Keywords

Introduction

Aluminum alloys appear as structural materials in various industries such as aerospace, automotive, electrical, and chemical [1]. For example, the aerospace industry demands a high mass fraction of aluminum alloys in airplanes. Especially thin-walled, monolithic structural components are used due to their beneficial properties, such as a high overall strength-to-weight ratio and good fatigue life [2]. Typically, those structural components are machined by the manufacturing process milling, removing up to 95% of the total volume of the semifinished product [3]. Part distortion is a common problem due to the required small wall thicknesses of those weight-optimized structural components [4]. Residual stresses (RS) in the form of machining-induced residual stresses (MIRS) and initial bulk residual stresses (IBRS) are known to be the main cause of those distortions [4]. The MIRS are induced by the machining process due to plastic deformations in a near surface layer of the part. Prior research has investigated the effects of cutting conditions and tool properties on MIRS [5,6,7,8]. The IBRS are present in the blank material because of upstream processes like rolling, casting, and especially the heat treatment, which is characterized for wrought and cast aluminum alloys by a three-step process to increase the material strength and hardness: solution heat treatment, quenching, and age hardening [9]. Especially the high thermal gradients during quenching lead to high IBRS in the range of −150 to +100 MPa within the material. Therefore, a RS relief through controlled stretching or compression is necessary. Although the RS can be reduced to a level of ±20 MPa or lower, distortion remains as a problem. Past investigations showed that the position of the finished part in the semifinished product has an influence on the part distortion due to the redistribution of the IBRS [10,11,12,13,14]. However, it was not investigated yet how IBRS in different batches of A7050-T7451 vary and if that affects the distortion of thin-walled structural parts.

Numerical simulation models, typically based on the finite element method (FEM), are the preferred choice for predicting the part distortion due to known RS, because of the reduced effort of the modelling process especially for complex part geometries in comparison to analytical methods. The RS used as input for the FEM distortion model are either measured [14,15,16] or predicted analytically or numerically [2]. The FEM distortion models are mostly based on linear material elasticity. The modelling of the material removal process, e.g., realized by element deletion techniques [15, 16] or the application of the RS to the final machined part geometry [2, 14], was presented in the literature. Either way, forces and moments act as a consequence of the RS imbalance, which leads to the distortion of the part due to the re-equilibrium of the RS as soon as the component is released from its constraints (clamping).

In our past research, we investigated the effect of varying MIRS on distortion [17]. Furthermore, we developed a FEM model to predict the part distortion due to both MIRS and IBRS [18,19,20]. This study investigates how the IBRS in different 7050-T7451 semifinished products vary. With the help of the FEM distortion model, we assess how this variation affects distortion of structural parts.

Methods

Prior to investigating the effect of IBRS on distortion, the IBRS in three different configurations of material A7050-T7451 were measured by the slitting method. Then, machining of different part geometries and measuring their distortion was done to validate predictions from the FEM distortion model.

Initial Bulk Residual Stress Measurements

To investigate the effect of IBRS on distortion, IBRS in three different A7050-T7451 materials were determined:

  • A: Vendor I (USA; 102-mm-thick plate): 206 × 28 × 102 mm3 (x-direction is longitudinal (L), rolling direction; y-direction is long-transverse (LT) direction; z-direction is short transverse (ST) direction)

  • B: Vendor II (Ger; 30-mm-thick plate) batch i: 206 × 102 × 30 mm3 (x- is L direction; y- is LT direction; z- is ST direction)

  • C: Vendor II (Ger; 30-mm-thick plate) batch ii: 206 × 102 × 30 mm3 (x- is L direction; y- is ST direction; z- is LT direction)

For two material batches, B and C, small beam specimens (see Fig. 1a), measuring 100 × 5 × 30 mm3, were cut from the original larger stock. For each material batch, one beam specimen had its length along the rolling (L) direction and the other along the long transverse (LT). The IBRS component acting along the length of each beam specimen was measured using the slitting method, which comprises cutting the sample by wire EDM as shown in Fig. 1a (lower portion) in increments of cut depth, measuring strain after each cut depth and computing residual stress from the strain versus cut depth data [21]. Slitting provides a profile of the stress component perpendicular to the slitting plane (i.e., along the beam length in these experiments) as a function of distance along the slitting direction; the stress so determined reflects an average through the part depth (here along the 5 mm dimension of the beam). Strains were measured using metallic foil gages with active length 1.57 mm that were mounted on the back face of the beam specimens, opposite the start of the cut (see Fig. 1). Strains were measured after each of 40 equal cut depth increments, the final cut depth being equal to 95% of the 30 mm beam width. Residual stresses were computed using pulse regularization, as described earlier [21]. The residual stress measurement procedure for batch A was quite similar but for a larger plate thickness. The procedure and measurement results are presented in [22]. Measured IBRS are compared with literature values from Prime and Hill [21] (see section “Results”) and used as an input for the FEM distortion model (see section “FEM Distortion Model”).

Fig. 1
A series of diagrams and drawings of a C N C machine, along with its top view and bottom view. The text on the image labels different parts of the machine, including the screws, clamps, mill, and specimens along with dimensions for some of the parts.

Orientation of samples with slitting measurement plan (a) and experimental setups for machining of feature samples (b) and wing ribs (c)

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Distortion Experiments

To validate the FEM distortion model, different samples, varying in their part geometry, IBRS, and milling path strategy, were manufactured. Besides, the position of the final part within the original block, here called “z-offset,” was also varied. Two part geometries, varying in size and complexity, were machined: a simple small rib-typed structural part with two pocket features and one stiffener in the center (here called “feature sample,” dimension 200 × 98 × 20 mm3; see Fig. 1b) and a more complex and bigger geometry imitating a small-scaled airplane wing rib with multiple pockets and stiffeners (here called “wing rib,” dimension 480 × 170 × 20 mm3; see Fig. 1c) were analyzed. The feature sample was machined out of material batch B, originating from the same raw material, whereas the wing rib corresponds to material batch C. All components were machined on a five-axis DMG Mori DMU 70 CNCFootnote 1 machine. The manufacturing steps of the feature sample can be found in the literature [19]. The machining of the wing rib was similar (initial block size, 485 × 172 × 30 mm3), but the order and clamping strategy deviated slightly (see Fig. 1c):

  • Step 1: Face milling of backside in side clamps (feed per tooth fz = 0.2 mm, cutting speed vc = 730 m/min, radial cut depth ae = 40 mm, axial cut depth ap = 1.5 mm)

  • Step 2: Side milling in side clamps (fz = 0.055 mm, vc = 450 m/min, ae = 2.5 / 0.5 mm, ap = 4.4 / 22 mm)

  • Step 3: Drilling holes in side clamps

  • Step 4: Face milling of top in side clamps and screws (fz = 0.2 mm, vc = 730 m/min, ae = 40 mm, ap = 1.5 mm)

  • Step 5: Milling of pockets in side clamps and screws (fz = 0.2 mm, vc = 200 m/min, ae = 4 mm, ap = 3 mm)

A cutter with indexable inserts (Sandvik1 R590-110504H-NL H10) was used to face mill the top and backside surface (step 1, 4) and a regular end mill (Kennametal1 F3AA1200AWL) to side mill the walls (step 2) and pockets (step 5). MIRS from the cutting operations face milling (step 1, 4) and pocket milling (step 5) were measured in the previous research and plotted in Fig. 2. For more information we refer to [17,18,19,20]. Since the total machined part is 20 mm thick, different z-offsets of the part in the 30 mm stock are possible: a symmetrical position, removing 5 mm each at top and bottom, and an asymmetrical one, removing 1.5 mm at the bottom and 7.5 at the top were investigated. To achieve high feed rates, the pockets were milled in multiple layers with constant cutting parameters. The milling path strategy was varied from part to part from zig (machining in horizontal lines) to spiral path (machining from the inside out in spirals following the contour of the pockets). To prevent the distortion of the parts during pocket machining, the parts were held down by screws in addition to the clamping with side clamps. The backside surface was measured after the part was released from its clamping after step 5 with the coordinate measuring machine Tesa micro Hite 3D DCC1 (repeatability limit ISO MPE-p 3.5 μm) to determine the distortion – here defined as the out of plane displacement in z-direction – caused by the RS. For the feature sample (wing rib), a spacing of the measured points of 2 mm (4 mm) with a distance to the edge of 1 mm (2 mm) was chosen, which resulted in 4714 (4419) measurement points in total. The final part distortion was analyzed by first leveling the data set (fitting a flat plane and subtracting it) and then setting a zero height at the resulting minimum, which was determined by averaging of the 10 (5) lowest measured points.

Fig. 2
3 cross-sectional views of the f e m distortion models present machined pocket surface along with various marked dimesions. There are 2 graphs for the residual stress versus depth of m i r s pockets and m i r s top and backside portion plots data for sigma x x, sigma y y, and t x y.

FEM distortion model for feature sample and wing rib with MIRS from [23]

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FEM Distortion Model

The developed FEM distortion model was presented and validated in previous research [17,18,19,20] and is now used to investigate the effect of varying IBRS on distortion for different part geometries. It is summarized here as follows: a static, linear elastic FEM model was set up in ABAQUS1 (E = 71,700 MPa, ν = 0.33). The measured MIRS and IBRS were implemented as an initial condition (type = stress) to the final part shape without modelling the material removal process. The MIRS were limited to a near surface layer (pocket floor, 200 μm; backside/top, 70 μm; see Fig. 3). IBRS were applied to the rest of the bulk. All RS σ(z) were linearly interpolated over depth z at the element centroids. For the spiral milling strategy, a coordinate transformation of the MIRS according to the direction of milling was achieved (for more information see [20]). Previous research showed that MIRS in the walls have neglectable impact on the distortion in z-direction [20] and were therefore not considered in the distortion model. The mesh of the feature sample (wing rib) consisted of 670,308 (2,096,508) eight-node brick (C3D8) elements. The global mesh size was 1.5 mm and was refined in the near surface layer down to 10 μm to resolve the MIRS properly. The parts were minimally constrained (3-2-1 constraint principle [15]) to avoid rigid body motion but to enable a free part distortion (see Fig. 2). After one simulation step (reaching RS equilibrium), the displacement at the parts backside was analyzed according to experiments (leveling and shifting data) and compared to the measured distortion.

Fig. 3
2 multi-line graph plots residual stress versus depth into plate thickness for sigma x x rolling and sigma y y long transverse.The plotted lines are for batches A to c, and prime and hill. The curves in rolling are fluctuating with larger peaks while in long transverse they form M-shape.

Initial bulk residual stress comparison of measured and literature values of AA7050-T7451

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Results

The results section is divided into two parts: the IBRS results and the distortion results including measurements and simulations.

Initial Bulk Residual Stress Measurements

Figure 3 depicts the measured IBRS and literature values from Prime and Hill [24] in x- and y-direction over the beam thickness normalized by the plate thickness. Most RS depth profiles showed the typical M shape of stresses with compressive RS close to the surface and tensile RS in the center. Batch C showed a ∩ shape rather than an M shape, which could be due to the distribution of strength through the thickness of the corresponding plate (see [24]). The peak magnitudes of IBRS in the three batches were similar, being 10–15 MPa, with stress magnitudes slightly larger along the rolling (x) direction than along the long transverse (y). The stress magnitudes in the present samples are smaller than those from the literature, which reached peak levels of 20 MPa. The trend in σxx for batch B at depths less than 20% of the plate thickness reflects outlying behavior, the cause for which is unclear. Overall, the results show residual stress with a clear, symmetric M shape in batch A, a less clear and less symmetric M shape in batch B, and a ∩ shape in batch C. The results are reasonably consistent with the prior work [24], which found similar trends in two plate thicknesses (80 mm and 25 mm), the thicker plate having a more distinct M shape.

Distortion

Figure 4 depicts the color maps of the measured distortion of the feature samples with different machining paths and z-offsets, as well as their simulated counterparts with different IBRS used as input. The orientation of the color maps is top view, meaning looking down to the milled pocket surface with positive distortion into the surface in positive z-direction. First the measurements are discussed before comparing simulated and measured distortions.

Fig. 4
12 heat maps arranged in 3 columns for zig strategy, column strategy z 1.5, and spiral strategy z 5 and 4 rows for experiment, simulation of i b r s, i b r s b, and i b r s c. The color coded regions of the map denote data for out of plane deformation z color scale.

Color maps of the measured and simulated distortions of the feature sample for different milling paths, z-positions and IBRS: zig strategy z1.5 (a), spiral strategy z1.5 (b) and spiral strategy z5 (c)

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A slightly twisted distortion with the minima at the bottom left and top right corner and their maxima close to the top left and bottom right corner (zmax = 0.211 mm) was evident for the feature sample milled with zig milling strategy (see Fig. 4a). The shear MIRS induced a torsional moment in addition to the bending moment of the IBRS and the normal compressive MIRS [17,18,19,20, 23]. Changing the milling direction also resulted in a change of the distortion shape: a U shape with the maximum distortion in the middle of the part’s length (x = 100 mm) and regions where the tool cut first in the material (highlighted with black arrows in Fig. 4) was evident (zmax = 0.134 mm). Due to the change of direction of the milling path to a spiral path, the distortion was reduced compared to the zig milling path, because the sign of the shear MIRS changed in 90° rotated regions. This led to an equilibration of the shear MIRS [20] and to a shift of the RS type dominating from MIRS to IBRS [23]. Choosing a z-offset of 5 mm of the final part in the raw material (Fig. 4c) instead of 1.5 mm decreased the distortion (zmax = 0.104 mm), because the IBRS were then symmetrically distributed over the height z, inducing therefore a smaller bending moment [23].

The shape, including the position of the maximum distortion, was predicted correctly by all simulations using different IBRS inputs – except for regions where the tool ramped in for the spiral milling path (highlighted with black arrows in Fig. 4). This could be attributed to the presence of deviating MIRS in those regions due to different machining kinematics. Surprisingly, the level of distortion varied significantly when using different IBRS as input for all investigated cases, although IBRS magnitude varied only by about 5 MPa. The distortion level was predicted best with the simulations using the IBRS literature values from Prime and Hill [24] instead of the measurements done on samples from the same batch B material. Deviations (in terms of differences between prediction and measurement) of the maximum distortion down to 22% (Fig. 4a; zig – z1.5), 21% (Fig. 5b; spiral – z1.5), and 19% (Fig. 4c; spiral – z5) were found. All trends discussed for the measured distortions were matched by the simulations.

Fig. 5
8 color maps arranged in 2 columns for zig strategy and spiral strategy and 4 rows for experiment, simulation of i b r s, i b r s b, and i b r s c. The color coded regions of the map denote data for out of plane deformation z color scale.

Color maps of the measured and simulated distortions of the wing rib for different milling paths and IBRS: zig strategy z5 (a) and spiral strategy z5 (b)

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Figure 5 highlights the color maps of the measured distortion of the wing rib with different machining paths, as well as their simulated counterparts with different IBRS used as input. For the distortion measurements, the same trends as discussed for the smaller feature sample were found: a twisted distortion shape for zig milling (zmax = 0.739 mm) and a U-shaped reduced distortion for spiral milling (zmax = 0.676 mm) were evident.

The wing rib shape was predicted correctly by all simulations using different IBRS inputs. Small deviations for the position of the maximum distortion for zig milling strategy were found. This could be attributed to the fact that in experiments outer machining paths were not perfectly horizontal as assumed in the simulation, due to the curved shape of the part. Again, the highest accuracy of the simulation was reached when using the IBRS from the literature as input. Deviations down to 7% (Fig. 5a; zig – z5) and 28% (Fig. 5b; spiral – z5) were achieved. Using the measured IBRS led to an underestimation of the distortion for both investigated cases. One possible explanation for this trend could be that the IBRS in the beam specimens deviate from the IBRS in the remainder of the plate stock (which is perhaps closer to the literature values); this could occur if the beams were closer to the edges of the original plate stock, but this remains unknown.

Conclusion

IBRS measurements of different batches of A7050-T7451 are reasonably consistent with what was found in the literature by Prime and Hill [24] with a clear, symmetric M shape in batch A, a less clear and less symmetric M shape in batch B, and a ∩ shape in batch C. The magnitude of the measured IBRS was slightly smaller than literature values (by about ~5 MPa). When using the different IBRS as input for the FEM distortion model in addition to the MIRS, the shape of distortion was predicted correctly for different geometries and milling strategies and for different z-offsets. However, the level of distortion, identified by the maximum, was underestimated when using the measured IBRS as input. The best results were achieved when using the IBRS literature values as input, in which case deviations of the maximum distortion of 28% (spiral-strategy) and 7% (zig-strategy) were evident.