Study of scale effects on mechanical strength of the AA1050 and AA1085 alloys

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1 Study of scale effects on mechanical strength of the AA1050 and AA1085 alloys Olivier R. Marques Instituto Superior Técnico, Universidade de Lisboa, Portugal Abstract Microfabrication technologies have been driven by the demands of the consumer market for more compact electro-mechanical systems with new and more features. A consequence of this miniaturization of the manufacturing processes is the appearence of challenges related with the scale effects. We have as an example the reduction of plastic hardening with the reduction of the volume of material involved in the manufacturing process. Thus, it is important to understand how the volume of material involved in the plastic forming, for the same metallurgical condition, can affect the mechanical response and which constitutive equations best reproduce this change of the mechanical behavior of the material. The present dissertation investigates the scale effects involved in orthogonal cutting by performing uniaxial compression tests with specimens of different dimensions. The reduction of the size of the specimens (from 8 to 0.5 mm) seeks to approximate the typical section of the chips and to simulate the plastic flow on the face of the tool. The results show that the materials used in the investigation (AA1050 and AA1085) do not present the softening of the yield stress for the range of sizes studied, however, they show a high sensitivity to the scale effects associated with the friction on the contact interface between the material and the tool. Keywords: Scale effects, plasticity, compression tests, yield stress, AA1050, AA Introduction The demand of products increasingly smaller has led to the development of technologies at the level of micro-manufacturing (having at least two dimensions below the millimeter). One of the most common technological processes of the machining industry is the orthogonal cutting that can be applied to lathes or, for example, to the complex machining centers. To predict the mechanical behavior of the materials, without machining it, it can be used softwares of finite elements method (FEM). To do so, it is necessary to know the mechanical properties of the materials, normally studied with the evolution of the stress with the real strain. Scale effects

2 can appear on many ways, and, despite of being effects also existing on macro-scale, they are negligible and many times unknown, due to the small impact comparatively to the size of the specimen. For example, in the uniaxial compression of a cylinder, the roughness of the compression plates and the cylinder cannot be zero, due to physical impossibility of having a perfectly plane surface. When minimizing the size of the specimen that initially was considered polished, it can have its surfaces completely rough, due to being working on specimens with the same scale as the roughness of the superficies, resulting on an example of a scale effect, present in this dissertation. On orthogonal cutting, it is known that the strain hardening of the materials decrease with the decreasing of the cutting thickness, but this variation is not quantified. This work serves to discover this variation, so we can include this scale effect on computational cutting models and predict better the mechanical behavior of the Aluminum alloys AA1050 and AA1085 (with a specimen relation of when subjected to cutting processes with different thicknesses and to any study of the mechanical behavior. The objective of this present study is to prepare a bench tests, valid it, get the mechanical behavior of the two Aluminum alloys with the dependency of (being D the diameter of the cylinder to compress and d the grain size) and obtain models that characterize this behavior. This analysis is meant to support researchers in future developments and to guide future researches so it can be increased the precision of the predictions of the mechanical behavior, when subjected to external forces. 2. Literature review In practice, micro-forging quickly became a promising manufacturing process for micro-scale, due to its potential for high productivity, low cost and good mechanical properties (M. Geigerl, 2001) and (F. Vollertsen, 2004). By reducing the size of components to be manufactured, the scale effect appears. This causes the classic modeling theories of conventional forming processes become inefficient (J. Liu, 2012). These scale effects can not only be linked to the size of the components to manufacture, but also by the microstructure of the material. The grain size is as important in the behavior of the material. According to (C. Keller, 2010), the scale effect is linked to, being T the characteristic size of the piece and D the cylinder diameter subjected to compression. The scale effects can be classified into intrinsic and extrinsic. When the size of the microstructure is variable, such as grain size, for example, called the intrinsic-scale effect, dwell on the mechanical characteristics of the material (Figure 1.a). When considering constant intrinsic conditions, by varying the size of the component, this is called the effect of extrinsic scale (Figure 1.b).

3 (a) Figure 1 Scale effects: (a) Intrinsic and (b) Extrinsic ( (G.Y. Kim, 2007). (b) If we consider the ratio λ, it is possible to understand that the higher the ratio, the better the surface finish of the workpiece, as would happen otherwise if the ratio decreased, because the grains are irregular and are increasingly pronounced. The effects of intrinsic and extrinsic scale may be combined, which is the most frequent case in engineering. This can be classified into polycrystalline samples (components with a ratio ), multi-crystalline ( ) and almost mono-crystalline (when the specimen order of magnitude to deform approach the order of magnitude of the metallurgical grain) [(C. Keller E. H., 2010) (C. Keller E. H., 2011)]. The reduction in strain hardening in micro and macro compression tension tests have been extensively investigated experimentally [ (Julia R. Greer, 2011), (W.L. Chan, 2011) and (C. Keller E. H., 2015)] and concluded that the effects of scale only appear when the parameter λ is less than or equal to 10. Thus, it is considered that the effects of scale may appear for any of the classes of polycrystalline samples. As the response of each material when changing the parameter λ may be different, there was made a study in two aluminum alloys with different degrees of purity to estimate the change in the material response, depending on its degree of purity of aluminum. The mechanical behavior of the forecast study of polycrystalline metal has given rise to several constitutive models that can describe this behavior. Some of them are described below. The Hall-Petch model is a very common and widely used model to characterize materials in which the effect of grain size is taken into account on the mechanical strength of polycrystalline metals: (1) Where σ 0(ε) and k hp (ε) are constants of the material that depends on the stress. Fleurier Gwendoline (Gwendoline Fleurier, 2015) states that, regardless of the deformation level, the Hall-Petch law does not meet the full range of metallurgical grain sizes. In an attempt to use the most appropriate models for each situation, appears the need to make some changes. Some generalizations of the Hall-Petch equation were used in determining the mechanical behavior of materials in this case study, then presenting the models used.

4 The model of Ludvik-Holloman (equation 2, (P., 1909) e (J.H., 1945)) is used for conditions of constant values of strain rate and temperature relating the stress behavior with the true strain of the material, being a simpler equation capable to characterize the stress with the true strain of the materials. (2) Where K is a constant that depends on the material and the conditions of the material, and n is an exponent that depends on the work hardening of the material. The model of Voce (E., 1948) is described by the equation 3, and is an equation that features elastic-plastic materials. This model introduces the concept of saturation stress and is used to relate stress with true strain to materials which exhibit reduced strain hardening to higher extensions values, (3) where a, b and c are constants that depend on the material and operating conditions ((Silva, 2013) and (E., 1948)). The mechanical behavior of the model proposed by Carlos Silva (Silva, 2013) to cold materials processing combines the concept of multiplicative terms studied in (Silva, 2013) with a structure of the terms and constants contained, allowing to know specific aspects in cold behavior. The proposed model has been changed to not account the strain rate, which, in spite of knowing, is quasi-static, thus decreasing the equation and entering the same input data in all models. (4) Where the constants A, B, m and n depends on the material and should be determined using the experimental tests of mechanical characterization, with the aid of MATLAB software. 3. Materials and experimental procedure The specimens used in the experiments are cylindrical, subjected to uniaxial compression. In the case of samples with dimensions of up to 500 micrometers, manufacturing these test pieces originate many problems, which leads and appear the need to minimize internal and external defects in the samples, to obtain valid test pieces. Thus, this was made using a numerically controlled milling machine and after that, the two alloys were annealed for two hours at 500 C so as to make the material as free of residual stresses as possible. In Figure 2 you can see the steps of the machining process of the specimens, which involves machining the contours of the cylinders of the raw material (point a), leaving the raw material with the cylinders. After this, the material has been filled with Super Glue 3 in the area where the material was removed in order to improve the structural rigidity (point b), reversed the machining material (point c) to take out the base of the cylinders, without deforming them because of the lack of structural rigidity. After this, appears the cylinders inside the glue (point d), which is removed with acetone, getting the final samples with the desired geometry (point e).

5 (a) (b) (c) (d) (e) Figure 2 Manufacturing sequence of compression specimens. For obtaining the mechanical behavior of materials, it is necessary to have a sensor that provides information of the force being exerted. To do so, we used the Kistler brand load cell, named 9102 with a pre-load of 10 kn, because the load cell manufacturer recommends the use of a pre-tension of 50% of the maximum force value to be exerted on the cell. This force sensor by itself only sends information in the form of voltage, which is too low, so it was used an amplifier to increase the output signal. The amplifier used was the Kistler Type 5011B. Despite the sensitivity value provided by the manufacturer to be used in the amplifier be of, this figure showed not properly represent the data, and it was studied the most accurate value of T, having obtained. Beyond the force, it is necessary to relate the instantaneous height of the specimen with the force exerted. In this way, and to account the deformation of the test specimen (with no chance to be measured the deformation of the structure), it was made up of magnetic electro distance sensors, sending a magnetic field (preset by a generator signals called TG550, of the brand AIM & TTi ) from one coil to another (one being the signal generator and the other the receiving), using the principle of electromagnetic induction. Having the need to rectify the signal, it was made a rectifier for full-wave phase for using in the output coil, which will turn on the data acquisition board and turn the computer (Figure 3). Figure 3 Esquema do processo de aquisição da distância entre sensores. The data acquisition board is called National Instruments NI USB This equipment receives the signal voltage from the distance sensors and force with a frequency of 500 Hz each one. The software used for data acquisition was LabView. The force sensor behavior is translated into a curve relating the input voltage of the data acquisition board with the distance at which the coils are located, having improved the curve

6 obtained with hundreds of points. This last curve has been approximated to a straight line on a logarithmic scale, making it easier and flexible to obtain the height data of the samples. The compression tool used is a rod-crank press type, where is possible to adjust the final height to be obtained in the cylinders. It is presented in Figure 5 the test bench with the equipment used. Label 1- Data processing 2- Data acquisition board 3- Amplifier 4- Signal generator 5- Electric circuit 6- Secondary motor 7- Original motor 8- Compression Figure 4 Test bench.. tool The experimental conditions used in this study were composed by considering height and diameter of the cylinders with the same size, for four different steps (4, 2, 1 and 0.5 mm), and making the compressions in two different Aluminums Alloys (AA1050 and AA1085). Thus, four tests were conducted for each type of aluminum. It was joined another electric motor to the original one to reduce the speed to almost static values. For incremental compression tests used in this work, the achieved speeds were all between 0 mm/s and 0.2 mm/s. The compressor plates suffered various changes in form and material, to minimize friction that is present in these tests, where initially altered the values to the point in which it was not able to consider the results for the study. The final version of the compressors plates, which it was obtained the results of this study were made of stainless steel with a recessed tungsten carbide cylinder. The machine was validated by comparing the experimental results obtained in this bench tests with Alcino Reis (Reis, 2016), demonstrating coincident results for testing under the same conditions. Nevertheless, the friction effects noted in tests are increasingly higher the greater the extension and the smaller the sample size to be tested. Since the stress versus true strain curve has values influenced by friction (Figure 6), tests were done incrementally with lubrication at each increment. It can be seen that the increments 8 and 10 have a slope of the elastic region different from the other extension increments, which may be related to a non-homogeneity of the compressed surfaces.

7 Stress (MPa) 350 1º Increment 2º Increment 3º Increment 4º Increment 5º Increment 6º Increment 7º Increment 8º Increment 9º Increment 10º Increment Continuous compression ,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 True strain [adimensional] Figure 5 Difference between results obtained by continuous and incremental compressions of a AA1050 specimen, with 6 mm of diameter and height, and strain rate between 0.3 and 0 mm/s for incremental compressions and between 1.2 and 0 mm/s for continuous compressions. Comparison of the results was made with respect to λ, and the results obtained for the compression of specimens of AA1050 are in the Figure 6, where λ values range between 1.9 and The curves do not show a dependence on λ in the plastic zone, presenting a generally σ AA1050 (ε=1.5) = 180 MPa, but show that there is a tendency of increasing the Young s modulus with decreasing λ, thus entering faster in plasticity. This variation is not normal, as the differences between different λ s is 6 times bigger in the 0.5 mm specimen than in the others, showing that something might be wrong with this result (this situation was understood later and show that this elastic region cannot be possible). This variation appears to be increasingly significant, the lower the λ value from values below Analysis and discussion of results The results of the stress versus true strain curves are shown in the Figure 7 and 8, presenting the differences of the two different Aluminum alloys.

8 Stress [MPa] 250,0 4 mm 2 mm 1 mm 0,5 mm 200,0 150,0 100,0 50,0 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 Strain [dimensionless] Figure 6 Stress versus True strain for the AA1050, for strain rate between 0 and 0.3 mm/s and for the following cases: H=D=4 mm, H=D=2 mm, H=D=1 mm and H=D=0.5 mm. The results for AA1085 demonstrate poor influence of λ in the elastic zone, unlike AA1050, and a tendency of a decreasing in hardening with the decreasing of λ. The larger samples of up to 1 mm, ie, λ 4 mm = 58.2 to λ 1 mm = 3.4, have approximately matching values, and there is no tendency among them. Already in λ 0.5 mm = 0.8, the difference is presented clearly, with less work hardening, from σ AA1085 (ε=1.5, λ > 3.4) = 170 MPa for σ AA1085 (ε=1.5, λ = 0.8) = 122 MPa. It seems like there is a high dependence on λ, but only from values less than 1, a value within the proposed by [(Julia R. Greer, 2011), (WL Chan, 2011) and (C. Keller EH, 2015) ], with appearance of scale effects for for both the AA1050 and the AA1085.

9 Stress [MPa] mm 2 mm 1 mm 0,5 mm ,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 Strain [dimensionless] Figure 7 Stress versus True strain for the AA1085, for strain rate between 0 and 0.3 mm/s and for the following cases: H=D=4 mm, H=D=2 mm, H=D=1 mm and H=D=0.5 mm. Looking at the quality of the results, it is found that there is an increase in dispersion results by reducing the sample size and with increasing extension. Having been taken precautionary measures in order to obtain the results as little as possible scattered. The characterization of the mechanical behavior with the scale effects in AA1050 and AA1085 were made in three different models, including one with elastic-plastic behavior and two hardplastic. The calculation tool used was the MATLAB, based on the code used by Alcino Reis (Reis, 2016), modified for the case study, it appears that the extracted theoretical curves correctly represent the experimental curves showing that the equations are valid for the characterization of the mechanical behavior of AA1050 and AA1085, having as a variable not only the strain, but the grain size compared with the size of the sample to deform. In the model Ludwik-Holloman (elasto-plastic model) presented in equation 2, it is seen that the curves for the AA1050 follow the evolution of the curves, both in the initial part, as at the final. For AA1085, the equations describe this material better than AA1050, following with confidence the experimental points, and showing that the equations describe with success the mechanical behavior of the material taking into account the effects of scale. It is found that for any of the models, the influence of λ is low, being visible even in the equation, but it is only a reflection of the low real influence of λ in the experiments in question. The model proposed by Ludwik-Holloman proved that it describes best and fully the mechanical behaviors of the material for the case study, being also the simplest. Thus, the model proposed by the author that best characterizes the influence of λ (the average diameter ratio of metallurgical grain to the size of the deformed specimen) in the mechanical behavior of materials is the modified equation of Ludwik Holloman.

10 5. Conclusions and future work The conclusions are inherently linked to the experimental development, computational and analytical results. The lack of information on this subject, made overcome several obstacles in order to obtain valid results demonstrating that scale effects exists on the mechanical behavior of aluminum alloys. Although the study focus on the characterization of scale effects on experimental results, this was not the component that I have spent more time and effort. The development of the experimental apparatus and all the implications and obstacles raised was where I have spent more time and work, so that had to reconcile many issues so far theoretical to practical. This helped me a lot in my personal and professional development, making me learn a lot about many different subjects. It is also concluded that the mathematical model studied that best describes the behavior of the two alloys studied considering λ in the model is the model of Ludvik Holloman, modified for the case study. For future work, I suggest to do some changes on the compression tool, in order to improve the results (Marques, 2016). Since the hardening of the results of the material present variations to λ values below 1, it would be important to make a study of λ values from this value down, if it could be possible to make the tests, due to the implications that arise by decreasing λ. I suggest studying the mechanical behavior of materials when subjected to different deformation speeds, as the machine developed in this study is adapted from a frequency inverter that can work to any speed within the minimum and maximum speed of the two motors. Being the experimental bench operational and tested, it becomes much simpler and faster to do testing, as such, I suggest studying the mechanical response of materials in pure materials, in order to obtain the properties of each and try to create a general model that can predict computationally the mechanical behavior of any league, just knowing its constitution, linking the properties of each alloy constituent in the equation. It is an ambitious proposal, but this would make possible the study and know-behavior of any league with only computing resources, with very low expenditure of time and money.