Modeling and Simulation for Material Selection and Mechanical Design Part 15 pot

Wp for full plastified cross-section is used (Wp ¼ pdo3=12) Step 7 offers the lead angle of the thread profile j Step 8 formulates the theory of maximum distortion energy for producing a material failure (this is also called ‘‘vMises theory of failure’’) This is the background-formula for step 1 to combine equivalent stress and axial stress General information about theories of failure can be found in Ref [3] In general, the friction coefficient m is defined as the ratio of normal force acting over produced tangential frictional force in a sliding motion of two bodies (Fig 17) The frictional force is always directed against the direction of motion For a screw, the normal force is the preload Fp The tangential force can be formulated as mtÁFp in the thread contact zone and as mhÁFp in the head support area These tangential forces cause frictional torques, because of the radii of thread and head contact zones due to screw axis (diameters Deb resp d2, see also Fig 16) Therefore, the frictional Figure 17 Definition of friction coefficients mh and mt Copyright 2004 by Marcel Dekker, Inc All Rights Reserved coefficients define the part of preload, which acts tangentially in the contact areas of a screw Table 4 proposes classes of frictional coefficients valid for bolted joints, based on the VDI 2230 guideline [70] and experience [17] If no exact value is available, one can select a value from this table which is valid for low surface roughness But one must always remember that the friction coefficient depends on complex influences like materials surfaces, lubrication incl homogeneity, hardness ratio of the two surfaces in contact, local stress peaks or stress distribution in contact zone, tolerances for contact geometry as well as tightening level and number of (re) tightenings A selection table can only provide rough approximations The supplier of screws can provide information related to friction behavior In practice, all parameters for calculations of Fig 16 have deviations Main influences are based on minimum and maximum strength of screw material (e.g heat treatment process) as well as minimum and maximum friction coefficients (e.g roughness and lubricant) Geometry is usually very precise, so tolerances from diameters are not significant for screw tightening This situation is shown schematically in Fig 18 with two corresponding diagrams for highest material stressing in the screw shank The upper case A refers to conditions with minimum friction mmin (both, mtmin and mhmin) and maximum screw strength Rmsmax On the abscissa axis, the Table 4 Values for Guidance of frictional Coefficients mt and mh in Classes A–E [17,70] mt, mh (—) Characteristics=Typical examples A 0.04–0.10 B 0.08–0.16 C 0.14–0.24 D 0.20–0.35 E 0.30–0.45 Hard polished surfaces, thick lubrication with wax or grease, high pressure lubricants, anti-friction coatings, e.g polished magnesium and screw with PTFE-low friction coating and MoS2, no peak pressure at edges of support area Commonly used conditions with defined friction by optimized lubricants, such as oil, wax, grease for fasteners; suitable for ferritic steel metallic blank, phosphate, zinc and microlayer surfaces as well as nonferrous metals with relevant lubricant Usual conditions with only thin or inhomogeneous lubricant, austenitic steel screws with suitable lubricant; zinc, zinc alloy, and nonelectrolytical applied surfaces without lubricant Austenitic steel with oil, rough surfaces and Zn=Ni coating without lubricant Austenitic steel, aluminum, and nickel alloys blank without lubricant Copyright 2004 by Marcel Dekker, Inc All Rights Reserved plastification of the screw shank (transition of the strong gradient of the tightening curve in Fig 18 to the low gradient in the range of plastified screw) Another possibility to reach high tightening levels is using the angular controlled tightening method (also called ‘‘turn-of-the-nut-method’’): After applying a snug-torque Ts an additional, fixed defined tightening angle Du is added, so the screw is plastified to a certain grade in any case (comp markings in Fig 18) For yield point controlled tightening and angular controlled tightening the ratio of Fpymax=Fpymin resp Fpanmax=Fpanmin is about 1.1–1.3 The deviation in practice is reduced drastically For this reason, the greatest advantage of overelastic tightening methods is a significant increase of the minimum preload and a slight increase of the maximum preload But one must always note the resulting torque value can vary extremely for overelastic tightening methods, because torque is no controlled parameter Some hints for selection of parameters considering deviations in practice are: for calculating the highest preload (related to the highest screw stressing) always take minimum friction coefficients and maximum screw strength This is relevant for maximum contact pressure under head) If the lowest preload has to be determined, maximum friction coefficients and lowest screw strength are relevant To obtain maximum assembly torque for overelastic tightening method, take maximum friction coefficients and highest screw strength This is relevant for maximum screw drive loading If new tightening devices have to be designed for a production line with screw assembly, these devices should be able to apply a high torque value for angular controlled tightening In practice, more than the double torque limit should be designed compared to torque controlled tightening E Loading During Operation 1 Mechanical Loading If a threaded fastening system is tightened, then screw, clamped part, and nut thread component are loaded mechanically by the flow of preload without external force (Fig 19) The preload leads to head contact pressure pch between screw head support and clamped part surface as well as to thread contact pressure pct at engaged thread flanks Between clamped part and nut thread component, the component contact pressure pcc is generated (important for sealing) Following considerations due to force—elongation-behavior which are based on Ref [70], details are discussed in Refs [7,67,72] Copyright 2004 by Marcel Dekker, Inc All Rights Reserved This idealized model reduces all elastic contributions within the system to rigid bodies and two springs with defined resilience: The screw shank is modeled as one tensile spring with ds, the clamped part is represented by a compressive spring with elastic resilience dp Before tightening, all ‘‘springs’’ are unloaded (left side of Fig 20) After tightening, usually the tensile spring of the screw is elongated much more than the compression spring of the clamped part (right of Fig 20) If an external axial force Fax is induced within the clamping length lc, the inducing factor n determines which part of the clamped part is additionally loaded (towards the screw head) and which part is unloaded by Fax (towards the nut thread component) These parts of additional loading and unloading by an external axial force Fax influence the relevant elastic resiliences of ds and dp, if the fastening system is loaded Therefore the resiliences vary between tightening and operating, if n < 1 Fig 20 leads to the following force–elongation diagram shown in Fig 21 The diagram shows on the x-axis the elongation of screw (left of ‘‘0’’) and clamped part with clamping length lc (right of ‘‘0’’) On the y-axis, the corresponding preload Fp in the screw shank is drawn For Figure 21 Force–elongation-characteristics of screw and clamped part Copyright 2004 by Marcel Dekker, Inc All Rights Reserved the stable tightening level Fp0, a (positive) screw elongation of Fp0Áds and at clamped part an (negative) elongation of Fp0Ádp is generated The representative curves of screw and clamped part are linear up to the yield point of each material Here, the stable tightening level Fp0 is completely within the linear range If screw or clamped part show plastification, each nonlinear behavior has to be considered for force–elongation diagram (degressive dashed lines in Fig 21) If a tensile external axial force Fax is applied to the fastening system, on the one hand, the screw is loaded additionally by nfFax and on the other hand the clamped part is unloaded by (1 À nf)Fax, because the two springs are a parallel arrangement The consequence is that Fax reduces the residual clamping load and increases the tension in the screw shank, but always only a part of Fax acts in any ‘‘spring’’ The additional operating force of screw (nfFax) besides the load factor f is dependent on the inducing factor n For this reason, Fig 22 gives some examples for the value of n, which are approximations Some references propose a calculation of n [70], but an analytical solution is usually a lot of work, and a simple approximation often gives the same range in practice Figure 22 Examples for approximation of inducing factor n (From Ref 70.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Numeric calculations like FEM are very suitable to determine nf ¼ Faxscrew shank=Fax external directly for a given geometry by selecting the nodes of the screw shank cross-section for Faxscrew shank and all nodes, which are loaded externally for Fax external With the result of nf, the analytical calculation can be continued; therefore, FEM can be used to consider all influences from geometry and inhomogeneous stress distribution (e.g for clamped part) The determination of the inducing factor n is an example, to show that very detailed design modifications lead to significant changing in screw loading In general, it is valid that a small inducing factor n decreases the additional operating force of screw (interesting for increasing the fatigue loading capacity of the fastening system), and reduces also the residual clamping force under axial loading with an operating force (compare also Fig 21) If no numeric calculation is done, the load factor f can be approximated with the analytical model of Fig 23, see also Ref [70,72] This load factor can be calculated from f ¼ dp=(ds þ dp), if the axis of screw, clamped part centerline and external axial force Fax is the same If these axes have different positions, additional bending of the screw and clamped part occurs, so that the elastic resiliences and in consequence the load factor f are changed Figure 23 Linear model for determination of load factor F (From Ref 17.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved For the model shown in Fig 23, the force Fax, the distances of axes s and a, the through-hole diameter dh as well as the elastic resiliences ds and dp from Figs 12 and 15 and the substituted area Asub must be known From these, the substituted diameter Dsub can be calculated This constant diameter corresponds to Asub for the same resilience dp The model is assuming a linear stress distribution s(x) within Dsub For the use of Fig 23, it is necessary that the real stress distribution is similar to the linear distribution in the model The size of the clamped part may not be much larger than Dsub, so the moment of inertia Ifull keeps valid Then, the moment of inertia Ifull can be obtained and as a next step f can be calculated Ifull does include the cross-section area of the screw, because the screw gives also a bending resistance during loading with Fax After tightening, any threaded fastening system shows relaxation effects This short time relaxation often is called ‘seating’: it leads to a preload reduction as demonstrated in Fig 24 Important influence for this is the roughness and strain hardening of all surfaces in contact zones between screw, clamped part(s) and nut thread component as well as the direction of mechanical loading due to a normal vector on the contact area Under contact pressure, the high surface spots are deformed axially which leads to a seating distance fz of the fastening system and in consequence to a reduction of preload down to a stable preload level Fp0 Significant short time relaxation always occurs if the fastening system is partially overloaded, such as when thread engagement is too small Figure 24 Preload reduction by seating (short time relaxation) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved (see Fig 33) or if contact pressure under the head is too large (see Fig 39), material mismatch (e.g material strength of clamped part is too low) or geometric mismatch (e.g nonperpendicular nut thread or screw head, oversized underhead fillets) The approximational equation for fz given in Fig 24 can be used if there is no partial overloading An eccentric loading of a threaded fastening system can lead to component separating Figure 25 demonstrates this for an external force Fax acting with a distance a from the axis of symmetry 0–0 of clamped part The configuration of Fig 25 is the same as in Fig 23 Figure 25 Mechanics of component separating as a result of eccentric loading by Fax (From Ref 17.) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved There exists a point of tilting on one side of clamped part; on the opposite side, of the first component separating occurs With the given values Fp0, Fax, s, a, dh, Dp and f after calculating the area Ap of clamped part in the contact zone between components and the moment of inertia Ip, the preload for first separating Fps can be estimated for a given axial force Fax If the preload Fp0 is larger than Fps, then component separation does not occur for loading with Fax On the other hand, if a stable preload after tightening Fp0 is given, Faxcrit determines the beginning of component separating, if Fax > Faxcrit This leads to two cases indicated in Fig 25 Case 1 is determined by elastic screw loading regarding the force–elongation diagram of a threaded fastening system The additional operating load of screw Fsa is equal to nFFax Case 2 refers to the situation of a beam lever system, built by Fp and Fax and the length values a, s, Dp Component seperation must be avoided (case 2) because it leads to extensive additional loading of the screw Fsa and to early failure either by static overloading or by fatigue fracture But in some cases, for optimized components with high resilience dp and with exactly defined tightening by loading, a partial component separation can be allowed without problems (e.g bolted joints at lightweight piston rods) For more details regarding component separation under eccentric mechanical loading, see Refs [67,70] Figure 26 Preload behavior for overelastic tightening Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 26 explains the preload behavior for overelastic tightening of screw The corresponding force–elongation diagram illustrates the screw plastification with a degressive curve for exceeded elastic limit under the tensile and torsional stressing during tightening The first preload level after tightening Fp1 is reduced to the stable preload Fp0 by the reason of seating effects Besides this, a general aspect is that after tightening a screw the torsional stress is reduced significantly—to app 30–50% of the torsional stress under applied torque This leads to an increased elastic limit of screw and leading to a higher preload limit during operating compared to tightening A screw, which was tightened overelastic, can be loaded by a large operating force Fax In practice, there is almost no difference between the tightening methods due to the loading capacity during operation (for dynamic loading, see also Fig 52) Up to now, no time dependence of mechanical load is considered Fig 27 displays the effects for an alternating axial force Fax For positive axial force Fax (tensile loading), the preload in the screw shank will be increased and the clamping force will be reduced, producing the same effect as for static loading If a threaded fastening system is loaded axially, the preload in the screw shank is not the same as the clamping force between components For a negative axial force ÀFax, just the opposite aspects are true: the preload in the screw shank will be reduced and the clamping force between Figure 27 Preload behavior for mechanical dynamic axial loading Copyright 2004 by Marcel Dekker, Inc All Rights Reserved the components will be increased In this case, by the negative axial loading ÀFax, a plastification of the clamped part can be generated which does not occur during tightening and leading to relaxation effects that are not acceptable during operation But overall, also for dynamic axial loading, the screw has to bear only the part (nfFax) due to the complete axial force Fax For a well-designed threaded fastening system, this part normally should be smaller than 10– 20% of Fax 2 Thermal Loading Often, a threaded fastening system must be used at different temperatures, e.g tightening at room temperature (t1) and operating at elevated temperature (t2) If screw material and material of clamped part have different thermal properties like Young’s modulus (Es, Ep) or thermal expansion coefficient (as, ap) or if the properties are temperature-dependent in the range of temperatures applied, the preload Fp varies, and this can be significant The design engineer must check if the thermal loading of the paricular threaded fastening system does not lead to overloading by preload increasing or missing of clamping force by preload reduction Figure 28 shows a linear approximation of the temperature-dependent preload change DFp Again, the screw is tightened to its stable preload level Fp0 at temperature t1 The temperature change DT ¼ t2 À t1 leads to thermal elongations at screw and clamped part Dl1, Dl2 and to changed elastic constants Es, Ep Therefore, the force-elongation diagram is modified so that, a Figure 28 Ref 17.) Approximation of preload changing by thermal loading (From Copyright 2004 by Marcel Dekker, Inc All Rights Reserved preload change DFp is generated Influences from nut thread component are neglected because the main part of the preload is transmitted by the first thread flanks, therefore only a very short expansion length is relevant compared to the clamping length lc This preload change DFp can be positive or negative It is positive, if Young’s moduli are constant and the clamped part has a larger thermal expansion coefficient than the screw (typical for threaded fastening systems with light metals and steel screws) For example, it is negative for titanium screws and steel components A positive preload change DFp can result in a screw failure (static fracture of screw by too large yielding=plastification) For example, in an extreme relaxation of preload by plastification of clamped part or screw, a negative DFp can result in a component separation and finally in a fatigue failure of screw The preload change demonstrated in Fig 28 is valid for the same temperature of screw and clamped part (steady state); during heating up or down a peak difference in temperature can occur, which generates even more preload change The equation indicates what can be done to minimize DFp: reduce the thermal expansion mismatch (ap À as), reduce temperature difference DT, maximize for given clamping length lc both the resiliences ds and dp (e.g by low Young’s moduli) This means that in practice the positioning of screws away from extreme hot or cold places using the same materials for screw and clamped part (e.g Al-screws for Al-components) and using long thin walled distance tubes (e.g for pipe constructions) Figure 29 proposes a fundamental example for thermal loading with numeric values A description of the situation is given with the sketch on the leftside of Fig 29 A screw with nominal diameter d and support diameter da is tightened with a clamped part with through-hole diameter 1.1d, then heated to a temperature difference between tightening and operating of DT This generates a preload change DFp which results in an axial stress change Dsp in the screw shank and also in a change of contact pressure under head Dpch The diagram contains values for ferritic steel screws and aluminum screws combined with a clamped part made of aluminum or magnesium (Young’s moduli are set to constant for this calculation) The highest thermal stress increase takes place for steel screw with magnesium component If applying DT ¼ 1008C, this combination has about 250 MPa stress increase which means 170 MPa contact pressure increase If a standard ISO 4014 screw is used only 65 MPa contact pressure increase using a flange head with da ¼ 2d will be obtained The result from this thermal stress increase can be the plastification of clamped part and leading to extensive relaxation; see also examples in Fig 66 Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 5 1 2 3 General Types of Corrosion Chemical corrosion Chemical reaction of the material surface with electrolyte; the metal dissolves in a corrosive liquid until either it is consumed or the liquid is saturated (in practice, the ‘‘liquid’’ also can be humid air atmosphere, possibly with solvents of compounds, such as SO2 or salt at sea coasts) Galvanic corrosion Chemical reaction of two electrically coupled metals using an electrolyte as transmitter for electrons (electrochemical cell) Then, the corrosion rate of the less corrosion-resistant metal is increased significantly Therefore, this type of corrosion normally shows high corrosive speed, but the corrosion-rate depends on many parameters, such as potential-difference, temperature, purity, grain structure, convection=diffusion, influence of corrosion-products, ratio of cathodic and anodic areas, geometry In practice galvanic corrosion is always a subject, if only one of two coupled metals is attacked and if the attack is reduced with increasing distance from the borderline between the two materials Selective Corrosion Chemical reaction located within a part of a material This corrosion type is typical for alloys where different elements=phases with different sensibility for corrosive media exist e.g dezincification of brass Stress corrosion cracking is an intercrystalline reaction at grain boundaries, induced by the existing mechanical loading of special material=electrolyte=environmentcombinations Examples for this are stainless steel and chloride-electrolyte (seawater) or some high-strength aluminum alloys and electrolyte with saltsolvent Another type of selective corrosion is the so-called ‘‘hydrogenembrittlement’’ of high-strength steels (see also text) When designing for corrosive behavior of different material surfaces, Table 6 with normal potential, measured against a standard H-electrode (flat electrode, 258C, 1 M-solution of ions in the electrolyte) is used for theoretical estimation of suitable metal combinations But galvanic corrosion is determined by system behavior so that any table can only provide a tendency not quantitative information Metals with low (negative) potential are called anodic (base metals, likely to corrode) The materials with high potential are called cathodic (noble metals, unlikely to corrode) The existing corrosion current in a galvanic cell is determined by the combination of the metals For a minimum corrosion activity, the design engineer should combine materials with low difference in electrochemical potential One can conclude that the ideal situation would be a screw made of the same material as the clamped part Besides the corrosive stability, this also has almost no thermal loading under changing temperature (see Fig 29) Exceptions are passivated metals (indicated with à ) They build a thin oxide layer on their surface which has a dense structure and, therefore, Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 7 Galvanic Series for Seawater from [3,50] in part, Measured Against Saturated Calomel Reference Electrode (SCE) Metal=Alloy Titanium Ni–Fe–Cr-alloys Ni–Cu-alloys Silver Platinum Stainless steels, active Stainless steels, passive Copper Brass Cast iron Low-carbon steel Low-alloy steel Aluminum alloys Zinc Magnesium Bronze Cu–Sn Range of potential (mV) À40 to þ40 À30 to þ30 À150 to À30 À150 to À100 þ180 to þ230 À300 to À50 À550 to À350 À350 to À250 À400 to À270 À730 to À590 À730 to À590 À610 to À580 À1000 to À750 À1200 to À900 À1650 to À1580 À320 to À240 Measured against SCE, flow of seawater 2.4–4.0 msec; temperature 5–308C during operation, e.g H atoms from corrosion reactions As a result, screws made of steel should be coated nonelectrolytically for class 12.9 or higher The data is shown in Fig 31 suggests fundamental corrosion mechanisms of threaded fastening systems The characteristics are printed to each part in the figure itself If the screw material is a base metal and the component material is noble chemical, the screw material corrodes (e.g steel screw in copper component) If the difference of electrochemical potential is opposite the component corrodes (e.g steel screw in magnesium component) This is shown in part (a) of Fig 31 (left and right) Any corrosion product like oxide generates a limited appearance and can increase the speed of corrosion For a further state of corrosion, destroying the support area leads to extreme relaxation because the residual original material cannot bear the initial preload from tightening In general, the first step of corrosion is relevant for appearance, the second step of corrosion is relevant for preload function Part (b) of Fig 31 demonstrates the same situation for a coated component and coated screw with internal drive An internal screw drive can collect electrolyte, and therefore, is set to a severe corrosive environment This is the reason why often screws with internal drive configura- Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 30 1000  SEM image of fracture from screw M12-12.9; loosened grains are typical for hydrogen embrittlement, magnification Copyright 2004 by Marcel Dekker, Inc All Rights Reserved then the protection is partly reduced For coated screws with high corrosion resistance, a hexagon drive configuration should be avoided by the reason of the high bit contact pressure and possibly high edge-deformation of screw (see also Fig 36) Coating systems make the chemical corrosion complex (four materials in Fig 31b), which can react: two bulk materials, two coating materials) The noble material does not corrode (compare damaged component coating and the resulting local corrosion) Coating systems for screw protection must provide a high quality adhesion, because they have to work under extreme mechanical surface pressure (explanations of Fig 31b) Besides electrolytical coatings, there are also very effective nonelectrolytical coating-systems for enhanced corrosion protection of steel screws known For established suppliers of nonelectrolytical coatings, see Refs [54,12,13,53,54]); for standardization see Ref [23] Part (c) of Fig 31 focuses on electrical insulation as a mechanical way to prevent from corrosion Remarks are given in the figure Part (d) summarizes general aspects for corrosion of threaded fastening systems in practice III DESIGN STRATEGY FOR THREADED FASTENINGS For realizing an optimized threaded fastening system, an effective development procedure is necessary Figure 32 demonstrates this with a flow diagram by distinguishing three columns: calculation=design, verification, and realization The main topics of calculation=design are: tightening= operating (determination of loadings the bolted joint has to bear), screw, clamped part, nut thread component (specifications of all parts of the bolted joint), and design analysis (engineering results based on theory and experience) If the design analysis meets the requirements and is proposing a reliable function of the bolted joint, the verification column is started Prototypes are the very first practical realization of the theoretical design With these parts, the laboratory tests and the field tests can be done, if the prototypes are representative for series production The realization column contains assembly process (parameters often are determined by assembly process capability as a result of laboratory tests), purchase, series production and field service Today, basic aspects of quality management are teamwork, documentation of results and history, failure modes and effects analysis as well as feasibility reviews These concepts can be transferred to several topics of Fig 32 (only drawn for design analysis and prototypes, because here they are necessary in any case, see also Ref [19]) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 8 Check List for Screw Material Selection No Question for Theoretical Checking of the Selected Screw Material 1 Is the screw material suitable for sufficient preload (material strength high enough)? Is the screw material suitable for required dynamic loading (notch-sensitivity, material fatigue behavior)? Is the screw material suitable for operating temperature? Is the thermal expansion coefficient of screw material suitable for permitted change of preload under temperature? Is the screw material resp screw surface suitable for corrosion requirements (climate, fluids=electrolytes, material contacts)? Is the screw material suitable for tightening (adhesion, friction in mechanical contacts)? Is the screw material suitable for screw manufacturing (availability of raw material, forming, cutting, heat treatment, large batch production requirements)? Has the screw material good-natured behavior if overloading (ductility resp significant plastification before fracture, no embrittlement)? Has the screw material sufficient long-term properties under tensile stress (stable grain-structure, no creeping, no embrittlemement)? Is the screw material economic? 2 3 4 5 6 7 8 9 10 1 Operating Environment and Material-Related Standards The operating environment determines the materials that are suitable Table 9 gives fundamental selection criteria and a few examples for alloys (for established materials, see Tables 10–12) Only when standard materials cannot be used should special solutions be considered In this case, the supplier of fastening elements can give support, e.g Refs [2,62] The European standard EN 10269 provides steels and nickel alloys for fasteners at elevated or low temperatures with temperature-related properties [11] As a rough estimation, the material strength at limiting temperature of the material is approximately half of the strength at room temperature The European designation system for steels is defined in standard EN 10027 The Vickers hardness test procedure is defined in standard ISO 6507 [39] Electrolytical surface coatings for fastening elements are defined in ISO 4042 [31] (types of coatings, coating thickness, tolerances, hydrogen-embrittlement, designations of coating systems), nonelectrolytical coatings for fastening elements are defined in ISO 10683 [23] Detection of hydrogen embrittlement is dealt in ISO 15330 [25] Surface discontinuities are proposed and evaluated in ISO 6157 [37] Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 11 Some Properties of Screws made of Stainless Steels, Defined in ISO 3506 [29], for Design Purpose and Details, Refer to Standard Steel group and grade Minimum tensile strength Rm (MPa) Minimum proof stress Rp0.2 (MPa) Minimum elongation after fracturea (%) Minimum vickers hardness HV 10 Maximum vickers hardness HV 10 A2-70 700 450 %24 — — A2-80 800 600 %16 — — A4-70 700 450 %24 — — A4-80 800 600 %16 — — 700 1,100 800 600 410 820 640 410 %8 %8 %8 %8 220 350 240 180 330 440 340 285 C1-70 C1-110 C3-80 F1-60 a Example for suitable Material (not defined in ISO 3506) X5CrNi-18-9, X5CrNi1816 X5CrNi-18-9, X5CrNi1816 X5CrNiMo17-12-2, X2CrNiMo17-13-3 X5CrNiMo17-12-2, X2CrNiMo17-13-3 X12Cr13 X12Cr13 X19CrNi16-2 X3Cr17, X6CrNb12 in ISO 3506 originally measured at manufactured screw as elongation over total length in mm retightened by nonprofessionals (e.g wheel bolts of cars, Fig 73) Also, misuse has to be tested during verification of the design (Fig 32) 2 Established Materials for Screws If searching for established screw materials, three main groups can be found: low alloyed- or carbon-steels (mostly used, ISO 898 [46]), stainless steels (ISO 3506 [29]) and nonferrous metals for screws (ISO 8839 [44]) In ISO 898 and ISO 3506, only grades for groups of materials are specified Besides this, in ISO 7085 [41], mechanical properties of case hardened and heat treated screws and in ISO 2702 [27] mechanical properties of heat treated tapping screws are defined The well-known property classes of screws (3.6, 4.6, 4.8, 5.6, 5.8, 6.8, 8.8, 9.8, 10.9, 12.9) are defined in ISO 898 are only valid for screws made of carbon steel or alloy steel (definition of property classes: first number: minimum tensile strength Rmmin of material=100 in N=mm2; second number: 10  ratio of proof stress Rp0.2 over tensile strength Rmmin) ISO 898 does not apply to high temperatures above 3008C or low temperatures under À508C Table 10 summarizes the important properties defined in ISO 898 Another material group is also well established: screws made of stainless steels Related properties for fasteners are defined in ISO 3506 [29] Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 11 contains some properties of screws made of stainless steels regarding ISO 3506 Austenitic steels cannot be hardened and are usually nonmagnetic Alloys of steel grade A2 are most frequently used (kitchen equipment, apparatus industry), but they are not stable in environments with chlorides (e.g swimming pools or chemical devices) Alloys of grade A4 are the so-called ‘‘acid proof steels’’ with molybdenum as alloy element to increase corrosion resistance, to a certain extent, also against chloride ions (used for chemical industry, food industry, ship-building industry) Steels of martensitic grades C1 and C3 can have higher strength than austenitic steels and can have relatively higher proof stress Rp0.2, but they have a limited corrosion resistance, so they are widely used in machines with high loading and controlled environment, such as pumps and turbines Ferritic steels of grade F have a permanent ferritic grain structure at room temperature, so they cannot be hardened, but they are magnetic They are an alternative for steels of grade A2 For all situations, where ISO 898 and ISO 3506 cannot offer suitable materials for screws or bolts, the materials of ISO 8839 should be checked Table 12 proposes the nonferrous metals of this standard which are used for electrical contacts (screws made of copper, brass), special corrosive conditions, lightweight design or constructional elements (screws made of aluminum) AL5 and AL6 of Table 12 can be sensitive for stress corrosion cracking, depending on their grain structure Currently, additional aluminum alloys for screws are available, which provide high strength without stress corrosion cracking (e.g alloys 6013 and 6056, in work standards often called AL9, see also Refs [15,16]) B Determination of Screw Thread Size The screw thread size normally is the main parameter used to determine the initial preload of a threaded fastening system The other parameters are in many cases preselected, such as screw material (determined by environment), assembly method (determined by assembly line, field maintenance or philosophy), and frictional situation (determined by surfaces in contact) But the design engineer always has to distinguish both initial preload (generated during tightening, see also Fig 18) and residual preload (stable preload level during operating, see also Fig 24) The initial preload can be calculated in a detailed manner, the residual preload strongly depends on the material’s behavior and the local contact conditions Therefore, this value often is estimated from experience or if necessary measured (preload measurement by ultrasonics or strain gauges) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 13 Estimated Preload Level for Different Metric Screw Types Preload Level (kN), Metric Screw Thread Tensile strength and yield strength ratio of screw Thread size M1 M2 M3 M4 M5 M6 M8 M10 M12 M12 M14 M14 M16 M16 M18 M18 M20 M22 M24  1.5  1.5  1.5  1.5 Nominal As (mm2) 0.458 2.069 5.000 8.800 14.20 20.10 36.60 58.00 84.30 88.10 115.4 124.6 156.7 167.3 192.5 216.2 244.8 303.4 352.5 Rm (MPa) kR (À) 300 0.6 400 0.6 400 0.8 500 0.6 500 0.8 600 0.8 800 0.8 900 0.8 1,000 0.9 1,100 0.9 1,200 0.9 1,400 0.9 0.06 0.28 0.68 1.20 1.94 2.75 5.01 7.93 11.5 12.1 15.8 17.0 21.4 22.9 26.3 29.6 33.5 41.5 48.2 0.08 0.38 0.91 1.61 2.59 3.67 6.68 10.6 15.4 16.1 21.0 22.7 28.6 30.5 35.1 39.4 44.7 55.3 64.3 0.11 0.50 1.22 2.14 3.45 4.89 8.90 14.1 20.5 21.4 28.1 30.3 38.1 40.7 46.8 52.6 59.5 73.8 85.7 0.10 0.47 1.14 2.01 3.24 4.58 8.34 13.2 19.2 20.1 26.3 28.4 35.7 38.1 43.9 49.3 55.8 69.2 80.4 0.14 0.63 1.52 2.68 4.32 6.11 11.1 17.6 25.6 26.8 35.1 37.9 47.6 50.9 58.5 65.7 74.4 92.2 107.2 0.17 0.75 1.82 3.21 5.18 7.33 13.4 21.2 30.8 32.1 42.1 45.5 57.2 61.0 70.2 78.9 89.3 110.7 128.6 0.22 1.01 2.43 4.28 6.91 9.78 17.8 28.2 41.0 42.9 56.1 60.6 76.2 81.4 93.6 105.2 119.1 147.6 171.5 0.25 1.13 2.74 4.82 7.77 11.00 20.0 31.7 46.1 48.2 63.1 68.2 85.7 91.5 105.3 118.3 134.0 166.0 192.9 0.31 1.42 3.42 6.02 9.7 13.7 25.0 39.7 57.7 60.3 78.9 85.2 107.2 114.4 131.7 147.9 167.4 207.5 241.1 0.34 1.56 3.76 6.62 10.68 15.12 27.5 43.6 63.4 66.3 86.8 93.7 117.9 125.9 144.8 162.7 184.2 228.3 265.2 0.38 1.70 4.10 7.22 11.7 16.5 30.0 47.6 69.2 72.3 94.7 102.3 128.6 137.3 158.0 177.5 200.9 249.0 289.3 0.44 1.98 4.79 8.43 13.6 19.2 35.0 55.5 80.7 84.4 110.5 119.3 150.1 160.2 184.3 207.0 234.4 290.5 337.6 Copyright 2004 by Marcel Dekker, Inc All Rights Reserved M24  2 M27 M30 M36 (  4) M36  3 M36  2 M36  1.5 M39 M48 M56 M64 M80 M90 M100 384.4 459.4 560.6 816.7 864.9 914.5 940.3 975.8 1,475 2,032 2,678 4,490 5,594 6,998 52.6 62.8 76.7 111.7 118.3 125.1 128.6 133.5 201.7 278.0 366.4 614.3 765.3 957 70.1 83.8 102.3 149.0 157.8 166.8 171.5 178.0 269.0 370.6 488.5 819.1 1,020 1,277 93.5 111.7 136.3 198.6 210.3 222.4 228.7 237.3 358.6 494.2 651.4 1,092 1,361 1,702 87.6 104.7 127.8 186.2 197.2 208.5 214.4 222.5 336.2 463.3 610.7 1,024 1,275 1,596 116.9 139.7 170.4 248.3 262.9 278.0 285.9 296.6 448.3 617.7 814.2 1,365 1,701 2,128 140.2 167.6 204.5 297.9 315.5 333.6 343.0 356.0 538.0 741.2 977 1,638 2,041 2,553 187.0 223.5 272.7 397.2 420.7 444.8 457.4 474.6 717.3 988 1,303 2,184 2,721 3,404 210.3 251.4 306.8 446.9 473.3 500.4 514.5 534.0 806.9 1,112 1,466 2,457 3,061 3,830 262.9 314.2 383.5 558.6 591.6 625.5 643.2 667.4 1,009 1,390 1,832 3,071 3,826 4,787 289.2 345.7 421.8 614.5 650.8 688.1 707.5 734.2 1,110 1,529 2,015 3,379 4,209 5,266 315.5 377.1 460.1 670.3 709.9 750.6 771.8 800.9 1,210 1,668 2,198 3,686 4,592 5,744 368.1 439.9 536.8 782.1 828.2 875.7 900.4 934.4 1,412 1,946 2,565 4,300 5,357 6,702 Boundary conditions: (1) Yield point controlled tightening; (2) Friction tot ¼ 0.16; (3) As is smallest area of cross-section; (4) proper screw section design, so failure is located at threaded cross-section, (no thread stripping, no head stripping) Notes (1) For torque controlled tightening in practice, the preload can be reduced (app  0.7); (2) for utilization of eq ¼ 90%; of Rp0.2, multiply relevant preload by 0.9; (3) yield strength ratio kR ¼ Rp0.2=Rm; (4) for angular controlled tightening, multiply relevant preload by [1 þ 0.3(1 À kR)=kR ] Copyright 2004 by Marcel Dekker, Inc All Rights Reserved  ... same materials for screw and clamped part (e.g Al-screws for Al-components) and using long thin walled distance tubes (e.g for pipe constructions) Figure 29 proposes a fundamental example for. .. Material Selection No Question for Theoretical Checking of the Selected Screw Material Is the screw material suitable for sufficient preload (material strength high enough)? Is the screw material. .. Is the screw material suitable for tightening (adhesion, friction in mechanical contacts)? Is the screw material suitable for screw manufacturing (availability of raw material, forming, cutting,