we43mg espi draft final

7/28/2019 WE43Mg Espi Draft Final

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Short Communication

Notch root strain measurement of WE43 magnesium alloy using

electronic speckle pattern interferometry

Haw Ling Liewa, Judha Purbolaksonoa,*, Azmi Bin Ahmadb

aDepartment of Engineering Design and Manufacture, Faculty of Engineering, University of Malaya,

Lembah Pantai, 50603 Kuala Lumpur, Malaysia

bDepartment of Mechanical Engineering, College of Engineering, Universiti Tenaga Nasional, ,

Malaysia

*Corresponding author. E-mail address: [email protected]

Abstract

The notch root elasto-plastic strain for circumferentially grooved round specimens of

cast magnesium WE43-T6 was experimentally measured. Hexagonally close-packed

magnesium has intrinsic limited ductility, and its potential implications on the validity

of various rules for the prediction of maximum notch root strain such as Neubers and

Glinkas motivate this work. The measurements were performed on circularly notched

specimens with small radii of 1.6 mm and 0.8 mm; together with the opening angle of

60, they are moderately deep and sharp. The technique of electronic speckle pattern

interferometry (ESPI) is used with the objective of confirming its accuracy in

measuring three dimensional surface deformations on large negatively curved

manifolds. The measured nominal stress for rupture is well beyond the ultimate

strength, this suggests the existence of significant biaxial stress at the notch root.

Comparing to the results of finite element simulation, ESPI-based strain

measurement on notch surfaces with negative Gaussian curvature is concluded to be

accurate. Furthermore, we report on the distribution of the simulated plastic zone at

the notch root.

1. Introduction

The interest for research and applications involving magnesium (Mg) and its alloys

has been steadily increasing. This inexorable trend of magnesium toward a

ubiquitous material is attributed to its high specific strength and promising potential


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comparison to cubic materials [8], for example the elongation of WE43 is 7% at room

temperature [2]. Notwithstanding the obvious sanguine proposition to employ

Neubers and Glinkas for such materials, their validity have not being established;

this work on notch root strain measurement is a first step toward this goal. In a

broader sense, the accurate knowledge of strain field around the notch root may

support the understanding, development, and evaluation of various analytical and

empirical models for stress and strain distributions, see e.g. [9, 10]. In this report, we

provide for the experimental measurement of the maximum strain for specimens of

WE43-T6 magnesium alloy with moderately sharp notches. The strain measurement

at the notch root is performed using ESPI, a non-contacting technique that is capable

of resolving full field deformation of the order of sub-micrometer. Comparison with the

results of finite element (FE) simulation is provided.

2. Material and methods

2.1 Specimen material and geometry

The material used was cast magnesium WE43 with T6 treatment. Table 1 lists some

of the mechanical properties from the material datasheet [2].

Table 1. Mechanical properties of WE43-T6 [2].

Modulus of elasticity (GPa) 44

Poissons ratio 0.27

Yield stress (0.2%) (MPa) 180

Tensile strength (MPa) 250

Elongation (%) 7

Circumferentially notched round bar with radii of 1.6 mm and 0.8 mm as depicted in

Fig. 1 were used in this study, the elastic stress concentration factors are =


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1.94, 2.53 respectively from interpolation on nomographs in [11]. With an opening

angle of 60, the depth (2 / ) for both notches is high at the value of 0.29. The

sharpness ( / ) is moderate with value of 0.38 and 0.19 respectively for notch

radius of 1.6 mm and 0.8 mm. These configurations are roughly drawn from ASTM

E602 [12], and they are similar to those used in Zeng and Fatemi [7]. In relevance to

the ESPI measurement described next, the grooved surfaces are curved with

negative Gaussian curvatures of the order of 0.1mm.

Fig 1. The geometry of the circularly notched specimens.

2.2 EPSI strain measurement

Electronic pattern speckle interferometry (see e.g. [13]), a non-contact and full-field

three-dimensional surface deformation measurement technique, has recently evolved

to the level of reliability and accuracy that meets the rigorous requirements of

research standard. Full field displacement measurements, easy application for in-situ

measurements, nonrequirement of fiducial marking, and displacement of sub-

micrometer accuracy are some of the main features of this seemingly becoming


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technique in experimental mechanics and material testing. We cite Bottlang et al. [14]

for measurement of full field continuous strain distribution in a biological material with

steep functionally graded stiffness, Tay et al. [15] for experimentally studying the

plastic zone around the tip of a through thickness crack, and Cavaco [16] for using

the theory of elasticity and ESPI-based measurement to develop a hybrid

experimental theoretical technique for residual stress analysis.

For measuring notch root strain of moderately sharp notches with small radii of

curvature that implicate large strain gradient, the ESPI-based displacement

measurement is advantageous: (1) As the displacement field is numerically

differentiated to compute the strain field, the error is greatly amplified by

measurement noise for instance the maximum accuracy when the fourth-order

Richardson extrapolation is used is 10 for noise level of 10 [17]; (2) for notches

with small radii of curvature, the conventional technique of strain gages is but very

difficult and less accurate because of the gage length requirement [7].

The 3D-ESPI System of Dantec Dynamics is the center piece of the instrumentation

in our work, Fig 2 shows the set-up. The ESPI unit is attached to the crosshead of a

tensile testing machine through a pulley system so that the position of the optical

camera that capture images of the notch root could remain static relative to the notch

root during the tensile testing. A built-in software, ISTRA, controls the sensor-head

for alignment, and processes the images.


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Fig 2. The set-up of the ESPI system.

2.3 Finite element model

Numerical simulation of the elasto-plastic strain behavior at the notch root of the

notched WE43 magnesium specimen is performed using the finite element method

via ANSYS. The finite element mesh of the physical domain is shown in Fig 3, and

linear quadrilateral isoparametric element is used for the discretization. In order to

minimize computational error due to the expected behavior of large strain gradient,

the characteristic size of the element at the vicinity of the root is set to be 4 m;

translating into 400 and 200 elements over respectively a length of the size of the

notch radius of 1.6 and 0.8 mm. The material plasticity for stresses exceeding the

yield stress is represented using a multi-linear uniaxial stress-strain constitutive

relationship. We also assume a homogeneous and isotropic continuum material and

microstructures such as grain size that becomes relevant at this length scale are

ignored.


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Fig 3. The finite element meshes for the axisymmetric circularly grooved specimens.

3. Results and discussion

The three dimensional full field axial strain contour on the grooved region obtained

using the ESPI measurement system prior to rupture is shown in Fig 4. By averaging

the surface strain on the circumference of the notch root, we obtained the uniaxial

notch root strain; and this result is plotted in Fig 5 together with the prediction from

the finite element simulation.

The results of ESPI measurements of the notch root strains on both specimens, as

plotted in Fig 5, agree very well with the strains computed using the finite element

method over the elastic region. Deviation of the finite element results from the

experimental measurement in the plastic zone is expected since the multi-linear

uniaxial stress-strain relationship used in the simulation does not include the plane

strain effects of the round bar specimen. Such deviation is also observed in Zeng and

Fatemi [7]. The nominal stress for rupture is observed to be well beyond the ultimate

strength listed in Table 1 when the area reduction factor of 2.03 at the notch root is


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taken into account; this is due to the moderately sharp notch root that produces

significant hoop stress.

In the ESPI image for strain contour, several distinct color fringes are observed at the

root, indicating that the axial strain is well resolved in both specimens. The anomaly

of non-uniform root strain on the circumference observed in Fig 4(a) is likely due to a

small offset in the alignment of the test specimen. This accidental imperfection in the

set-up is not unbeneficial; for it is detected, and hence validating the sensitivity of this

measurement system. The high degree of axisymmetry of the contour field also

suggests that this technique is capable of measuring strain on curved surfaces; and

the case in point are surfaces with negative Gaussian curvatures of the order of

0.1mm.

In Fig 6, the decomposition of the elastic strain and the plastic strain are shown.

These strain fields correspond to the last three loading steps in the finite element

simulation. The plane strain effect at the notch root is obvious, as the plastic zone

remains small and localized for both specimens at a nominal stress of about 180

MPa that corresponds to the yield stress for the nominal cross-section.


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Fig 4. ESPI strain contour displaying full field axial strain on the specimen prior to

rupture failure. (a) 1.6 mm notch, and (b) 0.8 mm notch.

Fig 5. Notch root strains with uniaxial tensile loading. Three tests were conducted

with each notched configuration. The last data point indicates state prior to rupture.

Comparison with the finite element calculation is included.


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Fig 6. The elastic and plastic strain fields simulated by the finite element method.

The nominal stresses correspond to the last three load increment steps in the

simulation.

4. Conclusion

The notch root strain measurement for cast magnesium WE43-T6 is reported for

moderately deep and sharp notches. Three dimensional full field surface strain

measurement at the notch with negative Gaussian curvature of the order of 0.1mm

are obtained using the technique of ESPI. Finite element simulation confirms the


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accuracy of ESPI, and the plane strain effect is found to be pronounced at these

notch roots.

Acknowledgment

The third author is grateful for the access to the set-up of ESPI at UMIST,

Manchester, UK. The corresponding author is funded by the UM-MOHE-HIR grant.

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8. Avedesian M, Baker H. Magnesium and Magnesium Alloys ASM Speciality

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we43mg espi draft final

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