Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures CHALMERS UNIVERSITY OF TECHNOLOGY Master’s Thesis BOMX02-17-101 Gothenburg, Sweden 2017 Material Characterization of Weld Toe Region Using Digital Image Correlation Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology ANDREA DEZŐ MASTER’S THESIS BOMX02-17-101 Material Characterization of Weld Toe Region Using Digital Image Correlation Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology ANDREA DEZŐ Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2017 I Material Characterization of Weld Toe Region Using Digital Image Correlation Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology ANDREA DEZŐ © ANDREA DEZŐ 2017 Examensarbete BOMX02-17-101/ Institutionen för bygg- och miljöteknik, Chalmers tekniska högskola 2017 Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: Strain field of the test specimen, obtained by means of DIC and the corresponding finite element model. Department of Civil and Environmental Engineering. Göteborg, Sweden, 2017 I Material Characterization of Weld Toe Region Using Digital Image Correlation Master’s thesis in the Master’s Programme Structural Engineering and Building Technology ANDREA DEZŐ Department of Civil and Environmental Engineering Division of Structural Engineering Steel and Timber Structures Chalmers University of Technology ABSTRACT Material models, properties of steel, the changes that occur during welding and different testing procedures were investigated as a starting point of the thesis work. The thesis project investigated the feasibility of using digital image correlation (DIC) in the process of material calibration. This consisted of the examination of local material properties at the weld toe of a welded joint, using digital image correlation in order to obtain the true strain field over the investigated area. The real stress-strain curves of the three material regions at the weld toe, namely, the weld material, base material and heat affected zone were obtained by means of material calibration, using an optimization function in Matlab, combined with the structural analysis capability of Abaqus. Since all weld geometries are significantly different, and the investigated area is very local, the accuracy of the Abaqus model is very important. Thus, in order to ensure a good correlation between the real test specimens and the Abaqus model, the test specimens were 3D scanned, and the obtained contour line was used in the creation of the model. The difficulty of the task arises from the presence of three different materials in a region where stress concentration is also present. Therefore, a test-run of the material calibration was performed on a statically loaded plate having a hole in the middle, serving as source of stress concentration and consisting of two materials. The results showed that deviation between the obtained stress-strain curves and the reference stress-strain curves was under 5 %, proving that the proposed material calibration procedure worked well. The DIC was performed on three test specimens, two of which were loaded statically and one was subjected to cyclic loading. One of the statically tested specimens was in its as welded state, while the other together with the cyclically loaded test specimen were treated with High Frequency Mechanical Impact (HFMI) treatment. The results of all three testing procedures were examined. The material calibration was performed only on the as welded statically tested test specimen. However, a detailed stress-strain curve for all three materials could not be obtained, since the plastic deformation of the investigated area was deemed to be too small. Key words: Digital image correlation (DIC), Material calibration, Optimization function, 3D scanning, Weld toe, Base material (BM), Heat affected zone (HAZ), Weld material (WM), High Frequency Mechanical Impact (HFMI) treatment II Click here to enter text. Click here to enter text. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 III Contents 1 INTRODUCTION 1 1.1 Aim and scope 1 1.2 Methodology 1 1.3 Limitations 2 2 MATERIAL PROPERTIES 3 2.1 Overview of material properties 3 2.2 Characteristic tests 4 2.2.1 Tensile test 4 2.2.2 Hardness tests 6 3 MATERIAL CHARACTERISATION OF WELDED JOINTS 12 3.1 Introduction (welding) 12 3.2 Base material (BM) - structural steel (S355-S460) 13 3.3 Weld material (WM) 16 3.4 Heat affected zone (HAZ) 19 4 HIGH FREQUENCY MECHANICAL IMPACT TREATMENT 24 4.1 Introduction 24 4.2 HFMI treatment process 26 4.2.1 Treatment defects 28 4.3 Consequences of HFMI treatment 30 5 PLASTICITY MODELS 32 5.1 Yield condition 33 5.1.1 The von Mises yield criterion 33 5.1.2 The Tresca criterion 34 5.1.3 The Hill criterion 37 5.2 Hardening rules - overview 38 5.3 Isotropic hardening 41 5.3.1 Johnson-Cook isotropic hardening 42 5.4 Kinematic hardening 43 5.4.1 Bi-linear kinematic hardening (Melan-Prager) 45 5.4.2 Multilinear kinematic hardening (Mroz) 46 5.4.3 Nonlinear kinematic hardening (AF and Chaboche) 47 5.5 Mixed hardening 48 CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 IV 6 EXPERIMENTAL PROCEDURES 51 6.1 Test specimens 51 6.1.1 Geometry 51 6.1.2 Material 53 6.2 Testing 55 6.3 Digital image correlation 56 6.3.1 Introduction 56 6.3.2 Specimen preparation 57 6.3.3 Convergence study – Analyzed area size 60 6.4 Results 63 6.4.1 Static test results – As welded specimen 63 6.4.2 Static test results – HFMI treated specimen 66 6.4.3 Cyclic test results 69 7 MODELLING PROCEDURES (ABAQUS + 3D SCAN) 73 7.1 3D scanning of test specimen 73 7.2 Abaqus model 76 8 MATERIAL CALIBRATION PROCEDURE 79 8.1 Simple case study 80 8.1.1 Abaqus model 80 8.1.2 Calibration procedure 82 8.1.3 Results 84 8.2 Test specimen (SAW) 87 8.2.1 Elastic region 87 8.2.2 Plastic region 90 9 DISCUSSION\CONCLUSION 93 10 FUTURE RESEARCH 94 11 REFERENCES 95 APPENDIX I: MATLAB CODE FOR MATERIAL CALIBRATION OF SAW TEST SPECIMEN 97 Main Matlab code for Elastic material models 97 Main Matlab code for Plastic material models 98 Matlab Function script code: simulationEl 101 Matlab Function script code: simulationYield 105 Matlab Function script code: simulationPl 108 Matlab Function script code: simulationYieldHAZ 111 Matlab Function script code: IntElas 114 CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 V Preface This Master’s thesis is focused on the investigation of the materials present at the weld toe region of a welded detail, using digital image correlation (DIC) in the process of material calibration in order to obtain the stress – strain curves of these materials. The study was carried out at the Division of Structural Engineering of the Department of Civil and Environmental Engineering at Chalmers University of Technology. Many people have contributed either directly or indirectly to this study, without whom it would have been impossible to complete this research. First and foremost, I would like to show my greatest appreciation to my supervisor, Prof. Mohammad Al-Emrani, who was an endless source of wisdom and support. His invaluable assistance and comments helped me throughout my research, while his personality and sense of humour brightened my day on multiple occasions. I am deeply grateful to Prof. Mathias Flansbjer, for conducting the tests in the laboratory of the Research Institutes of Sweden (RISE - former SP), helped me understand the testing procedures and gave me valuable insight regarding DIC. Special thanks to Ignasi Fernandez for granting me his time and for giving me his assistance regarding the manipulation of the 3D scanner. Finally, I would like to thank my opponents, Josef Makdesi and Fabio Lozano Mendoza for their continuous feedback. Göteborg June 2017 Andrea Dező CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 VI Notations Roman upper case letters A Constant equal to the yield stress in Johnson-Cook isotropic hardening 0A Initial cross-sectional area of test specimen B Constant representing the strain hardening in Johnson-Cook isotropic hardening C Constant representing the strain rate in Johnson-Cook isotropic hardening CEV Carbon equivalent value D Diameter of indenter in Brinell hardness test Db Depth of HFMI treatment in base material Dw Depth of HFMI treatment in weld material E Elastic modulus HRE Constant indention in Rockwell hardness test F Force   ijF  Initial yield surface G Shear modulus H Plastic modulus HB Brinell hardness test value HR Rockwell hardness test value HV Vickers hardness test value K Strain hardening coefficient K Hardening parameter K Strain concentration factor 0L Initial length of test specimen ijR Stress ratio T̂ Homologous temperature in Johnson-Cook isotropic hardening Roman lower case letters d Diameter of indent in Brinell hardness test e Depth of indention n Strain hardening exponent m Thermal softening constant in Johnson-Cook isotropic hardening ijs Deviatoric stress tensor Greek upper case letters A Cross sectional area difference due to tensile testing L Length deformation due to tensile testing Greek lower case letters d ij Deviatoric back-stress ij Back-stress  Engineering strain CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 VII p Plastic strain p eff Effective plastic strain p ij Plastic strain rate nom Nominal strain value p true True plastic strain  Plastic multiplier  Poisson’s ratio  Engineering stress e Equivalent von Mises stress ij Given stress in Abaqus M ij Mapping stress point max Maximum principal stress min Minimum principal stress true True stress U Maximum stress x Stress in x direction y Stress in y direction Y Yield stress z Stress in z direction max Maximum sheer stress Abbreviation AF Armstrong and Frederick AW As-Welded BM Base Material CCT Continuous Cooling Time DIC Digital Image Correlation HAZ Heat Affected Zone HFMI High Frequency Mechanical Impact HiFiT High Frequency Impact Treatment IIW International Institute of Welding PIT Pneumatic Impact Treatment PWT Post-Weld Treatment SEM Scanning Electron Microscope UPT Ultrasonic Peening Treatment WM Weld Material Special characters El% Percent elongation (ductility) Ra% Percent reduction of cross section area (ductility) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 VIII CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 1 1 Introduction The behaviour of a material subjected to tension can be described by the stress-strain curve of that specific material. In the case of structural steel, this can be divided into two regions, an elastic region described by Hook’s law and a plastic region following the Power law. Usually, this stress-strain curve is obtained by Tensile testing, where a homogeneous test specimen, having regular geometry is subjected to uniformly increasing tensile force, until failure. When multiple steel elements are desired to be joined, the most common method is welding. This procedure introduces not only residual stresses, but it also changes the crystalline structure of the weld zone. Thus, due to the welding of the elements, three different materials can be differentiated at the weld toe, the base material to be welded, the weld material which was added during welding and the heat affected zone, which is the area of the base material which suffered changes due to the heat input of the welding. In order to obtain the stress- strain curves of these three materials, the above mentioned tensile testing is no longer adequate, since the test specimen is not homogeneous and stress concentration appears due to the change in geometry. Thus, another method must be used. 1.1 Aim and scope The aim of the thesis work is to investigate the feasibility of using Digital Image correlation (DIC) in the process of material calibration, in order to obtain the material parameters of a welded joint at the weld toe region. During the thesis work, three test specimens are tested and the result of the experimental procedures are analysed. The material calibration is performed only on the simplest case, this being the statically tested welded test specimen, without any post weld treatments, due to the time limitation of the thesis work. The other two test specimens are subjected to High Frequency Mechanical Impact (HFMI) treatment in order to increase the strength of the materials at the weld toe region, and improve the weld toe geometry. One of these is tested statically, while the other is subjected to cyclic loading. The thesis work also serves as a stepping stone for future research in using DIC for the investigation of the effect of HFMI post-weld treatment on the stress- strain curve of the materials present at the weld toe and in the description of their cyclic behaviour, when subjected to fatigue loading. 1.2 Methodology Initially an extensive literature study is performed regarding the material models and material properties of steel, in order to understand what happens with the material during welding and how the material is described by different parameters and models. The test specimens are prepared and tested, which is followed by the analysis of the test results. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 2 The material calibration is performed by continuously comparing the strain data of the test specimen during static loading, obtained by means of DIC with the strain data obtained from the Abaqus analysis, which is simulating the experimental procedure. In order to use an optimisation function from Matlab, as well as the structural analysis capabilities of Abaqus, a link is created between the two softwares by using the Abaqus2Matlab toolbox. The used optimisation function produces an educated guess of the input material properties, which is then introduced into the Abaqus model and the analysis is run again with the new material input. The input material parameters are improved until the obtained strain field from the Abaqus model is as close as possible to the strain field from the DIC experimental procedure. 1.3 Limitations The conducted study is restricted to test specimens having a steel grade of S460, considered as regular structural steel. The investigated test specimens are slices of two full-size filet weld details, one with and one without HFMI-treatment. Thus, the only post-weld treatment method considered is HFMI treatment. The material calibration is limited to the statically tested as-welded test specimen, considering only three different materials located at the weld toe region, without a gradient in the case of the heat affected zone. Thus, each material is regarded as homogeneous and the exact locations of these are determined using the magnified image captured for the DIC procedure. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 3 2 Material Properties This chapter serves as a short overview of typical material properties and tests which are carried out in order to understand a material's behaviour under loading. 2.1 Overview of material properties The short description of the following material properties is based on Damone, Illston (2010) and Brockenbrough, Merritt (1999). Stress-strain curve: The stress-strain curve is most commonly used in order to show the behaviour of a specific material under steadily increasing tensile or compressive loading. Some significant material properties can be obtained by analyzing these curves, like yield strength, tensile strength, modulus of elasticity or ductility. Two distinct regions can be differentiated on most material stress-strain curves, an initial linear region, or also called elastic region and a non-linear, plastic region. The curve can change depending on the composition and the crystalline structure of the material. Figure 2.1 shows the schematic stress – strain curve for different types of steel. Figure 2.1 Stress strain curves for different types of steel. Yield strength: The yield strength is the stress value, at which a sudden increase of strain can be observed, without the increase of stress. This delimits the point up to which the material undergoes elastic deformation, having the ability to recover its initial shape in the case of unloading and above which the material experiences plastic, permanent deformation due to the applied load. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 4 Tensile strength: The maximum stress before failure recorded on the stress-strain curve indicates the ultimate tensile stress, or tensile strength. Modulus of elasticity: The modulus of elasticity is defined as the ratio between the stress and strain of the material or the slope of the stress-strain curve in the elastic region and it shows the ability of the material to withstand elastic deformation. Ductility: Ductility measures the ability of the material to deform plastically before failure. It is expressed as percent elongation at failure or percent reduction of cross section area in a tensile test. Hardness: Hardness is defined as the capability of the material to resist indentation or penetration by another material, showing the resistance of the material against plastic deformation. 2.2 Characteristic tests 2.2.1 Tensile test This test can be performed in order to determine the tensile stress-strain curve of a material. It is regarded as a destructive test, since the specimen is destroyed in the process of obtaining the relevant material data. After placing the test specimen into the testing machine, a steadily increasing traction force is applied, acting in the longitudinal direction of the test specimen, usually until failure, while the elongation and the force acting on the specimen is recorded in time. Equation (1.1) and (1.2) can be used to calculate the engineering stress and strain values. Dividing the force ( F ) by the initial cross sectional area ( 0A ) of the specimen will result in the engineering stress ( ) value expressed in MPa in the SI system, while dividing the deformation ( L ) in the direction of the applied force with the initial length ( 0L ) of the specimen gives the strain ( ) value, which is dimensionless. All these parameters are presented in Figure 2.2, showing the schematic representation of the specimen before and after testing. 0A F  (1.1) 0L L  (1.2) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 5 Figure 2.2 Schematic representation of the stress rupture test parameters. As mentioned before, as a consequence of obtaining the stress-strain curve, the test will also provide values for yield strength, tensile strength, ductility and other tensile properties. Ductility is expressed as percent elongation ( El% ) at failure or percent reduction of cross section area ( Ra% ) during tensile testing and it is calculated using the equation (1.3) and (1.4). %100% 0L L El   (1.3) %100% 0A A Ra   (1.4) Figure 2.3 shows an example of a test machine used for the tensile testing. Figure 2.3 Hualong stress rupture testing machine - RCW series. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 6 The general behavior of a structural steel specimen during tensile testing can be seen in Figure 2.4. At stress values below the yield stress ( Y ), the material exhibits elastic behavior, characterized by elastic deformation. This is followed by the plastic region, which can be divided into two parts. Until the maximum stress is reached ( U ), the specimen experiences uniform plastic deformation. After this point, the stress starts decreasing while a localised decrease in the cross sectional area, also called necking can be observed somewhere along the length, which leads to a ‘cup and cone’ failure type in the case of medium-strength steel. Figure 2.4 Schematic stress –strain curve of structural steel and general behaviour of the structural steel specimen during tensile testing. 2.2.2 Hardness tests The hardness value can be obtained using multiple testing methods, usually by measuring the indentation surface left by an indenter, which is pushed into the material with a specific force and for a specific time period. Some of the most widely used hardness testing methods are the Brinell hardness test, the Vickers hardness test and the Rockwell hardness test, these being presented in this subchapter. The information regarding these tests is based on Herrmann (2011). The hardness value is governed by the chosen measurement procedure, being regarded as a reference value scale, thus lacking a unit of measurement. The value is denoted as the hardness value obtained by the test followed for example by the letters ‘HB’ in the case of the Brinell hardness test, or ‘HV’ for the Vickers hardness test. The direct CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 7 comparison of the obtained values by different methods is not possible, however certain tables and charts are available for converting or finding the equivalent values from a different testing method. However, these are regarded as approximate equivalents. The hardness value of a specific material is directly proportional with the bonding forces between the molecules. Since the bonding force between different molecules is stronger than between similar molecules, the hardness of steel is greater than the hardness of its individual alloying components. The hardness value is also inversely proportional to the grain size and directly proportional to the yield strength, meaning that hardness value is larger if the grain size is smaller and if the yield strength is higher. Brinell hardness test: This test was invented in 1900 by a Swedish engineer named Johan August Brinell and it is the oldest hardness test method, which is still in use. It is a nondestructive test. Thus the test specimen may be reused. The indentation is produced by a carbide ball. The diameter of the ball, the applied force and the time interval of the load application may vary according to the tested material, however the relationship between the applied force and the ball size has to be the same in order to have comparable results. The correct steps and regulations concerning the Brinell hardness test can be found in the standards: ASTM E10 and ISO 6506. For example, the minimum thickness of the test piece has to be 8-10 times higher than the depth of the produced indentation. This rule is set in place due to fact that the material zone affected by the indentation process has to be located completely inside the test specimen, otherwise the surrounding materials, like the support table would influence the outcome of the test. The distance between two indentations is also regulated, as well as the distance of the indentation from the edge of the test specimen. Under normal circumstances the indenter is pushed against the test specimen with a given force, which is maintained for 15-30 seconds, depending on the material. The diagonal of the indentation left behind is measured, by taking the average value of two perpendicularly measured diagonals, using a portable microscope or a microscope integrated in the device. The hardness value is calculated with the formula given in equation (1.5), using the parameters presented in Figure 2.5. )( 2 22 dDDD F HB    (1.5) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 8 Figure 2.5 Schematic representation of the Brinell hardness testing. In the notation of the test result, after the hardness value and the abbreviation of the test method (HB for Brinell hardness test) the diameter of the carbide ball in millimeters, the applied force in kilogram and the force application time in seconds are also presented - or denoted (ex. 270 HB 10/300/15). An example of the test machine can be seen in Figure 2.6. Figure 2.6 Fasne Optical Brinell Hardness Testing Machine, OPAB – 3000 model. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 9 Vickers hardness test: This test was created by Robert L. Smith and George E. Sandland at Vickers Ltd in 1921. In this case the indenter has a diamond pyramid shape, with a square base, having an angle of 136 degrees between the opposite faces. The procedure of the test is similar in many ways to the Brinell hardness test, however one of the main advantages it possesses is that the indenter is kept the same for all materials tested. The test has to be in accordance with the regulations presented in ISO 6507, for example the indentation has to be located at a distance of 2.5 times the diagonal of the indentation from the edge, and 3 times the diagonal from adjacent indentations. When calculating the hardness value, the arithmetic mean of the two measured diagonals is used in the formula, inserted in millimeters, while the applied load is introduced as kilogram force, as presented in equation (1.6). The schematic representation of the procedure can be seen in Figure 2.7. Figure 2.7 Schematic representation of Vickers hardness testing and the indention left on the material after testing. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 10 22 854.12 136 sin2 d F d F HV    (1.6) The obtained hardness value should be followed by the letters ‘HV’, denoting the used testing method and the value of the applied force (ex. 270 HV/100). An example of the used testing machine can be seen in Figure 2.8. Figure 2.8 Jinan precision testing equipment Vickers hardness tester, 200HVS-5 model. Rockwell hardness test: This test was developed by Stanley P. Rockwell and is regulated by the ASTM E18 and ISO 6508 standards. The indention is produced by either a diamond cone, or a steel ball, having different dimensions and different applied loads depending on the scale on which the test is performed. There are a total of 15 scales, which depend on the material that has to be tested. An initial minor load (F0) is applied, followed by a major load (F1). The major load is then removed, while keeping the minor load applied on the material, this way allowing a partial recovery of the indention. The depth of indention ( e ) produced only by the major load is recorded and divided by 0.002 mm. The principle of this hardness test is shown in Figure 2.9. The Rockwell hardness value ( HR ) is obtained as presented in equation (1.7), by subtracting this value from a constant ( HRE ), which is 100 units in the case of diamond indenters and 130 for steel ball indenters. eEHR HR  (1.7) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 11 Figure 2.8 Schematic representation of Rockwell hardness testing. The key advantage of this test compared to the other hardness tests is the test duration, since it only takes a few seconds. However, a basic knowledge of influencing factors is necessary in order to choose the correct scale, which can be considered as a disadvantage. The hardness value is usually denoted by the obtained value, followed by the letters “HR”, showing that the testing was performed with the Rockwell method and a letter corresponding to the used scale. For example, 70 HRC, if the obtained hardness value is 70 and the chosen scale is C. In the case of regular steel, the scale C is usually chosen. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 12 3 Material Characterisation of Welded Joints 3.1 Introduction (welding) Welding is the process by which elements can be joined, usually metals, in the process of which due to application of heat or pressure, or both simultaneously the base material is melted locally and then left to cool down naturally. During the welding process filler material may be added, if desired. However, the filler material should have at least equivalent yield strength, ultimate tensile strength, elongation at failure and minimum Charpy V-notch energy value to the one specified for the base material, as stated in Eurocode 3-1-8 (2005). According to the Oxford Dictionary of Construction, Surveying and Civil Engineering (2012) welding is defined as: A technique for joining metals in which actual melting of the pieces to be joined occurs in the vicinity of the bond. A filler metal may be used to facilitate the process. In this process both similar and dissimilar metals can be used; several welding techniques exist including arc welding, gas welding, brazing, and soldering. This joining process is widely used in the construction industry due to the advantages it presents, which include simplicity of execution, a more direct way of stress flow, and the possibility of creating complex cross sectional geometries. Due to the applied heat, a temperature gradient can be observed in the base material, along the weld zone, which leads to metallurgical changes in the material. This is referred to as the heat affected zone (HAZ) around the weld, in the base material. Figure 3.1 Fillet weld, showing the material regions and the location of the weld toe. Thus in welded joints three different material regions can be differentiated at the weld toe region, as presented in Figure 3.1: CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 13 1 - Base material (BM) - Structural steel 2 - Weld material (WM) - Filler material 3 - Heat affected zone (HAZ) due to the welding process. The material properties of the base material around the weld change due to the heat input from the welding process. In the following subchapters, the material properties of these 3 layers will be analysed. 3.2 Base material (BM) - structural steel (S355-S460) Structural steel is a steel type used in the construction industry. In the notation of the steel grade, the letter ‘S’ stands for ‘structural’, while the upcoming number marks the minimum yield strength in MPa in the case when the specimen has a smaller thickness than 16 mm (ex. S355). Until the yield point is reached, the material exhibits elastic behavior, characterized by linear variation between the stress and strain values and described by Hook’s law:   E (3.1) The law states that the stress ( ) is equal with the product between the elastic modulus ( E ) and the strain value ( ). Beyond this point, the material experiences strain hardening, up to the point of maximum stress. The variation between stress and strain is no longer linear, but can be described by a power law relationship, which states, that the change in one parameter will induce a proportional change in the second parameter. Hallomon proposed such an empirical equation, where the stress ( ) is expressed as a function of plastic strain ( p ) (Samuel, Rodriguez, 2005):  npK   (3.2) , where K is the strain hardening coefficient and n is the strain hardening exponent. These constants can be identified from a log-log plot of experimental true stress and true strain curve, as shown in Figure 3.2. If the strain hardening exponent ( n ) is equal to 0, the described material is considered perfectly plastic solid, whereas a value of 1 would indicate an elastic solid material. Ludwik’s equation is a modification of equation (3.3), which includes the yield stress ( Y ) (Samuel, Rodriguez, 2005):  np Y K   (3.3) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 14 Figure 3.2 Log/log plot of true stress-strain curve. Concerning the chemical composition of steel, it is composed of iron mixed with other alloying elements, like carbon and manganese. Some of the alloying elements are due to the steelmaking process, while other chemical elements are added deliberately to modify the material properties of the steel, as desired. For example, carbon increases the tensile strength and the hardness of steel (Brockenbrough, Merritt, 1999). The following material properties of steel, can be considered as constant, regardless the steel type (Domone, Illston, 2010): Modulus of elasticity, E = 205 GPa Shear modulus, G = 80 GPa Poisson’s ratio,  = 0.3 Coefficient of thermal expansion = 12 x 10-6 /C° The chemical composition, yield strength, tensile strength and minimum elongation of the most common structural steel grades are listed in the Table 3.1 (Domone, Illston, 2010). The data corresponds to flat, long, hot-rolled test specimens, having a thickness of maximum 16 mm. CEV stand for ‘Carbon Equivalent Value’ and shows the sensitivity of the material to rupture due to the heating and cooling experienced by the material, when welded. It is calculated, using the percentage of alloying elements in the formula:     15/5/6/ CuNiVMoCrMnCCEV  (3.4) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 15 Table 3.1 Material properties of common hot-rolled structural steel grades, after Domone and Illston (2010). Grade Min yield strength (MPa) Tensile strength (MPa) Min elong. at fracture (%) Chemical composition limit (max %) C Si Mn P S N Cu CEV S235 235 360-510 26 0.19 1.5 0.04 0.04 0.014 0.6 0.35 S275 275 410-560 23 0.21 1.6 0.04 0.04 0.014 0.6 0.40 S355 355 470-630 22 0.23 0.6 1.7 0.04 0.04 0.014 0.6 0.47 S450 450 550-720 17 0.23 0.6 1.8 0.04 0.04 0.027 0.6 0.49 Microscopically, steel is characterized by a crystal structure, which crystallizes cubically. Two patterns can be observed, regarding the emplacement of iron atoms: cubic system with centered volume (CC crystals) and cubic system with centered faces (FCC crystals) as presented in Figure 3.3 (Lemaitre, Chaboche, 1990). The first one is characterized by the fact that the iron atoms are located in the corners of the cube and in its center, while in the second case the iron atoms are located in the corners and in the middle of each face. Figure 3.3 CC crystal (left) and FCC crystal (right). Electromagnetic forces are acting between electrons of neighbouring atoms, keeping the atom structures together. The material properties and crystalline structure of steel can change due to temperature changes, and carbon percentage. In the case of structural steel, with carbon content less than 0.8 % and at normal temperature, the crystals appear in a cubic network with centered volume. It is composed of alpha iron, also called ferrite and small regions of pearlite, located at grain boundaries. By uniting several monocrystals with random orientation a polycrystal is formed, also referred to as a crystal lattice. Since steel is a ductile material, certain defects are present in the crystal lattice, which induce the plastic deformation of the material beyond the yield limit (Lemaitre, Chaboche, 1990). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 16 3.3 Weld material (WM) The welding material is typically chosen according to the base material that needs to be welded. This is because the weld material has to have similar or better properties than the base material, as mentioned before and stated in Eurocode 3. Easterling (1992) gives a good overview of the changes that occur in the weld material, induced by the welding process as well as the transformations due to the cooling period. In order to understand and be able to characterize the material properties, all the various contributions that affect the final composition of the weld deposit has to be taken into account and analyzed. A simplified portray of the different contributions can be seen in Figure 3.4 in the case of fusion welding. Figure 3.4 Fusion weld composition contributions, after Easterling (1992). The chosen welding process has an influence on the weld metal composition, for example in the case of fusion welding, the basicity of the flux is of great importance. This can be expressed by the ratio between sum of basic oxides and sum of acid oxides, and it ranges usually between 0.5 and 3. According to Easterling (1992), the effect of the inclusion content is important, since the increase of the inclusion content will decrease the toughness of the weld material. More so, certain welding processes use inert shielding gases in order to protect the welding. During these welding processes, elements from the gases have the tendency to enter the weld material. Other contributions may arise from the ambient air and from the base material to be welded. The toughness of the weld is also effected by the speed of welding. If the welding speed is increased, the orientation of crystal growth must change in order to maintain continuity, which increases the risk of segregation at the weld center line and decreases the toughness of the weld. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 17 Due to the high heat input of the welding process, the weld becomes liquid, thus a solidification process occurs, which can be divided in three stages, epitaxial, cellular and dendritic. During epitaxial solidification, the preliminary crystal size is governed by the grain growth zone of the base metal. Thus welding processes that cause large grain growth in the heat affected zone, like submerged arc welding will also lead to large initial crystal size of the weld metal. As a result, to the solidification process, the weld material develops a cellular-dendritic structure. This is characterised by coarse columnar austenitic grains and a fine cellular network inside the grains. Additional changes in the microstructure appear during the cooling period, from solidification temperature to ambient temperature. However, these changes are dependent on the cooling rate. With a slow cooling rate, the obtained microstructure is a mixture of ferrite and pearlite. Medium-slow cooling rate yields either Widmanstätten side plates or acicular ferrite microstructures, whereas medium-high cooling rate creates periodic pearlite microstructure. All of the above mentioned microstructures are presented in Figure 3.5. a) Ferrite and pearlite b) Widmanstätten side plates c) Acicular ferrite d) Periodic pearlite Figure 3.5 Transmission electron micrographs showing microstructures observed after cooling in weld metals, after Easterling (1992). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 18 Upper bainite plus cementite as well as upper bainite and retained austenite microstructures occur in the case of fast cooling, see Figure 3.6 a) and b). In the case of very fast cooling lower bainite can form. However, if the time is not sufficient for carbon diffusion, lath martensite will form instead. a) Upper bainite plus cementite b) Upper bainite and retained austenite c) Lower bainite d) Lath martensite Figure 3.6 Transmission electron micrographs showing microstructures observed after cooling in weld metals, after Easterling (1992). The influence of carbon percentage in the welding material is a good example concerning the role of alloying elements in the microstructure transformation of the weld material. Thus by increasing the carbon percentage, the bainitic and the martensitic fields get wider concerning the CCT (continuous cooling time) curve of the material. In Figure 3.7 below, the influencing factors and their effect are marked with arrows, showing the tendency of modifying the transformation fields of the CCT curve to longer or shorter transformation time periods. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 19 Figure 3.7 CCT diagram for steel weld material, after Easterling (1992). 3.4 Heat affected zone (HAZ) The applied heat on the base material due to welding process introduces metallurgical changes in the material close to the weld, which have an influence on its mechanical properties, while also introducing tensile residual stresses (Phillips D. H., 2016). Some of the observed changes include grain growth, recrystallization, phase transformation, annealing and tempering. There are two phase transformations taking place during cooling, one from 𝛿 − 𝐹𝐸 to 𝛾 − 𝐹𝐸 , followed by a transformation from 𝛾 − 𝐹𝐸 to 𝛼 − 𝐹𝐸 (Boumerzoug et al., 2010). The iron-carbon equilibrium diagram can be seen in Fig 3.8, which shows the phase transformations of steel, depending on the applied heat and carbon percentage of the material. It should be noted, that this diagram applies only in the case of slow cooling, since the equilibrium is not kept in the case of fast cooling (Brockenbrough, Merritt, 1999). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 20 Figure 3.8 Iron-carbon equilibrium diagram, after Brockenbrough and Merritt (1999). Since a temperature gradient is observed in the HAZ, it is understandable that it can be divided in subzones, depending on the temperature and metallurgical changes that take place under the temperature of that specific subzone. The temperature is the highest right at the fusion line, next to the weld and it decreases gradually as the distance from the weld increases, until it reaches the temperature of the BM. Figure 3.9 presents the partitioning of the HAZ. Figure 3.9 Different subzones of the heat affected zone (HAZ), after Barzin (2015) and Easterling (1992). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 21 In the zone with the highest temperature, significant increase in grain size, compared to the base material grain size, can be observed. This zone is called the grain growth zone and it has a temperature range of approximately 1200 – 1500 °C. If the steel material has a higher CEV value (approximately 0.4), then the formation of martensite is more likely, which would also indicate a higher hardness value in this region (Easterling, 1992). The grain refined zone is delimited in the temperature range of 900 – 1200 °C. This zone is characterised by fine grained ferrite – pearlite structure, which is produced during cooling. In the temperature range of 650 – 900 °C the produced structure depends highly on the cooling rate and it is called the partially transformed zone. Possible developed structures are: pearlite, upper bainite, autotempered martensite or high carbon martensite. Below 650 °C, in the annealed zone, there is no change in the microstructure of the material. However, dynamic strain ageing can take place, due to the heating cycle and residual stresses produced by the welding process. This will lead to locking the position of dislocations, increasing the brittleness of the material. Figure 3.10 presents image quality maps of the heat affected zone and the base material, provided by Mikkola (2016). It shows significant grain size difference between the two regions. a) HAZ b) BM Figure 3.10 Image quality maps of the heat affected zone (HAZ) and the base material (BM), from Mikkola (2016). A more detailed analysis of the zones located in the HAZ was performed by Easterling (1992), by presenting optical micrographs on all of the zones and the BM as reference. These can be seen in Figure 3.11, showing clear differences in the microstructure of the zones. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 22 a) Fusion zone b) Grain growth zone c) Grain refined zone d) Partially transformed zone e) Unchanged base material (BM) Figure 3.11 Optical micrographs of various zones in HAZ, from Easterling (1992). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 23 Figure 3.12 Vickers hardness values along the HAZ of structural steel, from Easterling (1992). In Figure 3.12 it can be seen that the zone with maximum hardness value coincides with the zone with maximum grain size, close to the fusion line Easterling (1992). The cooling rate is dependent on the welding process, the ambient temperature and the geometry of the welded joint. Thus it is possible to plot the maximum hardness close to the fusion line taking into account different cooling rates, of different welding processes. The relation between hardness value and cooling rate is presented in Figure 3.13 (Easterling, 1992). Figure 3.13 Mean vickers hardness values along the HAZ of medium strength 20 mm thick C-Mn steel based on several different welding processes, adapted from Easterling (1992). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 24 4 High Frequency Mechanical Impact Treatment 4.1 Introduction The fatigue strength of a welded joint is decreased because of three main reasons, namely the stress concentration due to geometry changes, the tensile residual stresses introduced by the welding process and the defects of the weld, like undercuts or porosity, which shorten the crack initiation period or in some cases even eliminates it altogether. In order to increase the fatigue strength of welded joints, a number of post-weld treatment (PWT) methods were developed and divided in two categories, weld geometry improvement methods and residual stress improvement methods. An overview of existing improvement methods is presented in Figure 4.1 below. Figure 4.1 Overview of weld improvement techniques, adapted from Marquis and Barsoum (2016). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 25 Some methods concentrate solely on geometry improvement, or the introduction of compressive residual stresses into the material, while others offer a combination of beneficial effects, which act together in order to increases the fatigue strength. Table 4.1 offers an overview of the manner in which certain methods are improving the overall performance of the welded joint. Table 4.1 Weld improvement methods and their effects, after Marquis and Barsoum (2016). Method Geometry improvement Introduce compressive residual stresses Grinding x - TIG-remelting x - Shot peening (blasting) - x Hammer/needle peening x x HFMI x x Since the different methods have different ways of enhancing the fatigue strength, it is understandable that some will have greater influence on the global behaviour of the joint than others. Figure 4.2 displays a comparison between PWT methods, with respect to their effect on the fatigue life of the joint. Figure 4.2 Effect of weld improvement techniques, adapted from Johnson and ProcessBarron (-). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 26 In the current chapter the focus is set on one of the residual stress improvement methods, more exactly the high frequency mechanical impact treatment (HFMI), also referred to in relevant literature as ultrasonic peening treatment (UPT), pneumatic impact treatment (PIT) or high frequency impact treatment (HiFiT). It is regarded as having similar improvement capability as hammer peening or needle peening (Marquis, Barsoum, 2016). 4.2 HFMI treatment process The high frequency mechanical impact (HFMI) treatment method is classified as a mechanical, residual stress method, belonging to the peening methods subcategory (see Figure 4.3). As the name suggests, the method is based on mechanical impact of a cylindrical indenter, using high frequency, of approximately 90 Hz. It has three main improvement effects, the insertion of compressive residual stresses, the reduction of stress concentrations by improving the weld toe geometry, and strain hardening of the material at the treatment surface. The treatment is applied to the weld toe, since it is considered a critical region, because of the stress concentration induced by sudden change in geometry. Thus the method will have a significant effect on all three material layers located in this region, namely the WM, the HAZ and BM. a) As-welded state b) After HFMI treatment Figure 4.3 Weld toe profile before and after HFMI treatment, from Marquis and Barsoum (2016). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 27 Figure 4.4 HFMI treatment process. Schematic illustration of the HFMI treatment process can be seen in Figure 4.4. The areas that are affected by the treatment are presented in Figure 4.5. The red arrows, from the same figure, mark the extent of the strain hardening effect. Figure 4.5 Areas affected by the HFMI treatment. Various HFMI machines were developed during the last decade, which led to a large variety of indenter configurations. The machine is composed by two parts, a power unit and a tool with a high strength steel cylinder indenters. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 28 Before applying HFMI treatment on the weld toe region, the area has to be cleaned from any traces of slag, oxide or other foreign materials. Grinding should be avoided, since it could reduce the visibility of the weld toe. The International Institute of Welding (IIW) defines the typical values of the HFMI grove geometry as ranging between 0.2 and 0.6 mm considering the depth and between 2 and 5 mm for the width. In a study conducted by Ghahremani et al. (2014), regarding the quality assurance of HFMI treated welded steel, it was found that average between the depth of treatment in the base material (Db) and weld material (Dw) has to be between 0.25 and 0.5 mm, anything above this value is considered as over-treated and anything below this value is considered as under-treated. These measurements are represented schematically in Figure 4.6. Figure 4.6 Measurements of the HFMI treatment. It should be noted, that this treatment method is appropriate for joints that are likely to develop weld toe cracks. In the case of other welded joint types, where the occurrence of root cracking is expected, the improvement of the fatigue life is limited and special measures should be taken, as using full penetration welds or increasing the weld throat. 4.2.1 Treatment defects If the treatment procedure is performed correctly, a smooth and shiny HFMI grove is created along the weld toe region. However, certain defects may appear, which are easily detectable during surface inspection. A dark crack-like line may appear in the HFMI grove, if the contact area between indenter and treated surface is inadequate or if the chosen indenter is inadequate. The schematic representation of this defect is presented in Figure 4.7 and a real life example of this type of defect is observable in Figure 4.8 below. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 29 Figure 4.7 Potential crack like defect due to treatment carried out with a steep angle of the indenter or too large indenter, after Marquis and Barsoum (2016). Figure 4.8 Example of improperly treated weld toe, from Marquis and Barsoum (2016). Defects can appear in the case of under-treatment as well, implying that the number of applied passes are insufficient and the indenter strikes are observable along the treated surface. However, this defect is easily fixable by additional passes with the HFMI device. Figure 4.9 shows an example of under-treated weld toe with the individual indenter strikes still visible, adapted from Marquis and Barsoum (2016). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 30 Figure 4.9 Example of under-treated weld toe, from Marquis and Barsoum (2016). Another common defect is due to the cold working of the material, which induces plastic deformations. In this situation, a crack-like line may appear if a specific point is over treated. The schematic representation of a proper HFMI groove and one having a crack-like line is presented in Figure 4.10. Figure 4.10 Proper HFMI groove (left) and HFMI groove having crack-like lines (right), from Marquis and Barsoum (2016). 4.3 Consequences of HFMI treatment As mentioned in Chapter 3, the welding process produces tensile residual stresses in the metal, which have a negative influence on the fatigue life of the joint. However, these tensile residual stresses are counteracted by the compressive residual stresses resulted by the HFMI treatment. Local stress concentrations appear when there is a sudden change in the geometry, as in the case of a weld toe. As a result of the HFMI treatment, the weld-toe region deforms plastically, creating a smooth transition between the weld and the base material, this way reducing the stress concentration at the weld toe. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 31 During the treatment process, the material undergoes strain hardening, thus increase in the local yield strength, hardness and fatigue strength is expected. The most significant microstructural change induced by the HFMI treatment, is the decrease in average grain size. However, according to Mikkola (2016) this reduction occurs only in one direction, resulting in the elongation of the grains. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 32 5 Plasticity Models Ductile materials, like structural steel, exhibit large irreversible, plastic deformations, if they experience stresses beyond their yield strength. The crystal structure rearranges and due to shear stresses acting on the material, a slip displacement occurs, which leads to permanent strains. The plastic deformation is possible due to defects in the crystal lattice, like edge dislocation, screw dislocation or dislocation loop, which are presented in Figure 5.1 (Lemaitre, Chaboche, 1990). a) Edge dislocation b) Screw dislocation c) Dislocation loop Figure 5.1 Defects in the crystal lattice, from Lemaitre and Chaboche, (1990). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 33 5.1 Yield condition The yielding strength of a material in a uniaxial stress state is easily determined by uniaxial testing. However, generally a structure experiences a multiaxial stress state, characterized by a stress tensor, having six stress components.                       zyzxz yzyxy xzxyx zzyzxz yzyyxy xzxyxx        (5.1) The yield condition relates the multiaxial stress state with the uniaxial one, in order to determine if the combined effect of the stress components induce yielding of the material or not. In other words, it determines the stress state, at which yielding starts. It is represented by a yield surface in the stress state coordinate system delimiting the elastic region from the plastic region (Ottosen, Ristinmaa, 2005). Every point in the coordinate system marks a stress state. The stress states located inside the yield surface, induces elastic deformations in the material. Thus it can also be used, as a limit considering the state of stress in structures, if elastic analysis of the structure is desired. The most commonly used yield criterion in the case of metals is the Tresca and the von Mises, the former being implemented in the finite element method (FEM) software, Abaqus. 5.1.1 The von Mises yield criterion The general formula, of the equivalent von Mises stress, taking into account all the stress components is (Krenk, Høgsberg, 2013):         222222 6 2 1 xyxzyzzzyyzzxxyyxxe   (5.2) Expressed in principal stresses, the formula can be rewritten as:       222 2 1 zyzxyxe   (5.3) Yielding occurs, when the equivalent stress is equal to the yield strength ( Y ), obtained by uniaxial testing. Thus the von Mises yield condition can be written in terms of the equivalent stress and the uniaxial yield strength (Ottosen, Ristinmaa, 2005): Ye   (5.4)        0 2 1 222  Yzyzxyx  (5.5) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 34       2222 2 Yzyzxyx   (5.6) By plotting the equation (5.6) in 3D principal stress space, the von Mises yield surface is obtained, in the form of a cylinder, aligned with the 321   axis (see Figure 5.2). Any stress state located inside the above defined cylinder is inducing elastic behaviour in the material. Stress states directly on the surface of the cylinder leads to yielding of the material (Krenk, Høgsberg, 2013). The Von Mises cylinder is graphically represented in Figure 5.2. Figure 5.2 Von Mises stress cylinder in principal stress space, after Krenk and Høgsberg (2013). 5.1.2 The Tresca criterion According to the Tresca criterion, the material is yielding, when the maximum shear stress is greater than a characteristic stress value, which is regarded as half of the yield stress ( Y ) (Krenk, Høgsberg, 2013. Ottosen, Ristinmaa, 2005). The maximum shear stress is defined as the radius of the Mohr’s circle, expressed as half of the difference between the maximum and minimum principal stress. Thus the general expression for the Tresca yield criterion can be written as: Y  minmaxmax2 (5.7) According to Krenk and Høgsberg (2013), the Tresca yield surface can be obtained in a simple way by considering three situations in the yx ´ - plane, when 0z . Therefore, when x and y are of different signs, the yield equation will be: Yyx  max2 (5.8) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 35 Figure 5.3 Tresca stress polygon in plane stress, after Krenk and Høgsberg (2013). Equation (5.8) will mark the inclined lines of the yield surface trace in the yx ´ - plane, as shown in Figure 5.3. The horizontal and vertical lines are provided by the case, when x and y have the same sign, the yield criterion being defined by the largest stress. Yx   02 max (5.9) Yy   02 max (5.10) As seen in Figure 5.4, the Tresca yield surface has the shape of a hexagon, which is inscribed in the von Misses ellipse, having the same intersections with the axes. Thus for stress states located in the apexes of the hexagon, the two yield conditions, predict the same yield limit. However in some cases, the Tresca criterion predicts lower yield stresses with up to 13.4%, compared to those predicted by the von Mises (Ottosen, Ristinmaa, 2005). In the 3D principal stress space, the Tresca yield surface will have the shape of a hexagonal prism, aligned with the 321   axis. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 36 Figure 5.4 Tresca stress surface in principal stress space, after Krenk and Høgsberg (2013). A study conducted by Taylor and Quinney (1931), comparing the von Mises yield condition and Tresca yield condition to experimental results is presented by Ottosen and Ristinmaa (2005) and Chakrabarty (2006). The experiment was realized considering copper, aluminium and mild steel thin walled tubes subjected to combined tension and torsion. The study clearly showed, that the von Mises yield condition has a better concordance with the experimental results, than the Tresca yield condition. This comparison can be seen in Figure 5.5. Figure 5.5 Tresca and Mises ellipses on the ( 𝜎, 𝜏 ) plane together with the experimental results of Taylor and Quinney, from Chakrabarty (2006). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 37 5.1.3 The Hill criterion The Hill criterion is an extension of the von Mises yield condition, which is used to model anisotropic plasticity. It can be expressed with the following formula (Lemaitre, Chaboche, 1990):       1222 222222  xzyzxyzxzyyx NMLHGF  (5.11) where the parameters F, G, H, L, M and N are scalar numbers representing the state of anisotropic hardening. These can be determined from pure tension and pure shear tests. An example concerning Hill criterion can be observed in Figure 5.6. Figure 5.6 Example of plastically anisotropic material, Hill criterion, from Lemaitre and Chaboche (1990). In the FEM software, Abaqus, Hill’s yield criterion can be introduced in the sub option ‘Potential’, by defining the stress ratios (equation (5.12)), between the given stress and CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 38 the reference yield stress ( Y ), which was defined using Mises plasticity (Abaqus Analysis User's Guide, 2013). Y ij ijR    (5.12) 5.2 Hardening rules - overview According to Ottosen and Ristinmaa (2005), the hardening rule is defined as the rule governing the way in which the yield surface modifies as a consequence of plastic loading, since the yield stress generally changes its value according to the plastic deformation. In the case of perfectly plastic materials, the yield surface stays the same during loading, thus keeping its initial yield strength even after the yield stress is reached. However, when the material shows signs of strain hardening, as in the case of structural steel, at stresses above the initial yield stress, the yield surface changes as guided by the chosen hardening rule (Araújo, 2002). Three types of hardening rules may come into effect after plasticity takes place: isotropic, kinematic or a combination of these two. Over the years, a large number of models were developed in order to simulate the different hardening rules, making it possible to include various effects that may appear. Table 5.1. offers an overview of the different hardening models and their validity concerning the inclusion of certain phenomena, which were observed during experiments. Table 5.1 Hardening rules and their validity, after Lemaitre and Chaboche (1990). Models Monotonic hardening Bauschinger effect Cyclic hardening / softening Ratcheting effect Isotropic x - x - Linear kinematic x x - - Multilinear kinematic x x x - Nonlinear kinematic x x - x Mixed (isotropic + kinematic) x x x x CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 39 Monotonic hardening appears, when the material is subjected to static loading. This can be simulated by all of the above presented hardening rules. However, these are significantly different, when we consider effects due to cyclic loading. A so called, Bauschinger effect, is observable, when tensile loading is followed by compressive loading. According to which, the yield stress in compression is much lower than the maximum reached stress in tension. Thus the yield stress in compression is inversely proportional to the yield stress increase in tension. This phenomenon is presented in Figure 5.7. Figure 5.7 Bauschinger effect, after Ottosen and Ristinmaa (2005). Depending on the analyzed material, either cyclic hardening or cyclic softening can be detected, when subjected to cycling between fixed and symmetrical strain or stress values. This phenomenon, is depicted in Figure 5.8 and 5.9. a) Cyclic hardening b) Cyclic softening Figure 5.8 Strain cycling between , after Ottosen and Ristinmaa (2005). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 40 a) Cyclic hardening b) Cyclic softening Figure 5.9 Stress cycling between , after Ottosen and Ristinmaa (2005). If the cycling is performed between fixed stress values, which are not symmetrical about zero, the observed phenomenon is called ratcheting effect. This is characterized by a strain increase, after each cycle, if the mean stress is positive, as shown in Figure 5.10. Figure 5.10 Stress cycling between unsymmetric stress values with ratcheting, after Ottosen and Ristinmaa (2005). When modeling the plastic behavior of the material in a FEM software, special attention should be accorded to the input stress-strain data. The regularly used engineering stress- strain data is no longer adequate input data, thus the true stress vs. logarithmic plastic strain data must be provided. These can be calculated using the engineering stress-strain values. Until twice the yielding strain, the true stress and true plastic strain values are equal to the engineering values. Between this point and the point when necking initializes, the following formula can be used:    1true (5.13) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 41                E pp true   1ln1ln (5.14) Figure 5.11 shows the difference between engineering stress-strain curve and true stress and true strain curve. Figure 5.11 Engineering stress-strain curve and true stress-strain curve. In the current chapter the focus is fixed on plasticity models that can be implemented in the FEM software Abaqus. 5.3 Isotropic hardening Isotropic hardening is characterised by a uniform increase or decrease of the yield surface, while sustaining its centre point in the same position throughout the change, as well as maintaining its initial shape. Depending on the exhibited behaviour, in the case of softening, the yield surface shrinks in size, while during hardening, it expands. The rate of expansion is governed by the increase of equivalent plastic strain during loading or the dissipated plastic work. The isotropic hardening of a yield function can be generally expressed as (Ottosen and Ristinmaa, 2005):   0),(  ijij FKf   (5.15) }{KK  (5.16) , where   ijF  is the initial yield surface. K represents the hardening parameter, in the form of K, as a function of equivalent plastic strain ( p eff ), which increases with the increase of plastic strain. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 42 The effective plastic strain can be calculated as presented in equation (5.17), where p ij stands for plastic strain rate (Ottosen and Ristinmaa, 2005). p ij p ij p eff   3 2  (5.17) In the case of von Mises yielding criterion, experiencing isotropic hardening, equation (5.18.) can be rewritten as:        0 2 1 ),( 222  KKf Yzyzxyxij   (5.18) The yield surface translation in isotropic hardening is depicted in Figure 5.12. Figure 5.12 Yield surface translation in isotropic hardening, after Ottosen and Ristinmaa (2005). This hardening model is most commonly used in the case of modelling large strains or proportional loading. It cannot describe cyclic behaviour of the material on its own, thus in case of cyclic loading it is usually combined with the kinematic hardening model. According to the isotropic hardening rule, when the material experiences tensile loading, followed by compressive loading, the yielding stress in compression will be equal to the highest stress reached during the tensile loading. Meaning, that the isotropic hardening model of the von Mises criterion leads to equal yield stresses in compression as in tension, this being in contradiction with experimental results carried out on steel, concerning the Bauschinger effect (Ottosen and Ristinmaa, 2005). 5.3.1 Johnson-Cook isotropic hardening It is considered a type of isotropic hardening, which utilizes an analytical function. The equation is composed of three parts, taking into account the equivalent plastic strain, CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 43 strain rate and thermal softening. It is most often used in the case of modelling high- strain-rate deformation (Abaqus Analysis User's Guide, 2013). According to Johnson-Cook hardening, the yield stress has the following equation (Johnson and Cook, 1983):     m p effnp eff CJ Y TCBA ˆ1ln1 0                        (5.19) , where 𝐴 is a constant, equal to the yield stress, 𝐵 and 𝑛 are constants representing strain hardening and 𝐶 is the strain rate constant. The exponent 𝑚 is the thermal softening constant and T̂ is the homologous temperature, defined as in equation (5.20). In order to determine the homologous temperature, the reference temperature (𝑇𝑟), the melting temperature (𝑇𝑚) and the current temperature (𝑇) has to be defined (Dorogoy and Rittel, 2009).              m mr m r r TTfor TTTfor TT TT TTfor T 1 0 ˆ (5.20) The constants can be obtained by using a least square method curve fitting of the experimental data. 5.4 Kinematic hardening Considering the kinematic hardening rule, the yield surface will not change its size or shape after the occurrence of plasticity, but it translates in the direction of yielding. The kinemtic hardening of a yield function can be generally expressed as (Ottosen and Ristinmaa, 2005):   0),(  ijijij FKf   (5.21) The translation is induced by the tensor ij , also referred to as back-stress, which marks the centre of the von Mises surface in the stress space and has an initial value of 0. Thus in the case of von Mises yield criteria, the generalised formula becomes:    0 2 3 ),( 2/1        Y d ijij d ijijij ssKf   (5.22) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 44 }{ d ijK   (5.23) , where K is the hardening parameter, in the form of the deviatoric back-stress ( d ij ) and ijs is the deviatoric stress tensor.                               0 0 0    zyzxz yzyxy xzxyx zyzxz yzyxy xzxyx ij sss sss sss s (5.24) 3 0 zyx     (5.25) The yield surface translation in kinematic hardening is depicted in Figure 5.13. Figure 5.13 Yield surface translation in kinematic hardening, after Ottosen and Ristinmaa (2005). In order to approximate the Bauschinger effect, in the case of tensile loading followed by compressive loading, the yield stress in compression is decreased with the same amount as the tensile yield stress is increased. Leading to a constant difference between the two yield stresses of two times the initial yield stress in tension ( Y ). The kinematic hardening models can be divided into three main groups: linear kinematic, multilinear kinematic and nonlinear kinematic hardening models, a few of which being presented in the current sub-chapter. Table 5.2 presents an overview of the availability of certain kinematic hardening models in a few finite element analysis software (Halama, Sedlák and Šofer, 2012). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 45 Table 5.2 Availability of kinematic hardening models in certain FE software, after Halama, Sedlák and Šofer, (2012). Kinematic hardening Ansys 13 Abaqus MSC.Marc MSC.Nastran Bilinear x x x x Multilinear x - - - Armstrong- Frederick x x x x Chaboche x x - - 5.4.1 Bi-linear kinematic hardening (Melan-Prager) This is the simplest kinematic hardening model, which assumes that the back-stress varies linearly with the plastic strain. The back-stress expressed by the Melan-Prager’s evolution law (Ottosen and Ristinmaa, 2005): p ijij c   (5.26) , where p ij denotes the plastic strain rate and c is the constant material parameter, obtained from uniaxial stress-strain curve, equal with two-thirds of the plastic modulus H. The interpretation of the plastic modulus is presented in Figure 5.14. Hc 3 2  (5.27) Figure 5.14 Interpretation of plastic modulus H, from Ottosen and Ristinmaa (2005). The linear kinematic hardening model is presented in Figure 5.15. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 46 Figure 5.15 Linear kinematic hardening, from Dahlberg and Segle (2010). Due to the assumed linearity, the consideration of the Bauschinger effect becomes rather rudimentary, which makes the linear kinematic hardening model unsuitable for very large strain simulations. Thus most often being utilised in the modelling of low cycle fatigue, with small strains. 5.4.2 Multilinear kinematic hardening (Mroz) The multilinear kinematic hardening model, considers several linear segments, having different hardening modulus values. Thus every linear segment considered, is described by a different yield function, and different yield surface. Elastic response is only possible, when the stress state is within the smallest yield surface. This concept is depicted in Figure 5.16. Figure 5.16 The Mroz concept of several yield surfaces, from Dahlberg and Segle (2010). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 47 The back-stress is defined by the Mroz evolution law in the following manner (Ottosen and Ristinmaa, 2005):  ij M ijij q    (5.28) , where M ij is the mapping stress point, ij is the current stress point and  is a plastic multiplier. The positive quantity 𝑞 can be calculated as:   ij M ij d ijij Y sss H q     3 2 (5.29) The Bauschinger effect is simulated in a correct manner in this model. However, the obtained loops are always symmetrical, thus material ratcheting is not possible to be described (Dahlberg and Segle, 2010). 5.4.3 Nonlinear kinematic hardening (AF and Chaboche) The main advantage of this model is that it can simulate the ratcheting effect, due to asymmetric stress cycling, while introducing the Bauschinger effect in an accurate manner. However, it has a clear disadvantage when describing the shape of the hysteresis loop (Halama R., Sedlák J., Šofer M., 2012). One of the most well-known nonlinear kinematic hardening model, is the Armstrong and Frederick (AF). The constants appearing in the evolution law of the back-stress tensor can be determined from uniaxial tests (Araújo, 2002). Armstrong-Frederick evolution law (Ottosen and Ristinmaa, 2005):           p eff ijp ijij h      3 2 (5.30) , where p ij is the plastic strain rate, p eff is the effective plastic strain rate, h and  are constant. The last term in the Armstrong-Frederick back-stress evolution law can be regarded as a recall term, since if the second constant (  ) tends to infinity, the evolution law becomes the same as the Melan-Prager linear kinematic evolution law (Ottosen and Ristinmaa, 2005). This implies, that the second term is responsible for the introduction of nonlinearity in the evolution law. As seen in Figure 5.17, the yield surface is limited by a bounding surface, which is fixed in the stress space. When the yield surface comes in contact with the bounding surface, the hardening modulus becomes zero, simulating an ideally plastic material. In all other cases, the hardening modulus will have a variable value, while loading (Halama R., Sedlák J., Šofer M., 2012). CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 48 In some literature, the constants from the Armstrong-Frederick evolution law are marked as C and . Thus the evolution law is written as: p effij p ijij C    3 2 (5.31) Using this expression, the yield surface can be represented in the following way: Figure 5.17 The yield surface and bounding for the AF-model, from Dahlberg and Segle (2010). The Chaboche model is an improvement of the Armstrong-Frederick hardening model, by summing multiple nonlinear kinematic models. The improvement is observable in the simulation of the ratcheting effect, making it possible to describe ratcheting decay. It should be noted, that with the superimposition of a higher number of nonlinear kinematic models, the capability of the model is increased, and while choosing the number of superimposed models as 1, it will return to the Armstrong-Frederick model (Dahlberg and Segle, 2010). Chaboche evolution law:                   n i p eff i ip iiij h 1 3 2      (5.32)          n i p effii p iiij C 1 3 2   (5.33) 5.5 Mixed hardening The mixed hardening model is obtained by combining the isotropic hardening model with the kinematic hardening model. The yield surface keeps a constant shape, while modifying its size and position during plastic deformation. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 49 The mixed hardening is generally expressed as (Ottosen and Ristinmaa, 2005):   0),(  KFKf ijijij   (5.34) By rewriting the generalised formula for the von Mises yield criterion, we obtain:    0 2 3 ),( 2/1        KssKf Y d ijij d ijijij   (5.35) },{ KK d ij  (5.36) Setting the hardening parameter K to 0, will result in a kinematic hardening model, while setting the back-stress hardening parameter to 0, we obtain an isotropic hardening model. This model is used in the case of cyclic loading, when the cyclic hardening or softening is of interest. It also approximates the Bauschinger effect accurately, as well as the ratcheting effect. The deviatoric plane and the uniaxial loading of mixed hardening von Mises material can be seen in Figure 5.18. Figure 5.18 Mixed hardening of von Mises material, after Ottosen and Ristinmaa (2005). In order to obtain a mixed hardening model between isotropic hardening and Armstrong-Frederick hardening, the isotropic hardening parameter is expressed in a similar manner as the back-stress tensor for Armstrong-Frederick hardening. By introducing a mixed hardening parameter (m), determining the amount of mixing between the two hardening models, the following hardening parameters are obtained (Ottosen and Ristinmaa, 2005):             p eff ijp ijij hm      3 2 1 (5.37) p eff K K mhK          1 (5.38) CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 50 , where m represents the mixed hardening parameter and K is a constant. The deviatoric plane and the uniaxial loading of mixed AF hardening material can be seen in Figure 5.19. Figure 5.19 Mixed AF hardening model, after Ottosen and Ristinmaa (2005). CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 51 6 Experimental Procedures 6.1 Test specimens The tested specimens are “slices” of two full-size weld details, one with and one without HFMI-treatment. The weld details consist of a base plate, having a perpendicular plate welded to it, using filet welding, as seen in the figure below. Figure 6.1 Analyzed weld detail. A total of 4 test specimens were analyzed during the thesis work, two of them were loaded statically, while the other two have been subjected to cyclic loading. The specifications of the specimens are presented in the table below, together with the test specimen ID, which are used throughout the thesis work. Table 1.1 Test specimen specifications. Test specimen ID Loading type Treatment Max. load [kN] Steel grade SAW Static No treatment (AW) 25 S460 SHFMI Static HFMI 25 S460 C18 Cyclic HFMI ±18 S460 6.1.1 Geometry Two different testing specimen geometries were adopted for two different loading conditions, namely static and cyclic loading. In both cases, in order to maintain symmetry, the base material was water jet cut on the opposite side of the weld, imitating the outline of the welding as seen in Figure 6.2. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 52 Figure 6.2 Symmetric cut of base material. The specimen used for static testing are presented in Figure 6.3. It had a thickness of 4 mm and was flat on both sides. This enabled fine grinding of the two surfaces, exposing the micro-structure of the specimen. Due to the change in geometry and the presence of welding, stress concentration is expected to localise at the weld toe. Figure 6.3 Specimen used in the case of static loading. In the case of cyclic testing, the specimen having 4 mm thickness is no longer adequate, because of the risk of buckling of the specimen in compression. Thus in order to eliminate the buckling possibility during cyclic loading, the thickness of the specimen CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 53 used for cyclic testing was increased to 8 mm and a circular cut-out, with a radius of 4 mm and depth of 3.5 mm was made around the area of interest from both sides, leaving a thickness of 1 mm in this specific area. This circular cut-out was performed in order to ensure that the highest stresses will appear in the area of interest. To maintain symmetry of the test specimen, the circular cut-out was made in the other side of the specimen as well, as seen in Figure 6.4. Due to slicing of the test specimens the residual stresses from welding and HFMI disappear, thus the only effect due to HFMI treatment left behind is the strain hardening of the material in the vicinity of the treatment zone and the geometry improvement at the weld toe. Figure 6.4 Specimen used in the case of cyclic loading. 6.1.2 Material Only one structural steel type was chosen as base material, namely S460, because of the time limitation of the thesis project. Table 6.1 lists the steel properties of the used steel, provided by the manufacturer. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 54 Table 6.1 Steel properties provided by manufacturer. State t [mm] Steel fy [MPa] fu [MPa] As-welded (AW) 60 S460 494 597 HFMI treated 40 S460 566 639 Table 6.2 gives an overview of the welding parameters used for the welding of the specimens. The welding method used was flux-cored arc welding. Table 6.2 Welding parameters. Method Voltage Current Average welding speed No. of weld passes FCAW 136 27.5 V 260 A 370 mm/min 3 on each side of attachment As described in Chapter 3, three different materials can be found at the weld toe region. These areas, can be seen in the pictures from Figure 6.5, which were taken on both the as-welded and the HFMI treated weld detail, using a scanning electron microscope (SEM). Due to the difference in micro-structure, these three regions can be easily distinguished between each other. a) As-welded (AW) b) HFMI treated Figure 6.5 SEM pictures of the two welded details. More in-depth pictures were taken on the HFMI treated weld detail, showing the micro- structure of the different regions, these are presented in Figure 6.6. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 55 a) HFMI treated surface b) Base material (BM) surface c) Base material (BM) d) Weld material (WM) e) Heat affected zone (HAZ) f) HFMI treated material Figure 6.6 SEM pictures of the HFMI treated welded detail. 6.2 Testing The tensile testing was performed at room temperature, with steadily increasing load, reaching a maximum load of 25 kN. The load increase speed was 4 kN per minute. The cyclic testing was performed at a loading rate of 60 seconds per cycle, having a total of 25 cycles. The two specimens tested cyclically were subjected to different cycle loads. Specimen C18 was subjected to a load of ±18. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 56 6.3 Digital image correlation 6.3.1 Introduction The deformation behavior of the specimens, during the static and cyclic testing was monitored using the Aramis 4M measuring system. This provides a non-contact and material independent measuring procedure, which consists of high resolution image capturing, during the experiment. Subsequent images are then analyzed, using Digital Image Correlation (DIC) techniques. The DIC, returns the strain field over the area of interest, by comparing the acquired images. More exactly, the area of interest is divided in square zones, of a specified size, called facets. These are identified by the software, in every image, considering the stochastic pattern of the specimen. The position of the facet is searched in the images, by means of minimizing the quadratic difference between the observed patterns inside the facets. The location changes of the facets, throughout the image series, gives possibility of calculating the local strain field for the tested specimen. The first image can be considered as the reference frame, i.e. when strain is considered to be equal to 0 in every point. If desired, an initial strain value can be introduced, calculating the strain field of upcoming images based on the applied, fix reference strain value of the first image. The facet size is specified by the software user as a number of pixels, marking the edge length of the square facet. This should be chosen as small as possible, in order to reduce computation time and increase the acquisition of local effects within the facet, while being also large enough to enable the computation of the facet (GOM mbH, 2015). The accuracy of the result can be increased by overlapping the facets, both in vertical and horizontal direction. This can be achieved by the point distance parameter in the software, describing the distance between two contiguous facets. With a smaller point distance, the measurement point density is increased, creating a finer mesh, which also influences the computation time. Thus, with smaller point distance, the mesh is finer, but the computation time is longer. The recommended overlapping percentage interval is considered to be between 20 % and 50 % (GOM mbH, 2015). The DIC was performed using the software GOM Correlate 2016, in the current study. An area of 7.9 x 7.9 mm was monitored, right at the weld toe in the case of static loading, using a digital camera (2048 x 2048 pixel). Since the analyzed area was very small, the camera was equipped with a magnification device. By trial and error, a facet size of 39 x 39 pixels was considered adequate in this case, with an overlap of 33 %. Thus the point distance was set to 26 pixels, this corresponding to 0.1 mm. In the case of cyclic loading, the monitored area was increased to 12 x 12 mm, thus magnification was no longer necessary. In both cases, i.e. static loading and cyclic loading, the image accusation rate was 1Hz. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 57 6.3.2 Specimen preparation In order to obtain better results, the specimens had to undergo certain preparations, consisting in surface pattern enhancements, to improve the facet creation. Two different methods were used for the static, respectively cyclic testing, prior testing. In the case of static loading, the specimens were polished, to expose the crystalline structure of the 3 material regions (BM, WM and HAZ). This enabled the use of microstructure pattern, as reference points for the facets. The polished test specimen, the monitored area and the location of the monitored area can be seen in Figures 6.7, 6.8 and 6.9. On the other hand, the cyclic test specimens were painted with a speckle pattern before testing, as seen in Figure 6.10. The monitored area and the location of the monitored area is presented in Figure 6.11 and 6.12. Figure 6.7 Polished test specimen for static testing. Figure 6.8 Monitored area (7.9 x 7.9 mm) for DIC, of static test specimen. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 58 Figure 6.9 Location of monitored area (7.9 x 7.9 mm) for DIC, of static test specimen. Figure 6.10 Painted test specimen for cyclic testing. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 59 Figure 6.11 Monitored area (12 x 12 mm) for DIC, of cyclic test specimen. Figure 6.12 Location of monitored area (12 x 12 mm) for DIC, of cyclic test specimen. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 60 6.3.3 Convergence study – Analyzed area size The strain field in the area of interest was obtained by means of DIC. In order to reduce the noise from the strain measurements, the strain values were averaged over a specific area, and a convergence study was carried out to examine the used area size. Two locations were chosen to analyze the influence of the chosen area size, one right at the weld toe where high stress concentrations are found, and one in the base material, which is located far from the stress concentration zone. In both locations, six different area sizes were selected over which the averaged strain values were determined. As seen in Figure 6.13, the selected area sizes were ranging between 0.2 x 0.2 mm and 1 x 1 mm. Figure 6.14 and Figure 6.15 shows the variation of strain in the two locations for the different area sizes during loading. It is observable that in both graphs, the smallest area size (0.2 x 0.2 mm) shows significant fluctuation, while with the increase of the area size the fluctuation is reduced. The fluctuation appears due to the noise of the experimental results, and it has as consequence the loss of accuracy in the measured data. Since the monitored area is very small (7.9 mm x 7.9 mm for static loading and 12 mm x 12 mm for cyclic loading), accuracy on a local scale is very important. Thus a balance has to be reached between localized data and accurate data. It was concluded that an area size of 0.6 x 0.6 mm is sufficiently small in order to capture the important localized strain data, while also being sufficiently large to reduce the noise of the experimental values and obtain converging strain data. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 61 a) Area size of 0.2 x 0.2 mm b) Area size of 0.4 x 0.4 mm c) Area size of 0.5 x 0.5 mm d) Area size of 0.6 x 0.6 mm e) Area size of 0.8 x 0.8 mm f) Area size of 1 x 1 mm Figure 6.13 Area sizes for convergence study. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 62 Figure 6.14 Maximum principal strain during loading in base material, averaged over different area sizes. Figure 6.15 Maximum principal strain during loading at the weld toe, averaged over different area sizes. 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 M a x . P ri n ci p a l S tr a in [ % ] Force [kN] 1.1 (0.2 x 0.2 mm ) 1.2 (0.4 x 0.4 mm ) 1.3 (0.5 x 0.5 mm) 1.4 (0.6 x 0.6 mm ) 1.5 (0.8 x 0.8 mm ) 1.6 (1 x 1 mm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 M a x . P ri n ci p a l S tr a in [ % ] Force [kN] 2.1 (0.2 x 0.2 mm ) 2.2 (0.4 x 0.4 mm ) 2.3 (0.5 x 0.5 mm) 2.4 (0.6 x 0.6 mm ) 2.5 (0.8 x 0.8 mm ) 2.6 (1 x 1 mm) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 63 6.4 Results 6.4.1 Static test results – As welded specimen Figure 6.16 displays the maximum principal strain color plot of the specimen, at different load levels. The figures show that stress concentration appears at the weld toe region, as expected. a) F = 0 kN b) F = 5 kN c) F = 10 kN d) F = 15 kN e) F = 20 kN f) F = 25 kN Figure 6.16 Maximum principle strain [%] color plots of statically tested as-welded test specimen, at different load levels. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 64 In order to analyze the strain data in different material regions, areas of 0.6 x 0.6 mm were placed along the area of interest, as shown in Figure 6.17 and the E11 strain value was averaged over these areas. Figure 6.17 Displacement of analyzed areas on the SAW specimen. The area with the highest strain value was area 4.1, located in the weld material, right at the weld toe. The strain concentration factor ( K ) of this area was calculated at the load level of 15 kN, by dividing the strain value obtained from DIC with a calculated nominal strain value ( nom ), using the equations below. EA F E nom nom    (6.1) 372.1 0012755.0 0017505.0  nom K    (6.2) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 65 The obtained strain concentration factor at 15 kN, at the weld toe was 1.372 and the strain – force diagram of this area is presented in Figure 6.18. Figure 6.18 E11 strain [%] – Force [kN] diagram of area 4.1. 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 S tr a in ( E 1 1 ) [% ] Force [kN] 4.1 Strain concentration factor of 1.372, at 15 kN CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 66 6.4.2 Static test results – HFMI treated specimen Figure 6.19 displays the maximum principal strain color plot of the HFMI treated and statically tested specimen, at different load levels. The figures show that stress concentration appears at the weld toe region, as expected and that the area having strain above 0.3 % at maximum load is smaller than in the case of the untreated specimen. a) F = 0 kN b) F = 5 kN c) F = 10 kN d) F = 15 kN e) F = 20 kN f) F = 25 kN Figure 6.19 Maximum principle strain [%] color plots of statically tested HFMI treated test specimen, at different load levels. CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 67 Areas of 0.6 x 0.6 mm were positioned in the different material regions, in order to establish the area with highest strain concentration, as shown in Figure 6.20 and the E11 strain value was averaged over these areas. Figure 6.20 Displacement of analyzed areas on the SHFMI specimen. The strain concentration factor was calculated using the equation (6.1) and equation (6.3), obtaining 1.417. 417.1 0012755.0 0018078.0  nom K    (6.3) Under normal circumstances, the stress concentration factor for the HFMI treated specimen should have been smaller than the one for the untreated specimen, which was equal to 1.372. This was expected due to the geometry improvement induced by the HFMI treatment. However, this was not the case concerning the analyzed test specimens in the current thesis project. This can be explained by the fact that the radius at the weld toe was smaller for the HFMI treated test specimen than for the untreated test specimen and smaller radius causes higher strain concentration. CHALMERS, Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 68 Figure 6.21 E11 strain [%] – Force [kN] diagram of area 5.1. Figure 6.22 Comparison of maximum E11 strain areas of statically tested as-welded and HFMI treated specimens. 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 S tr a in ( E 1 1 ) [% ] Force [kN] 5.1 Strain concentration factor of 1.417, at 15 kN 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0 5 10 15 20 25 30 S tr a in ( E 1 1 ) [% ] Force [kN] 4.1 (AW) 5.1 (HFMI) CHALMERS Civil and Environmental Engineering, Master’s Thesis BOMX02-17-101 69 Figure 6.22 shows the strain – force curves of the areas with highest strain from the as- welded specimen, respectively the HFMI treated specimen, when loaded statically, both areas being located in the weld material, right at the weld toe. The circular marks on the curves have the purpose of showing the point when the curves start to deviate from a linear behavior. These can be associated in a qualitative manner to the point when yielding occurs in the specific area. Taking this into account, it can be observed, that yielding occurs much later (at higher load level) in the HFMI treated specimen, at the specific area location, than in the as-welded specimen. This coincides with the behavior expected due to the HFMI treatment of the weld toe. 6.4.3 Cyclic test results A grid of areas was established in order to analyze the extent of the plastic zone. The areas were deemed to deform plastically if they exhibit a substantially larger strain in the first compressive cycle than in the previous tension cycle. Thus after analyzing every area separately, it was concluded that the areas marked with red, in Figure 6.23 are experi