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Procedia Engineering 10 (2011) 3273-3278

Engineering

Procedia

The effect of residual stresses on the fracture behaviour of a cracked body under mixed mode loading

K. Sedighiania*, J. Mosayebnejada, H. Zakerhaghighib, and H. Ehsasic

"Fatigue and Fracture Laboratory, Department of Mechanical engineering, Iran University of Science > Technology, Tehran, Iran bDepartment of Mechanical engineering, Department of Mechanical engineering, Shiraz University, Shiraz, Iran cDepartment of Mechanical engineering, Razi University, Kermanshah, Iran

Abstract

Many of engineering structures operate under the presence of residual stresses due to welding or other manufacturing processes. Because of the magnified effects of residual stress on crack growth behaviour, corrections for residual stress are needed for appropriate fatigue life estimation and fracture resistance analysis of cracked structures subjected to mixed mode I and II loading. In this paper, the effect of various residual stress profiles on the crack tip parameters is studied. To make the results more general, two types of butt welds are assumed and the corresponding residual stresses due to the weld are estimated. Than, the effect of residual stress on the crack tip parameters are calculated for complete range of mode mixities from pure mode I to pure mode II and for different crack lengths. It was found that the influence of welding residual stress on the crack tip parameters can be considerable, depending on the stress field, the loading direction, and geometry. In this research, the finite element method is employed to determine the residual stresses and the related stress intensity factors.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of ICM11

Keywords: Fracture mechanics; Residual Stress, Weld, Mixed mode I/II; Stress intensity factors; T-stress

1. Introduction

Residual stress can be classified as the stresses that exist in a component after all external forces have been removed. Accurate determination of residual stresses is a key issue in the strength analysis of welded structures. Experimental techniques to measure residual stresses are often very expensive and

i Corresponding author. Tel.: +98-21-66364252; fax: +98-21-77240488. E-mail address: karosedighiani@gmail.com.

1877-7058 © 2011 Publi d by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.540

finite element analysis has been traditionally recognized as the most general technique for evaluating the residual stresses [1-3].

It is well known that the behaviour of cracks located inside or near the heat affected zone is seriously influenced by the welding induced residual stresses. Many efforts have been devoted to the prediction of residual stress effect on crack initiation angle, fracture resistance, and fatigue crack growth rates [4-8]. Linear elastic fracture mechanics analysis is the most common technique for assessing the behaviour of the cracked structure in the presence of residual stresses. After determination of the crack tip parameters simple formulas for fatigue crack propagation, like Paris law [9], or more sophisticated criteria, like the maximum tangential stress criterion [10] can be used for the calculation of stable or unstable crack propagation.

For the calculation of crack tip parameters under residual stress fields, only limited works have been published. Usually because of lack of information on residual stress distributions, recommended upper-bound residual stress profiles [4-6] have been used by many researchers to evaluate cracked specimen in the presence of residual stresses.

In this study, three-dimensional finite element analysis is performed to determine the residual stress distributions in a welded plate. Subsequent to the derivation of the appropriate residual stress in the component, a fracture mechanics analysis is, generally, required to determine the appropriate fracture mechanics parameter to account for the effect of the residual stress on cracks. In the second step in this paper, the calculated residual stress are projected on the cracked specimen and the crack tip parameters are derived directly based on the 3-D residual stresses calculated from the first step.

2. Finite Element Analysis

2.1. Weld modeling

Three-dimensional finite element models of the welded specimen were simulated and analyzed in the finite element code ABAQUS. Two types of butt welding are studied in this paper: single V weld bevel with a single pass and double V weld bevel with two passes. The geometry of the welded specimens is shown schematically in Fig. 1(a). The plate considered is square with 300 mm long, 300 mm wide, and 6 mm thickness, resulting from the welding of two identical segments made of stainless steel 304. The material properties are chosen according to the [11].

A sequentially thermo mechanical elastic plastic analysis was used for modeling residual stresses in a butt welding of two flat plates. Firstly, transient thermal heat transfer analysis were performed by using semi 3-D finite element with about 120,000 cubic elements, to obtain the history of temperature distribution in the welding by considering following assumptions

• Temperature dependent material properties

• Combined heat loss due to radiation and convection heat transfer through surfaces

• Body heat generation due to weld torch in the form of Gaussian distribution in the directions of normal to the weld line and uniform in the direction of weld line.

The heat input model was considered according to the following body heat generation model

where TC is the total welding time for one pass (TC=60S) and Tws is time for welding torch to travel the weld pool (TC<=2S). c denotes the half of the weld pool width (2c=6 for single V weld and 2c=3 for double V weld), b the depth of weld pool (6=6 for single V weld and b=3 for double V weld), L length of

the plate, $ welding efficiency ($=85%), V welding voltage (F=15V), and I welding current (9=200A for single V weld and /=120A for double V weld).

After obtaining transient temperature history of welding an Elastic-plastic mechanical analysis was performed to obtain stress and strain history due to applied temperature from welding heat transfer analysis. The following assumptions were made for mechanical analysis:

• Temperature dependent material property

• Elastic-Plastic analysis with kinematics hardening

• Von Mises yield criterion

• Element activation and deactivations of weld filler material

2.2. Fracture modeling

A central crack of length 2a inclined at an angle / with the vertical axis (weld line) is considered at the centre of the plate, as shown in Fig. 1(b). The second-order elements (20-node bricks) were used to analyze the cracked specimen. The singular elements with nodes at quarter-point positions, which are

(a) (l>)

Fig. 1. Geometry and main parameters of (a) welded specimen; (b) cracked specimen.

• Single V weld Double V weld

-50 0 50

Position from weld line (mm)

0. 40 H S

0 tfl tfl

-100 -50 0 50 100

Position from weld line (mm)

Fig. 2. Variation of the residual stresses (a) parallel to the weld line; (b) perpendicular to the weld line.

Fig. 3. Variation of crack tip parameters versus crack length for different loading angles.

highly recommended for crack modeling, were used for the first ring of elements around the crack tip. In the circular partitions surrounding the crack tip where the contour integrals are calculated, the mesh was biased toward the crack tip. The stress intensity factors and T-stress were extracted directly from ABAQUS which makes use of an interaction integral method to compute the stress intensity factors for a crack under mixed-mode loading [12]. The crack length 2a is parametrically varying from 20 to 60 mm, while the crack inclination angle in respect to weld line varies between 0 and 90. The 3-D residual stresses calculated from the pervious step were used to analyze the cracked components.

¡t 16

1 2 3 4 5

Thickness, t (mm)

2 3 4 5

Thickness, t (mm)

Thickness, t (mm)

Thickness, t (mm)

Thickness, t (mm)

Thickness, t (mm)

Fig. 4. Variation of crack tip parameters through the specimen thickness for .=10 mm.

3. Results and discussion

-100 -

-150 -

Fig. 2(a) and 2(b) show, respectively, the variation of the residual stresses parallel to the weld line (y-direction) and perpendicular to the weld line (x-direction) through the plate width. Clearly, the residual stress field is symmetric relative to the weld line. The residual stress profile depends on several factors, such as the plate materials, specimen geometries and welding parameters. The maximum residual stress was found to be near the weld line with a distance about 15 mm.

In the present study the effect of external loads was ignored for calculating the crack tip parameters. By taking advantage of the stress intensity factor superposition principle, stress intensity factors for cracked body problems combining residual stresses and different external loadings can be calculated, by adding the stress intensity factors due to the different external loadings to the stress intensity factors due to residual stresses.

Fig. 3 shows the variation of K9, Kn, and T-stress as a function of a for various crack inclination angles /at the mid surface of the plate for both type of welds. It is clear from this figure that for large value of / the mode I stress factor is first increased as the crack length increases, and then it decreases when crack length becomes larger. This means a smaller driving force for a deeper crack. An increase can be observed for the mode II stress intensity factor with increase in / and it reaches a maximum at /=45°. After that the mode II stress intensity factor decreases with an increase in the crack inclination angle. Also, for large value of /and for small crack lengths the value of T-stress is considerable.

The variation of K9, Kn, and T-stress through the thickness of the specimen for a=10 mm are shown in Fig. 4. It is clear from this figure that for single V weld type there is a sensible variation in the crack tip parameters through the specimen thickness. Whereas for double V weld type the variation of crack tip parameters is almost symmetric relative to the mid plane of the specimen. The results for double V weld are almost symmetric relative to the weld line, while the amount of crack tip parameters decreases through the specimen thickness for single V weld.

4. Conclusion

In this paper 3-D finite element method was used to analyze a welded plate for two types of welding. The calculated residual stresses were used to compute the crack tip parameters. It was shown that crack tip parameters are influenced considerably by the residual stresses due to welding. Also, it was shown that the mode II stress intensity factor and T-stress are not negligible compared to the mode I stress intensity factor. Therefore, for analyzing the fatigue life or the fracture load of such cracked structures, appropriate mixed mode crack growth criteria should be employed.

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