SAE-TPS-332004-01-0627.pdf

400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2004-01-0627 Fatigue Analysis of Steel MIG Welds in Automotive Structures R. Potukutchi, H. Agrawal and P. Perumalswami Ford Motor Company P. Dong Center for Welded Structures Research, Battelle Reprinted From: Fatigue Research and Applications, and Fatigue Analysis and Creative Problem Solving (SP-1839) 2004 SAE World Congress Detroit, Michigan March 8-11, 2004 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. 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Printed in USA 1 ABSTRACT MIG weld failures are commonly seen in chassis and frame structures in automobile industry. Until now, testing and CAE analysis based on local stresses in the vicinity of MIG weld were driving the design of these welds. With the advent of advanced methods and tools, it is possible to estimate fatigue life of MIG welds and support the design in the early stages of the vehicle program. Recently, fatigue damage models are developed for assessing the durability of MIG welds in aluminum auto structures. These damage models are based on advanced technologies like mesh-insensitive structural stress method, virtual node method, estimation of notch stress intensities and life predictions based on two-stage crack growth law. This paper outlines the theoretical aspects involved in deriving the master S-N curve. The applicability of steel MIG weld damage model developed based on the same structural stress approach in assessing the life of MIG welds in automotive steel structures is verified by analyzing different automotive components and correlating with test data. The results are very promising and it can be used to support the design of MIG welds in automotive steel structures. INTRODUCTION MIG (Metal Inert Gas) or MAG (Gas Metal Arc) welding is the most common way of joining steel components in automotive chassis and frame structures. There is also a trend towards cars built on space frame structures made up of MIG welded tubes. The main design benefits of MIG welding are however the ability to join the parts with only single side access and the reduction or elimination of flanges. In general, durability assessment of MIG welded automotive structures is achieved by measuring stiffness (bending and torsion), loads and stresses far away from MIG welded areas. In the absence of weld fatigue data that is suitable for automotive applications, solid models of the steel welds have been made and surface stresses were recovered using a coat of very thin plate elements for fatigue analysis. These stresses were analyzed using a typical sheet metal fatigue analysis tool with pseudo fatigue weld properties. A notch factor was used to simulate heat-affected zones. These methods are not reliable since many types of variability are not accounted for. It is well known that due to highly localized heating and cooling induced by welding processes, the major effects may be summarized as follows as far as manufacturability and structural integrity are concerned: a. Material property changes occur in both weld metal and HAZ, particularly for high-strength steel applications. b. Weld defects such as micro cracks, porosity and other discontinuities can develop. c. Residual stresses can reach as high as yield magnitude that can significantly impact the structure's fatigue. d. Weld induced distortions can not only affect the fabricability at component level, but also contribute significantly to the overall dimensional variation stack up in the final body assembly. Fatigue life assessment is complex, costly and time consuming due to these fundamental issues of MIG welded joints. Therefore, to avoid the costly and complex analysis, traditionally, the fatigue life of the joint for structural applications followed the S-N type of approach. In this approach, a suitable structural stress parameter is related to the fatigue life of a test specimen. Several approaches are available in selecting the structural stress parameter. 2004-01-0627 Fatigue Analysis of Steel MIG Welds in Automotive Structures R. Potukutchi, H. Agrawal and P. Perumalswami Ford Motor Company P. Dong Center for Welded Structures Research, Battelle Copyright © 2004 SAE International 2 Notch Stress Approach- Welds are classified based on joint type and loading. Notch case catalogues (S-N curves) containing permissible stress ranges are developed for each weld class based on test data. These catalogues are implemented in codes such as Eurocode 3(1) and DIN 15018(2). Types and loading conditions of welded connections in automotive structures are often not contained in the notch case catalogues. Hot Spot Stress Approach - The structural stress parameter is obtained by extrapolation of the stress distribution outside of the weld to the weld toe(3,4,5). The structural stress based on this approach is highly dependent on finite element size, type, extrapolation position etc.,. The membrane and bending components of structural stress cannot be separated. Also, the extrapolation procedures available to date still lack of consistency for general applications(5). Nominal Stress Approach In this approach, the remote loads in the vicinity of MIG weld are converted into nominal stresses. Recently, this approach has been used to develop steel MIG damage model at Volvo Car Corporation(6). All the coupon data could not be fitted on to a single S-N curve. Two S-N curves (one for stiff weld joints and the other for flexible weld joint) are proposed for predicting the live of MIG welds in thin steel structures. Additionally, the method is finite element mesh sensitive. Stress Intensity Approach Many researchers(7,8) view weld fatigue as a crack growth problem. A simplistic formulation will consider stress intensity solution based on Mode I crack opening and use some uni-axial crack growth data to estimate life. To improve S-N curve approach, mesh-size insensitive structural stress method and stress intensity based master S-N curve approach for weld joints have been developed by Dong(9,10). In this approach, mesh independent consistent force and moment distributions along the weld line are calculated using discrete nodal forces and moments. The S-N relationship is derived using fracture mechanic principles. The single master S- N curve developed based on the derived S-N relationship will cater the variability in geometry (different MIG weld types), loading (tension and bending) and thickness. Recently, MIG weld damage models that account all weld types in aluminum vehicular structures have been developed using these advanced technologies and are implemented in Ford Proprietary CAE fatigue analysis tool FLOW (Fatigue Life of Welds)(11). The steel MIG weld master S-N curve developed using the same structural stress approach is taken from ASME Div 2(12) and is also implemented in FLOW. Following sections briefly describes the salient features of the structural stress methodology and application of steel MIG weld damage model in assessing the life of MIG welds in steel automotive structures. MASTER S-N CURVE STRUCTURAL STRESS APPROACH A robust analytical procedure for developing the fatigue damage models should consolidate all coupon S-N data generated by varying the geometry, thickness and load modes on to a single master S-N curve. MIG welds develop cracks at weld toe because of presence of undercuts at weld toe. Also there will be stress concentration at weld toe due to weld notch effect. In this approach, a relation is derived between life of weld (the number of cycles required to propagate infinitely small surface crack at weld toe through the thickness of the sheet) and equivalent structural stress parameter using Mode I crack growth fracture mechanics principles. Stress intensities in the region of short crack growth are considered using modified Paris law. Mesh independent remote loads for Mode I crack growth analysis are derived using work equivalent arguments. A special virtual node method is also used to capture the stress concentrations at weld start and stop locations. A global- local analysis technique has been used for this purpose. GLOBAL ANALYSIS - MIG welds are modeled as plate/shell elements in the global model. Grid point forces for the nodes along the weld line are obtained using linear static analysis. The grid point forces are transformed to weld local co-ordinate system (x'-axis is perpendicular to the weld line and y'-axis is along the tangent to the weld line at node under consideration Fig. 1). The nodal forces along the weld line are converted into distributed forces (line forces and moments) using work equivalent argument the work done by the nodal forces is equal to the work done by the line forces and moments along the weld line. A portion of a curved MIG weld is shown in Fig. 1. Eqn.1 shows a system of simultaneous equations derived using the work equivalent argument. FFF (3) 2 (2) 2 (1) 2 and , are the grid point force contributions at node 2 from the elements 1, 2 and 3 in the weld local co-ordinate system and n21 .f ,f ,f are line forces at node 1,2,n. Similar equations in terms of line moments can be obtained from the nodal moments along the weld line. The line forces and moments obtained by solving these system of equations are mesh-independent and consistent along a curved weld line. To capture the weld concentration at weld ends, a special virtual node method has been developed at Battelle(13,14). The line forces and moments at the weld ends are modified using the virtual node method. 3 LOCAL ANALYSIS - The complex geometry and loading in the global FE analysis is transformed to simple geometry and loads (Fig. 2) - a finite width plate with a surface crack subjected to remote loads (tension and bending). Fig.2 Simple model for Mode I crack growth analysis Remote loads or structural stresses (membrane and bending) at the node under consideration can be obtained from the mesh-independent line force and moments. If 'f' is the line force along the local weld x'- axis and 'm' is the line moment about the local weld y'- axis, the membrane and bending loads are given as, m = t f and b = 2 t m6 (2) where t is the thickness of sheet The rate at which crack grows is governed by the cyclic range of stress intensity,K. A two-stage crack growth model that relates crack growth rate and stress intensity range can be written in the form of modified Paris law and is given by where m corresponds to the conventional Paris law exponent and the exponent n (taken as n = 2) unifies the short crack growth rate induced by notch effects with long crack growth. The stress intensity magnification factor Mkn is defined as (4) ) and thicknesson through (based n K effects)notch localwith ( notch K kn M b m = The detailed discussions on the two-stage growth model are given in detail in 14. The Mode I stress intensity factor range due to remote tension load(15) is given by, where, ? ? ? ? ? ? t a m f is membrane compliance function. The Mode I stress intensity factor range due to remote bending load(15) is given by, where ? ? ? ? ? ? t a b f is bending compliance function. The Mode I stress intensity factor range due to combined loading can be expressed as (using superposition principle), ?K = ?Km + ?Kb (7) By defining the bending ratio, r as the stress intensity factor range ?K can be expressed as Line forces (1) f . . f f f 6 6 00 636 0 0 636 00 63 F . . FF FFF F F . . F F F 3 2 1 3 3322 2211 11 )( )4( 3 )3( 3 )3( 2 )2( 2 )1( 2 )1( 1 3 2 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + + = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? n n n n n l . l l)l(ll l)l(ll ll Element Force contributions GP forces Fig.1 Weld axis system (3) K)()(M C dN da mn kn = (5) t a m f m t m K ? ? ? ? ? ? = (6) t a b f b t b K ? ? ? ? ? ? = (8) r s b bm b = + = t m b a Crack size 4 Fracture mechanics based prediction of life in cycles to final failure can be expressed as: After substituting forK and Mkn, the above equation can be written as, where I(r) is a dimensionless function of r and is given by, I(r) function can be expressed in actual test loading conditions (e.g. displacement controlled condition or load controlled condition). The relation between ?Ss and N uniquely describes a family of structural stress based S- N curves (N s ) as a function of the Paris Law exponent m, thickness effects (t) and bending ratio effects r. The equivalent structural stress parameter, Ss is used to consolidate S-N data by calculating the mesh-insensitive structural stresses. DAMAGE MODEL - The master S-N curve method has been adopted by the new ASME Div 2 Code 12 for developing steel MIG damage model. The detailed procedures and data processing for ASME community can be found in 16. There exists a large amount of S-N data from a variety of weld joint types, thicknesses, loads (tension and bending loads) and steel material with varying yield strengths. Some of the weld joint types, loading and thickness are shown in Fig. 3. Often, such data are presented in terms of nominal stress range versus cycles to failure (or S-N). A large collection of such S-N data from the open literature is plotted in S- N format in Fig. 4(16). Fig. 3 S-N coupons As expected, the nominal stress based plot in Fig. 4 shows drastically different S-N behaviors among the joint types and loading modes. Also, the scatter in the data is so large that the nominal stress based S-N representation cannot be used as fatigue correlation parameter. In Fig. 5, once the structural stress based parameter is used, all data are collapsed into a narrow band. It proves th