Wim Nagy

Fatigue strength application of fracture mechanics to orthotropic steel decks

Modern fatigue design in civil constructions is mainly limited to the use of S-N curves and the hypothesis of Palmgren-Miner, as described in design standards and Eurocode. While using the latter, the fatigue evaluation may be conservative, since the outdated S-N curves are compared to current construction technology and weld properties. This shortcoming has a direct influence on the current design of orthotropic steel decks. To increase the understanding of the fatigue behaviour, an improved analysing tool using linear elastic fracture mechanics and extended finite element model is proposed. As a result, thickness effects are evaluated for both the longitudinal stiffener and the deck plate. These calculations indicated that increasing the thickness of the deck plate and the longitudinal stiffener increases the fatigue life of the structure. However, the thickness should be limited to maintain the advantage of a light-weighted construction.

Measuring Residual Stresses in Orthotropic Steel Decks Using the Incremental Hole-Drilling Technique

Manufacturing processes such as welding cause residual stresses which exist in most steel civil structures, causing plastic deformations without any external loads. This type of stress is often overlooked during design. Nevertheless, residual stresses can have serious influence on the material strength and the fatigue life of the construction. This is also true for orthotropic steel decks which have many complex welding details. Since little is known about the distribution of residual stresses due to welding, a semi-destructive experimental test setup is developed for a stiffener-to-deck plate connection of an orthotropic steel deck. In particular, hole-drilling is used. The test procedure has been optimized to reduce measurement errors. The most important influencing factors on measurement accuracy are the surface preparation and the precision of the determination of the zero-depth. Once these measurement errors are optimized using proper grinding and visual inspection tools, a clear residual stress pattern becomes visible. The results confirmed the theoretical assumption of high tensile yield stresses near the weld location. However, at small distance from the weld, the residual stresses tend to decrease to almost zero.

Effect of plasticity on residual stresses obtained by the incremental hole-drilling method with 3D FEM modelling

The incremental hole-drilling method is used to determine high residual welding stresses in an orthotropic bridge deck. When comparing the measurement results with a theoretical residual stress distribution of an orthotropic steel deck, a large difference in sign and magnitude of the residual stress values is observed. These measurement results are presented in another paper [1]. The test method, specified in ASTM E837-13a only applies when the material behavior is linear-elastic. Relaxed-plastic strain can be detected in the region of the bored hole for the evaluation of high residual welding stresses. This plastic behavior can result in a significant error of the residual stresses. In this paper, the hole-drilling procedure is simulated and the effect of plasticity on the determination of residual stresses is studied with three-dimensional finite element modelling. The calculation software Siemens NX 9.0 is used to simulate the hole-drilling procedure with both linearelastic and elastic-plastic material behavior. First, a 3D model is set up for uniform in-depth residual stress fields with a linear-elastic material behavior to determine the calibration coefficients. The same model is used to determine similar calibration coefficients but this time with a simplistic model of material plasticity. The effect of plasticity on the uniform in-depth residual stresses is determined. The residual stresses obtained under the assumption that the material behavior is linear-elastic are an overestimation. In future research, residual strains for non-uniform in-depth residual stresses can also be studied with similar models. This will result in a more accurate determination of the residual weld stresses present in bridge constructions. Introduction The incremental hole-drilling method is widely used for measuring residual stresses in steel components. Plastic relaxed strain can be induced in the region of the borehole. Since this test method only applies when the material behavior remains linear-elastic, significant errors can be introduced by this plastic behavior during the determination of residual stresses [2]. In this paper, the effect of plasticity on the determination of residual stresses for uniform in-depth residual stresses is studied. Incremental hole-drilling method The residual stresses introduced by a welding operation can be evaluated making use of the incremental hole-drilling technique. A small hole is drilled through the center of a strain gauge rosette into the test material (Fig. 1) [3]. The surface material of the test specimen has to be exposed by drilling only through the material of the strain gauge rosette. This drilling depth is called zero depth. The initial uncertainty of the separation of the cutter from the outer surface by the strain gauge rosette and coating can be disregarded by establishing this zero depth [4]. The relieved surface strains caused by the introduction of a hole in a series of small steps are recorded. Residual stresses are calculated according ASTM E837-13a [3] taking into account the measured strains and calibration coefficients. Reliable measurements are only achieved by limiting Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 235-240 doi: http://dx.doi.org/10.21741/9781945291173-40 236 the residual stresses to 80% of the material’s yield stress in order to take into account that the test method only applies when material behavior is linear-elastic [3]. However, the level of residual stress can be comparable with the material yield stress and then, the stress concentration due to the introduction of the hole produces zones in which the elastic limit of the material is reached. The plastic region arises at the lower circumference of the hole and when the hole depth is increased, it spreads towards the strain gauges located on the strain gauge rosette. Fig. 1. Hole-drilling machine (left) and hole-drilled strain gauge rosette (right) A type A strain gauge rosette which follows the Rendler and Vigness [5] geometry is considered in this paper to determine the effect of plasticity on the determination of residual stresses with the incremental hole-drilling method. This pattern is available in several different sizes and is recommended for general-purpose use [3]. The strain gauge rosette type CEA-06-062UL-120 is used for the finite element modelling. A schematic representation of the geometry of a strain gauge rosette used for hole drilling is shown in Fig. 2(a) and a detail of one strain gauge is shown in Fig. 2(b). The dimensions of a strain gauge for the considered strain gauge rosette can be found in Table 1. The hole diameter of this strain gauge rosette is 2mm while the maximum hole-drilling depth is 1mm. Fig. 2. Schematic geometry of strain gauge rosette (a) and detail of one strain gauge (b) [2] Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 235-240 doi: http://dx.doi.org/10.21741/9781945291173-40 237 Table 1. Strain gauge rosette dimensions in mm Rosette Type D GL GW R1 R2 CEA-06-062UL-120 5.13 1.59 1.59 1.77 3.36 3D finite element model A three dimensional finite element model is set up in Siemens NX 9.0 to evaluate the plastic relaxed strain readings of the considered strain gauge rosette. The geometry of the strain gauge rosette is exactly modelled by defining element nodes corresponding with the number and length of grid lines and their spacing. The strain gauge rosette’s material and its bonding to the test surface is not taken into account. It is assumed that the measured strains by the strain gauge rosette are identical to the relaxed strains of the test specimen [6]. Nodal displacements for both ends of every grid line are simulated and they are used to calculate the radial strains. The hole-drilling procedure is simulated by deactivating elements with the element birth/death feature of the Nastran Solver in NX. Element layers are incrementally deactivated in a number of steps corresponding to the hole-depth increment specified in ASTM E837-13a. For each step, strains are simulated which are used to calculate residual stresses according to the ASTM standard. Only radial strains 1 and 3 (Fig. 2 (a)) will be considered for the evaluation of the residual stresses since the only interest are the normal xand y-stresses. The used mesh for the model is shown in Fig. 3 and it contains 436410 three-dimensional elements. Fig. 3. Mesh of finite element model with drilled hole Geometry, constraints, material properties and loading conditions. The hole-drilling simulation of a flat plate with a thickness of 6mm is performed. The effect of increasing the plate thickness is studied and it has no influence (less than 1%) on the results. Due to symmetry, only a quarter of the total plate is modelled. Therefore, symmetry constraints are applied on the sides of the model where the hole will be situated which means that the displacements along xand y-axes are zero. The displacement of the bottom surface along the z-direction is set to zero. The model width is chosen 15 times the hole diameter and the thickness is larger than the rosette’s mean diameter according to the minimum thickness for thick plates recommended by ASTM E837-13a. The steel grade S235 is used as material for the modelling. The presence of a residual stress field is simulated by imposing a uniform pressure distribution of 50MPa on the sides not containing the drilled hole. In order to make the distinction between linear-elastic and elastic-plastic material behavior, a different stress-strain curve is specified. For linear-elastic material behavior, a linear stress-strain curve is specified until the yield stress is reached (Fig. 4). Elastic-plastic material behavior is Residual Stresses 2016: ICRS-10 Materials Research Forum LLC Materials Research Proceedings 2 (2016) 235-240 doi: http://dx.doi.org/10.21741/9781945291173-40 238 specified with bilinear stress-strain curve (Fig. 5) and isotropic strain hardening plasticity model. A simplistic model of material plasticity has been used. Fig. 4. Linear-elastic stress-strain behavior Fig. 5. Elastic-plastic stress-strain behavior Residual stress calculation. The principal residual stresses σx and σy can be calculated from the measured relaxed strains ε1 and ε3, the calibration coefficients a and b, the material’s Young’s modulus E and Poisson’s ratio ν. The following relationships apply: σx = − E(ε1+ε3) 2a(1+ν) − E(ε1−ε3) 2b σy = − E(ε1+ε3) 2a(1+ν) + E(ε1−ε3) 2b (1) The calibration coefficients are calculated with finite element modelling by applying a known uniform stress distribution on the sides not containing the hole and evaluating the relaxed strains [2]. These imposed pressures are assumed to be equal to the principal residual stresses before a hole was drilled [7]. Determination of calibration coefficients Linear-elastic material properties. First, a test piece with uniform in-depth residual stress field is considered in order to numerically calibrate the hole-drilling process and determine the calibration coefficients. A linear-elastic material law is used and the uniform residual stress field is split up into hydrostatic (σx = σy) and deviatoric (σx = -σy) residual stress fields. The model with hydrostatic residual stress field is used to determine the calibration coefficient a and the model with deviatoric residual stress field results in calibration coefficient b. Both models are evaluated for ten depth-step increments of 0.1mm until a final hole depth of 1mm is reached. The relaxed strains for each depthstep are evaluated and the calibration coefficients are determined. In Table 2 the calibration coefficients determined with the 3D-model are shown. The results for elastic-plastic material behavior are also already mentioned. When a comparison is made between the calibration coefficients obtained by the 3D model with linear-elastic material behavior

INFLUENCE OF TEMPERATURE EFFECTS IN STEEL BOX GIRDERS

A number of recent monitoring project of steel box girders in Belgium have indicated that daily temperature variations can be an important load condition. The resulting behavior is not always included in the design loads according to the codes. As part of a large-scale project in order to improve the accessibility of the Belgian capital by train, the existing railway line between Brussels and Ghent is expanded from 2 to 4 tracks over a length of 25 km. This line crosses the valley of the river Pede by a 523 m long historic viaduct, built in the 1930s. In those days the viaduct was chosen over large backfills in the valley due to poor soil conditions. With respect to the protected work of art, two additional lateral fly-overs consisting of steel box girders with variable hollow section are integrated in the existing viaduct. This paper shows the results of the detailed monitoring program verifying the design and behavior of the newly built superstructure. Extensive strain measurements were performed during a two-day load test, together with acceleration measurements in order to evaluate the dynamic response of the structure. In addition long term strain monitoring was carried out in order to study the effects of temperature gradients on the closed steel box girders of the fly-overs. The measured temperatures are introduced into a finite element model. Stresses resulting from this model are compared with measured stresses and stresses based on calculation using the same model but based on Eurocode load combinations. While the size of temperature variations is more or less as was expected the resulting behavior is more complex and less homogeneous than is generally assumed.