Electric strain gauge measurement of residual stress ... - SAGE Journals

SPECIAL ISSUE PAPER 117

Electric strain gauge measurement of residual stress in welded panels G Ivetic, A Lanciotti, and C Polese Department of Aerospace Engineering, University of Pisa, Pisa, Italy The manuscript was received on 10 June 2008 and was accepted after revision for publication on 22 September 2008. DOI: 10.1243/03093247JSA456

Abstract: The current paper describes a destructive, sectioning method for measuring residual stress in welded panels, using electric strain gauges. Since this method is carried out rather simply, it has a wide range of possible applications. For this reason, a more thorough analysis of the method is performed. The potential limits of its application are investigated, together with the parameters that can influence the obtained results. The sectioning method is verified by determining residual stress in welded panels numerically. The results show it is possible to estimate the residual stress field in a welded structure rapidly and accurately, by using reasonably priced equipment. Keywords: analysis

1

residual stress, sectioning method, strain measurement, finite element method

INTRODUCTION

Many technological processes introduce residual stresses in mechanical components. These residual stresses can have negative effects on the performance of structures by influencing fatigue life and fatigue crack propagation significantly. Some of these processes, however, are executed intentionally in order to introduce a favourable state of residual stress. Shot peening, hole expansion, and rolling, for example, introduce residual stress states that can have a positive influence on the nucleation and the propagation of fatigue defects, as well as fracture and stress corrosion resistance. From a metallurgical point of view, three different types of residual stress are identified, based on the scale of the observed material. The macroscopic stresses (stresses of the first kind) are defined on the level of several metal grains; micro stresses of the second kind are defined over one single grain, while micro stresses of the third kind are defined on a part of a grain. This paper refers to the macroscopic state of residual stress, the only state that can interact *Corresponding author: Department of Aerospace Engineering, University of Pisa, Via G. Caruso 8, Pisa 56122, Italy. email: [email protected] JSA456 F IMechE 2009

with external loads and produce visible component deformations. Because of the common presence of residual stresses and their considerable contribution to the fatigue properties of a material, they need to be taken into account during the design of mechanical components. Therefore, the correct characterization of residual stresses is of great importance. Various techniques for characterizing residual stresses exist, and a broad description of them can be found in references [1] to [3]. A brief overview of the most widespread methods is given here. Among the non-destructive techniques, X-ray diffraction and neutron diffraction are the most commonly used. However, in addition to the fact that these methods require expensive equipment and are not easily applicable, there is a limitation in the maximum dimensions of the test sample. X-ray diffraction can measure residual stress in crystalline materials to a maximum depth of about 0.05 mm. Subsurface measurement requires electrolytic polishing to remove layers, making the measurement destructive. Neutron diffraction can measure residual stresses to depths up to 10 cm, where measurements are made typically in volume elements of the order of 1 mm3. According to reference [4], with the neutron diffraction method, it is possible to charJ. Strain Analysis Vol. 44

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G Ivetic, A Lanciotti, and C Polese

acterize residual stresses in components of a diameter up to 1 m and of a weight up to several hundred kilogrammes. Other non-destructive techniques commonly used are the ultrasonic method [5], based on variations in the velocity of ultrasonic waves that can be related to the residual stress state, and the magnetic method, the application of which is limited to ferromagnetic materials only. The most common destructive methods for measurement of residual stresses are hole drilling, ring core, crack compliance, and sectioning methods. These methods are sensitive to the macroscopic residual stresses only. The hole drilling method is considered to be a semi-destructive technique for the measurement of residual stresses. It is executed by introducing a hole at the centre of a strain gauge rosette [6], which is connected to the test specimen. The measurements are performed at various depths, recording the residual stress values along the thickness of the specimen. This method is considered to be semi-destructive if the measurements are limited to only one point of the structure that can be repaired easily. The hole drilling method is usually applied to a limited area of the specimen and is successfully used in structures where no major variations in residual stress are present, e.g. on the shot peened surfaces. The ring core method [7] for the measurement of residual stresses is a variation of the hole drilling method. It is a mechanical strain gauge technique used to determine the principal residual stresses as a function of depth in materials, where linear elastic theory can be assumed (metal, ceramics, polymers). The annular groove needed to release the stresses can be machined with a suitable mechanical dissection device, or removed by electrolytic polishing or by electrical discharge machining. Strain gauge rosettes are usually used to measure the relieved strains on the surface of the cylindrical core. The crack compliance (slitting) method is described in reference [8]. The determination of the residual stress variation with depth is performed by successive extension of a slot or cut and measurement of the resulting strains. The method itself includes analytical, experimental, and application components that can differ in various implementations of the method. The analytical part of the compliance method has two components: forward solution, which finds the strains as a function of slot depth; and inverse solution, which finds the residual stress distribution that matches the actually measured strains. The experimental component can J. Strain Analysis Vol. 44

differ when deciding how to introduce the slot (saw, cutter) and how to measure the resulting deformations (strain gauge, micrometer). The application component refers to the different types of materials that are being tested using the crack compliance method (metals, polymers, composites). The sectioning method [9] is based on the principle that internal stresses are relieved by cutting the specimen into strips. The method is best applied on specimens where the residual stresses are important in one direction alone. The residual stresses are determined by measuring strain before and after the sectioning and applying Hooke’s law. Another technique that uses sectioning is contour measurement [10, 11], where the specimen is cut by electric discharge machining and the resulting displacements out of the cut surface, due to the relaxation of the residual stress, are measured experimentally (with laser scanning or touch trigger probe). Later, the measured displacements are compared with the flat original surface contour analytically, and the residual stress field is calculated. Other possible destructive methods, used for determination of the triaxial residual stress field, are reviewed in reference [12]. In addition to the commonly used techniques, as discussed above, recent studies have described more advanced applications of some of these techniques. Schajer and Steinzig [13] describe the use of electronic speckle pattern interferometry (ESPI) measurement of surface displacement for the hole drilling method which allows full-field results to be obtained. In reference [14], the application of an interferometric strain/slope rosette (ISSR), combined with incremental hole drilling, is reported, used for measuring of in-plane residual stresses that may vary in depth. The destructive mechanical methods of measuring residual stresses are often more cost-effective and efficient with respect to other techniques, when determining deep residual stresses. Welding is one of the most common processes that introduces detrimental residual stresses in structures. A residual stress field is formed in a welded structure as a consequence of high thermal gradients developed during the welding process. These residual stresses are only partially relaxed during the phase of cooling, causing undesired deformations of the welded structure. Thermal relaxation of the remaining residual stresses is not always applicable, since it requires that the welded structure is placed in an oven for several hours. Apart from difficulties with the availability of an JSA456 F IMechE 2009

Electric strain gauge measurement of residual stress

oven of proper dimensions and the associated costs, by placing welded structures in an oven, further deformations can be introduced. The geometry of the structure can exceed the allowable limits and further mechanical deformations are required in order to re-establish the original dimensions of the component. Because of this, the current trend in the space industry for the realization of pressure vessels is to use components in their ‘as-welded’ state. Therefore, it is essential to evaluate accurately the state of residual stress before placing the welded component in operational conditions, in order to minimize the residual stress-related failures. In welded structures, the residual stress values vary from one point to another and the measurement needs to be carried out in different positions. The measurement is usually executed on panels designed specifically for this purpose. The most common specimen, if not explicitly specified otherwise, is a rectangular, butt-welded panel. Since the panels are being designed for testing purposes only, even a destructive test can be considered if this facilitates the measurement considerably. So far, there is no standard procedure that describes the measurement of the complete residual stress field in rectangular, welded test specimens. The measurements are based on hypotheses that introduce simplifications on different levels and it is not possible, at this point, to unify them together in a possible standard procedure. This paper describes possible applications, limits, and advantages of a destructive, sectioning method for the determination of residual stress in a welded panel, based on utilization of electric strain gauges.

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MEASUREMENT OF RESIDUAL STRESS IN A RECTANGULAR, BUTT-WELDED PANEL

A welding process generates a significant residual stress in the longitudinal (welding) direction, sy, that generally has a peak tensile stress in the centre of the weld bead and a peak compressive stress in lateral zones (Fig. 1(a)). At the same time, stress in the transversal direction is present, sx; this reaches lower values with respect to the stresses acting in the longitudinal direction (Fig. 1(b)). Obviously, the residual stress field, in the absence of external loads, is in an auto-equilibrated state. Regarding possible symmetries, a panel designed conveniently for measuring residual stress will have a double symmetric geometry (xz and yz symmetry planes in Fig. 1). This, however, does not imply a complete symmetry of temperature field during the JSA456 F IMechE 2009

Fig. 1

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(a) Longitudinal sy and (b) transversal sx residual stress in a welded panel

welding process. The joint in fact is not realized simultaneously along its length and differences can be found between the areas at the beginning and at the end of the joint. Related to the distribution of the residual stress along the thickness of the panel, experimental results show that it is possible to assume a constant distribution of the stress along the z axis, where thicknesses are up to 1 in (25.4 mm) [15]. Assuming double symmetry (xz and yz symmetry planes in Fig. 1), can limit the measurement to two segments on which the strain gauges are attached. Double symmetry implies the absence of tangential stresses, txy, on the axes, making the values sx and sy, measured along the axes x and y, principal stresses. The number of strain gauges needs to be determined beforehand, predicting a possible distribution of internal stress. The quantity of heated material, i.e. the concentration of the energy source, determines the dimension of the zone of interest where significant values of residual stress can be expected. Obviously, a larger number of strain gauges is used where higher stress gradients are expected. After the bonding of the strain gauges, it is necessary to produce the relaxation of the internal stresses. This is executed by isolating the area where the strain gauges are applied using a mill cutter or a band saw or by electrodischarge machining. During the sectioning, the strain gauges need to be opportunely protected, e.g. with silicone coating, in order to avoid contact with chips of removed material or accidental damage. Strain gauge electric connections need to be positioned in order to avoid interfering with the cutting path. During the cutting process, the panel needs to be fixed in a suitable way. In some cases, it can be interesting to examine the residual stress J. Strain Analysis Vol. 44

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relaxation and redistribution during the sectioning; for example, simulating the propagation of a fatigue crack using the sectioning method. In this case, it is advisable to remove the restraints before each measurement in order to keep their influence away from the strain gauge measurement. The sectioning parameters must be selected in order to produce insignificant heating of the panel. Nevertheless, it is advisable to leave the panel to cool down for a certain period of time between sectioning and strain gauge measurement, in order to avoid a possible influence of the heat on the results. Obviously the strain gauges are reset to zero before the start of the sectioning. Whichever sectioning method is adopted, the first limit of the method is the distance between the cutting line and the position of the strain gauges. This distance obviously cannot be zero and it needs to be compatible with the dimensions of the strain gauges. It is possible to reduce the number of strain gauges applied, using some simplifying hypotheses. It is well known that the transversal stress, sx, in the centre of the weld bead is about 10–20 per cent of the maximum value of the longitudinal stress, sy, and disregarding it in the first approximation, strain gauges oriented in the direction of the y axis only can be used. In addition, the distribution of longitudinal stress sy along the longitudinal, y axis, is practically constant and decreases to zero at the edges of the panel, so it is not necessary to perform measurement along the entire weld bead. Therefore, a simplified analysis can be performed using y-axis-oriented strain gauges, positioned along the x axis only, the transversal direction of the panel. The following section illustrates the results of experimental measurements and numerical simulations. The numerical simulations are used to show the effects of the simplifications introduced.

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EXPERIMENTAL MEASUREMENT OF RESIDUAL STRESS

Measurements were carried out on a butt–plasmawelded 2219-T851 aluminium panel, dimensions 550 mm6890 mm, thickness 7 mm. The welded panel was provided by a company specialized in the aerospace sector. The residual stresses present in the welded panel were measured using the previously described sectioning method. It is possible to assume the symmetry of the panel in respect to the weld bead, yz plane. As a consequence, the strain gauge measurement was limited to one half of the panel only (Fig. 2). Strain gauges used for the J. Strain Analysis Vol. 44

measurement, numbered from 0 to 9, were of type XY, that measured deformations in one single point in two perpendicular directions. All other strain gauges measured deformations in one direction only. The strain gauges were bonded to the front side of the panel, the welding side. The instrumented panel was mounted on a milling machine and restrained in a suitable way in order to allow free deformation of the panel in the xy plane. The sectioning itself started from a central hole (produced with a cylindrical mill with diameter of 4 mm), that was progressively extended. The instrumented zone was isolated as illustrated in Fig. 2, by performing two cuts, 15 mm above and 15 mm below the reference line. When using the results of strain gauges oriented in the y direction only, ey, it is possible to evaluate, in the first approximation, the longitudinal residual stress present in the examined panel by using the equation for the uniaxial stress state sy ~Eey

ð1Þ

where E is Young’s modulus. Otherwise, when using the results of all strain gauges, oriented in both x and y directions, ex and ey, together with the biaxial stress–strain equation sy ~

E ey znex 1{n2

ð2Þ

a more accurate stress field can be obtained (where n is Poisson’s ratio). However, it will be illustrated with the experimental measurements and with finite element method (FEM) analyses that strain gauges oriented in the longitudinal direction only are enough to characterize the residual stress correctly. In all the evaluations, a Young’s modulus, E of 70 000 MPa was assumed. The results obtained are illustrated in Fig. 3. First of all, an anomaly in the centre of the weld bead can be observed; this is, almost certainly, associated with the lower mechanical properties of the weld bead in respect to the base metal. This feature is characteristic for all the welding processes of aluminium alloys. The yield stress of 338 MPa reduces in the weld bead to 165 MPa [16]. Figure 3 shows the results after the first and the second cut, considering either longitudinal strains only or the strains measured in both the directions. The results demonstrate that the first cut does produce the major part of the relaxation, but the second cut is necessary to release the internal stresses more completely. In order to perform two cuts, it was JSA456 F IMechE 2009


Fig. 2

Disposition of strain gauges for determination of residual stress

required, however, to dispose all the electric cables of the strain gauges horizontally in order to avoid interference with the cutting paths, and this complication was inevitable. The second observation considers the stress state; the residual stress determined by longitudinal strain ey only is practically equal to the one determined by combining the transversal and longitudinal strains, ex and ey. This justifies the hypothesis of neglecting the residual stress acting in the transversal direction and using the strain gauges that are oriented in the longitudinal direction only, thus reducing the total number of strain gauges necessary by one-half.

4

NUMERICAL EVALUATION OF THE MEASUREMENT METHOD USED

4.1 4.1.1

Longitudinal residual stress distribution sy obtained experimentally

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FEM model definition Geometry definition

The sectioning method for measurement of residual stress was evaluated numerically by simulating the welding process in a panel that has the same dimensions as that used in the experimental measurements, 550 mm6890 mm. The FEM model used was a two-dimensional plane stress model, since the thickness of the plate was small enough to assume constant stress distribution in the z axis direction. Owing to its double symmetry, in respect to the x and y axes, it could have been possible to model onequarter of the panel only. However, the heat input associated with the welding process does not correspond to this simplification, so one half of the panel was modelled instead, assuming symmetry with respect to the y axis only. The circular heat input zone, over which the thermal load is applied (the weld bead area), was realized with a denser mesh in order to describe more accurately the zone where higher temperature and stress gradients are expected.

4.1.2 Fig. 3

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Material definition

The material used in the numerical analysis was the same as that used in experimental tests, 2219-T851 aluminium alloy. Unfortunately, all the necessary J. Strain Analysis Vol. 44

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information for the FEM analysis was not available, i.e. Young’s modulus, thermal properties and their temperature-dependent variations. Therefore, with these properties lacking for the material examined, the properties of 5052 aluminium alloy, available in reference [17], were used instead. On the other hand, the temperature-dependent mechanical properties of 2219-T851, i.e. yield stress and maximum strength, are available in reference [17]. In the FEM model, the weld bead thermal properties, as well as Young’s modulus and density, were assumed equal to the properties of the base material. Yield stress and maximum strength of the 2219 weld bead are available for room temperature only [16]; therefore, without other experimental data accessible, the assumption introduced was that the temperature dependence of weld bead properties could be defined proportionally to the temperature-dependent mechanical properties of the base material. In the FEM model, the conductivity and specific heat were defined, both for base and welded material, as temperature dependent, while the thermal expansion coefficient and the density were assumed to be constant.

4.2

Numerical analysis

Numerical analysis was performed using the commercial finite element analysis code ABAQUS. Numerical analysis was divided in two stages: a thermal analysis followed by a mechanical static stress analysis. The thermal analysis stage was performed by referring to reference [18]. In this paper, experimental and numerical analyses of a welding process were performed in a panel with similar dimensions to the panel examined in the present work. In the experimental stage, thermocouples were positioned in the surrounding area of the weld bead, positioned in both longitudinal and transversal directions. In addition, a number of thermocouples were placed along the thickness of the panel. These experimental results were used in the present work to calibrate the quantity of heat to be inserted during the numerical simulation, which was adjusted in order to obtain a comparable temperature field to that measured in reference [18]. The thermal analysis results were inserted in the mechanical static stress analysis in order to obtain the residual stress field in the model. Therefore, the scope of the present FEM analysis was not creating a model of a welding process, which should also consider effects such as material fusion, phase transformations, etc. The present analysis J. Strain Analysis Vol. 44

simply served to insert a realistic state of residual stress in a welded panel, that could be used for the verification of the sectioning method. For this reason, it was considered acceptable to use the results presented in reference [18], even if they are referred to another welding process (friction stir welding), differing from the process used in the experimental part of the present work.

4.2.1

Heat transfer analysis

The heat transfer analysis was performed by defining the area on which the thermal load is applied: semicircular areas, visible in Fig. 4, with radius, r 5 12 mm, that correspond to the radius of the shoulder of the friction stir welding tool. Each semicircular area was meshed with 36 elements, and the heat input distribution was considered constant over the area. A total of 150 areas were defined. The model consisted of 25 920 nodes with 25 520, two-dimensional solid homogeneous elements, type DC2D4. A starting temperature of 20 uC was defined on the entire panel. Simulated welding speed was 360 mm/min, obtained by sequentially activating and deactivating overlapping heat sources, one semicircular area at a time. In the last step of the analysis, the panel cooled down by the effect of heat diffusion, meaning that the quantity of heat inserted is distributed uniformly in the panel and by the effect of natural convection, with an assumed heat transfer coefficient of 10 W/m2 uC and a sink temperature of 20 uC.

Fig. 4 Longitudinal residual distribution sy for the model with zones with different mechanical properties JSA456 F IMechE 2009


4.2.2

Stress analysis

The stress analysis was performed after the thermal analysis. The main result of the thermal analysis, i.e. the obtained temperature field at each step, was introduced as the initial state for the corresponding step of the mechanical analysis. The duration of each step in the mechanical analysis corresponded to the step duration of the thermal analysis. The geometry and the number of elements of the model were equal for both thermal and mechanical analysis. Two-dimensional elements, type CPS4R, were used. One half of the panel was modelled, with symmetry boundary conditions with respect to the y axis and one point restrained in the y direction, in order to avoid the rigid body motion. In the first FEM analyses, the residual stresses obtained in the weld bead were much higher than the yield stress of the weld bead material. Typically, in aluminium alloys this yield stress is around 50 per cent lower that the yield stress of the base material. In order to remove this incongruence, the variation of the mechanical properties of the material as a consequence of the welding process was simulated in the analysis. At the beginning of the analysis, the mechanical properties of the entire panel were those of the base material. As the heat source advanced, the mechanical properties of the weld bead were being sequentially activated, replacing the mechanical properties of the base material. In order to avoid non-gradual variations of mechanical properties, two transition zones were introduced, characterized by mechanical properties intermediate between those of the base metal and those of the weld bead.

4.3

FEM results

The distribution of the longitudinal residual stress, sy, after importing the results of the thermal analysis into the mechanical analysis, together with the definition of the zones with different mechanical properties, is given in Fig. 4. The developed model took into consideration the change of material properties during the welding process. It can be observed in Fig. 4 that the residual stress distribution has an atypical shape that should be associated with the zones with different yield stresses, introduced to simulate the gradual transition from the mechanical properties of the weld bead to those of the base material. This problem was resolved by defining the mechanical properties of the weld bead in the entire panel. In fact, outside the weld bead, the material experiences only elastic deformations and defining JSA456 F IMechE 2009

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zones with different mechanical properties does not bring significant variations of results. With this simplification taken into account, the new results, shown in Fig. 5, do not show the previously met anomaly. The maximum stress in the sy direction, in the centre of the weld bead is around 180–190 MPa, a slightly higher value than the yield stress introduced in the model (165 MPa). This feature can appear to be an irregularity at first, but it is actually a consequence of the yield criterion used in the analysis (von Mises criterion), which is not a simple excess of the uniaxial yield. In fact, in plane stress conditions, even if one component of the stress, in this case sy, is slightly higher than the nominal uniaxial yield stress, yielding does not occur, since the equivalent von Mises does not reach the value of 165 MPa. The model with constant mechanical properties in the entire panel (one field) was taken as the base model for performing all further analyses. In order to evaluate the sectioning method for the measurement of residual stresses, the elastic strain values were taken from the FEM analysis. The elastic strain values were read from the FEM analysis before and after the sectioning of the panel, and, by using either the uniaxial (equation (1)) or the biaxial stress–strain equation (equation (2)), the longitudinal stress values were calculated. In this first example, two cuts were positioned 3 mm above and 3 mm below the line where the elastic strains were read (the virtual position of the strain gauges). The numerical results obtained (Fig. 6), are qualitatively comparable with the experimental results (Fig. 3), but their numerical values are visibly higher. When evaluating the residual stresses using the

Fig. 5

Longitudinal residual stress sy distribution for different models analysed J. Strain Analysis Vol. 44

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elastic longitudinal strains ey only, the result obtained is practically exact. The effects of the partial or total relaxation of the residual stress (one or two cuts), observed in experiments, were observed in the numerical analyses as well. Numerically, the second cut seems to be important only if longitudinal strains ey alone are being considered. The effect of the distance of the cut from the position of the strain gauges, d, was evaluated using the same model. The results obtained, given in Fig. 7, show that it is not crucial to perform the sectioning as close as possible to the line where the strain gauges are positioned; the results begin to change significantly when passing from two cuts at d 5 21 mm to cuts at d 5 30 mm, a value that is much higher than the size of the electric strain gauges.

4.4

Additional effects verified by the FEM model

Fig. 7 The effect of the height of the panel (i.e. the distance of the cut from the path where the elastic strain is read) on the maximum values of longitudinal residual stress sy

The created FEM model was used to verify other effects as well, such as the size of the panel and a possible alternative to the simulation of the welding process. It is evident that the welded specimen needs to have a certain width, in order to contain significant residual stresses. The redistribution of the residual stresses with the change in panel dimensions was evaluated by removing progressively two lateral strips from the model (Fig. 8). Figure 8 shows the distribution of maximum longitudinal residual stresses sy, measured at the centre of the panel, as a function of the width of the panel. It can be seen from the results that the width of the panel that was used in the tests, 550 mm, is enough to develop practically the entire stress state. Even a panel with smaller width, e.g. 300 mm, would have contained

the residual stresses that are around 95 per cent of the asymptotic value. Moreover, it was also interesting to evaluate the effect of the transversal cut, along the x axis, on the transversal residual stress sx distribution along the y axis. This stress reaches values that can be disregarded, apart from the extremes of the panel. After performing the first cut, two new terminal zones were created. This effect is shown in Fig. 9. An asymmetry can be observed with respect to the first cutting line, caused by the different thermal conditions in the panel at the beginning and at the end of the welding bead. After the first cut, the peak of the negative stress in the terminal zone was moved to the central zone. As a consequence of a high stress

Fig. 6

Fig. 8 The effect of the width of the panel on the maximum value of longitudinal residual stress sy

Longitudinal residual stress sy distribution obtained numerically

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gradient that is present in this zone, interference with the measurement of the longitudinal residual stress is possible. Basically, for this reason, it is necessary to perform the second cut as well, in order to isolate the instrumented area completely. This area, after performing two cuts, has a height that is practically equal to the dimensions of a strain gauge (obviously, for practical reasons, in experimental tests a minimum distance from the instrumented area has to be maintained). The negative transversal residual stresses, sx, after two cuts, have values that are significantly lower than those present after performing one cut only. This effect was confirmed numerically, where the peak of negative stress changed from 2169 MPa after the first cut, to practically zero after the second cut (Fig. 9). Finally, the effect of the welding simulation was examined. Instead of performing the complete simulation that requires an elevated amount of time, one simplified thermal analysis was considered, conducted in two steps only: a heating step lasting 5 s and a cooling step lasting 500 s. All other parameters remained unaltered. When compared with the complete analysis, which lasted approximately 7 h 15 min (1 h 45 min for the thermal and 5 h 30 min for the mechanical analysis), the simplified analysis lasted significantly less, about 26 min (6 min for the thermal and 20 min for the mechanical analysis). All the analyses were performed using a PC with 3.2 GHz processor and 3 GB of RAM. During the heating step, the heat input was defined along the entire weld bead, instead of simulating the movement of the heat source that is travelling along the bead. The residual stress distribution, obtained as a result of the simplified

mechanical analysis, compared with the results of the complete analysis, shows a satisfactory correspondence (Fig. 10). Additionally, a sensibility analysis was performed, changing – within the range of possible values – the maximum temperature reached in the thermal analysis, the hardening properties of the material, and the mechanical properties of the weld bead. As a consequence of these variations, the maximum longitudinal residual stress sy at the centre of the weld bead oscillated between 160 and 190 MPa. These values still remain higher than the values determined experimentally.

5

CONCLUSIONS

This paper has described one possible method of measuring residual stress in a butt-welded panel using electric strain gauges. It is possible to derive the following conclusions from the work carried out. 1. It has been shown, experimentally and numerically, that the stress state present in a welded panel can be characterized using strain gauges oriented in the direction of the weld bead only. The differences between stress values calculated using uniaxial and biaxial stress–strain equations are +2.6 per cent for the experimental analysis and +2 per cent for the numerical analysis. 2. Since it is not possible to perform a cut exactly along the line where the strain gauges are positioned, it is necessary to perform two cuts, one above and one below the instrumented zone, in order to relax the internal stresses more

Fig. 10 Fig. 9

Distribution of transversal residual stress sx along the y axis of the panel


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Longitudinal residual stress distribution sy for the full 150-step analysis and for the simplified 2-step analysis J. Strain Analysis Vol. 44

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completely. The effect of the second cut observed in experiments was confirmed numerically. 3. The effect of the distance between the cut line and the line that contains the strain gauges was evaluated numerically. Even when performing cuts at a distance of 20 mm, a dimension that is much bigger than the size of a strain gauge, the values of the (simulated) strain gauge readings did not show notable variations. 4. Finally, one simplified model was developed, in which the simulation of the welding process was performed by inserting heat in the entire weld bead in one step only, instead of simulating the moving heat source. This model was extremely efficient in terms of the computational time necessary, requiring only 6 per cent of the time needed for the full analysis. Nevertheless, the results were practically coincident. REFERENCES 1 ASM International ASM handbook, vol. 8, Mechanical testing and evaluation, 2000 (ASM International, Materials Park, Ohio). 2 ASM International ASM handbook, vol. 6, Welding, brazing and soldering, 1993 (ASM International, Materials Park, Ohio). 3 Withers, P. J. and Bhadeshia, H. K. D. H. Overview: residual stress. Part 1 – Measurement techniques. Mater. Sci. Technol., 2001, 17, 355–365. 4 The Helmholtz Centre Berlin for Materials and Energy website, http://www.hmi.de/bensc/stress/ stress_instruments_en.html, accessed 9 June 2008. 5 Bray, D. E., Kim, S.-J., and Fernandes, M. Ultrasonic evaluation of residual stresses in rolled aluminum plate. In Proceedings of the Ninth International Symposium on Nondestructive characterization of materials, Sydney, Australia, 28 June–2 July 1999. Am. Inst. Physics Conf. Proc., 1999, 497, 443–448. 6 ASTM E 837-01, Standard Test Method for Determining Residual Stresses by the Hole drilling StrainGauge Method, 2001 (ASTM, West Conshohocker, Philadelphia). 7 Schajer, G. S., Roy, G., Flaman, M. T., and Lu, J. Hole-drilling and ring-core methods. In Handbook of measurement of residual stresses (Ed. J. Lu), 1996, pp. 5–34 (The Fairmont Press Inc., Georgia). 8 Prime, M. B. Residual stress measurement by successive extension of a slot: the crack compliance method. Appl. Mechanics Rev., 1999, 52(2), 75–96. 9 Tebedge, N., Alpsten, G., and Tall, L. Residual stress measurement by the sectioning method. Exp. Mechanics, 1973, 13, 88–96.

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10 Prime, M. B., Gna¨upel-Herold, T., Baumann, J., Lederich, R., Bowden, D., and Sebring, R. Residual stress measurement in a thick, dissimilar aluminum-alloy friction stir weld. Acta Mater., 2006, 54(15), 4013–4021. 11 Woo, W., Choo, M., Prime, M., Feng, Z., and Clausen, B. Microstructure, texture, and residual stress in a friction stir processed AZ31B magnesium alloy. Acta Mater., 2008, 56(8), 1701–1711. 12 Hill, M. R. and Nelson, D. V. Determining residual stress through the thickness of a welded plate. In Proceedings of the ASME Conference on Pressure Vessels and Piping, Montreal, Canada, July 1996, 327, 29–36. 13 Schajer, G. S. and Steinzig, M. Full-field calculation of hole drilling residual stresses from electronic speckle pattern interferometry data. Exp. Mechanics, 2005, 45, 526–532. 14 Tjhung, T. and Li, K. Measurement of in-plane residual stresses varying with depth by the interferometric strain/slope rosette and incremental hole-drilling. J. Engng Mater. Technol., 2003, 125, 153–162. 15 Masubuchi, K. Analysis of welded structures, 1980 (Pergamon Press Ltd, Oxford). 16 Lanciotti, A. and Belmondo, A. Mechanical properties of Al 2219 VPPA weldments. In Proceedings of the 48th International Astronautical Congress, Turin, 6–10 October 1997, paper IAF-97-1.4.07, pp. 1–14. 17 ASM International ASM handbook, vol. 2, Properties and selection: non-ferrous alloys and special purpose materials, 1990 (ASM International, Materials Park, Ohio). 18 Chao, Y. J., Qi, X., and Tang, W. Heat transfer in friction stir welding – experimental and numerical studies. J. Mfg Sci. Engng, 2003, 125, 138–145.

APPENDIX Notation d E W

height of the isolated area of the panel after sectioning Young’s modulus width of the panel

ex ey n sx sy txy

transversal elastic strain longitudinal elastic strain Poisson’s ratio transversal residual stress longitudinal residual stress tangential stress
