Residual stresses at a longitudinal stiffener — Web frame intersection and their effects on crack growth

MarineStructures8 (1995) 603 616

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O 1995 Elsevier Science Limited Printed in Great Britain.All rights reserved 0951-8339/95/$9.50 ELSEVIER

0951 -8339(94)00022-0

Residual Stresses at a Longitudinal S t i f f e n e r - W e b Frame Intersection and Their Effects on Crack Growth

Rutger T. Ogeman*, B. Lennart Josefson t and Anders Ulfvarson* * D i v i s i o n o f Marine Structural Engineering, Chalmers University of Technology, S-412 96 G6teborg, S w e d e n

lDivision o f Solid Mechanics, Chalmers University of Technology, S-412 96 G6teborg, Sweden (Received 7 December 1994)

ABSTRACT Stress coining at geometrical discontinuities may introduce compressive residual stresses which will lower the propagation of surface cracks and thus increase the fatigue life. In a non-linear finite element analysis, the residual stresses after welding of a transverse web-frame to a ship hull plating is first estimated. Stress coining of one corner of a longitudinal cutouJ! in a transverse web-frame is then simulated in detail. The calculated residual compressive tangential stresses in the corner of the cut-out is seen to lower the propagation of edge cracks. Experiments performed on webframes taken from a shipyard after manufacturing show indeed that large tensile residual stresses exist in the web-frame after welding. Stress coining is therefore believed to have a beneficial effect on the fatigue life.

Key words."welding residual stresses, non-linear FEM, crack propagation, experiments, stress-coining. INTRODUCTION

Background Cut-outs and brackets in web-frames are the most common structural discontinuities in ship structures. With a good detail design the stress 603

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concentration at the edge of a cut-out may be limited to about four times the nominal stress in the region. The stress concentration is here described as the relation between the maximum tangential stress at the edge of the cut-out and the nominal principal stress in the non-disturbed stress field of the region. Aluminium is sensitive to welding. Hence, in welded aluminium structures the maximum permitted design stresses are in many design codes only about 40% of the yield limit. 1"2 Despite this drawback welded aluminium is often used in lightweight structures, such as high speed crafts. In those ships the deadweight is small compared to the total displacement. A fully loaded ship will go only marginally deeper than an empty ship. Consequently, pressure from wave-loads will dominate as cause of stress variations in the side and bottom web-frames. Stresses will be seen to vary around one fairly distinct mean value as shown in Fig. 1. The conditions described mean that the stress-range at a highly stressed edge of a cut-out is limited to about four times forty percent of the yield limit, that is 1.6 times the yield limit, while the stress-range needed to shake out high compressive residual stresses is almost twice the yield limit. This leaves the designer with a good opportunity to increase fatigue life by a controlled introduction of residual stresses by coining. Coining is a method where residual stresses are intentionally introduced. The plate containing the hole to be coined is placed between two steel mandrels which are pressed together by approximately 1.5% of the plate thickness. Hereby the material surrounding the hole will be plastically deformed.

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Fig. 1. Time variations of normalised stress in fast passenger ships due to extreme dynamic loads.

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When the mandrels are released the still elastic surrounding area will compress the plastically deformed zone and create tangential compressive stresses. 3 Present investigation

A typical detail, present in almost all ship-structures, is studied: the intersection between a longitudinal stiffener and a transverse web-frame. Figure 2 shows an example of such an-intersection from a fast passenger ship built of aluminium. The present investigation consists of three parts. The first part deals with the assessment of the residual stresses which emanate from manufacturing. The manufacturing process includes the punching of the cutouts in the web-frame, see Fig. 2 (D), when applicable; also, the forming of the web-frame to fit the curvature of the ship side or bottom, and the welding of the web-frame, see Fig. 2 (B), to the ship side-plating, see Fig. 2 (C). Secondly, a fully 3 dimensional non-linear FE-analysis of the effect of coining on the residual stresses at the corner of the cut-out in the web-frame is performed. Thirdly, the influence of the residual coining stresses on the propagation of a macroscopic edge crack, starting from the corner, is discussed, using formulas from fracture mechanics, see Fig. 2 (D).

Fig. 2. Intersection between longitudinal stiffener (A) and web-frame (B). Web-frame is fillet welded (C) to plating. Blow up shows corner of cut-out with possible fatigue crack (D) initiated.

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EXPERIMENTAL RESIDUAL STRESS ASSESSMENT In order to assess the residual stresses present in the web-frame three test specimens have been produced. Figure 3 shows one of these test specimens. They were produced in the workshop at a shipyard, where normal routines for punching and welding were folloWed during the assembly of the test specimens. These particular specimens were plane since no forming of the web-frame to fit the ship side was necessary. The side-plating part of the specimens consists of five extruded profiles, each 320 mm wide, which are welded together in a MIG welding machine handling 5 m long sections. In this hull profile the longitudinal T-shaped stiffener is incorporated, see Fig. 2 (A). The cut-outs in the web-frame, where the longitudinal stiffeners are to come through, are punched out. The web-frame is welded to the side-plating by use of manual MIG equipment. To assess the magnitude of the tangential residual stresses in the most interesting area, namely in the corners of the cut-outs, where there is a considerable stress-concentration, foil strain-gauges were placed symmetrically, and on both sides of the plate, at a line which starts from the centre of the corner and is directed 45 ° from the vertical direction, see Fig. 4. The gauges were placed 7.5 mm from the corner. To release the residual stresses, a saw-cut was made along the line between the gauges.

Fig. 3. Test specimenused for determinationof residual stresses from manufacturing.

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55

(@7 t Fig. 4. Location of strain gauges on web-frame. Gauges with number within brackets are located on opposite side of web-frame.

At a point between two cut-outs, about 10 mm from the weld connecting the web-frame to the plating, a type of strain-gauge for residual stress determinations, drill-out rosette strain gauges, are placed. In this latter type of strain gauge the three measuring directions are 0 °, 90 ° and 135 °. They are surrounding a hole in the gauge with a diameter of 1.5 mm. By the use of drilling device and a fixture, a 1.5 mm diameter hole is drilled to a depth of 5.0 mm in the web-frame. The differences, for the three directions, in strain prior to and after the hole drilling process give the residual stresses at the location of the gauge. 4 With the same type of equipment measurements were also made in an area 40 mm from the upper flange of the web-frame.

Results The experiments show, as anti~pated, that a rather complex residual stress field exists in the web-frame, in particular close to the weld zone where, the heat input during welding creates compressive plastic strains. The measured tangential strains, close to the corner of the cut-out in the web-frame, indicate that out-of-plane bending occurs. Tensile tangential strains on one side of the web-frame is balanced by compressive tangential strains on the other side. Tensile residual strains were always present on the inlet side of the punch. It seems most probable that these tangential

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residual strains are the consequence of the punching process making the cut-outs in the web-frame. The result from the measurements made 12-0 m m from the corner show the same tendency, but not as clear. The experimentally found released tangential strains, from the experiments made at different distances from the corner are shown in Fig. 5, as function of the saw-depth. These strains correspond, roughly, to stresses of half the yield stress level. It is more difficult to evaluate the results from the measurements using the drill-out rosette gauges. The observed dependence of the drilling depth indicates that the assumption of a plane stress field is in no way fulfilled. Therefore, no conclusions can be drawn, other than the obvious one that the residual stresses are of large magnitude and vary in a most unpredictable manner. FE-CALCULATIONS To simulate the mechanical effect of coining o f a corner in a cut-out in a web-frame a fully 3-dimensional FE-model has been designed, see Fig. 6.

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5. Released tangential strains in the c o m e r of the cut-out. See Fig. 4 for location of strain gauges.

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Fig. 6. FE-model of the intersection between the longitudinal stiffener (not shown) and the web-frame. Blow-up of corner of cut-out also showing mandrel used for stress coining.

This FE-model includes both the web-frame and the ship hull plating. Also, the influence from the welding process, which creates considerable residual stresses, is accounted for. The residual stresses from the welding process are simulated using a zone close to the joint in the model where the material model includes temperature dependence. The tensile stresses in the area around the weld and also elsewhere in the web-frame are obtained in the FE-model by lowering the temperature of the elements which are closest to the weld. 5 A commercial non-linear FE-code, SOLVIA, 6 was used for the calculations. Finite ,element model The entire FE-model is built-up by 8-node isoparametric solid ,elements. In the part surrounding the cut-out the FE-mesh is considerably refined, see Fig. 6. Three planes of symmetry are used. The mandrels are built up of 8-node isoparametric solid elements together with linear contact elements in the zones where the plate and the mandrels come into contact. 7 Corresponding contact elements are attached to the surface of the web-frame in the area close to the corner of the cut-out. The material is assumed to be elasto-plastic, as modelled with von Mises' yield function and associated flow-rule with isotropic strain hardening, in the solid elements closest to the cut-out, while only elastic properties are considered in the remaining part of the web-frame. The elastic

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properties are Young's modulus, E = 69,000 MPa and Poisson's ratio, v = 0.3. In the area closest to the weld, where the temperature is lowered to simulate welding, the coefficient of thermal expansion is taken as = 23.10 -6 1/K. Values of material parameters for the elasto-plastic constitutive model were obtained from uni-axial tensile tests on the specific aluminium alloy used for the ship structure, AA6082 with a 2% offset stress of 280 MPa. Some cyclic uni-axial tests were performed to verify the assumption of isotropic hardening. These tests showed that the tangent modulus has a value, Er = 1800 MPa, and the entirely isotropic expansion of the yield surface. The mandrels are assumed to be made of high strength steel with E = 210,000 MPa and v = 0.3 and to remain elastic during the analysis. From the measured energy input during the weld process the size and the temperature difference of the zone that was cooled are calculated. 5"8.9 Here, a temperature difference, A T = -200°C, and a width of 20 m m are assumed. This zone is extended both in the web-frame plate and in the hull plate. The coining load is applied as a prescribed plane displacement field at the top of the mandrel. The maximum coining depth, measured at the contact surface, is 1.5% of the plate web-frame plate thickness. This depth has been found to be reasonable 3 when applying coining of circular holes in aluminium plates. Calculated results

The FE-calculations show that considerable residual tangential stresses appear at the corner of the cut-out after the simulations of the fillet welding process. The von Mises effective stresses, shown in Fig. 7, are high in an area close to the weld zone. Relatively high effective stresses are also present in the area close to the corner of the cut-out. The most detrimental crack driving force in the corner is the tangential stress which are shown in Fig. 8 (left). Here, also, the tangential stress field after coining is shown. Here, the calculated stress field after the simulated welding process and also after the subsequent coining process are shown. Fig. 9 shows, in detail, the calculated stresses along lines starting from points at the corner directed 45 ° . The lines correspond to different locations in the thickness direction.

DISCUSSIONS A N D C O N C L U S I O N S In welded designs where large residual stresses in tension often appear, the coining method can be used to reduce stresses, or even to introduce resi-

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Fig. 7. Calculated von Mises' effective stress (MPa) distribution in web-frame and ship plating after simulation of weld process (left). Blow-up shows part of intersection between web-frame and plating.

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Fig. 8. Calculated tangential residual stresses (MPa) in the corner of the cut-out before (left) and after (right) coining. dual compressive stresses. This will have a reducing effect on the propagation o f a macroscopic crack growing in the area. An attempt to quantify this reduction is presented below. This m e t h o d o f introducing residual compressive stresses in areas with original large tensile residual stresses m a y be useful both in new designs

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Fig. 9. Calculated tangential residual stresses (MPa) along lines, oriented 45 ° to the horizontal line, at corner of cut-out before (upper) and after (lower) coining. Lines in figure correspond to different locations in the thickness direction.

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and also as a tool when already cracked parts are to be repaired. The risk for a detrimental redistribution of the intentionally introduced compressive stresses, during subsequent operation, depends on the loads acting on the structure. In, for example, ship structures the loads are stochastic in character and the large load magnitudes which may cause stress redistribution are rare. Therefore, it seems possible that this method can be used successfully on ship structures. This may be particularly true for fast ships which are often subjected to loads of high frequency but of low magnitudes.

Growth of edge crack emanating from cut-out The possible beneficial effect of stress coining can be quantified by estimating the growth of an edge crack at the corner of the cut-out which is directed 45 ° to a horizontal line (direction often found in practice), see Figs 2 and 3. The stress intensity factor KI for a crack starting from a stress concentration can be estimated as: 10,11 K I = K t . Ki, nom

(1)

where K, is the stress concentration factor for the corner and Kt. ~o,,, is the 'nominal' stress intensity factor for an edge crack in a semi-infinite half plane without stress concentration. For the present case, where the radius in the corner of the cut-out, p = 5 mm, is very small compared to other dimensions one finds Kt to be high (Kt = 6-8 depending on the type of remote loading). However, elastic FE-calculations show that the tangential stress oriented normal to the thought crack line will decrease very rapidly (after roughly 1 mm) to a constant value. Hence, for the case when the crack has propagated outside the stress concentration region we can, approximately, assess the effect of coining by considering an edge crack in a half-plane subject to residual stresses without or including coining residual stresses and stresses from a typical remote design load, see Fig. 10. The total crack length is then taken as the.crack length, a, plus the radius, p.10,11 The nominal stress variation along the crack line without stress coining or after stress coining can be extracted from the FE-calculations presented above, see Fig. 9. This variation along the crack line is here approximated as linear and constant throughthe-thickness. Using the stress intensity factor Kz, res from Sih 12 for a linear normal stress variation along a crack surface and the stress intensity factor KI for a remote constant stress ¢r0, see for example Rooke et al., ~3 corresponding to a constant shear stress along the upper and vertical surfaces of the transverse web-frame, the propagation of an edge crack can be predicted.

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J Fig. 10. The cut-out in the web-frame together with the corresponding handbook reference cases for the total stress intensity factor.

The growth of the edge crack is calculated using Paris' law, hence, the crack growth per cycle, d a / d N , is taken as: da d-N = C . (AK~,eif) m

(2)

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In eqn (2) above C and m are material parameters. Here we have used the values for an aluminium alloy with a similar chemical composition, used in aircraft structures, A A 6061-T6, hence C = 2.94 × 10 -l° and m = 2-63 (stresses in M P a and lengths in m).14 Consider now the case with an alternating external load with constant amplitude, a0 : 15 M P a on the web-frame, that is R = 6 0 , m i n / f O , max : - - 1 . Assume that the initial crack length a0 : 1-0 mm, thus disregarding the crack initiation phase and the possible effect o f the stress concentration in the corner. When integrating eqn (2) it is first discretized, thus the increment A a for a finite number o f cycles is obtained as Aa = ( d a / d N ) . A N . It is seen in Fig. 9 that the normal stress along the thought crack line is

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Fig. 11. Propagation for a through the thickness edge crack with initial length a0 = 1 mm starting from the corner of the cut-out.

influenced by the coining process over a length of about 10 mm. The edge of the mandrel is located at this radius. Figure 11 shows the calculated growth ,7, up to the length a = 8 mm, of the edge crack for two cases: when no coining has been applied (the residual stresses on the crack surfaces originate from the welding of the web-frame to the ship plating, see above), and when coining has been applied. It is clearly seen that coining of the corner of the cut-out may reduce the growth of an edge crack, in particular for the case when R = - 1 for the external load. As seen in Josefson e t al. ]4 the reduction of the crack growth may be lower when R has a higher value, like for a pulsating external load, R = 0. The curves in Fig. 11 have been derived after several engineering simplifications. However, it is believed that they are accurate enough to demonstrate the beneficial effect of stress coining. ACKNOWLEDGEMENTS Marinteknik Verkstads AB in Oregrund, Sweden supplied the test specimens used in the experimental part of the study. This work has been

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financially supported by The Swedish Board for Industrial and Technical Development ( N U T E K ) and The Swedish Shipowners Association (SFR).

REFERENCES 1. Lloyd's Register, Rules and Regulations for the classification of ships. Part 3 chapter 2, London, UK, 1991. 2. Det Norske Veritas, Rules for classification, High speed craft, Part 3 chapter 3, Hovik, Norway 1991. 3. Ogeman, R., Coining of holes in aluminium plates: finite element simulations and experiments. AIAA J. of Aircraft, 29 (1992) 947-952. 4. Determing residual stress by the hole-drilling straingauge method. ASTM Standard E837-85, American Society of Testing and Materials, Philadelphia, PA., USA, 1985. 5. Radaj, D., Heat effects of welding. Springer Verlag, Berlin, Germany 1992. 6. SOLVIA-PRE, Users manual. Report SE 90-1, SOLVIA Engineering AB, V~ister~s, Sweden, 1991. 7. Chaudhary, A. B. & Bathe, K. J., A solution method for static and dynamic analysis of three-dimensional contact problems with friction. Computers & Structures, 24 (1986) 855-873. 8. Kamtekar, A. G., White, J. D. & Dwight, J. B., Shrinkage stresses in a thin plate with a central weld. J. of Strain Analysis, 12 (1977) 140-147. 9. Kamtekar, A. G., The calculation of welding residual stresses in thin steel plates. Int. J. of Mechanical Sciences, 20 (1978) 207-227. 10. Fatigue Design Handbook, Second Edition, Society of Automotive Engineers, Inc, Warrendale, PA, USA, 1988. 11. Barsom, J. M. & Rolfe, S. T., Fatigue and Fracture Control in Structures, Second edition, Prentice-Hall, Englewood Cliffs, N J, USA, 1987. 12. Sih, G. C., Handbook of Stress Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA, USA, 1973. 13. Roooke, D. P. & Cartwright, D. J., Compendium of Stress Intensity Factors, H.M.S.O., London, UK, 1976. 14. Josefson, B. L., Karlsson, S. & Ogeman, R., Influence of residual stresses on fatigue crack growth at stress-coined holes. Engineering Fracture Mechanics, 47 (1994) 13-27.