# Simulation based investigation on the effect of the topology and size of milled thin-walled monolithic aluminum parts on the distortion due to residual stresses

Daniel Weber, Benjamin Kirsch, Christopher R D'Elia, Julianne E Jonsson, Barbara S Linke, Michael R Hill, Jan C Aurich

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Daniel Weber, Benjamin Kirsch, Christopher R D'Elia, Julianne E Jonsson, Barbara S Linke, et al. Simulation based investigation on the effect of the topology and size of milled thin-walled monolithic aluminum parts on the distortion due to residual stresses. ICRS 11 – The 11th International Conference on Residual Stresses, Mar 2022, Nancy, France. hal-03869964

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# SIMULATION BASED INVESTIGATION ON THE EFFECT OF THE TOPOLOGY AND SIZE OF MILLED THIN-WALLED MONOLITHIC ALUMINUM PARTS ON THE DISTORTION DUE TO RESIDUAL STRESSES

D. Weber<sup>a*</sup>, B. Kirsch<sup>a</sup>, C.R. D'Elia<sup>b</sup>, J.E. Jonsson<sup>b</sup>, B.S. Linke<sup>b</sup>, M.R. Hill<sup>b</sup>, J.C. Aurich<sup>a</sup>

## ABSTRACT

Thin-walled monolithic aluminum parts are common in the aerospace industry because of their advantages such as favorable material properties for lightweight applications, proven design methods, good machinability, predictable performance, and reliable inspection techniques. After milling of those weight-optimized, monolithic components, distortion is a common problem. It is known that residual stresses (RS) in the part cause these distortions, which are divided in machining-induced residual stresses (MIRS) and initial bulk residual stresses (IBRS).

This study assesses the effects of both RS types and the milling strategy on the distortion of part geometries varying in size and topology. A previously developed and validated 3D linear elastic finite element (FEM) model, that considers both types of RS and the true milling path as input, is used to predict the resulting part distortion.

The results show that the part topology, size and the machining strategy in terms of the milling path and the orientation of the IBRS have a mutual effect on the distortion. This relation does not allow for making general statements about what the crucial wall-thickness is when MIRS are driving the distortion. Furthermore, it could be shown that gained knowledge from investigating smaller and simpler parts could partially be transferred to bigger ones. Preferred methods to minimize the distortion of the investigated geometries were a spiral milling path and a favorable position (symmetric distribution of IBRS) of the final part within the initial block.

**Keywords:** Residual stress, Distortion prediction, milling, Finite element model

## 1. Introduction

Aluminum is the most common metal and the third most common element in the earth [1]. Aluminum alloys are used as constructional materials in numerous fields such as automotive engineering, aerospace engineering, electrical engineering, installation and apparatus engineering, food technology, chemical industry, and optical industry [2]. Particularly in aerospace industry, a high mass proportion of aluminum alloys of airplanes was, is and will be required, especially in the form of thin-walled monolithic structural components, because of their good properties such as a high overall strength-to-weight ratio and a good fatigue life [3].

<footnote><sup>a</sup>Institute for Manufacturing Technology and Production Systems, TU Kaiserslautern, Gottlieb-Daimler-Str.,
67663 Kaiserslautern, Germany</footnote>

<footnote><sup>b</sup>Department of Mechanical and Aerospace Engineering, University of California, One Shields Avenue, Davis,
CA 95616, USA</footnote>

<footnote>* Corresponding author. daniel.weber@mv.uni-kl.de</footnote>
Although the ongoing COVID-19 pandemic has reduced the global air passenger traffic, the aeronautical engineering expects an average annual growth of 4 % until the year 2040 according to the most recent published commercial market outlook by Boeing [4]. In this period 43,610 new airplane deliveries are expected, of which 75 % are single aisle airplanes [4]. Especially for those types of airplanes the mass proportion of aluminum alloy is high: For example, the A320 consists of 72 mass-% aluminum [5]. In this case aluminum alloys were chosen over composites due to their comparatively lower manufacturing and maintenance costs [6].

Typically, those weight-optimized, monolithic components are milled, where up to 90 % of the initial material is removed [7]. A known problem is the distortion of those parts [8], which leads to high follow-up costs due to the required quality control, remanufacturing or even part rejection [9]. Residual stresses (RS) in form of initial bulk residual stresses (IBRS) and machining-induced residual stresses (MIRS) are the main driver of the part distortion [8]. The IBRS exist in the blank material because of upstream processes like rolling, casting and especially heat treatments (e.g. quenching). Usually, a process to relief the high IBRS, e.g. by controlled compression or stretching, is required after the quenching of the aluminum alloys [10]. The MIRS, on the other hand, are introduced into the boundary layer of the material during the machining process due to plastic deformation [8].

Simulations based on the finite element method (FEM) are a common tool to predict the distortion due to RS [8]. The RS are known and used as an input to predict the part distortion by linear elastic FEM models [3,7, 11, 12, 13, 14]. Either the MIRS were measured [7, 11, 12, 13] or they were predicted analytically or numerically [3, 14]. In general, two main approaches were applicable for predicting the distortion: Applying the RS to the final part shape [3, 7, 12] or modelling the material removal process [11, 13, 14] by element deletion. Either way, as a consequence of the applied dis-equilibrium of the RS in the initial simulation step or during the material removal, the RS aim for the re-equilibrium once the part is removed from its (clamping) constraints. As a result, the part distorts [8].

The literature review by Li et al. highlights, that the main factor of the distortion of thick structures are the IBRS and for thin wall thicknesses both RS types must be considered [8]. But there is apparently a disagreement what the crucial wall-thickness for MIRS driving the distortion is [8]. However, a lot of different parameter combinations, that effect the RS and therefore the part distortion, were investigated. The prevailing RS in form of their magnitude and orientation and their penetration depth (MIRS) are influenced by the machining strategy including the position of the final part in the raw material [15], the machining sequence [16] and the machining path itself [12].

Therefore, in this study the combined influence of the part geometry, including its topology (angle of stiffeners, wall thickness, size, complexity), and the machining strategy (IBRS orientation, position of final part in initial block, milling path) on the part distortion is analyzed in detail to also highlight when which RS type plays the leading role. For this purpose, a FEM simulation model is used, which was presented and validated in previous research by the authors [17], to predict the distortion of simple small rib-typed structural parts.

## 2. Simulation methods

### 2.1. Part geometries

Different part geometries, varying in size and complexity, and topologies (different stiffener angles) were investigated to show their effect in combination with different machining strategies on the distortion. First the distortion of a simple small rib-typed structural part with two pockets and one stiffener in the middle (dimension: 200 x 98 x 20 mm³) was analyzed. Herby the angle of the stiffener was varied from 45° over 90° to 135° (see Fig. 1a). Furthermore, the distortion of a more complex geometry (dimension: 480 x 170 x 20 mm³) mimicking a small-scaled airplane wing-rib with multiple pockets and stiffeners was simulated (see Fig. 1b).
<figure><img src="image_2.png" /><figcaption>Fig. 1. (a) Small part with different stiffener angles; (b) more complex geometry: small-scaled airplane wing-rib.</figcaption></figure>

## 2.2. Model input: residual stresses

The RS used for the simulation as input were presented and explained in detail in previous research (for more information see [17]). The MIRS resulting from the different milling operations are typical RS found for milling (see Fig 2): Compressive RS with its maximum near the surface. A face milling operation with a tool with indexable inserts is typically used to mill the top and bottom of the initial block to its desired height. Whereas an end mill was used to mill the pockets. The resulting MIRS were measured by the hole-drilling technique (for more information see [18]). Two different machining paths for milling the pockets were investigated: A zig strategy with linear tool movement and a spiral milling path. The information on the tools and the machining parameters can be found in Fig. 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2. (a) MIRS depth profiles for face milling; (b) pocket milling: x feed- and y orthogonal feed direction.</figcaption></figure>

The effect of the magnitude of the IBRS was investigated in previous research [17]. It could be shown that IBRS are the main factor for the distortion of AA7050-T74 parts, which have not undergone a stress relief process and therefore contain IBRS of roughly ±100 MPa. But a systematic influence of the MIRS for thin wall thicknesses (3 mm) was also noticeable [17]. In this investigation however the effect of the orientation of the low IBRS (stress relieved parts AA7050-T7451: $\sigma < 20$ MPa) and the position of the final part in the initial block are analyzed. Therefore, two different IBRS orientations are investigated: The longitudinal (L) rolling direction is the x-direction, which corresponds to the length of the initial block l (see Fig. 3a - I). The longitudinal transverse (LT) corresponds to the z-direction (height of block h) and the short transverse (ST) to the y-direction (width w) (see Fig. 3a), because of the way the block was cut from the original rolled plate. Especially for larger workpieces orientation I is not feasible, because the rolled plates usually have a limited thickness. If the desired final part width exceeds this plate thickness, an orientation corresponding to the rolled plate is required. This means that the longitudinal (L) rolling direction remains the x-direction, but the directions ST and LT are exchanged in comparison to orientation I (see Fig. 3b - II).
It is known that the in-plane IBRS σ<sub>xx</sub>, σ<sub>yy</sub> mainly depend on the ST direction of the rolled plate [19]. In previous research the IBRS were measured via the slitting method on samples of the size 206 x 102 x 28 mm<sup>3</sup> (1 x w x h) with orientation I (for more details see [20]). For orientation II the applied IBRS were derived from both the measured stresses (I) and the literature [19]: The stress profile of σ<sub>xx</sub> with its magnitude stays the same as for the measured stresses but depends now on the z-direction, which corresponds to the measured stresses presented by Prime et al. for the same material but different size. Initial stresses σ<sub>yy</sub> are assumed to have the same M-shape as σ<sub>xx</sub> but are 45 % smaller in magnitude [19].

For varying geometry sizes, it is assumed that the magnitude of the IBRS within the initial block stays the same. This means that only its extension on the length axis is scaled accordingly to the length, width or depth of the part, respectively. Since the total machined part is 20 mm thick, there is the option to vary the position of the part in the 28 mm stock: Position IIa indicates a position at the center (z-offset of 4 mm) and IIb towards the top (z-offset of 1.5 mm). The z- offsets are shown on the horizontal axis of Fig 3b.

<figure><img src="image_4.png" /><figcaption>Fig. 3. (a) Measured [20]; (b) derived IBRS according to [19,20] of AA7050-T7451.</figcaption></figure>

2.3. Model

The model to predict the distortion due to the measured RS is a static, linear elastic FEM model and was created in ABAQUS¹. A superposition of the MIRS and the IBRS is assumed: The MIRS are considered in the near-surface region and the IBRS in the bulk of the sample, neglecting the interaction of both stress types. This assumption is possible, since only small IBRS (σ < 20 MPa) are considered. The presented RS were implemented as an input via the command “initial condition type = stress” [17]. The measured MIRS (plane stress: σ<sub>xx</sub>, σ<sub>yy</sub>, τ<sub>xy</sub>, see Fig. 1) were linearly interpolated over depth z at the element centroids in the boundary layer of the milled surfaces (backside, top, bottom of pockets) (see Fig. 4). For milling the pockets in a spiral milling path, a transformation of the MIRS according to the direction of milling (imported from G-Code) is required. For depths smaller than the first measured point the first measured MIRS was used. Whereas for depths greater than the last measured depth, the measured or derived in-plane IBRS (σ<sub>xx</sub>, σ<sub>yy</sub>, see Fig. 3) were linearly interpolated according to their position and orientation. Eight-node brick elements (C3D8) with different sizes were used: A refinement of the mesh at the machined surfaces in z-direction was chosen to precisely resolve the MIRS. To reduce the calculation time, a coarser mesh was used elsewhere. Due to the 3-2-1 constrain principle rigid body motion was avoided, while enabling a free distortion of the body (see Fig. 4) [11]. Linear elastic material behavior (E = 71,700 MPa, ν = 0.33) was given. After equilibrium was calculated, the displacement at the backside was analyzed by first leveling (fitting polynomial plane of order 1x1 and subtracting it) and setting the surface to zero height at its minimum.
<figure><img src="image_5.png" /><figcaption>Fig. 4. FEM distortion prediction model [modified from 17].</figcaption></figure>

**3. Results and discussion**

**3.1. Stiffener angle and machining path variation**

Fig. 5 depicts the color maps of the simulated displacement in z-direction (here defined as distortion) of the backside of each sample for the different stiffener angles and machining paths. They mimic looking down at the milled surface of the pockets with positive distortion in the z-direction (into the surface). Orientation I of the IBRS was chosen for each investigated case. To further highlight which RS is driving the distortion, simulations with only IBRS applied, neglecting MIRS, were investigated additionally.

For milling the 90°-part in zig strategy the highest distortion occurs with $z_{max} = 0.202$ mm (see Fig. 5a). An X-shaped distortion shape with the maximum displacement on the two opposite corners is visible. This is due to the presence of a torsional moment induced by the negative shear RS in addition to the bending moment caused by the compressive normal MIRS, leading therefore to a rotation of the principal axes towards ±45°. Whereas for only applying the IBRS (Fig. 5c) a U-shaped distortion with significantly lower magnitude $z_{max} = 0.036$ mm is found. The maximum is towards the mid-length, because IBRS $\sigma_{xx}$ are the greatest (without any shear stresses), inducing therefore a bending moment in x-direction. By assuming the superposition of both RS types, the MIRS are responsible for 82% (= 1-0.036/0.202) of the maximum distortion for the zig strategy. When the milling path is changed from lines to a spiral path, the shear stresses within the bottom of the pockets almost equilibrate each other and less distortion occurs with $z_{max} = 0.066$ mm (see Fig. 5b). The distortion maximum shifts towards the opposite corners compared to Fig. 5d because the low shear RS at the backside inducing a torsional moment in the opposite direction. Now both RS types are almost equally responsible for the distortion with a contribution of the MIRS of 45% (= 1-0.036/0.066%).

When changing the angle of the stiffener from 90° towards 45° the distortion of the part machined in zig milling strategy (Fig. 5d) is significantly lower ($z_{max} = 0.068$ mm), because the sample is now stiffened along the principal direction, where the maximum displacement was found. This leads to a reduced MIRS contribution to the overall maximum distortion of 46% (= 1-0.037/0.068%). Machining in a spiral path increases the distortion for the 45°-part ($z_{max} = 0.102$ mm, see Fig. 5e), because shear stresses do not fully equilibrate each other anymore (as for the 90°-part). For this case MIRS are responsible for 64% of the maximum distortion.

The 135°-part machined in lines has a similar distortion shape and magnitude ($z_{max} = 0.191$ mm) as the 90°-part, but fundamentally different distortion compared to the 45°-part, although the stiffener is only mirrored (see Fig. 5g). This is due to the mentioned alignment of the 45°-stiffener with the principal direction where the maximum displacement was found. MIRS are accounting for 81% of the maximum distortion. A spiral milling path can reduce the distortion to $z_{max} = 0.127$ mm and the contribution of the MIRS to 71% (see Fig. 5h).

In general, it can be highlighted that the choice of the milling path is strongly connected to the part topology in form of the angle of the stiffeners. A spiral milling path for the 90°-part showed the lowest distortion and is therefore selected for following investigations.
<figure><img src="image_6.png" /><figcaption>Fig. 5. Color maps of predicted distortion for stiffener angle and machining path variation.</figcaption></figure>

## 3.2. Wall thickness variation

Fig. 6 shows the variation of the wall and floor thickness (2, 3, 5 mm) of the 90°-part machined with the spiral milling strategy and IBRS orientation I. The distortion increases with decreasing wall thickness. For this part topology and a 3 mm wall-thickness the MIRS and IBRS are almost equally responsible for the part distortion (MIRS 45 %). For parts with 2 mm thick walls and floor the MIRS are dominating by 63 % and a maximum distortion of $z_{max} = 0.112$ mm is found, because of the reduced stiffness of the part. Contrary for parts with thicker walls and floor respectively (5 mm), the IBRS are driving the distortion (74 %) and a maximum distortion of $z_{max} = 0.03$ mm is found.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Color maps of predicted distortion for wall thickness variation.</figcaption></figure>

## 3.3. Initial bulk residual stress variation

Fig. 7 depicts the predicted distortion of the 90°-parts, machined in spiral milling strategy, for parts with different IBRS. The shape and magnitude of the distortion due to the different IBRS orientations is similar to each other with a maximum distortion of 0.066 mm, 0.069 mm respectively (compare Fig. 7a to Fig. 7b). Choosing an offset of 1.5 mm of the final part in the raw material (Fig. 7c) increases the distortion ($z_{max} = 0.085$ mm), because the IBRS are not symmetrically distributed over the height z anymore.
<figure><img src="image_8.png" /><figcaption>Fig. 7. Color maps of predicted distortion for IBRS variation</figcaption></figure>

### 3.4. Part size

Fig. 8 shows the distortion of a more complex part, a small-scaled airplane wing-rib, machined with the spiral milling path and different IBRS. Comparable conclusions as for the smaller part can be drawn: Similar U-shaped distortions are evident for all three investigated cases. The smallest distortion is found for orientation IIa ($z_{max}$ = 0.376 mm). Applying IBRS of orientation I leads to higher distortions than case IIa, since more material is removed in y-position (compared to the small parts). This is due to the curved rim, disturbing the IBRS equilibrium more than for IIa, where the IBRS do not depend on the y-direction.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Color maps of predicted distortion of small-scaled airplane wing-rib for different IBRS.</figcaption></figure>

Fig. 9 shows the effect of the different milling strategies on the part distortion of the small-scaled airplane wing-rib. Similar conclusions as for the small parts can be drawn: The X-shaped distortion with the highest distortion $z_{max}$ = 0.494 mm is found for the zig strategy (see Fig. 9c). The MIRS contribute to 57 % of the distortion, which is less than for the small part. The distortion can be reduced for choosing a spiral path ($z_{max}$ = 0.272 mm). Thereby the effect of the MIRS on the distortion is minimized (22 %) and the IBRS are driving the distortion (78 %).

<figure><img src="image_10.png" /><figcaption>Fig. 9. Color maps of predicted distortion of small-scaled wing-rib for different milling strategies.</figcaption></figure>

## 4. Conclusion

It could be shown that the part topology, part size, the machining strategy in terms of milling path and orientation of the IBRS have a mutual effect on the distortion. It was shown that a decreasing wall thickness led to increasing distortion with a shift of the RS type dominating the
distortion towards the MIRS. Specifying a general crucial wall thickness when MIRS are
driving the distortion for thin-walled monolithic structural parts is not possible, because that
depends on the specific part geometry and the machining strategy.

The results furthermore showed that knowledge gained from investigating smaller and
simpler parts (size and complexity) could partially be transferred to bigger parts: For the
investigated geometries it can be stated that milling the pockets in spiral paths (for 90° stiffener
angles) reduces the distortion. Positioning the final part symmetrically in the initial block
minimized the distortion as well. However, the percentage to the contribution of each RS type
depends on the part size and topology.

**5. Acknowledgements**

The authors would like to thank the German Research Foundation (DFG) and the National Science Foundation (NSF) for the financial support within the project AU 185/64-1 (351381681) “NSF DFG Collaboration to Understand the Prime Factors Driving Distortion in Milled Aluminum Workpieces” (NSF funding Award No. 1663341). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the DFG or NSF.¹Naming of specific manufacturers is done solely for the sake of completeness and does not necessarily imply an endorsement of the named companies nor that the products are necessarily the best for the purpose.

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