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

W
p
for full plastified cross-section is used (W
p
¼pd
o
3
=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 fail-
ure 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 F
p
. The
tangential force can be formulated as m
t
ÁF
p
in the thread contact zone and
as m
h
ÁF
p
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 D

eb
resp. d
2
, see also Fig. 16). Therefore, the frictional
Figure 17 Definition of friction coefficients m
h
and m
t
.
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 co-
efficient 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 tight ening.
This situation is shown schematically in Fig. 18 with two correspond-
ing diagrams for highest material stressing in the screw shank. The upper
case A refers to conditions with minimum friction m

min
(both, m
tmin
and
m
hmin
) and maximum screw strength R
msmax
. On the abscissa axis, the
Table 4 Values for Guidance of frictional Coefficients m
t
and m
h
in
Classes A–E [17,70]
m
t
, m
h
(—) Characteristics=Typical examples
A 0.04–0.10 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
MoS
2
, no peak pressure at edges of support area
B 0.08–0.16 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

C 0.14–0.24 Usual conditions with only thin or inhomogeneous lubricant,
austenitic steel screws with suitable lubricant; zinc, zinc alloy,
and nonelectrolytical applied surfaces without lubricant
D 0.20–0.35 Austenitic steel with oil, rough surfaces and Zn=Ni coating
without lubricant
E 0.30–0.45 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 T
s
an additional, fixed defined tightening angle Du is
added, so the screw is plastified to a certain grade in any case (comp. mark-
ings in Fig. 18).
For yield point controlled tightening and angular controlled tightening
the ratio of F
pymax
=F
pymin
resp. F
panmax
=F
panmin
is about 1.1–1.3. The devia-
tion in practice is reduced drastically. For this reason, the greatest advan-
tage 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 overelas-
tic tightening methods, because torque is no controlled parameter.
Some hints for selection of parameters considering deviations in prac-
tice 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 with-
out external force (Fig. 19). The preload leads to head contact pressure p
ch
between screw head support and clamped part surface as well as to thread
contact pressure p
ct
at engaged thread flanks. Between clamped part and
nut thread component, the component contact pressure p
cc
is generated

(important for sealing). Following considerations due to force—elonga-
tion-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 d
s
, the clamped part is represented by
a compressive spring with elastic resilience d
p
.
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 F
ax
is induced within the clamping length l
c
, the
inducing factor n determines which part of the clamped part is additionally
loaded (towards the screw head) and which part is unloaded by F
ax
(towards
the nut thread component). These parts of additional loading and unloading
by an external axial force F
ax
influence the relevant elastic resiliences of d
s
and d

p
, 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 l
c
(right of ‘‘0’’). On
the y-axis, the corresponding preload F
p
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 F
p0
, a (positive) screw elongation of F
p0
Ád
s
and at
clamped part an (negative) elongation of F
p0
Ád
p
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 F
p0
is com-
pletely 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 F
ax
is applied to the fastening system,
on the one hand, the screw is loaded additionally by nfF
ax
and on the other
hand the clamped part is unloaded by (1 Ànf)F
ax
, because the two springs
are a parallel arrangement. The consequence is that F
ax
reduces the residual
clamping load and increases the tension in the screw shank, but always only
a part of F
ax
acts in any ‘‘spring’’.
The additional operati ng force of screw (nfF
ax
) 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 ¼F
axscrew shank

=F
ax external
directly for a given geometry by selecting the
nodes of the screw shank cross-section for F
axscrew shank
and all nodes, which
are loaded externally for F
ax 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 approxi-
mated with the analytical model of Fig. 23, see also Ref. [70,72]. This load
factor can be calculated from f ¼d
p
=(d
s
þd
p
), if the axis of screw, clamped
part centerline and external axial force F
ax

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 F
ax
, the distances of axes s
and a, the through-hole diameter d
h
as well as the elastic resiliences d
s
and d
p
from Figs. 12 and 15 and the substituted area A
sub
must be known. From
these, the substituted diameter D
sub
can be calculated. This constant
diameter corresponds to A
sub
for the same resilience d
p
. The model is assum-
ing a linear stress distribution s(x) within D
sub
.
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 D
sub
, so the moment of inertia I
full
keeps
valid.
Then, the moment of inertia I
full
can be obtained and as a next step f
can be calculated. I
full
does include the cross-section area of the screw,
because the screw gives also a bending resistance during loading with F
ax
.
After tightening, any threaded fastening system shows relaxation
effects. This short time relaxation often is called ‘seating’: it leads to a pre-
load 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 a s well as the direction of
mechanical loading due to a normal vector on the contact area. Under con-
tact pressure, the high surface spots are deformed axially which leads to a
seating distance f
z
of the fastening system and in consequence to a reduction
of preload down to a stable preload level F
p0
.
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 geo-
metric mismatch (e.g. nonperpendicular nut thread or screw head, oversized
underhead fillets). The approxim ational equation for f
z
given in Fig. 24 can
be used if there is no partial overloading.
An eccentric loading of a threaded fastening system can lead to com-
ponent separating. Figure 25 demonstrates this for an external force F
ax
act-
ing 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
F
ax
(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 oppo-
site side, of the first component separating occurs. With the given values
F
p0
, F
ax
, s, a, d
h
, D

p
and f after calculating the area A
p
of clamped part in
the contact zone between components and the moment of inertia I
p
, the pre-
load for first separating F
ps
can be estimated for a given axial force F
ax
. If the
preload F
p0
is larger than F
ps
, then component separation does not occur for
loading with F
ax
.
On the other hand, if a stable preload after tightening F
p0
is given, F
ax-
crit
determines the beginning of component separating, if F
ax
> F
axcrit
. 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 sys-
tem. The additional operating load of screw F
sa
is equal to nFF
ax
. Case 2
refers to the situation of a beam lever system, built by F
p
and F
ax
and the
length values a, s, D
p
.
Component seperation must be avoided (case 2) because it leads to
extensive additional loading of the screw F
sa
and to early failure either by
static overloading or by fatigue fracture. But in some cases, for optimized
components with high resilience d
p
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 ten-
sile and torsional stressing during tightening.
The first preload level after tightening F
p1
is reduced to the stable pre-
load F
p0
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 F
ax
. In practice, there is almost no
difference between the tightening methods due to the loading capacity dur-
ing 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 F
ax
. For positive axial force
F
ax
(tensile loading), the preload in the screw shank will be increased and
the clamping force will be reduced, producing the same effect asfor static load-
ing. 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 ÀF
ax
, 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
ÀF
ax
, a plastification of the clamped part can be generated which does not
occur during tightening and leading to relaxation effects that are not accep-
table during operation.
But overall, also for dynamic axial loading, the screw has to bear only
the part (nfF
ax
) due to the complete axial force F
ax
. For a well-designed
threaded fastening system, this part normally should be smaller than 10–
20% of F
ax
.
2. Thermal Loading
Often, a threaded fastening system must be used at different temperatures,
e.g. tightening at room temperature (t
1
) and operating at elevated tempera-
ture (t
2
). If screw material and material of clamped part have different ther-
mal properties like Young’s modulus (E
s
, E

p
) or thermal expansion
coefficient (a
s
, a
p
) or if the properties are temperature-dependent in the range
of temperatures applied, the preload F
p
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 increas-
ing or missing of clamping force by preload reduction.
Figure 28 shows a linear approximati on of the temperature-dependent
preload change DF
p
. Again, the screw is tightened to its stable preload level
F
p0
at temperature t
1
. The temperature change DT ¼t
2
À t
1
leads to thermal
elongations at screw and clamped part Dl
1
, Dl
2

and to changed elastic con-
stants E
s
, E
p
. Therefore, the force-elongation diagram is modified so that, a
Figure 28 Approximation of preload changing by thermal loading. (From
Ref. 17.)
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
preload change DF
p
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 l
c
.
This preload change DF
p
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 DF
p
can result in a screw failure (static frac-
ture of screw by too large yielding=plastification). For example, in an
extreme relaxation of preload by plastification of clamped part or screw,
a negative DF

p
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 tem-
perature 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
DF
p
: reduce the thermal expansion mismatch (a
p
Àa
s
), reduce temperature
difference DT, maximize for given clamping length l
c
both the resiliences
d
s
and d
p
(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 d
a

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 DF
p
which results in an axial stress change Ds
p
in the screw shank and also in a change of contact pressure under head Dp
ch
.
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 ther-
mal stress increase takes place for steel screw with magnesium component. If
applying DT ¼1008C, 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
d
a
¼2d 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.
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 pro-
vide 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 gal-
vanic 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
Ã
). They build a thin
oxide layer on their surface which has a dense structure and, therefore,
Table 5 General Types of Corrosion
1. 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 SO
2
or salt at sea coasts).
2. 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 corro-
sion-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.
3. 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 =environment-
combinations. Examples for this are stainless steel and chloride-electrolyte
(seawater) or some high-strength aluminum alloys and electrolyte with salt-
solvent. Another type of selective corrosion is the so-called ‘‘hydrogen-
embrittlement’’ of high-strength steels (see also text).
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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 mech-
anisms 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 corro-
sion 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 relax ation 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 environ-
ment. This is the reason why often screws with internal drive configura-
Table 7 Galvanic Series for Seawater from [3,50] in part,
Measured Against Saturated Calomel Reference Electrode (SCE)
Metal=Alloy

Range of potential
(mV)
Titanium À40 to þ40
Ni–Fe–Cr-alloys À30 to þ30
Ni–Cu-alloys À150 to À30
Silver À150 to À100
Platinum þ180 to þ230
Stainless steels, active À300 to À50
Stainless steels, passive À550 to À350
Copper À350 to À250
Brass À400 to À270
Cast iron À730 to À590
Low-carbon steel À730 to À590
Low-alloy steel À610 to À580
Aluminum alloys À1000 to À750
Zinc À1200 to À900
Magnesium À1650 to À1580
Bronze Cu–Sn À320 to À240
Measured against SCE, flow of seawater 2.4–4.0 msec; temperature 5–308C
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Figure 30 SEM image of fracture from screw M12-12.9; loosened grains are typical for hydrogen embrittlement, magnification
1000 Â.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
then the protection is partly reduced. For coated screws with high corro-
sion resistance, a hexagon drive configuration should be avoided by the
reason of the high bit contact pressure and possibly high edge-deforma-
tion of screw (see also Fig. 36).
Coating systems make the chemical corrosion complex (four materi-
als in Fig. 31b), which can react: two bulk materials, two coating materi-
als). The noble material does not corrode (compare damaged component

coating and the resulting local corrosion). Coating systems for screw pro-
tection 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 nonelectrolyti-
cal 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 develop-
ment 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 experi-
ence). If the design analysis meets the requirements and is proposing a reli-
able 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 his-
tory, 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 necessa ry in any case,

see also Ref. [19]).
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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 sup-
plier 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 temperatur e. The European des-
ignation 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, designa-
tions 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].
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)?
2 Is the screw material suitable for required dynamic loading (notch-sensitivity,
material fatigue behavior)?
3 Is the screw material suitable for operating temperature?
4 Is the thermal expansion coefficient of screw material suitable for permitted
change of preload under temperature?
5 Is the screw material resp. screw surface suitable for corrosion requirements

(climate, fluids=electrolytes, material contacts)?
6 Is the screw material suitable for tightening (adhesion, friction in mechanical
contacts)?
7 Is the screw material suitable for screw manufacturing (availability of
raw material, forming, cutting, heat treatment, large batch production
requirements)?
8 Has the screw material good-natured behavior if overloading (ductility resp.
significant plastification before fracture, no embrittlement)?
9 Has the screw material sufficient long-term properties under tensile stress
(stable grain-structure, no creeping, no embrittlemement)?
10 Is the screw material economic?
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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 trea-
ted screws and in ISO 2702 [27] mechanical properties of heat treated tap-
ping 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: mini-
mum tensile strength R
mmin
of material=100 in N=mm
2
; second number:

10 Â ratio of proof stress R
p0.2
over tensile strength R
mmin
). ISO 898 does
not apply to high temperatures above 3008C or low tempe ratures under
À508C. Table 10 summarizes the important properties defined in ISO 898.
Another material group is also well established: screws made of stain-
less steels. Related properties for fasteners are defined in ISO 3506 [29] .
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
R
m
(MPa)
Minimum
proof stress
R
p0.2
(MPa)
Minimum
elongation
after
fracture

a
(%)
Minimum
vickers
hardness
HV 10
Maximum
vickers
hardness
HV 10
Example for
suitable Material
(not defined
in
ISO 3506)
A2-70 700 450 %24 — — X5CrNi-18-9,
X5CrNi1816
A2-80 800 600 %16 — — X5CrNi-18-9,
X5CrNi1816
A4-70 700 450 %24 — — X5CrNiMo17-12-2,
X2CrNiMo17-13-3
A4-80 800 600 %16 — — X5CrNiMo17-12-2,
X2CrNiMo17-13-3
C1-70 700 410 %8 220 330 X12Cr13
C1-110 1,100 820 %8 350 440 X12Cr13
C3-80 800 640 %8 240 340 X19CrNi16-2
F1-60 600 410 %8 180 285 X3Cr17, X6CrNb12
a
in ISO 3506 originally measured at manufactured screw as elongation over total length in mm.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Table 11 contains some properties of screws mad e 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 ele-
ment 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 R
p0.2
, 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. Fer-
ritic steels of grade F have a permanent ferritic grain structure at room tem-
perature, 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 condi-
tions, lightweight design or constructional elements (screws made of alumi-
num). AL5 and AL6 of Table 12 can be sensitive for stress corrosion
cracking, depending on their grain structure. Currently, additional alumi-
num 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 environ-
ment), 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
Nominal
A
s
(mm
2
)
R
m
(MPa) 300 400 400 500 500 600 800 900 1,000 1,100 1,200 1,400
k
R
(À) 0.6 0.6 0.8 0.6 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9
M1 0.458 0.06 0.08 0.11 0.10 0.14 0.17 0.22 0.25 0.31 0.34 0.38 0.44

M2 2.069 0.28 0.38 0.50 0.47 0.63 0.75 1.01 1.13 1.42 1.56 1.70 1.98
M3 5.000 0.68 0.91 1.22 1.14 1.52 1.82 2.43 2.74 3.42 3.76 4.10 4.79
M4 8.800 1.20 1.61 2.14 2.01 2.68 3.21 4.28 4.82 6.02 6.62 7.22 8.43
M5 14.20 1.94 2.59 3.45 3.24 4.32 5.18 6.91 7.77 9.7 10.68 11.7 13.6
M6 20.10 2.75 3.67 4.89 4.58 6.11 7.33 9.78 11.00 13.7 15.12 16.5 19.2
M8 36.60 5.01 6.68 8.90 8.34 11.1 13.4 17.8 20.0 25.0 27.5 30.0 35.0
M10 58.00 7.93 10.6 14.1 13.2 17.6 21.2 28.2 31.7 39.7 43.6 47.6 55.5
M12 84.30 11.5 15.4 20.5 19.2 25.6 30.8 41.0 46.1 57.7 63.4 69.2 80.7
M12 Â 1.5 88.10 12.1 16.1 21.4 20.1 26.8 32.1 42.9 48.2 60.3 66.3 72.3 84.4
M14 115.4 15.8 21.0 28.1 26.3 35.1 42.1 56.1 63.1 78.9 86.8 94.7 110.5
M14 Â 1.5 124.6 17.0 22.7 30.3 28.4 37.9 45.5 60.6 68.2 85.2 93.7 102.3 119.3
M16 156.7 21.4 28.6 38.1 35.7 47.6 57.2 76.2 85.7 107.2 117.9 128.6 150.1
M16 Â 1.5 167.3 22.9 30.5 40.7 38.1 50.9 61.0 81.4 91.5 114.4 125.9 137.3 160.2
M18 192.5 26.3 35.1 46.8 43.9 58.5 70.2 93.6 105.3 131.7 144.8 158.0 184.3
M18 Â 1.5 216.2 29.6 39.4 52.6 49.3 65.7 78.9 105.2 118.3 147.9 162.7 177.5 207.0
M20 244.8 33.5 44.7 59.5 55.8 74.4 89.3 119.1 134.0 167.4 184.2 200.9 234.4
M22 303.4 41.5 55.3 73.8 69.2 92.2 110.7 147.6 166.0 207.5 228.3 249.0 290.5
M24 352.5 48.2 64.3 85.7 80.4 107.2 128.6 171.5 192.9 241.1 265.2 289.3 337.6
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
M24 Â 2 384.4 52.6 70.1 93.5 87.6 116.9 140.2 187.0 210.3 262.9 289.2 315.5 368.1
M27 459.4 62.8 83.8 111.7 104.7 139.7 167.6 223.5 251.4 314.2 345.7 377.1 439.9
M30 560.6 76.7 102.3 136.3 127.8 170.4 204.5 272.7 306.8 383.5 421.8 460.1 536.8
M36 ( Â4) 816.7 111.7 149.0 198.6 186.2 248.3 297.9 397.2 446.9 558.6 614.5 670.3 782.1
M36 Â 3 864.9 118.3 157.8 210.3 197.2 262.9 315.5 420.7 473.3 591.6 650.8 709.9 828.2
M36 Â 2 914.5 125.1 166.8 222.4 208.5 278.0 333.6 444.8 500.4 625.5 688.1 750.6 875.7
M36 Â 1.5 940.3 128.6 171.5 228.7 214.4 285.9 343.0 457.4 514.5 643.2 707.5 771.8 900.4
M39 975.8 133.5 178.0 237.3 222.5 296.6 356.0 474.6 534.0 667.4 734.2 800.9 934.4
M48 1,475 201.7 269.0 358.6 336.2 448.3 538.0 717.3 806.9 1,009 1,110 1,210 1,412
M56 2,032 278.0 370.6 494.2 463.3 617.7 741.2 988 1,112 1,390 1,529 1,668 1,946
M64 2,678 366.4 488.5 651.4 610.7 814.2 977 1,303 1,466 1,832 2,015 2,198 2,565

M80 4,490 614.3 819.1 1,092 1,024 1,365 1,638 2,184 2,457 3,071 3,379 3,686 4,300
M90 5,594 765.3 1,020 1,361 1,275 1,701 2,041 2,721 3,061 3,826 4,209 4,592 5,357
M100 6,998 957 1,277 1,702 1,596 2,128 2,553 3,404 3,830 4,787 5,266 5,744 6,702
Boundary conditions: (1) Yield point controlled tightening; (2) Friction 
tot
¼0.16; (3) A
s
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. Â0.7); (2) for utilization of 
eq
¼90%; of R
p0.2
, multiply
relevant preload by 0.9; (3) yield strength ratio k
R
¼R
p0.2
=R
m
; (4) for angular controlled tightening, multiply relevant preload by
[1 þ0.3(1 Àk
R
)=k
R
].
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.