• J.E Ritter, Ed., Erosion of Ceramic Materials, Trans Tech Publications, Switzerland; also published as Key Engineering Materials, Vol 71, 1992 Sliding Contact Damage Testing Introduction SURFACE DAMAGE from sliding contact is related to the adhesion of the mating surfaces in contact Adhesion is a major contributor to sliding resistance (friction) and can cause loss of material at the surface (i.e., wear) or surface damage without a loss of material at the surface (e.g., galling or scuffing) Adhesion is clearly demonstrated in sliding systems when a shaft seizes in a bearing The types of surface damage caused by sliding contact include adhesive wear, galling, and fretting These three damage mechanisms are all influenced by adhesion of the mating surfaces, but these categories also reflect the nature of the surface damage and the type of sliding contact For example, galling is considered a severe form of adhesive wear that occurs when two surfaces slide against each other at relatively low speeds and high loads Fretting is also a special case of adhesive wear that occurs from oscillatory motion of relatively small amplitude The third damage type, adhesive wear, is a little more ambiguous Often adhesive wear is defined by excluding other forms of wear For example, if no abrasive substances are found, if the amplitude of sliding is greater than that in fretting, and if the rate of material loss is not governed by the principles of oxidation, adhesive wear is said to occur In most cases, however, adhesive wear involves a transfer of material from one surface to another Adhesive wear also occurs typically from the sliding contact of two surfaces, where interfaces in contact are made to slide and the locally adhered regions must separate, leaving transferred material Breakout of this transferred material will form additional debris This separation of material results in a wide range of wear rates, depending on the type of contact and the adhesion between the mating surfaces This article describes the methods for evaluation of surface damage caused by sliding contact The first section, “Adhesive Wear,” describes wear testing from long-distance sliding of nominally clean and dry (unlubricated) surfaces This is followed by sections on test methods for galling and fretting wear, which are more unique forms of adhesive wear and surface damage Additional information on sliding contact damage can be found in Friction, Lubrication, and Wear Technology, Volume 18 of ASM Handbook Sliding Contact Damage Testing Adhesive Wear W.A Glaeser, Battelle Adhesive wear typically occurs from sliding contact and is often manifested by a transfer of material between the contacting surfaces As an example, Fig shows bronze transfer to a steel surface under sliding contact Transfer can be minute and only visible in the microscope Deformation wear, or plastic deformation of a thin surface layer during sliding contact, can also fall under the definition of adhesive wear Adhesive wear can occur along with abrasive or chemical wear conditions A transfer layer can build up on the harder surface of a sliding pair in the form of a mechanically mixed material (Ref 1) The transfer layer can also contain compacted wear debris This layer will tend to break out and form wear debris Fig Bronze transfer to a steel surface after adhesive wear during sliding contact Adhesive wear is a function of material combination, lubrication, and environment For instance, austenitic stainless steels (AISI 304, 316, etc.) sliding against themselves are very likely to transfer and gall with severe surface damage Other materials that are prone to adhesive wear include titanium, nickel, and zirconium These materials make very poor unlubricated sliding pairs and can wear severely in adhesive mode even when lubricated Other metals are apt to show adhesive wear when dry sliding contact occurs Rubber tends to bond to smooth, dry surfaces (glass and polymers) by weak van der Waals forces and slide in a stick-slip mode that involves adhesion A gaseous environment is an important factor in promoting adhesive wear The lack of oxygen and water vapor in a wear environment can aggravate adhesive wear High vacuum conditions as found in outer space will make adhesive wear likely Wear tests run in simulated space conditions (10-10) torr reveal tendencies for various material combinations to develop adhesive wear in that environment (Ref 2) Adhesive wear testing can be carried out with a variety of sliding contact systems These include four-ball, block-on-ring, pin-on-disk, crossed cylinders, flat-on-flat, and disk machines Examples are shown in Fig Fig Diagrams of contact types for various test machines Adhesive wear testing (sliding contact wear, no lubrication, slow motion, heavy load) may be chosen deliberately to investigate the resistance of a material to excessive wear and material transfer for a given application Adhesive wear can also occur unexpectedly in a sliding contact test and should be recognized from the wear morphology Typical wear scars associated with adhesive wear are shown in Fig and Figure 4(a) shows a scanning electron microscope (SEM) micrograph of an embedded steel particle in an aluminum bearing surface; the particle is identified by the energy-dispersive x-ray spectrometry (EDX) pattern for iron shown in Fig 4(b) The test can be designed to determine load capacity or effects of temperature on the onset of adhesive wear These data would then be used in the design of a bearing or gear system that could operate safely in the conditions simulated in the test Fig SEM micrograph of adhesive wear of cast iron Fig Scar from adhesive wear (a) SEM micrograph of wear scar on an aluminum bearing with embedded steel particle from the shaft 200× (b) EDX pattern for iron in the particle 200× References cited in this section P Heilman, J Don, T.C Sun, W.A Glaeser, and D.A Rigney, Sliding Wear and Transfer, Proc Int Conf Wear of Materials, American Society of Mechanical Engineers, 1989, p 1–8 W.R Jones, S Pepper, et al., The Preliminary Evaluation of Liquid Lubricants for Space Applications by Vacuum Tribometry, 28th Aerospace Mechanisms Symposium, National Aeronautics and Space Administration, May 1994 Sliding Contact Damage Testing Adhesive Wear Terms Adhesive wear from sliding contact occurs from the transference of material from one surface to another due to a process of solid-phase welding (Ref 3) Particles that are removed from one surface are either permanently or temporarily attached to the other surface There are also a number of other terms used to describe adhesive wear conditions, defined as follows Asperity refers to an isolated high spot in a given surface-roughness profile or a protuberance in the small-scale topographical irregularities of a solid surface Cold welding is the bonding of surface contact points after localized softening or melting caused by the frictional heating of contacting asperities during sliding Galling is a severe form of scuffing and is often associated with gross damage to the surfaces or failure The usage of the term galling has different intents, and therefore its meaning must be ascertained from the specific context of the usage Galling can be considered to be a severe form of adhesive wear, where cold welding of asperities causes heavy transfer of surface material Scuffing is the formation of severe scratches in the sliding direction Also referred to as scoring, scuffing is considered a milder form of galling It occurs when cold-welded junctions leave hardened protrusions, which tend to plow and scratch the softer mating surface much like abrasion Seizure is the stopping of relative motion as a result of interfacial friction or by gross surface welding Seizure is an adhesive wear condition, where cold welding and material transfer result in loss of clearance between mating surfaces Wear coefficient is a nondimensional number that is typically defined as the proportionality k factor in the Archard wear formula (Ref 4): W = kLD/H where W is wear volume, L is normal load or force, D is distance of sliding, H is hardness, and k is wear coefficient This equation assumes a linear process; that is, wear is proportional to the applied load and distance, and inversely proportional to hardness This equation is used extensively in developing data from wear tests As an example, assume a pin-on-disk wear test is run using a copper pin The operating conditions are as follows (a detailed description of the calculation and use of the wear coefficient can be found in Ref 5): Normal load, N (kgf) 19.6 (2) Disk speed, rpm 80 Track diameter, mm (in.) 32 (1.3) Test duration, h Pin weight loss, mg (grains) 23.1 (0.35) Hardness of pin, HV 80 3 Density of copper, g/cm (lb/in ) 8.9 (0.3) The wear coefficient is calculated as follows: W = 23.⅛.9 = 260 mm3 D = π × 32 × 80 × 120 = 9.65 × 105 mm k = 2.60 × 80/9.65 × 105 × = 1.08 × 10-4 Wear Life Determination Assume a 10 mm diam copper pin electrode rides against a rotating steel surface running at 100 rpm and the allowable shortening of the pin due to wear is 10 mm The pin load is kg The track diameter is 70 mm What is the approximate life of the pin? k = 1.08 × 10-4 Pin wear volume = π × 100 × 10 = kLD/H D = (3.14 × 103 × 80)/1.08 × 10-4 = 2.32 × 109 mm D = π × 70 × 100 × time Time = 2.32 × 109/2.2 × 104 = 1.05 × 105 min, or 1750 h Specific wear is similar to wear coefficient, except that the hardness factor is not included This is often used when determining the wear properties of materials of similar hardness References cited in this section Glossary of Terms, Friction, Lubrication, and Wear Technology, Vol 18, ASM Handbook, P Blau, Ed., ASM International, 1992 E Rabinowicz, Wear Coefficient—Metals, Wear Control Handbook, American Society of Mechanical Engineers, 1980, p 475–506 E Rabinowicz, Wear Coefficient—Metals, Wear Control Handbook, American Society of Mechanical Engineers, 1980, p 475–484 Sliding Contact Damage Testing Selecting Standard Adhesive Wear Tests Generally, adhesive wear testing involves sliding contact between unlubricated parts For instance, such testing might help identify a material combination for a slow-moving brake or clutch system Testing also could assist in operating a sleeve bearing in a high vacuum or oxygen and water-vapor-free environment The purpose might be to estimate the wear life of such an operating system The wear coefficient can be obtained from an appropriate wear test apparatus, and the maximum wear loss can be specified Simulation of Operating Conditions In selecting a standard wear test, it is important that the test come close to simulating the prospective operating conditions of the mechanism of concern The test should simulate the following conditions: Contact Point contact (ball-on-flat, ball-on-ball, crossed cylinders) Line contact (roller-on-flat; roller-on-roller, axes parallel) Flat-on-flat Conforming (sleeve or journal bearing) Velocity and load (high speed, low load; low speed, high load; low speed, low load) Temperature Vibration Gaseous environment Contact conditions can be selected from a number of wear test configurations as are shown in Fig These are taken from standard wear tests, and many can be found in ASTM specifications The Amsler and Falex vee block represent line contact systems Point contact is represented in pin-on-disk, crossed cylinders and four-ball tests, while flat-on-flat is shown in ring-on-ring, fretting bridge, and flat-on-flat configurations The following ASTM standards apply to the configurations shown in Fig 2: Title Test ASTM No Block-on-ring G 77 Standard Test Method for Ranking Resistance of Materials to Sliding Wear, Using Block-on-Ring Test Crossed G 83 Standard Test Method for Wear Testing with a Crossed Cylinder Apparatus cylinders Pin-on-disk G 99 Standard Test Method for Wear Testing with a Pin-on-Disk Apparatus Falex vee D 2670 Standard Test Method for Measuring Wear Properties of Fluid Lubricants block (Falex Pin and Fee Block Method) Four-ball D 4172 Standard Test Method for Wear Preventive Characteristics of Lubrication Fluid (Four-Ball Method) These standards are also available in Ref Temperature and Friction Wear tests should have continuous measurement of both specimen temperature and friction Temperature can be measured by a thermocouple inserted in the stationary specimen near the contact surface A number of standard tests found in ASTM specifications have friction measuring devices included in the description of the apparatus Velocity and Load Archard's equation, as a general model of wear, assumes that wear is proportional to the applied load and sliding distance Distance and velocity are related, and so wear is also proportional to velocity by Archard's equation Because it is desirable and economical to run wear tests as quickly as possible, both the load and the velocity can be increased to speed up a test However, increasing these parameters will also increase the frictional heat generation and can lead to overheating Overheating will change the wear mode (increasing galling and surface damage) and will result in misleading wear data This is particularly important in wear testing of polymers Polymers have low thermal conductivity and low melting and softening points compared to metals Therefore, before embarking on a series of wear tests for statistical analysis, a set of preliminary tests should be run to establish the most efficient method, while keeping the wear mode as expected in the application Reference cited in this section Friction and Wear Testing: Source Book of Selected References from ASTM Standards and ASM Handbooks, ASM International, 1997 Sliding Contact Damage Testing Statistical Analysis of Wear Data Data scatter is inherent in any testing, and using a statistical approach to the analysis of wear data is desirable The method in ASTM G 83 (Ref 7) recommends sample sizes over 10 However, because 10 samples may not be possible owing to availability of samples and cost, ASTM G 83 does provide a method for analysis with sample sizes less than 10 The method uses the range of test results, where the range, R, is the difference between the highest and lowest test values for an initial set (2 to 10 samples) of measurements For these small sample sizes, the standard deviation (s) can be calculated from the R value instead of from the root mean square value For sample sizes from to 10, the standard deviation is calculated from the range of the first few test results as follows: s = R/d2 where the values for d2 are listed in Table for different sample sizes Table Factors for estimating standard deviation for sample sizes 10 and less Sample size d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 10 3.078 Standard deviation s = R/d2 for small sample size, where the range R is the difference between the highest and lowest test values for an initial set (2 to 10 samples) of measurements Source: Ref Sample size (n) estimate can be derived from the relation: n = 1.96 ν/e2 where ν is the percent coefficient of variation = (s/x) × 100(%), e is the sampling error, and x is the average for n tests For example, if s = 0.9 mg and x = mg, then the coefficient of variation is 11% If an allowable sampling error (e) is selected as 10%, the sample size for 95% confidence limits should be (1.9 · 11/10)2 = The results of round-robin tests from several laboratories using block-on-ring test apparatus are reported in the appendix of ASTM G 77 (and also Ref 8) This reference shows the expected scatter in such wear tests References cited in this section “Standard Test Method for Wear Testing with a Crossed-Cylinder Apparatus,” ASTM G 83, Annual Book of ASTM Standards Friction and Wear Testing: Source Book of Selected References from ASTM Standards and ASM Handbooks, ASM International, 1997, p 110–114 Sliding Contact Damage Testing Measuring Wear A wear test should be run long enough to produce measurable wear What constitutes measurable wear depends on the measuring method The easiest way to determine measurable wear is to measure weight loss This is also the coarsest method Weight loss must be sufficient to be uninfluenced by condensed moisture, contaminants such as dust and oil, and minute transfer Dimensional change is a more sensitive method If a well-defined contact geometry is used such as ball-on-flat, ball-on-ball, or ring-on-flat, a scar length can be translated to volume loss Equations for calculating wear volume from scar dimensions are shown in Fig Fig Wear volume calculations for various shapes in contact with a flat surface Source: Ref Adhesive wear testing often involves some transfer from one surface to another It is good practice to use two methods to measure wear: scar measurement and weight loss The volumes determined from both methods can be compared, and effects of transfer, deformation, or pitting can be detected Reference cited in this section A.W Ruff, Wear Measurement, Friction, Lubrication, and Wear Technology, Vol 18, ASM Handbook, P Blau, Ed., ASM International, 1992, p 362–369 Sliding Contact Damage Testing Galling John H Magee, Carpenter Specialty Alloys Galling is a severe form of adhesive wear or surface damage that occurs when the surface of two components slide against each other at relatively low speeds and high loads Lubricants or coatings, designed to reduce friction and prevent galling, are sometimes either ineffective or cannot be used due to product contamination concerns Thus, gross surface damage occurs and is characterized by localized material transfer or removal This gross surface damage is known as galling and can occur after just a few cycles of relative movement between the mating surfaces Severe galling can cause seizure of these parts When galling takes place, mated surfaces typically show distinct junctions where severe plastic deformation has occurred (Fig 6) These contact surfaces contain areas where asperities, or surface protrusions, from one surface have bonded together with those on the other surface Under low stresses, these junctions are minute and break apart with movement resulting in adhesive wear debris However, higher stresses produce much larger junctions and galling (Ref 11) Fig Galling test button specimens, after testing (a) No galling exhibited (b) Severe galling Source: Ref 10 Components that encounter galling conditions include threaded fasteners from a typical bolt/nut connection to large threaded tubular used in oil exploration Valve parts have mating surfaces that are designed to encounter infrequent sliding movement Galling damage on these surfaces affects valve performance, for example, leaking The interface of a roller and side plate on a continuous chain-link conveyor belt can gall when lubrication is not used This is an important design consideration for the conveyance of food and drug products because lubricants are prohibited due to contamination concerns (Ref 12) The term galling has also been used to describe surface damage caused during metalworking Metalworking processes include rolling, extrusion, wire drawing, deep drawing of sheet, and press-forming operations Insufficient lubrication sometimes causes metal transfer and galling In Japan, the term galling is used mainly to describe damage in sheet metalforming processes Tests to characterize this gross surface damage usually involve production equipment or laboratory simulation of various plastic metalworking processes Additional information can be found in Ref 13 and in Friction, Lubrication, and Wear Technology, Volume 18 of ASM Handbook This section describes in detail the ASTM G 98 button-on-block galling test The purpose of this test is to rank material couples resistant to galling Several variations of this test are also discussed that either increase the severity of the test or attempt to quantify the surface damage using profilometry Data obtained from button-onblock testing are very useful in screening materials for prototype testing This section also describes prototype testing of threaded fasteners Three threaded connection tests are discussed as examples of prototype tests designed to closely simulate field service for a specific application This type of testing tends to be expensive, but vital before use in-service Also, these tests can be used to solve a specific galling problem 25 P Parikh, Report on Bending Stress Relaxation Round Robin, STP 676, Stress Relaxation Testing, A Fox, Ed., ASTM, 1978, p 112–125 26 J Henderson and J.D Sneddon, Complex Stress Creep Relaxation on Commercially Pure Copper at 250 °C, Advances in Creep Design, A.I Smith and A.M Nicolson, Ed., John Wiley & Sons, Inc., 1971, p 163–180 27 A Fox, Effect of Temperature on Stress Relaxation of Several Metallic Materials, Residual Stress and Stress Relaxation, Proceedings 28th Sagamore Army Materials Research Conference, E Kula and V Weiss, Ed., Plenum Press, 1982, p 181–203 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Introduction DESIGN OF PRESSURIZED COMPONENTS is normally based on uniaxial data because all the material data is generated using uniaxial tests However, typical industrial piping components operate under a multiaxial state of stress as a result of the internal pressure, temperature gradients, and system stresses Very general effective stress concepts have been used in component design codes to calculate the creep life of the material under triaxial state of stress These concepts are based on the principle that the life of a component with a multiaxial effective stress corresponds to the rupture time at the same uniaxial stress according to the uniaxial design data Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Multiaxiality and Principal Stresses Any complex stress combination with stresses in three directions and six different shear stresses can be reduced to just three stresses, the principal stresses σ1 > σ2 > σ3 The highest of these is called the maximum principal stress (MPS) In the principal stress coordinate system there are no shear stresses The stress state is biaxial if σ3 = 0, as is often assumed for thin-walled tubes The stress system is reduced to uniaxial when σ1 = σ and σ2 = σ3 = In thick-walled pipes and components the stress state is triaxial In the stress distribution figures in this article, a tube under internal pressure that has a ratio of inner radius to outer radius of 0.6 has been used as an example Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Effective Stress Equations The basic idea of effective stresses is to calculate a stress for complex stress situations with a value that gives the correct failure time when applied to uniaxial data, which is often the basis for engineering design—and often the only data available in absence of representative multiaxial test data The effective stresses can be calculated for different cases, each of which will be described in detail in this article: • • • • Elastic stresses (see the section “Elastic Stress Distribution in a Tube”) Steady-state creep stresses (see the section “Steady-State Creep Stress Distribution in a Tube”) Stresses in a fully plastic case (see the section “Plastic Stresses in a Tube”) Thermal stresses (see the section “Thermal Stresses in a Tube”) The thermal stresses are often superimposed with one of the former stress systems Von Mises Criterion The most commonly used effective stress concept is the one presented in 1913 by von Mises, based on a concept of maximum energy of distortion: (Eq 1) The von Mises effective stress is most widely used in engineering design, both in the low and high temperature ranges It has been found to govern the deformation of materials under complex loading situations It is also the controlling parameter for creep rupture at high stresses where the rupture is associated with large deformations and a ductile failure mechanism However, in long-term service, the rupture is controlled either by MPS or a mixed MPS-von Mises criterion Also in brittle materials, the rupture tends to be more MPS controlled Much work has been focused on whether or not creep rupture would occur under a complete tensile triaxiality when σ1 = σ2 = σ3 = σ Under these circumstances, von Mises would go to zero, which means that there is no deformation or rupture in the short term, but it is believed that creep rupture would occur under MPS control after a long exposure time with a constrained grain-boundary cavity nucleation and growth mechanism Experimentally this is extremely difficult to verify because of the difficulty of triaxial loading using a cruciform specimen, for example For practical reasons, the von Mises equation is often used in engineering design in a different form where, instead of principal stresses, the engineering stresses are used, including torsion stress: (Eq 2) where σh is hoop stress (circumferential), σa is axial stress, σr is radial stress, and τ is torsion stress Often an effective stress concept has been used in the background when design rules have been determined, but it is not always apparent to the user from the design code itself Similarly, plenty of detailed analyses have often been hidden behind the design safety factors Tresca Criterion The yield criterion generally known as the Tresca criterion is based on the concept of maximum shear stress energy and is expressed simply as: σTR = σ1 - σ3 (Eq 3) Huddleston Criterion This multiaxial effective stress concept is a modified version of the von Mises stress, and it is claimed to better take the multiaxiality into account (Ref 1, 2) Here the equation is shown in the simplified form (Eq 4) J1 = σ1 + σ2 + σ3 (Eq 5) (Eq 6) While under the steady-state creep conditions, the von Mises predicts highest stresses on the inner surface; the Huddleston distribution, on the other hand, is quite contrary and would probably provide a more reliable basis for damage and life predictions than von Mises, at least if only stress is considered in life prediction and not ductility (See Fig in the section “Steady-State Creep Stress Distribution in a Tube” in this article.) This criterion was originally developed for stainless steels but has proved to be useful for ferritic high-temperature engineering materials as well The Huddleston criterion was incorporated into ASME Code Case N-47-29 Fig Distribution of normalized steady-state creep stresses in a pressurized tube with a ratio of inner radius, Ri, to outer radius, Ro, of 0.6 The principal facet stress values have been normalized by dividing by a factor of 2.24 Mixed Criteria Often mixed criteria have been proposed because, in practical cases, none of the classical parameters describe the material behavior sufficiently in various stress cases One of the most common criterion is the one developed at the former Central Electricity Generating Board in the United Kingdom, presented by Cane and Hayhurst (Ref 3, 4): σeff = ασ1 + (1-α) (Eq 7) where α is the coefficient of thermal expansion A similar empirical effective stress concept for hightemperature materials has been proposed by the Russian research institute CKTI: σCKTI = ( + 0.47 )1/n (Eq 8) where n is the Norton creep exponent The concept of principal facet stress σF has been developed (Ref 5) based on the observations that creep damage will first appear on grain boundaries transverse to the axis of MPS, and that on inclined boundaries there will be shear deformation, which is mainly controlled by von Mises effective stress: σF = 2.24σ1 - 0.62(σ2 + σ3) (Eq 9) The principal facet stress has been found to bring uniaxial and multiaxial data together especially for ferritic and austenitic steels However, this stress does not apply directly to engineering calculations because the stress values calculated by Eq are high Therefore, in Fig 1, σF has been normalized by a factor of 2.24 The principal facet stress is then seen to coincide with the von Mises stress on the outer surface of the pressurized tube Normalization by a factor of would make σF coincide with the von Mises stress in the skeletal point and with the distribution of the Huddleston stress The Effect of Stress System on the Damage Processes At least in the short term, the creep damage process of cavity nucleation seems to be von Mises controlled because cavity nucleation requires accumulation of shear strain On the contrary, for brittle materials the number of cavities formed is a function of MPS and intergranular fracture is promoted by the increasing ratio of σ1/σVM (Ref 3) Similarly, the effect of MPS becomes more pronounced under long service times, under which the uniaxial ductility is known to reduce remarkably and fracture becomes more brittle According to Cane (Ref 3), the growth of grain-boundary cavities is controlled by MPS at low effective stress levels and by von Mises at high stress levels If component-integrity and life-assessment methods not give proper consideration to the change of the damage mechanism, they are likely to be conservative at high stresses and short times when σ1/σVM < and not conservative at low stress levels in the long term when σ1/σVM > References cited in this section R.L Huddleston, An Improved Multiaxial Creep-Rupture Strength Criterion, J Pressure Vessel Technol (Trans ASME), Vol 107, Nov 1985, p 421–429 R.L Huddleston, Assessment of an Improved Multiaxial Strength Theory Based on Creep-Rupture Data for Type 316 Stainless Steel, J Pressure Vessel Technol (Trans ASME), Vol 115, May 1993, p 177– 184 B.J Cane, Creep Damage Accumulation and Fracture under Multiaxial Stresses, Proc Advances in Fracture Research (Fracture 81), 1981 (Cannes, France), Vol 3, Pergamon Press, 1982 B.J Cane, Representative Stresses for Creep Deformation and Failure of Pressurised Tubes and Pipes, Int J Pressure Vessel Piping, Vol 10, 1982, p 119–128 H.K Kim, F.A Mohamed, and J.C Earthman, “High Temperature Rupture of Microstructurally Unstable 304 Stainless Steel Under Uniaxial and Triaxial Stress States,” Metall Trans A, Vol 22, 1991, 2629–2635 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Effective Strain In a multiaxial stress system as well, strains occur in three different directions, which are assumed to coincide with the principal stress axes It is assumed that failure will occur when the effective strain reaches the uniaxial rupture strain value The effective strain equation is almost identical with the respective stress equation (Eq 2): (Eq 10) Similarly, the effective strain rate can be expressed as: (Eq 11) The relationship between stress and strain rate can then be expressed: (Eq 12) Further, a simple criterion comes from the fact that most engineering materials are considered to be incompressible This rule applies for both strains and strain rates: + + =0 (Eq 13) Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Elastic Stress Distribution in a Tube The equations for the elastic stress distribution for hoop, axial, and radial stress (Ref 6) were first published by Lame in 1852 and can be expressed as: (Eq 14) (Eq 15) (Eq 16) where p is pressure, Y is the outer radius divided by the inner radius (Ro/Ri), and r is the radius The elastic stress distribution is shown in Fig for an example tube (Ri = 0.6Ro) without any stress relaxation due to plasticity or creep Fig Distribution of normalized elastic stresses in a pressurized tube with a ratio of inner radius, Ri, to outer radius, Ro, of 0.6 The thicker the tube, the steeper the stress gradient becomes The radial (compressive) stress on the inside is, by definition, equal to the inner pressure and gradually decreases to zero towards the outer surface This radial stress has to be taken into account when calculating the effective stress On the other hand, in a thin-walled tube, the radial stress is often considered negligible, and, therefore, the stress state is simplified to biaxial Reference cited in this section R Seshardi, Design and Life Prediction of Fired Heater Tubes in the Creep Range, J Pressure Vessel Technol (Trans ASME), Vol 110, Aug 1988, p 322–328 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Steady-State Creep Stress Distribution in a Tube The analytical solutions for a tube under steady-state creep (Ref 6, 7, 8) were published first in 1935 by Bailey, and therefore, the following equations for hoop, axial, and radial stresses are often referred to as the Bailey equations: (Eq 17) (Eq 18) (Eq 19) The stress distribution is shown in Fig These stresses are related by a correlation, which can be used to check numerical calculations: σa = 0.5(σh + σr) (Eq 20) With creep, the initial elastic stresses are redistributed and the stresses are “reversed.” Under pressurization, the maximum elastic stresses appear on the inner surface of the tube, but, due to creep, these stresses relax and, under steady-state conditions, the maximum stresses move to the outer surface The maximum initial elastic hoop stress of 2.13p on the inner surface is reduced to only 1.16p under steady-state creep Meanwhile, on the outside, the initial elastic hoop stress of 1.13p increases to 1.76 under creep conditions It should also be noted that the elastic stress distribution is a special case of creep stress distribution when n = References cited in this section R Seshardi, Design and Life Prediction of Fired Heater Tubes in the Creep Range, J Pressure Vessel Technol (Trans ASME), Vol 110, Aug 1988, p 322–328 R.W Bailey, Creep Relationships and Their Application to Pipes, Tubes and Cylindrical Parts under Internal Pressure, Proc Inst Mech Eng A, Vol 164, 1951, p 425 I Finnie and W.R Heller, Creep of Engineering Materials, McGraw-Hill, 1959 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Plastic Stresses in a Tube These equations assume a completely plastic case: (Eq 21) (Eq 22) (Eq 23) A reference stress equal to the von Mises effective stress value can be calculated for the fully plastic case using Eq 24: (Eq 24) The plastic stress distribution for the example tube is shown in Fig It should be noted that the plastic stress distribution in a cylindrical body is very similar to the creep stress distribution This similarity has been used in the limit load analysis where plastic finite-element (FE) stress analysis is used to determine representative failure loads for various components Second, both von Mises and Tresca distributions are constant through the wall thickness Third, it should be noted that the Tresca value is equal to the maximum hoop stress value on the outer surface Fig Distribution of normalized plastic stresses in a pressurized tube with a ratio of inner radius, Ri, to outer radius, Ro, of 0.6 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Thermal Stresses in a Tube Often thermal stresses appear in plant components, which can have a significant influence on the stresses In heat exchangers, tubes operate continuously under a thermal gradient, and, in many plants, thick-walled components experience severe thermal gradients, especially during transition periods like start-up and shutdown of the plant Often these thick-walled components set a limit to the start-up speed just because of the maximum allowable thermal stress in the wall During operation, thermal stresses are often superimposed on primary stresses originating from the pressure The thermal stresses are called secondary because, in long-term operation, they may relax as a result of creep In that case, after long-term operation (after complete stress redistribution), the stresses follow the steady state distribution; at shut-down, the initial elastic stresses and thermal stresses have to be subtracted Then the remaining stress at zero pressure with zero temperature gradient becomes: Remaining stress = steady state stress - elastic stress from pressure - thermal stress The thermal hoop, axial, and radial stresses can be calculated using the following equations Here the temperature gradient has been defined as a result of external heating For the cases of internal heating (applicable to the start-up of a cold component), the thermal gradient, ΔT, becomes negative and the stress distribution is reversed (Eq 25) (Eq 26) (Eq 27) where E is the modulus of elasticity and ν is Poisson's ratio An example of the distribution of multiaxial thermal stresses is shown in Fig for the example tube Fig Distribution of normalized thermal stresses in a pressurized tube with a ratio of inner radius, Ri,to outer radius, Ro, of 0.6 and with a temperature gradient of 50 °C (90 °F) under external heating Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Comparison of Life Predictions By Different Effective Stress Criterion Figure contains data generated for P91 steel at 600 °C (1100 °F) using tubular specimens (outside diam 38 × mm, thinner than the example tube in other figures) under internal pressure and axial end load with different ratios of hoop and axial stress It should be noted that all the tests were started with the same initial von Mises stress In the same figure, the continuum damage mechanics (CDM) model predictions are shown for three different multiaxial stress rupture criterion: von Mises, Tresca, and Huddleston Fig Multiaxial creep test results for a pressurized P91 tube with end load at 600 °C (1100 °F) under various ratios of hoop stress to axial stress and with constant initial von Mises stress One would assume then that the von Mises prediction would be a flat curve, but the CDM model predicts always a slightly curved shape Similarly, one would assume that at stress ratios of and 0.5, the life would be the same, but it does not seem to be the case The reason for this is that at a stress ratio of 2, the hoop stress is dominant and the hoop strain leads to an increase of the inner diameter, which will reduce the life in a pressurized test On the other hand, at a stress ratio of 0.5 (hoop stress is half of the axial), the axial stress is dominant and the diameter actually remains constant (the necking as a result of the axial stress is balanced by the internal pressure) This leads to a slightly increased life When the initial von Mises stress is the same in all tests, the shape of the Tresca (or MPS) curve is explained by the hoop and axial stress components Figure clarifies this The MPS in this figure consists of axial stress between stress ratios to and hoop stress when stress ratio is greater than unity The MPS life curve in Fig is a “mirror image” of the MPS curve in Fig Fig Hoop and axial strain components in an internally pressurized tube when the von Mises effective stress is kept constant The plots like Fig can be used to tell whether the stress rupture criterion is von Mises or MPS For many materials, the experimental points lie somewhere in the middle It has been observed that the Huddleston stress, described by, Eq correlates fairly well with this data It should be noted, however, that plots like Fig are time dependent This figure describes the short-term behavior where the failure is associated with large deformation In long-term service, the damage mechanism is constrained grain-boundary cavitation, which is associated with very little deformation Therefore, under the long-term service conditions, the creep behavior tends to become more MPS dominated Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Commonly Used Stress Equations for Design Often, the design of pressurized components is based on simple and desirably conservative design rules, and, in many cases, a simple mean diameter hoop (MDH) stress equation is used only because experience has proved it to be conservative in most cases: (Eq 28) where is the outside diameter, and t is the tube thickness According to Cane (Ref 4), the mean diameter hoop stress well describes the life at high pressures and underestimates it at low stresses; that is, MDH is conservative in design for long-term operation The axial stress component in a pressurized tube with axial loading can be calculated using the following equation: (Eq 29) where F is the axial load and di is the inside diameter These simple stress equations are insensitive to system (bending) stresses, which may appear, for example, in a piping as a result of thermal expansion between fixed points This can result in severe secondary bending stresses, which should be taken into account in piping design Omission of bending stresses can lead to premature failure in, for example, welds close to fixed points (type IV cracking) For tubes, a skeletal stress has been found to correlate fairly well with the stress rupture data: (Eq 30) The basis for this definition is the observation that in approximately the middle of the wall thickness there is a point where the stresses are not dependant on the Norton creep exponent, n, as demonstrated in Fig Calculation of the von Mises stress in the mid-wall using the steady-state creep stresses leads to Eq 30 The skeletal stress value for the tube used in the example of Fig becomes 1.71p Fig Stress distributions in a creeping tube at different creep exponents showing the appearance of a skeletal stress in a point where the hoop stress value is practically independent of the Norton creep exponent (n) Ro, outside radius of tube Reference cited in this section B.J Cane, Representative Stresses for Creep Deformation and Failure of Pressurised Tubes and Pipes, Int J Pressure Vessel Piping, Vol 10, 1982, p 119–128 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) Multiaxial Creep Ductility It is well known that triaxiality has a strong effect on the ductility of materials Under high degrees of tensile triaxiality, ductility will decrease remarkably Therefore, a constraint parameter, h, is introduced (Ref 9): (Eq 31) Then the ratio of multiaxial and uniaxial ductility can be expressed by an exponential equation: (Eq 32) where εf is failure strain and εfmx is the failure strain under multiaxial conditions An alternative solution is to define a triaxiality factor (TF), which is three times the h parameter: (Eq 33) Then multiaxial ductility (Ref 10) can then be calculated from a simple formula: (Eq 34) These ductility equations give very different predictions of the multiaxial behavior at both extremes The reciprocal Eq 34 gives very high values when TF approaches zero (equal tensile principal stresses) and does not work if TF is negative The exponential Eq 32 gives lower multiaxial ductility values at small and negative values of h and is more conservative at high degrees of multiaxiality Both curves go through the uniaxial point, which is TF = and h = ⅓(Fig 8) Fig Multiaxial ductility as a function of the triaxiality factor using Eq 32 and 34 High degrees of multiaxiality can be found especially at notch roots or in front of a crack tip Also, in the soft zone of the heat-affected zone of a weld there is a strong element of tensile triaxiality, which will have an effect on the life The multiaxial ductility for our model tube (Ri = 0.6Ro) gives the values shown in Table when calculated using the Eq 32 and 34 This result is extremely important because it explains the discrepancy between the two observations: • • Creep stress analysis for a cylindrical body gives always the maximum effective stress values on the inner surface of the tube The service experience shows that the creep damage always appears on the outer surface of the tube—at least for materials other than the most brittle ones Table Ratio of multiaxial and uniaxial ductility calculated at various locations in the wall of a tube Location on tube wall Ratio of multiaxial ductility to uniaxial ductility 1/TF(a) 1.65 exp(-3h/2)(b) Inner surface 7.60 1.54 Mid wall 1.01 1.00 Outer surface 0.58 0.69 Tube has a ratio of inner radius to outer radius of 0.6 (a) See Eq 34 (b) See Eq 32 In a creeping tube, the strains are proportional to 1/radius Therefore, both the effective stress and the strain on the inner surface of the tube are the highest, but the multiaxial ductility is clearly higher than the uniaxial ductility, as shown in Table This is why the damage does not initiate on the inside of the tube (except in materials where the uniaxial creep ductility is very low—then the relaxation of the high initial elastic stresses can cause failure on the inside) On the other hand, according to Eq 32 and 34, the ductility on the outer surface is much less than the uniaxial ductility, which leads to the initiation of the damage on the outer surface first Fortunately, the nature of creep rupture itself seems to simplify the problem of multiaxiality in plant components In long-term service, creep rupture occurs with a constrained grain-boundary cavity nucleation and growth mechanism, it seems to be more MPS controlled, and damage appears predominantly on the outer surface (which is fortunate from an inspection point of view) This finding could simplify the necessary engineering calculations of multiaxial stress systems to some extent However, the present-day design codes for plant equipment not necessarily reflect this idea, although design lives can be well above 100,000 h where MPS would become the controlling parameter Further, it should be remembered that for components in the creep regime, the MPS should not be calculated according to the initial elastic distribution but according to the steady-state creep stress distribution References cited in this section P Segle, P Andersson, and L.Å Samuelson, A parametric study of creep crack growth in heterogeneous CT specimens by use of finite element simulations, Mater High Temp., Vol 15, 1998, p 101 10 B.W Roberts, Influence of Multiaxial Stressing on Creep and Creep Rupture, Mechanical Testing, Vol 8, ASM Handbook, ASM International, 1985, p 343–345 Influence of Multiaxial Stresses on Creep and Creep Rupture of Tubular Components R.C Hurst and J.H Rantala, European Commission, Joint Research Centre, Institute for Advanced Materials (The Netherlands) ... 1 0-3 171 191 Variation of torque coefficient, % +7, -6 -1 6 +9 +11 +3, -2 +18 -1 4 +5, -6 +7, -7 +9, -1 3 +21 -1 4 -1 6 -2 2 -3 1 -1 4 -2 3 -3 0 -1 6 -2 1 +9 -7 -1 1 -1 0 -3 +10 -9 -1 5 +11, -1 … +1, -1 4 -1 7... Test and condition MoS2-Sb2O3-epoxyester film None 10 Torque coefficient(a) at first makeup 73 × 1 0-3 102 121 124 139 125 1 46 125 149 127 189 314 165 164 202 175 1 46 167 159 159 161 153 152 160 ... contact (ball-on-flat, ball-on-ball, crossed cylinders) Line contact (roller-on-flat; roller-on-roller, axes parallel) Flat-on-flat Conforming (sleeve or journal bearing) Velocity and load (high