Review on finite element analysis for estimation of residual stresses in welded structures

Review on finite element analysis for estimation of residual stresses in welded structures

Available online at www.sciencedirect.com ScienceDirect Materials Today: Proceedings 4 (2017) 10230–10234 www.materialstoday.com/proceedings ICEMS ...

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Available online at www.sciencedirect.com

ScienceDirect Materials Today: Proceedings 4 (2017) 10230–10234

www.materialstoday.com/proceedings

ICEMS 2016

Review on finite element analysis for estimation of residual stresses in welded structures Bhanu Prakash Mahur*, Yogesh Bhardwaj, Vikas Bansal Mechanical Engineering Department, Rajasthan Technical University, Kota 324010, India

Abstract In this review various finite element analysis approaches available for estimation of residual stresses in welded structures are presented. FEA can effectively estimate residual stresses, especially the relaxation of residual stresses in weld region and region in close vicinity under repeated loading. The amount of the residual stress relaxation depends on the magnitude of applied repeated loading. Comparison revealed that rapid dumping approach have least computational time and shows qualitatively good agreement with experimental values for welding residual stresses whereas gradual weld bead deposition approach estimated more exact results as compared to experimental and various other approaches. Using substructuring approach computation is remarkably reduced without any loss to acceptable accuracy of predicted welding residual stresses. In this composition various assumptions required to carry out finite element analysis of welded structures are also explained. Conclusion indicates that it is important to include all weld sequences for accurate estimation of residual stresses in a structure but even before that it is required to analyze the weld sequences in critical area as a starting point in initial design stage. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of International Conference on Recent Trends in Engineering and Material Sciences (ICEMS-2016). Keywords: Residual stresses; Stress based fatigue analysis; Finite element analysis; Welding simulation.

1.

Introduction

Welding, a efficient metal joining technique widely used for development of structures and machines in all engineering sectors is third widely used process in manufacturing [1]. Welding induces residual stresses which pose

* Corresponding author. Tel.: +91-7737302465. E-mail address: [email protected] (B. P. Mahur ) 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of International Conference on Recent Trends in Engineering and Material Sciences (ICEMS2016).

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serious problem for quality of finished welded structure making estimation of residual stress pattern very crucial. In order to mitigate negative impacts of welding on service life, a large-scale research work on welding residual stresses is being carried out by researchers throughout the world. Analysis using experimental, analytical, and computational modelling are carried out in order to study evolvement of residual stresses in welded structures. Conventionally, Methods of estimation of residual stresses were only experimental. These can be categorized in terms of the extent of damage they bring out to the metal i.e. destructive, semi-destructive and non-destructive methods. In the destructive and semi-destructive, the residual stresses are measured by means of stress-relaxation i.e. by measuring the elastic-strain release induced when a sample is segmented, drilled or milled using mechanical/electrical strain gauges. Generally, resistance strain gauges, removable extensometers and photoelastic surface layers are mainly used for measurements. Though they are destructive and semi-destructive, the stress relaxation techniques provide dependable data and are the most widely accepted and are frequently referred [2-5]. In crystalline material, elastic strain can be prescribed non-destructively by evaluating lattice specification using XRD. Due to limitations of either cost or accuracy, its practical application is less. Numerical simulation based on Finite Element Analysis (FEA) offers a radical approach for the prediction of residual stress in welded structure. Ueda [6] and Nomoto [7] initiated the use of finite element methods to analyze residual stresses in welded joints. In same series, Ueda [8–11] evolved a modern method of measuring axisymmetric, 3-D residual stresses such that inherent strains are treated as parameters. This work further formulated a foundational theory using FEM. Brown and Song [12,13] performed 2-D axisymmetric and full 3-D analysis of welded ring-stiffened cylinder to investigate the elastic coupling between the welded zone and global three dimensional geometry. Similarly, Michaleris and DeBiccari [14] used 2-D generalized plane strain models of local weld zones in conjunction with subsequent 3-D elastic analyses. Residual stresses and various welded defects are unavoidable in welding, and the impact of these stresses on the welded structures cannot be overseen and hence determining residual stresses is an important problem. However, accurate estimation of residual stresses and deformations induced by welding is extremely difficult because thermal and mechanical functioning in welding include localised high temperature, temperature dependence of material properties, and a dynamic heat source. FE simulation of the welding process is highly effective in predicting thermomechanical behavior. This investigation performs thermal elastoplastic analysis using FEA techniques to study the thermomechanical behavior and estimate the residual stresses in welded structures. 2. Finite element simulation approaches FEA can effectively estimate residual stresses, especially the relaxation of residual stresses in weld region and in close vicinity under cyclic loading. The amount of the residual stress relaxation depends on the magnitude of applied repeated loading. In a succession to fabricate a framework for efficient prediction of residual stresses in welded structures different finite element simulation approaches are employed. In all FE approaches mentioned, three dimensional sequentially coupled thermomechanical simulations are performed. The flowchart of residual stress analysis is as depicted in Fig. 1. 2.1. Gradual weld bead deposition approach Generally, three dimensional welding simulations are processed using gradual weld bead deposition approach [15-17]. In this approach the filler material deposition is simulated by activating and deactivating elements characterizing filler material (element death-birth technique) in both thermal and mechanical analysis. During thermal simulation the heat inputs in welded region are provided using steady volumetric and surface heat input model. The heat provided by the welding arc is modelled as uniform surface heat flux while the heat provided by molten droplets is modelled as volumetric heat generation body load. Elements that represent filler material are first deactivated followed by activation of block of filler elements in progression as they come under the influence of welding arc. The heat inputs are put into a block of active elements at a particular heating load step for certain time depending upon the speed of

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Fig. 1. Flowchart of residual stress analysis [15]

welding (i.e heating cycle) and activation length. In the succeeding load step the heat inputs to the previous block is cleared, next adjoining filler elements block is activated and same heat inputs are implemented. This activity is iterated till welding is completed. In due course the temperature of entire model is allowed to cool down (cooling cycle). Volumetric and surface heat input model used in analysis is expressed as following: Q=Qsurface + Qvolume

(1)

Q surface is the surface heat input [J/m2s] applied to the external area of the corresponding activated block, while Q volume volumetric heat input [J/m2 s] applied to the activated block. Eq. (1) can be modified to be written as (2) where η is the arc efficiency, U and I represent arc voltage and current respectively. Volume (bv) and surface (bs) heat factors have no real meaning and are adjusted manually so as to achieve desired temperature distributions and fusion in HAZ.

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2.2. Block and rapid dumping approach Block dumping or lumped pass is an efficient welding approach for estimation of residual stresses in welded structures [19-21]. This approach also makes use of activation and deactivation of the elements for simulating filler material deposition in thermal as well as mechanical analysis. In thermal analysis all filler elements within structure are brought to deactivation. Followed by all filler elements belonging to first weld sequence in welding are activated and heat input (volumetric and surface) are applied for a particular time depending on the welding speed a well as activation length. Afterwards, the heat input from the previous weld bead is cleared and all filler elements in the progressive welding sequence are activated and same heat input is stored. This process is repeated until welding is concluded. Ultimately the structure is allowed to cool down to normal temperature. The mechanical analysis is performed in a same manner as in gradual weld bead deposition approach. The difference is that dissimilar of using block of filler elements, whole weld bead is considered. Rapid dumping approach [22] is the hybrid of weld deposition in thermal and dumping approach in the mechanical analysis. 2.3. Substructuring technique During welding, the region in close vicinity of heat source is extremely nonlinear whereas the remaining region in the structure behaves almost linearly elastic. In FE analysis the whole structure is assumed as a non-linear model and the element matrices of whole structure are again and again calculated at every equilibrium iteration resulting in extra computation. The computation time can be lessened by substructuring the linear portion of the model thus only element matrices of the nonlinear portion are repeatedly calculated at every equilibrium iterative point. Substructuring reduce size of the matrix equations by condensing a group of elements inside a structure into one single element. The elimination of the degree of freedom in the super element is performed by static condensation. For a substructure S, the equilibrium equation based on FEM is given by [KS]. {US}= {FS}

(3)

where KS is the stiffness matrix of substructure S, US and FS represents the corresponding node displacement and load vector. 
To perform the static condensation, KS, US, FS of the super element should be partitioned as shown in [23]. 3. Assumptions for FE simulation of welded structures In multipass welding different assumption exist so as to simplify the simulation. Evaluating multi-pass welds as a set of single-pass welds is rigorous. Lumping sequential passes collectively is another way to reduce the computation time. Other assumptions of the thermal and mechanical process are to either merge weld passes into larger welds or accounting for some of the weld passes. To simulate the filler material, particularly in multi-pass weld the technique of “birth-death” of elements is appropriate as described in the FE-software ANSYS [24]. All the elements are defined in the model and born in the later stage of the analysis. Another approach by Lindgren [25] is called quiet element where the structure is included in the computation model. The elements, corresponding to non-laid welds are given material properties so that they do not affect the rest of the model. The elements are given normal material properties at the beginning of the weld pass, and all the tensors that have been accumulated are removed. 4. Conclusion Comparing various FE simulation approaches it is revealed that rapid dumping approach have least computational time and shows qualitatively good agreement with experimental values for welding residual stresses whereas gradual weld bead deposition approach estimated more exact results as compared to experimental and various other

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approaches. Using substructuring approach computation is remarkably reduced without any loss to acceptable accuracy of estimated welding residual stresses. It is also concluded that it is crucial to include all weld sequences for close prediction of residual stresses but even before that it is promoted to analyze the weld sequences in critical area as a starting point in the initial design stage. References [1] D.S. Naidu, K.L. Moore, S. Ozcelik, Modeling, sensing and control of gas metal arc welding, Elsevier, Kidlington, 2003.
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 [7] T. Nomoto, Finite element analysis of thermal stress during welding, Ph.D. thesis, University of Tokyo, 1971. 
 [8] Y. Ueda, K. Fukuda, M. Tanigawa, New measuring of three dimensional residual stress based on theory of inherent strain, Transactions of JWRI 8 (2) (1979) 89–96. 
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