International Journal of Fatigue 23 (2001) 865876 www.elsevier.com/locate/ijfatigue
A structural stress denition and numerical implementation for fatigue analysis of welded jointsP. Dong*
Center for Welded Structures Research, Battelle, Columbus, OH 43016-2693, USA Received 10 December 2000; received in revised form 11 May 2001; accepted 12 June 2001
Abstract A mesh-size insensitive structural stress denition is presented in this paper. The structural stress denition is consistent with elementary structural mechanics theory and provides an effective measure of a stress state that pertains to fatigue behavior of welded joints in the form of both membrane and bending components. Numerical procedures for both solid models and shell or plate element models are presented to demonstrate the mesh-size insensitivity in extracting the structural stress parameter. Conventional nite element models can be directly used with the structural stress calculation as a post-processing procedure. To further illustrate the effectiveness of the present structural stress procedures, a collection of existing weld S-N data for various joint types were processed using the current structural stress procedures. The results strongly suggests that weld classication based S-N curves can be signicantly reduced into possibly a single master S-N curve, in which the slope of the S-N curve is determined by the relative composition of the membrane and bending components of the structural stress parameter. The effects of membrane and bending on S-N behaviors can be addressed by introducing an equivalent stress intensity factor based parameter using the structural stress components. Among other things, the two major implications are: (a) structural stresses pertaining to weld fatigue behavior can be consistently calculated in a mesh-insensitive manner regardless of types of nite element models; (b) transferability of weld S-N test data, regardless of welded joint types and loading modes, can be established using the structural stress based parameters. 2001 Elsevier Science Ltd. All rights reserved.Keywords: Structural stress; Finite element analysis; Welded joints; Fatigue; Notch stress; Stress concentration; Mesh-size sensitivity
1. Introduction At present, fatigue design of welded structures is primarily based on a nominal stress or hot spot stress approach with a series of classied weld S-N curves [1 4], although a local stress or initiation-based fatigue life approaches [5,6] provide an alternative method for fatigue life predictions of welded joints. Without going into a detailed discussion of the merits of the two different approaches, the premise of this paper is that the nominal stress or hot spot stress approach has been well accepted by major industries, and recommended by numerous national and international codes and standards (e.g. [3,4]). A series of S-N curves corresponding to each class of joint types and loading mode were well documented in some of the codes and standards. With such an
* Tel.: +1 614-424-4908; fax: +1 614-424-3457. E-mail address: [email protected] (P. Dong).
approach, nominal stresses with appropriate geometric or structural stress concentration factor (SCF) for a particular class of joints must be determined against the corresponding S-N curve to calculate fatigue damage. Two critical issues remain unresolved in this context. First, both nominal stresses and geometric SCFs cannot be readily calculated from nite element models due to their strong dependence on element size at weld discontinuities. Secondly, the selection of an appropriate S-N curve for damage calculation can be very subjective, since the weld classications were based on not only joint geometry, but also dominant loading mode. There are numerous on-going international efforts to address the above two issues. A majority of the effort has been on developing effective hot-spot stress extrapolation procedures and an ability to correlate various available S-N curves (e.g., [7,8]). However, the extrapolation procedures available to date still lack consistency for general applications . This is in part due to the fact that extrapolation procedures are based on the
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P. Dong / International Journal of Fatigue 23 (2001) 865876
assumption that the surface stresses on a structural member provides an indication of the stress state at a weld fatigue prone location, such as a weld toe. This underlying assumption may become questionable if the structural member is not a dominant load-transfer member in a joint. Under such circumstances, the surface stresses at some distance away from a weld toe may not be relevant to the stress state of concern. In addition, a reference nominal stress in such a structural member may not be readily identied for conventional SCF calculations. Among the various extrapolation procedures proposed in the open literature (e.g., [7,8]), a typical one is based on a linear extrapolation from stress values at both 0.4t and 1t from a weld toe [8,9], as shown in Fig. 1, where t represents the plate thickness of a structural member. The drawback in such an extrapolation scheme becomes immediately clear in view of Fig. 1 in which some of the well-studied joints in the research community are illustrated. The stress concentration behaviors can be categorized into two types : one is rather localized stress concentration behavior (Type I) at weld toe, while the other is more global in length-scale (Type II). In order to correlate the fatigue behavior in various joint types, stress concentration behavior at the weld toe of various joint types must be captured. However, as shown in Fig. 1(b), any stress concentration effects in Type I
joints cannot be captured in this extrapolation scheme, resulting in little stress concentration effects from this calculation. On the other hand, for Type II joints, Fig. 1(b) shows that extrapolation from the two reference positions (open circles) should provide some indication of the concentrations at the weld toes. Then, one obvious question is if such calculation procedures provide a reliable stress concentration measurement or hot spot stresses. As discussed in Neimi , the results are often questionable due to the fact that these stresses can be strongly dependent on mesh-size and loading modes. To improve the S-N curve approach (using either nominal stresses or hot spot stresses) for welded structures, a relevant stress parameter must satisfy the two basic requirements: (a) mesh-size insensitivity in nite element solutions; (b) ability to differentiate stress concentration effects in different joint types (e.g., butt joints versus T-llet cruciform joints) in welded structures. In the following, such a stress parameter is presented and the corresponding nite element procedures using both solid and shell element models are given. The validation of such a structural stress parameter is demonstrated by reprocessing a series of existing S-N data for joint types listed in Fig. 1(a).
2. Structural stress denition and formulation As discussed in Dong  and Dong et al. , a structural stress denition that follows elementary structural mechanics theory can be developed with following considerations: (a) It can be postulated that for a given local throughthickness stress distribution as shown in Fig. 2(a) obtained from a nite element model, there exists a corresponding simple structural stress distribution as shown in Fig. 2(b), in the form of membrane and bending components that are equilibrium-equivalent to the local stress distributions in Fig. 2(a). (b) The structural stress distribution must satisfy equilibrium conditions within the context of elementary structural mechanics theory at both the hypothetical crack plane [e.g., at weld toe in Fig. 2(a)] and a nearby reference plane, on which local stress distributions are known a priori from typical nite element solutions. The uniqueness of such a structural stress solution can be argued by considering the fact that the compatibility conditions of the corresponding nite element solutions are maintained at this location in such a calculation. (c) While local stresses near a notch are mesh-size sensitive due to the asymptotic singularity behavior as a notch position is approached, the imposition of the equilibrium conditions in the context of elementary structural mechanics with respect to this regime
Stress concentration behavior in welded joints.
P. Dong / International Journal of Fatigue 23 (2001) 865876
a membrane component (sm) and bending component (sb), consistent with elementary structural mechanics denition: ss sm sb. (1)
The normal structural stress (ss) is dened at a location of interest such as Section AA at the weld toe in Fig. 2(b) with a plate thickness of t. In the above, the transverse shear (tm) of the structural stress components [to be calculated based on local transverse stress distribution from Fig. 2(a)] is not considered in the structural stress denition in the present discussions. In practice, the transverse shear component can play an important role in controlling crack propagation path if the remote loading imposes a signicant transverse shear at the weld toe. A second reference plane can be dened along Section BB in Fig. 3(a), along which both local normal and shear stresses can be directly obtained from a nite elements solution. The distance, d, represents the distance between Sections AA and BB (in local x direction) at the weld toe. For convenience, a row of elements with same length of d can be used in the nite element model. By imposing equilibrium conditions between Sections AA and BB, the structural stress components sb and sm must sati