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3D Fracture Analysis of Cold Lap Weld Defect in Welded Structures
AYJWAT AWAIS BHATTI
Master of Science Thesis in Lightweight Structures Dept of Aeronautical and Vehicle Engineering Stockholm, Sweden 2010
1
2
A MASTER THESIS ON THE 3D FRACTURE ANALYSIS OF COLD LAP WELD DEFECT IN WELDED STRUCTURES Ayjwat Awais Bhatti A Master Thesis Report written in collaboration with Department of Aeronautical and Vehicle Engineering, Division of Lightweight Structures Royal Institute of Technology Stockholm, Sweden
December, 2010
I
II
Preface
The work in this master thesis has been carried out at the Division of Lightweight Structures at the Department of Aeronautical and Vehicle Engineering at KTH between July and December 2010.
Firstly I want to express gratitude to my supervisor Dr. Zuheir Barsoum, without whom this thesis would not have been possible. He has helped me throughout my work, given me his precious time, and taught me a lot and solved my problems.
I want to thank my parents as well who though are not here with me in Sweden but they have been a great moral help and their prayers have to do a lot with what I have been finally able to achieve. Lastly I want to thank my wife for her love, and patience.
Stockholm, December 2010
Ayjwat Awais Bhatti,
II
Abstract This thesis is concerned with the classification and effect of cold lap weld defect on the fatigue strength of a welded structure. Cold lap is a type of weld defect which occurs when molten metal does not completely fuse with the cold plate surface. This produces a crack like defect, often very small, which is parallel to the plate. The cold lap weld defect has been classified into three types namely spatter, overlap and spatter-overlap cold lap. Study showed that all three types of cold lap defects have the corresponded lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. Fatigue life assessment of the above mentioned three types of cold lap defects was carried out using finite element and crack growth analysis in 2D and 3D. In the 2D analysis the cold lap defects were modeled as line crack (assuming a/c=0). Based on the experiments the cold lap defects were visualized as having two probable crack shapes; penny shaped and part through, which required 3D crack growth analysis. Results showed that in 2D analysis the three types of cold lap defects have same influence on fatigue life of the weld. In 3D analysis, the shape of the cold lap defects did not show any difference in fatigue life. Overall penny shaped and part through cracks in 3D analysis predicted 1.75 times longer fatigue life as compared to line crack in 2D analysis.
Keywords
Cold lap defects, classification, crack growth modeling, fatigue.
III
Table of Contents INTRODUCTION..................................................................................................1 1.1 Background...........................................................................................................1 1.2 Cold Lap Weld Defect ........................................................................................1 1.3 Fatigue Life Assessment Methods.....................................................................3 2 METHODS...............................................................................................................4 2.1 2D Fracture Modeling.........................................................................................4 2.2 3D Fracture Modeling.........................................................................................5 3 RESULTS ..................................................................................................................7 4 DISCUSSION.........................................................................................................17 5 CONCLUSIONS....................................................................................................18 6 REFERENCES ......................................................................................................19 7 APPENDIX ............................................................................................................20 7.1 Spatter Cold Lap ................................................................................................20 7.2 Overlap Cold Lap ..............................................................................................21 7.3 Spatter-Overlap Cold Lap.................................................................................23 7.4 Penny Shape Crack ............................................................................................24 7.5 Part Through Shape Crack ...............................................................................26
1
IV
1 INTRODUCTION 1.1
Background
In vehicle, mining, agricultural, offshore industry, cranes and construction machineries the load carrying components are often composed of complex welded steel. Normally 60-80% of the vehicle weight consists of steel plates and steel castings in thickness 6-70mm with welding as the primary ing process [1]. The welding without improvement give rise to local stress concentrations and different defects and this combined with complex variable amplitude loading on welded components results in fatigue failure. In order to avoid fatigue failure along with increasing the performance to the weight ratio efficient and accurate fatigue design methods are to be used. It is well known fact that welding process creates crack like defects for instance cold laps, undercuts and root defect like lack of penetration etc in the structure. Along with these defects the local weld geometry e.g. toe angle, toe radius and throat thickness controls the fatigue life as well as give rise to local stress concentration making the welds the weakest part in fatigue loaded structures. Cold lap weld defect is one of the most important defects. An investigation [2] proved that 80 % of all discovered weld defects in MAG (Metal Active Gas) welds are cold laps. The range of a typical cold lap size is between 0.01 – 0.14 mm. Moreover, there seems to be an obvious connection between high speed welding and the occurrence frequency of cold laps [3]. A new novel weld class system [4-5] has been developed within Volvo to revise the old standards which had a poor relation between weld geometry, defects and fatigue strength. Therefore, in order to develop new updated acceptance criteria for weld defects within the weld class system, it is important to investigate the formation of cold laps, their different shapes and their effect on fatigue strength of welded structures.
1.2
Cold Lap Weld Defect
Cold lap is a type of weld defect which occurs when molten metal does not completely fuse with the cold plate surface. This produces a crack like defect, often very small, which is parallel to the plate. In a study [6] three types of cold lap weld defects have been defined on basis of batch of tandem arc MIG/MAG welding experiments namely 1.
Spatter cold lap
2.
Overlap cold lap
3.
Spatter-overlap cold lap
The micro camera and schematic figures [6] of three types of cold lap weld defects are shown in following figures.
1
Figure 1 - Spatter cold lap weld defect.
Figure 2 - Overlap cold lap weld defect.
Figure 3 – Spatter-Overlap cold lap weld defect. Specimens containing three types of cold lap defects according to the above classification were collected; sections were polished and investigated by optical microscope [6]. Results showed that all three types of cold lap defects have the corresponded lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the fatigue life assessment of the above mentioned three types of cold lap weld defects.
2
1.3
Fatigue Life Assessment Methods
Over the years several methods have been developed to assess the fatigue life of welded structures and components. Some methods are regarded as global approach methods in which the stresses far from the weld are taken into for fatigue life evaluation. These methods are acceptable for simple structures but for complex welded structures they are not very well connected with fatigue life prediction and hence new methods were required. With the introduction of FEA some local approach methods were developed in which stresses at the local weld geometry are considered for fatigue life prediction. Following are the methods for fatigue life assessment which are frequently used in connection with welded structures and components. •
Nominal Stress Approach
•
Hot Spot Stress Approach
•
Effective Notch Stress Method
•
Linear Elastic Fracture Mechanics
First two methods are global approach methods and the last two are local approach methods. All of these methods are outlined in [7] and a detailed procedure for implementing them is also described. Assessment and comparison of these methods can be found in [8] and [9]. Figure below shows the schematic illustration of the work effort required for fatigue analysis of welded ts for the different assessment methods.
Figure 4 - Schematic illustration of the relation between accuracy, complexity and work effort required for fatigue analysis of welded structures [1]. All three types of cold lap defects have lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the implementation of Linear Elastic Fracture Mechanics approach in which a cold lap can be modeled as a crack for assessment of the fatigue life.
3
2 METHODS As discussed earlier all three types of cold lap defects have lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the implementation of Linear Elastic Fracture Mechanics approach in which a cold lap can be modeled as a crack for assessment of the fatigue life. Fatigue life assessment of T-t fillet weld containing all three types cold lap weld defect as shown in the figure 1 is carried out using crack growth analysis in 2D and 3D. Isotropic elastic material is assumed with material constants E=210GPa and υ = 0.3.
Figure 5 - Two sided fillet weld T-t.
2.1
2D Fracture Modeling
FRANC2D [10] is used as a tool for 2D fracture analysis. It is a two dimensional, finite element based program for simulating curvilinear crack propagation in planar (plane stress, plane strain, and axisymmetric) structures [10]. Symmetric boundary condition is used therefore half of the model is constructed. Three types of the cold lap defects are constructed in 2D as shown in the figure 6. Spatter
Overlap
Spatter-Overlap
Figure 6 - Model, boundary conditions and the construction of different cold lap defects in 2D.
4
Figure 7 - Non cohesive initial crack of 0.25mm is modeled in all three cold lap defects. Crack is propagated in the direction of maximum hoop stress around the crack tip. In FRANC2D Displacement correlation technique is used for computing stress intensity factors and fatigue life analysis is based on Paris model as shown in equation below.
and are the material parameters and following values are selected for steel according to Where IIW recommendations [12].
2.2
3D Fracture Modeling
FRANC3D [11] is used as a tool for 3D fracture analysis. It is hybrid software that combines solid modeling, mesh generation and fracture mechanics for nucleating and propagating cracks in the model geometry [11]. Again symmetric boundary condition is used therefore half of the model is constructed in FRANC3D. Three types of the cold lap defects are constructed in 3D as shown in the figure 8. Boundary conditions are same as in 2D analysis.
(a)
(b)
(c)
Figure 8 - Model and the construction of different cold lap defects in 3D a) Spatter Cold Lap b) Overlap Cold Lap and c) Spatter-Overlap Cold Lap.
5
In 2D fracture analysis the crack is modeled like a line crack but in 3D fracture analysis we do not know the exact shape of the lack of fusion (cracks). Therefore two different shapes are assumed in all three types of cold lap weld defects namely. • •
Penny Shape Crack Part Through Crack
(a)
(b)
(c)
Figure 9 - Penny Shape Crack modeled in a) Spatter Cold Lap b) Overlap Cold Lap and c) SpatterOverlap Cold Lap.
(a)
(b)
(c)
Figure 10 - Part through Crack modeled in a) Spatter Cold Lap b) Overlap Cold Lap and c) SpatterOverlap Cold Lap. In FRANC3D Crack Propagation is based on the computed fracture parameters (SIF’s) and a rule to predict the new crack front, orientation and advance. The stress intensity factors (SIF) are calculated using Displacement Correlation Technique [13]. Crack propagation is handled by breaking the crack front into a series of discrete points and then using two dimensional theories to predict the crack growth direction in the plane normal to the crack front tangent at each of these points [13]. The amount of crack growth at each point is based on equation given below [13].
is the maximum extension provided manually and is a constant comparable Here to Paris constant. Smaller values of is recommended regardless of Paris constant as this factor is simply a way of trying to equalize the values along the crack front at discrete steps. Furthermore, larger value of sometimes result in unreasonable and distorted crack front therefore smaller values can be chosen.
6
A history of stress intensity factors as a function of the flaw size can be used in conjunction with the crack growth properties of material and load history to make a prediction of fatigue life.
3 RESULTS Firstly 2D fracture analysis of three types of cold lap defects is carried out. The crack is propagated using automatic propagation technique available in FRANC2D. Final length of the crack is 13 mm. The crack increments used in all three cold lap defects are given below.
(a)
(b)
(c)
Figure 11 - 2D propagation of line crack in a) Spatter Cold Lap, b) Overlap cold Lap and c) SpatterOverlap Cold Lap. For fatigue crack growth analysis Stress Intensity Factor history and values are extracted for all three types of cold lap defects and plotted as a function of crack length as shown in figure 12 and 13.
Figure 12 -
as a function of crack length.
7
Figure 13 -
as a function of crack length.
Fatigue life analysis based on Paris model is shown in figure 14.
Figure 14 - Fatigue Life as a function of crack length.
8
3D fracture analysis of three types of cold lap defect with different shapes of initial crack i.e. Penny Shape and Part Thru is carried out. The top and front view of crack propagation for first ten increments is shown in the figures 15, 16, 17 and 18.
(a)
(b)
(c)
Figure 15 - Top view of propagation of Penny Shape crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
(a)
(b)
(c)
Figure 16 - Top View of propagation of Part Thru crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
(a)
(b)
(c)
Figure 17 - Front view of propagation of Penny Shape crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
9
(a)
(b)
(c)
Figure 18 - Front View of propagation of Part Thru crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap. For fatigue crack growth analysis average values of Stress Intensity Factor ( ) for all three types of the cold lap defects containing Penny Shape and Part Thru crack are extracted by defining a path along the crack front and plotted as a function of crack length as shown in figure 19 and 20.
Figure 19 -
as a function of distance along crack front for Penny Shape Crack.
10
Figure 20 -
as a function of distance along crack front for Part Thru Crack.
Fatigue life analysis based on Paris model for Penny Shape and Part Thru crack in all cold lap defects is shown in figure 21 and 22.
Figure 21 - Fatigue life as a function of crack length for Penny Shape crack.
11
Figure 22 - Fatigue life as a function of crack length for Part Thru crack. Average values of Stress Intensity Factor (
Figure 23 -
) are also extracted as shown in figure 23 and 24.
as a function of distance along crack front for Penny Shape Crack.
12
Figure 24 -
as a function of distance along crack front for Part Thru Crack.
Since the results for of all three types of cold lap defects are identical therefore only Overlap Cold Lap having Penny Shape and Part Thru crack is presented here. It’s comparison with the 2D overlap defect is also presented here. The rest of the results can be consulted in the Appendix A attached herewith. ) for Overlap Cold Lap defect containing Penny Shape and Part Stress Intensity Factor ( and Thru crack are extracted by defining a path along the crack front and plotted as a function of crack length as shown in figure 25 and 26.
Figure 25 -
as a function of distance along crack front for Overlap cold lap.
13
Figure 26 -
as a function of distance along crack front for Overlap cold lap.
Fatigue life analysis based on Paris model for Penny Shape and Part Thru crack in Overlap cold lap defect is shown in figure 27.
Figure 27 - Fatigue life as a function of crack length for Overlap Cold Lap. A comparison of the results for Overlap cold lap defect in 2D and 3D is also presented. The variation of and values as a function of crack length are shown in figure 28 and 29. In case of 3D overlap cold lap defect containing penny shape and part thru crack average values of and are taken and plotted against the distance along the crack front.
14
Figure 28 -
as a function of crack length.
Figure 29 -
as a function of crack length.
15
Fatigue life analysis based on Paris model for 2D and 3D Overlap cold lap defect containing Penny Shape and Part Thru crack is shown in figure 30.
Figure 30 - Fatigue life as a function of crack length in 2D and 3D LEFM for Overlap Cold Lap defect.
16
4 DISCUSSION In 2D LEFM analysis the behavior of all three types of cold lap defects namely Spatter, Overlap and Spatter-Overlap is identical as shown in figure 12. There is a slight difference in the initial value of among cold lap defects which results in the difference in the predicted fatigue life. The difference among the predicted fatigue life is 3-7% and hence negligible. After 2mm of crack growth 84% of the life is consumed as shown in figure 14. in all three cold lap defects, therefore, Since the cold lap defect is modeled as a line crack during the first crack growth increment mixed mode crack growth will occur that results in higher value. This give rise to a kink angle of around at the first step and very quickly the crack will start growing in mode , and, values start to diminish shown in figure 13. In 3D LEFM analysis the behavior of three types of cold lap defects when modeled as penny shape and part thru crack is identical as shown in figures 19 and 20. There is an insignificant difference in predicted fatigue life for penny shape crack and part thru crack which ranges from 1-13% as shown in figures 21 and 22. The difference among predicted fatigue life is because the LEFM approach is sensitive to the initial crack length and also because of the error in numerical integration of the Paris Law. In 3D crack growth analysis of all three types of cold lap defects containing penny shape and part and thru crack the crack growth in depth (a direction) is very much influenced by mixed mode resulting in higher kink angle around for penny shape crack and for part thru crack which is pretty much similar to the behaviour of line crack in 2D. And the crack growth along surface and resulting in a small deflection angle around (c direction) is influenced by mixed mode . After the first crack growth increment the mixed mode quickly diminshes and the mode 1 crack propagation will dominate the subsequent crack growth steps as shown in figures 23 and 24. Since the results for of all three types of cold lap defects are identical therefore only Overlap Cold Lap having Penny Shape and Part Thru crack is presented in results section. If 2D and 3D LEFM value is much higher for the 2D analysis analysis of overlap cold lap is compared we can see that (when cold lap defect is modeled as a line crack) as compared with 3D analysis (when cold lap defects are modeled as penny shape and part thru cracks) as shown in figure 28. It is because the simple formula for stress intensity factor calculation gives lower values for penny shape and part thru crack [14]. Consequently the overlap cold lap containing penny shape and part thru crack has 1.75 times higher fatigue life as compared to the line crack as shown in figure 30. This result is in contrary with work done by Zuheir [14] in which 2.7 times higher fatigue life was predicted when cold lap defect is modeled as penny shape crack and inserted at the weld toe (without modeling the exact shape of the cold lap defect).
17
5 CONCLUSIONS •
In 2D LEFM the behavior of all three types of cold lap defects is identical.
•
In 2D LEFM simple line crack modeled at the weld toe (without modeling the exact shape of the cold lap defects) is sufficient for the analysis since its behavior is identical to the behavior of three types of cold lap defects.
•
In 3D LEFM the behavior of all three types of cold lap defects is identical regardless of the shape of the lack of fusion i.e. penny shape or part thru.
•
Since 3D LEFM analysis predicts 1.75 times higher fatigue life as compared to 2D LEFM analysis which is not a very significant difference therefore 2D LEFM analysis is recommended though it is conservative but cost effective.
•
It is difficult to validate these results in the laboratory since it is difficult to have the desired shape of the cold lap defect and crack shape. Therefore FEA results can be considered as a good approximation for the estimation of fatigue strength.
18
6 REFERENCES [1]
Barsoum, Z., Residual stress analysis and fatigue assessment of welded structures, Doctoral Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2008.
[2]
Lopez Martinez L. and Korsgren P., Characterization of welded defect distribution and weld geometry in welded fatigue test specimens, Fatigue under Spectrum Loading and Corrosive Environments, Warley, UK, EMAS, 1993.
[3]
Samuelsson J., Cold laps and weld quality acceptance limits, Design and analysis of welded high strength steel structures, Stockholm, EMAS, 2002.
[4]
Jonsson B. and Samuelsson J., A new weld class system, IIW Doc. XIII-2235-08, IIW Annual Assembly Graz, Austria, 2008.
[5]
Volvo weld quality standard, STD 181-0004, Version 1, April 2008.
[6]
Li, P., Characterization of cold lap defects in tandem arc welding, Proceedings of Swedish conference on lightweight optimized welded structures, Borlange, March 2009.
[7]
Hobbacher A., Fatigue design of welded ts and components, IIW doc. XIII-1539-96, 1996.
[8]
Martinsson J., Fatigue assessment of complex welded steel structures, Doctoral Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2005, ISBN 91-2783-968-6.
[9]
Pettersson G., Fatigue assessment of welded structures with non-linear boundary conditions, Licentiate Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2004, ISBN 91-7283-948-1.
[10] FRANC2D Version 3.2 http://www.cfg.cornell.edu/. [11] FRANC3D Version 3.2 http://www.cfg.cornell.edu/. [12] Hobbacher A., Recommendations for Fatigue design of welded ts and components, IIW doc. XIII1965-03/XV-1127-03, June 2005. [13] FRANC3D Concepts and s guide version 2.6 http://www.cfg.cornell.edu/. [14] Barsoum Z. and Jonsson B., Fatigue assessment and LEFM analysis of cruciform ts fabricated with different welding processes, IIW, 2007.
19
7 APPENDIX 7.1
Spatter Cold Lap
Figure 31-
Figure 32 -
SIF as a function of distance along the crack front.
as a function of distance along the crack front.
20
Figure 33 - Fatigue Life as function of crack length.
7.2
Overlap Cold Lap
Figure 34 -
SIF as a function of distance along the crack front.
21
Figure 35 -
as a function of distance along the crack front.
Figure 36 - Fatigue Life as function of crack length.
22
7.3
Spatter-Overlap Cold Lap
Figure 37 -
SIF as a function of distance along the crack front.
Figure 38 -
SIF as a function of distance along the crack front.
23
Figure 39 - Fatigue Life as function of crack length.
7.4
Penny Shape Crack
Figure 40 -
SIF as a function of distance along the crack front.
24
Figure 41 -
SIF as a function of distance along the crack front.
Figure 42 - Fatigue Life as function of crack length.
25
7.5
Part Through Shape Crack
Figure 43 -
SIF as a function of distance along the crack front.
Figure 44 -
SIF as a function of distance along the crack front.
26
Figure 45 - Fatigue Life as function of crack length.
27
TRITA-AVE 2011:01 ISSN 1651-7660
www.kth.se www.lightweightstructures.se
28
AYJWAT AWAIS BHATTI
Master of Science Thesis in Lightweight Structures Dept of Aeronautical and Vehicle Engineering Stockholm, Sweden 2010
1
2
A MASTER THESIS ON THE 3D FRACTURE ANALYSIS OF COLD LAP WELD DEFECT IN WELDED STRUCTURES Ayjwat Awais Bhatti A Master Thesis Report written in collaboration with Department of Aeronautical and Vehicle Engineering, Division of Lightweight Structures Royal Institute of Technology Stockholm, Sweden
December, 2010
I
II
Preface
The work in this master thesis has been carried out at the Division of Lightweight Structures at the Department of Aeronautical and Vehicle Engineering at KTH between July and December 2010.
Firstly I want to express gratitude to my supervisor Dr. Zuheir Barsoum, without whom this thesis would not have been possible. He has helped me throughout my work, given me his precious time, and taught me a lot and solved my problems.
I want to thank my parents as well who though are not here with me in Sweden but they have been a great moral help and their prayers have to do a lot with what I have been finally able to achieve. Lastly I want to thank my wife for her love, and patience.
Stockholm, December 2010
Ayjwat Awais Bhatti,
II
Abstract This thesis is concerned with the classification and effect of cold lap weld defect on the fatigue strength of a welded structure. Cold lap is a type of weld defect which occurs when molten metal does not completely fuse with the cold plate surface. This produces a crack like defect, often very small, which is parallel to the plate. The cold lap weld defect has been classified into three types namely spatter, overlap and spatter-overlap cold lap. Study showed that all three types of cold lap defects have the corresponded lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. Fatigue life assessment of the above mentioned three types of cold lap defects was carried out using finite element and crack growth analysis in 2D and 3D. In the 2D analysis the cold lap defects were modeled as line crack (assuming a/c=0). Based on the experiments the cold lap defects were visualized as having two probable crack shapes; penny shaped and part through, which required 3D crack growth analysis. Results showed that in 2D analysis the three types of cold lap defects have same influence on fatigue life of the weld. In 3D analysis, the shape of the cold lap defects did not show any difference in fatigue life. Overall penny shaped and part through cracks in 3D analysis predicted 1.75 times longer fatigue life as compared to line crack in 2D analysis.
Keywords
Cold lap defects, classification, crack growth modeling, fatigue.
III
Table of Contents INTRODUCTION..................................................................................................1 1.1 Background...........................................................................................................1 1.2 Cold Lap Weld Defect ........................................................................................1 1.3 Fatigue Life Assessment Methods.....................................................................3 2 METHODS...............................................................................................................4 2.1 2D Fracture Modeling.........................................................................................4 2.2 3D Fracture Modeling.........................................................................................5 3 RESULTS ..................................................................................................................7 4 DISCUSSION.........................................................................................................17 5 CONCLUSIONS....................................................................................................18 6 REFERENCES ......................................................................................................19 7 APPENDIX ............................................................................................................20 7.1 Spatter Cold Lap ................................................................................................20 7.2 Overlap Cold Lap ..............................................................................................21 7.3 Spatter-Overlap Cold Lap.................................................................................23 7.4 Penny Shape Crack ............................................................................................24 7.5 Part Through Shape Crack ...............................................................................26
1
IV
1 INTRODUCTION 1.1
Background
In vehicle, mining, agricultural, offshore industry, cranes and construction machineries the load carrying components are often composed of complex welded steel. Normally 60-80% of the vehicle weight consists of steel plates and steel castings in thickness 6-70mm with welding as the primary ing process [1]. The welding without improvement give rise to local stress concentrations and different defects and this combined with complex variable amplitude loading on welded components results in fatigue failure. In order to avoid fatigue failure along with increasing the performance to the weight ratio efficient and accurate fatigue design methods are to be used. It is well known fact that welding process creates crack like defects for instance cold laps, undercuts and root defect like lack of penetration etc in the structure. Along with these defects the local weld geometry e.g. toe angle, toe radius and throat thickness controls the fatigue life as well as give rise to local stress concentration making the welds the weakest part in fatigue loaded structures. Cold lap weld defect is one of the most important defects. An investigation [2] proved that 80 % of all discovered weld defects in MAG (Metal Active Gas) welds are cold laps. The range of a typical cold lap size is between 0.01 – 0.14 mm. Moreover, there seems to be an obvious connection between high speed welding and the occurrence frequency of cold laps [3]. A new novel weld class system [4-5] has been developed within Volvo to revise the old standards which had a poor relation between weld geometry, defects and fatigue strength. Therefore, in order to develop new updated acceptance criteria for weld defects within the weld class system, it is important to investigate the formation of cold laps, their different shapes and their effect on fatigue strength of welded structures.
1.2
Cold Lap Weld Defect
Cold lap is a type of weld defect which occurs when molten metal does not completely fuse with the cold plate surface. This produces a crack like defect, often very small, which is parallel to the plate. In a study [6] three types of cold lap weld defects have been defined on basis of batch of tandem arc MIG/MAG welding experiments namely 1.
Spatter cold lap
2.
Overlap cold lap
3.
Spatter-overlap cold lap
The micro camera and schematic figures [6] of three types of cold lap weld defects are shown in following figures.
1
Figure 1 - Spatter cold lap weld defect.
Figure 2 - Overlap cold lap weld defect.
Figure 3 – Spatter-Overlap cold lap weld defect. Specimens containing three types of cold lap defects according to the above classification were collected; sections were polished and investigated by optical microscope [6]. Results showed that all three types of cold lap defects have the corresponded lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the fatigue life assessment of the above mentioned three types of cold lap weld defects.
2
1.3
Fatigue Life Assessment Methods
Over the years several methods have been developed to assess the fatigue life of welded structures and components. Some methods are regarded as global approach methods in which the stresses far from the weld are taken into for fatigue life evaluation. These methods are acceptable for simple structures but for complex welded structures they are not very well connected with fatigue life prediction and hence new methods were required. With the introduction of FEA some local approach methods were developed in which stresses at the local weld geometry are considered for fatigue life prediction. Following are the methods for fatigue life assessment which are frequently used in connection with welded structures and components. •
Nominal Stress Approach
•
Hot Spot Stress Approach
•
Effective Notch Stress Method
•
Linear Elastic Fracture Mechanics
First two methods are global approach methods and the last two are local approach methods. All of these methods are outlined in [7] and a detailed procedure for implementing them is also described. Assessment and comparison of these methods can be found in [8] and [9]. Figure below shows the schematic illustration of the work effort required for fatigue analysis of welded ts for the different assessment methods.
Figure 4 - Schematic illustration of the relation between accuracy, complexity and work effort required for fatigue analysis of welded structures [1]. All three types of cold lap defects have lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the implementation of Linear Elastic Fracture Mechanics approach in which a cold lap can be modeled as a crack for assessment of the fatigue life.
3
2 METHODS As discussed earlier all three types of cold lap defects have lack of fusion in the interface, which could be considered as initial macro cracks in different shapes where a possible fatigue crack growth could start. This motivates the implementation of Linear Elastic Fracture Mechanics approach in which a cold lap can be modeled as a crack for assessment of the fatigue life. Fatigue life assessment of T-t fillet weld containing all three types cold lap weld defect as shown in the figure 1 is carried out using crack growth analysis in 2D and 3D. Isotropic elastic material is assumed with material constants E=210GPa and υ = 0.3.
Figure 5 - Two sided fillet weld T-t.
2.1
2D Fracture Modeling
FRANC2D [10] is used as a tool for 2D fracture analysis. It is a two dimensional, finite element based program for simulating curvilinear crack propagation in planar (plane stress, plane strain, and axisymmetric) structures [10]. Symmetric boundary condition is used therefore half of the model is constructed. Three types of the cold lap defects are constructed in 2D as shown in the figure 6. Spatter
Overlap
Spatter-Overlap
Figure 6 - Model, boundary conditions and the construction of different cold lap defects in 2D.
4
Figure 7 - Non cohesive initial crack of 0.25mm is modeled in all three cold lap defects. Crack is propagated in the direction of maximum hoop stress around the crack tip. In FRANC2D Displacement correlation technique is used for computing stress intensity factors and fatigue life analysis is based on Paris model as shown in equation below.
and are the material parameters and following values are selected for steel according to Where IIW recommendations [12].
2.2
3D Fracture Modeling
FRANC3D [11] is used as a tool for 3D fracture analysis. It is hybrid software that combines solid modeling, mesh generation and fracture mechanics for nucleating and propagating cracks in the model geometry [11]. Again symmetric boundary condition is used therefore half of the model is constructed in FRANC3D. Three types of the cold lap defects are constructed in 3D as shown in the figure 8. Boundary conditions are same as in 2D analysis.
(a)
(b)
(c)
Figure 8 - Model and the construction of different cold lap defects in 3D a) Spatter Cold Lap b) Overlap Cold Lap and c) Spatter-Overlap Cold Lap.
5
In 2D fracture analysis the crack is modeled like a line crack but in 3D fracture analysis we do not know the exact shape of the lack of fusion (cracks). Therefore two different shapes are assumed in all three types of cold lap weld defects namely. • •
Penny Shape Crack Part Through Crack
(a)
(b)
(c)
Figure 9 - Penny Shape Crack modeled in a) Spatter Cold Lap b) Overlap Cold Lap and c) SpatterOverlap Cold Lap.
(a)
(b)
(c)
Figure 10 - Part through Crack modeled in a) Spatter Cold Lap b) Overlap Cold Lap and c) SpatterOverlap Cold Lap. In FRANC3D Crack Propagation is based on the computed fracture parameters (SIF’s) and a rule to predict the new crack front, orientation and advance. The stress intensity factors (SIF) are calculated using Displacement Correlation Technique [13]. Crack propagation is handled by breaking the crack front into a series of discrete points and then using two dimensional theories to predict the crack growth direction in the plane normal to the crack front tangent at each of these points [13]. The amount of crack growth at each point is based on equation given below [13].
is the maximum extension provided manually and is a constant comparable Here to Paris constant. Smaller values of is recommended regardless of Paris constant as this factor is simply a way of trying to equalize the values along the crack front at discrete steps. Furthermore, larger value of sometimes result in unreasonable and distorted crack front therefore smaller values can be chosen.
6
A history of stress intensity factors as a function of the flaw size can be used in conjunction with the crack growth properties of material and load history to make a prediction of fatigue life.
3 RESULTS Firstly 2D fracture analysis of three types of cold lap defects is carried out. The crack is propagated using automatic propagation technique available in FRANC2D. Final length of the crack is 13 mm. The crack increments used in all three cold lap defects are given below.
(a)
(b)
(c)
Figure 11 - 2D propagation of line crack in a) Spatter Cold Lap, b) Overlap cold Lap and c) SpatterOverlap Cold Lap. For fatigue crack growth analysis Stress Intensity Factor history and values are extracted for all three types of cold lap defects and plotted as a function of crack length as shown in figure 12 and 13.
Figure 12 -
as a function of crack length.
7
Figure 13 -
as a function of crack length.
Fatigue life analysis based on Paris model is shown in figure 14.
Figure 14 - Fatigue Life as a function of crack length.
8
3D fracture analysis of three types of cold lap defect with different shapes of initial crack i.e. Penny Shape and Part Thru is carried out. The top and front view of crack propagation for first ten increments is shown in the figures 15, 16, 17 and 18.
(a)
(b)
(c)
Figure 15 - Top view of propagation of Penny Shape crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
(a)
(b)
(c)
Figure 16 - Top View of propagation of Part Thru crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
(a)
(b)
(c)
Figure 17 - Front view of propagation of Penny Shape crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap.
9
(a)
(b)
(c)
Figure 18 - Front View of propagation of Part Thru crack for first ten crack increments in a) Spatter Cold Lap, b) Overlap cold Lap and c) Spatter-Overlap Cold Lap. For fatigue crack growth analysis average values of Stress Intensity Factor ( ) for all three types of the cold lap defects containing Penny Shape and Part Thru crack are extracted by defining a path along the crack front and plotted as a function of crack length as shown in figure 19 and 20.
Figure 19 -
as a function of distance along crack front for Penny Shape Crack.
10
Figure 20 -
as a function of distance along crack front for Part Thru Crack.
Fatigue life analysis based on Paris model for Penny Shape and Part Thru crack in all cold lap defects is shown in figure 21 and 22.
Figure 21 - Fatigue life as a function of crack length for Penny Shape crack.
11
Figure 22 - Fatigue life as a function of crack length for Part Thru crack. Average values of Stress Intensity Factor (
Figure 23 -
) are also extracted as shown in figure 23 and 24.
as a function of distance along crack front for Penny Shape Crack.
12
Figure 24 -
as a function of distance along crack front for Part Thru Crack.
Since the results for of all three types of cold lap defects are identical therefore only Overlap Cold Lap having Penny Shape and Part Thru crack is presented here. It’s comparison with the 2D overlap defect is also presented here. The rest of the results can be consulted in the Appendix A attached herewith. ) for Overlap Cold Lap defect containing Penny Shape and Part Stress Intensity Factor ( and Thru crack are extracted by defining a path along the crack front and plotted as a function of crack length as shown in figure 25 and 26.
Figure 25 -
as a function of distance along crack front for Overlap cold lap.
13
Figure 26 -
as a function of distance along crack front for Overlap cold lap.
Fatigue life analysis based on Paris model for Penny Shape and Part Thru crack in Overlap cold lap defect is shown in figure 27.
Figure 27 - Fatigue life as a function of crack length for Overlap Cold Lap. A comparison of the results for Overlap cold lap defect in 2D and 3D is also presented. The variation of and values as a function of crack length are shown in figure 28 and 29. In case of 3D overlap cold lap defect containing penny shape and part thru crack average values of and are taken and plotted against the distance along the crack front.
14
Figure 28 -
as a function of crack length.
Figure 29 -
as a function of crack length.
15
Fatigue life analysis based on Paris model for 2D and 3D Overlap cold lap defect containing Penny Shape and Part Thru crack is shown in figure 30.
Figure 30 - Fatigue life as a function of crack length in 2D and 3D LEFM for Overlap Cold Lap defect.
16
4 DISCUSSION In 2D LEFM analysis the behavior of all three types of cold lap defects namely Spatter, Overlap and Spatter-Overlap is identical as shown in figure 12. There is a slight difference in the initial value of among cold lap defects which results in the difference in the predicted fatigue life. The difference among the predicted fatigue life is 3-7% and hence negligible. After 2mm of crack growth 84% of the life is consumed as shown in figure 14. in all three cold lap defects, therefore, Since the cold lap defect is modeled as a line crack during the first crack growth increment mixed mode crack growth will occur that results in higher value. This give rise to a kink angle of around at the first step and very quickly the crack will start growing in mode , and, values start to diminish shown in figure 13. In 3D LEFM analysis the behavior of three types of cold lap defects when modeled as penny shape and part thru crack is identical as shown in figures 19 and 20. There is an insignificant difference in predicted fatigue life for penny shape crack and part thru crack which ranges from 1-13% as shown in figures 21 and 22. The difference among predicted fatigue life is because the LEFM approach is sensitive to the initial crack length and also because of the error in numerical integration of the Paris Law. In 3D crack growth analysis of all three types of cold lap defects containing penny shape and part and thru crack the crack growth in depth (a direction) is very much influenced by mixed mode resulting in higher kink angle around for penny shape crack and for part thru crack which is pretty much similar to the behaviour of line crack in 2D. And the crack growth along surface and resulting in a small deflection angle around (c direction) is influenced by mixed mode . After the first crack growth increment the mixed mode quickly diminshes and the mode 1 crack propagation will dominate the subsequent crack growth steps as shown in figures 23 and 24. Since the results for of all three types of cold lap defects are identical therefore only Overlap Cold Lap having Penny Shape and Part Thru crack is presented in results section. If 2D and 3D LEFM value is much higher for the 2D analysis analysis of overlap cold lap is compared we can see that (when cold lap defect is modeled as a line crack) as compared with 3D analysis (when cold lap defects are modeled as penny shape and part thru cracks) as shown in figure 28. It is because the simple formula for stress intensity factor calculation gives lower values for penny shape and part thru crack [14]. Consequently the overlap cold lap containing penny shape and part thru crack has 1.75 times higher fatigue life as compared to the line crack as shown in figure 30. This result is in contrary with work done by Zuheir [14] in which 2.7 times higher fatigue life was predicted when cold lap defect is modeled as penny shape crack and inserted at the weld toe (without modeling the exact shape of the cold lap defect).
17
5 CONCLUSIONS •
In 2D LEFM the behavior of all three types of cold lap defects is identical.
•
In 2D LEFM simple line crack modeled at the weld toe (without modeling the exact shape of the cold lap defects) is sufficient for the analysis since its behavior is identical to the behavior of three types of cold lap defects.
•
In 3D LEFM the behavior of all three types of cold lap defects is identical regardless of the shape of the lack of fusion i.e. penny shape or part thru.
•
Since 3D LEFM analysis predicts 1.75 times higher fatigue life as compared to 2D LEFM analysis which is not a very significant difference therefore 2D LEFM analysis is recommended though it is conservative but cost effective.
•
It is difficult to validate these results in the laboratory since it is difficult to have the desired shape of the cold lap defect and crack shape. Therefore FEA results can be considered as a good approximation for the estimation of fatigue strength.
18
6 REFERENCES [1]
Barsoum, Z., Residual stress analysis and fatigue assessment of welded structures, Doctoral Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2008.
[2]
Lopez Martinez L. and Korsgren P., Characterization of welded defect distribution and weld geometry in welded fatigue test specimens, Fatigue under Spectrum Loading and Corrosive Environments, Warley, UK, EMAS, 1993.
[3]
Samuelsson J., Cold laps and weld quality acceptance limits, Design and analysis of welded high strength steel structures, Stockholm, EMAS, 2002.
[4]
Jonsson B. and Samuelsson J., A new weld class system, IIW Doc. XIII-2235-08, IIW Annual Assembly Graz, Austria, 2008.
[5]
Volvo weld quality standard, STD 181-0004, Version 1, April 2008.
[6]
Li, P., Characterization of cold lap defects in tandem arc welding, Proceedings of Swedish conference on lightweight optimized welded structures, Borlange, March 2009.
[7]
Hobbacher A., Fatigue design of welded ts and components, IIW doc. XIII-1539-96, 1996.
[8]
Martinsson J., Fatigue assessment of complex welded steel structures, Doctoral Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2005, ISBN 91-2783-968-6.
[9]
Pettersson G., Fatigue assessment of welded structures with non-linear boundary conditions, Licentiate Thesis, Dept. of Aeronautical and Vehicle Engineering, KTH, Sweden 2004, ISBN 91-7283-948-1.
[10] FRANC2D Version 3.2 http://www.cfg.cornell.edu/. [11] FRANC3D Version 3.2 http://www.cfg.cornell.edu/. [12] Hobbacher A., Recommendations for Fatigue design of welded ts and components, IIW doc. XIII1965-03/XV-1127-03, June 2005. [13] FRANC3D Concepts and s guide version 2.6 http://www.cfg.cornell.edu/. [14] Barsoum Z. and Jonsson B., Fatigue assessment and LEFM analysis of cruciform ts fabricated with different welding processes, IIW, 2007.
19
7 APPENDIX 7.1
Spatter Cold Lap
Figure 31-
Figure 32 -
SIF as a function of distance along the crack front.
as a function of distance along the crack front.
20
Figure 33 - Fatigue Life as function of crack length.
7.2
Overlap Cold Lap
Figure 34 -
SIF as a function of distance along the crack front.
21
Figure 35 -
as a function of distance along the crack front.
Figure 36 - Fatigue Life as function of crack length.
22
7.3
Spatter-Overlap Cold Lap
Figure 37 -
SIF as a function of distance along the crack front.
Figure 38 -
SIF as a function of distance along the crack front.
23
Figure 39 - Fatigue Life as function of crack length.
7.4
Penny Shape Crack
Figure 40 -
SIF as a function of distance along the crack front.
24
Figure 41 -
SIF as a function of distance along the crack front.
Figure 42 - Fatigue Life as function of crack length.
25
7.5
Part Through Shape Crack
Figure 43 -
SIF as a function of distance along the crack front.
Figure 44 -
SIF as a function of distance along the crack front.
26
Figure 45 - Fatigue Life as function of crack length.
27
TRITA-AVE 2011:01 ISSN 1651-7660
www.kth.se www.lightweightstructures.se
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