance. If a second conductor is present in the magnetic field associated with the current through the first conductor, it induces a voltage proportional to the ratio of the field common to both conductors to the total field of the first conductor This phenomenon is the base for various transformer designs which, as a rule, seek "tight coupling" between the first (primary) and second (secondary) wires This coupling is further enhanced by use of ferromagnetic flux concentrators A second, less desirable, effect occurs when two or more signal transmission lines are in proximity of each other The mutual inductance between them is, as a rule, accompanied by mutual capacitance The combined effect is known as "crosstalk." Typically, it is very small (close to zero) at the far end (away from the driver of the first line) and sizeable at the near end A "directional coupler" utilizing this phenomenon permits separation of two waves propagating

in opposite directions along the first line (Ref 5)

Trang 34

18 S Ramo and J.R Whinnery, Fields and Waves in Modern Radio, 2nd ed., John Wiley and Sons, Chapman

& Hall, 1953

19 D.K Chang, Field and Wave Electromagnetics, 2nd ed., Addison-Wesley, 1990

20 J.P Schaffer, A Saxena, S.A Antolovich, T.H Sanders, and S.B Warner, The Science and Design of

Engineering Materials, Irwin, 1995

Overview of Parameters and Materials Properties Other than Electric and Magnetic

As already briefly indicated, the temperature dependence of many properties, singly and in the context of an electronic structure, is of paramount importance to proper functioning of devices, circuits, and equipment The malfunctions can be immediate, for example, caused by the drift of device characteristics outside of design limits, or they can be the result of failures caused by time or cycle-dependent disruptions of the structural integrity, for example, cracking of the solder joints The mechanical stresses can also originate from a hostile operating environment: shocks and vibrations being the major ones A hostile operating environment (salt water, for example) may chemically attack the electronic components

Temperature and Temperature Dependencies. An important consideration, especially in semiconductor-based components and ICs is the strong temperature dependency of the conduction mechanism; it often limits the temperatures

at which a circuit functions reliably There are several other temperature considerations, temperature values, and their effects:

• Temperatures required for processing (manufacturing) of the semiconductor devices and IC chips, such

as diffusion or sputtering

• Temperatures required for packaging (assembly) of the electronic equipment, for example, solder

• Environmental temperatures encountered during the product life, for example, transportation in an unheated compartment of a jet plane, products under the hood of a vehicle in tropic and arctic environments

• Temperature rise above the environment caused by power dissipation

The effects of these temperature variations are many:

• Shift in the electrical characteristics already mentioned

• Shift in the device switching speed (bipolar digital circuits are faster at higher temperatures, complementary metal-on-silicon, or CMOS, circuits are slower)

• Excessive mechanical stresses caused by mismatches in the thermal coefficients of expansion

• Instability of the materials such as decomposition of polymers and melting of solder

The designs for temperature control become increasingly difficult with wider range of operating temperatures (e.g., in automotive applications from arctic to tropic) and greater power densities Thermoelectric coolers/heaters may be required They increasingly employ Peltier-effect junctions

Interface Adhesion. Essentially all electronic structures have thin-film layers of insulators and conductors The interlayer adhesion is, as already mentioned, an extremely important design consideration that often requires compromises in the choice of materials, their deposition/lamination techniques, and surfaces treatments to facilitate the adhesion

Trang 35

An additional consideration is the quality and integrity of the vertical electrical connections between two or more conducting layers Such connections require creation of apertures in the insulating layer, commonly called vias or via holes, and their subsequent filling with conducting materials Additional challenge results from diminishing dimensions, currently in the submicron range The integrity of the via connections requires sufficient removal of the insulating material and metal deposition that has a good bond to the conductor at the via hole bottom as well as to the via hole sides This integrity is threatened during the subsequent product manufacturing and through its life in the field, mainly by mechanical stresses

Stress-Strain, Creep, and Fatigue. There is an unavoidable mismatch in the thermal coefficients of expansion (TCE) between the semiconductor IC bodies, the aluminum and insulator thin films on them, and the packaging to which the chips are attached The need for low thermal resistance further compounds the challenge of providing adequate stress relief The packaging structures usually employ copper conductors and various organic and inorganic insulators, each with their own challenges Creep is often relied upon to provide stress relaxation However, repeated temperature cycling fatigues the bonds and, thus, limits the product life The mechanism is sufficiently understood (Ref 5) to offer design guidance The failures may result from structural damage that disrupts either electrical or thermal conduction paths

Reference cited in this section

5 R Tummala, E.J Rymaszewski, and A.G Klopfenstein, Ed., Microelectronics Packaging Handbook, Part 1,

2nd ed., Chapman & Hall, 1997

Electronic Applications

The electronic applications (as opposed to electric power) are still growing rapidly, doubling in dollar volume every decade They seem to penetrate every appliance and gadget, and even go beyond dreams of science-fiction writers; just think of cell phones, personal digital assistants, and small, easily portable geopositioning equipment Yet, many of these applications share the same basic technologies: semiconductor IC chips, packaging (supporting chips and other components, such as resistors, capacitors, and inductors), source(s) and distribution of electric power, and means of interfacing with humans and other equipment This section deals with the components of the electronic circuits analog and digital The next section discusses the augmenting technologies: magnetic and special technologies such as electrooptical

Semiconductors. Understanding of the operational principles of a semiconductor junction is barely half a century old; the IC technology is two decades younger Yet the progress has been spectacular, as demonstrated in Fig 4 The fabrication of ICs is a highly specialized, still rapidly evolving field (Ref 3, 21, 22) The IC chips consist of two major domains: the semiconductor devices and the thin-film interconnections (conductors, insulators, and interlayer connections) for signal and power distribution An integration of IC chips with the rest of the components occurs in the packaging, the task of which is to provide mechanical support and protection, signal and power connections, and to conduct away the inevitable heat Thus, sufficient electrical, thermal, and mechanical interfaces must be established during manufacture and assembly and maintained through the useful product life Depending on the application, there may be a need to disassemble the package in order to remove and replace one or several of the failed chips

Resistors. The very definition of electrical parameters (Ohm's law) includes the resistor Yet, the real-life realization of just about any resistor has several challenges, made especially severe in demanding applications The thermal coefficient

of resistivity had been already mentioned, the value and sign of which are controlled by the composition of materials and

by the physical dimensions The range of resistor values of interest extends over at least 6 to 10 orders of magnitude The additional considerations are the variation of the value when first manufactured and within the operating temperature and frequency ranges, and the power-handling capability The very recent challenges are presented by the quest for the lowest manufacturing and assembly costs and smallest area or volume Such challenges drive development of "embedded" resistors, as well as capacitors and inductors, labeled imbedded passives (Ref 13) They are produced with thin films of

Trang 36

proper composition, dimensions, and processing In addition to determining the power-handling capabilities, the structural dimensions of resistors control their high-frequency characteristics The impedance of low-value resistors (below 100 ) has the tendency to acquire a sizeable series inductance, and high-value resistors (above 1 k ) tend to have a parallel capacitor component The skin effect is less pronounced in thin-film resistors, but its effect should at least be considered

Capacitors. The range of capacitance value is even greater than those of resistors, from fraction of a picofarad (pF) to one or several Farads, or at least 12 orders of magnitude Some of the applications require tight tolerances (initial value, throughout the life, versus temperature and frequency) while others are open-ended toward higher values requiring only some minimum value The operating and breakdown voltage and leakage currents are another important consideration that may dictate the choice of materials, as, for example, shown in Fig 7 The embedded capacitors often require compatibility with organic materials used in packaging structures This need rules out many excellent processing techniques that require high temperatures

The series inductance of the capacitor with its connections, Ls, affects the high-frequency behavior in a peculiar way

there is an apparent increase in the capacitor value because total Xc = (1/ C - Ls) < 1/ C To make matters worse, above the resonance frequency, at which 1/ C = Ls, the inductance dominates the total impedance (plus the losses

represented by a series resistance Rs) Just as with the resistors, careful control of geometry is required to push the resonance frequency to values higher than the highest operating frequency (Ref 23)

Signal Transmission. Transmission of electrical signals tolerates only relatively minor distortion, be it injected noise

or signal amplitude degradation The signal delay is unavoidable and is factored into designs, but it is often required to be

as small as achievable as well as to remain constant The signal transition time limits the maximum transmittable data rate It is controlled by the losses in the conductors (series resistance) and insulators (dielectric losses and, in extreme situations, leakage currents) The quest for higher densities (Ref 14) drives cross-sectional geometries toward smaller values, requiring low-loss materials For example, aluminum served the IC industry well since its inception a third of a century ago While copper offers lower losses, and will eventually replace aluminum, the IC industry will use it with greatest reluctance By contrast, the electronic packaging industry has been copper based from the start Both are seeking dielectric materials with permittivities below 2 to minimize signal delay time and degradation of the signal transition time Nonisometric values of permittivity are of concern

Power Distribution. The power distribution system resides between the source of power a battery or power supply circuits that convert the power line ac voltage into appropriate value dc voltage and the power users: a multitude of circuits connected to the distribution at a multitude of locations Ideally, all power users should have the same voltage (within tight tolerance) free of superimposed ac noise The conductivity is, again, a key parameter, along with proper geometries Suppression of the ac noise (decoupling) is usually accomplished with discrete capacitors whose high-frequency behavior sets the limits (Ref 5, 23)

21 S.A Campbell, The Science and Engineering of Microelectronic Fabrication, Oxford University Press,

1996

22 J.W Mayer and S.S Lau, Electronic Materials Science: For Integrated Circuits in Si and GaAs,

Macmillan, 1990

23 J.N Humenik, J.M Oberschmidt, L.L Wu, and S.G Paul, Low-Inductance Decoupling Capacitor for the

Thermal Conduction Modules of the IBM Enterprise System/9000 Processors, IBM J Res Dev., Vol 36

(No 5), Sept 1992, p 935-942

Trang 37

Magnetic Applications

Some of these applications are as old as the electromagnetic technology, or even its precursor, the electricity and magnetism branch of physics The unwanted (parasitic) effects of magnetic field energy associated with a current flow are described elsewhere in this section The desired effects can be classified into several major groups: those requiring flux enhancers such as ferromagnetic cores and those without, sometimes referred to as having an air core Some applications require conversion of the magnetic energy into energy other than electrical, for example, mechanical or thermal

Inductors and transformers require no energy conversion Some conversion is unavoidable and is considered parasitic The inductors have only one set of terminals and one coil associated with the magnetic flux The transformers have at least two coils (primary, to which the input voltage or current are applied, and the secondary) that provide isolation and, depending on the ratio of the turns in the coils, a voltage or current transformation The volume of magnetic core is determined by the transmitted power

Electromagnets, relays, motors, and activators utilize the magnetic field(s) to exert mechanical force either by interaction with the field of a permanent magnet, or between two electromagnets or (in most relays) by the attractive force between a solenoid core and the structure carrying contacts

Magnetic storage requires initial magnetization and subsequent interrogation (readout) that causes minimum alteration

of the magnetization to enable multiple readouts The main advantages of the magnetic storage are the ability to store without continued application of electric power and high storage capacity and essentially an unlimited number of the write/read cycles The main disadvantage is the need to move the storage elements with respect to the readout head, by either a moving tape or a spinning disk Another disadvantage is a relatively long read-out time

permanence Properties Needed for Electronic and Magnetic Applications

as watches and tuning circuits for radio receivers and transmitters

Optoelectronics are gaining in popularity because modulated coherent light enables very high data transfer rates over large distances The transmission medium is a fiber light guide whose refraction coefficient confines the light beam to the interior and transmits it with very low losses However, generation and modulation of light at the sending end still poses challenges, and these challenges are greater than those at the receiver: the wide-band demodulation of light and conversion to electrical signals

Display panels use two types of technology: the well-established cathode-ray tubes (CRTs) used in most television sets and desktop computers, and flat-panel displays, which begin to challenge the bulky and heavy CRTs in area and are far superior in total volume and mass

Trang 38

Optoelectronic storage applications are best known by the compact disc (CD), its bigger cousin, laser disc (LD), and the emerging DVD, which originally stood for a digital video disc All offer a very low-cost, high-capacity storage, mostly for read-only use the information is permanently embedded during the manufacturing These discs supplement the magnetic storage and, to a degree, compete Write/read variants are also available, but at high cost

References

1 J.F Shackelford, Introduction to Materials Science for Engineers, 3rd ed., Macmillan, 1992, Fig 11.7.1

2 L Solymar and D Walsh, Lectures on the Electrical Properties of Materials, 3rd ed., Oxford University

Press, 1984

6 S.P Murarka and M.C Peckerar, Electronic Materials Science and Technology, Academic Press, 1989, p

272

7 E.J Rymaszewski, High-Dielectric Constant Thin Films for High-Performance Applications, Proc DARPA

Physical Electronic Packaging Program Review, Washington, DC, March 1993

8 W.-T Liu, S Cochrane, P Beckage, D.B Knorr, T.-M Lu, J.M Borrego, and E.J Rymaszewski, Deposition, Structural Characterization, and Broadband (1 kHz 40 GHz) Dielectric Behavior of BaxTi2-xOy

Thin Films, Proc Mater Res Soc., Spring, 1993

9 W.D Callister, Jr., Materials Science and Engineering: An Introduction, 3rd ed., John Wiley & Sons, 1994,

Fig 19.20

2, Semiconductor Packaging, 2nd ed., Chapman & Hall, 1997

3, Subsystem Packaging, 2nd ed., Chapman & Hall, 1997

16 R.C Weast, D.R Lide, M.J Astle, and W.H Reyer, Ed., CRC Handbook of Chemistry and Physics, 70th

19 D.K Chang, Field and Wave Electromagnetics, 2nd ed., Addison-Wesley, 1990

20 J.P Schaffer, A Saxena, S.A Antolovich, T.H Sanders, and S.B Warner, The Science and Design of

Engineering Materials, Irwin, 1995

21 S.A Campbell, The Science and Engineering of Microelectronic Fabrication, Oxford University Press,

1996

22 J.W Mayer and S.S Lau, Electronic Materials Science: For Integrated Circuits in Si and GaAs,

Trang 39

Macmillan, 1990

23 J.N Humenik, J.M Oberschmidt, L.L Wu, and S.G Paul, Low-Inductance Decoupling Capacitor for the

Thermal Conduction Modules of the IBM Enterprise System/9000 Processors, IBM J Res Dev., Vol 36

(No 5), Sept 1992, p 935-942

Design with Brittle Materials

Stephen F Duffy, Cleveland State University; Lesley A Janosik, NASA Lewis Research Center

Introduction

BRITTLE MATERIALS (e.g., ceramics, intermetallics, and graphites) are increasingly being used in the fabrication of lightweight components From a design engineer's perspective, brittle materials often exhibit attractive high-strength properties at service temperatures that are well beyond use temperatures of conventional ductile materials For advanced diesel and turbine engines, ceramic components have already demonstrated functional abilities at temperatures reaching

1370 °C (2500 °F), which is well beyond the operational limits of most conventional metal alloys However, a penalty is paid in that these materials typically exhibit low fracture toughness, which is usually defined by a critical stress intensity

factor, and typically quantified by KIc This inherent undesirable property must be considered when designing components Lack of ductility (i.e., lack of fracture toughness) leads to low strain tolerance and large variations in observed fracture strength When a load is applied, the absence of significant plastic deformation or microcracking causes large stress concentrations to occur at microscopic flaws These flaws are unavoidably present as a result of fabrication or in-service environmental factors Note that nondestructive evaluation (NDE) inspection programs cannot be successfully implemented during fabrication The combination of high strength and low fracture toughness leads to relatively small critical defect sizes that cannot be detected by current NDE methods As a result, components with a distribution of defects (characterized by various sizes and orientations) are produced, which leads to an observed scatter in component strength Catastrophic crack growth for brittle materials occurs when the crack driving force or energy release rate reaches

a critical value and the resulting component failure proceeds in a catastrophic manner

The emphasis in this article is placed on design methodologies and characterization of certain material properties Of particular interest to the design engineer is the inherent scatter in strength noted above Accounting for this phenomenon requires a change in philosophy on the design engineer's part that leads to a reduced focus on the use of safety factors in favor of reliability analyses If a brittle material with an obvious scatter in tensile strength is selected for its high-strength attributes, or inert behavior, then components should be designed using an appropriate design methodology rooted in statistical analysis However, the reliability approach presented in this chapter demands that the design engineer must tolerate a finite risk of unacceptable performance This risk of unacceptable performance is identified as the probability of failure of a component (or alternatively, component reliability) The primary concern of the engineer is minimizing this risk in an economical manner

This article presents fundamental concepts and models associated with performing time-independent and time-dependent reliability analyses for brittle materials exhibiting scatter in ultimate strength However, the discussion contained within this article is not limited to materials exposed to elevated service temperatures The concepts can be easily extended to more mundane applications where brittle materials such as glass or cements are used Specific applications that have utilized ceramic materials at near-ambient temperatures include wear parts (nozzles, valves, seals, etc.), cutting tools, grinding wheels, bearings, coatings, electronics, and human prostheses Other brittle materials, such as glass and graphite materials, have been used in the fabrication of infrared transmission windows, glass skyscraper panels, television cathode ray tubes (CRTs), and high-temperature graphite bearings Thus, in this article the design methodologies used to analyze these types of components, as well as components exposed to elevated service temperatures, are presented Reliability algorithms are outlined, and several applications are presented to further illustrate the utilization of these reliability algorithms in structural applications For further background material on statistical methods, see the article "Statistical Aspects of Design" in this Volume

Trang 40

Design with Brittle Materials

Stephen F Duffy, Cleveland State University; Lesley A Janosik, NASA Lewis Research Center

Time-Independent Reliability Analyses

An engineer is trained to quantify component failure through the use of a safety factor By definition, the safety factor for

a component subjected to a single load L is given by the ratio:

(Eq 1)

where R is the resistance (or strength) of the material from which the component is fabricated Making use of the concept

of a safety factor, the probability of failure (Pf) for the component where a single load is applied is given by the expression:

(Eq 2)

In making the transition from a deterministic safety factor for a component to a probability of failure, for the most general

case, the assumption is made that both R and L are random variables Under this assumption Pf is the product of two finite probabilities summed over all possible outcomes Both probabilities are associated with an event and a random variable

The first event is defined by the random variable L taking on a value in the range:

(Eq 3)

The probability associated with this event is the area under the probability density function (PDF) for the load random

variable (f L) over this interval, i.e.,

To interpret this integral expression, consider the graphs in Fig 1 In this figure, the graph of an arbitrary PDF for the

resistance random variable is superimposed on the graph of an arbitrary PDF for the load random variable Note that R and L must have the same dimensional units (e.g., force or stress) to superimpose their graphs in the same figure A

Tiêu đề	Operational Classification of Wear Situations
Trường học	Unknown Institution
Chuyên ngành	Materials Selection and Design
Thể loại	Lecture Notes
Năm xuất bản	2010
Thành phố	Unknown City

Định dạng
Số trang	120
Dung lượng	2,11 MB