Simulations of a Large-scale Four Point Bending Experiment; Influence of Residual Stresses from a Repair Weld Academic research paper on "Materials engineering"

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Procedía Materials Science 3 (2014) 1599 - 1605

20th European Conference on Fracture (ECF20)

Simulations of a large-scale four point bending experiment; influence of residual stresses from a repair weld

Son Doa*, David J. Smitha

aSolid Mechanics Group, Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK.

Abstract

The presence of welding residual stresses is known to influence fracture of welded metallic structures. Where there is significant ductile deformation prior to fracture, welding residual stresses are often perceived to be removed as plasticity is accumulated and do not subsequently contribute to fracture. To explore this, a large scale experiment was conducted as part of the EU-STYLE project. One experiment was performed on a repair welded stainless steel pipe subjected to four-point bending. There was evidence of limited ductile tearing prior to collapse of the pipe. Prior to testing, residual stress measurements were made through the repair weld and opposite the repair weld in the original girth weld of the pipe. These measurements were used as input to a finite element (FE) model. An iterative technique was employed to map measured residual stresses onto an uncracked FE model, and an equilibrium state determined. The residual stress state was then mapped onto a cracked pipe FE model which was then used to simulate the pipe's behaviour. The simulations reveal that the presence of tensile residual stresses contributes significantly to initial yielding behaviour but as plasticity progresses the residual stresses are removed.

© 2014PublishedbyElsevierLtd. Thisis anopenaccess article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering

Keywords: Residual stress; 3D mapping; fracture; simulation

* Corresponding author. E-mail address: son.do@bristol.ac.uk

2211-8128 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering doi:10.1016/j.mspro.2014.06.258

Nomenclature

a Stress matrix in 3D FE model

P Adjustment factor

1. Introduction

Residual stress present in metallic components is known to have influence on their fracture. Some early experiments with residual stress were provided by Formby and Griffiths (1977) where they showed a marked reduction in fracture load at low temperature with the presence of the tensile residual stress. The influence of the residual stress diminished at higher temperatures. A set of experiments with and without residual stresses was carried out by Sharples et. al (1999) to validate procedures for the treatment of residual stress in fracture. Residual stress also appears in the warm pre-stressing process. Experiments showing the effect of preloading on the fracture of the metallic components were carried out by Smith and Garwood (1990a). Experimental studies using a variety of models include those by Smith and Garwood (1990a, 1990b), Hadidi-moud et. al (2004), Panontin and Hill (1996) and Mirzaee-Sisan et. al (2007). Recent work has explored the rate of residual stress relaxation during loading to fracture such as those by Aird et. al (2008), Smith et. al (2009), Song et. al (2013) and Horne et. al (2013). Whether or not a residual stress completely relaxes was shown to depend on the associated elastic-follow up.

There is therefore a considerable body of research that has studied the significance of residual stress on fracture. There are still some areas which are not well understood such as the interaction between a primary and secondary stresses during loading and elastic-follow up level in a structure.

A large scale experiment was conducted in CEA, Saclay, as part of the EU-STYLE project, Nicak and Keim (2010), to explore the influence of welding residual stress on fracture. The experiment was performed on a repair welded stainless steel pipe subjected to four-point bending. There was evidence of limited ductile tearing prior to collapse of the pipe. The significance of the particular welding residual stress during fracture is explained in this study.

Fig 1. (a) Dimensions of LC3 pipe and representation of the though-thickness part circumferential crack; (b) Post-test crack surface, scale

dimension is in mm.

2. Summary of the experiment

A large-scale four point bending experiment was carried out on a welded Esshete stainless steel pipe. This is called the LC3 pipe in this study. Post-test data were employed to develop a finite element model. Initially the measured residual stresses were introduced into the FE model. The model was then subjected to bending loads to

replicate the large scale experiment.

The LC3 pipe in the STYLE project was a repair welded Esshete 1250 pipe that contained an idealised through thickness part-circumferential crack within the repair weld. The main section of the repair weld pipe is shown schematically in Figure 1a. Two extension arms, manufactured from 304L stainless steel were then welded to the LC3 pipe to provide a 5m four point bending span for the four-point bending experiment, Figure 2. There were two main phases to the experiment; fatigue pre-cracking and then sequences of loading and unloading to promote ductile crack extension from the initial fatigued pre-crack. The CMOD was measured using the two attached clip gauges. Post-test examination of the fracture surfaces revealed that ductile tearing of the repair weld metal had occurred. This is illustrated in Figure 1b.

F/2 Crack F/2

Welded ^^extension arm

LC3 pipe

F/2 F/2

Fig 2. Four point bending arrangement of the experiment. The dimensions are in m.

3. Finite Element Model

3.1. Basic details

A one quarter model of the Esshete pipe was created by assuming two symmetries on the cracked pipe, one symmetry plane at the crack plane and the other symmetry in the axial direction at the mid span of the repair weld, normal to crack plane. The pipe in the experiment, however, had two unsymmetrical fatigue pre-cracks about 5mm and 8mm at the outer surface of the pipe. These values were averaged for the FE model. In a quarter model this led to a crack being equivalent to 23 degrees either side of the axial symmetry plane, as shown in Figure 3. Consequently, the two planes of symmetry were based on an assumption that the repair weld was at the centre of the girth weld on the pipe and the fatigue crack was symmetrical about the centre line of the repair weld. A quarter model was used in the analysis assuming pure bending applied to the LC3 pipe, and contained only the original 600mm Esshete pipe.

3.2. Loading condition

Pure bending was applied to the FE model by applying rotation to a rigid surface at the end of the FE model. The rigid surface was initially positioned parallel to the crack plane and perpendicular to the axial symmetry plane. The bending moment was obtained from the reaction moment on the rigid surface. The crack mouth opening displacement (CMOD) was obtained from a location on the FE model which corresponded to the clip gauge positions in the experiment.

4. Mapping in measured residual stresses

4.1. Measured residual stresses

The measured residual stresses, obtained from the application of the deep hole technique, were introduced into a FE model of the same size as the pipe model in Figure 2 but without the presence of a crack. The measurement method and the results obtained are described by Do et. al (2012). Two lines of measurements were obtained, one along the centre line of the repair weld and through the pipe wall thickness, and a second directly opposite at 180° in the centre of the original weld in its as-welded. In both cases only the in-plane (i.e. hoop and axial) residual stresses were measured, Figure 4.

4.2. Mapping technique

An iterative technique was used to map the residual stresses onto the quarter model. The technique was a combination of an iterative technique and a proportional integral adjustment explained in Ficquet (2007), Lei et. al (2000) and Do et. al (2013). The iterative method assumed that the parent and weld metals exhibited elastic-plastic deformation. The measured stresses were only available in the axial and hoop directions and the finite element solver determined the other stress components. As a starting point, it was assumed that the stresses along the line were the same everywhere within the volume of the repair weld. Similarly, line measurements in the original weld were assumed to be the same everywhere in the remainder of the original weld. The repair weld corresponded to mapping zone 1 and the remainder of the original weld to mapping zone 2. This is illustrated in Figure 2. The angular extent of Mapping zone 1 was 28.6 degrees from the symmetric crack plane based on the extent of the repair. Mapping zone 2 covered the remainder of the circumference in the quarter model. Both mapping zones extended 15mm along the axis of the pipe from the symmetric crack plane. The measured values in Mapping Zone 1, which is the repair weld region, were taken from the DHD measurement on LC3 pipe at the repair weld centre. The measured values in Mapping Zone 2, the remainder of the girth weld region, were extracted from DHD measurement on an unaged girth weld pipe (Do et. al (2012)).

! 15mm : Weld

285mm Parent

Repair 28.6

Mapping Zone 1

Through thickness Crack, 23 o angular span

Mapping Zone 2

Opposite Repair

Fig 3. The allocation of materials and mapping zones on the FE model.

Having introduced the initial residual the FE solver was used to generate an equilibrium stress state in both the two mapped zones and outside these zones. When the initial measured residual stresses was introduced, there was a redistribution of the stresses during an equilibrium step into regions where residual stresses were initially not imposed as explained before by Lei et. al (2000). The method consisted of taking values of the complete stress state outside of the mapping zones from the previous iteration, i, and also re-assigning the known values in the mapped zones and applying these to the next iteration, i+1. Outside of the mapping zone the stresses at each increment are given by

output

where r, 0, z are the cylindrical coordinates. In the mapping zone 1, the stresses are given by

°ee °er °9z' input aee 0 0 " input f aee 0 0 " measured aee 0 0 " output ^

°rr = 0 0 0 0 0 0 - 0 0 0 (2)

CTzz _ i+1 0 0 CTzz _ i V 0 0 CTzz _ 0 0 CTzz _ i )

where ft is an adjustment factor, taken to be 1 here. Finally, in mapping zone 2, the stresses are given by

°ee aer input " 0 output °ee 0 0 " measured+mod

are arr = °rr + 0 0 0 (3)

CTzz _ i+1 az6 0 i 0 0 CTzz _

Since the crack was within the repair weld region, the mapping zone 1, an adjustment factor was applied to mapping zone 1 only. This was to obtain output values as close as possible to the measured values for the repair weld region. Outside of a mapping zone, six stress components were remapped from the previous iteration. The initial stress input at the mapping zones had only two non-zero components which were the hoop and axial stresses.

0 10 20 30 40

Distance from pipe inner surface (mm)

0 10 20 30 40

Distance from pipe inner surface (mm)

™ ™ Measured stress, Iterated stress, —O" Measured + mod stress, O Iterated stress,

Repair Repair Opposite Repair Opposite Repair

Fig 4. Measured stresses and their corresponding iterated values after equilibrium steps.

4.3. Mapped stresses

The iterative technique was applied until converged stress fields at the original measured paths were obtained. This was achieved after 15 iterations. Figure 4 show the results. The output values, compared with their measured values, are plotted in Figure 4. The iterative technique mapped the hoop stresses well to the mapping zones with only small differences between mapped and measured hoop values at the repair weld. The difference was also insignificant opposite the repair weld except for a region between 22.5mm and 32mm distance from pipe inner surface. The maximum difference in the mapped and measured hoop stress values was about 100MPa at around 29mm from the pipe inner surface. The overall agreement between mapped and measured axial stress values was not as good. The difference between mapped and measured values in the repair weld was a minimum near the pipe inner surface and increased towards the pipe outer surface. The maximum difference was about 90MPa, which is 25 percent of the measured axial stress' membrane level, 350MPa. The difference in stresses opposite the repair weld was more significant with the largest difference of around 147MPa occurring near the mid pipe thickness.

These stresses were then mapped onto the cracked pipe model for the subsequent simulations of loading. A crack was modelled by releasing boundary conditions for nodes which lie on the crack plane and corresponded to the crack size.

5. Results of FE simulations of loading

5.1. Elastic and Elastic-plastic loading

The pure bending FE model was first loaded elastically with and without residual stresses. In all cases, the

model was run with the crack present. The mechanical response obtained from the model is shown in Figure 5. The compliance of the cracked model without residual stress was 1.33 10"3 mm/kN, which was 1% higher than the experimental value. Note however, the compliance measured in the experiment was obtained during compressive loading of the cracked faces whereas the FE obtained from simulation was obtained from tensile loading. Nevertheless, the compressive fatigue loading in the experiment was relatively low such that non-linear effects and the influence of crack closure were small. The compliance for the FE model containing the mapped residual stresses was also 1.33 10-3 mm/kN which was the same for loading without residual stresses.

The pure bending model was then loaded assuming that the materials exhibited elastic-plastic behaviour and was run with and without residual stresses, Figure 5. When residual stresses were not present, there occurred at about 85kN non-linear behaviour of the load-CMOD response, as shown in Figure 5a. In contrast, with residual stress present, non-linear behaviour occurred as soon as the pipe was subjected to external loading. This was because the process of mapping initial stresses also included elastic and plastic strains to the crack model. There existed plastic strain in mapping zone 1 from the iterated residual stress model and then a further redistribution due to the introduction of a crack. As a result, the crack tip was surrounded by plastic strains before the external load was applied. The behaviour of the pipe with residual stress present is approximately in agreement with the measured behaviour of the pipe for both pure and four point bending up to loads of around 130kN.

CMOD (mm)

CMOD (mm)

— Experiment--Elastic only 9 Pure bending, without RS A Pure bending, with RS

Figure 5. Comparison of CMOD versus force between experiment and simulations using pure bending model a) CMOD between 0mm-0.5mm; b)

full scale CMOD.

However, as the loading increased beyond 130kN there were significant differences between the FE model and the experiment. This is shown in Figure 5b. In the case of the models with and without residual stress and between CMOD values of 0mm and 1.32mm, the presence of residual stresses reduced the loading bearing capacity of the cracked pipe. However, with increasing load and beyond a CMOD of 1.32mm, the responses of the pipe models with and without RS were virtually the same.

6. Conclusions

A large-scale four point bending experiment on LC3 pipe was completed during the EU-STYLE project. The post-test data were used to design the FE models to mimic the experiments, with and without residual stresses. Measured residual stresses were mapped into an uncracked FE model and then onto a cracked pipe model for subsequent loading. In the early stages of loading of the pipe there was good agreement between the experiment and FE simulations at initial crack size that contained residual stresses. The presence of tensile residual stresses were shown to promote onset of earlier yielding in the cracked pipe than would be the case if residual stresses were not present. However, for higher applied loads the experiment had lower load bearing capacity relative to the results from the FE simulations.

Acknowledgements

The authors would like to acknowledge the EU-STYLE project for the financial support for this work. The large scale experimental test was conducted at the SEMT/LISN laboratory at CEA, Saclay, France, and we are grateful for their contribution. David Smith would like to acknowledge the support provided by the Royal Academy of Engineering, Rolls Royce plc and EDF-Energy.

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