A modified nominal stress method for fatigue assessment of steel plates with thermally cut edges

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Juha Peippo

A modified nominal stress method for fatigue assessment of steel plates with thermally cut edges

Thesis for the degree of Doctor of Science (Technology) to be presented with due permission for public examination and criticism in the Auditorium 1382 at the

Lappeenranta University of Technology, Lappeenranta, Finland on the 18th of December, 2015, at 12:00.

Acta Universitatis Lappeenrantaensis 684

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Finland

Reviewers Professor Per Jahn Haagensen

Department of Structural Engineering

Norwegian University of Science and Technology Norwegian

Dr. -Ing. Majid Farajian

Fraunhofer-Institut für Werkstoffmechanik IWM Germany

Opponent Assistant Professor Heikki Remes Department of Applied Mechanics Aalto University

Finland

ISBN 978-952-265-905-7 ISBN 978-952-265-906-4 (PDF)

ISSN-L 1456-4491 ISSN 1456-4491

Lappeenrannan teknillinen yliopisto Yliopistopaino 2015

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A MODIFIED NOMINAL STRESS METHOD FOR FATIGUE ASSESSMENT OF STEEL PLATES WITH THERMALLY CUT EDGES

Lappeenranta 2015 Pages 227

Acta Universitatis Lappeenrantaensis 684 Diss. Lappeenranta University of Technology

ISBN 978-952-265-905-7, ISBN 978-952-265-906-4 (PDF), ISSN 1456-4491 Thermal cutting methods, are commonly used in the manufacture of metal parts.

Thermal cutting processes separate materials by using heat. The process can be done with or without a stream of cutting oxygen. Common processes are Oxygen, plasma and laser cutting. It depends on the application and material which cutting method is used.

Numerically-controlled thermal cutting is a cost-effective way of prefabricating components. One design aim is to minimize the number of work steps in order to increase competitiveness. This has resulted in the holes and openings in plate parts manufactured today being made using thermal cutting methods. This is a problem from the fatigue life perspective because there is local detail in the as-welded state that causes a rise in stress in a local area of the plate. In a case where the static utilization of a net section is full used, the calculated linear local stresses and stress ranges are often over 2 times the material yield strength. The shakedown criteria are exceeded.

Fatigue life assessment of flame-cut details is commonly based on the nominal stress method. For welded details, design standards and instructions provide more accurate and flexible methods, e.g. a hot-spot method, but these methods are not universally applied to flame cut edges.

Some of the fatigue tests of flame cut edges in the laboratory indicated that fatigue life estimations based on the standard nominal stress method can give quite a conservative fatigue life estimate in cases where a high notch factor was present. This is an

undesirable phenomenon and it limits the potential for minimizing structure size and total costs.

A new calculation method is introduced to improve the accuracy of the theoretical fatigue life prediction method of a flame cut edge with a high stress concentration factor. Simple equations were derived by using laboratory fatigue test results, which are published in this work. The proposed method is called the modified FAT method (FATmod). The method takes into account the residual stress state, surface quality, material strength class and true stress ratio in the critical place.

Keywords: Fatigue, flame cut edges, stress analysis, residual stress

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Lappeenranta University of Technology, Finland.

Firstly, I would like to thank my supervisor Professor Timo Björk. His guidance, comments and motivation helped me throughout the research work for and the writing of this thesis.

I would also like to thank the following people for their advice on technical issues: Dr.

Timo Nykänen for his help, comments, tough questions, and ideas for developing the contents of this thesis; Dr. Risto Laitinen for his time and the advice he gave me about metallurgy issues; Emeritus Professor Erkki Niemi for his support at the beginning of my studies; Dr. Teuvo Partanen for his time and comments concerning the work; Matti Koskimäki, Lic.Sc., for his experience in arranging fatigue tests, and the laboratory staff of the Department of Mechanical Engineering for their help in carrying out the

experimental tests.

I thank my workplace teammates and my employer, Konecranes Corporation, for all support they gave me during this long working process. In addition, I want to express my gratitude towards FIMECC for their generous support during this thesis project.

I want to express my thanks to Professor Per Jahn Haagensen and Dr. Majid Farajian who gave valuable comments and suggestions for improving the manuscript.

I would also like to thank my opponent Professor Heikki Remes who kindly accepted this request.

Last, but not least, I would like to thank my wife Tiina and my children Sanni and Kaisa for their patience. They provided the much needed balance to my thesis work and were very understanding during the whole process.

Juha Peippo December 2015 Lappeenranta, Finland

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Nomenclature

CEV Carbon equivalent value

CGHAZ Coarse grained heat affected zone

D_CGHAZ Depth of CGHAZ

D_FGHAZ Depth of FGHAZ

D_HAZ Depth of HAZ

D_ICHAZ Depth of ICHAZ

FAT [MPa] Fatigue class, fatigue strength at 2 million cycles FATc,lin [MPa] Characteristic fatigue class at 2 million cycles,

relative value calculated using Nfcmod result and linear stress component.

FATc,Rtrue,ref=0 [MPa] Characteristic fatigue strength at 2 million cycles, Rtrue,ref = 0

FATcc [MPa] Characteristic fatigue class at 2 million cycles, constant FATmean/ FATchar ratio

FATcc,Rtrue,ref=0 [MPa] Characteristic fatigue strength at 2 million cycles, Rtrue,ref=0, FATmean / FATchar constant 1.37

FATchar [MPa] Characteristic fatigue class at 2 million cycles, ps (Survival probability) = 95 %

FATchar [MPa] Characteristic fatigue class at 2 million cycles, ps = 95 %

FATKt,mean [MPa] Mean fatigue class at 2 million cycles, stress calculation with Kt factor

FATm,Rtrue,ref=0 [MPa] Mean fatigue strength at 2 million cycles, Rtrue,ref = 0

FATmean [MPa] Mean fatigue class at 2 million cycles, p = 50 %

FEM Finite element method

FGHAZ Fine grained heat affected zone

HAZ Heat affected zone

HB Brinell hardness

ICHAZ Inter-critical heat affected zone

KT Kitagawa and Takahashi

LEFM Linear elastic fracture mechanics

OES Optical emission spectroscopy

SCHAZ Subcritical heat effective zone

S-N Stress vs. cycles

A [mm²] Cross-section area

a [mm] Crack size

a* [-] Material constant

a0 [mm] Short crack characteristic size

A5 [ % ] Ultimate elongation

A95% [mm²] Area, where stress is greater than 95 % of maximum stress

af [mm] Final crack size

ai [mm] Initial crack size

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aR [-] Roughness constant

Averagei [%] Moving average value, 5 results

B [mm] Width in general

b [-] Fatigue strength exponent

b’ [-] Fatigue strength exponent. Includes the size factor and surface quality factor.

C [mm/cycles] Material constant, crack growing speed

c [-] Fatigue ductility exponent

Cτ,R [-] Roughness correction factor for shear stress Cσ,R [-] Roughness correction factor for axial stress

c’ [-] Fatigue ductility exponent

Cchar [mm/cycles] Material constant, characteristic crack growing speed

CD [-] Size factor

CE,T [-] Temperature factor

Change [%] The value of the change

Cmean [mm/cycles] Material constant, mean crack growing speed

CR [-] Reliability factor

CS [-] Surface treatment factor

Cσ,E [-] Endurance factor

Cτ [-] Fatigue strength factor for steel

D [mm] Diameter in general

d [mm] Diameter of shaft

dequ [mm] Equivalent diameter of the non-shaft component

E [MPa] Young’s modulus

F [N] Force component

F(a) [-] Correlation factor that takes into account the crack position

Fexternal [N] External force

fu [MPa] Ultimate strength

Fx,y,z [N] Force in x, y or z direction

fy [MPa] Yield strength

H [mm] Height

HB [-] Brinell hardness number

HVmart [-] Vickers hardness number of martensite

I [mm⁴] Bending Moment of inertia

K [MPa] Monotonic strength coefficient

K^’ [MPa] Cyclic strength coefficient

Kf [-] Fatigue notch factor

KfC [-] Fatigue notch factor corrected with surface quality Ks [-] Hot-spot stress concentration factor

Kt [-] Elastic stress concentration factor

Ktr3 [-] Linear stress concentration factor at corner 3 Ktr4 [-] Linear stress concentration factor at corner 4

m [-] Wöhler curve exponent

M(a) [-] Correlation factor that takes into account the stress distribution through the plate thickness

Mb [Nmm] Bending moment

mfixed [-] Wöhler curve exponent, fixed

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mfree [-] Wöhler curve exponent, free

n [-] Strain hardening exponent, monotonic load

n’ [-] Cyclic strain hardening exponent

Nf [cycle] Number of cycles to failure

Nfc [cycle] Number of cycles to failure, calculated

Nfcmod [cycle] Fatigue time estimation base on FATmod method

Nft [cycle] Number of cycles to failure, tested

Nsample [pcs] Number of samples

Nt [cycle] Number of cycles in transition point

q [-] Notch sensitivity factor

R [-] Stress ratio. External load

r [mm] Radius or notch root radius

R² [-] The coefficient of determination

Ra [µm] Profile roughness, arithmetic average of absolute values

rA, rB [mm] Measured radius of the corner on side A and B

reff [mm] Effective radius

Rq [µm] Profile roughness, root mean squared

Rref [-] Reference stress ratio

Rtrue [-] True stress ratio

Rtrue,ref [-] Reference true stress ratio

Rz [µm] Average roughness value of the surface

Rz5 [µm] Arithmetic mean of the single profile elements of five bordering single measured distances

s [-] Material constant

Su,min [MPa] Minimum ultimate tensile strength

T [mm] Plate thickness

t8/5 [s] Cooling time (800^o – 500^o)

u [mm] Tolerance factor

W [mm³] Bending resistance

We [J] Elastic energy

Wp [J] Plastic energy

ρ [mm] Transition radius of notch

ν [-] Poisson’s ratio

α [deg] Angle

αangle [deg] Angular misalignment

σ ^[MPa] Stress in general

σ(x) [MPa Stress distribution function

ρ* [-] Micro-support length

σa,E [MPa] Endurance limit, amplitude at 2⋅10⁶ cycles

θangle [deg] Weld flank angle

σb [MPa] Bending stress component

σben [MPa] Shell bending stress

σgross [MPa] Nominal stress in cross-section

εgross [-] Nominal strain in cross-section

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σHS [MPa] Structural stress component σ1max [MPa] Maximum 1^st principal stress

σmem [MPa] Membrane stress

σyy [MPa] Stress component in material y-axis direction σmt [MPa] True mean stress in the material

σNL,max [MPa] Maximum stress value based on non-linear stress

calculation

σNL,min [MPa] Minimum stress value based on non-linear stress

calculation

σnlp [MPa] Nonlinear peak stress

σnom,max [MPa] Maximum nominal stress

σnom,min [MPa] Minimum nominal stress

σnom,net [MPa] Net nominal stress

εnom,net [-] Net nominal strain

∆u [mm] Distance from plate surface

∆x [mm] Distance between measured points

fForce [-] Coefficient for force load

fTemp [-] Coefficient for temperature load

α_angle [deg] Joint angle

∆σf [MPa] Fatigue strength

∆σ0 [MPa] Fatigue limit at selecter R of unnotched speciment

∆σKt [MPa] Stress range calculated with notch factor Kt

∆σKf [MPa] Stress range calculated with notch factor Kf

∆σKfC [MPa] Stress range calculated with notch factor KfC

∆σlin [MPa] Stress range base on linear stress calculation

∆σNL [MPa] Stress range base on non-linear stress calculation

∆σnotch [MPa] Stress range at the notch

∆σref [MPa] Reference stress range

∆σref1 [MPa] Stress range base on Kt – factor

∆σref2 [MPa] Stress range base on Kf – factor

∆σref3 [MPa] Stress range base on KfC – factor

∆σref4 [MPa] Stress range base on KfCR – factor and Rtrue = 0 value

∆T [C°] Temperature difference

∆Κ _[_MPa _m_] Range of stress intensity factor

∆Κth [MPa m] Range of threshold intensity factor

∆Κc [MPa m] Range of critical intensity factor

∆εe [-] Elastic strain range

∆εp [-] Plastic strain range

ε [-] Strain in general

εa [-] Strain amplitude

εf’ [-] Fatigue ductility coefficient

εsg [-] Strain gauge result

σf’ [MPa] Fatigue strength coefficient

σr [MPa] Residual stress

∆ [-] Range

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∆σKfCRtrue,ref=0 [MPa] Stress range calculated with notch factor KfC taking into account Rtrue effect = KfCRtrue,ref=0

Indices

1,2 Component number

i Index

max Maximum

mean Mean value

min Minimum

n Normal

nom Nominal

dev Deviation

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1 Introduction

A new theoretical approach is created to solve the fatigue strength of cut plates that have been made of different steel grades. This theory is based on the combination of theories and models by Ramberg-Osgood, Neuber, Lawrence and Smith-Watson- Topper.

Experience has shown that the FE-method and direct utilization of the nominal stress method gives some times quite conservative estimation for fatigue prediction and lead to the need to increase material thickness or redesign of detail. This leads directly to the questions weight-optimization, cost optimization, manufacturability and availability.

The great questions of modern industry.

1.1 Background

Thermally cutting is very common and widely used method in the plate parts

manufacturing process. Numerically controlled thermal cutting is a cost-effective way to make prefabrication for components before the final assembly. The number of work steps is designed to minimize the increasing competitiveness. This has led to the practice of holes and openings in the plate parts being produced by thermal cutting methods. From the fatigue life perspective this is problem because there is local detail in the as-welded state that causes increased stress in a localised area of the plate. In a case where the static utilization of the net section is high, the calculated linear local stresses and stress ranges are often over 2 times the material yield strength and the shake down criterion is exceeded [1] [2]. Therefore, this study is aimed at determining the fatigue strength of thermally cut plate edges under conditions of high stress concentrations.

Commonly used calculation methods will be compared with the fatigue life test results and a new, more accurate nominal stress based method will be developed in this work.

Fatigue assessment of structures with flame cut plates are included in design rules and standards, such as SFS-EN 1993-1-9 [3], EN 13001-3-1 [4] and IIW document XIII- 1965-03 [5]. The main assumptions in presented sources are that the residual stress state is similar between a flame cut edge and welded structure. This means that whether the stress from an external force is compression or tension, its effect on crack propagation is equal. The most commonly used design rules for the fatigue life estimation of cut edges, are based on the nominal stress approach. Even if the nominal stress method is quite easy to use, the nominal stress determination itself can be quite complicated, for example in case in Fig. 1. In cases where the commonly used FE-method is used in stress analyses the nominal stress may be difficult to establish. The FE-method makes it possible to reduce the design time of a new product, minimize the weight and material costs and increase the safety of the product if the designer is familiar with fatigue design.

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Fig. 1 An example of a welded steel structure, where the structure weight has been minimized by using holes in the webs of beams [6].

The problem is how the designer manage high stress peaks which FE-method takes visible. Common constructional materials, e.g., steel and aluminium are ductile. The static design of the structures made of ductile material is normally reached without the need to consider the local stresses. It means that the local yielding is allowed and the surrounding material can carry the external load. This way of design is permitted, if the loads are static. The loads are static when the number of force reversals is a few

thousand. The pressure vessel design standard gives a limit of 500 cycles and Hobbacher has given a stress based limit in reference [5]. If the limited number of reversed cycles is exceeded, a fatigue assessments is required. According to SFS-EN 1993-1-1:1992 [7] and SFS-ENV 1993-1-1:2005 [8], the fatigue should be checked when the structure is subjected to an alternating load.

Over the last ten years, the material manufacturers have concentrated their development efforts on high strength steel structures. Current quench and tempering, together with continuous annealing process, make it possible to produce high strength steel whose ultimate strength can be up to 1200 MPa. The use of the high strength steel has increased in recent years. One driving force behind the increasing utilization of high- strength steels the hope of obtaining good, and even improved, structural performance at the lowest possible weight and cost. Generally, overall economy is the deciding factor for the final product or part. Decisive economic factors include production economy, material costs and, increasingly, life cycle costs. The term ‘life cycle cost’ refers to all the costs and benefits of a product over its entire fatigue life. A complex cost analysis of a product is needed to determine life cycle cost of the product. [9, 10]

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The low alloy steels S235, S355 and high alloy steel S960QC have been selected in this thesis, because recent test results have shown that the fatigue durability of the base material increases by increasing the strength of material. S235 and S355 are commonly used structural steel grades in the steel industry, while S960QC is a high-strength steel that has been developed to meet the evolving needs of the steel industry. The test samples manufacturing methods, residual stress states and external load’s stress ratio R have been varied in tests. The selected cutting methods were oxygen-, laser- and plasma. A couple of reference samples have been made by machining and some test parts have been annealed before testing [11, 12].

The shapes of the test samples are derived from the real products. A characteristic of the detail is that the stresses concentration is very large in the local area and the

manufacturing method is thermal cutting. Even if the geometry seems very simple, determination of the nominal stress is difficult or even impossible. In static calculations, checks can be made using the principle force divided by area, but stress determination to fatigue life calculation is not so simple. This can be a complicated problem for designers and the wrong stress level selection can cause a conservative fatigue life estimation that can increase the product weight.

1.2 Literature survey

The fatigue life behavior of tests of specimens with thermally cut test edges pieces have been studied in the past. Fatigue life tests have been carried out, almost without

exception, on straight standard test pieces. However, fatigue life test results for notched thermally cut specimens were not found in the earlier test results. Some previous research results, and a summary of key results are given in following paragraphs.

Plecki et al. [13] showed that the fatigue life is strongly influenced by the surface roughness of the oxygen cut. A high strength, low alloy ASTM A572 steel and quenched and tempered steels A514 were investigated. The reported fatigue life was longer for higher strength steel A572 than lower strength steel A514 [14].

Ho et al. [15] have analyzed the influence of the cutting method on fatigue resistance.

The plasma and oxygen gutting methods were selected in this study. A572 and A514 steel were tested in this investigation. They found that the fatigue life was slightly higher for the plasma cut surface than the oxygen cut surface. The reason was that the plasma cut surface had a smoother surface than the oxygen cut surface. The fatigue life resistance was also higher for A572 steel than A514 steel [14].

Thomas [16] has reported on the impact of the quality of the cut edges on the fatigue durability for S355 steel. Plasma cut methods using air and oxygen were used in this investigation. The results indicate that the cutting parameters have a significant effect on durability. The reported reason was the different characteristic surface and

microstructural features.

In the references, [17] and [18] were reported that the microstructure of the material is less important than the geometry of flame-cut surface in determining the fatigue strength. In the same reports it was indicated that the residual stress state and mean

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stress are important factors in fatigue life prediction. The compressive residual stress in the plate gives a longer fatigue life than tensile residual stresses.

Laura et al. [19] evaluated the influence of the different plate shearing method to fatigue life durability. The test pieces were manufactured using laser cutting- and mechanical shearing. The cutting surfaces were honed. The main results of this investigation were the defects that generated at the cut edges during laser cut and shearing process mainly governed the fatigue behaviour of high strength steel plates. When the cut edge defects were removed, the fatigue life was equal to the fatigue life resistance of the base material. This report also mentioned that the crack propagation resistance of the high strength steel was low, as they had limited toughness.

Maronne et al. [20] investigated different grades of carbon and micro-alloyed steels.

High cycle fatigue tests were performed on nine steel grades with ultimate tensile strengths from 300 MPa to 600 MPa. It was shown that the roughness that the cutting process generates decrease the fatigue strength of the material. It was concluded that the manufacturing process had detrimental effect on the fatigue resistance

Sperle [9], in his survey of high strength steels with yield stress up to 1200 MPa found that material strength has no influence on the fatigue strength of welded joints. The reason is the sharp notch or crack at the weld toes. Sperle also reported that when the stress concentration is moderate, the yield strength of the base material can affect the fatigue resistance.

Sperle [12, 21] presented his results of investigations on the effects of quality of cut plate edges in the IIW document. He investigated the fatigue strength of rolled plate specimens with machined, laser, plasma and oxygen cut edges. The results show that the fatigue resistance of high quality laser and plasma cut edges can reach the same level as a steel plate with machined edges. Sperle has also provided a tentative

recommendation for the yield strength of the material influence on fatigue strength as a function of surface roughness.

Abilop et al. [22] investigated the fatigue behaviour of normal construction steel S355 and the higher strength steel S690. The results show that the S690 steel has a higher fatigue crack initiation resistance than the S355 steel in the high cycle fatigue life area.

The fatigue crack propagation resistance was lower for the S690 steel grade than S355.

In the results, it was mentioned that there was not an advantage in using the S690 steel for a structure whose fatigue life was dominated by crack propagation, rather than crack initiation. Anders et. al [23] presented similar of results for pressed steel components, for yield strengths between 314 MPa to 639 MPa. The reported fatigue tests were made with smooth specimens.

Laitinen et al. [11, 24] investigated the yield strength effect on the fatigue resistance of base materials with different edge surface qualities. Several strength classes of the materials were used in this investigation. The manufacturing methods were machining, laser- and plasma cutting. The results showed that the fatigue resistance of the plates increased by increasing the yield strength. The fatigue durability of the laser cut samples was lower than plasma cut samples, whose yield strength was 500 MPa or lower. The

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fatigue resistance of the machined and laser cut samples that were made of ultra-high strength steel were almost at the same level.

Meurling et al. [25] made fatigue tests to determine the difference in fatigue properties of laser cut and sheared test pieces. They concluded that higher strength steels were more sensitive to the cutting method than lower strength steel lower. In several cases shearing produced a lower fatigue strength than laser cutting. In this investigation surface defects sizes were larger after shear cutting than after laser cutting. That was the main explanation for fatigue strength results.

Piraprez[26] analyzed the effect of preheating and shot-peening on the fatigue life strength of oxygen cutting surfaces. Based on the fatigue test results, shop-peening after cutting increased the characteristic (ps = 90%) fatigue resistance by 30 to 35 MPa and preheating by about 25 MPa.

Chiarelli et al. [27] reported that the fatigue strength of plasma cut specimens in Fe510 steel was at the same level as milled specimen. The beneficial residual stresses that were formed in plasma cut edges were reported to be the reason for that.

Barsoum et al. [28] examined the residual stress effect on the fatigue life of welded structures. In this investigation, the FE-method was used in residual stress state determination. The temperature results from the FE-models were compared with measured results. The measured and calculated results were close together. They mentioned that the compressive residual stresses had a beneficial influence on the fatigue resistance.

In the references, [29, 30, 28, 31] the effect of a residual stress state on the predicted fatigue life of welded detail was investigated. The main result was that the compressive residual stress state had an improving effect on the fatigue resistance of welded details and, on the other hand, the tensile residual stress state decreased the fatigue life

strength.

Belassel et al. [32] analyzed the relaxation of the residual stress in loading state where the applied loads exceed the cyclic yield strength of the material. The main results were the residual stress relaxation is a function of the applied load and the initial stress and also small plastic deformation in the specimens can relax the initial residual stresses.

Farajian et al. [33] reported the results of the residual stress relaxation under the static and cyclic loading. They investigated to relaxation of residual stresses in the welded detail. The results of this investigation show that some relaxation happens during of firsts few loading cycles and after that the residual stress state is almost constant.

Rörup et al. [34] investigated the influence of mean compressive stresses on the fatigue resistance of a welded structure. The detail was a plate with a longitudinal stiffener with non-load carrying fillet welds. The specimens were made from structural steel S355 J2 G3.

The authors concluded that the level of residual stress has a strong influence on fatigue life resistance under a compressive cyclic load.

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Mäntyjärvi et al. [35] and [36] evaluated the influence of cutting methods on the

fatigue life of ultra-high strength steel. Milling, water jet and laser cutting methods were used in this study. According to Mäntyjärvi [35] “there were no significant differences between milling and water jet cutting”. The lowest fatigue life resistance was observed in the laser cut specimens.

1.3 Goals and methods

The goal of this thesis is to establish a new calculation method to evaluate fatigue strength of cut edges of plates prepared from different steel grades and cut by different processes.

The goal will be reached by developing theoretical analysis, experimental tests and applying numerical simulation (FEM).

1.4 Scientific contribution

In this Thesis a novel design method to predict the fatigue strength of cut edge will be presented. This advanced method takes into account in addition to normal parameters such as stress range and notch shape, also the ultimate strength of the plate, roughness and residual stresses on the cut surface and applied stress ratio. This Thesis is the first proposal to combine those effects in one theoretical model.

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2 Materials

Three different materials were selected in this examination. Two of these were

structural steels called S235J2G3 and S355J2G3 and the third one was a high strength steel called S960QC. All of these steels are weldable steels and flame cutting is a suitable engineering workshop procedure to cut plates into shape [37]. However, the weldability of structural steels is better than high strength steel, because the carbon equivalent value (CEV) of high strength steel is typical higher than structural steel. The structural steels up to 420 MPa are specified in EN 10025 standard. Higher strength class steel is not yet specified in that one standard. To keep this investigation as close as possible to real life designer work, no material properties tests were made to clarify the actual static properties of the three steel grades. The standard EN10025 gives the minimum yield strength of the S235 as 235 MPa and the ultimate strength can vary between 340 MPa to 470 MPa, when the thickness area is below 16 mm. Respectively, the same standard gives a minimum yield strength of 355 MPa and the ultimate strength capacity can be between 490 MPa to 630 MPa for S355J2G3. The ultimate elongation is about 20 % for both of these mild steels. The steel manufactures data sheet gives a yield strength value of 960 MPa and an ultimate strength value of 1000 MPa for high strength steel S960QC. The minimum ultimate elongation that manufactures guarantee is 7%. It means that the ultimate elongation of the high strength steels is about half of the

ultimate elongation of the mild steels that were used in this investigation. The static material properties are tabulated in Table 1.

Table 1. Mechanical properties of test materials. Plate thickness area under 16mm. [38, 39]

fy fu A5 E

S235J2G3 235 MPa 340-470 MPa 24 % 207000 MPa

S355J2G3 345 MPa 490-630 MPa 19 % 207000 MPa

S960QC 960 MPa 1000 MPa 7 % 207000 MPa

Table 2 presents a comparison of the typical chemical compositions for the steels used in the tests, according to EN 10025 and manufacture’s data sheet. It is possible that the S960QC steel includes grain-refining elements, such as aluminium, niobium and titanium.

A couple of test samples were selected for chemical analyses. These analyses were carried out in SSAB’s research laboratory in Raahe. The total number of samples was 19 pcs. The raw material of 7 samples was S235 and 11 samples were manufactured using S355 and one sample’s raw material was high strength steel S960QC. The chemical components were evaluated with optical emission spectroscopy, OES. The results of the analyses were tabulated in Appendix 1. The nominal values of the chemical consumption will be given in the Table 2.

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Table 2. Compositions of materials. [%] [38, 39]

C Si Mn P S N Cu Ti Note

S235J2G3 0.19 - 1.50 0.035 0.035 - 0.60 S355J2G3 0.23 0.60 1.70 0.035 0.035 - 0.60

S960QC 0.11 0.25 1.20 0.029 0.010 0.070 (1)

(1) In addition, niobium (Nb), vanadium (V), molybdenium (Mo) or boron (B) may be used as alloying elements, either alone or in combinations

The Carbon equivalent value (CEV) and approximation hardness of martensite has been calculated with Equations (1) and (2), based on the results in Appendix 1. The average values of CEV values and the estimations for the hardness of the martensite have been collected in Table 3. The literature values of CEV values have been given in the same Table [40, 41, 42].

15 Cu Ni 5

V Mo Cr 6

C Mn +

+ + + +

+

=

CEV (1)

294 C 884⋅ +

mart =

HV ₍₂₎

Table 3. CEV values and estimation of hardness of martensite, based on chemical component analyses and nominal CEV values, based on material standard EN 10025 and the manufacturer’s data sheet in reference [43, 44].

Based on chemical analyses Literature values

CEV HVmart CEV

S235J2G3 0.290 411 0.35

S355J2G3 0.370 405 0.45

S960QC 0.513 368 0.52

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3 Plate cutting

3.1 Plate cutting methods

Fabrications of steel structure have a need to cut the steel plates into desired shapes.

Various methods exist for cutting steel plates. The plate cutting methods can be divided into the mechanical and the thermal cutting methods. The list of the main cutting methods is given in Fig. 2. The best method for a given situation depends on the thickness of the plate and the configuration of the steel being cut [45, 46, 47].

Fig. 2 The classification of the steel plate cutting methods.

The common processes that are used to cut the steel plates are thermal cutting methods.

The methods are easily automated and the methods can be used to cut complex shapes to the plate. When the thickness of the steel plate is 10 mm or larger, the thermal cutting methods are almost the only methods used. The suitability of different thermal cutting methods to different thicknesses of the steel palate is presented in Fig. 3 [47].

Cutting methods

Thermal cutting

Oxygen cutting Laser cutting Plasma cutting

Mechanical cutting

Guillotine shearing Punch shearing

Dial shearing Water jet

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Fig. 3 Suitability of the various cutting methods for different material thicknesses of steel plates.

Gas, Oxygen cutting process is common and perhaps the most used cutting process in industry. The flammable gas is used in gas cutting process. Normally used gas are either acetylene or propane. The gas burns in oxygen and produces a high temperature. In the process the flame preheats the work piece fist and when a sufficiently high temperature has been reached a jet of oxygen produces the cut by actually burning the metal and the gas jet blows out liquid slag of the cut. [39, 44]

The plasma method is very suitable for cutting, when the material thickness is less than 50 mm. In plasma cutting the needed heat produced different than in gas cutting, where needed heat produced primarily by burning the material using the oxygen in the cutting jet. In plasma cutting process the metal is melted and the molten material blown out of the cut by the pressure of the plasma jet. [42, 48]

A laser beam is also suitable for cutting. The thermal effects are small due to low heat input and the precision of the cut is excellent. When high productivity is required and the material thickness is relatively small, laser cutting is a suitable cutting method. The normal material thickness for laser cutting is smaller than 15 mm. Laser cutting can also be used for many non-metallic materials. [48].

The guillotine, punch and dial shearing are processes, in which the shearing is

performing with mechanical pressure. These methods are generally useful for cutting edges, angles and holes in the plates.

Abrasive water jet cutting is a cold, non-thermal, cutting method. The cutting system uses high-pressure water, which is passed through a fine bore nozzle into forms a coherent, high velocity jet. The operating pressures in the cutting region is normally

15 mm

60 mm

250 mm

0,1 1 10 100

Laser Plasma Oxygen

Thickness [mm]

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between 700 bar to 4000 bar and the kerf width is, approximately, 2 mm. Powerful jets are capable of cutting 100 mm thick steel plates [46].

3.2 HAZ – heat-affected zone

The surface part of thermally cut steel experiences a short-term heating and the

temperature is near the melting point of steel. The cut surfaces cool down quickly after cutting. That temperature change cause changes in the microstructure and properties of the materials. The cooling time from 800 ^oC to 500 ^oC, a so called t8/5 time, can vary quite much, depending on the cutting method, cutting parameters and dimensions of the cutting plate. Due to the quick temperature change in the cutting process the cut surface and material below the cut undergoes changes in the microstructure that are similar to the HAZ of welded joint. Typically the hardness of the outermost surface increases due to the thermally cutting process. If the cooling time is too fast, the cut surface may become too hard and brittle and susceptible to cold cracking. Maximum allowed hardness values of the cut surfaces are given in the standard EN 1090-2, [49] to avoid too hard and too brittle surfaces. There is a soft zone below the hard surface. The width of both zones, as well as the hardness level, depends on the cutting method and cutting parameters, as well as on the carbon contents of the cutting surface. The higher carbon content comes from the material which was melted during the cutting. [17, 50, 51]

The HAZ below under the cut surface can be divided into four regions: coarse-grained HAZ (CGHAZ), fine-grained HAZ (FGHAZ), inter critical HAZ (ICHAZ) with partially transformed microstructures and subcritical HAZ (SCHAZ) with tempered microstructures. The width of the HAZ is a function of the cutting method, carbon level and the cutting speed. A schematic illustration of the HAZ of the thermally cut edge is given in the Fig. 4. The width of the HAZ is wider on the nozzle side than the bottom side of the plate [17, 47, 48, 52, 53].

Fig. 4. Schematic representation of the HAZ for the thermal cut edge and the relative width of heat effective zones for laser, plasma and oxygen cut edges [17, 47, 54].

Cutting direction

Relative width of the HAZ (D_HAZ) Laser cutting 1

Plasma cutting 5 Oxygen cutting 20

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3.3 Classification of thermal cuts

The international standard ISO 9013 [55] applies to materials that are suitable for oxygen, plasma and laser cutting processes. The standard is relevant for following material thicknesses: flame cuts from 3 mm to 300 mm, plasma cuts from 1 mm to 150 mm and laser cuts from 0.5 mm to 40 mm. The most important terms concerning the work piece is given in ISO standard and in Fig. 5 [55].

Fig. 5 The terms related to the cutting process of the work piece. [55]

The flame cut surface quality has been divided in dimensions of the quality of the cut surface and dimension tolerances of the work piece. The perpendicularity and angular tolerance is controlled with factor u, the surface quality is controlled with factor Rz5. The accuracy of u factor has been divided into five different ranges. The surface quality is divided in four different ranges in the ISO 9013 standard. The accuracy of dimensions has been divided into two classes, class 1 and class 2. The limits of deviations are tabulated in Table 4. The graphical illustrations of the tolerance factor u and the

roughness factor Rz5 are given in Fig. 6 and Fig. 7. In ISO 9013:2002 it is specified how the cut surface tolerances should be measured.

1 Torch

2 Nozzlep kerf width 3 Beam

4 Kerf 5 Start of cut 6 End of cut

T Work piece thickness B Nozzle distance C Advance direction D Top kerf width E Cut thickness F Length of cut G Bottom kerf width H Cutting direction

H C

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Table 4. The limit deviations for nominal dimensions tolerance class 1 and 2. [55]

Work piece thickness

Limit deviations for nominal dimensions

Tolerance class 1 Tolerance class 2

Nominal dimensions Nominal dimensions

>0<3 ≥3<10 ≥10<35 >0<3 ≥3<10 ≥10<35

T≤1 ± 0.04 ± 0.1 ± 0.1 ± 0.1 ± 0.3 ± 0.4

1<T≤3.15 ± 0.1 ± 0.2 ± 0.2 ± 0.2 ± 0.4 ± 0.5 3.15<T≤6.3 ± 0.3 ± 0.3 ± 0.4 ± 0.5 ± 0.7 ± 0.8

6.3<T≤10 - ± 0.5 ± 0.6 - ± 1 ± 1.1

10<T≤50 - ± 0.6 ± 0.7 - ± 1.8 ± 1.8

Fig. 6 Perpendicularity or angularity tolerance u, according to ISO 9013:2002. The determination of u dimension is also given in figure. [55]

Range 1 Range 2 Range 3 Range 4 Range 5

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Fig. 7 The mean Rz5 value of the profile.

In IIW document XIII-823-77 [56], the surface quality of cut edges has been divided into four different structural classes, based on how critical the detail is under the design.

The main criteria are given in Table 5.

In reference [56], recommendations are given as to how the different class of structure members should be selected. For example, the crane applications document gives instructions concerning the selection.

Class I: Important members that are subjected to tensile fatigue load or impact load.

Class II: Important members that are subjected to static load or compressive fatigue load.

Class III: Members of ordinary importance for which are subjected to static load.

Class IV: Members of ordinary importance on which load condition is not severe.

Table 5. Quality criteria for gas cut surfaces not being subjected to welding.

Class of structural

members I II III IV

Surface roughness [µm] 50 100 200 500

Depth of notches [mm] 0 1 2 3

Range 1 Range 2 Range 3 Range 4

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When we comparing quality values in Table 5 with ISO 9013, it is observed that the surface roughness requirements are similar.

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4 Definition of stress components

Fatigue strength analyses of welded components required rather accurate stress

calculations. Sometimes, it can be difficult to decide upon the level of accuracy, which one should choose for a fatigue strength analysis. Normally, a welded structure has several geometric features that act as stress raisers. These effects can be global or local [57, 58, 59, 5].

The traditional way is to divide the total stress distribution of the component into three different categories:

• Nominal stress component

• Structural stress component

• Non-linear peak or peak stress

4.1 Nominal stress

The nominal stress is normally calculated by simple formulas of elastic theory.

Normally a stress calculation is based on basic cross-section properties, such as area A, bending resistance W or bending moment of inertia I. However, the effect of certain global geometric discontinuities has to be included into the nominal stress calculation.

So called macro geometric effects are presented in reference [5]. This type of feature can be for example, the shear lag effect in a wide flange [57].

In Fig. 8, an example of the nominal stress determination of the plate is illustrated. A hole was prepared in the plate. The diameter of the hole is assumed to be small

compared with the other dimensions of the plate. The hole is considered small when the diameter of the hole is smaller or equal than 5 % of width of the plate [60]. In these case where holes are small the cross section values can be calculated using net section values and holes are not considered in the cross section properties calculation. It means the nominal stress at the cross section a-a and b-b is the same at the outermost edges of the plate in Fig. 8.

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Fig. 8 The determination for nominal stress at the cross section a-a and b-b. In the figure it has been assumed that D < < H. The nominal stresses at the cross sections a-a and b-b are same.

4.2 Structural stress

Structural stress σHS, hot-spot stress, is a linear stress distribution in the cross section of the plate. The hot-spot stress can be calculated by using strain gauge measurements, FE- calculation or predefined parametric formulas. The structural stress is divided in two different stress components: uniform membrane stress across the plate thickness and linear shell bending stress component. The stress separation into three components is given in Fig. 9. The needed Equations to stress separation are given in Equations (3) - (5). The Equation for hot-spot stress calculation is given in Eq. (6). [61, 57]

Fig. 9 The Stress classification through the material thickness. θangle is weld flank angle and αangle is misalignment angle.

Membrane stress component:

∫

^⋅

=

T

mem x dx

T1 ₀ ( ) σ

σ (3)

T

θ_angle

α_angle

x

y F_n σ(x)=σ_mem+σ_ben(x)+σ_nlp(x)

b b

n n

W M A

F

−

=

= σ σ

Wa-a = Wb-b and Aa-a = Ab-b

if D << H

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Bending stress component:

∫

^⋅ ⁻ ^⋅

=

T

ben T x dx

T² ₀ x ) (2 ) 6 (

σ

σ ₍₄₎

Non-linear peak component:

ben mem

nlp

x σ x σ

σ

σ = − − − )⋅

1 2 ( )

( (5)

Hot-spot stress:

ben mem

HS σ σ

σ = + , (6)

4.3 Non-linear peak stress

The non-linear peak stress distribution, σnlp, is the stress distribution across the material thickness, minus the structural stress component, see Eq. (5)

4.4 Local notch stress

The notch stress can be calculated by the sum of the nominal stress, bending stress and non-linear peak stress components together.

Notch stresses can be determined with a numerical analysis to estimate the local stress vs. strain response at a notch, based on stress history from a linear elastic stress

analysis. The notch stress based on a linear analysis is possible to determine by finite element analysis or some simple case with a combination of nominal stress and stress concentration factors Kt. The nominal stress and strain calculation can be based on either the gross or net cross-section area as is shown in Fig. 10.

Fig. 10 The nominal stress and strain calculation, based on the gross section of the plate or net cross-section of the plate.

Fn

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As long as stresses and strains at the notch root are elastic, the notch stress and strain can be calculated by the Equations (7) and (8). [62]

net nom

Kt σ _,

σ = ⋅ ₍₇₎

net nom

Kt ε _,

ε = ⋅ , (8)

where

Kt is elastic stress concentration factor σnom,net is net nominal stress

εnom,net is net nominal strain

In case where the notch stress increases and the deformation becomes inelastic the stress concentration for nominal stress and strain are not the same any more. The stress

concentration factor decreases toward to 1 and concentration factor for strain increases [62].

The Ramberg-Osgood equation is widely used to represent the relation between stress σ and strain ε. In Eq. (9), it is assumed that there is no distinct yield point. At all values of stress, the elastic and plastic strain is assumed to obtain a total strain, resulting in a smooth continuous curve. Eq. (9) will be used in the monotonic stress state and the same equation for the cyclic stress state can be written, as shown in Eq.(10) [62, 63, 64].

,

/ 1n

K

E 



 

 +

=σ σ

ε (9)

' ,

' / 1 n

K

E 



 

 +

=σ σ

ε (10)

where

K is monotonic strength coefficient n is monotonic strain hardening exponent K’ is cyclic strength coefficient

n’ is cyclic strain hardening exponent σ is stress

ε is strain

Numerous ways have been presented in literature to calculate the local stress and strain at the notch tip. Neuber’s rule, Glinka’s strain energy density method and linear rule are widely used. [65]

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4.4.1 Neuber’s rule

Neuber’s rule [65] is most widely used approximate method to estimate notch stresses and strains. Eq. (11) describes Neuber’s rule for monotonic loading. The physical interpretation of the Neuber rule Eq. (11) is shown in Fig. 11. For the graphical

illustration both sides of Eq. (11) have been divided by 2. Then right side of the Eq. (11) is the same format as work done by the spring Equation. [65]

( )

E K_t σ_nom ² σ

ε⋅ = ^⋅ ⁽¹¹⁾

where

Kt is linear stress concentration factor E is Young’s modulus

σ is notch stress ε is notch strain

Fig. 11 The interpretation of the Neuber model in the monotonic stress-strain case.

In a cyclic loading, the case maximum notch stress σmax and strain εmax can be determined with Eqs. (12) and (13). For cyclic loading, the theoretical stress

concentration factor Kt was replaced with the fatigue notch factor Kf in reference [62]

has suggested because Kf gives a better agreement with an experimental fatigue strength. At the same time, the strength coefficient K and strain hardening exponent n were replaced with the cyclic strength coefficient K’ and cyclic strain hardening exponent n’. In this work K = K’ and n = n’. The monotonic and cyclic stress-strain curves are the same because an ideal kinematic hardening behavior is assumed.

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( )

E K_f _nom_,_max ²

max max

σ σ

ε ⋅ = ^⋅ ⁽¹²⁾

' ,

' / 1 max max

max

n

K

E 



 

 +

=σ σ

ε (13)

where

K’ is the cyclic strength coefficient Kf is the fatigue notch factor n’ is the cyclic strain hardening exponent

Respectively, the strain range ∆ε and the stress range ∆σ can be calculated with Eqs.

(14) and (15). Eq. (15) is cyclic stress-strain hysteresis curve.

( )

E K_f σ_nom ² σ

ε⋅∆ = ^⋅^∆

∆ ⁽¹⁴⁾

/ '

1

2 '

2

n

K

E 



 





⋅ + ∆

= ∆

∆ σ σ

ε (15)

Application of Neuber’s rule is illustrated in Fig. 12 for constant amplitude cyclic loading. For initial loading from zero to the maximum nominal stress level, the

maximum notch stress and strain are able to determined using Equations (12) and (13).

Use of the cyclic stress and strain curve assumes that the deformation behaviour is cyclically stable. [62] The point σmax, εmax is a reference point for unloading. The notch strain curve follows Eq. (15).

Fig. 12 The notch stress vs. strain determination by Neuber’s rule. The external load is constant amplitude.

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4.4.2 Strain energy density rule or Glinka’s rule

A more recent notch vs. strain analysis rule is Glinka’s or the strain energy density rule.

The linear elastic notch behaviour and elastic-plastic notch behaviour is assumed to be same in this rule. Based on that hypothesis the strain energy density at the notch root is also the same both in linear elastic and elastic-plastic case. It means the strain energy density at the notch root is related to the energy density due to nominal stress and strain by a factor of elastic stress concentration Kt, both in monotonic stress state and in alternating stress state [62, 66].

Fig. 13 illustrates the physical interpretation of the Glinka’s rule. The elastic energy We

can be calculated with Eq. (16) and, respectively, elastic-plastic energy can be calculated with Eq. (17). Setting the elastic energy equal to the elastic-plastic energy can be written Eq. (18).

( )

E W_e K^t ^nom

⋅

= ⋅ 2

σ 2

(16)

n

p E n K

W

/ 2 1

1

2 



 



⋅ + +

= σ⋅ σ σ

(17)

( )

E K K

n E

nom t

n 2

/ 2 1

1

2 σ σ σ

σ ⋅

 =



 



⋅ +

+ ⋅ (18)

Fig. 13 The graphical interpretation of strain energy density rule.

σ

ε K_t⋅ σ_nom

K_t⋅ ε_nom σ

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The maximum notch stress σmax and strain εmax in Fig. 13 can be determined by

Equations (16) and (17) for monotonic loading case. The theoretical stress concentration factor Kt should be used in both the monotonic and cyclic loading case. The cyclic material properties should be used in cyclic loading and Eqs. (16) and (17) can be written in the form that has been presented in Eq. (19) and Eq. (20). The material behaviour is assumed to be ideal in these Equations.

( )

E K K

n E

nom t

n 2

max , '

/ 1 max max

2 max

' 1

'

2 σ σ σ

σ ⋅

 =



 



⋅ +

+ ⋅ (19)

' / 1 max max

max '

n

K

E 



 

 +

=σ σ

ε ⁽²⁰⁾

Correspondingly, the strain range ∆ε and the stress range ∆σ can be calculated with Eqs.(21) and (22).

( )

¹^/ ^'

' '

2 2

2 1

4 ⁿ

nom t

K n

E E

K 



 





⋅

⋅ ∆ +

∆ + ⋅

= ∆

∆

⋅ σ σ σ σ

(21)

/ '

1

2 '

2

n

K

E 



 





⋅ + ∆

= ∆

∆ σ σ

ε (22)

4.4.3 Linear rules

When using the linear rule the terms σmax and εmax in Fig. 12 are calculated with Eqs.

(23) and (24) .

E K_t σ_nom_,_max

ε = ^⋅ (23)

' / 1 max max

max '

n

K

E 



 

 +

=σ σ

ε

(24)

The strain range ∆ε and the stress range ∆σ can be calculated with Eqs. (25) and (26).

E K_t σ_nom_,_net ε = ^⋅^∆

∆ (25)

' / 1

2 '

2

n

K

E 



 





⋅

⋅ ∆

∆ +

=

∆ σ σ

ε (26)

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4.4.4 Comparison of rules in the same curve

Comparing Notch stress and stain results obtained from previous rules are compared in the case where the linear tensile stress amplitude is 2 times the yield strength of S355 steel. The stress ratio R of the external load was set to 0. It was assumed that the linear stress concentration factor Ktand the fatigue stress concentration factor Kf was set 1 in this comparison. The cyclic material properties were utilized in the notch stress-strain curves determinations. It can be seen from Fig. 14 that the greatest strain range and stress range was given by Neuber’s rule and the smallest by the linear rule. The results from Glinka’s rule are located between these two rules.

In this particular case, the external linear stress was pulsating, R=0. The true stress ratio Rtruewas smaller than zero for three notch stress and strain calculation methods. The smallest Rtrue values were given by the linear rule and the greatest one by Neuber’s rule.

Fig. 14 Comparisons of stress-strain curves for constant amplitude cyclic loading. The external linear notch tensile stress was assumed to be 2 times the material yield strength,

∆σnotch= 700 MPa. The material is assumed to be S355.

4.5 Stress classification

The design stress or strain calculation can be processed, either by manual calculation, based on hand books or the FE-method, which is a common engineering tool nowadays.

The use of the FE-method for obtaining the design stress or strain information is needed in the fatigue life estimation. This requires good understanding and experience of the FE calculation method and philosophy behind the fatigue assessment methods. The stress separation in three different stress components that are used in the fatigue

Material S355 Load

K’ = 858 MPa ∆σnotch = 700 MPa n’ = 0.164 R = 0

A modified nominal stress method for fatigue assessment of steel plates with thermally cut edges