PSI - Issue 35

Available online at www.sciencedirect.com Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 35 (2022) 1–1 Structural Integrity Procedia 00 (2021) 000–000

www.elsevier.com / locate / procedia

2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials Editorial Tuncay Yalc¸inkaya a, ∗ a Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey

Keywords: Plasticity; Damage; Fracture Mechanics; Ductile Fracture; Micromechanics

This special issue contains a selection of research papers presented virtually at the 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials organized by Middle East Technical University in Ankara, Turkey on 18-20 August 2021. Participants were given live and pre-record options to present their contributions. Due to the challenging conditions caused by the COVID-19 pandemic throughout the world, the workshop is held online to contribute to the dissemination of scientific progress in the fields of plasticity, damage and fracture of engineering materials. There were 8 keynote lectures, 35 contributed talks and 53 pre-record presentations published on the Youtube channel. 117 researchers from 28 di ff erent countries participated in the meeting and only the papers that are accepted after a peer-review process are published in this special issue. After the successful organization of the first version of the IWPDF workshop held on 22-23 August 2019, in Ankara with various activities and trips, it has been a challenging task to organize the 2nd version due to pandemic conditions. However we are quite glad with the decision of organizing the event virtually, which attracted high level of contribu tions from all over the world. The scientific level of the workshop was set by the brilliant keynote lectures given by Prof. Laura De Lorenzis (ETH Zu¨rich, Switzerland) on phase-field modeling of brittle fracture, by Prof. Odd Sture Hopperstad (Norwegian University of Science and Technology, Norway) on plastic flow and fracture in anisotropic aluminium alloys, Prof. Erdogan Madenci (University of Arizona, USA) on recent progress in peridynamic theory, by Prof. Emilio Mart´ınez Pan˜eda (Imperial College London, UK) on phase field modelling of corrosion damage and hy drogen embrittlement, by Prof. Dierk Raabe (Max-Planck-Institut fu¨r Eisenforschung GmbH, Germany) on multiscale and multi-physics simulations of chemo-mechanical crystal plasticity and phase transformation problems for complex materials using DAMASK, by Prof. Timon Rabczuk (Bauhaus University Weimar, Germany) on machine learning based solutions of PDEs, by Prof. Javier Segurado Escudero (IMDEA-Materials, Spain) on modeling size e ff ects in metals using FFT homogenization and by Prof. Huseyin Sehitoglu (University of Illinois Urbana-Champaign, USA) on exploring the fundamental issues in modeling of twinning in materials. We would like to thank all the keynote speakers for their immeasurable contributions to the workshop. The organization process of the workshop was made very easy by the kind, attentive and e ffi cient support of the members of the organizing committee: Prof. Mehmet Dorduncu, Mr. Orhun Bulut, Mr. Can Erdogan, and Mr. Izzet Tarik Tandogan. Finally, I would like to acknowledge the support of the European Structural Integrity Society (ESIS) and its president Prof. Francesco Iacoviello for the organization of the meeting and for the publication of the special issue papers in Procedia Structural Integirty Journal.

∗ Corresponding author. Tel.: + 90-312-2104258 ; fax: + 90-312-2104250. E-mail address: yalcinka@metu.edu.tr

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yal ç inkaya 10.1016/j.prostr.2021.12.040 2210-7843 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalc¸inkaya.

ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceDire t Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 35 (2022) 66–73

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya Abstract Experimental and numerical studies on deformation-induced surface roughening in a commercial purity aluminum alloy are presented and discussed. Mesoscale surface profiles evolving in the experimental and numerical specimens in the course of tension are processed to reveal a correlation between roughness characteristics and in-plane plastic strains at the mesoscale. A dimensionless parameter calculated as a ratio of the rough profile length to the profile evaluation length has been used for quantitative estimations of the mesoscale roughness patterns. The dimensionless roughness parameter is shown to depend exponentially on the in-plane plastic strains at the mesoscale. The results support an early assumption that in-plane plastic strains accumulated in a loaded material can be evaluated from the estimations of mesoscale surface roughness. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer- review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya Keywords: deformation-induced surface roughness; mesoscale; plastic strain, aluminum alloys, crystal plasticity 1. Introduction Plastic deformation is commonly accompanied by free surface roughening at different scales. Since the early work of Osakada and Oyane (1971), extensive experimental and numerical data on this phenomenon commonly referred to as deformation-induced (DI) surface roughening have been accumulated for polycrystalline metals and alloys. A recent review on this subject is provided, e.g., by Li and Fu (2019). Examination of roughened surfaces 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials A Correlation between Deformation-Induced Surface Roughness and In-Plane Plastic Strain in an Aluminum Alloy at the Mesoscale V. Romanova a, *, V. Shakhidzhanov a , O. Zinovieva a , O. Nekhorosheva a,b , R. Balokhonov a a Institute of Strength Physics and Materials Science SB RAS, Tomsk 634055, Russia b National Research Tomsk State University, Tomsk 634050, Russia Abstract Experimental and numerical studies on deformation-induced surface roughening in a commercial purity aluminum alloy are pres nted and discussed. Me oscale surface prof les evolving in th experime tal and nu eri al s ec mens in the course of ten ion are proce sed to rev al a correlation betwe n rough ess characteristics and i -plane plastic stra ns at the m soscal . A dimensionless parame er calcul ted as ratio of the profile length to the profile evalua on length has be n used for quantitativ estim tions of the meso c le r ughness patterns. The dimensi nl ss r ughness parameter is shown to d pend exponentially on the i -plane plastic strains at the me oscal . The results supp rt an early assumption that in-plane plastic strai s accumulated in a loaded mat rial can be evaluated from the stimations of mes sc le surface roughness. © 2021 The Auth rs. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer- review u der re ponsibility of IWPDF 2021 hair, Tu cay Yalçinkay K ywords: deformation-induced surface roughness; mesosc le; plastic strain, aluminum alloys, crystal plasticity 1. Introduction Plastic deformation is commonly accompanied by free surface roughening at different scales. Since the early work of Osakada and Oyane (1971), extensive experim ntal and numerical data on this phenomenon common referred to s deformation-induced (DI) surfac rougheni g have been ac umulated for polycrystalline metals a d alloys. A recent review this subject i provided, e.g., by Li and Fu (2019). Examinati n of roughened surfaces 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials A Correlation between Deformation-Induced Surface Roughness and In-Plane Plastic Strain in an Aluminum Alloy at the Mesoscale V. Romanova a, *, V. Shakhidzhanov a , O. Zinovieva a , O. Nekhorosheva a,b , R. Balokhonov a a Institute of Strength Physics and Materials Science SB RAS, Tomsk 634055, Russia b National Research Tomsk State University, Tomsk 634050, Russia

* Corresponding author. Tel.: +7-960-969-2982 E-mail address: varvara@ispms.tsc.ru * Corresponding author. Tel.: +7-960-969-2982 E-mail address: varvara@ispms.tsc.ru

2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer- review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer- review u der responsibility of IWPDF 2021 hair, Tuncay Yalçinkay

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yal ç inkaya 10.1016/j.prostr.2021.12.049

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

67

2

with different spatial resolutions has revealed three distinct length scales of out-of-plane surface displacements attributed to different plastic deformation mechanisms. A detailed classification of the multiscale roughening events was given by Raabe et al. (2003). The intragrain displacements related to the slip bands are first to occur as plastic deformation begins. The heights of individual slip steps are comparable to interatomic distance so that even a pack of slip bands are capable of fitting rather limited out-of-plane strain. Thus, further deformation involves larger-scale surface displacements seen as grain clusters conjointly moving up and down relative to each other. The surface patterns formed by the collective grain displacements are classified as mesoscale. Finally, surface waviness is detected at the macroscale with a wavelength comparable to the specimen size. The DI waviness should not be confused with the initial waviness inherited from the sample manufacturing or elastic waviness disappearing after unloading. A pronounced bow-shaped surface region is formed in necking shortly before fracture. Being well-detected throughout the entire deformation process from the very beginning of plastic deformation to a macroscale necking, the mesoscale roughening events can be utilized in the material stress-strain attestation provided that a correlation between certain characteristics of roughness patterns and plastic strains is established. Since Osakada and Oyane’s (1971) pioneering work, many experimental and computational efforts have been made to link the surface morphology with the deformation parameters for different metals and alloys and various loading conditions (e.g., Ma et al. 2019; Messner et al., 2003, 2005; Paul et al., 2019; Shavshukov, 2020; Stoudt et al., 2011; Wang et al., 2013; Yoshida, 2014). Recently, Romanova et al. (2019a, 2020) have shown on the example of commercial purity titanium that the mesoscale DI roughness was nonlinearly related to in-plane strain through a so-called dimensionless roughness parameter. Being drawn for the particular case, this conclusion still needs further experimental and numerical evidence. This paper continues the experimental and numerical investigations along these lines to reveal a correlation between mesoscale DI roughening and in-plane plastic strains in a commercial purity (CP) aluminum alloy under uniaxial tension. 2. Experimental 2.1. Material The EBSD map and pole figures for a CP aluminum alloy presented in Fig. 1a and b provide information about the grain shape and orientations. Hereinafter, the X- and Y-axes lie along and transversely to the specimen axis, respectively, and Z-axis is perpendicular to the specimen top plane (Fig. 1c). The microstructure mainly consists of equiaxed grains with the size varied fro m 20 to 70 µm. The inverse and direct pole figures (Fig. 1a, b) indicate the presence of a two-component texture typical for rolled aluminum {100}<001>+{110}<001> with the cube grains (red colored in Fig. 1a) occupying a larger area.

a

b

c

Fig. 1. EBSD map (a) and pole figures (b) of an aluminum alloy and the experimental specimen after tension (c)

2.2. Stop-and-study measurements A dog-bone- shaped specimen with a 50×10×1.5 mm 3 gauge part was subjected to quasistatic uniaxial tension using an INSTRON Universal testing machine. In order to reveal a correlation between in-plane plastic strains and

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

68

3

mesoscale deformation-induced roughening, a stop-and-study technique developed by Romanova et al. (2019a) has been utilized. The specimen gauge section was divided into subsections by a set of control marks indented on the surface along its centerline (Fig.1c). The evaluation length was chosen, relying on the conclusions drawn by Romanova et al. (2019a) for a titanium alloy. In order to be representative of the mesoscale, the surface profile evaluation length should cover ~ 4-5 characteristic wavelengths of the mesoscale surface relief. Our recent experimental and numerical estimations for titanium (Romanova et al. 2019a) showed that the mesoscale clusters initially covering 3 to 5 grains consolidated into 15-20 grain units in the developed deformation stage. Relying on this, 5 mm subsection length was chosen to catch the mesoscale phenomena throughout the entire deformation process. Treating longer profiles is unreasonable since it might lead to averaging the mesoscale roughness effects. After certain deformation, the specimen was taken from the testing machine to examine strains and roughness profiles in its subsections. The in-plane tensile strain of each subsection was calculated as a ratio of the current distance between the control marks to the reference length of the subsection. In what follows, we denote the strains of the specimen and its subsections by  and sub  , respectively. The surface profiles in the subsections were measured by an Alpha- Step IQ contact profiler with a step of 1 µm. Then the specimen was set into the testing machine again and its loading was continued up to the next stop. In such a way, the subsection strains and surface profiles were measured throughout the deformation process with a strain step of 2.5-5%. Along with the periodical profilometry and strain measurements, surface patterns in some selected subsections were treated with a laser scanning microscope NewView. Standardized surface roughness quantification is provided in terms of the arithmetic mean roughness, the root mean-square roughness and other roughness parameters determined from the deviations of the surface peaks and valleys from the mean line. The roughness evaluation procedure is commonly preceded by filtering the raw surface profiles to remove high-frequency noise oscillations and low-frequency waviness. The resulting roughness estimates are expressed in microns. Romanova et al. (2017) proposed a new approach to quantify DI roughness in a loaded material, taking into account the origin of this event. Summarizing our previous results (Romanova et al. 2013, 2017, 2019a, 2020) and literature data on DI roughening in metals and alloys (Messner et al., 2003, 2005; Panin et al. 2020; Paul et al. 2019; Qin et al., 2013; Raabe et al., 2003; Shanyavskiy and Soldatenkov, 2020; Stoudt et al., 2011), we came to the conclusion that the rough patterns developing on the free surface under deformation are representative of the multiscale deformation mechanisms involved. In order to take into account the contributions from all length scales appearing within the evaluation length, we estimate mesoscale roughness for unfiltered profiles. By analogy with a strain measure, we have introduced a dimensionless roughness parameter Rd calculated as (1) where L r is the rough profile length and L e is the profile evaluation length. Expressed in this way, the roughness parameter is simply calculated and clearly interpreted: the larger is the Rd value, the stronger is the surface irregularity. The free surface of a uniaxially loaded homogeneous material is known to remain flat since no forces act normally to the surface to produce its out-of-plane displacements. Microstructure inhomogeneity in real materials produces nonuniform displacement fields not only along the load axis but also in the perpendicular direction. The latter are related to the surface out-of-plane displacements causing surface roughening in the absence of external forces. Thus, the R d parameter might reflect a degree of material inhomogeneity to a certain extent. 1 r e R L L d   2.3. Mesoscale roughness quantification

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

69

4

3. Numerical simulation Taking in mind that DI surface roughening in real materials is inextricably linked to their structural inhomogeneity, we employ an approach of microstructure-based simulations where the grain structure is taken into account explicitly. For incorporating the grain orientation effects, the constitutive behavior of grains is reasonable to describe in terms of crystal plasticity. The crystal plasticity finite-element approach and its dynamic implementation in simulations of aluminum polycrystals have been validated and discussed at length in many papers (see, e.g., Harewood and McHugh, 2007; Romanova et al., 2019, 2019b). Omitting a detailed mathematical description, let us briefly discuss the main points related to the simulations at hand. 3.1. Polycrystalline model Based on the experimental data, a polycrystalline model consisting of 1000 equiaxed grains with an average size of 70 µm was generated on a 150×150×50 mesh by the method of step -by-step packing (SSP) (Romanova et al. 2013) and subsequently translated four times along the X-axis and two times along the Y-axis to obtain 30 00× 15 00× 2 50 µm 3 model representative of the mesoscale. As input parameters of the SSP procedure, the grain seeds were randomly distributed over the meshed domain using a random number generator. In the subsequent SSP procedure, the grains were grown in accordance with the equation of a sphere. The resulting grain structure consisting of 8000 grains is shown in Fig. 2a. Each grain was assigned a Cartesian frame with the axes along the [100], [010] and [001] crystal directions (hereinafter referred to as the crystal frame). The orientations of the local frames with respect to the specimen XYZ frame (Fig. 2a) were given by a set of Euler angles describing subsequent XYX rotations. The first and the third angles were randomly determined in the range of 180 degrees while the second angle was ranged within 15 degrees in order to fit the experimental texture (cf. Figs. 1b and 2b).

200

150

50 100 Stress , MPa

Experiment Simulation

0

0

5

10

15

20

Strain, %

a

b

c

Fig. 2. Grain structure (a) and texture (b) of the model polycrystal and the experimental and numerical stress-strain curves (c).

3.2. Constitutive description, numerical implementation and loading conditions The dynamic boundary-value problem was solved using Abaqus/Explicit. In the numerical realization, the constitutive equations of grains were formulated with respect to their crystal frames on a consistent basis to relate the stress rate, σ , and the total and plastic strain rates, T ε and p ε , through the Hooke ’ s law (in order to differ scalar and tensorial quantities, the latter are written in bold type)   T p   σ C ε ε . (2)

Here T ε is calculated through the velocity field provided by the solution to the equation of motion. The plastic strain rate tensor is calculated through a summary slip over active slip systems

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

70

5

1..12     ε θ p

( ) ( )  

(3)

where θ is the tensor defining the  - th slip system orientation in the crystal frame and ( )   is the slip rate calculated as



( ) 

  ( )  



( )      ( ) a

.

(4)

sign

0 ( ) 



CRSS

Here  is the resolved shear stress, CRSS  is the critical resolved shear stress (CRSS) necessary to initiate slip, 0  is the reference slip rate,  is the strain rate sensitivity coefficient, a is equal to zero under the CRSS below CRSS  and turns to 1 otherwise; hereinafter, the superscript in parenthesis denotes the slip system  . The CRSS value is described by the phenomenological strain hardening function     ( ) 0 1 2 1 exp / p CRSS eq a a         , (5) eq  is the equivalent plastic strain accumulated in the finite element, and 1 a and 2 a are the approximating constants chosen to fit the experimental stress-strain curve. The material constants and model parameters used in the calculations were 1111 C =108 GPa, 1122 C =61 GPa, 2323 C =28 GPa, 0  =33 MPa, 1 a =37 MPa, 2 a =0.0526. A close agreement between the experimental and numerical stress-strain curves (Fig. 2c) proves the model validation. In every time step of the numerical implementation, the constitutive equations (2)-(5) were calculated within a VUMAT User Subroutine with respect to the crystal frames and then the stress tensor components were passed to the Abaqus main program to calculate the equation of motion. On the opposite faces perpendicular to the X-axis the displacement velocities were set to simulate uniaxial tension along the X-direction (Fig. 2a). The displacements of the bottom face were constrained in the vertical direction, and the free-surface boundary conditions were set on the top and lateral faces. The tension velocity was smoothly increased and then kept constant to minimize the acceleration effects unnatural for quasistatic processes (see, e.g., Romanova et al. (2019, 2019b) for further details). 4. Results 4.1. Mesoscale roughness patterns Representative roughness patterns formed in the experimental and model specimens are shown in Figs. 3a and 4a, respectively. Corresponding surface profiles measured in two subsections of the experimental specimen (Fig. 1c) and along the line A-A' in the model polycrystal (Fig. 2a) are plotted in Figs. 3(b, c) and 4b. The mesoscale roughness patterns became well-defined in the experimental and numerical specimens already in the initial deformation stage. In line with the conclusions made by Romanova et al. (2013, 2017, 2019a) for aluminum and titanium alloys, two distinct rough patterns began to develop simultaneously. Smaller round-shaped hills and dimples associated with the extrusion and intrusion of individual grains and grain clusters relative to the surrounding material are seen in the structure of larger surface undulations formed by extended parallel-like ridges lying by an angle to the axis of tension. Experimental and numerical surface profiles plotted in Figs. 3b-c and 4b additionally confirm that the two kinds of roughness irregularities simultaneously appear on the surface. In the course of deformation, the larger-scale undulations intensify while smaller hills and dimples retard their growth. It is worth noting that the peaks and valleys formed in the early deformation stage evolve under tension but do not change their positions relative to each other. where 0  is the reference CRSS value, p

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

71

6

1

200

1

2

200

3

2

4 5

3

6 5 4

150

150

6

100

7

100

7

 : 1

0%;

Height, mm

Height, mm

50

5%; 3 15%; 5 22.5% 7

10%;

2 4 6

50

20%;

24,8%

0 1 2 3 4 5 6 7 0

0 1 2 3 4 5 6 7 0

Position along Subsection 2, mm

Position along Subsection 5, mm

a c Fig. 3. Experimental surface image ( sub  =18%) (a) and evolution of surface profiles in Subsections 2 (b) and 5 (c) (refer to Fig. 1b). b

250

240

220 Height, m m 230

Tensile strain, % 0.8 2.5

210

5.5

8.5

11.3

15.0

200

0

1

2

3

Position along the line A-A', mm

a

b

Fig. 4. Calculated roughness pattern at a strain of 15% (a) and surface profiles in the model polycrystal at different strains (b). The Z displacements in (a) are plotted with a scale factor of 3.

Comparison of the evolving profiles with the grain structure (e.g., cf. Figs. 4b and 2a) suggests that the contributions of surface undulations to the overall roughness patterns are proportional to their characteristic size. The smallest mesoscale irregularities are formed by 3-5 grains and have a period of 200- 300 µm. Their heights do not exceed 2- 3 µm even in the neck region (Subsection 2 in Fig. 3b). Surface undulations with a characteristic wavelength of 700- 1200 µm make a major contribution to roughening throughout the deformati on process; their height being of 4- 5 µm at 5% strain reaches 30 - 40 µm in Subsection 2 shortly before necking (Fig. 3b). 4.2. Correlation between mesoscale surface roughness and in-plane plastic strains For quantitative analysis of the mesoscale roughness patterns, the R d parameter was calculated by Eq. (1) for the whole set of experimental profiles measured in the ten specimen subsections (Fig. 1b). Totally, 80 experimental profiles were processed to reveal a correlation between the mesoscale roughness and in-plane strains of the corresponding subsections. The bar graphs in Fig. 5a and b show the dependences of the in-plane strains and R d values in the subsections on the overall specimen strain. Fig. 5a shows that Subsection 2 where a neck is formed in a later deformation stage begins to deform at a higher strain rate than the other regions as early as 10% overall strain and this tendency is kept throughout the whole deformation process. The strain rate in Subsection 2 demonstrates almost linear growth up to necking (Fig. 5a), while the strains experienced by other subsections slow down or nearly stop growing. Accordingly, the mesoscale roughness evaluated over all the subsections takes on higher values in Subsection 2 than in the other regions (Fig. 5b). However, the R d value in Subsection 2 exponentially grows with the specimen strain. The roughness values in other subsections increase modestly in the initial deformation stage and nearly stop growing after 20% specimen strain (see Fig. 5b). Note, the standard roughness estimates generally provide a linear

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

72

7

roughness dependence on the tensile strain (see, e.g., Banovic and Foecke, 2003; Ma et al., 2019; Messner et al., 2003, 2005; Osakada and Oyane, 1971; Stoudt et al. 2011; Wang et al., 2013). In order to reveal a correlation between the roughness parameter and in-plane plastic strains at the mesoscale, the whole set of the experimental data representing the R d values versus subsection strains are brought together in Fig. 5c, d. Of importance is the fact that the data obtained for different subsections are perfectly approximated by a single fitting curve with the coefficient of determination equal to 0.99 (the red line in Fig. 5c). The fitting equation is expressed by a sum of two exponential functions         5 d R 61.4exp ( 0.1) / 0.18 0.000237exp 0.1 / 0.027 34 10 Sub Sub          (6) The first term of the sum describes the R d (ε Sub ) dependence in the range of moderate plastic strains developing in most specimen regions. The second term is responsible for the catastrophic R d growth in the neck region due to a contribution from the low-frequency macroscopic waviness component. In the case at hand, this term is negligible for the strains below 20%. By analogy with the experiment, the R d values were calculated for numerical profiles measured in the model polycrystal. The numerical strain-dependent roughness curve is plotted in the inset in Fig. 5d in comparison with the experimental data. The R d dependence, in agreement with the experimental evidence, demonstrates a non-linear growth in the course of deformation. The fact that the numerical and experimental R d dependences reasonably fit together additionally proves the model validity.

0 10 20 30 40 50 Subsection strain  Sub , % a

c

0,015

Experimental data for Subsections 1 2 3 4 5 6 7 8 9 10

d

Simulation

8x10 -4

0,010

Fitting curve, Eq. (6)

R d

5 10 15 20 22,5 24,8 26

R d

4x10 -4

0,000 0,004 0,012 0,014 b Subsection roughness, R d Model Equation Plot A Reduced Chi-Sqr R-Square (COD) Adj. R-Square 0,002

Exp1p1 Specimen subsections 1 2 3 4 5 6 7 8 9 10 y = exp(x-A) 12 30,28804 ± 0,05715 6,72355E-7 0,97167 0,97167

0,005

0

0,0

0,1

0,2

Subsection/Model strain

0,000

0,0 0,2 0,4 0,6

Subsection strain  Sub

5 10 15 20 22,5 24,8 26

Specimen strain  , %

Fig. 5. Subsection strains (a) and roughness values (b) vs. specimen tensile strain, and the R d values vs. experimental subsection strains (c, d) compared with the numerical data (d). 5. Conclusions Experimental and numerical studies were performed to reveal a correlation between mesoscale deformation induced surface roughness and in-plane plastic strains in a polycrystalline aluminum alloy under uniaxial tension. The roughness evolution was investigated throughout the specimen surface in a wide range of tensile strains. A dimensionless roughness parameter R d calculated as a ratio of the rough profile length to the profile evaluation length was used to quantify roughness patterns developing at the mesoscale. The R d values calculated for a set of mesoscale surface profiles were shown to depend exponentially on the in plane strains of the evaluated regions. A strong correlation between the mesoscale dimensionless roughness

V. Romanova et al. / Procedia Structural Integrity 35 (2022) 66–73 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

73

8

parameter and in-plane plastic strains has been revealed to confirm that plastic strain accumulated in a material can be evaluated from estimations of mesoscale deformation-induced roughness. Particularly, in the experiments presented in this study, the place of necking was predicted pretty in advance of its visible manifestation at the macroscale from the comparison of R d values in the specimen subsections. Acknowledgements This work is supported by Russian Science Foundation through the grant № 20 -19-00600. The microstructures were generated using the in- house software “SSP - design” developed according to the Government research assignment for ISPMS SB RAS, project FWRW-2021-0002. EBSD-data were obtained at Equipment Center for Collective Use at Tomsk State University. References Banovic, S.W., Foecke, T., 2003. Evolution of Strain-Induced Microstructure and Texture in Commercial Aluminum Sheet under Balanced Biaxial Stretching. Metall. Mater. Trans. A. 34, 657 – 671. Harewood, F.J., McHugh, P.E., 2007. Comparison of the Implicit and Explicit Finite Element Methods using Crystal Plasticity. Comput. Mater. Sci. 39, 481 – 494. Li, H., Fu, M., 2019. Inhomogeneous Deformation- Induced Surface Roughening Defects, in “ Deformation-Based Processing of Materials ”. Elsevier, pp. 225 – 256. Ma, X., Zhao, J., Du, W., Zhang, X., Jiang, Zh., 2019. Analysis of Surface Roughness Evolution of Ferritic Stainless Steel using Crystal Plasticity Finite Element Method. J. Mater. Res. Technol. 8(3), 3175 – 3187. Messner, C., Oberndorfer, C., Werner, E.A., 2005. Surface Roughness of Duplex Steels: Role of the Microstructure. Comput. Mater. Sci. 32(3-4), 455 – 462. Messner, C., Silberschmidt, V.V., Werner, E.A., 2003. Thermally Induced Surface Roughness in Austenitic – Ferritic Duplex Stainless Steels. Acta Mater. 51, 1525 – 1537; https://doi.org/10.1016/s1359-6454(02)00545-1 Osakada, K., Oyane, M., 1971. On the Roughening of Free Surface in Deformation Processes. Bull. JSME 14, 171 – 177. Panin, V.E., Egorushkin, V.E., Kuznetsov, P.V., Galchenko, N.K., Shugurov, A.R., Vlasov, I.V., Deryugin, Ye.Ye., 2020. Structural Turbulence of Plastic Flow and Ductile Fracture in Low-Alloy Steel under Lattice Curvature Conditions. Phys. Mesomech. 23, 279 – 290. Paul, S.K., Roy, S., Sivaprasad, S., Tarafder, S., 2019. Forming Limit Diagram Generation from In-Plane Uniaxial and Notch Tensile Test with Local Strain Measurement through Digital Image Correlation. Phys. Mesomech. 22, 340 – 344. Qin, L., Seefeldt, M., Van Houtte, P., 2013. Meso-Scale Modelling on Ridging or Roping of Aluminium Alloys. Mater. Sci. Technol. (MS&T) 2013 2, 1274 – 1283. Raabe, D., Sachtleber, M., Weiland, H., Scheele, G., Zhao, Z., 2003. Grain-Scale Micromechanics of Polycrystal Surfaces during Plastic Straining. Acta Mater. 51, 1539 – 1560. Romanova, V.A., Balokhonov, R.R., Batukhtina, E.E., Emelianova, E.S., Sergeev, M.V., 2019. On the Solution of Quasi-Static Micro- and Mesomechanical Problems in a Dynamic Formulation. Phys Mesomech 22, 296 – 306. Romanova, V., Balokhonov, R., Emelianova, E., Pisarev, M., Dymnich, E., 2020. Numerical Study of the Texture Effect on Deformation Induced Surface Roughening in Titanium Polycrystals. Eng. Fail. Anal. 110, 104437. Romanova, V., Balokhonov, R., Emelianova, E., Sinyakova, E., Kazachenok, M., 2019a. Early Prediction of Macroscale Plastic Strain Localization in Titanium from Observation of Mesoscale Surface Roughening. Int. J. Mech. Sci. 161 – 162, 105047. Romanova, V., Balokhonov, R., Emelianova, E., Zinovieva, O., Zinoviev, A., 2019b. Microstructure-Based Simulations of Quasistatic Deformation Using an Explicit Dynamic Approach. Facta Universitatis. Ser. Mech. Eng. 17(2), 243 – 254. Romanova, V., Balokhonov, R., Panin, A., Kazachenok, M., Kozelskaya, A., 2017. Micro- and Mesomechanical Aspects of Deformation Induced Surface Roughening in Polycrystalline Titanium. Mater. Sci. Eng. A 697, 248 – 258. Romanova, V.A., Balokhonov, R.R., Schmauder, S., 2013. Numerical Study of Mesoscale Surface Roughening in Aluminum Polycrystals under Tension, Mater. Sci. Eng. A. 564, 255 – 263. Shanyavskiy, A.A., Soldatenkov, A.P., 2020. Scales of Metal Fatigue Limit. Phys. Mesomech. 23, 120 – 127. Shavshukov, V.E., 2020. Extreme Strain Fluctuations in Polycrystalline Materials. Phys. Mesomech. 23, 13 – 20. Stoudt, M.R., Levine, L.E., Creuziger, A., Hubbard, J.B., 2011. The Fundamental Relationships Between Grain Orientation, Deformation Induced Surface Roughness and Strain Localization in an Aluminum Alloy. Mater. Sci. Eng. A 530, 107 – 116. Trusov, P.V., Sharifullina, E.R., Shveykin, A.I., 2019. Multilevel Model for the Description of Plastic and Superplastic Deformation of Polycrystalline Materials. Phys. Mesomech. 22, 402 – 419. Wang, Y, Meletis, E.I., Huang, H., 2013. Quantitative Study of Surface Roughness Evolution during Low-Cycle Fatigue of 316L Stainless Steel using Scanning Whitelight Interferometric (SWLI) Microscopy. Int. J. Fatigue 48, 280 – 288. Yoshida, K., 2014. Effects of Grain-Scale Heterogeneity on Surface Roughness and Sheet Metal Necking. Int. J. Mech. Sci. 83, 48 – 56.

ScienceDirect Structural Integrity Procedia 00 (2019) 000 – 000 Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceD rect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 35 (2022) 124–131

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya Abstract Nowadays, the phenomena of damage and fracture affect many machines and components in the good part of engineering. Hydraulic machines are also part of these components affected by these phenomena. Axial Piston Machine is undoubtedly one of the compact machines; however, it is also confronted with performance loss or even its destruction because of the complexity of the movements that perform its internal elements. A good part of the causes of loss of its performance and efficacies comes from the mechanism of rupture, fracture, and abnormal deformation that undergo its solid compounds. In this work, we implement an analysis of damage and fatigue on the slipper/swashplate interface by predicting the solid deformation, strain, wear of the solid bodies (slipper and swashplate) for given materials. As a result, the deformation and fatigue of both slipper and swashplate have been predicted. Furthermore, the lubricant thickness between slipper and swashplate is solved. For the validation of our research, the oil thickness and temperature are measured by the test rig and compared with the simulation results. Finally, some suggestions are given to improve or avoid the damage and failure of the slipper and swashplate. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials Analysis of Damage and Failure mechanism under a lubricated slipper/swashplate interface in Axial Piston Machines Gaston Haidak*, Dongyun Wang College of Engineering, Zhejiang Normal University, 688 Yingbin Avenue, Jinhua, Zhejiang, 321004, China, haidak@zjnu.edu.cn Abstract Nowadays, the phenomena of damage and fracture affect many machines and components in the good part of engineering. Hydr ulic machines are also part of th se components a fected b these ph nomena. Axial Pi to Machine is und ubtedly one of the compact machines; howeve , it is also confr ted with p rformanc loss r ven its destruction because of the complexity movements t at perform its intern l elements. A good part f the auses f loss of its performanc and fficacies com s from echanism of ru ture, fracture, and abnormal def rmation that undergo its solid com ounds. I this work, we implement an analysis of da age and fatigue on the slippe /swashplate interface by p edic ing the s lid deformation, strain, ar of the solid bodie (slipper nd swashplate) for given materials. As a result, the deformatio and fatigue of both slippe a d swashplat have een pred cted. Furthermore, the lubrica t thickne s betwe n slipp r and swashpl te is solv d. For the validation of our research, th oil thickness and t peratur are measured by the test rig and compared with th simu ation results. Finally, some suggestions ar g ven to improve or avoid th damage and failure of the slipper and swashplate. © 2021 The Auth rs. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of IWPDF 2021 hair, Tuncay Yalçinkay Keywords: Axial Piston Machines; Damage and Failure; Deformation, Lubrication 1. Introduction Axial piston machines face the problems of performance loss despite their compactness and capacity for driver fluid with higher pressure. It consists f several elements and three crit cal interfaces, including the one between the s ipper and swash late. Despite the lubrication mecha i m design d on the slipper/swashplate interfac , the damag 2nd International Workshop on Plasticity, Damage and Fracture of Engineering Materials Analysis of Damage and Failure mechanism under a lubricated slipper/swashplate interface in Axial Piston Machines Gaston Haidak*, Dongyun Wang College of Engineering, Zhejiang Normal University, 688 Yingbin Avenue, Jinhua, Zhejiang, 321004, China, haidak@zjnu.edu.cn Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya Keywords: Axial Piston Machines; Damage and Failure; Deformation, Lubrication 1. Introduction Axial piston machines face the problems of performance loss despite their compactness and capacity for driver fluid with higher pressure. It consists of several elements and three critical interfaces, including the one between the slipper and swashplate. Despite the lubrication mechanism designed on the slipper/swashplate interface, the damage

* Corresponding author. Tel.: +8613958419223. E-mail address: haidak@zjnu.edu.cn * Corresponding author. Tel.: +8613958419223. E-mail address: haidak@zjnu.edu.cn

2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yalçinkaya 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 hair, Tuncay Yalçinkaya

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IWPDF 2021 Chair, Tuncay Yal ç inkaya 10.1016/j.prostr.2021.12.056

Gaston Haidak et al. / Procedia Structural Integrity 35 (2022) 124–131 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

125

2

and ageing of these solid elements persist and lead to a substantial loss of energy and performance. In addition, it can lead to the destruction of slippers components. Many types of research have been conducted in this area. Some have effectively demonstrated the presence of elastic and thermodynamic deformation of the slippers and swashplate components. Other researchers (Bergada et al., 2012, 2010a, 2010b; Kumar et al., 2009) have also studied the hydrostatic and hydrodynamic behaviour and the flow process occurring within the axial piston machine. They experimentally demonstrated the enormous energy loss on the slipper/swashplate interface due to the leakage. The damage and failure mechanism on the slipper/swashplate interface comes from the nature of the slipper ’ s motion on the swashplate (Haidak et al., 2018; Ma et al., 2015) and lubrication failure on the other (Flegler et al., 2020; Haidak et al., 2019b, 2020; Lin et al., 2013). This requires a reliable understanding of the causes and origins of these defects. In this sense, a great deal of research was also carried out, firstly by analysing the thermoplastic model of lubrication of this interface and its impact on the elastohydrodynamic deformation(Hashemi et al., 2016; Schenk, 2014; Schenk and Ivantysynova, 2015); and the effect due to the structure of the solids themselves (Bhattacharya et al., 2016; Haidak et al., 2018). However, of all the works cited above, the damage and fatigue of the slipper were not taken into account. Therefore, we propose a model of damage and failure analysis of the slipper/swashplate set, taking into account the strain and fatigue of the slipper, as well as the experimental test. In addition, the lubrication process plays an essential role in this mechanism to minimise friction and possible contact between solids. For this reason, we have developed a rig test to understand the behaviour of the fluid during the regular operation of the axial piston machine. The following parts of this work will start with presenting materials and methods used, followed by the results and discussion and finally, a conclusion.

Nomenclature c p

Heat capacitance

Fluid film thickness [m]

h

MB Mixt Boundary NB Neuman Boundary P pressure [Pa] T temperature [K] T s T L Temperature of leakage [K] Oil viscosity [Pa.s] Rotational Angle [rad] 2. Materials and Methods. Temperature of solid [K]

The results of this work have mainly been done in two different parts, the simulation and experimental parts. For the simulation, part is subdivided into two subparts. First, the solid-body deformation and failure mechanism where the two pointed parts are slipper and swashplate as presented in Fig. 1; and the behaviour of the thickness of lubricant between slipper and swashplate.

Gaston Haidak et al. / Procedia Structural Integrity 35 (2022) 124–131 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

126

3

Fig. 1. (a) Slipper; (b) Swashplate.

The boundary conditions used are indicated in Fig. 1. The materials used for both slipper and swashplate are Leaded Commercial Bronze and Gray Cast Iron (Sn), respectively. The thermal boundary conditions illustrated in Fig. 1 are used to calculate the thermal stress from the thermal strain due to the loading. We used two different boundary conditions, Neuman Boundary, a natural boundary to specify a wall heat flux, and Mixt Boundary, which specifies a wall heat flux with temperature variation on the surface. The resulting non-uniform temperature distribution causes a thermal expansion of the slipper and swashplate. Thermal stress is calculated from the thermal strain, and this load vector is applied to the solid bodies. The lubricant used in this study is a viscous liquid, the characteristics of which are given in Table 2. The fluid thus described is used in two different aspects: for hydrodynamic simulation between slipper and swashplate and experimental testing. Table 1 presents the geometrical characteristics of the slipper.

Table 1. The geometric characteristics of the machine. Parameters Values

Parameters

Values

Outer diameter slipper [mm] Inner diameter slipper [mm]

25 15

Diameter orifice slipper [mm] Length orifice slipper [mm]

2.5

3.48

Table 2. Characteristics of fluid. Parameters

Values 1.5e-13 0.9000 9.6310 2.1025 3.7873

Parameters

values 0.073

Kinematic viscosity P coefficient Pc1[-] Kinematic viscosity weighting factor w [-] Kinematic viscosity T coefficient Tc1[-] Kinematic viscosity P coefficient Pc2 [-] Kinematic viscosity T coefficient Tc2 [-]

Dynamic oil viscosity [Pa.s]

Density oil at reference point [kg/m3] Heat capacitance [J/kg.K] Volumetric thermal expansion coefficient [1/K] Thermal conductivity of oil [W/m.K]

1048

05.76e-4

0.037 2000

The methodology used for the simulation part can be described in two parts. The first is devoted to the deformation of solid structures (slipper and swashplate), whose type of mesh used is the four-node linear tetrahedron. The summation of the weighted residual approximation over all the elements leads to a global solution approximation. Thus, the general governing elasticity equation (Eq. 1) commonly used, detailed by (Schenk and Ivantysynova, 2015), is used for the thermo-elastic deformation. The solid domain is discretised into many individual finite elements. Similarly, the temperature is assumed to be a weighted linear combination of the four nodal temperatures for the thermal conductivity analysis. ∇ + = 0 (1)

Gaston Haidak et al. / Procedia Structural Integrity 35 (2022) 124–131 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

127

4

where b represents the body forces and σ is the infinitesimal stress tensor. The second is that of the behaviour of the fluid. The instantaneous lubricating oil film thickness ( h), which is expressed as a function of three different points h 1 , h 2 , and h 3 on the outer edge of the slipper with the interval of 120° from each other, developed in (Haidak et al., 2018) can be used and transformed into cylindrical coordinate (Eq. 2) to calculate the fluid film thickness between slipper and swashplate; assuming that the slipper and swashplate surfaces are ideally smooth and neglecting the deformation of the slipper and the swashplate(Schenk and Ivantysynova, 2015). ℎ = . 0 . √3 ( ℎ 2 − ℎ 3 ) + . 3 . 0 (2. ℎ 1 − ℎ 2 − ℎ 3 ) + 1 3 ( ℎ 1 + ℎ 2 + ℎ 3 ) (2) where ℎ 1 represents the rigid film thickness, is the rotational angle varying between 0 and 2 , the radius varying between 0 and the outer diameter of slipper and 0 the slipper orifice radius. Therefore, the final fluid film thickness between the slipper and swashplate is the summation of ℎ 1 , the pressure/thermal deformation of the slipper ( ), and for swashplate ( ) as given in Eq. (3). ℎ = ℎ1 + − (3) Three primary loops for the numerical calculation are formed from combining these above equations. In Fig. 2, the first loop (green arrows) is executed at the beginning of every time step; this step is for the pre-processing of simulation, including setting initial conditions. The second loop (red arrows) helps to optimise mesh structure and its convergence; the balance of solid body deformation is checked under the loop (blue arrows). Finally, the pressure of structural body deformation is resolved and updating the temperature and viscosity of the fluid film. The modifications in the solid body deformation are relaxed at the beginning of the iterations of each loop.

Fig. 2. Flowchart of the proposed numerical simulation model