Micro-tension and micro-shear experiments to characterize stress-state dependent ductile fracture

Accepted Manuscript Micro-tension and micro-shear experiments to characterize stress-state dependent ductile fracture Maysam B. Gorji, Dirk Mohr PII:

S1359-6454(17)30226-4

DOI:

10.1016/j.actamat.2017.03.034

Reference:

AM 13640

To appear in:

Acta Materialia

Received Date: 5 November 2016 Revised Date:

17 February 2017

Accepted Date: 15 March 2017

Please cite this article as: M.B. Gorji, D. Mohr, Micro-tension and micro-shear experiments to characterize stress-state dependent ductile fracture, Acta Materialia (2017), doi: 10.1016/ j.actamat.2017.03.034. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Micro-tension and Micro-Shear Experiments to

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Characterize Stress-State Dependent Ductile Fracture Maysam B. Gorji1, and Dirk Mohr2 1

Impact and Crashworthiness Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA 2

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Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland

Abstract. In view of characterizing the local plasticity and fracture properties in structures with material property gradients at the millimeter scale, a micro-tension and micro-shear testing technique is developed. It makes use of flat dogbone-shaped, notched, central hole and smiley-shear micro-specimens that have been scaled down from their macroscopic counterparts in a way that the critical gage section dimensions do not exceed

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500µm. A new tensile loading device is designed to apply the loading at speed of less than 1µm/s to achieve strain rate of about 10-3/s at the gage section level. The device includes custom-made clamps without any floating parts that guarantee the alignment of the specimen with respect to the loading axis as well as the uniformity of the applied

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displacement fields. In-situ experiments on aluminum alloy 6016-T4 are carried out in an optical microscope. Planar digital image correlation is used to compute the surface strain

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fields. The parameters of the Swift-Voce hardening law and the Hosford-Coulomb fracture initiation model are identified based on the micro-experiments. The obtained material data is validated through numerical simulations of macroscopic fracture experiments that have been performed on the same material. Keywords: Micro-fracture experiments, ductile fracture, Hosford-Coulomb, aluminum alloy 6016-T4

ACCEPTED MANUSCRIPT M. Gorji and D. Mohr (revised version, February 2017)

1. Introduction Significant progress has been made over the past decade in developing robust experimental techniques to characterize the effect of stress state on the onset of fracture

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in structures with homogeneous material properties. The tension-torsion technique has been successfully extended from plasticity to fracture characterization [1-4] to provide insight into the effect of the Lode angle parameter in addition to the stress triaxiality. At the same time, new experimental techniques have been put in place to characterize the

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multiaxial plasticity and stress state dependent fracture initiation in sheet metal. This may be achieved by either varying the combinations of loadings applied onto the specimen boundaries (e.g. [5-7]) or varying the specimen geometry while applying a uniform axial

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displacement field onto the specimen boundaries. Candidate specimen geometries for the latter approach include dogbone-shaped, notched or central hole tension specimens (e.g. [8, 9]). Special efforts have been made to come up with flat specimen geometries for characterizing fracture under pure shear which includes single gage section (e.g. [10-12]) and double gage section [13] shear specimens.

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Aside from characterizing the fracture response of polycrystalline materials at the macroscale, i.e. through specimens whose smallest dimensions are still at the millimeter level, there is also a constant quest for experimental results that provide insight into the material response at smaller length scales. This is often motivated by the need to

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understand the governing failure mechanisms at the grain or sub-grain level (e.g. [14-18]) and/or by the small dimensions of structures from which the specimen needs to be

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extracted [19, 20]. Mechanical specimens with dimensions of a few microns or even less have been developed for characterizing thin-films [21-24]. In the present work, the downscaling of existing macroscopic experimental techniques is carried out to provide a means to identify the local plasticity and fracture properties in graded materials and structures such as weldments. The latter feature different zones (e.g. fusion zone, heat affected zone, basis material) of approximately constant material properties within regions that are less than 1mm wide. Micro-hardness testing is often used to characterize the property gradients in metallic structures, but tedious inverse material model parameter identification procedures are needed to extract an approximation of the stress-strain curve

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from such measurements (e.g. [25]) while no information on the material’s fracture response is obtained. To investigate the superplasticity in friction stir processed Al-MgZr alloy, miniature tensile specimens of 0.5mm thickness and 1.3mm gage length have been tested by Ma et al. [26] using a custom-built mini tensile tester. Peel et al. [27] made

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use of Vickers hardness measurements and tensile tests on flat dumbbell specimens with gage section dimensions of 2.6x12.5x50mm to characterize the mechanical response of friction stir welded aluminum 5083. In their experiments, the strain fields have been determined using electronic speckle pattern interferometry with a 780nm laser, providing

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a spatial resolution of 20-100µm. Their results demonstrate that the recrystallized weld zone exhibits a significantly lower hardness and yield stress than the base material.

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Genevois et al. [28, 29] extracted 25mm long micro-tensile specimens featuring a 0.8x4mm cross-section from welded aluminum 2024 plates using electro-discharge machining. They also performed macro-tensile experiments and demonstrated that the local tensile curves obtained through strain mapping agree reasonably well with the results from micro-tension experiments.

In the present work, a new experimental technique is proposed to perform tension

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experiments on miniaturized dogbone-shaped, notched and central hole specimens whose maximum gage section width does not exceed 500µm. At the same length scale, a microsmiley specimen is also proposed for characterizing the fracture response for stress states close to pure shear. In-situ experiments are performed on aluminum alloy 6016-T4 under

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an optical microscope to determine the displacement and strain fields through digital image correlation of microscopy images. Subsequently, the Swift-Voce hardening law

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and Hosford-Coulomb fracture initiation model parameters are identified using a hybrid numerical-experimental approach. In addition, conventional macroscopic fracture experiments are performed to validate the obtained “micro” material model parameters through simulations of macroscopic experiments.

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2. Experimental procedures

2.1. Material

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All specimens are extracted from aluminum alloy 6016-T4 sheets of 1.5mm nominal thickness. This heat-treated Al-Mg-Si sheet material has been provided by the manufacturer after requesting an isotropic sheet material. Figure 1 shows representative EBSD pictures of the polycrystalline microstructure. In the plane of the sheet, the average

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grain size is 50µm with an aspect ratio of 1.6 (Fig. 1a). In the RD-TD plane, i.e. the cross-sectional plane that contains the rolling and thickness directions, the average grain size is 37µm with an aspect ratio of 1.5 (Fig. 1b). In view of minimizing microstructural

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changes due to machining, all specimens are extracted using a combination of micro wire-EDM cutting and CNC micro-milling.

2.2. Micro-specimens

A typical basic plasticity and fracture testing program for sheet materials includes

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dogbone specimens for uniaxial tension (UT specimens), flat specimens with symmetric circular cut-outs (NT specimens), flat specimens with a central hole (CH specimens) and in-plane shear specimens (SH specimens). In view of characterizing the fracture response of structures with property gradients at the millimeter level, we design micro-specimens

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with cross-section dimensions of less than 500µm by downscaling the macro-specimens proposed by Dunand and Mohr [9] and Roth and Mohr [13].

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Figure 2 shows the resulting micro-specimen drawings. The in-plane specimen dimensions are typically scaled down by a factor of about 20x (from macro to micro), while a thickness of 200µm is chosen for all specimens to provide sufficient bending stiffness for specimen handling. With regards to the smallest specimen dimension, it is worth noting that the µ-specimens featured about six grains along the thickness directions. Given that both the grain size analysis and micro-hardness measurements did not reveal any noticeable property gradient in the thickness of the sheet, we did not make any special effort to verify the exact location of specimen extraction after receipt of the specimens. A micro wire EDM with a wire diameter of 50µm is employed to extract the 4

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specimens from the aluminum sheets. After an initial slicing operation, the 2D specimen contours are cut. An under-sized hole is first introduced into the µ-CH specimens using sinker EDM, before it is enlarged to a nominal diameter of 400µm using wire EDM

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machining. The gage section widths of the micro-specimens are 500µm for the µ-UT, µNT and µ-SH specimens, and 300µm for the µ-CH specimen. The total length of the first three specimen types is about 7.5mm . The µ-SH is almost twice as long which is due the

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required strength for the specimen shoulders.

2.3. Micro-testing device

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A micro-testing device is designed to load the above specimens under static loading conditions all the way to fracture. The specimen gripping and alignment is the most sensitive part of the entire testing procedure which led us develop a custom-made device instead of using a commercialized system. Simple limit analysis revealed that the maximum expected force for the micro-specimens is about 30N. In the uniaxial tension experiments, the initial yield point is expected to be attained after applying a

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displacement of 130/ 70000×1.5mm≅ 3µm . Furthermore, preliminary FE analysis revealed that fracture may be expected in all specimens at displacements ranging from 100µm to

500µm. To obtain a strain rate of the order of 10−3 / s , the displacement needs to be

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applied at a rate of the order of 1µm/ s . Given the above design considerations, we chose the following components for the micro-testing device (Fig. 3a): a strain gaged S-shaped load cell (Omega, model LCM101-100) of a

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maximum load capacity of 100N and an expected measurement accuracy of ± 0 . 1 N (component ① in Fig. 3a)

•

piezo-legs motor (Micromo, model LEGS Linear Twin 40N) which applies the loading quasi-continuously in 10 nm steps over a displacement range of ± 5mm (component ②)

These two elements are mounted onto a non-magnetic aluminum base frame (component ③) equipped with a linear low friction slide (component ④). The specimen clamps are

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designed as a single component without any floating parts. They feature a 2 mm long and

200µmthick slit that can be closed through bending by tightening an M2 hex cap screw. An important detail of the micro wire EDM machined clamps is a small step of 50µm

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height that facilitates the exact positioning of the specimen with respect to the clamp (Fig. 3b).

2.4. Displacement and strain measurement

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The overall weight of the device is 1100g which is sufficiently low for positioning the device onto the motorized x/y stage of an optical microscope (Keyence, model VHX-

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5000). To achieve a pixel size of about 1µm , images are taken at a magnification of 200x with a digital camera of a resolution of 1.1µm per pixel. At this magnification, the microstructural heterogeneities on the specimen surface become apparent. The natural surface contrast turned out to be sufficient for digital image correlation. For this, the planar DIC software VIC-2D (Correlated Solutions) is used in an incremental correlation model with a subset size of 21 pixels and a step size of 5. After calibrating the

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microscope, the relative axial displacements of the specimen shoulders are determined (i.e. the relative displacement of the blue dots shown in the specimen drawings in Fig. 2). In addition, the evolution of the effective von Mises strain fields within the specimen

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gage sections is determined through planar DIC.

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2.5. Testing procedure

Prior to testing, the initial distance between the grips is adjusted to the specimen

length. The specimen is inserted after setting the axial force to zero and the clamps are tightened. Subsequently, the in-plane specimen dimensions and the specimen thickness are measured using the microscope. The nominal actuator loading velocity (Table 1) is −3

chosen such that an average strain rate of the order of 10 / s is expected until the point of fracture initiation. It is kept constant throughout the entire experiment. Images are acquired at a frequency of 15 frames per second in the cameras video mode. After

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fracture, 3D pictures are taken of the fractured gage section before unmounting the specimen. The images are synchronized with the force recording using a custom-made

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Labview-based acquisition software (AGNES, V. de Greef, Ecole Polytechnique).

3. Finite element modeling

Most specimens undergo necking before fracture. As a consequence, the mechanical

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fields within the specimen gage section exhibit a through-thickness gradient. The surface strain measurements can thus not be used to determine the fracture strains. Instead, we

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make use of finite element simulations to determine the local loading paths to fracture.

3.1. Plasticity model

In a first approximation, the material will be treated as a homogenous solid even though the smallest specimen dimensions are close to the grain size, at which point the plasticity modeling assumption of separation of length scales might break down. In

employed.

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particular, the isotropic Levy-von Mises plasticity model with isotropic hardening is

With σ and s denoting the von Mises equivalent stress and the deviatoric part of the

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Cauchy stress tensor s, the yield condition reads

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f = σ − k = 0 with σ =

3 s:s 2

(1)

An associated flow rule is used to define the direction of plastic flow, while a Swift-Voce law [30-32] describes the evolution of the deformation resistance k as function of the equivalent plastic strain ε p ,

[ ]

(

(

)

(

k ε p = α A ε p + ε 0 + (1 − α ) k0 + Q 1 − e− β ε p n

))

(2)

with the Swift parameters {A, n, ε 0 }, the Voce parameters {k0 , Q, β } and the weighting factor α .

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3.2. Fracture initiation model

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The micromechanically-motivated Hosford-Coulomb damage indicator model is used to predict the onset of fracture initiation. Based on the results from three-dimensional unit cell computations [9,33] proposed the Hosford-Coulomb criterion to predict the onset of shear localization in polycrystalline materials. Assuming that ductile fracture is imminent

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with the onset of shear localization, Mohr and Marcadet [33] transformed the HosfordCoulomb criterion from principal stress space to a modified Haigh-Westergaard space defined by the equivalent plastic strain, Lode angle parameter and the stress triaxiality as

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coordinate axes. The obtained expression for the fracture strain after proportional loading is then embedded into a damage indicator framework (e.g. Johnson and Cook [34]) to predict ductile fracture after non-proportional loading. The damage indicator is defined as ε

D=

p

∫ε 0

dε

pr f

p

[η , θ ]

(3)

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The damage indicator is zero for the undeformed material (initial condition), while fracture is assumed to initiate when the condition D = 1 is met. The stress state is characterized by the stress triaxiality

σm tr (σ ) with σ m = σ 3

(4)

1 3 3 J3  J = s: s ; J 3 = det[s] arccos [ ] I = tr σ with ; 2 1 3/ 2  2 π  2 (J 2 ) 

(5)

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η=

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and the Lode angle parameter,

θ =1−

2

where s = σ − 1 3I1 I is the deviatoric tensor of the Cauchy stress. The heart of the fracture model is the function ε fpr = ε fpr [η , θ ] which provides the equivalent plastic strain to fracture after proportional loading as a function of the stress state (Fig. 9c). It is defined by the Hosford-Coulomb criterion in the mixed strain-stress state space,

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1   1 f 1 1  1  a a a a ε η , θ = b(1 + c ) p   ( f1 − f 2 ) + ( f 2 − f 3 ) + ( f1 − f 3 )  + c (2η + f1 + f 3 ) 2 2 2     

[ ]

with the transformation coefficient

p = 0 .1 ,

−

1 p

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and the material constants a , b and c .

2 π  f 2 θ  = cos  ( 3 + θ )  3 6 

3.3. Meshes and boundary conditions

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2 π  f 3 θ  = − cos  (1 + θ )  . 3 6 

(7)

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2 π  f1 θ  = cos  (1 − θ )  3 6 

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{ f1, f2 , f3} denote Lode parameter dependent trigonometric functions,

(8)

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The dynamic explicit FE-code LS-DYNA is employed to simulate the experiments.

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Given the symmetry of the mechanical systems, only one-eighth of the notched and central hole specimens is meshed; one-fourth of the shear specimen is modeled. All specimens are meshed with eight first-order solid elements along the (half-) thicknessdirection, while an element edge length of 0.01mm is used in the in-plane directions.

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Standard symmetry boundary conditions are applied along the planes of symmetry. Mass scaling is employed to shorten the CPU time within the limits of quasi-static loading

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conditions.

4. Results and discussion In the following we will present and discuss the results from our experiments and

simulations. We will focus primarily on the analysis of the mechanical fields. The reader is referred to Ghahremaninezhad and Ravi-Chandar [35] for a comprehensive analysis of the ductile fracture mechanism for a 6xxx series aluminum alloy.

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Throughout the discussion, two similar but different strain measures will be used: in the experiments, the effective strain is computed which is defined as

ε eff =

2 ε I2 + ε II2 + ε I ε II 3

(10)

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with ε I and ε II denoting the principal surface strains as obtained from DIC. In the numerical simulations, we report the equivalent plastic strain which is defined as

ε p = ∫ dε p

dε p =

2 ( dε Ip ) 2 + ( dε IIp ) 2 + ( dε Ip )( dε IIp ) 3

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with

(11)

A first difference is that the plastic strain components are used which creates only a

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small difference between the effective and equivalent plastic strains. For proportional loading paths the ratio of the strain components does not change and both definitions are identical except for the elastic strain contribution. Note that significant differences between these two strain measures will only arise for highly non-proportional strain

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paths.

4.1. Experimental results

The µ-UT force-displacement curve for an optical extensometer length of 1 . 5 mm is shown in Fig. 4. It exhibits a maximum of 18 . 9 N at a displacement of 0 . 28 mm . Up to

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this point (which corresponds to an average axial strain of 0 . 2 ), the surface strain fields are still homogeneous in a statistical sense, i.e. the strain variations occur at a length scale

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which appears to be related to the grain size. The average strain rate before the onset of necking is 2 ×10−3 / s . After the force maximum, we see clear localization of the deformation within a band whose width is comparable to that of 1 to 2 grains. Fracture then occurs at a force of 15 N while the maximum surface strains have exceeded 0.5. Figure 4b shows a 3D view of the fractured specimen. The overall crack orientation in the o

specimen plane is 72 with respect to the tensile axis, while it is slant when seen from the side. The local thickness reduction is clearly visible in Fig. 4b. Within the zone of

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localized plastic deformation (inside the neck), a significant surface roughness has developed which is tentatively attributed to varying grain orientations. Figure 5 summarizes the results for notched tension. A macroscopic gradient is

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introduced into the mechanical fields in addition to strain field fluctuations that are related to the polycrystalline microstructure. The force maximum of 21 . 5 N is reached after applying a displacement of 0 . 1mm . As in the uniaxial tension experiments, the deformation thereafter clearly localizes at a length scale that is comparable to the grain size. It is worth noting that the surface strain fields also loose symmetry when the

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localization sets in. In the last frame before fracture, an effective strain of 0.61 is observed on the specimen surface. The final crack is slant when the specimen is seen

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from the side. However, it is not straight when the specimen is seen from the top which suggests that microstructural heterogeneities influenced the crack path. The displacement and force at the instant of onset of fracture of the notched specimens are 0 .17 mm and 17 . 7 N , respectively.

In the experiments on central hole specimens (Fig. 6), a pronounced deformation

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concentration is observed near the hole boundary throughout the entire loading history. A maximum force of 23.4N is reached after applying a relative displacement of 0.09mm, while fracture initiates at a displacement of 0.14mm. As for the previous two specimen types, the localization appears to be influenced by the polycrystalline grain structure. For

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example, in picture ③, the maximum strain is observed at a location on the right ligament that is slightly above the horizontal line of symmetry, which is the location where the maximum would be observed in a homogenous material. For the most highly

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strained grains near the hole boundary, an effective strain of 0.8 is measured just before the crack forms.

The least pronounced force maximum is observed for the micro-shear specimens

(Fig. 7). A maximum force of 32.2N is observed at a displacement of 0.28mm, while fracture initiates at a force of 28.7N at a displacement of 0.36mm. The strain fields are remarkably homogenous within the two gage sections until the force maximum. Thereafter, a strain concentration becomes apparent near the free gage section boundaries that are under tension (in particular after the severe geometry change of the gage section

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contours induced by the loading). These strain concentrations are attributed to local necking of the gage section boundaries, which is reminiscent of the thickness reduction near the hole boundaries in the CH specimens. It is speculated that fracture also initiated from the gage section boundaries. The effective surface strains of 0.77 that are observed

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near the gage section center must thus be interpreted as lower bounds of the strain to fracture for pure shear. It is worth noting that both double gage section specimens (central hole and smiley shear) fractured in a remarkably symmetric manner, i,e, both gage section appears to have fractured almost simultaneously in these displacement-controlled

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experiments.

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4.2. Numerical simulation results

The Swift-Voce hardening parameters are identified through a first fit to the results from uniaxial tension up to the onset of necking, followed by an inverse parameter optimization procedure for central hole tension. Table 2 summarizes the final set of parameters for the aluminum alloy 6016-T4. A plot of the identified hardening law is shown next to the experimentally-determined true stress-strain curve in Fig. 8a. In

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addition, DIC results of µ-CH test show surface strain localization near the hole (see Fig. 6c). The experimentally-measured evolution of the maximum logarithmic strain at the hole boundary with respect to the applied displacement is shown as solid black dots in Fig. 8b; the surface strain reaches a maximum value of 0.93 prior to specimen fracture.

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This figure also provides the finite element prediction of local strain evolution, according to the Swift-Voce parameters listed in Table 2 (the curve is depicted in this figure as a

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blue solid line). The numerical and experimental curves almost lie on top of each other up to a displacement of about 0.1mm. Beyond this point, the FEM slightly underestimates the surface strain with a relative difference of less than 7%. The comparison of the numerically-predicted (blue curves) and experimentally-

measured (solid dots) force-displacement curves for all fracture specimens is shown in Figs. 8c to 8e. Overall, at the macroscopic level, we observe good agreement between the simulations and the experiments. It is worth noting that the simple macroscopic plasticity model can capture the micro-specimen response in the post-necking regime (for µ-CH

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and µ-NT) despite the apparent localization of deformation at the grain level in that regime. The final drop of the force-displacement curve for the smiley-shear specimen is not captured by the computational model. It is speculated that this drop is due to the first failure of one of the gage sections, which cannot be captured by the symmetric finite

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element model.

The loading paths to fracture are extracted at the gage section center for the µ-NT and

µ-SH specimens. In the case of the µ-CH specimen, we chose the highest strained

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element which is positioned on the horizontal axis of symmetry (on the specimen midplane) at the hole boundary. Figure 9b shows the evolution of the equivalent plastic strain as a function of the stress triaxiality. The stress state remains approximately constant in

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the µ-CH and µ-SH specimens, while the stress triaxiality increases from 0.38 at the beginning of the experiment to 0.74 at the instant of fracture initiation for the µ-NT specimen. The lowest strain to fracture is observed in the latter experiment ( ε f = 0 .64 ) , while fracture strains of 1.06 and 1.23 are achieved in the µ-CH and µ-SH experiments, respectively. The corresponding evolution of the Lode angle parameter is shown in Fig.

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9c. For reference, we also show the theoretical estimate of the Lode parameter based on the assumption of plane stress conditions (dashed curves). Note that the loading path for the µ-SH and µ-CH experiments is reasonably close to the plane stress path, while it deviates significantly from that for plane stress in the case of the µ-NT specimen. This

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observation just underlines that even in very thin foil-like specimens, significant out-ofplane stresses build up towards the specimen midplane.

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The three Hosford-Coulomb fracture initiation model parameters

{a, b, c}

are

identified using a standard inverse identification procedure (derivative-free minimization algorithm in Matlab) that accounts for the non-linear loading path in the calibration experiments. The final parameters are summarized in Table 3; a plot of the fracture envelope for proportional loading is included as a dashed black line in Figs. 9b and 9c. The model predictions for non-proportional loading (using the damage indicator framework) are represented by solid dots. These lie on top of the end point of the identified loading paths to fracture since the model identification is exact when using three experiments. The full 3D fracture surface for proportional loading showing the 13

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equivalent plastic strain to fracture as a function of the stress triaxiality and the Lode

5. Validation for conventional macro experiments

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angle parameter is depicted in Fig. 9a.

The goal of this section is to validate and assess the applicability of material model parameters identified from microscopic experiments through the simulation of

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conventional macroscopic experiments. Closely following the experimental procedures described by Dunand and Mohr [9] and Roth and Mohr [13], we therefore performed static experiments on the same aluminum alloy using conventional specimens of 1.5mm

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thickness: macro-NT, macro-CH and macro-SH (see Fig. 10 for specimen drawings). The experimentally-measured force-displacement curves for the macro experiments are depicted as black solid dots in Figs. 11a to 11d. The comparison of the micro and macro stress-strain curves up to the onset of necking reveals that a stronger hardening response in the macro experiments for strains greater than 0.05. At a plastic strain of 0.2,

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the stress in the macro experiments is about 12% higher than the µ-UT based stress-strain curve (blue curve in Fig. 11a). In close analogy with the simulation models for the micro specimens (see Section 3.3), we build finite elements models of all macro specimens with eight solid elements in the half-thickness direction. In the simulations of the macro

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experiments, the material model parameters identified from the micro experiments are used. In addition to using the micro-results for plasticity, we also make use of the fracture

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initiation model as calibrated from the micro-experiments for predicting the instant of fracture initiation in the macroscopic specimens. The numerically-predicted forcedisplacement curves are shown as blue solid lines in Figs. 11b to 11d. The experimental and numerical force-displacement curves agree reasonably well at the beginning of the experiments. However, the peak load in the macro NT and CH experiments is systematically underestimated by the micro plasticity model by about 8%. The corresponding error in the predicted peak load displacement is about 14%. As far as the displacement to fracture is concerned, a slightly smaller error is observed. The

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simulations underestimate the fracture displacement by less than 12% for the NT, CH and SH specimens, respectively. A detailed analysis considering the polycrystalline nature of the sheet material is in

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order to explain the systematic differences between the micro- and macro results. One speculation is that the grain boundary strengthening effect is weakened in the micro experiments due to the low number of grains along the thickness direction. It is thus recommended to repeat the present series of experiments with a fine grained material to demonstrate that the same plasticity and fracture properties are obtained by the micro and

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macro approaches. As an alternative, it may also be of interest to consider intermediate specimen sizes (i.e. a geometry scale factor of 5 or 10 instead of 20) to demonstrate the

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convergence of the measured mechanical properties with respect to the specimen size.

6. Conclusions

A new experimental technique is presented to characterize the stress-state dependent

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ductile fracture response for metals by means of micro-specimens. The latter feature gage sections with characteristic dimensions of less than 500µm. As result, the local plasticity and fracture properties in structures with high material property gradients such as welds can be identified. A novel micro testing machine is designed such that optimal alignment

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and uniform displacement boundary conditions may be achieved despite the small specimen dimensions of a few millimeters only. Experiments are performed on 200µm

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thick micro-specimens that are extracted from 1.5mm thick aluminum alloy 6016-T4 sheets using micro wire-EDM. To cover a wide range of stress states, uniaxial tension, notched tension, central hole tension and in-plane shear micro-specimens are included in the experimental program. The uniformity of the boundary conditions is confirmed by the symmetry in the strain fields obtained through digital image correlation of continuously recorded microscopy images. Aside from establishing the novel experimental procedure, the Hosford-Coulomb material model parameters are determined for the AA6016-T4 from the micro fracture experiments. The obtained material model parameters are validated through conventional 15

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macroscopic fracture experiments that have been performed on the same material. The proposed micro fracture testing technique provides a powerful means to assess local material properties that include far more information on a material’s plasticity and

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fracture response than conventional micro hardness tests.

Acknowledgements

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The partial financial support through the SNF (Swiss National Science Foundation) project P2EZP2_165243 is gratefully acknowledged. Thanks are due to Dr. Jürgen Timm (Novelis Switzerland) for providing the material and information regarding the

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microstructure, Mr. Colin Bonatti his help with the micro-tension experiments and Mr. Thomas Beerli for his help in designing the micro-testing device. Thanks are also due to Mr. Thomas Tancogne-Dejean and Dr. Christian Roth for valuable discussions.

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References

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[21] Haque, M.A. and Saif, M.T.A., 2003. A review of MEMS-based microscale and nanoscale tensile and bending testing. Experimental mechanics, 43(3), 248-255. [22] Espinosa, H.D., Prorok, B.C. and Fischer, M., 2003. A novel method for measuring

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global mechanical properties of 2024 T351, 2024 T6 and 5251 O friction stir welds. Materials Science and Engineering: A, 415(1), pp.162-170.

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[29] Genevois, C., Deschamps, A., Denquin, A., Doisneau-Cottignies, B., 2005. Quantitative investigation of precipitation and mechanical behaviour for AA2024 friction stir welds. Acta Materialia 53, 2447-2458.

[30] Swift, H.W., 1952. Plastic instability under plane stress. Journal of the Mechanics and Physics of Solids. 1, 1–18.

[31] Voce, E., 1948. The relationship between stress and strain for homogeneous

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deformation. J. Int. Metals. 74, 537–562. [32] Kessler L. and Gerlach J., 2006. The impact of material testing strategies on the determination and calibration of different fem material models. IDDRG International

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Conference, 113–120.

[33] Mohr, D. and Marcadet, S.J., 2015. Micromechanically-motivated phenomenological

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Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities. International Journal of Solids and Structures, 67, pp.40-55.

[34] Johnson, G.R. and Cook, W.H., 1985. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering fracture mechanics, 21(1), pp.31-48.

[35] Ghahremaninezhad, A. and Ravi-Chandar, K., 2012. Ductile failure behavior of polycrystalline Al 6061-T6. International journal of fracture, 174(2), pp.177-202.

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Tables Table 1. Micro- experiments conditions. Nominal actuator velocity [µm/s] 4 0.8 0.5 1

Average strain rate [/s] 2×10-3 5×10-4 3×10-4 2×10-4

Table 2. Hardening parameters of AA6016-T4 sheet sample.

0.185

353.4

Swift parameters

]

n [− ]

ε 0 [− ]

0.073

0.0015

Voce parameters β [− ] k 0 [MPa ] Q [MPa ] 106.9 153.8 9.98

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A [MPa

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ratio

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Micro- sample Uniaxial (UT) Notched (NT) Central hole (CH) Smiley shear (SH)

Table 3. Hosford-Coulomb parameters of studied AA6016-T4 sheet sample. b [-] 1.13

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a [-] 1.33

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c [-] 0.083

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(b)

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Figure 1. EBSD images showing the grain morphology: (a) plane of the sheet, (b) crosssectional view with the thickness direction being parallel to the vertical direction.

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(a) Uniaxial tension (UT) specimen

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(b) Notched tension (µ-NT) specimen

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(c) Central hole (µ-CH) specimen

(e) Smiley shear (µ-SH) specimen Figure 2. Drawings of micro-specimens; all units are in [mm]; blue dots indicate the start and end points of the DIC extensometer. 22

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Figure 3. Micro-testing device: (a) exploded view with load cell ①, linear motor ②, aluminum base frame ③ and linear low friction slide ④; (b) photograph of assembled device; (c) side view of clamped specimen.

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Figure 4. Micro-tension (µ-UT) experiment: (a) Force-displacement curve, (b) 3D view of fractured specimen, (c) evolution of the effective strain field.

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Figure 5. Micro-notched tension (µ-NT) experiment: (a) Force-displacement curve, (b) top view of fractured specimen, (c) evolution of the effective strain field.

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Figure 6. Micro-central hole (µ-CH) tension experiment: (a) Force-displacement curve, (b) top view of fractured specimen, (c) evolution of the effective strain field.

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Figure 7. Micro-shear experiment (µ-SH): (a) Force-displacement curve, (b) top view of fractured specimen, (c) evolution of the effective strain field.

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Figure 8. Comparison of simulation with experimental results for micro-specimens: (a) stress-strain curve for uniaxial tension (µ-UT), (b) evolution of the local strain at the hole boundary in a µ-CH specimen, and force-displacement curves for (c) notched tension (µNT), (d) central hole tension (µ-CH), and (e) in-plane shear (µ-SH).

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Figure 9. Hosford-Coulomb fracture model as identified from micro-fracture experiments: (a) fracture strain for proportional loading as a function of the stress state; and plane stress fracture envelope as a function of (b) the stress triaxiality, and (c) the Lode angle parameter; the solid dots in (b) and (c) show the model predictions for the non-proportional loading paths encountered in the micro-fracture experiments.

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(a) Uniaxial tension (UT) specimen

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(b) Notched tension (NT) specimen

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(c) Central Hole (CH) specimen

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Figure 11. Comparison of simulation (based on micro-data) with experimental results for macro-specimens: (a) stress-strain response, and force-displacement curves for (b) notched tension, (c) central-hole tension, (d) in-plane shear;

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