Series 07
Aerospace Materials 08
Fatigue Specimens for Sheet and
Plate Material
J.
Schijve
Fatigue Specimens for Sheet and Plate
Material
Fatigue Specimens for Sheet and
Plate Material
J.
Schijve
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Contents
Introduction 1
Characteristic aspects of experimental programs 2 Comparison of simple specimens 4
Criteria for selecting specimen type 6 Some experimental aspects 8
Summarizing conclusions 9 References 9
Fatigue specimens for sheet and plate material
Abstract - The usefulness of simp Ie sheet and plate specimens is discussed for various experimental research purposes. Specimens should be representati'!e as much as possible for the conditions offatigue problems in practice, which is more difficult to ach-;eve lor the fatigue crack initiation phase than for macro-crack growth. In many cases small specimens can not be recommended because of insufficieot similarity to the conditions of the engineering structure. Larger specimens have advantages for measurements of crack length and crack closure. The COr.1\l:lct tension specimen and a recently proposed derivative are asymmetric specimens, while the middle crack sDecimen, the central notch specimen and the double-edge notch specimen are symmetric. The latter specimens should be preferred for experimental reasons as weil as for reasons of a better similarity to the conditions of practical fatigue problems. A significant disadvantage ofthe asymmetric specimens is the high gradient ofthe stress intensity factor (dKJda).
Keywords -fatigue specimens; symmetric specimens; asymmetric specimens; K-gradient.
Nomenclature a CA CCT) D ECCT) K Kt Kf M(T) P = crack length = constant-amplitude = compact tension specimen = diameter
= extended compact tension specimen = stress intensity factor
= stress concentration factor = fatigue notch factor
= middle crack tension specimen = load = radius R = stress ratio S = stress t = sheet thickness V A = variable-amplitude W = specimen width
P
= geometry correction factorIntroduction
In a recent publication Piaseik, Newman,Jr and Underwood [1] have proposed a new type of specimen for application in fatigue and fracture investigations. The specimen has been defined as the "extended compact tension specimen" with EC(T) as an acronym. Several advantages of this new type of specimen were discussed with the classical compact tension specimen as a reference for comparison. In this paper the comparison is extended to include the center cracked tension specimen, the center notch tension specimen, and the double edge notch tension specimen. A survey of these types of simple specimens is given in Figure 1. In view of advantages and disadvantages ofthe specimens, characteristic aspects of experimental programs are briefly reviewed first. A comparison is then made between different types of simple specimens, which concentrates on the comparison between asymmetrie and symmetrie specimens. The relevanee ofthe specimens for experimental programs is then discussed. Finally, the major arguments are summarized in some conclusions.
Characteristic aspects of experimental programs
The literature on fatigue and fracture is extremely extensive, which is partly due to the large
number of variables involved. The broad scope of experimental fatigue programs can be
illustrated by the variety of incentives, types of specimens, and test load histories. Table I gives
a summary of different categories of specimens and load histories used in fatigue test programs.
Different types of specimens Different types of fatigue loads - Unnotched specimens (Kt'" I)
-
Constant-Amplitude (CA)-
simple riotched specimens, see Fig.l, Kt - Simple Variable-Amplitude (VA) loadweil known histories, e.g. two-step tests, tests with
- Joint specimens (welded, bolted, overioads, etc.)
riveted, bonded, lug type, etc.)
-
Complex V A load historiesComponents (full size component
-
Random load-Simulation of service load
testing)
-histories
- Full-scale testing (complete structure,
e.g. aircraft, cars)
Table 1: Different types of specimens and fatigue loads.
Going down in both columns ofthe table there is an increasing complexity ofthe test conditions. The main reason to accept such complex experiments is obvious, there is still a lack of
knowledge and accuracy in predicting the fatigue properties of engineering structures. As an
example, the fatigue strength of a riveted lap joint, abundantly used in aircraft structures, can not
be predicted from basic fatigue results of unnotched specimens. The same is true for welded
joints. As a consequence specimens are adopted which are supposed to be a relevant simulation
ofthe conditions in a structure. The same arguments apply to the load history, which must also
be representative.
Considering the more simple specimens shown in Figure 1, the question is for which purposes these specimens can profitably be used. Classes ofproblems to be mentioned are:
a Comparative experiments
b Compiling basic material data to be used for prediction purposes c Verification of prediction models
d Research on fatigue and fracture phenomena
Before commenting on these categories, it should be recalled that the fatigue life consists ofthree
phases as shown in Figure 2. As discussed in [2] crack initiation is a surf ace phenomenon, controlled by such aspects as surface roughness, surf ace damage (fretting, corrosion pits,
scratches, etc.), surface treatrnents (anodizing, nitriding, shot peening, etc.) and specific surface
material conditions (e.g. a soft cladding layer). In the second phase the crack penetrates into the
material away from the surface. Crack growth is then depending on the fatigue crack growth
resistance as a kind of a bulk property of the material. This property is no longer depending on
the surface conditions listed before. Final failure is the third and last phase, usually occurring as
.
,
a kind of a quasi-static failure. The occurrence of the final failure depends on the fracture toughness ofthe material. This property is related to the ductility of the material and material defects in a way which is different for crack initiation and crack growth. Some comments are now given on the problems a - d listed above.
Comparative experiments
A large percentage of experimental fatigue programs encompasses comparative fatigue tests. The purpose of such programs is to compare fatigue properties with respect to differences between materiais, surface treatments, production techniques, types of joints, environments, etc. In many practical cases possible improvements offatigue properties are the motivation for comparative test programs. The t;pe of specimen, the specimen dimensions, and the type of fatigue loading should be optimized for the real comparison to be made.
Compiling material data for prediction problems
The nature of prediction problems is that we extrapolate laboratory test results to practical conditions occurring in an engineering component. It requires "sirnilarity" between the laboratory experiment and the component conditions in service. The similarity approach is essentially based on the physically sound hypothesis that the same conditions imposed on the same system should have the same consequence. In the context of the present discus sion it should be translated as shown in Figure 3. Of course several refinements ofthe similarity approach are weil known. For instance, prediction techniques for the crack initiation fatigue life have been developed starting from similar strain cycles at the notch root instead of similar stress cycles. For crack growth predictions similar K -cycles have been replaced by similar ~1<...efT cycles in order to account for stress ratio effects. It anyhow is recognized that the similarity approach for predictions requires that all conditions are as much similar as possible. As an example, fatigue crack growth of through cracks can depend on the material thickness due to differences in plane stress/plane strain conditions. It implies that the crack growth prcr'erties should preferably be obtained from specimens with a similar thickness as in the structural application to be considered.
A more difficuIt issue is to maintain the similarity for the prediction of crack initiation fatigue lives. Because crack initiation is a surf ace phenomenon, it implies that the same surf ace conditions should apply. In Ol ~r words, the surf ace condition of the component should be simulated in the test specimen. This can be a difficult problem. Machining of the notch root should be done in a similar way. Also the root radius should be similar to avoid size effects. It easily leads to the idea that it might be much more effective to perform fatigue tests on the component itself.
The prediction of final failure based on the similarity approach offers problems of a different nature, especially for ductile materiais. The amount ofplasticity, and more specifically, the shape ofthe plastic zones should be similar in the specimen and the structure. Quite often this similarity requirement can not be satisfied.
Verification of prediction models
The verification of prediction models is usually done by comparing results of laboratory experiments with predictions based on results of simple laboratory experiments. Two typical examples are: (i) The prediction ofthe fatigue properties ofnotched specimens starting from the
basic fatigue properties of unnotched specimens. (ii) The prediction of fatigue lives and crack growth under Variable-Amplitude (VA) loading starting from results obtained in basic experiments under Constant-Amplitude (CA) loading. The basic CA tests and the VA tests, can be carried out in the same laboratory, which represents optimum similarity conditions for the purpose of verifying the prediction mode!. If a satisfactory agreement between predictions and test results is not obtained, the prediction model breaks down. If a good agreement is achieved,
a wider application to more realistic conditions can be considered.
Research on fatigue and fracture phenomena
The philosophy of science requires that the application of fracture mechanics should be preceded by a profound understanding of the relevant fracture mechanism. The mechanism should be studied by making observations and describing the fracture process. Microscopic observations are essential because "process zones" are smal!. Unfortunately, the materials are not transparent. Observations during fatigue cycling are therefore restricted to examination of the material surface. Of course the specimen can be sectioned to see the subsurface crack growth path, which is a destructive and tedious operation After completing a fatigue test the specimen can be opened and the fracture surface can be studied afterwards. This type of research work is a scientific challenge, but it requires minute and time consuming work. Special techniques are developed for this kind of research. Because the description of the fatigue process should be done in physical terms, knowledge of material science is essentia!.
Comparison of simpte specimens
The specimens in Figure I can be classified in two different groups: (i) Asymmetric specimens: CCT) and ECCT)
(ii) Symmetric specimens: M(T), CN(T) and DEN(T)
The asymmetric load introduction (load P) ofthe first group implies that the specimen is loaded under tension and bending at the same time. The free edge at the left hand si de in Figures la and I b does not offer any restraint to displacements perpendicular to the loading line. If crack growth occurs the asymmetry increases which increases the bending moment on the uncracked ligament. As a consequence, K does increase relatively fast for an increasing crack length. This is illustrated by Figure 4 by the geometry correction factor
p
,
generally defined as:K=pS[1ta
For the CCT) specimen the equation can be written as:
K=p~{7ta
Wt
(1)
(2)
with W as the specimen width and t as the material thickness. In the ASTM standard [3] the geometry factor adopted is:
.,
As shown by the curve for the C(T) specimen, the gradient of ~(a/W) is rather steep.
The stress-intensity factor for the EC(T) specimen was derived in [1] by the boundary-force method. Equations to fit the results were given as:
[P/(tJW)]FEC(T)
where FEC(T) =
cJI2
[1.4 +a]
[1 -ar
3!l G (4)G 3.97 - 10.88
a -
26.25a2 -
38.9a3
+ 30.15a4 -
9.27aS
a
=
aIW
In terms ofthe geometry correction factor Eq.(4) can be written as:
(5)
This geometry factor has also been plotted in Figure 4. Similarly to the C(T) specimen there is again a rather sharp increase of ~ for increasing crack length. In fact the K gradient is still steeper because of the [(rea) in Eq.(2). As a result plastic zone sizes in the asymmetric specimens increase rapidly during crack growth with significant and permanent crack opening as schematically shown in Figure 5b. For stilliarger plastic zones the uncracked ligament will become a plastic hinge. Of course this type of behaviour depends on the ductility of the material. The situation is obviously different for the symmetric specimens (Figures Ic, Id, Ie). In these specimens the central line of the specimen remains straight and there is a full restraint on horizontal displacements along the central line. Crack opening will be Ie ss and plastic zones remain smaller for a longer crack growth interval. If plastic zone tips reach the outer edges, net section yield occurs. The lower fuIlline in Figure 4 applies to the M(T) specimen and the same load as applied on the C(T) specimen. The other full lines are for higher loads on the M(T) specimen. It does require higher loads on the M(T) specimen to obtain similar Kvalues as obtained in the C(T) specimen. However, as illustrated by the lines the K-gradient (dKlda) is significantly lower for the M(T) specimen. The large difference is due to the difference between symmetry and asymmetry of the specimens.
A second important difference between the asymmetric and the symmetric specimen is related to the load introduction. In the asymmetric specimens it occurs by a pin loaded hole. The symmetric specimens, however, are c1amped at the specimen ends. It is usually supposed to lead to a homogeneous stress distribution at the specimen ends, which is theoretically not correct. A good c1amping of the specimen ends implies a homogeneous displacement. However, for sufficiently long specimens (say length/width ~2) this argument is insignificant for the net section of the notch or the crack. An essential difference between the asymmetric and the symmetric specimen remains: pinJhole loading versus c1amped specimen loading. The c1amped
end loading is a very weU defined load transmission, whereas that is less obvious for pinlhole loading. In theoretical analyses pin loading on a hole is approximated by some assumed pressure distribution on the bore of the hole. The cos<l>2 distribution is popular for this purpose. Other aspects to be considered in such an analysis are pin-deformation and friction between pin and hole. These features can be important for smaU cracks at loaded holes, but they are less significant for the C(T) and EC(T) specimen, where the crack tip is more remote from the loaded hole. ExperimentaUy an asymmetric pin loaded hole for load transmission is not attractive. In principle a smaU alternating rotation ofthe pin in the hole must occur in each load cycle. These alternating movements can lead to friction and fretting depending on lubrication. Although
skilled experimenters can manage this kind of problems, it should not escape attention.
Criteria for selecting specimen type
There are several criteria to be considered for selecting the type of specimen for aspecific research program, such as:
specimen production
ease of carrying out the experiments
reproducibility of test results
accuracy of test results
comparability to other test programs experimental efficiency and economy relevance to research topic.
It is not the intention to discuss these criteria in detail here, also because most aspects are weU known and accepted. However, some comments are appropriate in view of the different types of research programs and the differences between asymmetric and symmetric specimens. Two important questions to keep in mind are:
(i) Is the crack initiation phase or the crack growth phase the main issue of the research program?
(ii) Does the specimen provide arealistic similarity between the experimental conditions and the research topic to be studied?
The fatigue crack initiation phase
Options in Figure 1 are the EC(T) specimen with a rounded notch, the CN(T) specimen with a central notch and the DEN(T) specimen with two edge notches. Variables to be selected are the notch root radius, the specimen thickness, the notch root machining procedure, and possible surface treatrnents. Even for comparative experiments, the similarity between the specimens and the engineering conditions should be considered. It can imply that a realistic root radius and material thickness should be adopted to avoid size and thickness effects. It then should be realized that sheet and plate specimens have rectangular cross sections. In many cases it leads to initiation of corner cracks. However, if the background problem is related to circular cross sections non of the specimens in Figure 1 is useful.
Another example of comparative experiments is the evaluation of fatigue properties of Al-Li alloys with the classical 2024-T3 sheet material as a reference. Ifthe background problem is the application of sheet material for the skin of a pressurized aircraft fuselage, it should be recognized that riveted joints are probably the most fatigue critical issue. Comparative tests should then be carried out on riveted joints and not on the simp Ie notched specimens of Figure 1. 6
As amply shown in the literature, symmetrical notched specimens were extensively used for obtaining basic material fatigue data. Results revealed the notch sensitivity (e.g. the Kr Kt relation), as wel! as a size effect (e.g. the size ofthe root radius). It is general!y accepted that smal! root radii should be avoided for col!ecting material fatigue data. Smal! root radii results may suggest low Kf values which do not have a realistic engineering significance. Root radii should be selected to be in the range applied in real structures.
Symmetrically notched specimens were also abundantly used to verify cumulative damage rules, such as the PalrngrenIMiner rule. Other variants of the simple notched specimen, see Figure 6a and 6b, were also used for the same purpose. These specimens are stil! symmetrica!. It is difficult to see advantages ofthe EC(T) specimen for test programs on basic fatigue data and fatigue life prediction models for notch and size effects and V A loading.
A single edge notch specimen, SEN(T), see Figure 6c, was successful!y used in an extensive AGARD research program on fatigue crack initiation in an AI-alloy and the growth of short fatigue cracks [6]. As long as such cracks are still smal!, the nominalloading ofthe net section ofthis asymmetric specimen remains practical!y unchanged. However, a symmetric double edge notched specimens could also be used for the same purpose. Two notch roots in the same specimen have then to be observed, which appears to be more work. At the same time results from two notches in a single specimen become available. This dilemma should be recognized. The macro crack growth phase
Macro crack growth is no longer a material surface phenomenon. The variables affecting the fatigue crack initiation life are no longer a matter of concern, with the exception of environmental effects. The selection of a type of specimen for macro crack growth test programs thus appears to be more simple This is even more true for the crack growth specimens in Figure 1, because crack growth is supposed to occur as a through crack in these specimens. At first sight the crack length "a" is the single variabie to be studied. Complications ofthe latter concept are very weil known, such as the occurrence of crack closure, mixed mode cracking (e.g. shear lips), and the plane strain/plane stress transition (thickness effect).
In Figure 1 there are two asymmetric crack growth specimens, C(T) and EC(T), and one symmetrical specimen, M(T). Of course K-solutions for a crack growth specimen should be available. If a pure mode-I crack is assumed, K-solutions are no longer considered to be problematic within wel! defined specimen boundary conditions. Comparative crack growth experiments and test programs to obtain basic material crack growth data are usual!y carried out under CA loading. Prominent variables are the stress ratio R and the material thickness. As discussed before the gradient ofthe K(a) relation is quite different for the asymmetric and the symmetric specimens. For that reason the M(T) specimen should be preferred for comparative experiments as weil as for obtaining material crack growth data. This is even more true if comparative crack growth experiments should be made with a V A load history. If a mixture of cycles with high and low Smax values is applied, various plastic zone sizes occur along the crack growth path. That is a complication for the crack closure phenomenon during V A loading. It then should preferably occur in a way as much similar as possible as in the real structural component. As said before, in the asymmetric specimens of Figure 1 there is no constraint on the specimen edge displacements perpendicular to the loading line. However, for cracks in a real structure such a constraint will generally be present to a fairly effective extent. Even for an edge crack in a structure the bending deformations wil! usual!y be rather smal!. The symmetrical M(T) specimen 7
should therefore be preferred in view of the similarity of deforrnation constraints.
The above arguments were raised in relation to comparative experiments and material data test programs. Obviously they also apply to research programs to verify crack growth prediction models or to study fatigue crack growth mechanisms. It is purely a matter of the physical similarity to the engineering conditions in which we are interested.
Some experimental aspects
Specimen size and production
Sometimes the suggestion is heard that small specimens are "beautiful", which is supposed to be a positive feature. Similarly, it may be thought that small specimens are cheaper, which is highly questionable. Itcan be relevant ifthe specimens are made from an expensive and exotic materiaI. However, in general the material costs cover a very small fraction of the total costs of the experiments. Unfortunately we are sometimes obliged to use smal I specimens. Noteworthy examples are:
Properties in the short transverse direction of plate material can be obtained with small specimens only. The maximum length (or height) is equal to the plate thickness.
Properties of the material of a component which failed in service can be deterrnined on specimens cut from the component. That can imply limitations on specimen size.
Available testing machines with a low load capacity are not suitable for large specimens.
A vailable environmental chambers can set limitations to specimen dimensions.
In spite of these examples it should be clear that larger specimens have many advantages.
Specimen production to specific toleranees is easier, measurements of crack length, crack opening and crack closure are also easier and can be done more accurately. As pointed out in [1] an increased length of the specimen gives a better experimental accessibility, which can significantly facilitate various experimental observations to be made.
Test performance
Two major aspects ofperforrning a fatigue test are (i) clamping ofthe specimen in the fatigue machine, and (ii) carrying out various measurements during the fatigue test. Experimenters appreciate easy clamping procedures, but they are also aware ofthe fact that "accurate" clamping is a different issue. These aspects will not be discussed here, but it should be pointed out that alignment of the specimen needs considerable attention.
Crack length measurements and crack closure measurements can be made automatically, but it is still done manually or semi-automatically in many test programs. The potential drop method is used for automatic crack length measurements. The method appears to be more reliable for the MeT) specimen than for the qT) specimen. Automatic crack length measurements are essential for constant-t.K test in view ofthe required load shedding procedure. The M(T) specimen is also better suited for automatic load shedding because ofthe less steep K(a) relation in comparison to the asymmetrie specimens.
Crack closure measurements are still a subject of measurement technique problems. The problems are partly related to the deterrnination ofthe crack opening stress level at the transition between the non-linear and the linear part ofthe COD-P record. The result appears to depend on the location ofthe specimen, where the COD is measured. This issue will not be discussed any
further here. However, it is expected that the M(T) specimen is more suitable for exploring the crack closure behaviour than the asymmetrie specimens for reasons mentioned before.
Summarizing concIusions
In the present paper a discussion is presented on the usefulness of simple sheet and plate specimens for comparative tests, material data experiments, validation tests for prediction modeIs and research on fatigue mechanisms. Results ofthe discussion are summarized below.
I. Specimens should be designed to be representative as much as possible for the conditions of fatigue problems in practice. That is more difficuIt if the fatigue crack initiation phase is the main topic to be studied. In various practical cases a representative similarity can not be achieved by simple specimens. For macro crack growth the situation usually is more easy. 2. In many cases small specimens can not be recommended because of insufficient similarity to the conditions of the engineering structure. Small specimens can lead to unrealistic size effects. Small specimens are also undesirable from an experimental point of view. Larger specimens generally facilitate cxperimental observations (crack length measurements, crack closure measurements) and improve the reliability and accuracy ofthe results.
3. The C(T) and the EC(T) specimen are asymmetric specimens with a pin-Ioaded hole connection to the testing machine, whereas M(T), NC(T) and DEN(T) specimens are symmetric with clamped specimen ends. Symmetric specimens should be preferred for experimental reasons as weil as for reasons of a better similarity to the conditions of practical fatigue problems. A significant disadvantage ofthe asymmetric specimens is the high gradient of the stress intensity factor (dK/da) which is associated with the lack of constraint on defonnations perpendicular to the loading line and the asymmetry itself.
References
I. R.S. Piascik, J.C. Newman, Jr. and J.H. Underwood (1997) The extended compact tension specimen. Fatigue and Fracture of Engineering Materials and Structures, 20, 559-563.
2. J. Schijve (1996) Fatigue crack growth under variable-amplitude loading. Fatigue and Fracture, Vo1.l9, ASM Handbook, 110-133.
3. ASTM Standard E 561-86 (1986) Standard practice for R-curve determination.
4. G. Wällgren (1961) Review of some Swedish investigations on fatigue during the period June 1959 to April 1961. Report FF A-TN-HE 879, Stockholm.
5. H. Ostermann (1971) Stress concentration factors ofplate specimens for fatigue tests (in German). Laboratorium fijr Betriebsfestigkeit, LBF, Darmstadt, TM Nr.61.
6. P.R. Edwards. and J.C. Newman Jr (1990) An AGARD supplemental test program on the behaviour of short cracks under constant amplitude and aircraft spectrum loading. AGARD Report No.767, Short-Crack Growth Behaviour in Various Aircraft MateriaIs, paper 1.
p p W 1.5W i .... ~ ... ···{>gue crack
.-
,t
"
.
\ .l .... " ...1'85W
D = O.2W a W(
:~{5
mmho'.
".Fig.1 a Compact tension specimen.
10
s
0---> 2a
w
Fig.1c Middle crack tension specimen.
P
Fig.1 b Extended compact tension specimen with edge crack or edge notch.
s
o
--D
w
Fig.1 d Central notch tension specimen.
s
Fig.1e Double edge notch tension specimen.
crack micro crack macro crack final
nucleation growth growth failure
-
..
...
...
initiation period crack growth period
Kt K Klc K c
stress concentration stress intensity fracture
factor factor toughness
Figure 2: Different phases ofthe fatigue life and relevant factors.
I same conditions
I
+
fatigue life
IL-s_a_m_e __ o_-c_y_c_le __
---.l1
+
fatigue crack growth
same K-cycle two similar L -_ _ _ sy_s_te_m __ s ____ ~~ Similarity concept unnotched specimen root of notch, same material simple specimen ~ I---I~ complex cracked configuration same material
I
same consequenceI
same crack initiation lifesame da/dN
Figure 3: The similarity approach for fatigue predictions.
12 16~--~---~---~ , 14
/
12 10 8.
~~
.
:
~~/
' .: ...···
~
EC(T)
I
4 ... ) ...< ...
..
...
.
6 2 0.2 0.4 0.6 P' = P 0.8 afIN for C(T) 2afIN for M(T) 1.0Figure 4: Geometry correction factors for symmetrie and asymmetrie specimens.
o
--o
Fig. Sa Fig. Sb
crack opening
due to plastic zone
Fig. Sc
further crack opening
plastic hinge
Fig.6a
o
o
-
4 27 mm 2-hole specimen used by FAA [4] Kt=
2.7 Fig.6b d=8~
r=2 40 mm central notch used by LBF [5] Kt=
3.6 Fig.6c r=3.18 50 mmrl
-
rl
circular edge notch used by AGARD [6]
Kt
=
3.17Figure 6: Examples of simple specimens with notches.
Series 01: Aerodynamics
01. F. Motallebi, 'Prediction of Mean Flow Data for Adiabatic 2-D Compressible Turbulent Boundary Layers'
1997 / VI
+
90 pages / ISBN 90-407-1564-502. P.E. Skare, 'Flow Measurements for an Afterbody in a Vertical Wind Tunnel'
1997 / XIV
+
98 pages / ISBN 90-407-1 565-303. B.W. van Oudheusden, 'Investigation of Large-Amplitude 1-DOF Rotational Galloping'
1998 / IV
+
100 pages / ISBN 90-407-1566-104. E.M. Houtman / W.J. Bannink I B.H. Timmerman, 'Experimental and Computational Study of a Blunt Cylinder-Flare Model in High Supersonic Flow'
1998/ VIII
+
40 pages / ISBN 90-407-1567-X05. G.J.D. Zondervan, 'A Review of Propeller Modelling Techniques Based on Euler Methods'
1998 / IV
+
84 pages / ISBN 90-407-1568-806. M.J. Tummers / D.M. Passchier, 'Spectral Analysis of Individual Realization LDA Data'
1998 / VIII
+
36 pages / ISBN 90-407-1569-6 07. P.J.J. Moeleker, 'Linear Temporal Stability Analysis'1998/ VI
+
74 pages / ISBN 90-407-1570-X08. B.W. van Oudheusden, 'Galloping Behaviour of an Aeroelastic Oscillator with Two Degrees of Freedom'
1998/ IV
+
128 pages / ISBN 90-407-1571-809. R. Mayer, 'Orientation on Ouantitative IR-thermografy in Wall-shear Stress
Measurements'
1998 / XII
+
108 pages / ISBN 90-407-1572-610. K.J.A. Westin / R.A.W.M. Henkes, 'Prediction of Bypass Transition with Differential Reynolds Stress Modeis'
1998/ VI
+
78 pages / ISBN 90-407-1573-411. J.L.M. Nijholt, 'Design of a Michelson Interferometer for Ouantitative Refraction Index Profile Measurements'
1998/ 60 pages / ISBN 90-407-1574-2
12. R.A.W.M. Henkes I J.L. van Ingen, 'Overview of Stability and Transition in External Aerodynamics'
1998 / IV
+
48 pages / ISBN 90-407-1575-013. R.A.W.M. Henkes, 'Overview of Turbulence Models for External Aerodyna-mics'
Series 02: Flight Mechanics
01. E. Obert, 'A Method for the Determination of the Effect of Propeller
Slip-stream on a Static longitudinal Stability and Control of Multi-engined
Aircraft'
1997 I IV
+
276 pages I ISBN 90-407-1577-702. C. Bill I F. van Dalen I A. Rothwell, ' Aircraft Design and Analysis System
(ADAS)'
1997 I X
+
222 pages I ISBN 90-407-1578-503. E. Torenbeek, 'Optimum Cruise Performance of Subsonic Transport
Air-craft'
1998 I X
+
66 pages I ISBN 90-407-1579-3Series 03: Control and Simulation
01. J.C. Gibson, 'The Definition, Understanding and Design of Aircraft Handling
Oualities'
1997 I X
+
162 pages I ISBN 90-407-1580-702. E.A. lomonova, 'A System look at Electromechanical Actuation for Primary
Flight Control'
1997 I XIV
+
110 pages I ISBN 90-407-1 581-503. C.A.A.M. van der linden, 'DASMAT-Delft University Aircraft Simulation
Model and Analysis TooI. A Matlab/Simulink Environment for Flight
Dyna-mi cs and Control Analysis'
1998 I XII
+
220 pages I ISBN 90-407-1582-3Series 05: Aerospace Structures and
Computional Mechanics
01. A.J. van Eekelen, 'Review and Selection of Methods for Structural
Reliabili-ty Analysis'
1997 I XIV
+
50 pages I ISBN 90-407-1583-102. M.E. Heerschap, 'User's Manual for the Computer Program Cufus. Ouick
Design Procedure for a CUt-out in a FUSelage version 1 .0'
1997 I VIII
+
144 pages I ISBN 90-407-1584-X03. C. Wohlever, 'A Preliminary Evaluation of the B2000 Nonlinear Shell
Element 08N.SM'
1998 I IV
+
44 pages I ISBN .90-407-1585-804. l. Gunawan, 'Imperfections Measurements of a Perfect Shell with Specially
Designed Equipment (UNIVIMPI
Series 07: Aerospace Materials
01. A. Vasek I J. Schijve, 'Residual Strenght of Cracked 7075 T6 AI-alloy
Sheets under High Loading Rates'
1997 I VI
+
70 pages I ISBN 90-407-1587-402. I. Kunes, 'FEM Modelling of Elastoplastic Stress and Strain Field in
Centre-cracked Plate'
1997 I IV
+
32 pages I ISBN 90-407-1588-203. K. Verolme, 'The Initial Buckling Behavior of Flat and Curved Fiber Metal
Laminate Panels'
1998 I VIII
+
60 pages I ISBN 90-407-1589-004. P.W.C. Provó Kluit, 'A New Method of Impregnating PEl Sheets for the
In-Situ Foaming of Sandwiches'
1998 I IV
+
28 pages I ISBN 90-407-1590-405. A. Vlot / T. Soerjanto I I. Yeri I J.A. Schelling, 'Residual Thermal Stresses
around Bonded Fibre Metal Laminate Repair Patches on an Aircraft
Fusela-ge'
1998/ IV
+
24 pages / ISBN 90-407-1591-206. A. Vlot, 'High Strain Rate Tests on Fibre Metal Laminates'
1998 I IV
+
44 pages I ISBN 90-407-1592-007. S. Fawaz, 'Application of the Virtual Crack Closure Technique to Calculate
Stress Intensity Factors for Through Cracks with an Oblique Elliptical Crack
Front'
1998 I VIII
+
56 pages I ISBN 90-407-1593-908. J. Schijve, 'Fatigue Specimens for Sheet and Plate Material'
1998/ VI
+
18 pages I ISBN 90-407-1594-7Series 08: Astrodynamics and Satellite Systems
01. E. Mooij, 'The Motion of a Vehicle in a Planetary Atmosphere'1997 I XVI
+
156 pages I ISBN 90-407-1595-502. G.A. Bartels, 'GPS-Antenna Phase Center Measurements Performed in an
Anechoic Chamber'
1997 I X
+
70 pages I ISBN 90-407-1596-303. E. Mooij, 'Linear Quadratic Regulator Design for an Unpowered, Winged Re-entry Vehicle'
The usefulness of simple sheet and plate specimens is discussed for
various experimental research purposes. Specimens should be
representative as much as possible for the conditions of fatigue
problems in practice, which is more difficult to achieve for the
fatigue crack initiation phase than for macro-crack growth
.
In many
cases smal I specimens can not be recommended because of
insufficient similarity to the conditions of the engineering structure.
Larger specimens have advantages for measurements of crack
length and crack closure. The compact tension specimen and a
recently proposed derivative are asymmetrie specimens
,
while the
middle crack specimen, the central notch specimen and the
double-edge notch specimen are symmetrie. The latter specimens should be
preferred for experimental reasons as weil as for reasons of a better
similarity to the conditions of practical fatigue problems. A
significant disadvantage of the asymmetrie specimens is the high
gradient of the stress intensity factor (dKlda).
ISBN 90-407-1594-7
